An Extended Multi-Zone Combustion Model for PCI Simulation J ...

21st International Multidimensional Engine Modeling User’s Group Meeting, Detroit, MI, April 2011

An Extended Multi-Zone Combustion Model for PCI Simulation J. Kodavasal*, S. Keum, D. N. Assanis and A. Babajimopoulos Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 Abstract In recent years, fully coupled CFD-multi-zone chemistry combustion models have grown popular in modeling HCCI combustion. In this work, an improved CFD-multi-zone chemistry model is suggested for PCI combustion simulation. A new zoning scheme is proposed based on incorporating the internal energy of formation into an earlier conventional HCCI multi-zone approach, which considers a two-dimensional reaction space defined by equivalence ratio and temperature. It is shown that the added dimension improves zoning by creating more representative zones, and thus reducing errors compared to the conventional zoning approach, when applied to PCI combustion simulation. Introduction Increasingly stringent emission regulations and the pressure on engine manufacturers and automakers to deliver higher fuel economy have prompted research into the area of strategies that simultaneously reduce incylinder emissions, as well as reduce fuel consumption [1]. Homogeneous Charge Compression Ignition (HCCI) [2-4] and Premixed Compression Ignition (PCI) [5-7] are two novel combustion modes that aim to reduce fuel consumption and address soot and NOx emissions at the same time. CFD codes coupled with chemical kinetics have been shown to be useful in modeling HCCI and PCI combustion [8,9]. Various multi-zone approaches [10-14] have been used to solve chemical kinetics by grouping chemically and thermodynamically similar CFD cells into zones, and solving chemistry in these zones rather than in every individual cell, to save computational time. One of these approaches is the fully coupled CFDmulti-zone chemistry combustion model developed by Babajimopoulos et al. [13]. This combustion model will be referred to as the original MZ approach in this document. When the original MZ approach was applied to PCI combustion simulation in this work, the results from the multi-zone approach did not correspond well with the results from KIVA-3V [15] coupled with CHEMKIN-II [16] in every computational cell (referred to here as the detailed approach). The objective of this work is to improve the existing original MZ formulation, and extend it to diesel PCI simulation. This is done by introducing an additional parameter, the internal energy of formation, uf, to the zoning approach used by the original MZ, which creates zones for chemical kinetics based on the equivalence ratio (φ) and temperature (T) of computational cells. The new approach is referred to as the Extended Multi-Zone or Extended MZ [17] approach in this document. *

Corresponding author

Zone creation methodology in the original MZ model and its limitations The zone creation approach in the original MZ involves grouping cells having a similar progress equivalence ratio (φ) and a similar temperature (T). The progress equivalence ratio is defined as follows [13]:

ϕ=

2C

# −CO2

+

H −#H 2O

− z ' C −#CO2

(1)

2 O−#CO2 − H 2O − z ' C −#CO2

Here z’ represents the ratio of the number of oxygen atoms to the number of carbon atoms in the fuel. This equivalence ratio is based on the number of C, H and O atoms where the C, H and O atoms in complete combustion products (CO2 and H2O) are not considered in the calculation. After chemistry calculations in a zone, species composition information is mapped back onto the constituent cells using a procedure that aims to preserve thermal and compositional gradients in the cylinder. Details of both the mapping and the remapping approach may be found in [13]. When the original MZ was directly applied to diesel PCI simulation in this work, the errors compared to the detailed approach (chemical kinetics in every cell) were found to be large. The progress equivalence ratio, φ, is a good indicator of the combustion progress when the mixture is lean; however, under locally rich and stoichiometric conditions (characteristic of PCI combustion), φ may not be a suitable indicator of combustion progress by itself. The numerator of equation (1) no longer approaches zero with the progress of combustion under rich conditions. On the contrary, it reaches a finite value, while the denominator also approaches some finite non-zero value, but at a faster rate. This is due to the fact that oxygen is the limiting species in rich combustion. Moreover, in a stoichiometric mixture, both the

21st International Multidimensional Engine Modeling User’s Group Meeting, Detroit, MI, April 2011

numerator and the denominator of equation (1) go to zero at the same rate, since neither fuel nor oxygen is the limiting species. Consequently, the value of φ remains unity regardless of combustion progress. To illustrate the behavior of φ as a combustion progress variable, constant volume combustion of nheptane was modeled using CHEMKIN-II [16] for mixtures with different equivalence ratios. The initial temperature and pressure were set to 1000 K and 20 atm. respectively. The 44 species, 112 reaction, chemical kinetic mechanism for n-heptane developed by Liu et al. [16] was used in this adiabatic constant volume combustion simulation. Figure 1 shows the variation of φ with the progress of combustion under four different initial conditions; rich (φ0=1.5), lean (φ0=0.75, 0.50) and stoichiometric (φ0=1.0).

Introduction of internal energy as a new progress variable Let us consider combustion in a closed adiabatic constant volume reactor. With the progress of combustion, irrespective of initial conditions, the specific internal energy of formation (uf) of the mixture decreases as species like CO2 and H2O are produced, which have a relatively low internal energy of formation. In fact, the increase in temperature occurring from the progress of combustion is exactly compensated for by the decrease in the internal energy of formation of the mixture, according to the first law of thermodynamics. Consider combustion in the case with initial progress equivalence ratio φ0=0.50 described in the previous section. Plotted in Figure 2 is the variation of temperature (T), specific internal energy of formation (uf) and progress equivalence ratio (φ) with the progress of combustion. The values of T, φ and uf have been normalized and shifted suitably to vary from 0 to 1; 0 representing the initial value of the quantity at the start of the simulation, and 1 representing the final value of the quantity at the end of the simulation.

Figure 1. Irregular behavior of φ with combustion progress under different initial conditions of φ0; Pin = 20 atm., Tin = 1000K, constant volume adiabatic reactor. It may be seen that in the lean cases, φ reduces with the progress of combustion, while in the rich case it increases with the progress of combustion. More importantly, under stoichiometric conditions, φ does not change with the progress of combustion, thus diminishing its utility as a combustion progress variable. Also, comparing the variation of φ with the progress of combustion for the two cases starting off with initial values of φ0=0.75 and φ0=0.50, it can be seen that the values of φ for these two cases overlap during combustion. This indicates that two computational cells with completely different initial conditions and reaction histories could potentially be grouped in the same computational zone for chemistry at a given time-step in the simulation. From these observations, it can be concluded that φ may not be a good candidate by itself to represent species concentration and combustion progress in PCI simulations where the local equivalence ratio in the computational domain may vary from lean to rich.

Figure 2. Comparison of the variation of T, φ and uf with the progress of combustion in a constant volume, adiabatic reactor with Pin = 20 atm., Tin = 1000K and φ0=0.5. It can be seen that the uf and the T curves are almost coincident with each other. However, it should be noted that φ shows a small lag compared to the temperature (T) and the specific internal energy of formation (uf) near ignition, which occurs around 1.5 milliseconds into the simulation. Moreover, φ shows a more rapid change than the other two variables after ignition. As φ does not change until CO2 and H2O are produced, the production of intermediate species during the initial stages leading to ignition, is not captured by φ. The variable uf, on the other hand, is affected purely by the chemical composition of a computational cell. Also, unlike φ which varies in an irregular manner with the

21st International Multidimensional Engine Modeling User’s Group Meeting, Detroit, MI, April 2011

progress of combustion under rich, lean and stoichiometric conditions (Figure 1), uf only decreases with the progress of combustion irrespective of the initial composition of a cell. Based on these characteristics of uf, it is clear that it displays a more or less one to one relationship with the progress of combustion, and is an excellent combustion progress variable that contains species information implicitly. The premise of this work is that it is possible to introduce uf as an additional progress variable in the reaction space, since it is not affected by physical processes like heat transfer and evaporative cooling, and is solely affected by the chemical composition of the computational cell under consideration. To study the evolution of the reaction space, CFD (KIVA-3V [15]) coupled with chemistry (CHEMKINII [16]) in every cell (detailed approach) was run for a typical low load diesel PCI case, with a global equivalence ratio of 0.58, 49.8% residuals by mass and fuel injection at -7.0 crank angle degrees ATDC (injection duration was 3.4 crank angle degrees). Details of the engine, grid and simulation setup may be found in the Model Performance Evaluation section. Figure 3 shows the reaction space, visualized in T, φ and uf, at different crank angle degrees. The top row of the figure represents the post-injection stage (-3.0 degrees ATDC), the middle row represents the pre-ignition stage (0 degrees ATDC), and the bottom row represents the post-ignition stage (2.5 degrees ATDC).

Figure 3. Visualization of the reaction space in T, φ and uf at the post-injection, pre-ignition and post-ignition stages for a low load late PCI case with injection at -7.0 degrees ATDC and global equivalence ratio of 0.58. Reaction space during the post-injection stage (-3.0 degrees ATDC) Referring to the top row of Figure 3, it can be seen that right after injection, the temperature (T) and progress equivalence ratio (φ) are negatively correlated. This is explained based on the fact that right after injection, the fuel-rich regions, where the spray has vapo-

rized the most, have higher values of φ given by equation (1), and also lower temperatures due to evaporative cooling. It is also seen that φ and uf are almost perfectly correlated at this stage, since the spread in the value of uf in the cylinder is solely caused by different amounts of fuel being present in different cells. At this stage, uf is not a new dimension in the reaction space, as it is linearly dependent of the φ dimension. Reaction space during the pre-ignition stage (0 degrees ATDC) Referring to the middle row of Figure 3, it is interesting to note that the strong correlation between T and φ, and also between T and uf no longer exists. This is because at this stage, the temperature is primarily influenced by heat transfer and mixing which are both physical effects, while φ and uf are not influenced by heat transfer, but are affected to a certain extent by mixing. However, the most critical observation made is that φ and uf start going out of correlation at this stage. This occurrence forms the main basis of this work. The fact that T and uf are not correlated at this stage, along with the fact that φ and uf go out of correlation, indicates that uf presents a new dimension in the reaction space which is independent of T and φ. It is seen that for the same value of φ there is a small, but significant spread in uf. The reason for this is that uf changes with the occurrence of pre-ignition reactions in a cell, and the production of intermediate species with different values of uf. However, φ does not change with the occurrence of pre-ignition reactions, based on how it is determined from equation (1), and changes only when products of complete combustion (CO2 and H2O) are produced. Thus during the preignition stage uf presents itself, temporarily, as a new dimension in the reaction space, which enables us to separate cells with pre-ignition reactions occurring from those where these reactions have not yet commenced. This subtle difference is not picked up by the T- φ zoning used by the original MZ. Reaction space during the post-ignition stage (2.5 degrees ATDC) Right after ignition (2.5 degrees ATDC), it is observed that T and uf become quite correlated (Figure 3, bottom row), since both are primarily affected by the combustion process from this point onward. Also, φ is not correlated with either T or uf at this stage due to the irregular variation of φ under different initial conditions. Extended Multi-Zone Formulation Based on the above analysis, the original MZ approach of Babajimopoulos et al. was modified to include a uf consideration in the zoning scheme. The zoning approach used in the original MZ was also simplified such that the chemistry zones are created in a single step from the cells in the cylinder.

21st International Multidimensional Engine Modeling User’s Group Meeting, Detroit, MI, April 2011

At every computational time-step, before chemical kinetic calculations are performed, the physical space is divided into zones, based on information from the CFD solver. First the cells in the physical space are sorted based on their temperature. Cells are then added into a new chemistry zone starting from the coldest “nonzoned” cell as long as the following conditions are satisfied after adding the cell to the zone: • The spread in the temperature (T) of the zone is less than ∆T. • The spread in the progress equivalence ratio (φ) of the zone is less than ∆φ. • The mass of the zone does not exceed 1% of the total mass in the cylinder. • The spread in uf of the zone on a logarithmic scale does not exceed a certain fraction of the total spread in uf on a logarithmic scale in the whole cylinder. After performing chemistry calculations in the zones, composition information is mapped back onto the constituent cells using the remapping methodology proposed by Babajimopoulos et al. in [13] Figure 4 compares the number of zones created when only T and φ are used as zoning variables(∆T = 100 K, ∆φ = 0.02) to the number of zones created when T, φ and uf are used as zoning variables (∆T = 100 K, ∆φ = 0.02 and ∆log|uf|zone < 0.05 ∆log|uf|cyl), for the PCI simulation case studied in the previous section. It is seen that more zones are created by the T-φ-uf zoning approach in the pre-ignition stage, where uf presents itself as a new dimension in the reaction space. At this stage, uf which is not dependent on T or φ, brings in additional information into the reaction space. It is also observed that the number of zones created by both zoning approaches during the injection phase is the same, as φ and uf are correlated at this stage.

Figure 4. Comparison of the number of chemistry zones formed during the course of the simulation between T-φ zoning and T-φ-uf zoning. In the current implementation of the Extended MZ (used in the model performance evaluation section), ∆T is set to 100K, ∆φ is set to 0.05, and the criterion

∆log|uf|zone < 0.05 ∆log|uf|cyl has been used to introduce uf into the zoning scheme. Model Performance Evaluation In this section the performance of the Extended MZ with respect to the fully integrated CFD solution with detailed chemical kinetics in every cell for two PCI cases has been compared, with the view of demonstrating improved results compared to the original MZ approach which was developed for lean HCCI. The computational CFD mesh (Figure 5) used in these simulations is based on a high speed DICI engine with CR 16:1 (details in Table 1). It is a 60º bowl in piston sector mesh with 8800 cells at TDC. The CFD solver used in this work is KIVA-3V [15] and the chemical kinetics solver is CHEMKIN-II [16]. All simulations were run at 1500 RPM and natural aspiration. The fuel used for simulation was n-heptane and the chemical kinetic mechanism used was developed by Liu et al. [18]. The Zeldovich NOx mechanism [19] was used to predict NO emissions.

Figure 5. 60° sector mesh (8800 cells at TDC) of engine used in model performance evaluation studies. Table 1. Engine Specifications Parameter

Value

No. of Cylinders

4

Displacement (L)

1.7

Bore (m)

0.079

Stroke (m)

0.086

Connecting Rod Length (m)

0.1335

Wrist Pin Offset (m)

0.0006

Compression Ratio

16:1

Piston Geometry

Bowl-in-Piston

No. of Valves/Cylinder

4

IVO (°BTDC)

366

IVC (°BTDC)

136

EVO (°ATDC)

122

EVC (°ATDC)

366

Fuel System

Direct-Injection Common Rail

Injector Location

Centrally Mounted

Injector Nozzle No. of Holes

6

Injector Nozzle Spray Angle (deg.)

150

21st International Multidimensional Engine Modeling User’s Group Meeting, Detroit, MI, April 2011

Figure 6. Model performance evaluation Case 1: Low load late PCI with global equivalence ratio of 0.58, 49.8% residuals by mass and injection of 7.05 mg. of fuel at -5.0° ATDC.

Figure 7. Model performance evaluation Case 2: Low load early PCI with global equivalence ratio of 0.63, 49.7% residuals by mass and injection of 6.90 mg. of fuel at -25.0° ATDC. Figures 6 and 7 show the pressure traces, heat release rates and NO emissions predicted by the original MZ, the Extended MZ and the detailed approach. A comparison of the number of zones created by the original MZ and Extended MZ approaches has also been

shown. The computational time required (from IVC to 80° ATDC) for the detailed approach runs ranged between 30-40 hours on nodes with 2.8 GHz processor speed and 2 GB RAM. The number of computational zones formed for chemistry is comparable for both mul-

21st International Multidimensional Engine Modeling User’s Group Meeting, Detroit, MI, April 2011

ti-zone approaches for both the test cases, and the computational time was around 2.5 to 3.5 hours for both the original MZ and Extended MZ runs, indicating a reduction in computational time on the order of 90% compared to the detailed approach. It may be seen from Figures 6 and 7, that compared to the original MZ, the predictions of cylinder pressure, heat release rate and NO emissions from the Extended MZ correspond better with the detailed approach. It should also be noted that the number of computational zones used by both MZ approaches is comparable, which indicates that better predictions from the new approach are not due to increased resolution and thus increased computational effort. Conclusions The original Multi-Zone combustion model of Babajimopoulos et al. [13] was improved to extend its application to PCI simulation (Extended MZ [17]). It was shown that the progress equivalence ratio (φ) is not a good indicator of combustion progress in PCI cases, where locally rich and stoichiometric regions could occur within the cylinder. It was also demonstrated that the addition of uf as a combustion progress variable is beneficial in the critical pre-ignition stage since it is able to detect the occurrence of pre-ignition reactions, unlike φ. This results in the creation of zones that are more representative for chemistry, and smaller errors. References 1. Zhao, F., Asmus, T. W., Assanis, D. N., Dec, J. E., Eng, J. A. and Najt, P. M., Homogeneous Charge Compression Ignition (HCCI) Engines: Key Research and Development Issues. SAE, Warrendale, PA, 2003. 2. Onishi, S., Jo, S. H., Shoda, K., Jo, P. D. and Kato, S. Active Thermo-Atmosphere Combustion (ATAC) – A New Combustion Process for Internal Combustion Engines, SAE Paper 790501, 1979. 3. Najt, P. M. and Foster, D. E. Compression-Ignited Homogeneous Charge Combustion, SAE Paper 830264, 1983. 4. Thring, R. H. Homogeneous-Charge Compression Ignition (HCCI) Engines, SAE Paper 892068, 1989. 5. Takeda, Y., Keiichi, N. and Keiichi, N. Emission Characteristic of Premixed Lean Diesel Combustion and Extremely Early Staged Fuel Injection, SAE Paper 961193, 1996. 6. Nakagome, K., Shimazaki, N., Niimura, K. and Kobayashi, S. Combustion and Emission Characteristics of Premixed Lean Diesel Combustion Engine, SAE Paper 970898, 1997. 7. Iwabuchi, Y., Kawai, K., Shoji, T. and Takeda, Y. Trial of New Concept Diesel Combustion System – Premixed Compression-Ignited Combustion, SAE Paper 1999-01-1085, 1999.

8. Agarwal, A. and Assanis, D. N. Multi-Dimensional Modeling of Natural Gas Ignition under Compression Ignition Conditions Using Detailed Chemistry, SAE Paper 980136, 1998. 9. Opat, R., Ra, Y., Gonzalez D., M.A., Krieger, R., Reitz, R. D., Foster, D.E., Durrett, R.P. and Siewart, R. M. Investigation of Mixing and Temperature Effects on HC/CO Emissions for Highly Dilute Low Temperature Combustion in a Light Duty Diesel Engine, SAE Paper 2007-01-1093, 2007. 10. Aceves, S. M., Flowers, D. L., Westbrook, C. K., Smith, J. R., Pitz, W., Dibble, R., Christensen, M. and Johansson, B. A Multi-Zone Model for Prediction of HCCI Combustion and Emissions. SAE Paper 2000-01-0327, 2000. 11. Aceves, S. M., Flowers, D. L., Martinez-Frias, J., Smith, J. R., Westbrook, C. K., Pitz, W. J., Dibble, R., Wright, J. F., Akinyemi, W. C. and Hessel, R. P. A Sequential Fluid-Mechanic ChemicalKinetic Model of Propane HCCI Combustion. SAE Paper 2001-01-1027, 2001. 12. Flowers, D., Aceves, S., Martinez-Frias, J., Hessel, R. and Dibble, R. Effect of Mixing on Hydrocarbon and Carbon Monoxide Emissions Prediction for Isooctane HCCI Engine Combustion Using a Multi-zone Detailed Kinetics Solver. SAE Paper 2003-01-1821, 2003. 13. Babajimopoulos, A., Assanis, D. N., Flowers, D. L., Aceves, S. M. and Hessel, R. P. A fully coupled computational fluid dynamics and multi-zone model with detailed chemical kinetics for the simulation of premixed charge compression ignition engines, Int. J. Engine res., 6 (5), pp. 497-512, 2005. 14. Shi, Y., Hessel, R. P. and Reitz, R. D. An adaptive multi-grid chemistry (AMC) model for efficient simulation of HCCI and DI engine combustion, Combustion Theory and Modelling 13 (1), pp. 83104, 2009. 15. Amsden, A. A. KIVA-3V: A Block-Structured KIVA Program for Engines with Vertical or Canted Valves. Los Alamos National Laboratory Report LA-13313-MS, 1997. 16. Kee, R. J., Rupley, F. M. and Miller, J. A. CHEMKIN-II: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics. Sandia Report SAND89-8009, 1989. 17. Kodavasal, J., Keum, S., Assanis, D. N. and Babajimopoulos, A. An Extended Multi-Zone Combustion Model for PCI Simulation. Submitted to Combustion Theory and Modelling, 2011. 18. Liu, S., Hewson, J. C., Chen, J. H. and Pitsch, H. Effects of strain rate on high-pressure nonpremixed n-heptane autoignition in counterflow, Combustion and Flame 137, pp. 320-339, 2004. 19. Heywood, J. B. Internal Combustion Engine Fundamentals, McGraw-Hill, New York, 1988.