numerical modelling of abnormal combustion in high performance ...

UNIVERSITÀ DEGLI STUDI DI MODENA E REGGIO EMILIA DIPARTIMENTO DI INGEGNERIA “ENZO FERRARI"

PhD SCHOOL HIGH MECHANICS AND AUTOMOTIVE DESIGN&TECHNOLOGY MECCANICA AVANZATA E TECNICA DEL VEICOLO XXVII CYCLE

NUMERICAL MODELLING OF ABNORMAL COMBUSTION IN HIGH PERFORMANCE SPARK-IGNITION ENGINES

Advisors: Stefano Fontanesi, PhD Prof. Giuseppe Cantore PhD School Director: Prof. Paolo Tartarini

Candidate: Alessandro d’Adamo

Thesis Index Chapter 1. Fundamentals of CFD 1.1

Introduction to CFD

1.2

Mass conservation

1.3

Momentum Equation

1.4

Energy equation

1.5

Equations of state

1.6

Transport Equation for a Generic Variable

1.7

Direct Numerical Simulation

1.8

Large-Eddy Simulation

1.9

The 2-equations k-ε model

Chapter 2. Abnormal Combustion and Knock in SparkIgnition Engines 2.1

Relevance of Knock in Modern Spark-Ignition Engines

2.2

Methods for Knock Measurement 2.2.1 Intermediate radical species concentration 2.2.2 Exhaust gas temperature analysis 2.2.3 In-cylinder pressure signals

2.3 Knock Indices 2.3.1 M.A.P.O (Maximum Amplitude of Pressure Oscillations) 2.3.2 I.M.P.O. (Integral Modulus of Pressure Oscillations) 2.3.3 D.K.I. (Dimensionless Knock Indicator) 2.3.4 Knock Severity Index (K.S.I.)

Chapter 3. The ECFM-3Z Combustion Model 3.1 Motivation of The Model 3.2 Description of the ECFM-3Z Model 3.2.1

Mixing Representation

3.2.2

Reaction Progress Description

3.2.3

Evolution of the

̃ Description During Combustion

3.3

Global Species Equations

3.4

Progress variable ̃ and Tracers

3.5

The Three-Zones Mixing Model of ECFM-3Z

3.6

The ECFM-LES Combustion Model

Chapter 4. Numerical Modelling of the Spark-Ignition Process 4.1

Physics of Spark Ignition

4.2

Ignition Model for RANS Analyses

4.3

ISSIM-LES Model

4.4

4.3.1

Background of the ISSIM-LES Model

4.3.2

AKTIMeuler Ignition Model

4.3.3

Modified FSD equation for the ISSIM-LES Model

Validation of the ISSIM-LES Ignition Model

Chapter 5. UniMORE Knock Model 5.1

Background of the model

5.2

Integral Function for Knock Prediction

5.3

Empirical Correlation for the Autoignition Delay

5.4

Look-Up Table Approach Fundamentals

5.5

Neighbour Conditions

5.6

Interpolation Technique

5.7

Comparison of Empirical and Look-Up Table Interpolated AI Delays

5.8

Implementation of the UniMORE Knock Model in the Star-CD Code

5.9

The Knock Tolerance Function

Chapter 6. Engine Case - RANS Application 6.1

Introduction on RANS analysis

6.2

Numerical Setup for RANS Simulation

6.3

Analysis of the Mixing Process

6.4

Analysis of the Combustion Process

6.5

Knock Tendency for KLSA Condition

6.6

Comparison of Knock Tendency for the Douaud-Eyzat Knock Model

6.7

Knock Tendency for KLSA+3 Condition

6.8

Knock Model Sensitivity to Fuel Anti-Knock Rating

6.9

Conclusions

Chapter 7. Engine Case - LES Application 7.1

Introduction

7.2

Numerical Setup for Large-Eddy Simulation

7.3

Mesh Quality Assessment for LES

7.4

Analysis of Conditions at Spark-Ignition

7.5

Analysis of the Spark-Ignition Phase for KLSA

7.6

Knock Limited Spark Advance Condition 7.6.1

Combustion Analysis

7.6.2

Global Analysis of Knock Tendency for KLSA Condition

7.6.3

End-Gas Analysis of Knock Tendency for KLSA Condition

7.7

Combustion Results for KLSA+3 Condition

7.8

Mixture Quality Promoting Autoignition

7.9 – Conclusions

Bibliography Publications Abbreviations

1. Fundamentals of CFD 1.1

Introduction to CFD

Governing equations describing the flow motion are named “Navier-Stokes” equations. They are based on 3 fundamentals of fluid physics, i.e. mass conservation (also known as continuity), momentum conservation (also known as Newton’s second law) and energy conservation (also known as first law of thermodynamics). An important assumption is that the fluid is considered as a “continuum”, since the analyses are carried out on “macroscopic” scales (i.e. bigger than 1µm) and the molecular structure of the fluid and the molecular motion can be ignored and disregarded. Fluid behaviour is described in terms of macroscopic properties such as velocity, pressure, density, temperature and their spatial and temporal derivatives, all considered as average values over a huge number of single molecules which can be approximated as a point in space (or a single fluid particle), defined as the smallest fluid element which is not influenced by the single molecules’ behaviour. A fluid element of size δxi, δxj, δxk, with generic coordinates and volume δV is considered and a sketch of it is reported in Figure 1.1.

Figure 1.1 - Finite control volume.

All the fluid properties are functions of both time and space: (Eq. 1.1) (Eq. 1.2) (Eq. 1.3)

Chapter 1 – Fundamentals of CFD ̅

̅

(Eq. 1.4)

This dependency will not be further remarked for the sake of simplicity.

1.2

Mass conservation

Mass conservation equation is based on the balance between fluid mass entering and exiting the domain, i.e. the fluid element or “control volume”. The net rate of mass increase/decrease over time is:

(Eq. 1.5) Mass flow through a surface is the product of density, area and velocity component normal to the surface. It is positive if mass flow is entering and negative if exiting. The net balance of the contributions through each surface bounding the element is illustrated in Figure 1.2:

(Eq. 1.6) Figure 1.2 – Contributions to the momentum equation on the control volume.

Equating the two expressions and dividing by the control volume δV a compact notation is obtained: (Eq. 1.7) Which represents the compact form of the 3D continuity (or mass conservation) equation for a compressible fluid. The first term on the left is the rate of density (i.e. mass per unit volume) increase/decrease within the control volume, while the second is the algebraic sum of the fluxes

Chapter 1 – Fundamentals of CFD entering/exiting the volume through the bounding surfaces and is also named “convective term”, i.e. due to the fluid motion.

1.3

Momentum Equation

Following Newton’s Second Law, the acceleration a of a body is parallel and directly proportional to the net force F and inversely proportional to the mass m, i.e. F = ma. Also here, the variation of a physical quantity is caused by both the temporal variation of the quantity and the net flow through the surface bounding the control volume. Similarly to mass, the momentum variation for a fluid element can be expressed as: (Eq. 1.8) The first term represents the rate of increase of momentum per unit volume. The second term represents the variation of momentum due to convection through the control volume surface. The term can be further developed as: (Eq. 1.9) (Eq. 1.10) Using the above expression in the momentum equation, and using the continuity equation, the following expression is obtained: (Eq. 1.11) In Figure 1.3 a sketch of the forces acting on the control volume is illustrated.

Figure 1.3. Sketch of force acting on a finite control volume.

Chapter 1 – Fundamentals of CFD As for the forces acting on the fluid parcel we usually distinguish between mass forces f and surface forces, where the first type is grouped in a single term called the “mass force source”. Mass forces act “remotely” and act on the whole fluid mass. A typical example is gravity, for which the force per unit mass is the gravitational acceleration vector. The second term represents the surface forces acting on the fluid element. Stresses can be split in normal stresses and shear stresses, and are grouped in the tensor. The expression for the momentum conservation is of general use, and loses its generality only when peculiar expression are defined for the stress tensor: for example, for many gases and liquids a correlation between stresses and rate of deformation was observed. Fluids exhibiting that behaviour are usually referred to as Newtonian Fluids.

1.4

Energy equation

The energy equation is derived from the first law of thermodynamics, expressed as: (Eq. 1.12) As before, energy variation in time for a fluid particle and per unit volume can be expressed as the product of density and energy material derivative: (Eq. 1.13) The work done on the fluid particle in the infinitesimal time interval is that exerted by the forces acting on the element surface times the velocity component parallel to the forces themselves. The work can be derived from the previous equations. Considering the work along the i-direction we get:

(Eq. 1.14)

Summing the three previous equations and dividing by δV, we get the total work exerted on the fluid particle by the surface forces. The work by the mass forces, mainly due to the variation of potential energy, is described, as for the momentum equations, by a scalar source term S E, “source of energy per unit volume” in the considered time interval. The final expression is:

Chapter 1 – Fundamentals of CFD

(Eq. 1.15)

The heat exchanged by the fluid particle with the environment is now considered; naming the vector ̅ for the heat flux exchanged through conduction, and with reference to the Figure 1.4:

Figure 1.4. Sketch of energy fluxes on finite control volume.

The overall heat flux can be obtained by summing all the contributions (positive if entering, negative if exiting) through the element bounding surfaces: for example, the contribution along the direction is: (Eq. 1.16) The overall flux due to conduction exchanged by the fluid element per unit volume is equal to: (Eq. 1.17) The application of the Fourier’s Law for heat conduction allows to link the thermal flux to the local temperature gradient, which in compact notation is expressed as: (Eq. 1.18) Where k is the “heat transfer coefficient”. Combining the above expressions we get a new formulation for the heat exchange due to conduction by the fluid element per unit volume, defined as: (Eq. 1.19)


Substituting the above expressions we derive the energy equation for a fluid particle: (Eq. 1.20)

1.5

Equations of state

The 3D motion of a fluid is described by a set of 5 partial differential equations: equation of mass, three equations for the momentum and the equation for energy. Among the unknowns we have four thermodynamic variables: ρ, p, i and T. The thermodynamic equilibrium hypothesis permits to describe the state of the fluid through only two variables thanks to the set of “state equations”. For example, if the assumption of a “perfect gas” is adopted for the fluid we get the two well-known: (Eq. 1.21) (Eq. 1.22) Being R the universal Boltzmann’s constant and cv the constant volume specific heat. It is important to remind that in the case of uncompressible fluids (liquids and/or low-speed gases) density can be considered as a constant, which means that no connection exists between energy equation on one side and mass and momentum equations on the other side, since temperature (which defines the internal energy i) is not dependent on density itself. Under that assumption, the flow field is computed only through the continuity and momentum equations, while energy equation can be solved subsequently, once the velocity vector and the pressure field are known throughout the computational domain.

1.6

Transport Equation for a Generic Variable

Repeating the previous path for a generic variable ϕ, we get a similar equation which describes the transport of ϕ within the fluid flow-field:


(Eq. 1.23) The first term defines the temporal variation of ϕ within the control volume δV; the remaining three terms quantify the variation of ϕ by means of different phenomena. Clearly, ϕ within the control volume will change if any fluid particles crossing the fluid element at the given time drag the variable ϕ into or out of δV. This effect is expressed by the second term, which is named convective transport, i.e. due to the motion of the fluid particles. Nevertheless, even a still fluid can transport any variable ϕ by means of diffusion, i.e. due to molecular agitation, and this transport is quantified by the third term, named diffusive transport, where the constant

is referred to as “diffusivity of

ϕ”. The fourth (and last) term quantifies the so-called sources of ϕ; within this term, both “positive or production” and “negative or dissipation” sources are included. In common practice, the term defines the quantity of ϕ which is generated or destroyed within the control volume in the time interval t; it is important to remark that these are not flows entering into or exiting from δV; they are internal variations which have nothing to deal with either transport or diffusion through the elements surrounding the considered control volume.

1.7

Direct Numerical Simulation

Navier-Stokes equations describe the three dimensional flow field of a generic fluid; they are a system of 5 differential equations (together with two equations of state) in five space/time unknown variables. The most straightforward method for the numerical solution of a fluid-dynamic field, is the one based on the direct discretization of the Navier-Stokes equations in the same form as presented in the previous sections and it is called Direct Numerical Simulation (DNS). The obtained solutions are exact, that is they retain the fluctuation contributions typical of turbulent phenomena: a time average of the obtained solutions will then be needed to get a solution describing the mean flow motion of the fluid. Nevertheless, the direct solution of the Navier-Stokes equations leads to relevant problems: they mostly come from the computational cost: only using extremely fast and massively-parallel super computers with huge memory amounts, together with very refined numerical techniques, it is possible to get solutions within acceptable times. In fact, in order to have a correct solution, the computational grid must be so fine that it is able to capture all the temporal and spatial scales of the fluid-dynamic field. This leads to extremely fine grids and very small computational/integration time steps. Up to the present times, hardware evolution is still far away from allowing the

Chapter 1 – Fundamentals of CFD researchers to apply DNS for practical problems except for very “simple” cases. Nevertheless, DNS is extremely useful to provide a forecasts of the flow field in standard geometries which require “acceptable” computational demands, which can then become test-cases for the validation of the other subsequent approaches.

1.8

Large-Eddy Simulation

Direct integration of the Navier-Stokes equations still shows, up to the present times, many critical issues which strongly limit the use of DNS: among all, the Reynolds number limitation. As aforementioned the high computational cost of DNS is linked to the fact that the flow field is solved exactly, i.e. considering all the eddy scales within the fluid. The basic idea of Large-Eddy Simulation (LES) is that of exactly solving only the big-scale eddies while modelling the effects of the small-scale ones on the mean flow. The computational cost decreases by at least 20-40% (up to 50-60%), but it is necessary to “close” the system of equations since it is necessary to model the small scales of turbulence. Nevertheless, this operation shows some big advantages in comparison with the “classic” modelling of, as it will be shown later, the other turbulence models: while in this last case a single model will have to cover the full range of turbulent eddy scales (having an extremely broad range of characteristics), LES is limited to the modelling of small-scale eddies, that is those close to the Kolmogorov scales. This is far simpler and much more consistent from a formal point of view. Small scale eddies are substantially isotropic, since viscosity tends to dampen the dependence on the direction of the flow. This is not true for the big-scale eddies, which are strongly dependent on boundary conditions, on the geometry and on the geometrical constraints; this strongly limits the use of a general approach to the modelling of large-scale turbulence and it is the major limitation of the approaches based on averaged equations, as it will be shown later for RANS. Results obtained from high quality LES are comparable to those from DNS, mainly because turbulence modelling of the smallest-eddies is described in a univocal and general way, independent on the specific flow motion under investigation. Navier-Stokes equations for a compressible fluid are integrated using a filter function, usually named G, infinitely differentiable, having the specific aim of splitting the turbulent scales. Due to the linearity of the filtering operation with reference to both integration and differentiation, each generic term will undergo filtering. Naming a generic flow variable within the NS equations, the corresponding filtered variable will become:

Chapter 1 – Fundamentals of CFD (Eq. 1.24) where D indicates the flow field domain and Δ is the mean dimension of the computational cell. It is worthwhile to remark that the filtering operation is an integration over the whole fluid domain D of the considered variable, multiplied by the G function; the filter function is usually normalized, that is: (Eq. 1.25) The filter function has the property of reducing, or even eliminating, the amplitudes of the high frequency spatial Fourier harmonics (usually those having wavelengths lower than the cell size Δ) for each considered flow variable F. After the filtering operation is carried out the filtered Navier-Stokes equations are obtained. Neglecting the density variation within the cell, and using for the corresponding average value, the filtered equations of mass and momentum in compact notation become:

(Eq. 1.26)

(Eq. 1.27) where, except for the term

, all the other flow unknowns are the flow variables of the filtered

Navier-Stokes equations. As it will be valid for the RANS case as well, in these equations a new unknown term

appears which needs modelling to get a closed and solvable system; the unknown

tensor is called “subgrid scale” (sgs) tensor since it covers the effects of eddy-structures smaller than the computational cell, which are completely contained within the cell itself.

1.9

RANS Simulations and the 2-equations k-ε Model

The Reynolds-Averaged Navier-Stokes equations (RANS) are derived from the time-averaging operation performed on the Navier-Stokes original set of equations. Time-averaging is based on the decomposition of a generic fluctuating variable into a mean part and a fluctuation around the mean value. The resulting set of equations expresses the time-averaged behaviour, or in case of quasiperiodic flows such as those in internal combustion engines, phase-averaged flow realizations. RANS equations need closure terms to model the Reynolds Stresses, i.e. the product terms between velocity fluctuations.

Chapter 1 – Fundamentals of CFD In this context the 2-equations k-ε turbulence model is developed and it is still nowadays the most widespread and used model for turbulent flows in commercial CFD software. The idea is that of introducing two transport equation for k and ε. These have the form of:

(Eq. 1.28)

(Eq. 1.29)

The modelled equations give a relation for the energy transfer represented by the energy-cascade process, which is determined by the problem-dependent large-scale motions. The equations above, represents the turbulent kinetic energy and its dissipation rate process at a small scale. The origin of the model comes from experimental observations : at high Reynolds numbers, the energy dissipation rate and the turbulent kinetic energy undergo variations in time which are more or less proportional. An increase of k corresponds to an increase of ε of equal intensity, and vice versa; the same happens for decreasing rates. This fact, from a mathematical perspective, is converted into a direct proportionality between the productive and dissipative terms of k and ε: this assumption is called “turbulent equilibrium hypothesis”. The mentioned time correlation which stands between k (defined in m2/s2) and the dissipation rate ε (m2/s3) represents the inverse of the time-scale of the large scale eddies, i.e. it indicates the turn-over frequency of the large-scale eddies, measured in s-1. One major advantage of k-ε model is that it is based on the Boussinesq assumption typical of eddy viscosity turbulence models. It allows to simplify the evaluation of the turbulent stresses, reducing computational times and explaining why such models are the most used from an industrial point of view for the analysis of turbulent flows. Another advantage is their considerable robustness: from a computational point of view they are, surely, highly stable and efficient. On the contrary, some inner simplifications in the transport equations can lead to poor accuracy in the representation. Major error sources in two-equation models are the turbulent equilibrium assumption and the Boussinesq hypothesis. As for the turbulent equilibrium assumption, this is sufficiently true only for free-flows at high Reynolds numbers. Boussinesq hypothesis introduces the concept of eddy viscosity in perfect analogy with the molecular; the definition as a scalar, implicitly, imposes an isotropy condition to the eddy viscosity. This assumption leads to a linearity between the strain rate and the Reynolds stresses, which is never verified, except for very simple flows, far from solid

Chapter 1 – Fundamentals of CFD walls; for complex fields, highly distorted, where geometry effects are relevant (bended pipes, etc.), a linear relation is wrong.

2. Abnormal Combustion and Knock in Spark-Ignition Engines 2.1

Relevance of Knock in Modern Spark-Ignition Engines

The recent legislation in terms of passenger car tailpipe emissions and fuel consumption is more and more stringent. This pushed the engine manufacturers towards new concept in engine design, which can be summarized as namely the reduction of fuel consumption and of the global engine displacement. In order to keep the same target output of a given engine unit, several pathways are generally followed: 

Increase in volumetric compression ratio:



Increase in engine thermal efficiency;



Adoption of turbocharging systems.

;

Common to these strategies is the onset of abnormal combustion events. The most known of them is the so called engine knock, consisting in the spontaneous ignition of the unburnt mixture ahead of the propagating flame front. The resulting sudden heat release can potentially induce a set of pressure waves propagating in the cylinder volume and reflecting on the solid walls. The transition from autoigniting hot-spots to developing detonation waves is illustrated by Bradley and Kalghatgi (2009) and later refined by Peters et al. (2013) and it correlates the latter phenomenon to the temperature gradient field in the end-gas. In the present work autoignition is considered as a knocking event. The impact of the pressure wave on the combustion chamber walls (piston, head, lines, valves) is responsible for the typical engine ringing noise, which is the origin of the name “engine knock”. The travelling pressure wave is the main damaging actor inducing engine failure. A relevant example of experimental work regarding pressure wave visualization is from Kawahara et al. (2009).

Chapter 2 – Abnormal Combustion and Knock in Spark-Ignition Engine

Figure 2.1 – Knocking pressure wave propagation from autoigniting hot spot (from Kawahara et al., 2009).

The main effects of the pressure wave impact and reflection on solid components are: 

Increased thermal loss: the impact of the pressure waves on the solid walls promotes heat transfer. Several authors claim that the instantaneous heat transfer coefficient undergoes an increase by a factor ranging from 2 to 10, and examples of such are works by Grandin and Denbratt (2002), Ezekoye (1996) and Ollivier et al. (2006). During severe knocking conditions the thermal permeability of the combustion chamber is therefore much higher than the desired.



Reduced thermo-mechanical properties of the solid materials, as a consequence of the thermal overload of the solid components induced by the impacting pressure waves.



Removal of lubricant film by pressure wave reflections, increasing friction losses and supplementary wall heating.



Piston ring failure, due to the possible spontaneous-ignition of the unburnt mixture trapped in the crevices between cylinder liner and piston side when intense pressure impact on the cylinder wall. Another reason for piston rings failure is the aforementioned removal of lubricant film, since this prevents the direct contact of the ring itself with the cylinder liner.



Mechanical loading of all the solid components facing the combustion chamber, as peak pressure levels in severe knocking conditions can largely exceed the target maximum pressure for which components are designed.

Despite low/sporadic knock can be usually tolerated since it does not induce significant engine damage, heavy or recurrent knock is not acceptable. Figure 2.2 shows examples of highly damaged pistons from hard engine knock.


Figure 2.2 – Damaged piston examples from heavy engine knock.

2.2

Methods for Knock Measurement

A variety of methods for the measurement of the intensity of the knocking phenomenon are proposed in literature, and they are here briefly categorized. Extensive reviews are reported in works by Millo and Ferraro (1998) and by Corti and Forte (2009).

2.2.1 Intermediate radical species concentration These methods are based on the visualization of the end-gas radiation immediately before and during the autoignition event. It is known that knock occurrence can be correlated to local peaks of HCHO in the end-gases. However these methods are extremely expensive, as they require an optically accessible engine, and they are exclusively devoted to the research field.

2.2.2 Exhaust gas temperature analysis Since knock promotes heat transfer to the solid walls, exhaust gas temperature decreases due to the reduced energetic content of the in-cylinder charge. This was experimentally measured by AbuQudais (1995) and by Ollivier et al. (2005), where a clear correlation with engine running in knocking conditions was detected. A major advantage of such techniques is the non-intrusive measurement of exhaust gas temperature.

2.2.3 In-cylinder pressure signals Methods from this category are the most adopted for knock measurements and knock index definition. Measurements are carried out by pressure transducers flush-mounted on the combustion chamber. A typical measured pressure signal during knock occurrence is reported in Figure 2.3 for a progressive increase in SA.


Figure 2.3 – In-cylinder pressure trace for regular and knocking combustion (from Heywood, 1988).

In Figure 2.3 it is well visible as in the pressure trace of a knock-affected engine cycle is characterized by an initial portion of regular combustion until a sudden and fast-varying pressure signal is visualized. The typical procedure of signal processing is based on a software band-pass filtering of the same, in the range of 4-20 kHz. The low cut-off filtering frequency is needed to filter out the regular combustion noise which is associated with low frequencies. The high-pass filter is needed in order to avoid signal disturbance given by resonant frequencies of the sensor itself. The largest problem of this kind of knock measurements is the dramatic dependence of the measured signal on the sensor location.

2.3 Knock Indices The field of knock index definition is commonly recognized as a non-standardized research area, and the present taxonomy is limited to widespread knock indexes.

2.3.1 M.A.P.O (Maximum Amplitude of Pressure Oscillations) This index is defined as the maximum filtered pressure signal measured by the in-cylinder pressure sensor (Eq. 2.1): (| ̃| In Eq. 2.1 | ̃| is the modulus of the filtered pressure signal, and

)

(Eq. 2.1) is the crank angle of knock onset

is a measurement window needed to capture the complete evolution of the knocking event.

Chapter 2 – Abnormal Combustion and Knock in Spark-Ignition Engine Since M.A.P.O. is a cycle-resolved measurement, the usual practice in the experiments is to define knock onset when a given fraction over a pre-defined sample of cycle (i.e. the latest 100 or 200 cycles) exceed a threshold M.A.P.O. value.

2.3.2 I.M.P.O. (Integral Modulus of Pressure Oscillations) This index is based on an energetic content associated with the fluctuating pressure signals. It is usually based considering an ensemble average over N measured cycles, and it is defined as: ∑ ∫

| ̃|

(Eq. 2.2)

2.3.3 D.K.I. (Dimensionless Knock Indicator) This indicator was first proposed by Brecq et al. (2003) with the goal of defining a more general index than M.A.P.O. or I.M.P.O. The Dimensionless Knock Indicator is defined as: (Eq. 2.3) Therefore it is a combination of both M.A.P.O. and I.M.P.O., with the addition of W which is the angular amplitude of the observation window for knocking analysis. The D.K.I. index physically represents the ratio of the “pressure noise” generated by knock with respect to a total surface defined by

. The concept is illustrated in Figure 2.4.

Figure 2.4 – Graphical illustration of D.K.I. physical meaning (from Brecq et al. ,2003).

For regular combustion, the noise associated with deflagrating combustion is low, and the noise-tosurface ratio implicit in the D.K.I. definition assumed typical values in the range of 0.2-0.3. In the range of regular combustion, this value remains roughly constant for a wide range of SA variation. When knock originates and peak pressures are registered by transducers, the D.K.I. value drops to values close to zero. This trend is illustrated in Figure 2.5.


Figure 2.5 – Graphical illustration of D.K.I. variation as a function of SA (from Brecq et al. ,2003).

Since the D.K.I. indicator is based on commonly available M.A.P.O. and I.M.P.O. measurements, it is an appealing index for engine experimentalists. Moreover, it pursues the idea of a “general knock index” and tries to overcome the lack of standard threshold values for both the M.A.P.O. and the I.M.P.O. indices.

2.3.4 Knock Severity Index (K.S.I.) The Knock Severity Index proposed by Klimstra (1984) is a simple yet appealing alternative to the above mentioned indicators. It is not based on flush-mounted pressure transducers, instead it is defined starting from easily measurable quantities. The assumption of the K.S.I. is that at the instant of knock onset, all the remaining unburnt mixture is instantaneously consumed. This approximation is motivated by the consideration that after a detonating wave is originated in some point of the combustion chamber, the burn rate of the mixture involved by the shock wave is orders of magnitude higher than that of a deflagrating flame. Based on this, the hypothesis of attributing an infinitely fast chemistry to knocking phenomenon is considered acceptable. The result is that a constant volume combustion process is assumed for the knocking phenomenon. The K.S.I. is then defined as the product of two factors causing engine damage: 

A large residual mass fraction at knock onset

: the earlier a detonation wave develops

in the cycle, the larger is the air-fuel mixture which is involved in the knock process. This easily leads to severe engine damage.

Chapter 2 – Abnormal Combustion and Knock in Spark-Ignition Engine 

The higher is the pressure jump

associated with the instantaneous heat release. In

Klimstra’s work, this is calculated starting from thermodynamics considerations, while no pressure measurements are involved in the calculation process. After simple algebraic manipulation the pressure jump is defined as in Eq. 2.4: (Eq. 2.4) In Eq. 2.4 LHV is the fuel lower heating value, R is the universal gas constant, cp is the isobaric specific heat of the unburnt mixture while pKO and TKO are pressure and temperature at knock onset instant. Following these considerations the K.S.I. is defined as in Eq. 2.5: (Eq. 2.5) This index is based on easily measurable quantities at knock onset instant, and it does not considers a pressure fluctuation signal processing. It then represents an appealing indicator in absence of robust experimental data. For this reason the K.S.I. will be applied to numerical analyses in Chapter 6 and 7.

3. The ECFM-3Z Combustion Model 3.1 Motivation of The Model The origin of the ECFM-3Z combustion model comes from the evolution of the combustion modes encountered in modern internal combustion engines. Given to the more and more stringent regulations, the consolidated subdivision between perfectly premixed combustion and purely diffusion combustion is less and less able to cope with the modern combustion devices. A clarifying example of such combustion mixed mode is the combustion occurring in a modern GDI engine, where perfect mixture homogeneity is hardy obtained due to the reduced time allowed for mixing process. Even though combustion is mostly premixed, a broad range of mixture in-homogeneities is likely to be interested by the main flame front, as well as liquid droplets can still be present leading to a partially-diffusive combustion mode. Since the GDI technology is more and more present in recent passenger and racing car engines, computational models able to simulate the newly present phenomena, such as ECFM-3Z, must be developed.

3.2 Description of the ECFM-3Z Model The ECFM-3Z combustion model is based on a bi-dimensional representation of the state of the gas mixture. This is simultaneously represented as a 2D space (

̃ ) of the mixture fraction Z and of the

progress variable of combustion ̃ . A schematic representation of this is given in Figure 3.1.

Figure 3.1 – The cell separation between burnt/unburnt status and representation of the three mixing zones. Figure from Colin and Benkenida (2004).

Chapter 3 – The ECFM-3Z Combustion Model 3.2.1 Mixing Representation The mixing state of each fluid cell is represented in ECFM-3Z by a three-zone splitting: the unmixed fuel zone (named F), the unmixed air + EGR zone (named A) and the mixed zone (named M) containing fuel, air and EGR. This concept is a simplified representation of a Probability Density Function of the mixture fraction variable Z by a three-delta distribution (Eq. 3.1). (Eq. 3.1) The first delta function is relative to the unmixed air + EGR region A, the second to the unmixed fuel region F, while the third is the one pertaining the mixed region M. This mixing model follows a CMC-type approach (Conditional Moment Closure), with a Z-space discretization operated by three points. A dedicated mixing model is responsible for the mass transfer from unmixed region A and F to the mixing state M. This model is presented in Section 3.5 and it is based on a local turbulent time-scale.

3.2.2 Reaction Progress Description The only region where combustion is allowed to take place is region M, where fuel and air are simultaneously present. As a consequence, zones A and F only act as source regions for the mixed state F. Therefore combustion calculations are only conditioned on the mixed zone M, and only two possible states assumed for the gases: unburned and burned, hereafter named with the superscripts u and b (Figure 3.1). The relative amount of the unburned/burned gas in mixed zone M is given by the reaction progress variable ̃ , whose definition is given in Section 3.4. The reaction progress description is given by the local value of ̃ , ranging from 0 for completely unburned gases to 1 for fully burned mixture. The burned gases in region Mb have temperature Tb, while all the other five regions (Au, Fu, Mu, Ab, Fb) have temperature Tu.

3.2.3 Evolution of the (

̃) Description During Combustion

The description of the mixing and combustion evolution of the three-zone model is given for a direct injection combustion example. The characteristics mixing and combustion states are schematically represented in Figure 3.2.

Chapter 3 – The ECFM-3Z Combustion Model

Figure 3.2 – The cell separation between burnt/unburnt status and representation of the three mixing zones. Figure from Colin and Benkenida (2004).

Case A: the initial condition is an environment filled with pure air. The fluid cell is composed by the only region Au; the absence of any fuel concentration prevent any mixing or combustion modelling. A liquid fuel is injected and the unmixed fuel region Fu is created by fuel evaporation. Fuel and air are initially unmixed and region M is not present. Case B: the mixing model progressively transfer fuel and air from their respective unmixed region to the mixed state Mu. From this instant, both premixed and auto-igniting combustion are possible in region Mu. Case C: the common result from premixed combustion or auto-ignition event is the transfer of the unburned gas in Mu to the burned mixed region Mb. This situation represent a premixed-controlled combustion, as an infinitely fast chemistry is assumed for this combustion mode. Case D: a possible situation is that the unmixed fuel and air (regions F and A) are still characterized by a relevant mass fraction even in case of advanced combustion (i.e. ̃ > 0). The region Fb (respectively Ab) are created, corresponding to the ̃ fraction of region F (respectively A). The mixing operated by the dedicated model is still active and these unmixed gases are continuously mixed with the burned mixed region Mb. This case represent a typical diffusion-controlled combustion, i.e. the slowest limiting factor is the mixing process of the reactant species. The remaining fraction (

̃ ) of the unmixed region (i.e. Fu and Au states) is mixed with the unburned

Chapter 3 – The ECFM-3Z Combustion Model mixed Mu zone and they are consumed with the described premixed or auto-igniting combustion mode described in Case C. This schematic representation allows to describe all the possible combustion modes. The description of the fluid cell as a dynamic (Z, c) space allows the simultaneous representation of the different phenomena, and the occurrence of each is predicted by the relative weight of the mixing state, accounting for local turbulence levels, rather than on the mixture reactivity given by the fuel consumption rate. The predictive capability of the ECFM-3Z combustion model make it a suited tool for all types of combustion devices, in particular for internal combustion engines where a variety of combustion regimes can simultaneously occur.

3.3

Global Species Equations

In ECFM-3Z a transport equation is solved for the Favre average mass concentration of: fuel, O 2, N2, CO2, H2O, NO, CO, H2, O, H, N, OH and SOOT. These transport equation follow the generic modelling expressed by Eq. 3.2:

(Eq. 3.2) In Eq. 3.2

and

represent the laminar and turbulent viscosities respectively, while ̅ is the

source/sink term due to combustion. The model considers the fuel as subdivided in two regions: the fuel present in the fresh gases ̃ and the one present in the burnt gases ̃ . While the first portion is the one participating to premixed combustion or to autoignition, the last is the one involved in diffusive combustion. Their respective transport equations are Eq. 3.3 and Eq. 3.4:

(Eq. 3.3)

(Eq. 3.4) An important aspect to consider in GDI or Diesel engines is that fuel evaporation from liquid droplets can either occur in an unburned as well as in a burnt gas region. To account for this

Chapter 3 – The ECFM-3Z Combustion Model different behaviour the gaseous fuel produced ̃

is assigned to the unburnt or burnt region

following the local progress variable ̃ which is defined in the following section.

3.4

Progress variable ̃ and Tracers

The ECFM-3Z combustion model is based on the flamelet hypothesis stating that the flame can be seen as an infinitely thin region separating the burnt gases from the unburnt fresh mixture. The mass conservation through the flame front allows the local burnt mass fraction ̃ to be proportional to the fraction of fuel mass which was consumed since the beginning of combustion. This is expressed by Eq. 3.5:

(Eq. 3.5) In Eq. 3.5 ̃

is the mass fraction of fuel before the onset of combustion. For perfectly mixed

charges without vapour sources coming from droplet evaporation, ̃ constant in time. In practical application, such as engines, ̃

is uniform in space and

is a temporal and spatial dependent

variable since imperfect mixing and liquid fuel evaporation are typical situations. In order to account for the fuel tracer concentration, a transport equation is defined (Eq. 3.6):

(Eq. 3.6) The fuel tracer is diffused and convected in the same way as the actual fuel; also, its source term from spray evaporation is identically accounted for. The fundamental difference is that the tracer is not consumed by combustion, i.e. it is the fuel as a fictitious non-reactive species. This is the reason why Eq. 3.6 is the same as the fuel transport equation without the source term. The progress variable ̃ is only defined where the local fuel tracer concentration is positive. This simply indicates that combustion can only occur in a cell where fuel is (or was) present in some quantity. Tracer equations are also solved for other species in ECFM-3Z: O2, CO, NO, H2 and SOOT. In the same was as for fuel, tracers are used to track the reference species concentration before combustion reactions altered their presence.

Chapter 3 – The ECFM-3Z Combustion Model

3.5

The Three-Zones Mixing Model of ECFM-3Z

For the sake of description of the mixing model, two additional quantities need to be introduced: the unmixed fuel ̃ , representing the fuel concentration in regions

and

unmixed oxygen ̃ , accounting for the oxygen mass fraction in regions

in Figure 3.1, and the and

. These species

do not enter in the global species mass balance and they are considered as fictitious species for which ECFM-3Z solves Eq. 3.7 and Eq. 3.8:

(Eq. 3.7)

(Eq. 3.8) The mixing is described by the source terms ̃

and ̃

. The mixing rate for fuel and oxygen,

Eq. 3.9 and 3.10, is considered proportional to the respective volume fractions and to a mixing time scale

(Eq. 3.11). This latter is considered proportional to the turbulent time-scale given by the k-

ε turbulence model.

(Eq. 3.9)

(Eq. 3.10) (Eq. 3.11)

3.6

The ECFM-LES Combustion Model

The combustion model that will be used for LES simulations is the ECFM-3Z model adapted for LES studies and first proposed by Devessa et al. (2004) and Richard et al. (2007), which is available in the Star-CD code. This choice is mainly justified by the model fundamental nature which is the same as the FSD family of combustion models, with a minimum amount of assumptions required for adaptation to the LES context. In brief, the model belongs to the family of the coherent flame models where the flame surface density FSD (the flame surface area per unit volume) evolution is described by a balance equation which accounts for the effects of strain and curvature, both in their

Chapter 3 – The ECFM-3Z Combustion Model resolved and subgrid-scale contributions, along with the propagation of the flame itself in laminar unburnt gases zone. The FSD transport equation is reported in Eq. 3.12:

(Eq. 3.12)

In Eq. 3.12 Tres, Tsgs, P, Sres, Ssgs, Cres, and Csgs are the resolved transport, the subgrid-scale transport, the laminar propagation, the resolved strain, the subgrid-scale strain, the resolved curvature and the subgrid curvature, respectively. The Γ term represents an efficiency function that models the strain from sgs vortices onto the flame front and is taken from Colin et al. (2000): (Eq. 3.13) In Eq. 3.13 ̂ and

are the combustion filter size and the laminar flame thickness, respectively. In

the LES version of the FSD equation (Eq. 3.12) the presence of resolved terms, that require sufficiently fine grid size to be represented, and the laminar propagation term are what distinguishes the above equation from the RANS counterpart: in fact, for this last, every term has to be modelled and the turbulence viscosity is assumed to be much higher than the molecular one. The resolved terms and the propagation term actually make it possible to simulate (as opposed to model) the evolution of the flame surface even for very low (sgs) turbulence levels which, for example, are not too infrequent situations in the early stages after spark ignition. The FSD equation above is filtered at the combustion size rather than at the mesh size, where the combustion size is approximately equal to Nres times the grid size. With Nres typical = 5 and mesh characteristic sizes of approximately 0.5 mm, the combustion filter size is then approximately equal to the expected flame brush thickness. The use of this filter is justified by the circumstance that vortices smaller than the flame brush thickness are unable to wrinkle the flame and, therefore, they limit the ability of the Γ function to properly model the sgs strain rate.

4. Numerical Modelling of the SparkIgnition Process 4.1

Physics of Spark Ignition

In Spark-Ignition (SI) engines, the electrical discharge produced between the electrodes of the spark plug by the ignition system is needed to start the combustion process. The high-temperature plasma kernel develops into a self-sustaining flame front which propagates throughout the combustion chamber. The main phases characterizing a typical spark-ignition event are represented in Figure 4.1, in terms of their voltage and current levels.

Figure 4.1 – Voltage and current variation in time for a conventional coil spark-ignition system (from Heywood, 1988).

In traditional ignition systems the necessary condition for a spark discharge to develop is a sufficiently high voltage between the spark plug electrodes. The electrical potential is increased until an electrical breakdown occurs within the inter-electrode gas mixture. This phase is called breakdown phase and it is characterized by extremely high current intensity (up to 200 A) and voltage (up to 10 kV). The duration of this phase is extremely short, with typical time scales of the order of 10-9 s. The temperature in the plasma column that is created reaches up to 60000 K, generating an expanding shock wave in the surrounding gas. The breakdown phase is extremely short but its function is to generate the “electrical path” between the electrodes for the following stages.

Chapter 4 – Numerical Modelling of the Spark-Ignition Process

The breakdown phase is followed by the arc phase, when the cylindrical plasma expands largely due to heat conduction and diffusion. In this phase the exothermic chemical reactions leading to the propagating flame develops in the mixture. The voltage during this phase is lower (less than 100 V) and large voltage drops are measured in the proximity of both the electrodes. The final stage of the ignition process is the glow discharge phase, where the energy storage device (typically an ignition coil) dumps its electrical energy into the discharge circuit. In this stage the energy losses at the electrodes are higher than in all the preceding phases, exceeding values as high as 70%. The minimum energy required to ignite a quiescent stoichiometric fuel-air mixture is very low (about 0.2 mJ). However, this value can be one order of magnitudes higher when lean or rich mixtures are involved, which is a very common situation in modern direct-injection engines. Moreover, the ignition process is even more complicated in engines since the mixture is never quiescent and local velocities can be as high as 50 m/s. This has an impact on the glow phase, due to its longer duration with respect to the breakdown and the arc phase. The electrical arc is convected and lengthened by the flow, which reduces the relative importance of heat losses. As a consequence the ignition process results more efficient, even though the same energy is transmitted to the gas into a larger volume, hence the risk of misfiring events arises for extremely high flow velocities (in conjunction with lean mixtures).

4.2

Ignition Model for RANS Analyses

The model proposed by Boudier et al. (1992) is adopted for the RANS analyses proposed in Chapter 6. In this model, the ignition period is treated in two distinct phases. In the first phase, an electric discharge occurs between the electrodes and heats up the mixture to ignition point. An approximately spherical kernel forms with a rapidly expanding reaction zone. The propagation speed increases from its minimum value and asymptotically approaches the laminar flame speed for a planar unstretched flame, given by Eq. 4.1: (Eq. 4.1)

The assumed spherical kernel growth during this stage can be calculated from Eq. 4.2: (Eq. 4.2)


When the kernel propagation speed reaches the value of

, the first transition criterion is met.

During the second stage, it is assumed that the reaction zone of the laminar kernel still propagates with the laminar flame speed, augmented by the expansion ratio, but is simultaneously wrinkled and thickened by turbulence. The kernel radius is still calculated from Eq. 4.2 but the kernel surface area during this phase equals the sum of the area of the spherical laminar kernel and the area of the wrinkles. The rate of increase of the kernel area is calculated from Eq. 4.3, accounting for both the flame kernel surface increase due to the laminar propagation (first term on RHS) and to the contribution given by turbulent stretch. This latter is given by the ITNFS function proposed by Meneveau and Poinsot (1991).

(Eq. 4.3)

The second stage ends when the second transition criterion is met. This is defined as the time when the laminar stretch Kl (Eq. 4.4) decreases below the level of the turbulent stretch Kt.

(Eq. 4.4)

When this criterion is met the flame stretch is governed by the turbulent stretch

and the flame

modelling is completely handled by the ECFM-3Z combustion model. A flame surface density distribution is imposed at this stage and it represents an initial condition for the combustion model. One of the major drawbacks of the model is the lack of any modelling for the electric circuit. However this model was adopted in spark-ignition simulations over a wide variety of engine conditions and mixture qualities and a satisfactory agreement with experimental data was always obtained in past analyses.

4.3

ISSIM-LES Model

4.3.1 Background of the ISSIM-LES Model In this work an advanced ignition model is adopted for Large-Eddy Simulation analyses, i.e. the ISSIM-LES ignition model first proposed by Colin and Truffin (2011). The name is the acronym for “Imposed Stretch Spark Ignition Model” and it is based on the description of the flame kernel growth since the early phase thanks to a modified FSD transport equation. Since phenomena occurring during the early phases of flame kernel formation are considered to be the main


responsible of combustion variability, a detailed modelling of these is of high interest in the context of cycle-to-cycle variability simulation. The presented ISSIM-LES implementation in Star-CD was conducted within a joint project of University of Modena and CD-adapco. It was developed through an internship in the combustion modelling group where the relevant parts of the Star-CD source code and of ECFM-LES combustion model were modified to allow the implementation of ISSIM-LES.

4.3.2 AKTIMeuler Ignition Model In order to highlight the improvements brought in by the ISSIM-LES model, a brief description of the AKTIMeuler ignition model is given in this section. The reason for this is that this model was the adopted ignition model in several studies con combustion CCV carried out in a turbocharged DISI engine in Fontanesi et al. (2013) (1)-(2)-(3)-(4). A general lack of CCV of the early stages of combustion development (e.g. MFB5, MFB10 etc.) was measured from LES simulations with respect to experiments. The search for candidate causes of combustion repeatability was identified in the ignition process handled by the AKTIMeuler model. In this model an sphere of partially burnt gases is imposed in the domain in order to initialize the FSD equation. The volume of initial burnt profile is defined as the volume of a cylinder of radius the laminar flame thickness

and the electrode gap as length 〈

(Eq. 4.5):

〉

(Eq. 4.5)

This burnt profile is imposed following a Gaussian profile given by Eq. 4.6: ̅ In this equation the constant

(

) satisfies

| ∫

̅

| ̂

(Eq. 4.6)

, while ̂ is the combustion filter size.

Two major limitations are identified in the AKTIMeuler ignition model: 

instantaneous deposition of a flame kernel;



fully-resolved flame kernel.

The proper ignition phase is not modelled in space and time, and a developed flame is imposed to the calculated flow solution. The initial flame kernel is modeled by a 0-D model. These aspects depict a very loose coupling between flow field and flame development, being the latter imposed to


the first and not modelled in a coupled way. In the very common application to LES simulation of combustion in SI engines, this results in a very stiff and self-similar ignition phase throughout different cycles (i.e. different flow realizations), resulting in reduced levels of cycle-to-cycle variability (CCV) and/or CoV of IMEP/pmax. The mentioned aspects depict the framework for the ISSIM-LES model implementation.

4.3.3 Modified FSD equation for the ISSIM-LES Model The main incentive behind this model is the theoretical ability of the FSD equation to describe also the early phase of flame initiation by the spark. As most of the flame kernel creation and development occur at a subgrid scale for typical engine mesh sizes, the need to introduce dedicated terms or to suppress existing ones in the standard FSD arises. To this aim a modified FSD transport equation (Eq. 4.7) is proposed by Colin and Truffin (2011): ̅̃

̅

̅ ̃

̇

̃

(Eq. 4.7)

The detailed description of the different terms from the standard FSD transport equation is outlined in the referenced paper. Here the presence of the FSD source term ̇

is highlighted, which in this

model is calculated from the simulation of the spark discharge from the secondary circuit model. A fundamental requirement of a model able to treat both ignition and propagation is the continuity from early kernel development to a fully propagating flame. The transition is governed by a function

̅

, which is defined in as in Eq. 4.8 and illustrated in Figure 4.2: [

(

)]

with

⁄̂

(Eq. 4.8)


Figure 4.2 – α-function for subgrid to resolved transition in the modified FSD equation.

This formulation for the α-function is used throughout the present activity. For the sake of completeness it is however worth to notice that the only basic requirement of this function are:   

continuity; ̅ ̅

; ;

Once these are met, any different formulation can be adopted as a candidate to substitute Eq. 4.8. In Eq. 4.7 the terms of the modified FSD transport equation which are multiplied by α are suppressed during the ignition phase, while the term

̅ ̃ , which is not present

in the standard FSD equation, is called stretch during ignition and it is maximum during ignition and suppressed in developed flame.

4.4

Validation of the ISSIM-LES Ignition Model

The validation of the ISSIM-LES ignition model was carried out against experimental measurements conducted at the Leeds University by Lawes et al (2005). An extended description of their apparatus, the Leeds Mk2 bomb, is largely reported by Gillespie et al. (2000) and Bradley et al. (2011). The fundamental features are here recalled for the sake of completeness. The apparatus is a stainless spherical vessel of inner diameter 380 mm, in which a premixed fuel-air mixtures is ignited by means of two centrally mounted electrodes. Three orthogonal pairs of quartz windows are present and allow optical access for imaging and flame diagnosis. The ignition and


flame propagation characteristics of several fuels are examined, such as isooctane, methanol and methane. The experiments relevant to the validation of the ISSIM-LES model are carried out at initial temperature of 360 K and an absolute pressure of 50 bar. An homogeneous isotropic turbulent flow field is produced within the combustion volume by four fans driven by electric motor. Measurements conducted at Leeds University indicate an integral length scale for turbulence equal to 20 mm and a velocity fluctuation of 2 m/s. A premixed isoctane-air mixture is obtained is considered for the presented validation, although as mentioned methanol-air and methane-air were also tested. The choice of isoctane allows to consider a fuel whose properties are close to those of commercial gasoline, both in terms of physical properties and burning characteristics, while retaining the simplicity of a single-component fuel. Three mixture qualities are tested in the experiments: a lean mixture (Φ=0.8), a stoichiometric one (Φ=1.0) and a very rich one (Φ=2.0). In Figure 4.3 the flame radius and the pressure rise from the experiments are reported from Lawes et al. (2005) contribution.

Figure 4.3 – Flame radius and associated pressure rise for isooctane-air mixture (from Lawes et al., 2005).

The observation of Figure 4.3 allows to conclude that the initial part of combustion (before approx. 5 ms) does not produce a measurable pressure rise in the volume. This is due to the limited burnt mass originating just a modest heat release. This allows to introduce some approximations in the numerical simulations.




Boundary conditions: since the simulation is limited to the early combustion development (from ignition to 5 ms), the constant volume experiment in the closed combustion vessel can be assumed as a combustion in a constant pressure environment.



The shape of the combustion domain is not relevant since the simulation is limited to the formation and early development of the flame front. This allows to create a cubic fluid domain instead of a spherical one (as the actual combustion vessel), with an excellent mesh regularity.

A three-dimensional structured grid is created with hexahedral volumes with uniform cell size of 0.5 mm. This is a recommended typical cell size for Large-Eddy Simulations since it is considered as an upper limit to sufficiently resolve in-cylinder flow structures. The size of the domain is approx. 18x18x18 mm, with a total of about 7M fluid cells. Ignition is triggered in the centroid of the domain, so that a fully three-dimensional flame front is allowed. No symmetry planes can be adopted since the unsteadiness of Large-Eddy Simulation. In order to reproduce the turbulent flow field of the experiments, a statistically homogeneous isotropic turbulent flow field is imposed as initial condition, and a representation of the resolved flow field and of the subgrid-scale turbulence is reported in Figures 4.4 and 4.5 for a section cutting the ignition point. As for the latter, the static Smagorinsky model is adopted.

Figure 4.4 – Resolved flow field at ignition.


Figure 4.5 – Resolved velocity magnitude at ignition.

The combustion model is ECFM-LES with the ISSIM-LES ignition model. The modified transport equation for FSD (Eq. 4.7) is resolved, accounting for resolved and subgrid terms for flame kernel growth and development. The progress of combustion is represented by the Favre-averaged reaction progress variable ̃ . As anticipated in Chapter 3, ̃ is bounded between 0 in fully unburnt gases and 1 for combustion products. Since the region where ̃ is varying represents the flame front realization, it is interesting to observe this thanks to the ̃

̃ field. This scalar field is 0 for non-reactant gases (both

burnt and unburnt), while peaks 0.25 value for ̃ The ̃

, i.e. the central section of the flame front.

̃ scalar field is represented in Figure 4.6 for several instants after ignition, together

with the associated outer flame surface (iso-surface of ̃

).


Time = 1.00 ms

Time = 0.66 ms

Time = 0.33 ms

̃

̃

Iso-surface of ̃

Time = 2.00 ms

Time = 1.66 ms

Time = 1.33 ms


Figure 4.6 - ̃

̃ field and iso-surface of ̃

for a stoichiometric isooctane-air mixture.

As visible from Figure 4.6 the flame front is wrinkled by the homogeneous isotropic turbulent flow field, mimicking the fan-generated turbulence from the experiments.


The lack of a large-scale flow motion is responsible for the absence of preferential direction for flame propagation, which preserves a quasi-spherical shape during the whole combustion development. Another reason for this is that the mixture is imposed as perfectly premixed and homogeneous in the simulations (i.e. no subgrid scalar fluxes are present). Following the experimental practice, an useful approximation is carried out to recover an equivalent flame radius. The flame volume

is first calculated based on the resolved progress variable ̃

following Eq. 4.9: ∫

̃

(Eq. 4.9)

Three threshold levels are introduced for filtered ̃ values to be considered as flame edge marker. These are 0.1, 0.5 and 0.9, meaning that flame is assumed present when local ̃ value exceeds each of the respective values. The motivation of this multiple measurement is the expected difficulty in comparing numerical results with experimental flame radius measurements, which are based on optical techniques such as schlieren images and laser sheet acquisitions. If the assumption of spherical shape is introduced for the flame, the flame volume to that of a sphere. It is then immediate to calculate the equivalent flame radius

is related as reported in

Eq. 4.10: √

(Eq. 4.10)

The flame radius for the three mixture qualities is reported in Figure 4.7.

Flame Radius

Φ=1.0, ProgVar=0.1

1.00E-02

Φ=1.0, ProgVar=0.5

8.00E-03

Φ=1.0, ProgVar=0.9 Φ=0.8, ProgVar=0.1

6.00E-03 [m]

Φ=0.8, ProgVar=0.5 Φ=0.8, ProgVar=0.9

4.00E-03

Φ=2.0, ProgVar=0.1

2.00E-03 0.00E+00 0.00E+00

Φ=2.0, ProgVar=0.5 Φ=2.0, ProgVar=0.9 2.00E-03 Time [s]

4.00E-03

Figure 4.7 – Calculated flame radius against experiments (thicked dashed lines) for isooctane-air mixtures at Φ=0.8, Φ=1.0 and Φ=2.0..


Simulations for stoichiometric isoctane-air mixture are in good agreement with the experimental data, while results for rich (Φ=2.0) and lean mixtures (Φ=0.8) need more discussion. Simulation and experimental results agree in indicating the propagation speeds for both these mixtures as reduced with respect to the stoichiometric one. Where calculations and experiments differ is in the comparison between the lean and the rich mixture cases, with CFD cases predicting for the lean mixture a faster flame development while the rich isoctane-air case emerges as the slowest one. This is an expected consequence of the correlation for laminar flame speed proposed by Metghalchi and Keck (1980) for isoctane-air mixtures and adopted for the simulations. Experimental results show an opposite trend, with the Φ=2.0 mixture exhibiting a faster flame propagation than the Φ=0.8 case. The reason for this mismatch is attributed to the cellularity tendency of rich mixtures, which is an instability aspect typical of flame deflagrations at high pressure, temperature and for rich mixtures. This leads to an increase in burnt rate as resumed by Gillespie et al. (2000). It is inferred that this unstable behavior is not properly modelled by classical combustion models. Moreover, the adopted correlation for laminar flame speed is out of its validation range for such rich isoctane-air mixtures. As for the Φ=0.8 case, the numerical results gives a good agreement in the initial portion of flame development, while in the last simulated section the flame speed is overestimated compared to the experimental data. However the observation of the complete experiment reported in Figure 4.3 shows that the experimental flame speed undergoes an increase after 5 ms. It would be interesting to investigated whether this disagreement is reduced in later stages, since laminar flame speed is within its range of applicability. Moreover, it would be of analogous interest to observe the cyclic variability of the flame development process by performing several ignition realizations as experimentally carried out. However the computational cost of the simulations prevented at the current stages validation testing over a wider computational domain and for several combustion realizations.

5. UniMORE Knock Model 5.1

Background of the model

The simulation of the chemistry aspects leading to autoignition in SI engines is a key issue in modern internal combustion engine modelling. This study is usually divided into two main branches: 

Prediction of knock: chemical reactions in the unburnt mixture develop way before the main heat release and the pressure wave development. These follow chain and branching mechanisms, leading to the formation of intermediate products and active radicals, but they are characterized by negligible heat release. Since chemistry is observed in engine autoignition/knock analyses with the main focus on the heat release aspect, a relatively long and not relevant initial portion of chemical history is observed. As temperature and pressure levels increase, due to both piston compression and flame development, chemical kinetics rate exponentially increases and a sudden and intense heat release is finally measured. From a global perspective, the prediction of this instant is the first result that is pursued in engine knock modelling. The only way to predict the timing (or the phasing during the cycle) of engine knock is to simulate (or to model) the pre-reactions preceding the heat release.



Simulation of knock: autoignition resulting in detonation induces a pressure wave travelling throughout the combustion chamber and reflecting on concrete walls. The remaining endgases are exposed to this set of pressure waves and their knock resistance suddenly drops, due to the abrupt reduction of autoignition delay following the local pressure increase. The result is a rapid heat release from the total unburnt charge present in the cylinder. The CFD simulation of such phenomenon is usually referred to as “post-knock oxidation” and the numerical simulation of this imposes several challenges: o Numerical time-step: time-steps as low as 10-8 seconds are necessary to capture the high-frequency pressure fluctuations typical of knock. This is possible from a numerical point of view, but a comparison with experimental data is not immediate since pressure is experimentally filtered in a frequency range comprised between 4-6 and 20-25 kHz. Moreover, the local pressure signal has a dramatic dependence on the probe location, hence it is mandatory that the numerical measurement point is the exact same location as the experimental pressure transducer.

Chapter 5 – UniMORE Knock Model o Heat release is usually handled by the same flamelet combustion model as the main propagating flame front, while the actual engine knock does not present a flame front. Instead, it is a heat release closely following a travelling pressure wave and it does not involve the heat and mass exchange processes thought the reaction region of a typical deflagrating flame front. Moreover, the velocity of the pressure wave in the cylinder is the local speed of sound, while deflagration is a sub-sonic phenomenon. For these reasons the post-knock combustion (i.e. the heat release due to knock) is usually modelled by a modified (i.e. amplified) reaction rate operated by the same combustion code.

5.2

Integral Function for Knock Prediction

The traditional modelling of knock in SI engines relies on empirical correlations for the autoignition (AI) delay time τd. This is defined as the temporal interval between the imposition of constant pressure and temperature to a given mixture (i.e. to a fixed air/fuel/EGR ratio) before the main heat release occurs. This approach was first proposed by Livengood and Wu (1955), where the knowledge of the preknock chemical reaction rate can be neglected if a global delay time to autoignition is available. This is possible since the autoignition delay time expresses the fundamental time-scale of the observed phenomenon. Measurements of autoignition delay times are a commonly available data for a wide variety of fuels and initial conditions, and relevant examples of experimental tests characterizing the autoignition quality are conducted in rapid compression machines and/or shock tubes such as those reported by Wurmel et al. (2007), Fieweger et al., Vandersickel et al. (2012), Katsumata et al. (2011), Cancino et al. (2011). The main difficulty in knock prediction in internal combustion engines is that the physico-chemical conditions are continuously changing. Typical examples are: 

Pressure and temperature vary due to piston movement and energy release due to combustion;



Reactant ratio is extremely varying in DI engines, with region of pure air and other saturated by fuel vapour; in-between the continuous range of air-fuel ratios is present;



EGR mixing from the previous cycle can potentially add a further degree of mixture quality stratification.

Chapter 5 – UniMORE Knock Model For the mentioned reason the AI delay time τd is continuously changing, and its variation must be accurately considered based on local conditions. In their pioneering work Livengood and Wu (1955) proposed a simple relationship between the autoignition delay and the knock onset (Eq. 5.1): ∫

(Eq. 5.1)

In the reported equation, t0 is a conventional time where chemical reaction rate becomes relevant for the analysed case. In internal combustion engine analyses this time is commonly assumed as half of the compression stroke, where typical pressure and temperatures are such that chemical kinetics of the air-fuel mixture still presents an extremely slow reaction rate. These conditions vary based on engine operating point and on the air-fuel mixture considered, but they are in the order of 5-10 bar of absolute pressure and 700 K of temperature. At lower pressure and temperatures, reaction times are orders of magnitude higher than a typical engine cycle duration and chemistry can be considered as ‘frozen’ with regards to knock. Equation 5.1 is integrated in time as calculation proceeds and the unknown is the instant t where the unity value is reached. The crank angle corresponding to this condition is the knock onset angle. If in-cylinder conditions are such that the I < 1 is verified during all the combustion period, then the unburnt mixture is sufficiently knock resistant and autoignition does not occur. A regular deflagrating flame front propagates to the cylinder walls without any autoignition ahead of it. Conversely, is I = 1 condition is verified autoignition occurs and the integral function loses any physical meaning for I > 1. The Livengood-Wu Integral is a synthetic way to model the pre-knock reactions only based on the global autoignition delay time. The main advantage is that pre-knock chemical reactions are not modelled in the CFD code, with an evident saving of computational cost. An alternative formulation for an integral knock function was proposed by Lafossas et al. (2002), where a two-species framework was proposed. A knock precursor species is expressed by its concentration

, whose value is initially null. Its rate of increase is given by Eq. 5.2, which is

dependent on the local autoignition delay time

through Eq 5.3: (Eq. 5.2)

Chapter 5 – UniMORE Knock Model √

⁄

(Eq. 5.3) In Eq 5.2 and 5.3

is the fuel tracer mass fraction, i.e. the fuel as a passive non-reactive species.

As anticipated in Chapter 3, the fuel tracer is convected, diffused and produced (e.g. by liquid spray evaporation) as the actual fuel species, although it is not consumed by chemical reactions. In the Lafossas et al. model it represents the local concentration threshold for the species: when the equality

knock precursor

is verified, then the autoignition delay time

is reached and

knock is triggered. Several comparative tests were carried out between the Livengood-Wu Integral Function and the Lafossas et al. model for the same autoignition delay time

. The results were compared in terms

of knock prediction phasing and knock onset location in the combustion chamber. The excellent convergence of results between the two models made the choice between them driven by other considerations. In all the presented analyses, the Lafossas et al. knock model is adopted.

5.3

Empirical Correlation for the Autoignition Delay

Both the integral formulations presented in the previous section are based on the autoignition delay . A major difficulty arises from the observation that physical conditions are continuously changing during the integral calculations. Pressure and temperature in the unburnt gases rapidly increase due to compression and lower after the peak pressure angle. Equivalence ratio and EGR are mixing-related variables, and their evolution cannot be predicted in advance. This is especially true for GDI engines, where a level of air-fuel inhomogeneity is still present at the end of the compression stroke and during combustion development. This framework depicts the need of a detailed knowledge of the autoignition delay

for a large

variation of pressure, temperature, equivalence ratio and residuals. To this aim an empirical correlation was proposed by Douaud and Eyzat (1978), which is reported in Eq. 5.4: (

)

(

)

(

)

In Eq. 5.4

represents the Octane Index of the analysed fuel,

gases and

the temperature of the unburnt gases; the autoignition delay time

[s].

(Eq. 5.4)

the molar fraction of residual is calculated in

Chapter 5 – UniMORE Knock Model This relationship was obtained through a ‘four-octane number’ method, where combinations of RON and MON tests and operating conditions were experimentally tested. Validation was carried out for a range of commercial fuels with RON indices ranging from 80 to 100. The Douaud and Eyzat correlation is used to calculate the autoignition delay based on local and instantaneous conditions, which can be used in both the integral methods previously presented (Livengood-Wu Integral or the knock precursor model proposed by Lafossas et al.). This relationship is simple to implement in numerical codes since it is based on commonly available variables and it can be found as the reference correlation in many numerical codes for knock prediction. Several other empirical correlations are proposed in literature with the aim of adopting the presented correlation to account for fuel additives and/or high EGR levels. Examples of this are contributions from Iqbal et al. (2011) and Galloni et al. (2012).

5.4

Look-Up Table Approach Fundamentals

The UniMORE knock model is developed with the aim to overcome the use of empirical correlations such as the one by Douaud and Eyzat or similar. To this aim a variation of the synthetic Lafossas et al. knock model is developed based on an extended tabulation of autoignition delays for the adopted fuel. The aim of such a model are: 

Preserve the computational efficiency proper of a 2-species model (i.e. knock precursor YIG and fuel tracer YTF), where no chemical reactions are directly solved by the CFD solver.



Improve the calculation of autoignition delay times with respect to empirical correlations. Each fuel/blend presents specific non-Arrhenius behaviours, a relevant example of this is the Negative Temperature Coefficient (NTC) region typical of Diesel-like fuels. A fitting of these fuel-specific distinctive features would be necessary in case of empirical correlations. In the framework of a tabulation technique, these features are intrinsically described by the look-up table.



Decoupling from any flamelet combustion model: although originally developed on the ECFM-3Z embedded knock model, its formulation is general. In fact, the physical variables governing the autoignition delay time (i.e. pressure, temperature, equivalence ratio and residual level) are not related to a specific combustion model and/or their implementation in the CFD code. The coupling with the in-use combustion model is operated through a progress variable of combustion, which is common in most flamelet combustion models.

Chapter 5 – UniMORE Knock Model The developed model is based on an extended set of off-line calculated constant pressure autoignition delay calculations performed by a chemical kinetics solver. The results are used to define a look-up table of autoignition delays, which will serve as a database of calculated chemical conditions. During the CFD calculation, this is recalled for each fluid cell at every iteration and an interpolated autoignition delay is calculated based on the closest physical conditions stored in the look-up table. The CFD solver is not invoked in the preliminary stage. The chemical kinetics software used for the look-up table construction is the DARS-Basic software, but the same calculations can be performed with similar codes (e.g. CHEMKIN or Cantera packages). The range of physical conditions (i.e. pressure, temperature, equivalence ratio and EGR) must cover the entire design space of these physical variables which is experienced by the end-gases during the mixing and compression processes. As these conditions cannot be known in advance, a preliminary combustion analysis without the knock model is necessary with the only aim of investigating the range of physical conditions of interest for the autoignition delay calculation. The cost of this preliminary non-knocking case is largely overcome by the consideration that once a sufficiently large highly-resolved look-up table of autoignition delays is generated it can be later used for a wide variety of engine analyses. Typical examples are the knock tendency given by: 

Spark advance variations (if maximum pressure levels do not exceed the look-up table upper pressure bound);



Start of Injection variations, if maximum/minimum equivalence ratios are contained in the look-up table limit values;



Residual gases enrichment (Teodosio et al., 2015);



Charge cooling techniques, such as intercooling and/or water injection (d’Adamo et al., 2015).

The look-up table resolution should be as high as possible, in order to limit the interpolation job and to reduce the related error. Typical steps for each variable are: 

Pressure: 5 bar;



Temperature: 20 K;



Equivalence ratio: 0.1;



EGR: 2%;

Chapter 5 – UniMORE Knock Model The number of calculated cases is generally in the range of 104 to 105. Given the high parallelization which is possible for constant pressure reactor calculations, due to the fact that all the cases are independently calculated, even very large look-up tables can be created within few hours of CPU time for the chemistry solver.1 However as it will later shown the indexing technique used for the quest of reference conditions allows the use of such large look-up tables without affecting the CFD overall elapsed time. Once a set of discrete conditions is defined by the user, the deputed chemical kinetic software calculates a constant pressure reactor case for each (p,T,Φ,EGR) vector. The autoignition delay time is conventionally assumed for each case as the time of the maximum positive temperature derivative. Different criteria were evaluated for the autoignition delay time, such as the instant of maximum OH species molar concentration: given the almost null difference in term of results, the instant of maximum temperature rise is chosen. A look-up table is created containing the 4-dimensions hyperspace of physical conditions. For each (p,T,Φ,EGR) vector an autoignition delay time is available from the chemical kinetics solution. The structure of a typical look-up table is reported in Figure 5.1. The look-up table is created by an adhoc MATLAB script extracting the results from the chemistry solver and manipulating them to produce a formatted output file. 3222 4e+006 0.2 100 10 1e+006 5e+006 9e+006 1 1.2 900 1000 0 10 900 1e+006 1 0 5.5e+006 900 1e+006 1 10 7e+006 1000 1e+006 1 0 2.5e+006 1000 1e+006 1 10 4e+006 900 1e+006 1.2 0 1.6068 900 1e+006 1.2 10 1.1613 1000 1e+006 1.2 0 8.5e+006 1000 1e+006 1.2 10 2.7688 900 5e+006 1 0 6e+006 900 5e+006 1 10 7.5e+006 1000 5e+006 1 0 3e+006 1000 5e+006 1 10 4.5e+006 900 5e+006 1.2 0 1.4212 900 5e+006 1.2 10 1.0637 1000 5e+006 1.2 0 9e+006 1

The mentioned CPU time is indicative of semi-detailed chemical mechanisms composed by approximately 150 species. The CPU time needed for more detailed fuel surrogate models increases following the higher number of chemical species involved.

Chapter 5 – UniMORE Knock Model 1000 5e+006 1.2 10 2.203 900 9e+006 1 0 6.5e+006 900 9e+006 1 10 8e+006 1000 9e+006 1 0 3.5e+006 1000 9e+006 1 10 5e+006 900 9e+006 1.2 0 1.2785 900 9e+006 1.2 10 0.97958 1000 9e+006 1.2 0 3.9099 1000 9e+006 1.2 10 1.8516 900 1e+006 1 0 5.5e+006 900 1e+006 1 10 7e+006 1000 1e+006 1 0 2.5e+006 1000 1e+006 1 10 4e+006 900 1e+006 1.2 0 1.6068 900 1e+006 1.2 10 1.1613 1000 1e+006 1.2 0 8.5e+006 1000 1e+006 1.2 10 2.7688 900 5e+006 1 0 6e+006 900 5e+006 1 10 7.5e+006 1000 5e+006 1 0 3e+006 1000 5e+006 1 10 4.5e+006 900 5e+006 1.2 0 1.4212 900 5e+006 1.2 10 1.0637 1000 5e+006 1.2 0 9e+006 1000 5e+006 1.2 10 2.203 900 9e+006 1 0 6.5e+006 900 9e+006 1 10 8e+006 1000 9e+006 1 0 3.5e+006 1000 9e+006 1 10 5e+006 900 9e+006 1.2 0 1.2785 900 9e+006 1.2 10 0.97958 1000 9e+006 1.2 0 3.9099 1000 9e+006 1.2 10 1.8516 Figure 5.1 – Look-Up Table structure for the UniMORE Knock Model.

The first six lines of the look-up table are reserved for dedicated instructions related to the look-up table structure and size. These are read by the implemented routine in the CFD code, as later explained in the dedicated section, and they contain information regarding the database extension and resolution: 

Line 1: number of calculated states for p, T, Φ, EGR. These parameters are called n p, nT, nΦ and negr.



Line 2: steps adopted for discretization over p, T, Φ, EGR.



Line 3: calculated pressure values present in the look-up table.



Line 4: calculated equivalence ratio values present in the look-up table.



Line 5: calculated temperature values present in the look-up table.



Line 6: calculated EGR values present in the look-up table.

Chapter 5 – UniMORE Knock Model The remaining part of the look-up table contains the calculated states and their respective delay. Each line completely describes the autoignition delay time of a physical condition, hence the table contains as many lines as the number of calculated conditions. These can be more than 105 states, the only limit being the file size of the look-up table which will be allocated in the machine memory during the CFD run. However the text file of a few MB is typically created for very large tables, thus not representing a problem from the memory allocation point of view. A predefined order is applied for the data storage in the look-up table. This is fundamental in order to be able to operate an efficiently and fast neighbour data recovery during the CFD calculation. In the proposed model a series of nested loops of physical conditions is adopted, in particular: 

Pressure: 1st level loop (i.e. outermost loop);



Equivalence ratio: 2nd level loop;



Temperature: 3rd level loop;



EGR: 4th level loop (i.e. innermost loop).

Given such choice, when the index (or position) of the autoignition delay for a stored (p,T,Φ,EGR) vector is desired it is immediate to retrieve it by means of the following relationship (Eq. 5.5): (

)

(Eq. 5.5)

In Eq. 5.5 the I terms are the indexes relative to the calculated states whose physical conditions are the closest to the exact local ones: these are the neighbour states defined in the next section. For each of them the position in the look-up table is determined by the knowledge of the data storage criterion. This indexing technique allows the efficient handling of very large look-up tables with no evident increase in CPU cost. The reason for this is the absence of a retrieve algorithm based on DO-loops, which would be intrinsically sensitive to the database size. With the developed technique an overall increase limited to 5% of the total CPU time is measured. The choice of the look-up table convention for data storage has been arbitrary, and a different convention can be adopted for the look-up table data storage; in that case Eq. 5.5 should be accordingly adapted.

Chapter 5 – UniMORE Knock Model

5.5

Neighbour Conditions

A fluid cell in the unburnt gases is characterized by a generic (p*,T*,Φ*,EGR*) vector, whose values are given by the discrete Navier-Stokes solution as calculated by the CFD code. In principle the generic (p*,T*,Φ*,EGR*) vector can be stored in the look-up table as a set of calculated physical coordinates: in this case the autoignition delay would be immediately available from the database itself. Although theoretically possible, this is an obviously singular case and it is not of relevant interest. The most common situation that is verified is that the (p*,T*,Φ*,EGR*) vector is not present itself in the database, although autoignition delays for close conditions are. These are called neighbours states (or neighbours conditions). Since the look-up table stepping is known to the CFD code (from look-up table heading coordinates), an immediate variable bounding procedure is performed: Generic Variable (input data) p* T* Φ* EGR*

Lower Calculated Value (output data) pinf Tinf Φinf EGRinf

Upper Calculated Value (output data) psup Tsup Φsup EGRsup

Table 5.1 – Bounding variables for the generic (p*,T*,Φ*,EGR*) vector.

Other parameters immediately available are the exact coordinate positioning within the look-up table hyperspace, i.e. the number of (for example) pressure discrete steps to find the calculated p inf and psup values. This defines the Ip parameter needed in Eq. 5.5. The same applies to the other coordinates in Eq. 5.5, i.e. to calculate the IT, IΦ and IEGR parameters. The problem consists in identifying 16 neighbours states bounding the generic (p*,T*,Φ*,EGR*) vector, here listed: 1. (pinf, Tsup, Φinf, EGRinf) 2. (psup, Tinf, Φinf, EGRinf) 3. (psup, Tsup, Φinf, EGRinf) 4. (pinf, Tinf, Φinf, EGRinf). 5. (pinf, Tsup, Φsup, EGRinf) 6. (psup, Tinf, Φsup, EGRinf) 7. (psup, Tsup, Φsup, EGRinf) 8. (pinf, Tinf, Φsup, EGRinf)


9. (pinf, Tsup, Φinf, EGRsup) 10. (psup, Tinf, Φinf, EGRsup) 11. (psup, Tsup, Φinf, EGRsup) 12. (pinf, Tinf, Φinf, EGRsup) 13. (pinf, Tsup, Φsup, EGRsup) 14. (psup, Tinf, Φsup, EGRsup) 15. (psup, Tsup, Φsup, EGRsup) 16. (pinf, Tinf, Φsup, EGRsup) For each neighbour state the pre-calculated τd is available in the look-up table. The only requirement is the knowledge of the exact position of the neighbour states within the table. This is the scope of Eq. 5.5, providing the exact line of each state.

5.6

Interpolation Technique

Once the 16 neighbour states and their respective τd are found in the database, the problem moves to the calculation of the autoignition delay time τd* related to the generic (p*,T*,Φ*,EGR*) vector. This is the final result of the model, as it is the global indicator of the local end-gas reactivity and knock tendency. As the problem is defined starting from 4 independent variables (i.e. pressure, temperature, equivalence ratio and EGR), a 4-dimension interpolation procedure is necessary in order to calculate the interpolated delay time τd*. A procedure based on a series of linearly interpolating operation is defined. For the sake of clarity just the basic operations are described in detail, while for the repetitions just the modification in initial conditions is underlined. At first, Φ and EGR are fixed to their respective lower calculated states, i.e. Φinf and EGRinf. A bilinear interpolation is then carried out on the free variables (temperature and pressure). This is represented in the lower-left part of Figure 5.2. After the linear interpolation on the exact cellvalues T* and p*, a first delay is calculated in point 1. The same sequence of operations is repeated for fixed Φsup and EGRinf, and a second delay is calculated in point 2. The AI delays represented in 1 and 2 are interpolated over p and T, while

Chapter 5 – UniMORE Knock Model bound values are imposed for Φ and EGR. The interpolation over Φ is carried out based on the cell value Φ*, and an updated AI delay is calculated in A. All the operations performed to this point are at a fixed lower bound EGRinf value. These are repeated from the beginning for the upper bound EGRsup value: an AI delay in 3 is calculated for Φinf (analogous to the AI delay in 1), another is calculated for Φsup in point 4 (analogous to the AI delay in 2) and interpolation over equivalence ratio is performed to obtain the AI delay in point B. Finally, linear interpolation over EGR is performed and the final τd* is calculated. This represents the reactivity of the end-gas for the exact cell values (p*,T*,Φ*,EGR*). Since all the conditions reported in the look-up table come from a dedicated chemical kinetics simulation, all the global chemical information of interest (i.e. the AI delay) are retained in the presented procedure, and the final numeric error given by interpolation can be strongly limited by using high-resolution look-up tables. The accuracy of the generic (not calculated) τd* delay benefits from high-resolution look-up tables, as this increase the physical proximity of the calculated conditions to the unknown target one.

Figure 5.2 – Sketch of the 4-D interpolation technique for the AI Delay from the tabulated neighbour states.


5.7

Comparison of Empirical and Look-Up Table Interpolated AI Delays

In this Chapter the empirical correlation for autoignition delay

was presented in Eq. 5.4, then the

tabulated approach based on look-up table interpolation was introduced. The calculated delays are now compared for the two methods, with the aim of highlight the differences induced by the different calculation of

.

In Figure 5.3 a comparison is carried out for a RON98 fuel at stoichiometric conditions at an absolute pressure of 65 bar. The linear behaviour of the AI delays given by the Douaud and Eyzat correlation is given by the exponential dependence of temperature due to the Arrhenius-like formulation adopted represented on a logarithmic scale. An analogous comparison is reported in Figure 5.4, where the two methods are compared for increasing pressure levels.

10

Autoignition delay [ms]

10

10

10

10

10

Pressure =65 bar - Equivalence Ratio =1.0

3

2

EGR=0% (Look-Up Table) EGR=0% (Douaud&Eyzat Correlation) EGR=25% (Look-Up Table) EGR=25% (Douaud&Eyzat Correlation) EGR=50% (Look-Up Table) EGR=50% (Douaud&Eyzat Correlation)

1

0

-1

-2

0.7

0.8

0.9

1

1.1 1.2 1.3 1 / Temperature [1000/K]

1.4

1.5

1.6

1.7

Figure 5.3 – AI delays for a RON98 gasoline fuel model for increasing EGR levels: Douaud and Eyzat correlation and Look-Up Table output.


10


10

10

10

10

10

Equivalence Ratio =1.0 - Egr [%] =0

3

2

p=45 bar (Look-Up Table) p=45 bar (Douaud&Eyzat) p=65 bar (Douaud&Eyzat) p=65 bar (Look-Up Table) p=85 bar (Look-Up Table) p=85 bar (Douaud&Eyzat)

1

0

-1

-2

0.7

0.8

0.9

1

1.1 1.2 1.3 1 / Temperature [1000/K]

1.4

1.5

1.6

1.7

Figure 5.4 – AI delays for a RON98 gasoline fuel model for increasing absolute pressure levels: Douaud and Eyzat correlation and Look-Up Table output.

Two separate behaviours are observed when comparing the AI delays predicted for the same conditions by the two methods. A first tendency is identified at temperatures higher than 1000 K (left side on Figures 5.3 and 5.4), where the output from the Look-up table shows lower AI delays than those predicted by the empirical correlation. This states an underestimation of the chemical kinetics rate for the Douaud and Eyzat correlation which would lead to delayed autoignition onset. However, the range of involved temperatures is rather high and it is rarely found in internal combustion engines that endgases are subjected to compression levels such as those needed to increase their unburnt temperature over 1000 K. A second and more relevant trend is verified at temperatures lower than 1000 K (right side on Figures 5.3 and 5.4), the chemically calculated AI delays are systematically higher than the corresponding values from the Douaud and Eyzat formula. This states an overestimation of the autoignition chemical kinetics rate for the empirical correlation case in this range. This tendency is more important since it comprises all the unburnt mixture heating process due to piston compression. The chemical pathway experienced by the reacting mixture is comprised in this range and an evident delay in autoignition onset is to be predicted when adopting a chemically tabulated method for this reason. The path to autoignition is strongly and erroneously accelerated by the empirical correlation.


5.8

Implementation of the UniMORE Knock Model in the Star-CD Code

The presented knock prediction model is implemented in the framework of Star-CD provided by CD-adapco. The software capabilities on engine flow simulation and spark-ignition combustion are well known to the Internal Combustion Engine Research Group of University of Modena, and the close cooperation with CD-adapco allows a deep intervention into the implementation of large usercoding portions. The UniMORE knock model is implemented in Star-CD by means of an external Fortran-based routine called posdat.f. This routine allows the user to cell-wise post-process flow variables, among which are local (p*,T*,Φ*,EGR*) values. These are the input data to the knock model. At the first iteration the look-up table is addressed and stored in the machine memory. In this way a single I/O operation is performed for the complete engine calculation, without the repetition of a read-operation at every iteration. The look-up table heading is built to instruct the posdat.f code regarding the look-up table size. This is used to dynamically allocate arrays deputed to the storage of the database data. Thanks to this procedure, look-up table with different sizes or coordinate stepping can be used without any user intervention request (e.g. size parameters etc.), since the implemented code is completely selfadapting to the specific table. The 4-D interpolation code is nested in a loop over all the fluid cells contained in the cylinder domain. For each fluid cell, the previously described operations are carried out and they are here listed: 

Reading of cell-averaged values (p*,T*,Φ*,EGR*);



Calculation of bound coordinates: pinf, psup, Tinf, Tsup, Φinf, Φsup, EGRinf, EGRsup;



Retrieval of τd for neighbour states, using Equation 5.5;



4-D interpolation procedure for the calculation of the interpolated τd*;

Once an interpolated τd* is available at i-iteration, the cell-specific knock integral function adopted is updated with its instantaneous reaction rate, starting from the cumulated value at (i-1)-iteration: Livengood-Wu Integral Function: the integral function I is updated following Eq. 5.6: (Eq. 5.6) Lafossas Knock Precursor Model: the mass concentration of the knock precursor model YIG is updated following:


√

⁄

(Eq. 5.7) In Eq. 5.6 and 5.7, dt is the computational time-step. Finally a comparison is carried out whether the updated cumulated integral function overcomes its threshold value: 

If this condition is not verified, knock does not occur. The reaction status of the end-gases is still in the pre-knock phase where scarcely-exothermic (if not endothermic) chemical reactions occur, and the main heat release is yet to be verified. As described in the knock model assumptions, these chemical reactions are not modelled by the CFD code. In this phase the end-gases are represented in the CFD code as non-reacting, although correlated by a passive scalar (i.e. the knock integral function) which synthetically considers the global chemical pathway of the pre-knock reactions.



If this condition is verified, knock is triggered. In this region the reaction rate of the combustion model is modified to account for the different time-scales of a developing detonation with respect to a regular deflagrating flame front. After the knock condition is verified, both the interpolation of the τd* time and the increase in the knock integral function lose any interest. They are intrinsically defined to predict and foresee knock timing and its location and they are meaningless once knock onset has already occurred.

5.9

The Knock Tolerance Function

The model implementation in the Star-CD code allows to visualize local resistance to knock onset in each point of the unburnt mixture. In Figure 5.5 a snapshot of combustion progress is represented by the progress variable field of the adopted combustion model, which for the example is ECFM-LES. The blue area in Figure 5.5 is the unburnt mixture region, where the proximity to autoignition must be analysed.


Figure 5.5 – Progress variable field from a combustion simulation at +10 CA aTDC:

B A

Figure 5.6 – Knock Tolerance field from a combustion simulation at +10 CA aTDC:

In Figure 5.6 the output from the UniMORE Knock Model is reported for the same simulation. At first a filtering on the unburnt mixture is carried out, and only the portion with a value lower than 0.5 is retained. The visualized scalar field on the peripheral region of unburnt mixture is the difference between the fuel tracer YTF mass fraction and the knock precursor YIG concentration (Eq. 5.8). The scalar field resulting from this operation is called Knock Tolerance (KT), and it represents a comprehensive measurement of the local residual resistance to autoignition. ̅

̅

̅

(Eq. 5.8)

Chapter 5 – UniMORE Knock Model This function is meaningful for positive values, i.e. when YTF is higher than YIG and knock has not yet occurred. Conversely, if the KT local value is negative the knock precursor YIG has exceeded the threshold YTF concentration and knock has already occurred. Knock onset is triggered when Knock Tolerance is null, i.e. the residual resistance to autoignition is terminated. In Figure 5.6 it is visible how distant portions of the end-gases can experience different knock proximity levels. On one side, Point A in Figure 5.6 is the region showing the maximum Knock Tolerance value. This means that this region is the volume of unburnt mixture with the highest residual resistance to knock: this makes it the safest region in the unburnt mixture. On the other side, Point B shows the minimum Knock Tolerance value, rendering it as the most dangerous and knock-prone end-gas region.

6. Engine Case – RANS Application 6.1

Introduction on RANS analysis

The previously presented knock model is applied to a currently produced V8 spark-ignition engine which is currently under production. Experimental acquisition from the engine test bench are provided by the engine manufacturer and the simulated operating point is the same as the experiments, i.e. peak power point. Further details on the operating condition are confidential. In this section the analysed physical phenomena (i.e. fuel spray, mixing, combustion and eventual knock onset) are studied from an ensemble average perspective. For such analysis the ensemble average Navier-Stokes equations (also called RANS equations) presented in Chapter 1 are adopted, since the temporal averaging operated at the equation level is coherent with the aim of characterizing the mean behaviour of all the mentioned physical processes. Unsteady phenomena, such as mixing variability and combustion irregularity, are not treated in this Chapter and they will be the object of Chapter 7 dealing with Large-Eddy Simulation analyses. These last are able to describe cyclic-unsteady phenomena, thanks to the spatial (instead of temporal) filtering operated on the Navier-Stokes set of equations. The first characterization of the complex chain of physical processes, such as those occurring in a GDI engine, must necessarily proceed from an initial ensemble average characterization. To this aim RANS analyses are the right tool to numerically describe the global fluid dynamic system behaviour.

6.2

Numerical Setup for RANS Simulations

The numerical grid used for the current RANS simulations is created with the es-ice plug-in and it is composed of about 325000 cells at BDC and 580000 fluid cells at TDC. Details of the engine geometry can not be shown due to confidentiality reasons requested by the engine manufacturer. The computational grid represents just half of the analysed domain, thus allowing a considerable saving in computational cost for the simulations. This is possible thanks to the exact geometry of the simulated domain and to the use of a RANS simulation framework. It is important to underline that even if flow instabilities always occur in actual flows, RANS equations are by definition a mathematical model devoted to the ensemble average description of flow behaviour. Therefore, the

Chapter 6 – Engine Case: RANS Application use of half domain is exclusively possible with RANS simulations, while the entire fluid domain will be considered for the LES analyses. All the simulations presented in this chapter are carried out using Star-CD 4.20, licensed by CDadapco. The combustion model used in the RANS analyses is the ECFM-3Z, whose main features are described in Chapter 3. The possibility given by ECFM-3Z to handle different combustion modes (premixed and diffusive combustion, as well as autoignition) made it a logical choice for the investigation. As for turbulence modelling, the adopted model is the consolidated 2-equation k-ε RNG. Fuel injection is carried out through a 7-hole fuel injector placed between the intake valves and pointing towards an ad-hoc shaped bowl, machined in the piston crown. Spray atomization is not modelled in the simulations: a pre-atomized population of droplets is imposed at the nozzle exit. As for secondary break-up, the model by Reitz and Diwakar (1986) is adopted. The presented numerical framework for gasoline direct injection is validated against experiments in Malaguti et al. (2013). The fuel used in the numerical simulations is a single-component commercial gasoline surrogate, whose properties for the liquid phase are user-coded in the form of a polynomial law as a function of liquid temperature. Data for the liquid phase properties are provided by the fuel supplier and they fit the characteristics of the actual gasoline. The limitations of a single-component fuel formulation such as that adopted in this analysis must be recalled, the major of them being the impossibility to discern between the different rates of evaporation of the components actually present in a commercial fuel. Several studies are available in literature regarding the modelling soundness of a discrete-continuous multi component fuel modelling, such as Batteh and Curtis (2005) and Yang et al. (2012). Comparative analyses between the two formulations were conducted within the research group (Giovannoni et al. (2014), d’Adamo et al. (2014)). However, given the source of the singlecomponent fitted properties, which is the fuel manufacturer itself in this case, a simpler singlecomponent fuel formulation has been retained for the presented analyses. Start of Injection (SOI) for the analysed operating condition is at the beginning of the intake stroke and fuel injection proceeds during most of the intake valve opening period. Boundary conditions are imposed as time-varying profiles of pressure and temperature. They are applied at the intake and exhaust port boundaries of the domain represented in Figure 6.1, and

Chapter 6 – Engine Case: RANS Application values derive from a calibrated 1-D model developed by the engine manufacturer and validated against experimental acquisitions. Wall temperatures are imposed as uniform and constant values for ports, piston crown, cylinder liner, combustion dome and valve faces and stems separately, whose (confidential) values are extracted by the 1-D model. Given the wall-guided architecture of the analysed engine, particular care is devoted to the analysis of possible fuel impingement on the piston crown during injection. If a fuel liquid film is formed in this phase, it is well known that it will act as a liquid paddle with a relevantly slow evaporation rate. This in turn originates UHC (unburnt hydrocarbons) tailpipe emissions and soot. However, as the piston wall temperature is above the Leidenfrost fuel temperature, liquid film formation is prevented and no liquid film model is adopted in the simulations. Wall heat transfer is modelled thanks to the Angelberger et al. (1997) model. Finally, knock is modelled with the developed UniMORE Knock Model coupled with the ECFM3Z combustion model, although comparative analyses are carried out with the standard model as well as with other fuel qualities.

6.3

Analysis of the Mixing Process

Numerical simulations start before Exhaust Valve Opening (EVO) in order to properly simulate the burnt gas discharge and to obtain an accurate description of the in-cylinder flow structures and composition for the forthcoming charge intake process. A solution which is independent of the initial condition is necessary to represent the ensemble average behaviour of the fluid dynamic system; to this aim three consecutive full cycles are carried out. Since the solution of the third cycles shows negligible differences with that of the second cycle, both in terms of flow structures and combustion development, the procedure was not further repeated and the third cycle is assumed as representative of the engine mean behaviour. The flow field is represented in Figure 6.1 on two orthogonal sections cutting the intake valve. The well-organized tumbling flow structure created during the intake stroke is still recognizable at half of the compression stroke. The injection of liquid fuel is reported in Figure 6.2 for several CA.

Chapter 6 – Engine Case: RANS Application Crank Angle = 450 CA

Crank Angle = BDC

Crank Angle = 630 CA

Figure 6.1 – Flow field on two planes cutting the intake valve: longitudinal section (left column) and cross section (right column). Appropriate velocity components for each section are represented at 450CA (top row), BDC (middle row) and 630CA (bottom row).





Figure 6.2 – Liquid phase during the injection process at several CA:. (a) 420CA, (b) 450CA, (c) 480CA and (d) 510CA.

Part of the injected fuel backflows into the intake ports: this is due to both the early SOI and the long angular duration needed for the injection process. The result from these combined characteristics is that a major portion of spray break-up and fuel evaporation occur during the

Chapter 6 – Engine Case: RANS Application opening period of the intake valve. A fraction of fuel vapour is pushed back into the intake ports during the initial part of the compression stroke. Since this evaporated fuel is introduced in the cylinder in the following cycle it does not represent a fuel loss to the engine, and it is taken into account in the simulations thanks to the aforementioned multi-cycle procedure. The global equivalence ratio for the analysed operating condition is a fuel-rich mixture. The use of such a rich mixture is typical of highly turbocharged GDI engines. Even though this strategy is intrinsically non-efficient, since it represents a relevant waste of fuel, it is an effective strategy to limit the engine knock tendency and to reduce the turbine inlet temperature. This makes it a still adopted strategy on high-performance engines where knock tendency is a relevant issue. The resulting fields of equivalence ratio and laminar flame speed are illustrated in Figure 6.3 at the end of the compression stroke, depicting a rich mixture in the spark plug region. This is an optimal condition for spark ignition and flame propagation, as confirmed by the value of the laminar flame speed for which the Metghalchi and Keck (1980) correlation is adopted. Laminar Flame Speed

Longitudinal Section

Top View Section

Equivalence Ratio

Figure 6.3 – Equivalence ratio (left) and laminar flame speed (right) fields at -20CA aTDC.

6.4

Analysis of the Combustion Process

Combustion development is first studied neglecting any dedicated model for knock detection and energy release by autoignition. The motivation for this is the possibility to numerically simulate the regular flame propagation throughout the combustion chamber without any disturbance given by abnormal combustion events. Even though this practice could potentially represents a non-physical

Chapter 6 – Engine Case: RANS Application flow realization, due to the artificial impossibility for the end-gas to develop detonation, it is extremely useful to provide a “regular combustion benchmark” for following analyses. An equivalent practice would be to numerically set an extremely high fuel octane index. The Spark Advance (SA) used for the simulations is the same as the experiments, which is indicated as the Knock Limited Spark Advance (KLSA) by the engine test bed evidence. This is defined as the maximum spark advance allowable before a given fraction of cycles exhibits an excessive knock intensity. As outlined in Chapter 2, the definition of a knock intensity index and of the criteria to define a “threshold fraction of knocking cycles” are not a standardized field and most of the experimental practice is still based on the engine manufacturer expertise. The in-cylinder pressure trace as simulated by the ECFM-3Z combustion model is reported in Figure 6.4 and compared with the experimental ensemble average one. A satisfying agreement of the numerical result is obtained and the combustion simulation is considered in line with the experiments.

Figure 6.4 – Experimental and numerical ensemble average pressure trace. Values can not be shown due to confidentiality reasons.

The combustion progress is represented by the Favre-averaged reaction progress variable ̃. As anticipated in Chapter 3, ̃ is bounded between 0 in fully unburnt gases and 1 for combustion products. The region where ̃ is varying, illustrated in Figure 6.5 by the ̃ (

̃) scalar field,

represents in this case the ensemble average turbulent flame brush, and not the single flame front realization.

Chapter 6 – Engine Case: RANS Application Longitudinal Section

Crank Angle = +20 CA aTDC


Crank Angle = TDC

Top View Section

Figure 6.5 – Ensemble average flame brush on a cross section through the ignition point (left) and on a longitudinal axial section (right): TDC (top row), +10CA aTDC (middle row) and +20CA aTDC (bottom row).

6.5

Knock Tendency for KLSA Condition

The UniMORE knock model is activated on the presented combustion simulation in order to validate the edge-off knock condition indicated by the experiments. The aimed result for the validation of the knock model is the non-prediction of knock (or a negligible intensity knock level), since this result represents an ensemble average condition. Even if the sample of collected cycles presents a fraction of knocking cycles, they are a result from cyclic variability and the mean operating condition is still considered as knock-safe (even though at the edge of knock). The fuel model used for the knock prediction is different than that adopted for the flame propagation simulation handled by ECFM-3Z model. The focus for end-gas knock prediction is on chemistry anti-knock quality and a chemical mechanism is adopted to model the commercial

Chapter 6 – Engine Case: RANS Application European gasoline used in the experiments. The main characteristics of the fuel model used for knock prediction analysis are reported in Table 6.1. A chemical mechanism is provided by the fuel manufacturer aiming at reproducing the same antiknock quality as the actual gasoline. The mechanism is developed based on the Toluene Reference Fuel (TRF) scheme by Andrae and Head (2009). The gasoline model suggested by the fuel supplier is a blend of Toluene (C6H5CH3), Isoctane (C8H18), n-Heptane (C7H16) and Ethanol (C2H6OH), whose composition is reported in Table 6.1. Hydrocarbon Toluene (C6H5CH3) Isoctane (C8H18) n-Heptane (C7H16) Ethanol (C2H6OH) RON (Research Octane Number) MON (Motor Octane Number)

Volume Fraction [%] 53 35 12 0.00 98.80 88.20

Table 6.1 – Fuel surrogate composition for a RON98-E0 European commercial gasoline model.

In Figures 6.6 to 6.8 the AI delay time is reported a function of 1000/T for several pressure, equivalence ratios and EGR concentration.

10


10

10

10

10

10

Equivalence Ratio =1.0 - Egr [%] =0

3

2

45 bar 65 bar 85 bar

1

0

-1

-2

0.7

0.8

0.9

1

1.1 1.2 1.3 1 / Temperature [1000/K]

1.4

1.5

1.6

1.7

Figure 6.6 – AI delay sensitivity to absolute pressure for a stoichiometric RON98 mixture, without residuals. Conditions for low pressure (45 bar), medium pressure (65 bar) and high pressure (85 bar) are reported.

Chapter 6 – Engine Case: RANS Application

10


10

10

10

10

10

Pressure =65 bar - Egr [%] =0

3

2

Equivalence Ratio = 0.8 Equivalence Ratio = 1.0 Equivalence Ratio = 1.2

1

0

-1

-2

0.7

0.8

0.9

1

1.1 1.2 1.3 1 / Temperature [1000/K]

1.4

1.5

1.6

1.7

Figure 6.7 – AI delay sensitivity to equivalence ratio for a 65 bar RON98 mixture, without residuals. Conditions for lean mixture (Φ=0.8), stoichiometric mixture (Φ=1.0) and rich mixture (Φ=1.2) are reported.

10


10

10

10

10

10

Pressure =65 bar - Equivalence Ratio =1.0

3

2

EGR = 0% EGR = 25% EGR = 50%

1

0

-1

-2

0.7

0.8

0.9

1

1.1 1.2 1.3 1 / Temperature [1000/K]

1.4

1.5

1.6

1.7

Figure 6.8 – AI delay sensitivity to residuals for a stoichiometric RON98 mixture at 65 bar. Conditions without residuals, with 25% EGR and with 50% EGR concentration are reported.

A dedicated Look-Up Table is created with the physical coordinates and steps reported in Table 6.2. The choice of the extreme database values and the discretization steps is made following the

Chapter 6 – Engine Case: RANS Application analysis of the non-knocking case described in the previous section. The total number of stored physical states is 25578.

Absolute Pressure [bar] Absolute Temperature [K] Equivalence Ratio [-] EGR Mass Fraction [%]

Minimum Value

Maximum Value

Physical Step

Number of Points

5

205

10

21

600

1300

25

29

0.4

3.0

0.2

14

0

50

25

3

Table 6.2 – Look-Up Table boundaries and resolution for the investigated operating condition.

The UniMORE knock model is arbitrarily activated after 630 CA (i.e. half of the compression stroke). At that CA approximate values of pressure and temperature are 4.5 bar and 460 K respectively, which are not sufficient to trigger chemical reaction time scales comparable with the engine cycle lifetime. Moreover they are lower than the minimum boundaries of pressure and temperature of the adopted look-up table, hence allowing a smooth transition of end-gas states into the tabulated range for conditions with extremely reduced reactivity. The assumption to not consider any end-gas chemical reaction before this arbitrary limit is therefore justified since end-gas chemistry is substantially frozen in that range. When the knock model is activated, for each unburnt fluid cell and at each iteration an autoignition delay is multi-linearly interpolated from the dedicated look-up table, following the procedure detailed in Chapter 5. This synthesizes the complex chemical kinetics of the fuel model towards autoignition. The modelling effort in this phase is concentrated in the definition of an accurate chemical mechanism for the surrogate fuel model, which constitutes an input to the presented analyses. As illustrated in Chapter 5, the local AI delay time drives the rate of concentration increase of the “virtual” knock precursor species, i.e. the YIG concentration of Lafossas et al. (2002) knock integral function . An immediate way to visualize the local knock tendency of each portion of end-gases is to analyse the local difference between the Fuel Tracer YTF and the knock precursor YIG. In Chapter 5 a scalar variable called Knock Tolerance (hereafter KT) is introduced and it represents a synthetic measure of residual knock resistance. The KT variable is conditioned over the unburnt mixture, based on a threshold value of Favre-averaged progress variable ̃ arbitrarily set to 0.5 value.

Chapter 6 – Engine Case: RANS Application In Figure 6.9 the interpolated AI delay and the related Knock Tolerance fields are reported for significant CA position. A strong correspondence is visible between the regions with low AI delay, stating a high reaction rate of the end-gases, and areas characterized by a low knock tolerance, meaning a reduced local resistance to knock . This latter aspect is due to the faster growth rate of the YIG knock precursor species for regions with a low interpolated AI delay. Knock Tolerance




Autoignition Delay

Figure 6.9 – End-gas knock tendency on a section 1 mm below the flame deck: (left) AI delay and (right) Knock Tolerance scalar fields.

From the observation of Figure 6.9, it is recognizable that the most critical region of the combustion chamber for knock occurrence is the exhaust side region. This is due to the combination of two opposite considerations: 

Despite the residual tumble vortex at the end of the compression stroke, the propagating flame front reaches the outer cylinder walls on the intake side earlier than those on the

Chapter 6 – Engine Case: RANS Application exhaust one. This means that the volume of unburnt mixture that is required to resist for a longer time to autoignition is located on the exhaust side; therefore, one would desire this region to be the most anti-knock end-gas portion. 

The exhaust side region is the hottest portion of combustion chamber in an actual engine. This is mainly due to the lack of cooling operated by the incoming intake charge on the intake side and valve. Conversely, exhaust valve and the surrounding walls are exposed to the contact with combustion products and the cooling of this area is more problematic. This different thermal behaviour is represented in the simulation by the use of higher wall temperature for the exhaust valve face, valve body and port.

The combined effect of these factors is responsible for the large reduction of AI delays measured in this region and well visible in Figure 6.9, making it the least knock-resistant region of unburnt mixture. From the above analysis it clearly emerges how knock must be expected on the exhaust side earlier than in any other location of the combustion chamber.

6.6

Comparison of Knock Tendency for the Douaud-Eyzat Knock Model

A comparison between different knock models is carried out for the same operating condition. The prediction of knock for the same KLSA condition is carried out with the empirical correlation by Douaud and Eyzat (1978) and with the UniMORE Knock Model, in order to highlight and quantify the difference introduced by the chemistry modelling of the actual fuel. Both models are operated with a nominal fuel anti-knock quality equal to 98, following the RON index rating of the actual fuel: while for the Douaud-Eyzat knock model this is imposed as the anti-knock index value, for the proposed knock model the look-up table presented in Section 6.5 is used. In Figures 6.10 the average in-cylinder pressure and the fraction of burnt fuel are reported as a function of CA. The global heat release rate and the portion due to autoignition are reported in Figures 6.11. As for Figure 6.4, the global heat release trace for the case without numerical autoignition is also represented to evaluate the energy release difference from a regular combustion.


Figure 6.10 – In-cylinder average pressure and mass fraction burnt for the Douaud and Eyzat correlation and the UniMORE Knock Model. Values can not be shown due to confidentiality reasons.

Figure 6.11 – Global heat release rate and heat release rate due to AI for the Douaud and Eyzat correlation and the UniMORE Knock Model. Values can not be shown due to confidentiality reasons.

As it is visible from the above figures, the knock prediction according to the Douaud and Eyzat correlation is phased at approximately 753 CA, and the related MFB at this CA is approx. 85%. The heat release rate due to autoignition is a consequence of the remaining unburnt mixture at knock onset. This prediction for knock onset is not coherent with the experimental evidence of negligible knock for the mean cycle. The result from the same analysis performed with the UniMORE Knock Model, coupled with the dedicated look-up table for a RON98-E0 gasoline model, does not indicate any heat release given by autoignition and this is in agreement with the experimental knock-limited condition. In Figures 6.12 the Knock Tolerance field is compared between the UniMORE Knock Model and the standard knock model based on the Douaud-Eyzat correlation. The knock tendency (i.e. low Knock Tolerance value) in the end-gas is notably higher for the latter model, while in the former

Chapter 6 – Engine Case: RANS Application case the knock resistance is higher for the same physical conditions and knock prediction is




delayed.

Figure 6.12 – End-gas Knock Tolerance on a section 1 mm below the flame deck: (left) UniMORE Knock Model and (right) standard knock model based on the Douaud-Eyzat empirical correlation.

Both models agree in identifying the exhaust side portion of the end-gases as the most knock-prone region, i.e. the one with the lowest Knock Tolerance. The largest difference between the two is the phasing of knock onset prediction, and the reason is originated in the AI delay calculation. As the interpolation from a chemically-calculated look-up table for the specific fuel is considered more realistic than an empirical correlation valid for a wide range of fuels, the developed knock model is evaluated as more physically sound and it will be adopted for all the remaining analyses. Finally, images of flame propagation and knock onset region are reported in Figure 6.13 for several CA.

Chapter 6 – Engine Case: RANS Application Crank Angle = +32 CA aTDC



Figure 6.13 – Flame propagation (yellow iso-surface at ̃ ) and knock region (red iso-surface, defining AIreleased heat): (left) UniMORE Knock Model and (right) standard knock model based on the Douaud-Eyzat empirical correlation.

The knock onset location is identified in the exhaust side region, in coherence with the previous observations. The absence of autoignition hot spots is verified for the UniMORE Knock Model case, which is therefore considered validate with the experiments for this operating condition.

6.7

Knock Tendency for KLSA+3 Condition

In this Section the validation of the UniMORE Knock Model is carried out for knocking conditions. This is obtained by numerically increasing the Spark Advance by 3 CA (hereafter named KLSA+3 condition) from the experimental KLSA considered for the previous simulations. The aimed result in this section is the detection of a non—negligible heat release due to end-gas autoignition, since this particular operating condition is not allowable at the engine test-bed.

Chapter 6 – Engine Case: RANS Application In Figures 6.14 and 6.15 the average in-cylinder pressure, mass fraction burnt and heat release rates are reported for the KLSA+3 operating point, with knock prediction operated by the UniMORE Knock Model for the same RON98-E0 fuel model.

Figure 6.14 – In-cylinder average pressure and mass fraction burnt for the KLSA+3 condition. Values can not be shown due to confidentiality reasons.

Figure 6.15 – Global heat release rate and heat release rate due to AI for KLSA+3 condition. Values can not be shown due to confidentiality reasons.

Knock prediction is moved earlier in the cycle with the advance of SA, with a measured knock onset angle of 742 CA and a residual unburnt mixture of 18%. The advanced start of combustion induces a different flame interaction with the surrounding flow field. The difference with the flame propagation of the reference KLSA condition is reported in Figure 6.16.

Chapter 6 – Engine Case: RANS Application Crank Angle = -4 CA aTDC

Crank Angle = TDC



Figure 6.16 – Flow field and flame propagation (iso-lines around ̃=0.5) for several CA: (left) KLSA condition; (right) KLSA+3 condition.

Flame propagation towards the intake side is favoured by the combination of an intense intakeoriented flow deriving from the squish motion on the intake side (due to the reduced volume between the piston at TDC and the flat flame deck) with the residual tumbling vortex located in the core of the cylinder. As for the propagation on the exhaust side, it appears as less dependent on flow structures. When SA is anticipated, the overall flame interaction with flow structures is anticipated.

6.8

Knock Model Sensitivity to Fuel Anti-Knock Rating

A further testing of the developed knock model is carried out by comparing the knock prediction phasing and location for two different fuel models. The reference RON98-E0 case presented in the previous section is compared with a lower octane rating fuel model, which is developed to represent the autoignition quality of a RON95-E10 gasoline. The chemical mechanism used for the chemistry simulations is the same TRF scheme by Andrae and Head (2009) already presented for the RON98E0 fuel model. The main characteristics of the two fuels models are reported in Table 6.3, where the RON98-E0 model characteristics are recalled form Table 6.1 for the sake of comparison.


Toluene [volume %] Isoctane [volume %] n-Heptane [volume %] Ethanol [volume %] RON (Research Octane Number) MON (Motor Octane Number) AFRst

RON98-E0 Surrogate 53 35 12 0.00 98.80 88.20 14.4

RON95-E10 Surrogate 51 25 14 10.00 95.3 87.1 13.7

Table 6.3 – Fuel surrogate composition for a RON98-E0 and a RON95-E10 commercial gasoline models.

The comparison of the calculated AI delay time for the same physical conditions highlights the lower resistance of the RON95-E10 fuel model when compared to the RON98-E0 one, as it is visible from Figures 6.17 and 6.18 reporting AI delays as a function of temperature for lean and stoichiometric conditions and as a function of equivalence ratio and temperature respectively. These result confirm the octane grading of the actual fuels under investigations.

10

1

Pressure =90 bar - Equivalence Ratio =0.8 - Egr [%] =0 10

1

Pressure =90 bar - Equivalence Ratio =1.0 - Egr [%] =0

10

10

RON95-E10 RON98-E0



RON95-E10 RON98-E0

0

-1

0.9

1

1.1 1.2 1.3 1 / Temperature [1000/K]

1.4

1.5

10

10

0

-1

0.9

1

1.1 1.2 1.3 1 / Temperature [1000/K]

1.4

1.5

Figure 6.17 – AI delay dependence on the inverse of absolute temperature: (left) lean (Φ=0.8) and (right) stoichiometric mixture of RON98-E0 and RON95-E10 fuel models.

Chapter 6 – Engine Case: RANS Application Pressure =90 bar - Egr [%] =0 RON98-E0 1

1.5

1

1.4

0.8

1.4

0.8

0.6

1.3

End-Gas Region

1.2 1.1

0.4 0.2

1

0

0.9

-0.2

0.8

-0.4

0.7 0.6 0.5 700

750

800

850 900 950 1000 1050 1100 Temperature [K]

Equivalence Ratio [/]

1.5

1.3

Equivalence Ratio [/]

Pressure =90 bar - Egr [%] =0 RON95-E10

0.6 End-Gas Region

1.2 1.1

0.4 0.2

1

0

0.9

-0.2

0.8

-0.4

-0.6

0.7

-0.6

-0.8

0.6

-0.8

-1

0.5 700

750

800

850 900 950 1000 1050 1100 Temperature [K]

-1

Figure 6.18 – Colour map of log10 of AI delay as a function of end-gas temperature and equivalence ratio: (left) RON98-E0 model; (right) RON95-E10 model. Highlighted is the region of temperature and quality expected for endgases.

A dedicated look-up Table is created for the RON95-E0 fuel model. In order to carry out a rigorous comparison with the RON98-E0 fuel, the same physical conditions for the database are simulated. As a consequence, the discretization of the physical coordinates is unchanged and the resulting database is composed by the same number of points, which in this case is equal to 25578. The same combustion realization presented in the previous section is repeated with the RON95-E10 fuel model for knock prediction. In order to promote knock onset to better highlight the different knock tendency of the two fuel, the KLSA+3 conditions is chosen for this study. Combustion results for the two cases are reported in Figures 6.19 and 6.20 for the two cases.

Figure 6.19 – In-cylinder average pressure and mass fraction burnt for the RON98 and the RON95 fuel models for KLSA+3 condition. Values can not be shown due to confidentiality reasons.


Figure 6.20 - Global heat release rate and heat release rate due to AI for the RON98 and RON95 fuel models for KLSA+3 condition. Values can not be shown due to confidentiality reasons.

From the above figures it is visible that the regular combustion development is not affected by the fuel-specific anti-knock quality. This is due to two main reasons: 

The fuel anti-knock quality is a chemical property which is handled by the knock model only. Hence, its influence is inherently conditioned on the unburnt mixture and it does not affect flame propagation modelled by ECFM-3Z;



The fields of flow velocity and turbulence are identical for both cases, hence also the turbulence-flame interaction.

Combustion results confirm that for the same operating condition the RON95 fuel gives rise to an earlier and more intense knock phenomenon than the RON98 fuel model. Knock onset indicators are reported in Table 6.4 for the two fuel models.

CA of Knock Onset [CA aTDC] MFB at Knock Onset [%]

RON98-E0 Fuel

RON95-E10 Fuel

+22

+20

82 %

80 %

Table 6.4 – Crank angle and mass fraction burnt at knock onset for the RON98-E0 and the RON95-E10 fuel models, at the KLSA+3 condition.

The end-gas knock tendency is observed for the two fuels in Figure 6.21. In the most critical endgas region (marked by letter A) the RON95-E10 case systematically predicts lower AI delays than the RON98-E0 fuel model, as it could be expected by the higher octane rating of the latter. Quite curiously, an opposite trend is verified for the end-gases in the intake valve outer region (marked by letter B), where the RON95-E10 case predicts higher AI delay for the end-gases.

Chapter 6 – Engine Case: RANS Application Although this is not intuitive from a first analysis, the specific AFRst for the two fuel models reported in Table 6.3 must be reminded. This leads to a different equivalence ratio for the two cases. Crank Angle = +10 CA aTDC B

B A

A

Crank Angle = +16 CA aTDC B

B A

A

Crank Angle = +20 CA aTDC B

B A

A

Figure 6.21 – End-gas AI delay on a section 1 mm below the flame deck: (left) RON98-E0 and (right) RON95-E10 fuel model.

Finally, flame propagation and knock onset regions are illustrated in Figure 6.22 for several CA positions, confirming the exhaust side portion of end-gases as the first knock inceptor for both cases, with an advance of approx. 2 CA for the RON95-E10 fuel model. Crank Angle = 740 CA



Figure 6.22 – Flame propagation (yellow iso-surface at ̃ ) and knock region (red iso-surface, defining AIreleased heat): (left) RON98-E0 and (right) RON95-E10 fuel model.

6.9

Conclusions

In this chapter, the developed UniMORE Knock Model is applied to a currently produced turbocharged GDI for which experimental data are available at 7000 rpm peak power WOT condition. A RANS framework is chosen in this analysis as the aim is the evaluation of the mean combustion evolution. At first, the global spray evolution and fuel mixing are evaluated, confirming a mixture stratification still present at spark timing but with a mixture quality at ignition location optimal for spark ignition. Secondly, combustion is validated against ensemble averaged experimental data, without any numerical model devoted to knock modelling. Then, the developed knock model is applied and knock is not predicted in the cycle. This result is in agreement with the experimental evidence of edge-off knock condition, while the standard knock model based on the empirical correlation of Douaud and Eyzat (1978) predicts an anticipated knocking phenomenon. The most critical region for knock onset is identified as the exhaust side of the combustion chamber.

Chapter 6 – Engine Case: RANS Application Subsequently, the SA is numerically advanced by 3 CA in order to promote knock. An anticipation of the phenomenon by 9 CA is measured, which is in coherence with the experimental impossibility to operate the engine at such operating condition as the unit would be excessively damaged. Finally, the sensitivity of the developed knock model to the fuel anti-knock quality is carried out by a comparison with a lower octane rated RON95-E10 fuel. An advance in knock prediction by approx. 2 CA is measured in this case.

7. Engine Case – LES Application 7.1

Introduction

A Large-Eddy Simulation application of the developed knock model is described in this section for the same engine and operating condition previously presented in Chapter 6, i.e. 7000 rpm full load Wide-Open Throttle. Ten consecutive full-cycles are calculated, with the RANS field as initial solution. However, in order for the calculated fields to be independent of the initial solution, the first LES cycles is discarded from the analysed results. Therefore, nine consecutive full-cycles are performed for this analysis, since each numerical simulation is solely representative of a specific flow realization (i.e. spray realization, mixing realization, combustion realization and so on) in a Large-Eddy Simulation framework. A relevant number of realizations (in this case engine cycles) is therefore necessary in LES analyses for two main reasons: 

Ensemble averaging of LES results (i.e. first moment) is the numerical counterpart of experimental data averaging, and this constitutes the validation of the mean flow behaviour.



Flow instabilities and correlated phenomena such as Cycle-To-Cycle Variability (CCV) are typically measured by the second moment of LES results (e.g. the root mean square of peak pressure). Again, these are compared with experimental values in order to verify whether numerical LES is correctly capturing the experimental variability.

The necessity of a large number of LES flow realizations for consistent statistics has been a longtime known limitation for this technique, and it still constitutes the major restriction to the widespread application of LES to industrial applications, despite the relatively low-cost CPU availability. The use of LES has been restricted to academic flows for several years (e.g. backward facing step, flow separation, channel flows, etc.) such as in works from Le et al. (1996) and test cases contained in the AGARD Report, while just in the last decade the increase in available computational power made LES a suitable numerical analysis for real engine flows. Following Pope’s overview on the LES capabilities advance (Pope, 2004), it seems reasonable to affirm that the available computational power places the current state in-between a long past period, where LES was only applied to academic test cases with limited Reynolds number, to a situation where LES can be effectively seen as an industrial development tool. In this context, more complex flows with larger Reynolds number and a broader range on length scales to be resolved are the new application field for LES and internal combustion engine flows represent an excellent example of

Chapter 7 - Engine Case: LES Application this. In the recent years several research groups are moving towards LES simulation on both research and production engines, with valuable contributions from Institute Français du Petrole (IFP) (Lacour and Pera (2011), Enaux et al. (2012), Granet et al. (2012)), PennState University (Haworth (1999), Haworth and Jensen (2000) and Liu and Haworth (2010)) and TU-Darsmtadt (Goryntsev et al. (2011) and (2012)).

7.2

Numerical Setup for Large-Eddy Simulation

A numerical grid dedicated to Large-Eddy Simulation is created in the es-ice environment, comprising of both intake and exhaust ports. The resulting number of cells is about 910000 at TDC and 1.5M at BDC, with an average cell size of about 0.5 mm. The complete mesh with intake and exhaust ports and a close-up of the cylinder domain are reported in Figure 7.1.

Figure 7.1 – Computational grid used for LES simulations. (a), left: complete fluid domain; (b), right: cylinder domain close-up.

Subgrid scale turbulence is modelled by the algebraic Smagorinsky model (Smagorinsky, 1963), which belongs to the eddy-viscosity closure models and which is based on the hypothesis of a turbulent equilibrium for the subgrid scales. A mean gradient assumption allows to relate subgrid scale dissipation effects to a turbulent viscosity

calculated as: ⁄ 〈 〉

In the above equation 0.202 is the Smagorinsky constant, filtered strain rate due to the resolved scales:

(Eq. 7.1) is the average cell size and 〈 〉 is the

Chapter 7 - Engine Case: LES Application 〈

〉

(

〈

〉

〈

〉

)

(Eq. 7.2)

This turbulence model is widely recognized as one of the simplest subgrid scale models for LES turbulence representation, its essence being a relationship based on known quantities such as resolved velocity components. One of the major limitations of this model is the excessive energy dissipation even at large scales, involving a portion of energy content that should instead be handled by the filtered momentum equation. This effect is counteracted by the use of fine grids (typically not coarser than 0.6 mm of cell size), with the non-negligible drawback of large CPU-cost for fullcycle analyses. However, its robustness and stability are recognized as key distinctive features in engine LES analyses on highly unstructured computational grids, driving the choice on this model. As for two-phase flows, a Lagrangian treatment is adopted for fuel spray. A pre-atomized population of droplets is imposed at each nozzle exit, accounting for primary break-up, while secondary break-up is simulated using the Reitz approach (Reitz and Diwakar, 1986). Therefore, the same modelling setup as the RANS analysis is adopted also for LES simulations. This is a largely debated choice in LES-dedicated literature as illustrated by Rutland (2012) in his review on the LES status of art in engine flow analysis. The use of dedicated models based on the LES-formalism is a necessary long-term target in order to fully benefit from the higher predictive capability of LES analyses, though it is still far from being completed. Another strategy is the so-called “hybrid approach”, consisting in the adoption of RANS-based models (e.g. for spray, combustion, wall heat transfer and so on) coupled with a LES-resolved turbulent flow field. The interaction with a flow field representing a larger number of unsteady flow structures allows to get a first insight into several unsteady processes regarding liquid sprays, combustion and wall heat transfer, and it is therefore an acceptable compromise and a logical choice. For the same reasons the Angelberger et al. (1997) model is adopted for wall heat transfer, while wall temperatures are derived from a calibrated 1-D model of the engine provided by the engine manufacturer. In the 3-D CFD analyses they are imposed as uniform in space and constant in time values for each boundary. As for boundary conditions, time-varying pressure and temperature traces are imposed at the domain inlet and outlet. The imposed pressure condition derives from the ensemble average over 240 cycles recorded by the engine manufacturer through fast-pressure transducers located at the same sections at the experimental test-bed. A periodic pressure signal is adopted for all the cycles: a previous comparative analysis was carried out (Fontanesi et al., 2013 (1)) in investigating to what extent in-cylinder fluctuating quantities were affected by the use of cycle-specific boundary

Chapter 7 - Engine Case: LES Application conditions instead of periodic pressure signals. Results showed that the sudden deviation experienced through the intake valves and the abrupt expansion in the cylinder volume generates turbulence levels whose relevance was orders of magnitude higher than the cyclic variation experimentally measured in the ports. Finally, the relatively long flow path from the intake boundary to the valve and the industrial convenience in using a periodic signal for multi-cycle analyses were valued as favourable factors in this choice. The use of cyclic boundary conditions implies that no cause of CCV is introduced in the solution, i.e. the simulated flow unsteadiness is completely generated by the spatially filtered momentum equation. Temperature measurements are not experimentally carried out due to the difficulty in the measurement of fast-fluctuating thermal signal, and they are derived from a calibrated 1-D model adopted by the engine manufacturer. In analogy to pressure boundary conditions, time-dependent temperature signals are applied as a periodic signal. As a logical consequence of the analysis of the same operating condition as the one presented in Chapter 6, valve phasing and lift profiles are the same as the RANS analysis, as well as wall temperatures, fuel injection timing and profile and the experimental knock-limited SA. Also the fuel liquid and vapour properties are identical to the RANS analysis. Combustion is modelled by the ECFM-LES combustion model, which is based on the ECFMfamily combustion model formalism here adapted for LES (Vermorel et al., 2009) (Richard et al., 2007). The model belongs to the class of coherent flame models where the Flame Surface Density (hereafter FSD, the flame surface area per unit volume) evolution is described by a balance equation which takes into account the effects of strain and curvature (both resolved and unresolved) along with the propagation of the flame itself in laminar unburnt gases zone, as already presented in Chapter 3. The adoption of the ISSIM-LES ignition model (Colin, Truffin, 2011) allows to accurately simulate the flame kernel formation and development by means of the FSD transport equation. This is made possible by the use of a modified FSD transport equation, with the presence of terms explicitly devoted to the subgrid treatment of flame surface density. This is mandatory to accurately simulate flame sizes as small as the typical cell size. The details of the model are presented in Chapter 4. The model implementation in Star-CD was made possible by a joint cooperation with CD-adapco. This model constitutes a remarkable simulation improvement over traditional spark-ignition models based on the deposition of a resolved profile of fully-burnt gases.

Chapter 7 - Engine Case: LES Application The UniMORE Knock Model is adopted in this model with no modifications from the previously presented RANS analyses. Since it is based on the cell-average values of pressure, temperature and equivalence ratio, the same formalism is still valid in the LES framework. However a conceptual difference has to be underlined: the cell-average (p,T,Φ,EGR) vector, which is the input to the lookup table interpolation, represents in this context a mere realization of the fluid cell condition, and not its ensemble average status as it was for RANS application. Although the model operates in the same way both in the RANS and LES context, this important difference must be reminded. Also, the filtering of unburnt gases based on a threshold progress variable value is operated in the same way in the LES context by considering the filtered progress variable ̃ , allowing an immediate coupling with the ECFM-LES combustion model. As for the fuel model, a look-up table based the Andrae and Head (2009) semi-detailed mechanism and with a blend for a RON98-E0 commercial gasoline is adopted. This is the same database as the one applied to RANS analyses and here proposed for LES, with the same number of calculated states: this is motivated by the identical operating condition analysed, presumably leading to similar physical conditions for end-gases. Since the focus is on a multi-cycle LES analysis of a GDI engine, an expectation for a number of air-fuel mixing realizations is present, as well as different combustion development are expected to induce cycle-dependent end-gases compression. These cyclic variations in the boundary conditions of the developed knock model produce a CCV in knock tendency/onset as well. The cycle-resolved knock tendency will be carefully analysed.

7.3

Mesh Quality Assessment for LES

As a first step into the validation of the numerical grid adopted for the presented LES analyses, the filter length is visualized for characteristic CA. This is equal to the average cell size, which is calculated for each finite volume i as in Eq. 7.3: √

(Eq. 7.3)

The filter length is for the mesh at TDC is reported in Figure 7.2, showing that the filter length is about 0.5 mm in the central part of the domain while it increases to 0.6-0.7 mm in the outer region.

Chapter 7 - Engine Case: LES Application

Figure 7.2 – Filter length in mm on a longitudinal section of the domain at TDC.

Since the LES numerical framework implies a cut-off filter length adopted for scale separation between resolved flow structures and modelled sub-grid quantities, which is the average cell size in the presented analyses, it is necessary to verify the adequacy of the mesh for the simulated flows. It is dependent on the specific flow that is simulated; therefore, assessments on grid quality cannot be made in advance, neither a specific grid can be judged as valid or inadequate for different engine conditions (e.g. different engine speed and flow velocity). As a consequence, the indices and judgement that follow are to be intended as relative exclusively for the presented mesh and operating condition. To this aim, the Energy Resolution (ER) index (Eq. 7.7) is recalled and applied. It was first proposed by Pope (2004) and it is defined as the ratio between the ensemble average subgrid scale kinetic energy 〈

〉 (Eq. 7.4) and the total ensemble average kinetic energy 〈

〉 (Eq. 7.6),

accounting for both the energetic contribution of the resolved flow field (Eq. 7.5) and the subgrid modelled one. In the context of the Smagorinsky static model the subgrid scale kinetic energy is calculated following Yoshizawa’s approach (1986). 〈

〉

〈

〉

〈

〉

〈

‖〈 〈( ̅

〈

〈 ̅〉) ( ̅

〉

〈

〈

〉

〈

〉

〉‖ 〉 〈 ̅〉)〉

〉

(Eq. 7.4) (Eq. 7.5) (Eq. 7.6) (Eq. 7.7)

In this work the complementary to unity index is adopted (Eq. 7.9): (Eq. 7.9) The M index ranges from 0 (ideally a LES analysis approaching a RANS one) to 1 (limit for a DNS analysis. Typical accepted values for the M index are above 0.8, stating that at least the 80% of the

Chapter 7 - Engine Case: LES Application energetic content should be resolved, i.e. derive from the filtered momentum equation rather than from some subgrid closure model. The M index is calculated for two positions: at the beginning of the compression stroke (approx. 600 CA) and at the end of the same (approx. at 670 CA). The M index field for these two angular positions are reported in Figures 7.3. Transverse Section

670 CA

600 CA

Longitudinal Section

Figure 7.3 – M index on axial sections of the domain.

The M index field on both the observed CA is around 0.8 value. The mesh is then judged as adequate in order to correctly resolve approx. the 80% of the flow turbulent kinetic energy.

7.4

Analysis of Conditions at Spark-Ignition

During the intake and compression stroke a highly turbulent flow structure develops in the cylinder volume. After the intake valve closure, the main tumbling vortex decays in a continuous spectrum of smaller and smaller eddies until molecular viscosity dissipates their kinetic energy. This is mainly due to the ceasing of entering flow momentum (the inlet flow through the intake valves) and to the fluid interaction with the liquid spray and the solid walls. This process of flow structure breaking is referred to as energy cascade, describing the energy transfer process from large length scale flows to small turbulent eddies.

Chapter 7 - Engine Case: LES Application The Tumble Ratio (TR) is a common index to describe the residual tumbling quality of the incylinder flow field and it is calculated in terms of resolved velocity components as in Eq. 7.10: [(

∑ ∑

) [(

( )

) (

]

(Eq. 7.10)

) ]

The negative sign in Eq. 7.10 is needed to obtain positive Tumble Ratio values during the main intake stroke, while the adopted coordinate system would indicate a misleading negative index. A similar formulation as Eq. 7.10 is adopted for the Swirl Ratio (SR), regarding x and y-oriented flow components, and for the Cross-Tumble Ratio (CTR), regarding y and z-oriented flow components. These indices for the calculated nine LES cycles are reported in Figure 7.4.

Swirl Ratio

Cross-Tumble Ratio 0.4

1.5

0.1

0.2

1

0

0

0.5 0 630

[-]

0.2

[-]

[-]

Tumble Ratio 2

-0.1 660 690 Crank Angle

720

-0.2 630

-0.2 660 690 Crank Angle

720

-0.4 630

660 690 Crank Angle

720

Figure 7.4 – Flow structures for the nine LES cycles: (left) Tumble Ratio, (middle) Swirl Ratio and (right) CrossTumble Ratio. Values can not be shown due to confidentiality reasons.

Tumble is the most intense flow structure at the end of the compression stroke, its index being one order of magnitude higher than swirl and cross-tumble. This is expected given the lack of any geometrical asymmetry in the intake ports and in the combustion chamber with respect to the x and z axes. In Figures 7.5, 7.6 and 7.7 significant CA positions (half of the intake stroke , BDC and half of the compression stroke, respectively) are reported for the two cycles with the highest and lowest Tumble Ratio respectively.


Figure 7.5 – Resolved flow field at 450 CA on section planes for the cycle with the highest Tumble Ratio (left, Cycle no.7) and the one with the lowest Tumble Ratio (right, Cycle no.4). Top: longitudinal section plane through one of the intake valves; bottom: transverse section plane cutting the intake valves.




Local measurements of flow conditions at spark location are numerically carried out through a spherical observation region centred in-between the electrode gap and whose radius is 3 mm.

Chapter 7 - Engine Case: LES Application Measurements are relative to the mass-averaged values of the resolved velocity components measured by the probe. The u, v and w velocity components, along with the velocity magnitude, are reported in Figure 7.8 for the nine LES cycles, where cycle-to-cycle variability between consecutive flow realizations is well discernible. Since the exact value for KLSA cannot be mentioned due to confidentiality reasons, a window of CA for spark-ignition is reported.

Velocity u-comp. (Spark Region)

Velocity v-comp. (Spark Region)

50

40 Ignition Window

Ignition Window

20

[m/s]

[m/s]

0 -50 -100 680

0 -20

690

700 Crank Angle

710

-40 680

720

Velocity w-comp. (Spark Region)

700 Crank Angle

710

720

Velocity Magnitude (Spark Region)

40

80 Ignition Window

Ignition Window

60

[m/s]

[m/s]

20 0 -20 680

690

40 20

690

700 Crank Angle

710

720

0 680

690

700 Crank Angle

710

720

Figure 7.8 – Local resolved velocity components at spark plug region: u, v, w velocity components and velocity magnitude. Highlighted are the cycle with the fastest flow field at spark (red line) and the one with the slowest flow field (blue line).

The cyclic variability of the resolved flow field is also responsible for cycle-to-cycle fluctuation in mixture preparation. In particular, the local equivalence ratio at the spark region is reported in Figure 7.9 (a) and it ranges from stoichiometric to rich mixtures. This constitutes the range of equivalence ratios which is optimal for successful ignition events, thus making this operating condition safe from misfiring events as confirmed by experimental data. The laminar flame speed at spark is affected as well by mixture fluctuation, and its local value at spark is illustrated in Figure 7.9 (b).


Equivalence Ratio (Spark Region) 1.3

Laminar Flame Speed (Spark Region) 1

Ignition Window

Ignition Window

0.8

1.1

0.6

[-]

[m/s]

1.2

1

0.4

0.9

0.2

0.8 680

690

700 Crank Angle

710

720

0 680

690

700 Crank Angle

710

720

Figure 7.9 – Left (a): local equivalence ratio at spark plug region. Right (b): local laminar flame speed at spark plug region. Highlighted are the cycle with the fastest flow field at spark (red line) and the one with the slowest flow field (blue line).

In order to give an overall characterization of the variability of the flow field over the entire operating point, here represented by the sample of nine LES cycles, statistical analysis must be carried out over the collected data. A useful indicator is the Coefficient of Variation (CoV), which is defined as the ratio between the standard deviation and the ensemble average of a generic observed variable (Eq. 7.11): 〈 〉

[%]

(Eq. 7.11)

In this analysis the CoV field is calculated for the resolved velocity magnitude and for the equivalence ratio (Figures 7.10 and 7.11, together with the ensemble average fields), describing the cyclic variability measured for flow field and fuel-air mixing respectively. Figure 7.10 shows the entity of the flow variation which is expressed by individual measurements around the spark plug (see Figure 7.8). The CoV field exceeds values of 50% in a large portion of the represented sections and in particular at the spark plug region, confirming the occurrence of extremely variable flow conditions from one cycle to the consecutive one. As for the equivalence ratio field, the single-cycle measurements (see Figure 7.9) are the basis for the CoV field illustrated in Figure 7.11, with an average value of approx. 10% of mixture quality fluctuations in a large portion of the domain and around the spark plug.


Figure 7.10 – Resolved velocity magnitude field and its variability at -20CA aTDC. High: top view of the section containing the ignition point; bottom: longitudinal axial section. Left: ensemble average field of the resolved velocity field; right: CoV field of resolved velocity.

Figure 7.11 –Equivalence ratio field and its variability at -20CA aTDC. High: top view of the section containing the ignition point; bottom: longitudinal axial section. Left: ensemble average field of equivalence ratio; right: CoV field of equivalence ratio.


7.5

Analysis of the Spark-Ignition Phase for KLSA

At first a detailed output of the electrical model of the secondary circuit and of the arc-related phenomena (such as modelled arc elongation, heat losses to the electrodes, multiple re-strikes, etc.) is analysed for the nine simulated cycles. The equivalent flame radius is at first analysed. As aforementioned in Chapter 4, this is calculated based on the assumption that at least in the early stages a spherical shape can be assumed for the developing flame kernel. The equivalent flame radius for the nine cycles is reported in Figure 7.12. It is visible how the cycle that will produce the highest peak pressure (Cycle no.3) is the one whose propagation is promoted since the early stages, as witnessed by the systematically high flame radius. Conversely, the lowest peak pressure cycle (Cycle no.10) is not the one whose flame radius is constantly the smallest, even though it is one of the cycle whose spreading flame fronts are less enhanced. Equivalent Flame Radius 20 18 16 14

[ mm ]

12 10 8 6 4 2 0 700

705

710

715 Crank Angle

720

725

730

Figure 7.12 – Equivalent flame radius for the nine LES cycles. Highlighted are the highest peak pressure cycle (red dashed line) and the lowest one (blue line).

Another indicator of combustion progress is given by the total flame surface density (FSD) present in the domain, which is reported in Figure 7.13 for the nine cycles. Not surprisingly the same observations regarding the highest and lowest peak pressure cycles are supported as well by the total FSD.


2.5

x 10

Total Flame Surface Density

7

2

[-]

1.5

1

0.5

0 700

705

710

715 Crank Angle

720

725

730

Figure 7.13 – Total FSD present in the cylinder domain. Highlighted are the highest peak pressure cycle (red dashed line) and the lowest one (blue line).

As illustrated in Chapter 4, the fundamental variable governing the flame kernel growth in the ISSIM-LES ignition model is the α function, continuously varying between 0 (ignition phase, treated with subgrid-devoted terms in the modified FSD-LES equation) to 1 (propagation phase, handled by the standard FSD-LES equation). The evolution of the α function is reported in Figure 7.14 for the computed cycles, together with the dedicated terms in the modified FSD equation dedicated for the subgrid flame stretch during ignition (Figure 7.15). This term is multiplied by the quantity (

) in the modified FSD equation (see Eq. 4.7), therefore it is maximum immediately

after the first FSD deposition by the electric circuit model and it is gradually suppressed as function reaches unity value and the flame completes its transition to be fully resolved. Cycle no.3 is the first one completing the transition to a fully resolved treatment (α reaches its unity value earlier than all the other flame realizations), while Cycle no.10 is not the one with the slowest αfunction increase. Although CCV variation (here represented by the peak pressure value) is closely related to ignition related phenomena, this not always verified as other factors can contribute to burn rate modifications at later stages (e.g. mixture inhomogeneity or flame interaction with flow structures).

Chapter 7 - Engine Case: LES Application Alpha Function During Ignition 1 0.9 0.8 0.7

[-]

0.6 0.5 0.4 0.3 0.2 0.1 0 700

705

710

715 Crank Angle

720

725

730

Figure 7.14 – α-function during ignition for the ISSIM-LES ignition model. Highlighted are the highest peak pressure cycle (red dashed line) and the lowest one (blue line).

9

x 10

FSD Stretch During Ignition

9

8 7

[-]

6 5 4 3 2 1 0 700

705

710

715 Crank Angle

720

725

730

Figure 7.15 –Stretch during ignition term for the ISSIM-LES ignition model. Highlighted are the highest peak pressure cycle (red dashed line) and the lowest one (blue line).

Finally, the source term to the FSD transport equation is reported in Figure 7.16. Depending on the local thermo-physical conditions as well as on the local resolved flow field, the FSD transport equation of each cycle sees a specific source term deriving from the secondary circuit modelling, as well as from a different number of re-strikes depending on local physical conditions.

Chapter 7 - Engine Case: LES Application FSD Source Term 6000

5000

[-]

4000

3000

2000

1000

0 700

705

710

715 Crank Angle

720

725

730

Figure 7.16 – Source term for the modified FSD transport equation. Highlighted are the highest peak pressure cycle (red dashed line) and the lowest one (blue line).

7.6

Knock Limited Spark Advance Condition

7.6.1

Combustion Analysis

The set of nine LES combustion cycles obtained with the experimental KLSA is compared with the full dataset of 240 experimental cycles from the engine test bed. The in-cylinder pressure traces are reported in Figure 7.17 for experiments and for LES simulations. As visible, simulation results fall within the bounds of the most extreme experimental cycles, confirming the validity of the modelling framework adopted regarding flame kernel formation and flame propagation. Highlighted in Figure 7.17-b are the highest peak pressure cycle (Cycle no. 3, pmax=93.6 bar) and the lowest one (Cycle no. 10, pmax=78.5 bar); these will be recalled in the following post-process in order to better understand the consequences of combustion CCV on knock tendency variability. The filtered flame front for these extreme cycles is reported in Figure 7.18 for several CA and differences in flame shape are well distinguishable between the two.

Chapter 7 - Engine Case: LES Application In-cylinder Pressure (LES Simulation) KLSA

120

120

100

100

80

80

[ bar ]

[ bar ]

In-Cylinder Average Pressure (Experimental) KLSA

60

60

40

40

20

20

0 690

720

750

780

0 690

720

750

780

Crank Angle

Crank Angle

Figure 7.17. (a), left: experimental cycles (thin grey lines); highest and lowest p max cycles are highlighted (red dashed lines); (b), right: in-cylinder pressure traces from the 20 LES cycles (thin grey lines); highest and lowest p max cycles from the experiments are highlighted (red dashed lines). Values can not be shown due to confidentiality reasons

Crank Angle = -5 CA aTDC

Crank Angle = TDC







Figure 7.18 –Iso-surfaces of resolved progress variable ̃=0.5. Left: maximum peak pressure cycle (Cycle no.3); right: lowest peak pressure cycle (Cycle no.10).

Variations in pressure development are originated by non-repeatability of the combustion process, which is in turn originated by the cyclic variability of several factors: 

Mixture quality at spark plug (see Figures 7.9 and 7.11);



Flow field at spark plug (see Figures 7.8 and 7.10);



Residual large-scale tumble motion (see Figure 7.4).

Several analyses were conducted in order to establish a hierarchy amongst the aforementioned aspects and others, with the aim to identify which is/are the dominant factors for a successful and repeatable ignition and combustion process. Fontanesi et al. (2015) verified for the same engine and operating condition that a resolved flow velocity field below 35 m/s was a necessary condition for high pressure cycles, while flame propagation was poorly correlated to local equivalence ratio at spark. This latter was due to the rich operating condition, allowing a good mixture quality for all the realizations. The flame front development from the spark plug electrodes is observed for the two extreme cycles in terms of peak pressure, i.e. Cycle no.3 and Cycle no.10, at several CA. These are reported in Figures 7.19, 7.20 and 7.21.


Figure 7.19 – Resolved flow field and iso-surfaces of ̃ at -5 CA aTDC on section planes containing the ignition point. Left: maximum peak pressure cycle (Cycle no.3); right: lowest peak pressure cycle (Cycle no.10). Top: longitudinal section plane; bottom: transverse section plane.

Figure 7.20 – Resolved flow field and iso-surfaces of ̃ at TDC on section planes containing the ignition point. Left: maximum peak pressure cycle (Cycle no.3); right: lowest peak pressure cycle (Cycle no.10). Top: longitudinal section plane; bottom: transverse section plane.


Figure 7.21 – Resolved flow field and iso-surfaces of ̃ at +5 CA aTDC on section planes containing the ignition point. Left: maximum peak pressure cycle (Cycle no.3); right: lowest peak pressure cycle (Cycle no.10). Top: longitudinal section plane; bottom: transverse section plane.

Cycle no.3 is subjected to an intake-oriented flow in the spark plug region, and the residual tumbling vortex is located right below the intake valve. The developing flame is enhanced in its early propagation towards the intake side and when interaction with the large-scale tumble begins (e.g. at TDC and later) this is even more favoured. The final observation at +5 CA aTDC shows an equally distributed flame front between intake and exhaust side. Conversely, Cycle no.10 experiences an exhaust-oriented flow at spark and the tumble motion is little effective for flame propagation. The result is that at +5 CA aTDC the flame is largely skewed towards the exhaust side. The reduced number of calculated cycles prevents from converged statistics to be carried out. However, the comparison with the experimentally measured peak pressure data reported in Table 7.1 give an excellent agreement in terms of ensemble average peak pressure, while the reduced standard deviation of the LES simulations compared to the experimental counterpart is expected since the strong bias between the experimental dataset (240 cycles) and the computed one (9 cycles).

Chapter 7 - Engine Case: LES Application Experiments (240 cycles)

LES Simulations (9 cycles) -0.5% from exp. ensemble

Ensemble Average

-

Standard Deviation

7.08

4.70

Coefficient of Variation

8.14%

5.43%

average

Table 7.1 – Experimental and numerical results for peak pressure and its variation for KLSA condition. Exact values can not be mentioned due to confidentiality reasons.

7.6.2 Global Analysis of Knock Tendency for KLSA Condition Another fundamental part of validation for this condition is the confirmation of the knock-limit condition indicated by the experiments. The knocking signature of each cycle can be observed by the in-cylinder heat release rate and by its contribution due to autoignition. These are reported in Figure 7.22 where highlighted are the maximum peak pressure cycle (red dashed line) and lowest one (blue line). Heat Release Rate KLSA

Autoignition Heat Release Rate KLSA

6000

4000 3500

5000

3000 4000

[W]

[W]

2500 3000

2000 1500

2000

1000 1000

0 700

500 720

740 Crank Angle

760

780

0 700

720

740 Crank Angle

760

780

Figure 7.22 – Heat release rate as a function of crank angle: overall thermal power (left) and contribution due to autoignition (right). Highlighted are the highest peak pressure cycle (red dashed line) and the lowest one (blue line).

As visible, knock is observed just in a limited portion of cycles and this confirms the edge-off knock operating condition of the experiments. The fraction of heat released by autoignition alone can be separated in the numerical analysis from the overall heat released by combustion, and this is a first indicator of knock severity. In Figure 7.23 the fraction of heat release by AI over the total given by combustion is reported for each cycle and it is for most cycles less than 1% and just in few cycles exceeds 3%.

Chapter 7 - Engine Case: LES Application Percentage of Heat Released by AI 5

[%]

4 3 2 1 0

2

3

4

5

6 Cycle no.

7

8

9

10

Figure 7.23 – Fraction of heat released by AI over the total heat released by combustion for the nine simulated cycles at KLSA.

The Knock Severity Index (KSI) as proposed by Klimstra (1984) and resumed in Chapter 2 is here recalled in order to give a cycle-resolved measure of the knock-related damage. The resulting values are reported in Table 7.2 together with the CA where knock onset is detected, and both extremely low values of knock index and very late crank angles for knock onset are confirmed. Knock Severity Index [-] Cycle no.2 Cycle no.3 Cycle no.4 Cycle no.5 Cycle no.6 Cycle no.7 Cycle no.8 Cycle no.9 Cycle no.10

0.66 3.02 1.02 1.56 0.99 1.52 0.45 0.13 -

Crank Angle of Knock Onset [CA aTDC] 34.35 29.43 31.57 31.47 31.63 35.39 39.15 43.45 -

Mass Fraction Burnt at Knock Onset [%] 93.26 88.11 91.76 86.51 89.79 92.85 95.91 97.90 -

Table 7.2 – Knock Severity Index, CA and MFB at knock onset for all the LES cycles at KSLA condition.

Finally, the heat released by autoignition is illustrated in Figure 7.24 for the highest and the lowest peak pressure cycle at +35 CA aTDC. While the former presents a region in proximity of one of the exhaust valves where heat produced by autoignition is present, the latter is completely free from knock.


Figure 7.24 – Heat released by autoignition. Left: highest peak pressure cycle (Cycle no.3); right: lowest peak pressure cycle (Cycle no.10).

7.6.3 End-Gas Analysis of Knock Tendency for KLSA Condition A more detailed analysis of the end-gases condition is carried out by means of four peripheral probes placed in the outer region of the four valves. A sketch of the peripheral probes location is represented in Figure 7.25 and following. This analysis is intended to quantify the cycle-to-cycle variability of knock tendency as predicted by the developed knock model. Mixture quality variability is represented by the local equivalence ratio as seen by the probes and represented in Figure 7.25. In addition, EGR mixing is cycle-dependent as well, although the very limited residual EGR (mass fraction less than 1% for all the cycles) for this particular operating condition does not make this as a key factor; hence the EGR mixing is not interesting and it is not reported. It is visible that all the probes experience fuel-enriched end-gases, although fuel stratification is well visible for each individual cycle as witnessed by the location-dependent equivalence ratio trace representative of the aforementioned mixing hurdle of this high-speed fuelrich operating condition.


Equivalence Ratio (End Gas) Intake Valve 1

1.4

1.4

1.2

1.2

[-]

[-]

Equivalence Ratio (End Gas) Exhaust Valve 1

1 0.8 700

1

720

740 Crank Angle

760

0.8 700

780

1.4

1.4

1.2

1.2

1 0.8 700

740 Crank Angle

760

780

Equivalence Ratio (End Gas) Intake Valve 2

[-]

[-]

Equivalence Ratio (End Gas) Exhaust Valve 2

720

1

720

740 Crank Angle

760

780

0.8 700

720

740 Crank Angle

760

780

Figure 7.25 – Local equivalence ratio measured by four peripheral probes (red dots) for the nine LES cycles. Highlighted are the maximum peak pressure cycle (Cycle no.2, red line) and the lowest one (Cycle no.10, blue line).

Fuel-air mixing variability is combined with the pressure cycle-dependent history caused by combustion in the central region of the combustion chamber. End-gases compression heating is variable as a consequence of the aforementioned aspects. The final result is a cycle-resolved variability of the interpolated AI delays from the fuel-specific look-up table, whose values on the four probes are reported in Figure 7.26. Given the orders of magnitude of variability of AI delays over a few CA a logarithmic scale is adopted for these graphs, due to the exponential dependence of chemical reaction rate on in-cylinder pressure and temperature.


10 10

10

[ms]

10 10 10

10

-2

10

[ms]

[ms]

10

Autoignition Delay (End Gas) Exhaust Valve 1

-3

10

-4

700

720

740 Crank Angle

760

-1

Autoignition Delay (End Gas) Exhaust Valve 2

10

780

10

-2

10

[ms]

10

-1

-3

10

-4

700

720

740 Crank Angle

760

780

10

-1

Autoignition Delay (End Gas) Intake Valve 1

-2

-3

-4

700

720

740 Crank Angle

760

-1

Autoignition Delay (End Gas) Intake Valve 2

780

-2

-3

-4

700

720

740 Crank Angle

760

780

Figure 7.26 – Local AI Delay measured by four peripheral probes (red dots) for the nine LES cycles. Highlighted are the maximum peak pressure cycle (Cycle no.2, red line) and the lowest one (Cycle no.10, blue line).

Finally, the negligible knock signature of each cycle is confirmed by the local pressure wave measured by the peripheral probes, reported in Figure 7.27. This is defined as the difference between the local absolute pressure and the average in-cylinder pressure. From the point of view of pressure signal manipulation, the former acts as a high-frequency impulse given by the pressure waves produced by autoignition while the latter is the low-frequency noise due to regular combustion.


Pressure Fluctuation (KLSA) Intake Valve 1

60

60

30

30

[bar]

[bar]

Pressure Fluctuation (KLSA) Exhaust Valve 1

0 -30

-30 730

740 750 760 Crank Angle

770

-60 720

780

Pressure Fluctuation (KLSA) Exhaust Valve 2 60

60

30

30

[bar]

[bar]

-60 720

0

0


770

780

770

780

Pressure Fluctuation (KLSA) Intake Valve 2

0 -30

-30 -60 720

730

730


770

780

-60 720

730


Figure 7.27 – Local pressure wave signal measured by four peripheral probes (red dots) for the nine LES cycles at KLSA condition. Highlighted are the maximum peak pressure cycle (Cycle no.2, red line) and the lowest one (Cycle no.10, blue line).

Despite the absence of relevant knock events, a numerical investigation can be carried out on the interpolated AI Delay field and on the residual Knock Tolerance status of the end-gases. To this aim, both fields are reported in Figure 7.28 for the highest peak pressure cycle and the lowest one at +20CA aTDC.

Chapter 7 - Engine Case: LES Application Lowest peak pressure cycle

Knock Tolerance

AI Delay

Highest peak pressure cycle

Figure 7.28 – AI Delay and Knock Tolerance fields at +20 CA aTDC for the highest and the lowest peak pressure cycle.

The spatial distribution of the Knock Tolerance function in all the computed realizations is expressed by the PDFs of Knock Tolerance, reported in Figure 7.29 and relative to +20CA aTDC.

Chapter 7 - Engine Case: LES Application Intake Valve 1 (KLSA)

Knock Onset

0.08 0.06 0.04 0.02 0

0

0.02 0.04 0.06 Knock Tolerance

0.08

0.1

PDF of Knock Tolerance


Exhaust Valve 1 (KLSA) 0.1

0.1 Knock Onset

0.08 0.06 0.04 0.02 0

0



Knock Onset

0.06 0.04 0.02 0

0


0.08

0.08

0.1

0.08

0.1

Intake Valve 2 (KLSA)

Exhaust Valve 2 (KLSA) 0.1 0.08


0.1 0.08

Knock Onset

0.06 0.04 0.02

0.1

0

0


Figure 7.29 – Probability Density Functions of nock Tolerance at +20CA aTDC for the nine LES cycles at KLSA condition. Highlighted are the highest peak pressure cycle (red) and the lowest one (blue), together with the ensemble average PDF (black).

Figure 7.29 allows to carry out a knock tendency analysis even though no one of the calculated cycles developed knock. This is made possible by the distribution of the Knock Tolerance values, which are in the positive range for all the cycles but which highlight cycle-dependent knock tendency differences between consecutive cycles. This is evident by the comparison with the ensemble average PDF, with single cycles lying at lower Knock Tolerance values (more knockprone than the average cycles) while others exhibit higher Knock Tolerance (less knock-prone than the average cycles). In particular the highest peak pressure cycle (red line) is the one whose endgases are the closest to knock onset on the exhaust side of the combustion chamber (left sectors), while this is not rigorously found in the intake side portions (right sectors). The opposite is verified for the cycle with the lowest peak pressure, whose end-gases are generally amongst those which are the safest from a knock tendency point of view. Exceptions to this pressure-related trend are essentially due to mixing variability in the end-gases, which is not related to the regular combustion developing in the central region of the combustion chamber. Finally, the exhaust side of the combustion chamber emerges as the most knock-prone region of the combustion chamber, with Knock Tolerance values generally closer to zero (i.e. to knock onset) than those located in the intake side.


7.7 Combustion Results for KLSA+3 Condition The set of nine combustion cycles at KLSA is repeated for an increase in SA by 3 CA (hereafter named KLSA+3 condition), in order to evaluate the effect on combustion regularity and knock tendency. In Figure 7.30 to 7.32 the main combustion results are summarized for the two sets of nine combustion cycles: KLSA and KLSA+3 condition. Results for the experimental KLSA condition are repeated here for the sake of a better comparison between the two operating points. In-cylinder Pressure (LES Simulation) KLSA+3 CA

120

120

100

100

80

80

[ bar ]

[ bar ]

In-cylinder Pressure (LES Simulation) KLSA

60

60

40

40

20

20

0 690

720

750

780

Crank Angle

0 690

720

750

780

Crank Angle

Figure 7.30 – In-cylinder pressure traces for the nine LES cycles: (left) KLSA condition, (right) KLSA+3 condition. Values can not be shown due to confidentiality reasons


Heat Release Rate (LES Simulation) KLSA

Heat Release Rate (LES Simulation) KLSA + 3CA

12000

12000

10000

10000

8000

8000

[W]

14000

[W]

14000

6000

6000

4000

4000

2000

2000

0 700

720

740 Crank Angle

760

0 700

780

720

740 Crank Angle

760

780

Figure 7.31 – Heat release rate traces for the nine LES cycles: (left) KLSA condition, (right) KLSA+3 condition. Autoignition Heat Release Rate KLSA

Autoignition Heat Release Rate KLSA + 3CA

8000

8000

6000

6000

[W]

10000

[W]

10000

4000

4000

2000

2000

0 730

740

750 760 Crank Angle

770

780

0 730

740

750 760 Crank Angle

770

780

Figure 7.32 – AI heat release rate for the nine LES cycles: (left) KLSA condition, (right) KLSA+3 condition.

The increase in SA induces higher pressure levels, promoting favourable conditions for knock onset in a larger fraction of the simulated cycles. The fraction of heat released by AI over the entire combustion heat is reported in Figure 7.33. Compared to the same measurement relative to KLSA (see Figure 7.23) all the calculated cycles predict a moderate-to-mild fraction of AI heat. Cycle no.3 is the one exhibiting the highest value, with nearly 10% of heat released by AI.

Chapter 7 - Engine Case: LES Application Percentage of Heat Released by AI 10 8

[%]

6 4 2 0

2

3

4

5

6 Cycle no.

7

8

9

10

Figure 7.33 – Figure 7.23 – Fraction of heat released by AI over the total heat released by combustion for the nine simulated cycles at KLSA+3.

Similarly to the knock intensity estimation following Klimstra’s Knock Severity Index, the same observation is carried out for the KLSA+3 condition and values are reported in Table 7.3. Knock Severity Index [-] Cycle no.2 Cycle no.3 Cycle no.4 Cycle no.5 Cycle no.6 Cycle no.7 Cycle no.8 Cycle no.9 Cycle no.10

2.27 3.29 2.45 3.24 2.80 2.27 2.29 0.60 0.98

Crank Angle of Knock Onset [CA aTDC] 23.71 20.69 25.95 25.95 24.19 27.33 24.97 34.67 33.03

Mass Fraction Burnt at Knock Onset [%] 80.24 76.95 85.16 78.24 82.59 85.56 79.79 93.00 88.51

Table 7.3 – Knock Severity Index, CA and MFB at knock onset for all the LES cycles at KSLA condition.

The spatial distribution of the Knock Tolerance function in all the computed realizations is expressed by the PDFs of Knock Tolerance, reported in Figure 7.34 and relative to +20CA aTDC. Similarly to the same observation for the KLSA condition (still at +20 CA aTDC, see Figure 7.29) highest and lowest peak pressure cycles are characterized by the end-gases which are generally amongst the closest and the furthest from knock onset, respectively. This is driven by the different in-cylinder condition, enhancing knock tendency for high pressure cycles. However, the trend is not rigorous as local effects (e.g. air-fuel mixing) may increase or decrease the knock-prone quality of each cycle. The same fluctuations around the ensemble average knock tendency already observed in Figure 7.29 are here even more evident. In particular, the knock tendency for the most knock-prone cycles is much higher than the one predicted by the ensemble average, enforcing the cycle-specific signature of the knocking phenomenon.

Exhaust Valve 1 (KLSA+3)

0.1




Knock Onset

0.08 0.06 0.04 0.02 0

0


0.08

0.1

Intake Valve 1 (KLSA+3)

0.1

Knock Onset

0.08 0.06 0.04 0.02 0

0

Knock Onset

0.08 0.06 0.04 0.02 0

0


0.08

0.08

0.1

Intake Valve 2 (KLSA+3)

0.1



Exhaust Valve 2 (KLSA+3)


0.1

0.1 Knock Onset

0.08 0.06 0.04 0.02 0

0


0.08

0.1

Figure 7.34 – Probability Density Functions of nock Tolerance at +20CA aTDC for the nine LES cycles at KLSA+3 condition. Highlighted are the highest peak pressure cycle (red) and the lowest one (blue), together with the ensemble average PDF (black).

The local pressure wave measured by the peripheral probes is reported in Figure 7.34. If compared with the same measurement for the KLSA condition (see Figure 7.27), local pressure imbalance reaches up to 60 bar over the average in-cylinder pressure. This repeated mechanical overloading further confirms the KLSA+3 point to be a severely knocking operating condition.

Chapter 7 - Engine Case: LES Application Pressure Fluctuation (KLSA+3) Intake Valve 1

60

60

30

30

[bar]

[bar]

Pressure Fluctuation (KLSA+3) Exhaust Valve 1

0 -30 -60 720

0 -30

730


770

-60 720

780

60

60

30

30

[bar]

[bar]


770

780

Pressure Fluctuation (KLSA+3) Intake Valve 2

Pressure Fluctuation (KLSA+3) Exhaust Valve 2

0

0 -30

-30 -60 720

730

730


770

-60 720

780

730


770

780

Figure 7.34 – Local pressure wave signal measured by four peripheral probes (red dots) for the nine LES cycles at KLSA+3 condition. Highlighted are the maximum peak pressure cycle (Cycle no.2, red line) and the lowest one (Cycle no.10, blue line).

A final confirmation of the operating point moving into the knocking region when increasing the SA by 3 CA is the visualization of the pressure wave originated by knock. As recalled in Chapter 2 the pressure imbalance originated by autoignition is the main responsible of the set of damaging mechanisms for engine components. In Figure 7.35 the pressure wave field is reported. This is defined in Eq. 7.11 as the difference between the local pressure and the average in-cylinder pressure ̅ at that instant.

( ̅)

( ̅) ̅

(Eq. 7.11)


KLSA Cycle no.10

Cycle no.3

Cycle no.10

Knock Onset + 4 CA

Knock Onset + 2 CA

Knock Onset

Cycle no.3

KLSA+3

Figure 7.35 – Pressure wave evolution for highest and lowest peak pressure cycle for KLSA and KLSA+3 condition. Scale is +/- 15 bar from the mean in-cylinder pressure

As visible in Figure 7.35 knock is generally originated for both operating conditions from the exhaust side region. The entity of the knocking wave for Cycle no.3 (the highest peak pressure cycle for both operating conditions) is largely different, with a relevant increase for the KSLA+3 condition.

7.8

Mixture Quality Promoting Autoignition

The statistical analysis carried out through PDFs gives a statistical probability to have portions of fluid very close to knock onset or even potentially autoigniting. However, PDFs give an information about knock proximity without adding additional information regarding the quality of the end-gas portion which is first leading to spontaneous ignition. This is a useful information since it can help the engine designer to understand which portion of unburnt mixture is to be observed as

Chapter 7 - Engine Case: LES Application a first responsible of abnormal combustion. Based on this, evaluations can be made to avoid the formation of such reactive mixture pockets in order to postpone the onset of knocking event. The purpose of this section is to critically analyse the reactivity map such as those provided in Figure 6.18 by the sole chemistry at constant pressure, predicting a higher autoignition resistance for lean mixtures while for stoichiometric or rich ones a similar dependence on temperature is foreseen. The missing information from that kind of map is the degree of influence of the mixture strength on unburnt charge temperature. To this purpose, ‘Ф-T’ scatter plots are reported in Figures 7.36 and 7.37 for the unburnt mixture at +20 CA aTDC for the KLSA+3 condition. The choice of this particular condition is motivated by its higher knock tendency, which better clarifies this kind of analysis. The reaction rate of the mixture is once again represented by its AI delay for each unburnt fluid cell (Figure 7.36), and it is reported as a colour scale against the unburnt temperature and equivalence ratio. The Knock Tolerance field is reported in Figure 7.37 for the same CA. All the nine cycles are simultaneously reported in order to give an overall view of the whole operating condition. Figure 7.36 shows that the leanest portions of end-gas are those with the lower autoignition delay and they are located in the lower-rightmost part of the scatter plots. Being the most reactive regions, they are the first responsible of the autoignition event. This is due to the relatively higher mixture specific heat for richer portions of unburnt charge that helps in limiting their temperature. Fuel generally exhibits a much higher heat capacity than air, and the mixture property is given by the mass weighted average of the specific heat of the single components; therefore it increases linearly with fuel concentration. As expected, as far as Knock Tolerance is concerned, the charge portion which is the most prone to (or already exceeding) the autoignition criterion is the relatively lean one. In Figures 7.37 the increasing thermal loading in clearly visible, alongside with the decreasing level of Knock Tolerance. The conclusion from the maps below is that the partial leaning of end-gas for globally rich operating conditions may not be a good practice, as the cooling effect given by the high specific heat for fuel-rich mixtures is far more advantageous than the increase in their reactivity predicted by the chemistry alone. However, if a globally rich operating condition has to be chosen, then the utilization of the cooling effect given by the fuel evaporation can be beneficial for knock resistance purposes. To this aim, the adoption of early injection strategies is well confirmed and a further gain in knocking resistance could occur from even more advanced SOIs.


Figure 7.36 – Scatter plot of end-gas AI delay as a function of unburnt temperature and equivalence ratio at +20 CA aTDC.

Figure 7.37 – Scatter plot of end-gas Knock Tolerance as a function of unburnt temperature and equivalence ratio at +20 CA aTDC.


7.9 – Conclusions In this Chapter the developed knock model is applied to Large-Eddy Simulations of the same engine and operating condition as the one analysed in Chapter 6. The LES numerical technique allows to simulate the cycle-to-cycle variability affecting the in-cylinder turbulent combustion, as confirmed by the agreement of pressure trace results between experiments and LES simulations. The LES simulations at the experimental KLSA confirmed a negligible heat release due to knock limited to a fraction of the computed cycles, in agreement with the experimental criterion used to define the KLSA condition. A second set of simulations regarded the increase of SA by 3 CA. For this experimentally prevented condition, LES simulation show a larger heat release by autoignition for all the calculated cycles. The more intense knock intensity for the simulations at KLSA+3 is confirmed by local pressure fluctuations measurement, as well as from knocking pressure wave visualizations. Finally, an analysis regarding the end-gas composition acting as a first knock promoter is carried out. The lean portion of the unburnt mixture undergoes a more intense heating during piston compression, due to the lower specific heat than fuel-rich end-gases. Therefore knock is originated by lean end-gas regions at the analysed operating condition.

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Kawahara, N., Tomita, E., and Roy, M., "Visualization of Autoignited Kernel and Propagation of Pressure Wave during Knocking Combustion in a Hydrogen Spark-Ignition Engine," SAE Technical Paper 2009-01-1773, 2009, doi:10.4271/2009-01-1773. Klimstra, J. (1984) "The Knock Severity Index – A Proposal for a Knock Classification Method," SAE Technical Paper 841335, 1984, doi:10.4271/841335. Lacour, C., Pera, C. (2011) “An Experimental Database Dedicated to the Study and Modelling of Cyclic Variability in Spark-Ignition Engines with LES,” SAE Technical Paper 2011-01-1282 Lafossas, F A., Castagne, M. , Dumas, J. P., Henriot, S. (2002). Development and Validation of a Knock Model in Spark Ignition Engines using a CFD code,” SAE Technical Paper 2002-01-2701 Lawes, M., Ormsby, M.P., Sheppard, C.G.W. and Woolley, R. (2005) “Variation of turbulent burning rate of methane, methanol, and iso-octane air mixtures with equivalence ratio at elevated pressure,” Comb. Sc. and Techn., 177 (7). pp. 1273-1289 (2005). Le, H., Moin, P., Kim, J. (1996) “Direct numerical simulation of turbulent flow over a backwardfacing step,” J. Fluid Mech. (1997), vol. 330, pp. 349-374 Liu, K., Haworth, D. (2010) “Large-Eddy Simulation for an Axisymmetric Piston-Cylinder Assembly With and Without Swirl,” Flow Turbulence Combust (2010) 85:279-307 Livengood, J.C., Wu, P.C., Proc. Combust. Inst. 5 (1955) 347–356. Malaguti S, Fontanesi S, Cantore G, Montanaro A and Allocca L. (2013) “Modelling of primary breakup process of a gasoline direct engine multi-hole spray,” Atomization Spray 2013; 23(10): 861–888. Meneveau, C. and Poinsot, T. (1991) “Stretching and quenching of flamelets in premixed turbulent combustion”, Combust. Flame, 86, pp. 311-332. Metghalchi, M., Keck, J.C. (1980) “Laminar burning velocity of propane-air mixtures at high temperature and pressure,” Combustion and Flame 38, 143-154 (1980)

Millo, F. and Ferraro, C., "Knock in S.I. Engines: A Comparison between Different Techniques for Detection and Control," SAE Technical Paper 982477, 1998, doi:10.4271/982477. Moureau, V., Barton, I., Angelberger, C., Poinsot, T. (2004) “Towards Large Eddy Simulation in Internal-Combustion Engines: simulation of a compressed tumble flow,” SAE Technical Paper 2004-01-1995 Ollivier, E., Bellettre, J., Tazerout, M., (2006) “Detection of knock occurrence in a gas SI engine from a heat transfer analysis,” Energy Conversion and Management 47 (2006) 879–893 Ollivier, E., Bellettre, J., and Tazerout, M., "A Non Intrusive Method for Knock Detection Based on the Exhaust Gas Temperature," SAE Technical Paper 2005-01-1129, 2005, doi:10.4271/2005-011129. Ozdor, N., Dulger, M., Sher, E. (1994) “Cyclic Variability in Spark Ignition Engines A Literature Survey,” SAE Technical Paper 940987, doi: 10.4271/940987 Peters, N., Kerschgens, B., and Paczko, G. (2013) "Super-Knock Prediction Using a Refined Theory of Turbulence,"SAE Int. J. Engines 6(2):953-967, 2013, doi:10.4271/2013-01-1109 (2013). Pope, S. (2004) “Ten questions concerning the large-eddy simulation of turbulent flows,” New Journal of Physics 6 (2004) 35, DOI: 10.1088/1367-2630/6/1/035. Reitz R., Diwakar R. (1986) “Effect of Drop Breakup on Fuel Sprays,” SAE Technical Paper 860469, SAE Trans. 95, 3, 218-227. Richard, S., Colin, O., Vermorel, O., Benkenida, A., Angelberger, C., Veynante, D. (2007). “Towards large eddy simulation of combustion in spark ignition engines,” Proceedings of the Combustion Institute 31 (2007) 3059-3066 Rutland, C. J. (2011) “Large-eddy simulations for internal combustion engines – A review,” Int. J. Engine Res. Vol. 12, doi: 10.1177/1468087411407248. Smagorinsky J. (1963), “General circulation experiments with the primitive equations,” Mon. Wea. Rev. 91, 99-164.

Teodosio, L., De Bellis, V., Bozza, F. (2015) “Fuel Economy Improvement and Knock Tendency Reduction of a Downsized Turbocharged Engine at High Load Operations through a Low-Pressure EGR System”, SAE Technical Paper 2015-01-1244 Thobois, L., Lauvergne, R., Poinsot, T. (2007) “Using LES to Investigate Reacting Flow Physics in Engine Design Process,” SAE Technical Paper 2007-01-0166 Vandersickel, A., Hartmann, M., Vogel, K., Wright, Y.M., Fikri, M., Starke, R., Schulz, C., Boulouchos, K. (2012) “The autoignition of practical fuels at HCCI conditions: High-pressure shock tube experiments and phenomenological modeling,” Fuel 93 (2012) 492–501 Vitex, O., Macek, J., Tatschl, R., Pavlovic, Z., Priesching, P. (2012) “LES Simulation of Direct Injection SI-Engine In-Cylinder Flow,” SAE Technical Paper 2012-01-0138 Vermorel, O., Richard, S., Colin, O., Angelberger, C., Benkenida, A., Veynante, D. (2009) “Towards the understanding of cyclic variability in a spark ignited engine using multi-cycle LES,” Combustion and Flame 156 (2009) 1525–1541, ISSN 0010-2180 Würmel, J., Silke, E.J., Curran, H.J., Ó Conaire, M.S., Simmie, J.M. (2007) “The effect of diluent gases on ignition delay times in the shock tube and in the rapid compression machine,” Combustion and Flame 151 (2007) 289–302 Yang, S., Ra, Y., Reitz, R.D., VanDerWege, B., Yi, J.(2012) “Integration of a discrete multicomponent fuel evaporation model with a G-equation flame propagation combustion model and its validation, “International Journal of Engine Research 2012 13: 370 originally published online 28 February 2012 Yoshizawa, A. (1986) “Statistical theory for compressible turbulent shear flows, with the application to subgrid scale modelling,” Phys. Fluids, 29, pp. 2152-2164. Young, M. (1980) “Cyclic Dispersion - Some Quantitative Cause-and-Effect Relationships,” SAE Technical Paper 800459, doi: 10.4271/800459

Publications Journal Papers Fontanesi, S., Paltrinieri, S., D'Adamo, A., Cantore, G., Rutland, C. J., "Knock Tendency Prediction in a High Performance Engine Using LES and Tabulated Chemistry" SAE Int. J. Fuels Lubr. 6(1):2013, doi:10.4271/2013-01-1082. Oral presentation at SAE World Congress 2013 (Detroit, USA) Fontanesi, S., Paltrinieri, S., d’Adamo, A., Duranti, S., “Investigation of boundary condition effects on the analysis of cycle-to-cycle variability of a turbocharged GDI engine”, Oil & Gas Science and Technology – Rev. IFP Energies Nouvelles, DOI: 10.2516/ogst/2013142 Fontanesi, S., d’Adamo, A., Rutland, C.J., ‘Large-Eddy simulation analysis of spark configuration effect on cycle-to-cycle variability of combustion and knock’, International Journal of Engine Research, first published on January 9, 2015 as doi:10.1177/1468087414566253

Conference Proceedings S. Malaguti, A. d’Adamo, G. Cantore, P. Sementa, B.M. Vaglieco, F. Catapano, ‘Experimental and Numerical Investigation of the Idle Operating Engine Condition for a GDI Engine’’, SAE Technical Paper 2012-01-1144, 2012 Fontanesi, S., Paltrinieri S., Tiberi A., D'Adamo, A., “LES Multi-cycle Analysis of a High Performance GDI Engine,” SAE Technical Paper 2013-01-1080, 2013 Fontanesi, S., d’Adamo, A., Paltrinieri, S., Cantore, G., Rutland, C. J., “Application of Proper Orthogonal Decomposition for the Analysis of Combustion and Knock in a High Performance Engine,” SAE Technical Paper 2013-24-0031, 2013. Oral presentation at 11th International Conference on Engines & Vehicles – ICE2013 (Capri, NA)

Fontanesi, S., Cicalese, G., Cantore, G., and D'Adamo, A., "Integrated In-Cylinder/CHT Analysis for the Prediction of Abnormal Combustion Occurrence in Gasoline Engines," SAE Technical Paper 2014-01-1151, 2014, doi:10.4271/2014-01-1151. Fontanesi, S., Cicalese, G., d’Adamo, A., Cantore, G., ‘A Methodology to Improve Knock Tendency Prediction in High Performance Engines’, Energy Procedia, Volume 45, 2014, Pages 769–778, doi:10.1016/j.egypro.2014.01.082 Giovannoni, N., d’Adamo, A., Nardi, L., Cantore, G., ‘Effects of fuel composition on charge preparation, combustion and knock tendency in a high performance GDI engine. Part I: RANS analysis’, Accepted for publication on Energy Procedia D’Adamo, A., Giovannoni, N., Nardi, L., Cantore, G., D’Angelis, A., ‘Effects of fuel composition on charge preparation, combustion and knock tendency in a high performance GDI engine. Part II: LES analysis’, Accepted for publication on Energy Procedia

Abbreviations aSOC BCs CA CCV CoV DISI EA ER FSD GDI ICE IMEP IVC KLSA KT LES MFB NTC PDF PRF RANS RMS SA SI SOC SOI TDC THEO TRF WOT

After Start of Combustion Boundary Conditions Crank Angle Cycle-to-Cycle Variability Coefficient of Variation Direct Injection Spark Ignition Ensemble Average Equivalence Ratio Flame Surface Density Gasoline Direct Injection Internal Combustion Engine Indicated Mean Effective Pressure Intake Valve Closing Knock Limited Spark Advance Knock Tolerance Large-Eddy Simulation Mass Fraction Burnt Negative Temperature Coefficient Probability Density Function Primary Reference Fuels Reynolds-Averaged NavierStokes Root Mean Square Spark Advance Spark Ignition Start of Combustion Start of Injection Top Dead Center Toluene-n-Heptane-EthanolIsoctane Toluene Reference Fuel Wide-Open Throttle

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