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Seoul 2000 FISITA World Automotive Congress F2000A139 June 12-15, 2000, Seoul, Korea Numerical Simulation for Mixture Formation and Combustion

in Direct Fuel Injection Gasoline Engines

Yoshihiro Sukegawa* , Toshiharu Nogi, Yusuke Kihara1), Toshio Furuhashi2) 1)Hitachi Ltd., Hitachi Research Laboratory, 2520 Takaba, Hitachinaka-shi, Ibaraki-ken, Japan 2)Hitachi Ltd., Hitachi Automotive Products, 2520 Takaba, Hitachinaka-shi, Ibaraki-ken, Japan

The mixture formation and combustion process in direct fuel injection engines was analyzed using the simulation program developed by the authors. The following conclusions were obtained. (1) The swirl air motion generated in the cylinder plays an important rule for carrying fuel vapor around the spark plug. (2) The combustion period becomes shorter due to reduction of attachment of fuel on the piston when using the skewed spray. (3) There is an empirical correlation between homogeneity of the in-cylinder mixture and the engine torque obtained experimentally. (4) Generation of a uniform mixture in the cylinder is important to improve combustion efficiency.

Keywords: CFD, Direct Fuel Injection, Stratified Charge, Homogeneous Charge, Fuel Spray

INTRODUCTION

To reduce CO2 emission from automobile engines, development of low fuel consumption engines is strongly desired. Direct fuel injection gasoline engines (DI engines) are able to operate with an ultra lean mixture, so they are expected to be used as low fuel consumption engines.

To get stable combustion with DI engines under variable operating conditions, advanced controls of in-cylinder mixture formation are required. For this purpose understanding of in-cylinder phenomena is very important. Many studies have observed in-cylinder mixture formations or airflow in experiments using lasers [1-3]. But detailed observations in a cylinder during high-speed operation have difficulties, so observed sections and physical amounts are restricted. In this situation, numerical simulation of mixture formation and combustion has flexibility as a way for in-cylinder observations, with arbitrary sections, timings or physical quantities, so it is very useful for better understanding of in-cylinder phenomena and optimizations of mixture control.

The authors developed a numerical simulation program that can simulate in-cylinder spray behavior, mixture formation and combustion in DI engine cylinders. The simulation results were verified with experimental visualization results of free spray and in-cylinder flames.

This simulation program was applied to 4-valve DI engine calculations and the mixture formation and combustion process and combustion characteristics were evaluated. Furthermore influences of the spray direction on mixture distributions and combustion were studied.

MODELING

METHOD OF CALCULATION

The motions of air, fuel vapor and combustion gas were simulated by solving conservation equations for mass, momentum and energy with the standard k- model [4]. To take account of gas composition change by fuel vaporization and combustion, three mass conservation equations for air-fuel mixture, fuel vapor and burned gas were solved. Each equation was solved by the FLIC method [5], a second order fully explicit algorithm, based on a finite volume method. As the difference scheme of the convection terms, the QUICK scheme [6] was used for the N-S equations, and the first order upwind scheme was employed for the equation of turbulence energy k and its dissipation rate.

Combustion of the gasoline-air mixture was treated as oxidation of an octane-air mixture and its chemical reaction form was given as the following one-step reaction.

2N472O)1(5.12O2H92CO8

)2N472O5.12(18H8C

+++

++

(1)

The turbulent combustion model proposed by Inage et al. [7] was employed for calculation of reaction rate in turbulent flow.

( ) C1Ck3

40S8 2Lut

+

= (2)

LSupiCi4= (3)

Here the subscript i indicates mean temperature of burned and unburned gas. The laminar flame speed SL was calculated by Metghalchis equation [8].

( ){ } )s/cm(b0

a

0

u2L P

P13.172.8432.26S

= (4)

( )18.018.2a = (5) ( )16.0122.0b = (6)

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The fuel droplets motion was calculated by the Discrete Droplet Model (DDM) [9]. In this model, fuel droplets are treated as parcels. A parcel contains droplets that have the same diameter and velocity. The motion of parcels was obtained by solving the following momentum equation using the second order Euler scheme.

( ) ddd

Dd ~~d4

C3t

VVVVV

=

(7)

( ) 32eded

D R167.01R24C += (8)

= d~R ded VV (9)

The exchange of momentum, energy and mass between droplets and fluid was considered.

As a wall interaction model, Wakisakas impinging model [10] was employed. Droplet velocity and diameter after impinging on walls were determined using the model according to the incident Weber number of the droplet.

ENGINE MODEL AND BOUNDARY CONDITIONS

Table 1 shows the main specifications of the DI gasoline engine used in the simulation. Figure 1 shows its combustion chamber shape. A high-pressure fuel injector is attached between the two intake ports. The attachment angle of the injector is 36deg. A spark plug is located on the top-center of the cylinder head. A piston has a bowl on its crown. One of the two intake ports has a swirl control valve. This is a butterfly-type valve and during stratified charge operation, this valve is closed to generate swirl air motion in the cylinder.

The fuel injector is a swirl type and it injects fuel at a pressure of about 7MPa. Experimental data of free spray under atmospheric conditions were used as initial conditions for the spray simulations.

There are two kinds of operating modes for the DI engine, the stratified charge mode and the homogeneous charge mode. In the stratified charge mode, the swirl control valve is closed and fuel is injected at a late stage of the compression stroke. In the homogeneous charge modes, the swirl control valve is opened and fuel is injected during the induction stroke. So both operating modes were calculated and the mixture formation process and combustion characteristics were evaluated.

RESULTS AND DISCUSSION

VERIFICATIONS OF FREE SPRAY SIMULATION

To confirm the propriety of the simulation, free spray simulation results were compared with experimental data. The comparison is shown in figure 2. (a) is at atmospheric (0.1MPa) conditions and (b) is at pressurized (0.6MPa) conditions. The pressurized conditions match the typical in-cylinder pressure in the DI engine when fuel is injected during compression strokes in the stratified charge mode. For the atmosphere conditions, the spray has a hollow cone shape and the droplets are spread widely. On the other hand, at the pressurized conditions, the droplets roll in eddies on the outer edge of the spray, so spray penetration is shorter than the penetration obtained for atmospheric conditions. This is because shear stresses strongly affect the droplets and the surrounding gas due to the high pressure.

The simulation successfully portrays the influence of surrounding gas pressure on spray behavior and the simulation results agree with experimental ones.

VERIFICATION OF COMBUSTION SIMULATION

To confirm propriety of the combustion model, simulation results of in-cylinder combustion and experimental results were compared. Figure 3 shows the flame surfaces obtained from simulation and experiment. In this simulation, the flame surfaces were defined as iso-surfaces on which burned gas mass fraction was 0.5 each time. The burned gas areas surrounded by the flame surface agree between simulation and experiment.

Figure 4 shows the in-cylinder pressure for simulation and experiment. There is good coincidence. So it is confirmed that burning velocity in the cylinder is accurately evaluated using the combustion model.

MIXTURE FORMATION IN STRATIFIED CHARGE

The simulation results of spray motions, fuel-air ratio distributions and flame propagation in the stratified charge mode are shown in figure 5. The engine speed was 1400rpm, the start of injection timing was 70deg BTDC and the overall air-fuel ratio was 40. The fuel-air ratio distributions are shown on the cylinder symmetric planes.

The fuel spray injected at the last compression stroke goes into the piston bowl and evaporates there. The vaporized fuel goes toward the spark plug electrode. At near TDC, the fuel vapor concentrates around the spark plug and the air-fuel ratio around the spark plug is from 10 to 20, which would be a very ignitable mixture. Regarding the combustion stroke, the flame propagates from the spark point to the mixture in the piston bowl and then outside the bowl with a small lag. The flame propagates through the whole cylinder 30deg after the spark timing.

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To concentrate a rich mixture around the spark plug, swirl generated in the cylinder plays an important role. Figure 6 shows velocity vectors at the compression stroke. This figure indicates the velocity vectors on the vertical planes at 40deg BTDC and 20deg BTDC and on the horizontal plane at 20deg BTDC. The vectors show generation of 2 vortexes in the cylinder. One is swirl turning near the cylinder wall and the other is swirl in the piston bowl. At the center of each swirl, pressure is lower than other parts of the swirl because of centrifugal force. If the axis of each swirl center is different, flow goes from the outer side of the lower swirl where the pressure is higher to the center of the upper swirl where the pressure is lower. This flow carries fuel vapor generated in the piston bowl around the spark plug.

Figure 7 shows calculated heat release rate for two cases : where fuel was injected straight (non-skewed spray) and where the fuel injection direction was skewed upwards 7 degrees toward the cylinder head (skewed spray). With the skewed spray, the heat release rate rises more quickly after the ignition and is lower late in combustion compared with the non-skewed spray. Figure 8 shows the fuel-air ratio and burned gas mass fraction distribution. With the skewed spray, more fuel can reach around the spark plug, so a richer mixture is generated there. In this case, the flame propagation speed is faster than in non-skewed spray. On the other hand, with non-skewed spray, a too rich mixture is generated near the piston surface due to fuel impinging on the piston. This is because more heat is released at the late stage of combustion than for the skewed spray.

MIXTURE FORMATION IN HOMOGENEOUS CHARGE

The distribution of the fuel-air ratio for homogeneous charge is shown in figure 9. In this case, the engine speed was 2000rpm and the start of fuel injection timing was 270deg BTDC.

When using the non-skewed spray, fuel vapor near the injector nozzle goes toward the piston and enters the bowl. The air motion in the combustion chamber at the induction stroke is downward flow near the injector nozzle as shown in figure 10. This downward flow carries fuel vapor near the injector nozzle into the piston bowl. At the compression stroke, the air on the exhaust side of the cylinder enters toward the intake side by the squish effect. So at the late stage of the compression stroke, the mixture concentration on the intake side of the cylinder becomes richer than on the exhaust side. On the other hand, with the skewed spray, a lot of fuel vapor can reach the exhaust side of the cylinder, so the amount of fuel enters in the piston bowl is small. Therefore the mixture concentration at the compression stroke becomes more uniform than with the non-skewed spray.

Figure 11 shows a correlation for mixture homogeneity and measured engine torque. Here the mixture homogeneity is defined as follows.

1L

0 L

S

dS

=

= (10)

Equation (10) also implies mean laminar velocity of the in-cylinder mixture at ignition timing. Figure 11 shows that the case with higher homogeneity of mixture has higher engine torque. Therefore generation of a uniform mixture is important to improve combustion efficiency for the homogeneous charge mode.

CONCLUSION

The simulation program to calculate fuel spray, mixture and combustion gas behavior in an engine cylinder was developed by the authors and verified by using free spray and in-cylinder visualization data. This simulation program was applied to DI engine simulation and the following conclusions were obtained.

(1) The fuel vapor in the piston bowl was carried around a spark plug by the swirl generated in the cylinder.

(2) Using skewed spray, the combustion period for the stratified charge mode was shorter due to enrichment of mixture around the spark plug and reduction of attachment of fuel on the piston.

(3) For the homogeneous charge mode, a richer mixture was generated on the intake side of the cylinder when the non-skewed spray is employed due to downward flow near the injector nozzle.

(4) There was an empirical correlation between homogeneity of the in-cylinder mixture obtained by the simulation and the engine torque obtained by the experiment.

(5) Generation of uniform mixture in a cylinder was judged important to improve combustion efficiency for the homogeneous charge mode.

NOMENCLATURE

C: Burned gas mass fraction Cp: Specific heat f: Fuel component mass fraction k: Turbulent kinetic energy P: Pressure SL: Laminar burning velocity T: Absolute temperature V: Velocity

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: Air excess ratio : Flame thickness : Turbulent energy dissipation rate : Mixture homogeneity : Heat conductivity : Viscosity coefficient t: Turbulence reaction rate : Density : Equivalence ratio Subscripts d: Droplet st: Stoichiometric t: Turbulence condition u: Unburned condition 0: Standard state (0atm, 273K)

REFERENCES

[1]Tatsuta H. et al.,SAE 981435,1998. [2]Faure M.A. et al.,SAE 982705,1998. [3]Kiyota Y. et al.,FISITA 96,1996. [4]Launder B.E. et al.,Proc. NASA Conf. on Free Shear Flows, Langley,1972. [5]Gentry R.E. et al.,J. of Comp. Physics,1,p87, 1966. [6]Leonard B.P.,Comput. Meth. in Appl. Mech. and Engng.,19,p59,1979. [7]Inage S. et al.,JSME Ser.B,61,No.586, p2290,1995(in Japanese). [8]Metghalchi M. et al.,Combust. Flame 48,1982. [9]Amsden A.A. et al.,Los Alamos National Laboratory Report,LA-10245-MS,1985. [10]Wakisaka T.,et al.,JSME Proceeding No.934-2, p215, 1993(in Japanese).

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Piston bowl

Swirl control valve

Fuel injector

Spark plug

Intake ports

Exhaust ports

Fig.1 Engine configuration

Bore,StrokeCompression ratio

Displacement

Table 1 Engine specifications

Fuel pressure 7-9 MPa(Variable)

Cylinder head2,987cm3

93mm,73.3mm

4 valves pentroof

11:1Piston With piston bowlIntake port Straight port with

swirl control valve

Fig 3 Comparison of flame propagation between simulation and experiment (1400rpm, A/F=14.7, Injection=60deg ATDC, Ignition=30deg BTDC)

Simulation

Burned gast=02ms

3.1ms

Flame front

2mst=0

3.1ms

ExperimentC alc.Exp.

C rank angle

Pressure(MPa)

In-cylinder pressure(MPa)

Fig 4 Comparison of in-cylinder pressure (1400rpm, A/F=18, Injection=30deg ATDC, Ignition=40deg BTDC)

Sim ulationExperim ent

C rank angledegA TD C

*Defined as lapsed time after start of injection

0.82ms* 1.7ms 2.6ms

Sim

ulat

ion

Expe

rimen

t

(a) Atmospheric conditions (b) Pressurized conditions(0.6MPa)

0.82ms 1.7ms 2.6msSi

mul

atio

nEx

perim

ent

Fig.2 Comparison of free spray shape between simulation and experiment

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Fuel spray motion Fuel-air ratio Flame propagation

68deg BTDC

63deg BTDC

51deg BTDC

34deg BTDC

68deg BTDC

63deg BTDC

51deg BTDC

34deg BTDC

14deg BTDC

10deg BTDC

2deg BTDC

10deg ATDC

Fig.5 Simulation results of mixture formation and combustion in the DI engine cylinder (1400rpm, A/F=40, Injection=70deg BTDC, Ignition=20deg BTDC)

Horizontal section(A-A section)

A A

Vertical sections(center of cylinder)

Fig.6 Calculated velocity vectors for in-cylinder air (without fuel injection)

Low pressure

High pressure Swirl

Swirl

7

50m/s

Downward flow

Fig.10 Velocity vector on vertical cross section (Full load,2000rpm,at 240degBTDC)

Fig 9 Fuel-air ratio distributions of vertical cross section (Full load, 2000rpm, Injection start=270deg BTDC)

120BTDC 60BTDC 10BTDC

Fuel/Air

Non

-ske

wed

spra

ySk

ewed

spra

y

0.1

0

Bur

ned

gas f

ract

ion

Vap

or fr

actio

n

Skewed sprayNon-skewed spray40deg BTDC

20deg ATDC

Fig.8 Mass fraction of fuel vapor and burned gas

Unburned gas

Burned gas

Rich mixture

Crank angle

Skewed spray

Non-skewed spray

Hea

t rel

ease

rate

(Rel

ativ

e va

lue)

TDC

7deg

Fig 7 Heat release rate on stratified charge combustion (1400rpm,A/F=40,Injection=70degBTDC ,Ignition=20degBTDC)

2000rpm 4000rpm 6000rpm

1kgm

Skewed spray Non-skewed spray

10%

6000rpm4000rpm2000rpm

Torq

ueH

omog

enei

ty

Experiment

Simulation

Fig.11 Correlation between engine torque and mixture homogeneity

Engine speed