Large eddy simulation of fuel injection and mixing process in a diesel ...

Acta Mech. Sin. (2011) 27(4):519–530 DOI 10.1007/s10409-011-0485-1

RESEARCH PAPER

Large eddy simulation of fuel injection and mixing process in a diesel engine Lei Zhou · Mao-Zhao Xie · Ming Jia · Jun-Rui Shi

Received: 8 December 2009 / Revised: 11 August 2010 / Accepted: 24 January 2011 ©The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag Berlin Heidelberg 2011

Abstract The large eddy simulation (LES) approach implemented in the KIVA-3V code and based on one-equation sub-grid turbulent kinetic energy model are employed for numerical computation of diesel sprays in a constant volume vessel and in a Caterpillar 3400 series diesel engine. Computational results are compared with those obtained by an RANS (RNG k–ε) model as well as with experimental data. The sensitivity of the LES results to mesh resolution is also discussed. The results show that LES generally provides flow and spray characteristics in better agreement with experimental data than RANS; and that small-scale random vortical structures of the in-cylinder turbulent spray field can be captured by LES. Furthermore, the penetrations of fuel droplets and vapors calculated by LES are larger than the RANS result, and the sub-grid turbulent kinetic energy and sub-grid turbulent viscosity provided by the LES model are evidently less than those calculated by the RANS model. Finally, it is found that the initial swirl significantly affects the spray penetration and the distribution of fuel vapor within the combustion chamber. Keywords spray

Large eddy simulation · Diesel engine · Fuel

The project was supported by the National Natural Science Foundation of China (50806008) and the National Basic Research Program of China (2007CB210002). L. Zhou · M.-Z. Xie ( ) · M. Jia School of Energy and Power Engineering, Dalian University of Technology, 116024 Dalian, China e-mail: [email protected] J.-R. Shi Department of Power Engineering, Shenyang Institute of Engineering, 110136 Shenyang, China

List of symbols CD Fi,d G K md m ˙d p P Pr rd Red S ct S ij ui Vrel Ws Ym δi j εsgs ρ δi j τi j ∆ µ υt

Drag coefficient Drag force from gas to droplet LES spatial filter function Subgrid kinetic energy per unit mass Droplet mass Droplet evaporation rate Pressure Subgrid kinetic energy production Prandtl number Droplet radius Reynolds number Turbulent Schmidt number Rate of strain tensor Velocity Drop-gas relative velocity Spray source Mass fraction of species m Kronecker delta Dissipation rate for subgrid kinetic energy Gas density Shear stress Viscous shear stress Grid size Dynamic viscosity Eddy viscosity

1 Introduction With the rapid development of the global economy, the problems of energy crisis and environment pollution become more serious. As the main source of petroleum consumption and emissions to the atmosphere, automotive engines have received increased attention. Low-temperature diesel combustion strategies have shown promise in reducing nitrogen oxide, but these combustion modes have also been shown to produce higher unburned hydrocarbon and carbon monoxide emissions [1]. As a result, the combustion efficiency may

520

decrease for low-temperature combustion compared to traditional diesel combustion. Computational fluid dynamics (CFD) has become a reliable and effective tool for research on the engine combustion process. In CFD, direct numerical simulation (DNS) is the most precise method. Although DNS can describe the organized vortex structure in turbulent flows, it requires huge memory and calculation time for diesel spray application and hence, is not a practical method at the present [2]. Therefore, for most practical purposes, turbulent modeling is adopted. There are two types of turbulent modeling approaches: (a) Reynolds averaged Navier-Stokes (RANS), based on ensemble and time averaged governing equations, (b) Large eddy simulations (LES). In RANS, due to averaging, detailed information about the instantaneous unsteady characteristics of the turbulent flow are lost. Thus RANS simulation is not an ideal method of turbulent simulation, especially for highly transient flows, such as encountered in the engine cylinder. Consequently, LES is becoming popular in the field of fluid mechanics as a practical method for the analysis of turbulent phenomena [3]. Recently, some studies on the numerical analysis of fuel sprays by LES have been reported. Hori et al. [4–6] modeled non-evaporative and evaporative diesel sprays in a constant volume vessel using the LES approach. The results show that the solution of LES simulation of evaporative spray depends on the grid size, and, in comparison with RANS simulation, are in closer agreement with experimental results. Menon et al. [7–9] implemented the LES model into the KIVA-3V code to build a modified version, which is called KIVALES [10] and was used to model the fuel–air mixing process in a direct injection spark ignition engine with wide cycle-to-cycle variations. As a result, KIVALES shows an ability to capture the highly unsteady, anisotropic fuel–air mixing process and dynamically evolving fine-scale vortical and scalar structures. Rutland et al. [11, 12] performed a great deal of research on the combustion modeling of internal combustion engines with the LES method. Furthermore, Reveillon and Vervisch [13] showed that for evaporating sprays, droplet vaporization could add additional unclosed terms in the sources of fluctuations of mixture fraction. Moin et al. [14, 15] simulated multiphase, multi-scale turbulent reacting flows in realistic gas-turbine combustors using the LES model. They selected a series of validation cases to study the liquid evaporation, gas-phase combustion and droplet breakup. Apte et al. [16] have also performed simulation on an evaporating isopropyl alcohol spray in a coaxial combustor. Jones [17] performed a numerical investigation on the spreading and evaporation of liquid droplets in turbulent kerosene and acetone laden jets. Bini and Jones [18] presented a jet laden with liquid droplets of acetone with the large eddy model. Also, several works have been conducted for the case of liquid spray in diesel engines [19–22]. Accurate prediction of fuel injection and spray characteristics in an engine environment is an important step to-

L. Zhou, et al.

wards an accurate prediction of combustion and pollutants in a modern engine. The objective of this paper is to present a preliminary study to evaluate the feasibility and capability of the LES approach as applied to a real engine configuration. The LES approach based on the one-equation sub-grid turbulent kinetic energy model are employed for numerical computation of diesel sprays in a constant volume vessel and in a Caterpillar 3400 series diesel engine. The modeling accuracy of LES is compared with a traditional RANS model. The sensitivity of the LES results to mesh resolution is also discussed. 2 Numerical models 2.1 Filtering operation In LES, the flow field is decomposed into a resolved scale component, which is solved directly, and a sub-grid scale component, which is simulated by various models. To achieve this, a low-pass filtering operation is employed. There are many kinds of filtering kernels used for LES, among them the BOX filter is the most appropriate choice for the finite volume scheme, which KIVA-3V employs, because the filtered quantity at the filter center represents the spatial average of the filtered function within the filter domain. In KIVA, the finite-volume discretization itself implicitly provides the filtering operation Z 1 f (xi , t) = f (xi0 , t)dxi0 , (1) ∆V ∆V where ∆V is the volume of a computational cell. The filter function G implied here is then   xi ∈ ∆V,   1/∆V, G= (2)   0, otherwise. 2.2 LES equations Applying the filtering operator to the conservation equations of mass momentum, energy and species equations results in the following LES equations for gas–droplet two-phase flows [23] Continuity Equation ∂ρ ∂ρu˜j ¯ s + = ρ˙ , ∂x j ∂t Momentum Equation ∂ρ¯ u˜i ∂ sgs + ρ˜ ¯ ui u˜ j − τ¯ i j − τi j = F¯ is , ∂t ∂x j Energy Equation sgs ¯ u j e˜ ∂˜u j ∂h j ∂ρ˜ ¯ e ∂ρ˜ + p¯ + + ∂t ∂x j ∂x j ∂x j ∂q¯ j ∂˜ui + −σ ¯ ij − Θsgs = Q¯˙ s , ∂x j ∂x j

(3)

(4)

(5)

Large eddy simulation of fuel injection and mixing process in a diesel engine

Species Equation ∂ρ¯ Y˜ m ∂ ˜ ∂Y˜ m sgs + ρ¯ Ym u˜ j − ρ¯ D¯ m + Φ j,m = ρ¯˙ sm , (6) ∂t ∂x j ∂x j where the filtered viscous stress tensor and the heat flux vector are approximated respectively as 2 τ¯ i j = − pδ ¯ i j + 2µS˜ i j − µS˜ kk δi j , 3 N X q¯ j = −k∂T˜ /∂x j − ρ¯ h˜ m Dm (∂Y˜ m /∂x j ).

(7) (8)

M=1

In this paper, combustion is not considered, so chemistry terms are ignored. In the equations above, the following terms require closure sgs τi j = ρ¯ ug ˜ j u˜ j , (9) i ui − u sgs gi − E eu˜ i + (pui − p˜ui ), (10) hi = ρ¯ Eu sgs ˜ ˜j . Φ j,m = ρ¯ Y] (11) m u j − Ym u These terms represent, respectively, the subgrid stress tensor, subgrid heat flux, and sub-grid species mass flux. Another term Θsgs in Eq. (5) is the sub-grid viscous work. 2.3 Sub-grid model of LES sgs

The sub-grid stress tensor τi j is modeled using an eddy viscosity concept as 2 1 sgs ¯ sgs δi j , (12) τi j = −2ρυ ¯ t Sei j − Sekk δi j + ρK 3 3 where Sei j is the rate of strain tensor for the resolved scale defined by ∂˜u ∂˜u j i Sei j = 0.5 . (13) + ∂x j ∂xi The sub-grid eddy √3 viscosity is modeled as νt = Cv K ∆, where ∆¯ = ∆V is based on local grid size. The sub-grid kinetic energy K sgs is defined as K sgs = 0.5 ug iu j − u˜ i u˜ j and is obtained by solving the following equation proposed by Menon et al. [23] sgs 1/2

∂ρK ¯ sgs ∂ρ¯ u˜ K sgs + ∂t ∂x j = Psgs − Dsgs +

∂ νt ∂K sgs ˙ s ρ¯ +W , ∂x j Prt ∂x j

(14)

∂˜ui , ∂x j sgs and the sub-grid energy dissipation rate term D = Cε ρ(K ¯ sgs )3/2 /∆. Θsgs is modeled by Dsgs , Θsgs = Dsgs . In the above equations, the constant values of 0.916 and 0.067 are used for Cε and Cv , respectively [24]. The sub-grid species mass flux is modeled by a gradiνt ∂Y˜ m sgs ent diffusion model, Φ j,m = −ρ¯ , sub-grid heat flux S ct ∂xi sgs

where the production term Psgs is closed by −τi j

521 sgs

is modeled by heat gradient diffusion: h j = −ρ¯

νt C p ∂T˜ . Prt ∂x j

2.4 The droplet Lagrangian equation In KIVA-3V, a very efficient and accurate method for solving the spray dynamics is based on the ideas of the Monte Carlo method and of the discrete particle method [25]. With these methods, the total droplet population is represented by a number of parcels, each of which represents several physical droplets sharing the same size, position, velocity, and thermal properties. Thereafter, the Lagrangian operation keeps track of the motion of these parcels that is a set of ordinary differential equations which solve the mass, momentum, and energy exchange between the spray and the gas. The droplet Lagrangian equations are expressed as follows [25] dxd,i = vd,i , dt dvd,i Fi,d = , dt md dT d 1 = (Q + m ˙ d lv ), dt mdCp,l

(15) (16) (17)

drd dmd = 4πρl rd2 , (18) dt dt where xd,i and vd,i are the components of the droplet position and velocity, respectively, T d is the droplet temperature, md = 4/3πρl rd3 is the droplet mass, Q is the conductive heat flux through the droplet surface, Cp,l is the heat capacity of the liquid phase, and lv is the latent heat of vaporization. The acceleration due to the drag on a liquid drop is modeled as Fi,d 3 ρ Vrel = (˜ui − vd,i )CD , md 8 ρl rd

(19)

where Vrel is the magnitude of the relative velocity between the liquid droplet and the gas, ρl and rd are the liquid droplet density and radius respectively, and CD is the drop drag coefficient, modeled as follows  24    (1 + 1/6Re2/3 Red < 1 000,   d ), Re d CD =  (20)     0.424, Red > 1 000, where Red is the droplet Reynolds number. In this paper, the relative velocity between the droplet and the gas is replaced by the velocity interpolation model proposed by Nordin [26] which is employed in order to reduce the grid dependency of spray simulation. More details about this model can be found in Ref. [26]. 2.5 Drop breakup model In this study, the mechanism of the droplet breakup model is based on the modified TAB model [6].

522

L. Zhou, et al.

The model constants in the original TAB model proposed by O’Rourke and Amsden [27] are optimized to meet the diesel spray conditions. The TAB model is based on an analogy between a forced oscillating spring-mass system and an oscillating drop. According to the analogy, the equation of the drop surface oscillation is y¨ =

8σ 5µd 2 ρVrel + y− y˙ , 3 ρl rd2 ρl rd2 ρl rd3

the experimental picture it is clear that the liquid border also shrinks towards the jet center as the liquid is vaporized. In the images of the LES model, the liquid has vaporized almost completely at about 1.233 ms after the start of injection, while in the RANS model, after the injection ends all liquid drops concentrate on the head of the jet, and at about 1.233 ms there are still some liquid drops in the jet.

(21)

where subscript “d” indicates droplet, σ is surface tension. Droplet breakup occurs, if and only if y > 1. The Sauter mean radius after breakup is determined by the following equation 8K 6K − 5 ρl r3 2 −1 r32 = rd · 1 + + y˙ , (22) 20 120 σ where K is the ratio of the total energy in distortion and oscillation to the energy in the fundamental mode. The value of K is 0.89. And the droplet size after breakup is calculated based on the Sauter radius with a χ6 distribution. 3 Results and discussion In this study, to examine the feasibility of the LES approaches for application to diesel sprays in engines and to assess their performances, numerical simulations of an evaporative diesel spray in a constant volume vessel were conducted, and in the second part, LES simulations of the diesel spray in a real engine were carried out. It should be noted that a grid dependence study has been done in a previous study [28], so it is not repeated here . 3.1 Evaporative diesel sprays in a constant volume vessel In an early injection diesel spray, the short injection would limit the liquid penetration while permitting the vapor-phase to continue penetrating into the chamber. In this part, the short injection experiment of Lyle et al. [1] was used to validate numerical spray models for the evaporative spray simulation. In the experiment, 2# diesel oil was injected into the constant volume vessel. The ambient gas within the vessel was prepared inert, containing O2 0%, N2 89.7%, CO2 6.5% and H2 O 3.8%. The minimum grid size is approximately 0.25 mm and the number of computational cell is approximately 340 000. The detailed conditions are described in Table 1. Figure 1 shows images of mass fractions of the liquid and vapor phases at six different times after the injection start, which are predicted by the LES (left) and RANS models (middle), respectively. For comparison, the experimental images obtained by a high-speed CMOS camera are shown at the right [1]. In the images, the fuel drops are represented as black particles. It can be observed that the liquid phase moves downstream from the injector with time. From

Table 1 Computational conditions for evaporative spray simulation Injector hole diameter/mm

0.108

Injection duration/ms

0.35

Fuel

DF2

Injection pressure/MP

110

Fuel mass/mg

1.2

Fuel temperature/K

373

Ambient temperature/K

601

Ambient density/(kg·m−3 )

5.2

Ambient gas

N2 , CO2 , H2 O

Total parcels

7 000

SMR/mm

0.05

Max time step (dt)/s

1.0×10−6

Min time step (dt)/s

1.0×10−8

In this study, the spatial distribution of the vapor phase is of great importance. In Fig. 1, the vapor phase at 1.233 ms reaches a maximum penetration distance from the injector, which is about 80 mm in the LES model compared to 65 mm in the RANS model. The vapor phase structures predicted by the two models are significantly different. The LES results indicate complex three-dimensional structures with random turbulent eddies of various scales. The outer surface of the vapor phase shows wrinkled geometry and an unstable shape. This is because the LES model can capture the effect of the transient small-scale eddies. In contrast, the RANS model predicts a symmetric shape along the spray-axis without any significant three-dimensional structure. It is evident that the LES results are in much better agreement with the experiment than the RANS case. Figure 2 shows the evolution of vapor penetration computed by LES and RANS models. The vapor penetration by LES agrees very well with the measurement, while the RANS model under-predicts the experiment and LES results. This could be attributed to the more diffusive nature of RANS. Turbulent kinetic energy is one of most important parameters affecting the characteristics of the fuel spray. In this study, we used the RNG k–ε turbulence model in the RANS approach and the one-equation (k-equation) model for the sub-grid turbulence modeling in the LES. Figure 3 presents the temporal variation of the mean turbulent kinetic energy averaged over the entire volume of the vessel computed with the two models.


523

Fig. 1 Effect of the two turbulent models about short injection durations on liquid and vapor phases (left: LES model, middle: RANS model, right: experiment). a t = 206 µs; b t = 411 µs; c t = 617 µs; d t = 822 µs; e t = 925 µs; f t = 1 233 µs

In the fuel spray field, the droplets moving with high velocities induce additional turbulent kinetic energy. Therefore, the mean turbulent kinetic energy increases following the injection time through the injection duration. At the end of the injection it reaches the maximum and thereafter de-

creases. In the RANS simulation, the changes in the turbulent kinetic energy with injection times are much more obvious than the LES simulation. At the same time, it is extremely remarkable from Fig. 3 that the turbulent kinetic energy obtained by RANS is much higher than that by the LES

524

L. Zhou, et al.

simulation. The former is about several times larger than the latter. The reason for the difference is that the definitions of the turbulent kinetic energy are fundamentally different in LES and RANS. In RANS the turbulent kinetic energy, which is connected to the turbulent model, contains contributions from turbulent eddies of all scales, while in LES, it represents only those from the subgrid scale field (K sgs ), which is dependent on the filter scale. Figure 4 shows the ratios of the mean turbulent viscosity to molecular viscosity (µ/υ) and of the mean sub-grid turbulent viscosity to molecular viscosity (νt /υ). It is evident that the sub-grid viscosity is almost negligible in comparison to the turbulent viscosity predicted by the RANS model due to the different definitions.

Fig. 4 Temporal change in mean turbulent viscosity ratio with LES and RANS models

Fig. 2 Temporal change in vapor penetration with LES and RANS models

Fig. 3 Temporal change in mean turbulent energy with LES and RANS models

The difference in the predicted three-dimensional spray structure between the RANS and the LES models can be seen clearly from the fuel contour value. A three-dimensional fuel mass fraction isosurface for the case of short injection at 1.233 ms after the start of injection is presented in Fig. 5, in which an isosurface of fuel mass fraction equal to 0.015 6 is illustrated. It can be seen that the visible structure in the RANS model is very smooth and symmetric along the sprayaxis. On the contrary, the isosurface of the mass fraction produced by LES represents a significantly unsteady and asymmetric structure. Moreover, the instantaneous results reveal that the wrinkly isosurface of the mass fraction by LES is distributed more extensively in the space than the RANS simulation, which suppresses the effects of flow turbulence on the fuel dispersion. Overall, by using the LES model one can capture much more detailed structure and predict relatively realistic distribution and evolution of fuel droplets and vapors.

Fig. 5 Isosurface of fuel vapor for mass fraction 0.015 6


3.2 Diesel engine simulation In this section, a single-cylinder version of the Caterpillar 3400 series engine [29] is used for LES simulation. Some relevant details of the engine are listed in Table 2. In this engine, there are six nozzle holes distributed evenly over the azimuthal 360◦ space. In order to reduce the computational cost, only one sixth of the combustion chamber was simulated. The standard grid used to model this engine comprises of 192 486 cells at the intake valve closure. And a fine grid (266 586 cells) was also used as a reference case. At this stage of our study, only cold flow and fuel spray were simulated, combustion is not considered. The computational period covers the interval from the close of the intake valve (CIV) to 40 CA after TDC.

525

side-wall. With the RANS model, however, the penetration of the fuel spray is rather shorter and the droplets can not reach the side-wall. Second, a more complex and transient turbulent structure around the fuel spray and at the bottom as well as on the side-wall of the combustion chamber is obtained by the LES simulation. This is because a large amount of small-scale turbulent eddies captured by LES make the flow field more inhomogeneous and irregular, while these eddies directly reflect the transient character and randomness of the turbulent flow in the chamber. Besides, by comparing Fig.7b and 7c it can be observed that with the fine mesh the flow field becomes more complex with finer vortical structures.

Fig. 6 Computational grid at TDC Table 2 Caterpillar 3400 baseline engine conditions Engine base type

Caterpillar 3400

Number of cylinders

1

Bore/cm×Stroke/cm

13.76×16.51

Connecting rod length/cm

26.162

Displacement volume/l

2.44

Compression ratio

15.1 : 1

Number of nozzle

6 (equally spaced)

Diameter of nozzle orifice/mm

0.259

Spray angle/CA

27.5◦

Intake valve closure

−147◦

Injection pressure/bar

900

Engine speed/rpm

1 600 −1

Fuel mass/(g·cycle )

0.162 2

Start of injection/CA

−9◦

Duration of injection/CA

21◦

Figure 7 shows distributions of velocity predicted by the LES and the RANS models. The graphs clearly indicate the significant influence of the fuel spray on the in-cylinder velocity field. Furthermore, there are distinguished differences in the distributions of velocity between the LES model and RANS model. First, the LES result shows a high-speed gas motion area at the bottom and near the side-wall of the combustion chamber due to the spray tip colliding with the

Fig. 7 The distribution of velocity with LES and RANS models at 9CA after start of injection. a RANS model; b LES model (standard); c LES model (fine)

In the LES model, the turbulence viscosity and kinetic energy are computed based on the sub-scales (filter width) of computational fields; consequently, the grid size has an important influence on sub-grid viscosity and kinetic energy. To study the effect of gridsize, Figs. 8 and 9 show the two parameters computed with the standard and fine grids, respectively. It is noticeable that the sub-grid turbulent viscosity and kinetic energy mainly concentrate in the spray field, where higher velocities caused by the fuel spray exist (Fig. 7). Compared to the results with the standard grid, values of sub-grid turbulent viscosity and kinetic energy become smaller by refining the grid size. In fact, the conceptual division of the flow into the resolved and unresolved parts leads to a situation where theoretically LES with a very fine grid

526

would resolve almost all the flow field structures and the contribution of sub-grid energy would vanish. So, the sub-grid

L. Zhou, et al.

turbulent viscosity and kinetic energy in some sub-grid fields is very close to vanishing with a fine grid.

Fig. 8 Contours of turbulent kinetic energy at 9CA after start of injection. a LES-standard grid; b LES-fine grid

Fig. 9 Contours of turbulence viscosity at 9CA after start of injection. a LES-standard grid; b LES-fine grid

It should be noted that in LES the subgrid turbulent kinetic energy and turbulent viscosity, i.e. the physical diffusion (the contribution from subgrid eddies) introduced by the SGS model decreases as the grid is refined. Consequently, the accuracy of prediction increases with decreasing grid size. Hence in LES, unlike in RANS, there are no such things as grid-independence and optimum volume mesh. To assess the turbulence resolution of the LES model, a fraction M has been introduced by Pope [30], which is defined as the ratio of the SGS turbulence energy versus the overall turbulence energy. Thus, when M = 1, an RANS simulation is performed and when M = 0, a DNS simulation of performed. It is generally accepted that the reasonable requirement for a grid size of LES is to provide a turbulence resolution tolerance M < 0.2, which corresponds to a grid size of about 1 mm for a common engine cylinder. In this study, both the standard and fine grids fulfill this requirement for most of the mesh cells. In order to demonstrate the three-dimensional characteristics of turbulent flow structures in the engine predicted by the LES model, Figs. 10 and 11 show comparisons of thedistribution of the fuel mass fraction in the vertical and horizontal sections of the combustion chamber at TDC (9CA after start of injection) and ATDC 20CA predicted by LES and RANS, respectively. It is noted that LES predicts a more diffused field of mass fraction contours than RANS does. From the distribution of the vapor mass fraction shown in Figs. 10 and 11, it can be seen that the three-dimensional structures and asymmetric spray shape were captured by the LES model due to the diffusion, compared to the relatively

symmetric spray shape obtained by the RANS approach. The main focus of this section is to provide insight into the effect of swirling on the in-cylinder flow field and fuel distribution of a diesel engine using the LES model. Figure 12 shows computed fuel vapor and droplet distributions at TDC for four different initial swirl ratios of 0.5, 1.5, 2.0 and 2.5. It can be seen that the initial swirl affects the liquid phase penetration and mass distribution significantly. With increasing initial swirl ratio the liquid penetration in the piston bowl is reduced due to its peripheral motion forced by the gas swirling. Fuel vapor mass distributions in a cress section of the combustion chamber for swirl is 1.5 and 2.5 are presented in Fig. 13, which demonstrates clearly the peripheral motion of the fuel spray. It can be seen that the fuel vapor contours move clockwise more intensively as the swirl number increases. Figure 14 presents velocity vector distributions in the combustion chamber at TDC for swirl ratios of 0.5 and 2.5. These plots show clearly the interaction between swirl and fuel spray as well as the prominent effect of the swirl on the spray penetration and fuel distribution. This explains the differences in the fuel mass distributions between smaller and larger swirls shown in Figs. 12 and 13. Figure 15 depicts the evolution of the total vapor mass in the combustion chamber dependent on the initial swirl intensity. It can be observed that the vapor mass increases with rising swirl number, this is because enhanced gas motion promotes the evaporation of the liquid fuel. Especially, with the initial swirl number 2.5, the vapor mass is very close to the overall fuel mass injected, indicating that most fuel has been evaporated at such a high swirl intensity.


527

Fig. 10 Mass fraction distribution on cross sections at TDC injection. a Vertical section of the combustion with LES model; b Vertical section of the combustion with RAN model; c Horizontal section of the combustion with LES model; d Horizontal section of the combustion with RAN model

Fig. 11 The mass fraction distribution on cross sections at ATDC 20. a Vertical section of the combustion with LES model; b Vertical section of the combustion with RAN model; c Horizontal section of the combustion with LES model; d Horizontal section of the combustion with RAN model

528

L. Zhou, et al.

Fig. 12 Influence of initial swirl on spray at 9CA after start of injection. a Swirl=0.5; b Swirl=1.5; c Swirl=2.0; d Swirl=2.5

Fig. 13 Influence of initial swirl on the distribution of fuel mass. a Swirl=1.5; b Swirl=2.5

Fig. 14 Influence of initial swirl on the velocity vector. a and c Swirl=1.5; b and d Swirl=2.5


529

fuel injection, mixture preparation and combustion of internal combustion engines. References

Fig. 15 Influence of initial swirl on the vapor mass

4 Conclusion The present study was focused on the difference of the predicted spray characteristics between LES and RANS. An LES model with one turbulent equation based on the subgrid kinetic energy was implemented in the KIVA-3V code. Non-reacting simulations of evaporating spray in a constant volume vessel and Caterpillar 3400 series diesel engine were studied using modified TAB breakup model. Computational results were compared with those obtained by an RNG k–ε model as well as with experimental data. The results demonstrate that the LES approach is superior to the RANS model for predicting a highly transient flow field with random vortical flow structures. LES generally provides flow and spray characteristics in better agreement with experimental data than RANS; and the complex small-scale vortical structures of the in-cylinder turbulent spray field can be captured by LES. Furthermore, the penetrations of fuel droplets and vapors calculated by LES are larger than the RANS result, while the sub-grid turbulent kinetic energy and sub-grid turbulent viscosity provided by the LES model are evidently less than those calculated by the RANS model. To examine the sensitivity of the LES results to mesh resolution, comparison was conducted for two different meshes, which confirmed that LES results could benefit from mesh refinement. In a finer mesh, more of the turbulent energy is resolved, leading to a reduced sub-grid turbulent kinetic energy and, at the same time, more accurate predictions. Further, more detailed flow structures in very fine scales could be duplicated especially with the fine mesh. Finally, it is found that the initial swirl significantly affects the spray penetration and the distribution of fuel vapor within the combustion chamber. In conclusion, the LES approach should be used as a more advanced tool for predicting detailed characteristics of engine turbulent flow and fuel–air mixing processes. It can provide theoretical guidance for improving and optimizing

1 Lyle, M.P., Sanghoon, K.: Transient liquid penetration of earlyinjection diesel sprays. SAE Paper, 09010839 (2009) 2 Kimura, S., Kosaka, H.: A numerical simulation of turbulent mixing in transient spray by LES. SAE Paper, 2004-01-2014 (2004) 3 Bharadwaj, N., Rutland, C., Chang, S.: Large eddy simulation modelling of spray-induced turbulence effects. International Journal of Engine Research 10(2), 97–119 (2009) 4 Hori, T., Kuge, T., Senda, J., et al.: Large eddy simulation of diesel spray combustion with eddy-dissipation model and CIP method by use of KIVALES. SAE Paper, 2007-01-0247 (2007) 5 Hori, T., Kuge, T., Senda, J., et al.: Effect of convective schemes on LES of fuel spray by use of KIVALES. SAE Paper, 2008-01-0930 (2008) 6 Hori, T., Senda, J., Kuge, T., et al.: Large eddy simulation of non-evaporative and evaporative diesel spray in constant volume vessel by use of KIVALES. SAE Paper, 2006-01-3334 (2006) 7 Menon, S., Stone, C., Patel, N.: Multi-scale modeling for les of engineering designs of large-scale combustors. AIAA Paper, AIAA-2004-157 (2004) 8 Menon, S., Yeung, P., Kim, W.: Effect of subgrid models on the computed interscale energy transfer in isotropic turbulence. Computers & Fluids 25(2),165–180 (1996) 9 Sone, K., Menon, S.: Effect of subgrid modeling on the incylinder unsteady mixing process in a direct injection engine. Journal of Engineering for Gas Turbines and PowerTransactions of the ASME 125(2), 435–443 (2003) 10 Sone, K., Patel, N.V., Menon, S.: KIVALES: Large-eddy simulations of internal combustion engines. Part 1: KIVALES user’s manual. Technical Report CCL-00-008, Part 2: KIVALES user’s manual, Technical Report CCL-00-009, Georigia Institute of Technology, http://www.ccl.gatech.edu/home html (2000) 11 Hu, B., Rutland, C.J.: Flamelet modeling with LES for diesel engine simulations. SAE Paper, 2006-01-0058 (2006) 12 Jhavar, R., Rutland, C.J.: Using large eddy simulations to study mixng effects in early injection diesel engine combustion. SAE Paper, 2006-01-0871 (2006) 13 Reveillon, J., Vervisch, L.: Spray vaporization in nonpremixed turbulent combustion modeling: A single droplet model. Combustion and Flame 121(1-2), 75–90 (2000) 14 Moin, P., Apte, S.V.: Large-eddy simulation of realistic gas turbine combustors. AIAA Journal 44(4), 698–708 (2006) 15 Apte, S.V., Gorokhovski, M., Moin, P.: LES of atomizing spray with stochastic modeling of secondary breakup. International Journal of Multiphase Flow 29(9), 1503–1522 (2003) 16 Apte, S.V., Mahesh, K., Moin, P.: Large-eddy simulation of evaporating spray in a coaxial combustor. Proceedings of the Combustion Institute 32, 2247–2256 (2009) 17 Jones, W.P., Lyra, S., Marquis, A.J.: Large eddy simulation of evaporating kerosene and acetone sprays. International Journal of Heat and Mass Transfer 53(11-12), 2491–2505 (2010) 18 Bini, M., Jones, W.P.: Large eddy simulation of an evaporating acetone spray. International Journal of Heat and Fluid Flow

530 30(3), 471–480 (2009) 19 Jagus, K., Jiang, X., Dober, G., et al.: Assessment of large-eddy simulation feasibility in modelling the unsteady diesel fuel injection and mixing in a high-speed direct-injection engine. In: Proceedings of the Institution of Mechanical Engineers Part D-Journal of Automobile Engineering 223(D8),1033– 1048 (2009) 20 Jia, M., Zhou, L., Peng, Z.: The influence of breakup models on modeling diesel spray with large eddy simulation. In: The 13rd Annual Conference on Liquid Atomization and Spray SystemsAsia. Wuxi, China (2009) 21 Goryntsev, D., Sadiki, A., Klein, M., et al.: Large eddy simulation based analysis of the effects of cycle-to-cycle variations on air-fuel mixing in realistic DISI IC-engines. Proceedings of the Combustion Institute 32, 2759–2766 (2009) 22 Vuorinen, V., Larmi, M.: Large-eddy simulation on the effect of droplet size distribution on mixing of passive scalar in a spray. SAE Paper, 2008-01-0933 (2008) 23 Sankaran, V., Genin, F., Menon, S.: A sub-grid mixing model for large eddy simulation of supersonic combustion. AIAA Paper, 040801 (2004)

L. Zhou, et al. 24 Chakravarthy, V., Menon, S.: Modeling of turbulent premixed flames in the flamelet regime. Combustion Science and Technology 162, 1–50 (2000) 25 Amsden, A.A.: KIVA-II: A computer program for chemically reactive flows with sprays. Los Alamos National Laboratory, LA-11560-MS (1989) 26 Nordin, N.: The KIVA Jumpstation. http://www.tfd.chalmers. se/∼nordin/KJS/ 27 O’Rourke, P.J.: Statistical properties and numerical implementation of a model for droplet dispersion in a turbulent gas. Journal Computre Physics 83(2), 345–360 (1989) 28 Zhou, L., Xie, M.Z., Ming, J.: Application of large eddy simulation to a diesel spray. Transactions of CSICE 27(3), 202–206 (2009) 29 Montgomery, D., Reitz, R.: Six mode cycle evaluation of the effect of EGR and multiple injections on particulae and NO emissions from a D.I. Diesel Engine. SAE Paper, 960316 (1996) 30 Pope, S.B.: Ten questions concerning the large-eddy simulation of turbulent flows. New Journal of Physics 6(35), 1–24 (2004)