Numerical analysis of the effect of inhomogeneous pre-mixture on the pressure rise rate in an HCCI engine using multi-zone chemical kinetics

The HCCI (Homogeneous Charge Compression Ignition) engine is an internal combustion engine under development, which is capable of providing both high diesel-like efficiency and very low NOx and particulate emissions. However, several technical issues must be resolved before the HCCI engine is ready for widespread application. One issue is that its operating range is limited by an excessive pressure rise rate which is caused by the excessive heat release from its selfaccelerated combustion reaction and the resulting engine knock in high-load conditions. The purpose of this study was to evaluate the potential of thermal and fuel stratification for reducing the pressure rise rate in HCCI engines. The NOx and CO concentrations in the exhaust gas were also evaluated to confirm combustion completeness and NOx emissions. The computational work was conducted using a multi-zone code with detailed chemical kinetics, including the effects of thermal and fuel stratification on the onset of ignition and the rate of combustion. The engine was fueled with dimethyl ether (DME) which has a unique two-stage heat release, and methane which has a one-stage heat release.


INTRODUCTION
In HCCI engines, a premixed air/fuel mixture is inhaled to the combustion chamber and ignited by adiabatic compression. The HCCI engine, which uses bulk combustion, is a promising alternative for high efficiency and low emission engines (Yamashita et al., 2005). However, the power produced in an HCCI engine is limited by knocking caused by excessive heat release and a local area pressure rise under high load conditions (Sjoberg et al., 2005). Therefore, the main goal of our investigation was to avoid the knocking problem. Delaying the combustion angle and stratifying the temperature or fuel concentration for dispersion of the combustion timing is a well-known and effective method (Kwon and Lim, 2009;Kumano and Iida, 2004). In this study, the effect of a stratified temperature and fuel concentration in the pre-mixture on the pressure increase rate in the combustion chamber was investigated. A numerical analysis of the chemical reaction was conducted to study the emission properties.

COMPUTATIONAL METHODS
DME (dimethyl ether) and methane were used as fuels. The autoignition temperature of DME was 631K and methane was 810K. A numerical analysis was conducted for the purpose of investigating the effects of fuel and temperature stratification on the pressure rise rate and emissions using a multi-zone code with detailed chemical kinetics. DME has two stages of heat reaction called the HTR (High Temperature Reaction) and LTR (Low Temperature Reaction). The amount of the HTR is greater than that of the LTR. It is known that a greater DME concentration increases heat release during the LTR. Because of this, the existence of DME fuel stratification in the combustion chamber is expected to contribute to a reduction in the gas pressure rise rate because the heat release difference in the local area during the LTR causes stratification of the temperature before the HTR which extends the combustion duration. On the other hand, methane has only a one-stage heat release and its self-ignition temperature is high. The detailed specifications of HCCI engine shown in Table 1. Calculation was conducted between IVC (intake valve closed) to EVO (exhaust valve opened. Both CHEMKINII (Luz et al., 1989) and SENKIN (Luz et al., 1988), which were developed by Sandia National Laboratory, were adjusted and then used as calculation codes. Curran was used for the reaction in the DME model (Curran et al., 1998), GRI-Mech3.0 (GRI-Mech) was used for the reaction in the methane model, and Zeldovich was used for the NOx model. The calculation was conducted following assumption. Heat loss and residual gas were neglected. All chemical gases were considered to be ideal gasses, and the mass of the pre-mixture was assumed to be conserved. The *Corresponding author. e-mail: otlim@ulsan.ac.kr

O. T. LIM
multi-zone model created the stratification of temperature and fuel concentration in the combustion chamber by changing the gas temperature and equivalence ratio before the compression stroke of each zone. Each zone in the model had a constant gas temperature, and the homogenous chemical species was 0-demensional ( Figure 1). There was no chemical reaction or heat transfer between the zones, and the pressure was constant all over the combustion chamber. The definition of CA50, and the start and end timings of both the LTR and HTR are shown in Figure 2. The combustion reaction velocity ((dQ/dt)/Qin) was defined as the rate of heat production divided by the quantity of heat in one cycle (Figures 2 (a) and (b)). Figure  2 (c) shows the integral histories of heat production. The integral value of the heat production rate from LTRstart to HTRend was considered to be 100%, and then CA50 was defined as 50% of the heat production timing.

Effect of Thermal Stratification in the Pre-Mixture Gas on Reducing the Pressure Rise Rate
The calculated conditions for an equal equivalence ratio (Φ = 0.25), initial temperature T0 = 380K (Zone 1), and T1 = 420K (Zone 2) using DME/air methane/air are shown respectively in Figures 3 and 4. The volumetric rate was changed to equalize the heat quantity in each zone during one cycle. The gas pressure in the combustion chamber, the temperature and pressure in each zone when using DME fuel is shown in Figure 5. The magnified LTR and HTR are shown in Figure 6, in which the first graph is of the gas pressure in the combustion chamber. The second and third graphs represent the temperature and rate of heat release in each zone. The LTR-start temperature and HTR-start temperature were almost constant at 744 ± 3K and 1007 ± 5K. Before LTRstart, the gas temperature difference in the combustion chamber, which was nearly 40K before compression stroke, changed to 65.7K before LTR-start in Zone 2. Because the LTR-start temperature was almost constant, LTRstart was earlier by about 9.3 deg in Zone 2 than in Zone 1. The temperature difference between Zones 1 and 2 was constant after LTRstart, so HTRstart was earlier in Zone 2 than in Zone 1 by about 4.3 deg. Also, the     Compression ratio (ε) 8.0(DME) / 21.6(methane) gas pressure in the combustion chamber, the temperature, and the heat release rate in each zone when using methane is shown in Figure 7. The temperature of HTRstart was 1177 ± 3K. Zone 2 had a higher temperature than Zone 1, so HTRstart was earlier by about 4.5 deg before the compression stroke.

Effect of Fuel Stratification in the Pre-Mixture Gas on
Reducing the Pressure Rise Rate At the beginning of compression, the average gas temperature (T0 = 400K) was assumed. The calculation conditions are shown in Figures 8 and 9: Φ = 0.17 (Zone 1), Φ = 0.47 (Zone 2) using methane or DME. The gas pressure in the combustion chamber, the gas temperature in each zone are shown in Figure 10. A magnified graph is shown in Figure 11. The temperatures of LTRstart and Figure 5. Histories of in-cylinder gas pressure, in-cylinder gas temperature. Figure 6. Histories of in-cylinder gas pressure, in-cylinder gas temperature and heat release rate (DME, Thermal stratification, 2-zones).

O. T. LIM
HTRstart were 747 ± 3 K and 1009 ± 1. The temperature difference in the combustion chamber grew larger with piston rising before LTRstart due to the difference in specific heat caused by the different equivalence ratio. The temperature difference before the compression stroke changed from 0K to 17.3K before LTRstart in Zone 1. LTRstart was earlier in Zone 1 by about 2.3 deg. However, the large amount of heat released during the LTR in the higher equivalence ratio zone caused the trace of the gas temperature to reverse in Zone 2 at LTRend. Due to the reversal, HTRstart was earlier by about 2.3 deg in Zone 2 than in Zone 1. The gas pressure in the combustion Figure 10. Histories of in-cylinder gas pressure and incylinder gas temperature (DME, Fuel stratification, 2zones). Figure 11. Histories of in-cylinder gas pressure, in-cylinder gas temperature and heat release rate (DME, Fuel stratification, 2-zones). Figure 12. Histories of in-cylinder gas pressure, in-cylinder gas temperature and heat release rate (Methane, Fuel stratification, 2-zones). Figure 13. 50% heat release timing and maximum incylinder gas pressure rise rate (DME, Thermal stratification, 5-zone). Figure 14. 50% heat release timing and maximum incylinder gas pressure rise rate (DME, Fuel stratification, 5zone).
chamber, the gas temperature, and the heat release rate in each zone with methane is shown in Figure 12. The HTRstart temperature was 1163 ± 11 K. Similar to DME, the methane gas temperature difference in the combustion chamber grew large with piston rising. However, with onestage of heat release, methane doesn't have an LTR, so it can be seen that HTRstart in Zone 2 was later than in Zone 1 by about 3.1 deg because of the lean concentration in Zone 1.

Multi-Zone Analysis of the Reduction of the Maximum Pressure Rising Rate Effect and the Emission Features
Based on results from the two-zone model, the reduction of the gas pressure rate, the heat release, and emissions were investigated in the combustion chamber at more than one temperature and fuel distribution using the numerical analysis of a five-zone model to expand and vary the stratification. Using DME and methane, the relation between CA50% and the maximum pressure rise rate is shown in Figures13-16 under conditions of an average equivalence ratio (ϕ = 0, 25) and when changing the average temperature before compression from T 0 = 380K to T 0 = 420K. In terms of temperature stratification, an average of 5K was given for the pre-mixed gas temperature difference between each zone before compression, and the calculation was conducted under conditions of ∆T = 20K and ∆T = 40K between the highest and lowest zones. To investigate concentration stratification, the average equivalence ratio (ϕ = 0.25) was set up and the computation calculation was conducted with ∆ϕ = 0.10 and ∆ϕ = 0.30 between the highest and lowest zones. Then, these results were compared with those from conditions of equal temperature and concentration of pre-mixture gas, and it was found that, without any relation to the amount of temperature difference, the maximum pressure rise rate in case of temperature stratification was less than 50% that of homogeneous pre-mixed gas. As the reduction rate increased, so did the temperature difference. The reduction rate of decrease changed significantly in a range of concentration, although a energy density difference in each zone caused a maximum pressure rise rate less than that of the homogenous pre-mixed gas. The concentration ranges causing a reduction of the maximum pressure rise rate were different in DME and methane because the temperature difference caused by piston compression before the LTR disappeared, and the gas temperature trace reversed at LTRend due to the LTR in the DME. Figures 17~20 show the NOx and CO emission concentrations, the combustion Figure 15. 50% heat release timing and maximum in-cylinder gas pressure rise rate (Methane, Thermal stratification, 5zone). Figure 16. 50% heat release timing and maximum incylinder gas pressure rise rate (Methane, Fuel stratification, 5-zone).
Figure 17. CO and NOx mole fraction in exhaust gas, combustion efficiency and maximum in-cylinder gas temperature (DME, Thermal stratification, 5-zones). Figure 18. CO and NOx mole fraction in exhaust gas, combustion efficiency and maximum in-cylinder gas temperature (DME, Fuel stratification, 5-zones).
efficiency, and the maximum temperature in the combustion chamber at a gas average temperature before compression (T0) of 400K. The effect of temperature and concentration stratification on emission characteristics was studied by comparing pre-mixed gas under conditions of stratified temperature and concentration with that at equal temperature and concentration when T0 = 400K and at an equivalence ratio of 0.25. The concentration of CO increased below a maximum temperature of 1500 K, and NOx concentration increased above 2100K. The emission concentrations of NOx and CO were nearly the same when comparing the equal pre-mixed gas to DME and methane under the existing temperature stratification because the maximum temperature was between 1500K and 2100K in each zone. Under conditions of concentration stratification, the NOx and CO concentrations in the emission gas were larger than those from the equal pre-mixed gas because the maximum temperature was above 2100K with a high equivalence ratio.

CONCLUSION
The effect of temperature and concentration stratification on the pre-mixture reducing pressure rise rate was investigated. A numerical computation of the chemical reaction was conducted by assigning a temperature or concentration stratification to the pre-mixture. We chose DME and methane because of their different heat release characteristics, used a detailed reaction scheme, and conducted a multi-zone numerical computation. We determined the following: (1) Under conditions of stratified temperature, the temperature difference of the combustion chamber was increased by piston compression. The LTR and HTR occurred earlier in zones with higher gas temperatures.
(2) Under conditions of a stratified fuel pre-mixture, a temperature difference occurred in the combustion chamber. The LTR occurred earlier in zones with lower concentrations, and the HTR occurred earlier in zones with higher concentrations. (3) Under conditions of stratified temperature and concentration, the maximum pressure rise rate was significantly decreased compared to conditions with no stratification. In particular, restricting NOx and CO emissions under conditions of stratified temperature which is the same as equal conditions. (4) Concentration stratification control is needed to operate the engine between 1500K and 2100K under conditions of stratified concentration in the pre-mixture. (5) Investigation to determine the most efficient temperature and concentration stratification is needed to reduce the maximum pressure rise rate and emissions. Figure 19. CO and NOx mole fraction in exhaust gas, combustion efficiency and maximum in-cylinder gas temperature (Methane, Thermal stratification, 5-zones).
Figure 20. CO and NOx mole fraction in exhaust gas, combustion efficiency and maximum in-cylinder gas temperature (Methane, Fuel stratification, 5-zones).