**Numerical Analysis of the Effect of Inhomogeneous Pre-Mixture on Pressure Rise Rate in HCCI Engine by Using Multi-Zone Chemical Kinetics**

Ock Taeck Lim1 and Norimasa Iida2 *1University of Ulsan, 2Keio University, 1Republic of Korea 2Japan* 

### **1. Introduction**

26 Will-be-set-by-IN-TECH

140 Chemical Kinetics

Phys-Chem (2004). *Physical and Chemical Processes in Gas Dynamics: Physical and Chemical*

Present, R. (1960). Chapman-Enskog method in chemical kinetics, *J. Chem. Phys.*

Prigogine, I. & Xhrouet, E. (1949). On the perturbation of Maxwell distribution function by

Rydalevskaya, M. (1977). Formal kinetic description of gas mixtures with dissociation and

Seror, S., Druguet, M., Schall, E. & Zeitoun, D. (1997). A new vibration-exchange reaction

Shizgal, B. & Karplus, M. (1970). Nonequilibrium contributions to the rate of reaction. I. Perturbation of the velocity distribution function, *J. Chem. Phys.* 52: 4262–4278. Stupochenko, Y., Losev, S. & Osipov, A. (1967). *Relaxation in Shock Waves*, Springer-Verlag,

Treanor, C., Rich, I. & Rehm, R. (1968). Vibrational relaxation of anharmonic oscillators with

Polanyi, J. (1972). Some concepts in reaction dynamics, *Acc. Chem. Res.* 5: 161–168.

coupling model for hypersonic air flows, *AIAA Paper* 97-2556.

exchange dominated collisions, *J. Chem. Phys.* 48: 1798.

chemical reaction in gases, *Physica* 15: 913–932.

Press, Leningrad. (in Russian).

Berlin, Heidelberg, New York.

*Aeronautics*.

48: 4875–4877.

*Kinetics and Thermodynamics. Volume II*, Vol. I97 of *Progress in Astronautics and*

recombination, *Aerodinamika Razrezhennykh Gazov*, Vol. IX, Leningrad University

In HCCI, a premixed air/fuel mixture is inhaled to the combustion chamber and ignited by adiabatic compression. The HCCI engine, which is using the bulk combustion, is promising concept of the high efficient and low emission engine. However, power produced in HCCI engine is limited by knocking cause of excessive heat release and pressure rise at local area in condition of high load. Therefore, the main investigation of the HCCI is avoiding knocking problem to be able to operate at a high load. Delaying the combustion angle and stratifying temperature or concentration of fuel resulting in dispersion of combustion timing is the well-known effective method. In this study, effect of the pressure increase rate in combustion chamber by stratified temperature and fuel concentration of pre mixture according to fuel characteristic was investigated. Numerical analysis in chemical reaction was conducted for investigating an emission property.

#### **2. Experimental method**

In this paper, DME(Di-Methyle Ether) and Methane were used as a fuel. The Numerical analysis was conducted for the purpose of investigating that fuel or temperature stratification effect on pressure rise rate and emission using the multi-zone code with detailed chemical kinetics. DME has two stages of heat reaction which is called HTR(High Temperature Reaction) and LTR(Low Temperature Reaction). In case of DME, proportion of LTR is more than those of HTR. It is known that the more DME concentration make heat release increase during the LTR. Due to those facts, existing of DME fuel stratification in combustion chamber is expected to contribute reduction of gas pressure rise rate because heat release difference in local area during LTR causes stratification of temperature before the HTR which makes combustion duration extend. On the other hand, Methane has only 1 stage heat release and self-ignition temperature is high. The detailed specifications of the test engine are presented in Table 1. The hermetic gas is used for calculation duration from

Numerical Analysis of the Effect of Inhomogeneous Pre-Mixture

**3. Analytical method** 

**rate** 

consider 100% and then CA50 is defined 50% of heat production timing.

Fig. 3. Calculation condition (DME, Thermal stratification, 2-zones)

Fig. 4. Calculation condition (Methane, Thermal stratification, 2-zones)

on Pressure Rise Rate in HCCI Engine by Using Multi-Zone Chemical Kinetics 143

chemical gases were considered to be ideal gas and mass of pre mixture is assumed to be conservative. Multi-zone model is able to make stratification of temperature and fuel concentration in combustion chamber by changing the gas temperature and equivalent ratio before each of zones are compressed. Shown in Fig. 1, each zone model that is equally gas temperature and homogenous chemical species is 0-demension. Between the each zone, there is not chemical species and heat transfer but pressure is constant. The definition of CA50, start and end timing of both LTR and HTR are shown in Fig. 2 Shown in Fig. 2(a)(b), the combustion reaction velocity((dQ/dt)/Qin) was defined as rate of heat production divided by quantity of heat into the 1 cycle. Fig. 2(c) shows the integral hysteresis of heat production. The integral value of heat production rate from the LTR start to HTR end is

**3.1 The effect of thermal stratification in pre mixture gas for reducing pressure rise** 

The calculation condition of equal equivalent ratio (Φ=0.25) and initial temperature T0 = 380K(Zone1), T1 = 420K(Zone2) using the DME/air and Methane/air is shown in Fig. 3, 4. The volumetric rate is changed to equalize the heat quantity into the each zone during 1 cycle. Gas pressure in combustion chamber, temperature and heat release rate in each of the zone by using the DME with fuel is shown in Fig. 5. Magnified LTR and HTR shown in


Table 1. Engine specifications

Fig. 1. Concept of multi-zone model

Fig. 2. Definitions of LTR start, LTR end, HTR start, HTR end and 50% heat release timing

the time that intake valve closed to the time that exhaust valve opened. As a calculation code, both CHEMKIN-II(5) and SENKIN(6) which is developed by Sandia National Laboratory is adjusted and then used. Curran for reaction of DME model, GRI-Mech3.0 for reaction of Methane model and Zeldvich for NOx model are used. The calculation is conducted following consumption. Heat loss and residual gas was neglected. All the chemical gases were considered to be ideal gas and mass of pre mixture is assumed to be conservative. Multi-zone model is able to make stratification of temperature and fuel concentration in combustion chamber by changing the gas temperature and equivalent ratio before each of zones are compressed. Shown in Fig. 1, each zone model that is equally gas temperature and homogenous chemical species is 0-demension. Between the each zone, there is not chemical species and heat transfer but pressure is constant. The definition of CA50, start and end timing of both LTR and HTR are shown in Fig. 2 Shown in Fig. 2(a)(b), the combustion reaction velocity((dQ/dt)/Qin) was defined as rate of heat production divided by quantity of heat into the 1 cycle. Fig. 2(c) shows the integral hysteresis of heat production. The integral value of heat production rate from the LTR start to HTR end is consider 100% and then CA50 is defined 50% of heat production timing.

## **3. Analytical method**

142 Chemical Kinetics

Bore X Stroke 112mm X 115mm Displacement 1132cc Length of Conrod 205mm Crank Radius 57.5mm Intake Valve Close Timing ATDC-132 Exhaust Valve Open Timing ATDC-132

Compresstion Ratio 8.0(DME)/21.6(Methane)

**1 2**

**2-zones model**

**close up**

**HTRstart** **1 2 3 … N**

**n-zones model**

> **DME/Air =0.25** *T0***=400K** *P0***=0.1MPa** *Ne***=750rpm =8.0**

> > **0 0.05 0.1 0.15**

**50%**

 **HTRend 50%**

**Combustion Reaction Speed**

*(dQ/dt)/Qin*

**[1/ms]**

Fig. 2. Definitions of LTR start, LTR end, HTR start, HTR end and 50% heat release timing

**Crank Angle** 

**LTRstartLTRend**

**-30 -25 -20 -15 -10 -5 0 5 10**

**[deg ATDC]**

**CA50**

the time that intake valve closed to the time that exhaust valve opened. As a calculation code, both CHEMKIN-II(5) and SENKIN(6) which is developed by Sandia National Laboratory is adjusted and then used. Curran for reaction of DME model, GRI-Mech3.0 for reaction of Methane model and Zeldvich for NOx model are used. The calculation is conducted following consumption. Heat loss and residual gas was neglected. All the

Table 1. Engine specifications

Fig. 1. Concept of multi-zone model

**Combustion Reaction Speed**

**Total Heat Release**

*(dQ/d)* **[J]**

*(dQ/dt)/Qin* **[1/ms]**

**single zone model**

**a**

**b**

**c**

**0 0.5 1 1.5 2 2.5 3 3.5**

**1**

Process Only 1 Compression & Expansion

#### **3.1 The effect of thermal stratification in pre mixture gas for reducing pressure rise rate**

The calculation condition of equal equivalent ratio (Φ=0.25) and initial temperature T0 = 380K(Zone1), T1 = 420K(Zone2) using the DME/air and Methane/air is shown in Fig. 3, 4. The volumetric rate is changed to equalize the heat quantity into the each zone during 1 cycle. Gas pressure in combustion chamber, temperature and heat release rate in each of the zone by using the DME with fuel is shown in Fig. 5. Magnified LTR and HTR shown in

Fig. 3. Calculation condition (DME, Thermal stratification, 2-zones)

Fig. 4. Calculation condition (Methane, Thermal stratification, 2-zones)

Numerical Analysis of the Effect of Inhomogeneous Pre-Mixture

on Pressure Rise Rate in HCCI Engine by Using Multi-Zone Chemical Kinetics 145

Figure 6. First one is the graph of gas pressure in combustion chamber. Second and third one represent temperature and rat of heat release at each of the zone. LTR start temperature, HTR start temperature is almost constant as 744±3K, 1007±5K. Before LTR start, gas temperature difference in combustion chamber which is almost same as 40K according to piston rising is changed 65.7K before LTR start at zone 2. Because LTR start temperature is almost constant, LTR start is earlier about 9.3 deg at zone 2 than zone 1. Temperature difference between zone1 and zone2 is constant after LTR start so that HTR start is earlier about 4.3 deg than zone1. Also, using the fuel as a Methane, gas pressure in combustion chamber, temperature and heat release rate in each zone is shown in Fig. 7. The temperature of HTR start is 1177± 3K. Zone 2 with higher temperature than zone1, HTR start is earlier about 4.5deg than zone 1 before the compression stroke by using the Methane as a fuel.

Fig. 7. Histories of in-cylinder gas pressure, in-cylinder gas temperature and heat release

**-15 -10 -5 0 5 10**

**[ATDC deg]**

**zone1** *T0***=380K**

**1177**±**3K**

**Crank Angle** 

**zone2** *T0***=420K**

**<sup>1000</sup> <sup>600</sup>**

**=4.5deg**

**<sup>1800</sup> <sup>0</sup>**

**two-zones Thermal stratification**

**In-cylinder Gas Temperature**

**Methane/Air =0.25 =0** *T0***=400K** *T0***=40K** *P0***=0.1MPa** *Ne***=750rpm =8.0**

> *Tc* **[K]**

rate (Methane, Thermal stratification, 2-zones)

**Heat Release Rate** *dQ/d*

**[J/deg]**

> *T0* **=99.8K**

**In-cylinder Gas Pressure**

*Pc* **[MPa]**

Fig. 5. Histories of in-cylinder gas pressure, in-cylinder gas temperature

Fig. 6. Histories of in-cylinder gas pressure, in-cylinder gas temperature and heat release rate (DME, Thermal stratification, 2-zones)

**<sup>2500</sup> <sup>0</sup>**

**zone1** *T0***=380K**

Fig. 5. Histories of in-cylinder gas pressure, in-cylinder gas temperature

**Crank Angle** 

**two-zones Thermal stratification**

**zone2** *T0***=420K**

**Intake valve close** 

*IVC***=-132 deg**

**two-zones Thermal stratification**

**1**

*T0* **=40K**

**2**

*Pc* **[MPa]**

**In-cylinder Gas Pressure**

**In-cylinder Gas Pressure**

*Pc* **[MPa]**

**0**

*T0* **=65.7K**

> **=9.3deg**

**1**

**2**

**3**

**4**

**3**

**4**

**-150 -100 -50 0 50 100 150**

**[ATDC deg]**

**DME/Air =0.25 =0** *T0***=400K** *T0***=40K** *P0***=0.1MPa** *Ne***=750rpm =8.0**

**In-cylinder Gas Temperature**

*Tc* **[K]**

*Tc,max***=1790K** *Tc,max***=1658K**

**DME/Air =0.25 =0** *T0***=400K** *T0***=40K** *P0***=0.1MPa** *Ne***=750rpm =8.0**

**In-cylinder Gas Temperature**

*Tc* **[K]**

Fig. 6. Histories of in-cylinder gas pressure, in-cylinder gas temperature and heat release

**zone2** *T0***=420K**

**=4.3deg**

**-30 -25 -20 -15 -10 -5 0 5 10**

**[ATDC deg]**

**zone1** *T0***=380K**

**1007**±**5K 744**±**3K**

**Crank Angle** 

rate (DME, Thermal stratification, 2-zones)

**Heat Release Rate** *dQ/d*

**[J/deg]**

Figure 6. First one is the graph of gas pressure in combustion chamber. Second and third one represent temperature and rat of heat release at each of the zone. LTR start temperature, HTR start temperature is almost constant as 744±3K, 1007±5K. Before LTR start, gas temperature difference in combustion chamber which is almost same as 40K according to piston rising is changed 65.7K before LTR start at zone 2. Because LTR start temperature is almost constant, LTR start is earlier about 9.3 deg at zone 2 than zone 1. Temperature difference between zone1 and zone2 is constant after LTR start so that HTR start is earlier about 4.3 deg than zone1. Also, using the fuel as a Methane, gas pressure in combustion chamber, temperature and heat release rate in each zone is shown in Fig. 7. The temperature of HTR start is 1177± 3K. Zone 2 with higher temperature than zone1, HTR start is earlier about 4.5deg than zone 1 before the compression stroke by using the Methane as a fuel.

Fig. 7. Histories of in-cylinder gas pressure, in-cylinder gas temperature and heat release rate (Methane, Thermal stratification, 2-zones)

Numerical Analysis of the Effect of Inhomogeneous Pre-Mixture

*T0* **=0K**

**two-zones Thermal stratification**

**Intake valve close** 

*IVC***=-132 deg**

**1**

**Pressure** 

*Pc* **[MPa]**

**In-cylinder Gas**

**2**

**3**

**4**

stratification, 2-zones)

rate (DME, Fuel stratification, 2-zones)

**Heat Release Rate** *dQ/d*

 **[J/deg]**

**1**

*T0* **=17.3K**

> **=2.3deg**

*Pc* **[MPa]**

**2**

**In-cylinder Gas Pressure**

**3**

**4**

on Pressure Rise Rate in HCCI Engine by Using Multi-Zone Chemical Kinetics 147

**<sup>2500</sup> <sup>0</sup>**

**zone1 =0.17**

Fig. 10. Histories of in-cylinder gas pressure and in-cylinder gas temperature (DME, Fuel

**-150 -100 -50 0 50 100 150**

**[ATDC deg]**

**Crank Angle** 

**two-zones Fuel stratification**

**zone2 =0.47**

**DME/Air =0.25 =0.30** *T0***=400K** *T0***=0K** *P0***=0.1MPa** *Ne***=750rpm =8.0**

**1009**±**1K 747**±**3K** **In-cylinder Gas Temperature**

*Tc* **[K]**

**DME/Air =0.25 =0.30** *T0***=400K** *T0***=0K** *P0***=0.1MPa** *Ne***=750rpm =8.0**

*Tc,max***=2241K**

*Tc,max***=1447K**

**In-cylinder Gas**

**Temperature** 

*Tc* **[K]**

Fig. 11. Histories of in-cylinder gas pressure, in-cylinder gas temperature and heat release

**-30 -25 -20 -15 -10 -5 0 5 10**

**[ATDC deg]**

**zone1 =0.17**

**Crank Angle** 

**<sup>500</sup> <sup>400</sup>**

**zone2 =0.47**

**<sup>1800</sup> <sup>0</sup>**

**=2.3deg**

#### **3.2 The effect of fuel stratification in pre mixture gas for reducing pressure rise rate**

At the beginning of compression, the average gas temperature (T0 = 400K) is assumed. The calculation condition is shown in Fig. 8, 9 that is Φ = 0.17(zone1) Φ= 0.47(zone2) in each of the zone using the Methane or DME. Gas pressure in combustion chamber, gas temperature and rate of heat release in each of zone are shown in Fig. 10. Magnified graph was shown in Fig. 11. Temperature of LTR start and HTR start is 747±3 K, 1009±1. Temperature difference in combustion chamber is getting bigger according to piston rising before the LTR start due to difference of specific heat caused by equivalent ratio and temperature rising rate. Temperature difference before the compression stroke is changed from 0K to 17.3K before LTR start in zone1. LTR start is earlier at zone 2 about 2.3deg. However, Large amount of heat release during LTR in higher equivalent ration zone make trace of gas temperature be reversed in zone2 when LTR end. Due to gas temperature reversing, HTR start is earlier about 2.3 deg in zone 2 than zone1. Gas pressure in combustion chamber, gas temperature and heat release rate in each of the zone is shown in Fig. 12. HTR start temperature is 1163±11 K. Similar with DME, the Methane gas temperature difference in combustion chamber is getting big according to piston rising. However, Methane doesn't have LTR but 1 stage of heat release. So it can be expected HTR start in zone2 is later than zone 1 about 3.1 because of lean concentration of zone 1.

Fig. 8. Calculation condition (DME, Fuel stratification, 2-zones)

Fig. 9. Calculation condition (Methane, Fuel stratification, 2-zones)

**3.2 The effect of fuel stratification in pre mixture gas for reducing pressure rise rate**  At the beginning of compression, the average gas temperature (T0 = 400K) is assumed. The calculation condition is shown in Fig. 8, 9 that is Φ = 0.17(zone1) Φ= 0.47(zone2) in each of the zone using the Methane or DME. Gas pressure in combustion chamber, gas temperature and rate of heat release in each of zone are shown in Fig. 10. Magnified graph was shown in Fig. 11. Temperature of LTR start and HTR start is 747±3 K, 1009±1. Temperature difference in combustion chamber is getting bigger according to piston rising before the LTR start due to difference of specific heat caused by equivalent ratio and temperature rising rate. Temperature difference before the compression stroke is changed from 0K to 17.3K before LTR start in zone1. LTR start is earlier at zone 2 about 2.3deg. However, Large amount of heat release during LTR in higher equivalent ration zone make trace of gas temperature be reversed in zone2 when LTR end. Due to gas temperature reversing, HTR start is earlier about 2.3 deg in zone 2 than zone1. Gas pressure in combustion chamber, gas temperature and heat release rate in each of the zone is shown in Fig. 12. HTR start temperature is 1163±11 K. Similar with DME, the Methane gas temperature difference in combustion chamber is getting big according to piston rising. However, Methane doesn't have LTR but 1 stage of heat release. So it can be expected HTR start in zone2 is later than zone 1 about 3.1

because of lean concentration of zone 1.

Fig. 8. Calculation condition (DME, Fuel stratification, 2-zones)

Fig. 9. Calculation condition (Methane, Fuel stratification, 2-zones)

Fig. 10. Histories of in-cylinder gas pressure and in-cylinder gas temperature (DME, Fuel stratification, 2-zones)

Fig. 11. Histories of in-cylinder gas pressure, in-cylinder gas temperature and heat release rate (DME, Fuel stratification, 2-zones)

Numerical Analysis of the Effect of Inhomogeneous Pre-Mixture

Thermal stratification, 5-zone)

**Maximum In-cylinder Gas**

**Pressure Rise Rate**

**Maximum In-cylinder Gas**

**Pressure Rise Rate**

**d**

*Pc***/d***t*

**[MPa/ms]**

**d**

*Pc***/d***t*

**[MPa/ms]**

stratification, 5-zone)

on Pressure Rise Rate in HCCI Engine by Using Multi-Zone Chemical Kinetics 149

**Homogeneity** *T0***=0K**

Fig. 13. 50% heat release timing and maximum in-cylinder gas pressure rise rate (DME,

**50% heat release timing** 

**Thermal Stratification** *T0***=20K**

**Thermal Stratification** *T0***=40K**

**-25 -20 -15 -10 -5 0 510 15 20 25**

**[ATDC deg]**

**DME/Air =0.25 =0** *T0***=400K** *T0***=20, 40K** *P0***=0.1MPa** *Ne***=750rpm =8.0**

Fig. 14. 50% heat release timing and maximum in-cylinder gas pressure rise rate (DME, Fuel

**50% heat release timing** 

**Fuel Stratification =0.10**

**Homogeneity =0**

**-25 -20 -15 -10 -5 0 5 10 15 20 25**

**Fuel Stratification =0.30**

**[ATDC deg]**

**DME/Air =0.25** 

 **=0.10, 0.30** *T0***=400K** *T0***=0K** *P0***=0.1MPa** *Ne***=750rpm =8.0**

Fig. 12. Histories of in-cylinder gas pressure, in-cylinder gas temperature and heat release rate (Methane, Fuel stratification, 2-zones)

#### **4. Results and discussion**

#### **4.1 Analysis of reducing maximum pressure rising rate effect and emission feature by multi-zone**

Based on result of 2-zone model, reducing gas pressure rate, heat release and emission is investigated in combustion chamber when there is more temperature and fuel distribution by using the numerical analysis at 5 model-zone to expand and vary the stratification. Using the DME and Methane, the relation between CA50% and maximum pressure rise rate is shown in Fig..13-16 in condition of average equivalent ratio(φ=0,25) and changing the average temperature before the compression from T0=300K to T0=500K. In terms of temperature stratification, 5K average pre mixed gas temperature difference was given between each zone before compression and computation calculation was conducted in condition of T0=20K and T0=40K between highest and lowest zone. On the other hand, in terms of concentration stratification, average equivalent ratio(φ=0.25) is set up and computation calculation was conducted in condition of Δφ=0.10 and Δφ=0.30 between highest and lowest zone. Afterward, this result is compared with condition of equal temperature and concentration of pre-mixture gas. Comparing the result of temperature difference and concentration in pre-mixed gas, without any relation on amount of

**two-zones Fuel stratification**

> *T0* **=29.8K**

**<sup>1800</sup> <sup>0</sup>**

Fig. 12. Histories of in-cylinder gas pressure, in-cylinder gas temperature and heat release

**-15 -10 -5 0 5 10**

**[ATDC deg]**

**zone1 =0.17**

**zone2 =0.47**

**Crank Angle** 

**<sup>1000</sup> <sup>600</sup>**

**=3.1deg**

**1163**±**11K**

**In-cylinder Gas Temperature**

**Methane/Air =0.25 =0.30** *T0***=400K** *T0***=0K** *P0***=0.1MPa** *Ne***=750rpm =8.0**

> *Tc* **[K]**

**4.1 Analysis of reducing maximum pressure rising rate effect and emission feature by** 

Based on result of 2-zone model, reducing gas pressure rate, heat release and emission is investigated in combustion chamber when there is more temperature and fuel distribution by using the numerical analysis at 5 model-zone to expand and vary the stratification. Using the DME and Methane, the relation between CA50% and maximum pressure rise rate is shown in Fig..13-16 in condition of average equivalent ratio(φ=0,25) and changing the average temperature before the compression from T0=300K to T0=500K. In terms of temperature stratification, 5K average pre mixed gas temperature difference was given between each zone before compression and computation calculation was conducted in condition of T0=20K and T0=40K between highest and lowest zone. On the other hand, in terms of concentration stratification, average equivalent ratio(φ=0.25) is set up and computation calculation was conducted in condition of Δφ=0.10 and Δφ=0.30 between highest and lowest zone. Afterward, this result is compared with condition of equal temperature and concentration of pre-mixture gas. Comparing the result of temperature difference and concentration in pre-mixed gas, without any relation on amount of

rate (Methane, Fuel stratification, 2-zones)

**Heat Release Rate** *dQ/d*

**[J/deg]**

*Pc* **[MPa]**

**In-cylinder Gas Pressure**

**4. Results and discussion** 

**multi-zone** 

Fig. 13. 50% heat release timing and maximum in-cylinder gas pressure rise rate (DME, Thermal stratification, 5-zone)

Fig. 14. 50% heat release timing and maximum in-cylinder gas pressure rise rate (DME, Fuel stratification, 5-zone)

Numerical Analysis of the Effect of Inhomogeneous Pre-Mixture

condition of concentration stratification.

**1.0x10-14 1.0x10-12 1.0x10-10 1.0x10-8 1.0x10-6 1.0x10-4 1.0x10-2 1.0x10<sup>0</sup> 1.0x10<sup>2</sup> 1.0x10<sup>4</sup> 1.0x10<sup>6</sup> 0 20 40 60 80 100**

**CO Mole Fraction** 

**NOx** 

**Mole Fraction** 

*XCO* **[ppm]**

*XNO+NO2* **[ppm]**

**Combustion efficiency**

*c* **[%]**

**1500K 2100K**

on Pressure Rise Rate in HCCI Engine by Using Multi-Zone Chemical Kinetics 151

temperature difference, the maximum pressure rise rate is reduced below 50% beside homogeneous pre-mixed gas. The reduce rate is getting big, temperature difference is more. Its decrease rate is changed in a rage of concentration largely although the maximum pressure rise rate is reduced compared with homogenous pre-mixed gas when there is density difference. The rage of concentration which obtained reducing maximum pressure rise rate result is different comparing between DME and Methane. It can be expected that obtained result is different between DME and methane. The reason is that temperature difference by the piston compression before the LTR is disappeared and gas temperature trace is reversed at LTR end due to LTR existing in DME. In condition of 400K gas average temperature before the compression (T0), NOx, CO concentration in emission, combustion efficiency and maximum temperature in combustion chamber is shown in Fig. 17-20. The effect of temperature and concentration stratification on the emission characteristic was discussed by comparing pre-mixed gas with stratified temperature and concentration condition and equal temperature and concentration condition as T0=400K, equivalent ratio=0.25. Concentration of CO is increased bellow 1500K maximum temperature and NOx concentration is increased above 2100K. NOx and CO in emission gas concentration is almost same comparing the equal pre-mixed gas because maximum temperature is between 1500K and 2100K in each zone using DME and Methane existing temperature stratification in pre-mixed gas. NOx, CO concentration is getting big comparing with equal pre-mixed gas in emission gas because maximum temperature is above 2100K with high equivalent ratio in

Fig. 17. CO and NOx mole fraction in exhaust gas, combustion efficiency and maximum in-

**4 410K**

**5 420K**

**Maximum In-cylinder Gas Temperature**

**mass average of 5-zones**

**single zone**

**3 400K**

> **DME/Air =0.25 =0** *T0***=400K** *T0***=40K** *P0***=0.1MPa** *Ne***=750rpm =8.0**

*c* **NOx CO**

**Maximum In-cylinder**

**Gas Temperature** *Tc,max*

 **[K]**

cylinder gas temperature (DME, Thermal stratification, 5-zones)

**2 390K**

**1** *T0* **= 380K**

Fig. 15. 50% heat release timing and maximum in-cylinder gas pressure rise rate (Methane, Thermal stratification, 5-zone)

Fig. 16. 50% heat release timing and maximum in-cylinder gas pressure rise rate (Methane, Fuel stratification, 5-zone)

Fig. 15. 50% heat release timing and maximum in-cylinder gas pressure rise rate (Methane,

**50% heat release timing** 

**Thermal Stratification** *T0***=20K**

**Fuel Stratification =0.10**

**-25 -20 -15 -10 -5 0 5 10 15 20 25**

**Thermal Stratification** *T0***=40K**

**[ATDC deg]**

 **=0.25** 

 **=0.10, 0.30** *T0***=400K** *T0***=0K** *P0***=0.1MPa** *Ne***=750rpm =21.6**

**70 Methane/Air**

**Homogeneity** *T0***=0K**

 **=0.25 =0** *T0***=400K** *T0***=20, 40K** *P0***=0.1MPa** *Ne***=750rpm =21.6**

Fig. 16. 50% heat release timing and maximum in-cylinder gas pressure rise rate (Methane,

**50% heat release timing** 

**-25 -20 -15 -10 -5 0 510 15 20 25**

**Fuel Stratification =0.30**

**70 Methane/Air**

**Homogeneity =0**

**[ATDC deg]**

Thermal stratification, 5-zone)

**Maximum In-cylinder Gas**

**Pressure Rise Rate**

**d**

*Pc***/d***t*

**[MPa/ms]**

**Maximum In-cylinder Gas**

**Pressure Rise Rate**

**d**

*Pc***/d***t*

**[MPa/ms]**

Fuel stratification, 5-zone)

temperature difference, the maximum pressure rise rate is reduced below 50% beside homogeneous pre-mixed gas. The reduce rate is getting big, temperature difference is more. Its decrease rate is changed in a rage of concentration largely although the maximum pressure rise rate is reduced compared with homogenous pre-mixed gas when there is density difference. The rage of concentration which obtained reducing maximum pressure rise rate result is different comparing between DME and Methane. It can be expected that obtained result is different between DME and methane. The reason is that temperature difference by the piston compression before the LTR is disappeared and gas temperature trace is reversed at LTR end due to LTR existing in DME. In condition of 400K gas average temperature before the compression (T0), NOx, CO concentration in emission, combustion efficiency and maximum temperature in combustion chamber is shown in Fig. 17-20. The effect of temperature and concentration stratification on the emission characteristic was discussed by comparing pre-mixed gas with stratified temperature and concentration condition and equal temperature and concentration condition as T0=400K, equivalent ratio=0.25. Concentration of CO is increased bellow 1500K maximum temperature and NOx concentration is increased above 2100K. NOx and CO in emission gas concentration is almost same comparing the equal pre-mixed gas because maximum temperature is between 1500K and 2100K in each zone using DME and Methane existing temperature stratification in pre-mixed gas. NOx, CO concentration is getting big comparing with equal pre-mixed gas in emission gas because maximum temperature is above 2100K with high equivalent ratio in condition of concentration stratification.

Fig. 17. CO and NOx mole fraction in exhaust gas, combustion efficiency and maximum incylinder gas temperature (DME, Thermal stratification, 5-zones)

Numerical Analysis of the Effect of Inhomogeneous Pre-Mixture

**2100K**

**Combustion efficiency**

*c* **[%]**

**1.0x10-14 1.0x10-12 1.0x10-10 1.0x10-8 1.0x10-6 1.0x10-4 1.0x10-2 1.0x100 1.0x102 1.0x104 1.0x106**

**CO Mole Fraction** 

**NOx** 

**Mole Fraction** 

*XCO* **[ppm]**

*XNO+NO2* **[ppm]**

on Pressure Rise Rate in HCCI Engine by Using Multi-Zone Chemical Kinetics 153

**Maximum In-cylinder Gas Temperature 1500K**

> *c* **NOx CO**

**Maximum In-cylinder**

**Methane/Air =0.25 =0.30** *T0***=400K** *T0***=0K** *P0***=0.1MPa** *Ne***=750rpm =21.6**

**Gas Temperature** *Tc,max*

 **[K]**

Fig. 20. CO and NOx mole fraction in exhaust gas, combustion efficiency and maximum in-

**4 410K**

**5 420K**

**mass average of 5-zones**

**single zone**

**3 400K**

Chemical reaction numerical computation was conducted by giving a temperature or concentration stratification to pre-mixture. The reducing pressure rise rate effect is investigated by temperature and concentration stratification in pre-mixture. Choosing the DME and Methane that heat release characteristic is different, using the detailed reaction scheme and conducting numerical computation in multi-zone, following knowledge is

1. In condition of stratified temperature pre-mixture, temperature difference of the combustion chamber is expanded by piston compression. LTR or HTR occur earlier at

2. In condition of stratified fuel pre-mixture, temperature difference of the combustion chamber is occurred. LTR is occurred earlier in the zone which is lower concentration

3. In condition of stratified temperature and concentration, maximum pressure rise rate is decreased largely as compared with equal condition. Especially, maximum pressure rise rate is reduced restricting NOx, CO emission amount in condition of stratified

4. Concentrate stratification control is needed to operate the engine between 1500K and

5. Optimized succeeding investigation what temperature and concentration of stratification is most efficient is needed to reduce both maximum pressure rise rate and

cylinder gas temperature (Methane, Fuel stratification, 5-zones)

**2 390K**

**1** *T0* **= 380K**

the zone that gas temperature is higher.

temperature which is same as equal condition.

2100K in condition of stratified concentration in pre-mixture.

beside HTR is opposite.

emission together efficiently

**5. Conclusion** 

affordable.

Fig. 18. CO and NOx mole fraction in exhaust gas, combustion efficiency and maximum incylinder gas temperature (DME, Fuel stratification, 5-zones)

Fig. 19. CO and NOx mole fraction in exhaust gas, combustion efficiency and maximum incylinder gas temperature (Methane, Thermal stratification, 5-zones)

Fig. 20. CO and NOx mole fraction in exhaust gas, combustion efficiency and maximum incylinder gas temperature (Methane, Fuel stratification, 5-zones)

### **5. Conclusion**

152 Chemical Kinetics

> **DME/Air =0.25 =0.30** *T0***=400K** *T0***=0K** *P0***=0.1MPa** *Ne***=750rpm =8.0**

> *c* **NOx CO**

**Maximum In-cylinder**

**Methane/Air =0.25 =0** *T0***=400K** *T0***=40K** *P0***=0.1MPa** *Ne***=750rpm =21.6**

**Gas Temperature** *Tc,max*

 **[K]**

*c* **NOx CO**

**Maximum In-cylinder**

**Gas Temperature** *Tc,max*

 **[K]**

Fig. 18. CO and NOx mole fraction in exhaust gas, combustion efficiency and maximum in-

**4 410K**

**5 420K**

**Maximum In-cylinder Gas Temperature**

**mass average of 5-zones**

**single zone**

**3 400K**

Fig. 19. CO and NOx mole fraction in exhaust gas, combustion efficiency and maximum in-

**4 410K**

**5 420K**

**Maximum In-cylinder Gas Temperature**

**mass average of 5-zones**

**single zone**

**3 400K**

cylinder gas temperature (Methane, Thermal stratification, 5-zones)

**2 390K**

**1** *T0* **= 380K**

cylinder gas temperature (DME, Fuel stratification, 5-zones)

**1** *T0* **= 380K**

**2 390K**

**1500K 2100K**

**Combustion efficiency**

*c* **[%]**

**1.0x10-14 1.0x10-12 1.0x10-10 1.0x10-8 1.0x10-6 1.0x10-4 1.0x10-2 1.0x100 1.0x102 1.0x104 1.0x106**

**1500K**

**2100K**

**Combustion efficiency**

*c* **[%]**

**1.0x10-14 1.0x10-12 1.0x10-10 1.0x10-8 1.0x10-6 1.0x10-4 1.0x10-2 1.0x10<sup>0</sup> 1.0x10<sup>2</sup> 1.0x10<sup>4</sup> 1.0x10<sup>6</sup>**

**CO Mole Fraction** 

**NOx** 

**Mole Fraction** 

*XCO* **[ppm]**

*XNO+NO2* **[ppm]**

**CO Mole Fraction** 

**NOx** 

**Mole Fraction** 

*XCO* **[ppm]**

*XNO+NO2* **[ppm]**

Chemical reaction numerical computation was conducted by giving a temperature or concentration stratification to pre-mixture. The reducing pressure rise rate effect is investigated by temperature and concentration stratification in pre-mixture. Choosing the DME and Methane that heat release characteristic is different, using the detailed reaction scheme and conducting numerical computation in multi-zone, following knowledge is affordable.


**1. Introduction** 

mixing rate.

**7** 

**Ignition Process in a** 

*Graduate School of Energy Science,* 

Hiroshi Kawanabe

 *Kyoto University,* 

*Japan* 

 **Non-Homogeneous Mixture** 

An auto-ignition process of a non-homogeneous mixture is investigated using a numerical calculation based on chemical kinetics and the stochastic approach. This type of autoignition phenomenon is considered as a fundamental process of the initial stage of diesel combustion (Ishiyama, et al., 2003) or homogeneous charged compression ignition (Shimasaki, et al., 2003). In order to investigate these combustion processes, many numerical calculations have been performed and for many of those it has been assumed that the

However, the fuel-air mixing and chemical reaction progress happen simultaneously for these types of combustion processes. Due to the long ignition delay time and high homogeneity of the mixture, combustion characteristics, such as ignition delay and combustion duration, could be affected equally by non-homogeneity of the mixture, turbulent mixing rate and chemical reaction rate. Therefore, the understanding of those combustion mechanisms is incomplete due to the complexity of the phenomena in which the mixing and chemical processes interact with each other. The main purpose of this

Here, n-heptane is assumed as a fuel and its reaction process is calculated by means of a reduced mechanism (Seiser et al., 2000). The non-uniform states of turbulent mixing are statistically described using probability density functions and the stochastic method, which was newly developed from Curl's model (Curl, 1963). Focusing on the effects of mixture heterogeneity on combustion characteristics, such as ignition delay and combustion intensity (rate of temperature rise), the evolution of chemical reactions was calculated for the mixture in which variance in fuel-mass fraction decreases at given rates from the initial value under a fixed mean fuel-mass fraction and a constant pressure. The results show that the start timing of the low-temperature oxidation and ignition delay period are hardly affected by the equivalence-ratio variation, however, combustion duration increases with increasing variance. Furthermore, the combustion duration is mainly affected by the non-homogeneity at the ignition and is not much affected by the

ignition process is dominated by the turbulent mixing (Kong and Reitz, 2000).

chapter is to estimate these effects quantitatively using a numerical method.

#### **6. References**

