Development of a four-zone analytical combustion model for a D.I. compression-ignition engine

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CONSEIL INTERNATIONAL

DES MACHINES A COMBUSTION

20th INTERNATIONAL CONGRESS ON COMBUSTION ENGINES

DEVELOPMENT OF A FOUR-ZONE

ANALYTICAL COMBUSTION MODEL FOR A

D.I. COMPRESSION-IGNITION ENGINE

by

Dr Shao-Xi Shi, Mr Wan-Hua Su, Mr Kui-Han Zhao and Dr Yong Yue Tianjin University, China

LONDON 1993

INTERNATIONAL COUNCIL

ON COMBUSTION ENGINES

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m-= =

pis

DEVELOPMENT OF A FOUR-ZONE

ANALYTICAL COMBUSTION MODEL FOR

A D.I. COMPRESSION-IGNITION ENGINE

NAME OF AUTHORS

Dr. ShaoXi Shi, Professor, Tianjin University, China Mr. WanHua Su, Professor, Tianjin University, China

Mr. KuiHan Zhao, Professor, Tianjin University, China

Dr. Yong Yue, Lecturer, Tianjin University, China

ABSTRACT fr

In this paper, a fourzone analytical combustion model is developed for a D.I. compres-sionignition engine. In this model, the combustion chamber is divided into the following four zones, each being an open thermodynamic equilibrium system: (1) spray mixing zone(j), (2) burning zone(b), (3) combustion product zone(p), (4) air zone(a). The spray mixing zone is composed of air, fuel and combustion products. The burning zone is the volume swept by the flame front in the time interval of a calculation step. At the end of_{the calculation step, it is} as-Slimed that the mixture is uniformly mixed with the productzone.

Due to the differences in temperature, density and composition among the above men-tioned four zones, heat and mass transfer must occur among these zones. In this model, it is assumed that the heat transfer between zones takes place only when it is accompanied by the mass transfer. It is also considered that the fuel injection causes entrainment not only of air, but also of combustion products. The entrainment of combustion products, in fact, plays an important role in the fuel droplet evaporation. Besides, the mixing of the air with the combust tion products exert profound influences on the temperature and composition of the gas in the !combustion product zone, and in turn, on the exhaust emissions.

This combustion model has been applied to study the effects of the hardware parameters of the combustion system on the combustion parameters by inputting the conventional engine test data with a view to improving the combustion process of a high speed D.I. diesel engine having a bore of 130 mm and a stroke of 150 mm. The results show that by increasing the fuel injection pressure and the fuel pump plunger diameter and, at the same time, by reducing the rate of air swirl, the engine performance is considerably improved.

In short, the new combustion model can be used to calculate the. rate of heat release

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spray penetration, rate of medium entrainment, average fuel / air equivalent ratio,

tempera-tures of combustion and combustion products, rate of mass and heat transfer, rate of NOx formation etc. from the usual experimental data such as the indicator diagram, the injection pressure etc. and thereby to analyze the effects of design parameters on the combustion pro-cess. It is an effective tool for studying the combustion process of a DJ. compression ignition

engine.

RESUME

Dans cc memoire, un modele analytique de combustion

a quatrezone pour un moteur

diesel est developpe. Dans ce modele, la chambre de combustion est diviee dans quatre zones ciapre, chaqu'une etant un systeme ouvert dequilibre thermodynamique: (1) zone de melange par pulverisation (j), (2) zone de flamme (b); (3) zone de produit de la combustion, (4) zone

d'air(a). La zone de melange par pulverisation est composee par l'air, le combustible et les

produits de combustion, La zone de flamme est le volume par couru par le front de la flamme

pendant l'interval du tempt de pas de calcul. On suppose qu'au bout du pas de calcul, le.

melange est uniformement melange avec la zone de produit.

Par suite de differences de temperatures, de densites et de compositions entre les qutre

zones mentionnees cidessus, transferts de chaleur et de materiel doivent avoir lieu entre ces

zones. Dans cc modele, on suppose que le transfert de chaleur entre zone a lieu seulement

quand il est accompagnel par celui de materiel. On considere aussi que l'injection du

combusti-ble cause entratiements de l'air et aussi des produits de combustion. L'entrainement, en effet,

a un role important

dans la pulverisation des gouttelettes du combustible. D'ailleurs, le

melangement de l'air avec les produits de combustion et l'interaction entre la flamme et les

produits de combustion exerc,ent un influenceprofond sur la temperature et la composition du

gaz dans la zone de produit de combustion, et finalement, stir l'imission epuisee.

Ce modele de combustion a ete mis en oeuvre pour e'tudier les effects des parametres structuraux du systeme de combustion sur

les parametres de combustion en entrant

les

donnees de test de moteur conventionnel, a fin d'amelior er le procede de combustion &tin D.I. moteur diesel a grande vitesse, dont le calibre est 130 mm et la course est 150 mm, Les resultats montrent que, par l'accroissement de la pression de l'injection du combustible et du diametre du piston de la pompe de combustible, et en meme tempt, par reduction de la vitesse du remous d'air, la performance du moteur est considerablement amelioree.

Enfin, le nouveau modele de combustion peut etre utilise pour calculer

le taux de

decharge de chaleur, penetration de vaporisation, le taux d'entratnement de l'intermede, le rapport moyen d'equivalent de combustible / air, la temperature de combustion et celle de produits de combustion, taux de transferts de chaleur et de materiel, taux de formation de NOx etc., i partir des donnees experimentales ordinairees comme le diagramme d'indicateur,

le pression d'injection etc., et de c,ette maniere, on peut analyser les effects des parametres structuraux sur le procede de combustion. II est un outil efficace pour itudier le procede de,

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aair

acair entrained

bburning

jspray

pcombustion products

pcproducts entrained

SYMBOLS SUBSCRIPTS . INTRODUCTION

Due to the extreme complication of the combustion phenomena occurring in I.C. engines, the development of a new engine combustion system still mainly relies upon experimental work. However, experimental work often _{can not give the causality relations between the} combustion phenomena and the experimental results obtained. Combustion modelling is a

useful method for solving this problem.

MultiDimensional combustion modelling is extremely _{complicated. It is not yet well}

de-veloped and also not economically attractive for normal usage. Consequently,

zerodimensional or quasidimensional model is usually _{used,especially its single zone model}

which is most widely employed for analytical studies of the combustion and performance _of

diesel engines.

In the single zone model, the gas in the combustion chamber is assumed to be _a homoge-neous mixture in thermodynamic equillibrium, and the fuel is considered to be applied to the

3 apmixture of air and

combustion products

chcombustion chamber

eentrainment

ffuel

wwall jet

Cconstant

Vvolume

dodiameter of nozzle hole

acoefficient of product

hspecific enthalpy

_entrainment

Htotal enthalpy(mh)

_{flcoefficient of air / product}

mmass

mixing

Nnumber of nozzle holes

_{(pequivalent ratio}

nengine speed

_{(IDplunger diameter}

ppressure

0crank angle

)air swirl ratio

poneedle valve opening

_{p density}

pressure

_{Ethe rate of turbulent}

Qheat transfer

_{energy dissipation}

Sspray penetration

_{0iinjection advance}

Ttemperature

_{LAinjection duration}

ttime

I

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cylinder at the same rate as that it is consumed. Because of the assumption of spatially uni-form thermodynamic properties the calculated combustion temperatures are so low that mod-elling of pollutant formation processes becomes impossible due to the high sensitivity of these processes to gas temperature.

G.A.Szekely et al.[ II developed a twostage heat release model for diesel engines.

Al-though more reasonable calculated combustion temperatures were obtained ,the model by no means represents the complex nature of diesel combustion, and cann't correlate the engine combustion process with the engine design parameters.

An attempt was thus made to establish a 4Zone combustion model correlating the

ex-perimental data with the engine design parameters with a view to obtaining an effective tool for analyzing the combustion process in a D.I. diesel. In this model the combustion chamber is

divided into the following 4 zones, each being an open thermodynamic equilibrium system

(Fig.1): (1)mixing zone(j), (2) burning zone (b), (3) combustion product zone (p), (4) air zone

(a). The spray mixing zone is composed of air, fuel and combustion products. The burning zone is the volume swept by the flame front in the time interval of a calculation step. At the end of the calculation step, it is assumed that the mixture is uniformly mixed with the product zone. The input parameters are the basic engine test data including the cylinder pressure, the fuel injection pressure, the air swirl ratio etc. while the main outputs of the calculation are the ROHR, the process of spray development, the rate of air entrainment, the average fuel / air equivalent ratio co in the spray mixing zone, the temperatures in different zones and the pro-cess of NOx formation.

PHENOMENOLOGICAL COMBUSTION MODEL

1. The Model of Heat and Mass Transfer

Since there are differences

in

density, temperature and composition among the

thermodynamic zones defined above, there must be heat and mass transfer among different zones. Further, the fuel injection causes entrainment of both the air and the combustion prod-ucts. It is in fact the most important mass transfer in the engine combustion process. Besides, the mixing of the air and the combustion products will exert profound influence on the tem-perature and composition in the combustion product zone and, in turn, on the exhaust emis-sions. Fig. 2 shows the schematic diagram of heat and mass transfer involved in the model. It is assumed that the heat transfer proceeds only when accompanied by the mass transfer and that both the convection and radiation heat transfers are neglected.

Since the total mass flow rate of medium entrained dm is the sum of the mass flow rate

dO

of air entrained and that of combustion product entrained

dm Pe de de dm e

dm pe, dm

pe dO -t-de dO (1) dm

(6)

Assuming the mass flow rates of air and products are directly proportional to their respective

masses surrounding the free jet, then

dm.,

(1 -

a _{1 dm,}

where a coefficient of product entrainment( 0.35), mamass of air surrounding the jet, m mass of product surrounding the jet.

It is further assumed that the mixing rate of air and combustion product is proportional to the masses of air and products in their respective zones, and is controlled by the rate of dis-sipation of turbulent kinetic energy. It follows that:

dm

_{apflm a}

rn p

dO (4)

where '3 _{m i xi n g coefficient of air and product. The higher is the value of} _{the higher is the}

mixing rate of air and product, the lower is the rate of NOx formation because of the reduc-tion of product temperature Tp. _{T is turbulent mixing time which may be expressed by the folk}

lowing equation for large scale eddy structure,

r (L / e)

(5)

where E is energy dissipation rate of eddy structure, L is the length of scale. 2. Model for Spray Mixing

(a) Equivalent pressure difference and equivalent jet velocity

The ordinary empirical expressions cannot be used for computing the spray penetration and the rate of air entrainment because they are derived from fuel injection with a constant

pressure difference, whilst the pressure difference AP between the fuel _{line and engine cylinder} is variable during the injection_{process. In this case, the equivalent pressure difference APi and}

the equivalent jet velocity u _{by applying the principle of conservation of}

momen-tum to the fuel jet are usually used.

1 r uio mum f M f 5 (2) (6) dO Lame + (1 cOrn I dO

dm,

r CCM p dm, dO

Lm

+ (1 )ma i

dO (3) fl, obtained = a)m

(7)

28.6p do ₍₁₀₎ (13) (14)

AP; =

1 ci2pf U,

2 (7)

where mfquantity of fuel injected per cycle, uinstantaneous jet velocity, p1density of

fuel, Cdcoefficient of discharge. Spray penetration S

Using empirical expression derived by HiroyasuE21,

when t <tbraak, S =0.39(2Api )1/2

Pt

when t >tbak, S = 2.95(AP; )1,4 (da

PT

01/2

where:tbroakspray breakup time, doorifice diameter ofinjector hole.

it break

(pa Ap1)1/2

Penetration for wall jet Sw:

= (2.06u ,o . 01/2

Cl/0 is the equivalent jet orifice diameter and is defined as

=

do()1/2

(12)

Pa

where paair density, The origin of Sw is the pointof intersection of the jet axis and the

im-pinging surface.When air swirl exists, the penetration is given by:

Ss

(1 + id) n s / 30 / u,o)

aswirl ratio, nengine speed(r.p.m.).

Medium entrainment and turbulent mixing after injection

Medium entrainment into the free jet was calculated according to the expression of Ricou Spaldineover the time the jet penetrates to a distance S.

dm e drn

f

_)/

dm

f

_{C1 S/do}

dO dO dO

6

--(b) S (c) &

+

(8) (93

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where c1

is a constant (= 0.32), d'0

is

the equivalent jet

orifice diameter. Medium

entrainment into the wall jet may be calculated by Hertel's empirical expressionf41:

e.f

_)/

drn

f

c2S. /

dO dO dO

When too much fuel is impinged onto the chamber wall, the rate of air entrainment is reduced and a smaller value of c2 should be used. For the present test engine, when (S+Sw) / R<1.1,

c2= 0.86 and when (S+Sw) / R> 1.1,c2=0.20, Rradius of combustion chamber.

After the ending of injection, the jet momentum due _{to fuel injection will be zero, the} mix-ing process will be controlled by the turbulent kinetic energy dissipation in cylinder. The mass transfer rate of air by turbulent mixing into the unburned fuel from the unutilized air available in the jet and the surrounding regions can be expressed as c3 (ma

/ t ),

where ma is the mass of air,

t

is the turbulent mixing time for the breakdown of large_{scale eddies, and c3 is a}

con-dma

stant. The depletion rate of available air mass is . By conservation of mass, we have: dt

dma

c3(nza / ₍₁₆₎

di

3. Equations of Conservation of Mass

(a) Spray mixing zone

Rate of change of mass in spray mixing zone = Rate of fuel mass injected+Rate of _mass

of total medium entrainedRate of_{mass burned:}

dm, dm f dm, _dmh

dO dO dO dO

Air zone

Rate of change of mass in air

_{zone = (Rate of air mass entrained+Rate of air}

_mass

mixed with combustion products):

dma dmae dmap

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dO dO

Product zone

Rate of change of mass in product zone = Rate of mass burned+Rate of air mass mixed

with combustion productRate of product mass entrained:

dm,, din,, dma, dmpe dO dO de de (15) (17) (19) dm

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(d) Conservation of mass in cylinder

Rate of change of mass in spray mixing zone+Rate of change of mass in air zone+Rate of

change of mass in product zone+Rate of change of mass in burning zoneRateof fuel mass

injected = 0:

dm, dm dm, dm b dm f

dO dO dO dO dO

4. Equations of Conservation of Energy

(a) Air Zone

Rate of change of enthalpy in air zone = Volume of air zone x Rate of pressure

changeFlow rate of enthalpy of entrained air and that ofair

mixed with productsRate of

heat transfer to chamber wall:

d(h a m a)

v

dp dm ae dma, dQa

h.(

+ )

dO dO dO dO dO

Spray Mixing Zone

Rate of change of enthalpy in mixing zone Volume of mixing zone x Rate of pressure

change+Rate of change of enthalpy of entrained air+Rate of change enthalpy of entrained

product+Rate of change of enthalpy of injected fuelRate of change of

enthalpy of mass

burnedRate of heat transfer to chamber wall:

d(him;)dm

m f dm b dQ

V,dp

+

+h,

_{+hfdd0 h}

dO dO dO dO dO

Burning zone

Flow rate of enthalpy to burning zone = Flow rate of enthalpy to product zone (Assum-ing adiabatic combustion):

dn't b dni b

h b

dO dO

Product zone

Rate of change of enthalpy in product zone = Volume of product zone x Rate of

pres-sure change+Rate of change of enthalpy of mass burned-Flow rate of enthalpy of air in air / product mixtureRate of heat transfer to chamber wall:

d(hpm,) dp dm b + hadma, dQ p

V,,- +h,

dO dO dO dO dO + (24)

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5. Gas State Equation

piVi miRiTi

dpi dVi drni dTi

or

dO

/p+

i + dO dO

/ mi +

dO

/T1

Volume Equation

At any instant, the total combustion chamber volume is equal to the sum of the four

zones,

Veh =Va + VD Vp (27)

Heat Transfer to Chamber Walls

The total wall heat transfer Qch

is

calculated according the formula given by

Seitkei.[5] The heat loss from each zone is supposed to be proportional to the product ofmass

multiplied by temperature in the zone:

Qch= 18.788p" Tc--°.2C;;;7(2D

_{X., /(D +2X)-°3A}

(T, T.))

₍₂₈₎

dQi miTi dQch

)

dO Em iTi dO

where AArea of the chamber wall, pCylinder pressure, CmAverage velocity of piston,

XsPiston travel, DCylinder diameter, TwAverage temperature of the chamber wall, T,

Average temperature of the charge in cylinder. Combustion Temperature

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Due to the extreme complication of' the combustion process of a diesel engine, it isvery

difficult to make accurate calculations for the thermodynamic properties of the mixture in cyl-inder and the flame temperature. It is a very tedious and timeconsuming work. Toovercome

this difficulty and for convenient usage the following empirical expression for adiabatic flame

temperature was used.163

Tb 1{l + A 2Inyo + A 3(in(P)2] ₍₃₀₎

where A1, A2, A3

denote three numerical arrays, respectively related to the

initial

temperature, pressure and equivalent ratio co of the fuel / air mixture. The temperature in

product zone at the end of calculating step Tp can be calculated from the flame temperature

Tb, mass burned Lmb and the quantity of airmixed into products Atnap,

9

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The rate of NO formation is computed according to extended Zeldovich reaction

mecha-nism

Tpi mpi + CbTb(Amb)+ C. 7' a (AM aP)

T p2

C p2(M + AM b ± Amap)

where 1 denotes the beginning of calculating step, 2 denotes the end of calculating step, Cp,Cb,Caare specific heat of product zone, burning zone and air zone respectively.

9. Model for NO Kinetics

10

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The expressions for rate constants and equilibrium constants used are taken from Szekely

et.al.til

Di. RESULTS AND DISCUSSIONS

This model has been applied to the work of improving the combustion process of a high speed diesel engine produced by Tianjin Diesel Engine Works.Table 1. shows the main con-struction parameters of the single cylinder test engine. Table 2 gives the test results obtained under the following three operating conditions: Case 1: Original engine without any

modifica-02 = = 20

(32)

0 +N2= =NO +N

(33)

N+02= =N0+0

(34)

N+OH==NO+H

(35) d(NO) 2K IAN 21[0 2]1

(1_

x2 ₍₃₆₎

dt

Kbi2 1 v where [NO] ₍₃₇₎

x

_{KNo[02]1/2[N2P12} Kif[NO] ₍₃₈₎

v

_K2/1021+ and 1C31[02]1/4[H20]1/2 (39) KV4 -)

-C

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tion. Case 2: At higher injection pressure,, larger plunger diameter and lower air swirl. Case 3:

At lower engine speed.

Table 1. Main construction parameters of single cylinder ex erimental engine

Rate of Heat Release

Table 2. Experimental results for 3 typical cases

As shown in Fig. 3. the ROHR curve calculated from the new model is higher in the ini-tial period than that from the traditional single zone model (AVL) and somewhat lower inthe

later period. The reason for these differences is that in the single zone model the working me-dium is considered uniform, neglecting the existence of liquid fuel and its phase _{change, whilst} in the present model the heat absorption due to fuel evaporation and the temperature rise of fuel vapor is accounted for by changing the enthalpy of the fuel. The ROHR obtained should

be more accurate.

Fig. 4 shows the calculated accumulated ROHR for cases t and 2. The burning rate in case 2 during period 0--20°C A ATDC is higher and the combustion period is shorter than

those in case I. Consequently, st.c. is lower, thermal efficiency is higher, even though the in-jection timing is retarded by 3tA.

Z. The Fuel Spray Development and the Air / Fuel Mixing Rate

The calculated results of spray penetration s, air entrainment

_{rate dm./ de and average}

equivalent ratio cp in spray mixing zone for cases. 1

_{and 2 are given in Fig.5, 6 and 7}

respectively. As shown in these figures, the spray penetration S in case 1 and 2 is almost

unchanged although the injection pressure is increased and the timing of injection retarded in case 2. As the rate of fuel injection is increased due to higher injection pressure, the rate of air entrainment dm / dO is increased and, as a result, the equivalent ratio (I) in the spray mixing

zone is always lower than that in case 1, Especially in the period of diffusion combustion, the

11,

Cylinder Bore 130 mm Throat Dia. of

Combustion Chamber 67mm

Stroke 150 mm Fuel Pump, No.3 Pump

Compression Ratio 17 _Injector _{4 x0.35 mm x 144}

II J Case; Engine Speed Pe Injection ' Timing Pres. Swirl Plunger Dia. ' S.F.0 i I NO (r.p.m) (M Pa) (t A) (MN) (n) (mm) (g / kwh) (ppm) I

1,

2000 0.77

'-30

20 I 2.9 Illi 1 264.2 1450 , 2 . I 2000 0.77

-27

i 29 23 12' , 234.2 1750 3

um

037

21

29 2.5 12 218.6 1529 Bmep

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air and fuel is sufficiently mixed so that the ROHR of the diffusion combustion incase 2 is

in-creased.

Better overall engine performance in case 2 was obtained by varing simultaneously the plunger diameter, the fuel injection pressure and the air swirl ratio. According to the results of the analytical work made for a number of test data, the following conclusions were obtained:

(1) By increasing the fuel injection pressure pc, from 20MPa to 29MPa, dmaa / dO is increased by 13%; (2) By increasing the plunger diameter from 11 mm to 12 mm, dmaa / dO is increased by 15% approximately; (3) The reduction of air swirl ratio from 2.9 to 2.5 results in a reduc-tion of dmaa / dO by about 2%. It is evident that the improvement of air and fuel mixing pro-cess in case 2 is mainly due to the increase in plunger diameter and the fuel injection pressure.

When the engine operates at low speed with load kept unchanged (case 3), the spray

pen-etration S is increased due to the increase in the time duration of injection (Fig. 8). The

in-crease in S would cause excessive fuel injected onto the chamber wall. This may be the reason why smoke is increased at low engine speeds. On the other hand, the increase in spray penetra-tion would increase the rate of air entrainment dmaa / dO and decrease the combuspenetra-tion dura-tion in crank angle. This leads to the reducdura-tion of the specific fuel consumpdura-tion at low engine

speeds as shown in table 2.

3. Discussion on Mass Transfer

The mass transfer and the accompanied heat transfer have profound effects on the tem-peratures in the spray mixing zone and the product zone, and consequently on the process of

fuel evaporation and the rate of NOx formation. When a =0.5 from equation (2) and (3),

dmaa / dO and dmpe / dO are respectively proportional to ma and mp. When a=0, mpe = 0; While a = 1, ma, = O. Fig.9 shows the effect of a on calculated temperature in spray mixing

zone Tj and that in combustion product zone T. Just

before or after ignition, mp is very

small, the effect of on Ti is also very small. As mp is increased, the effect of a is also in-creased, but mainly on Ti. The calculated Tp is not sensitive to the value of a. The increase in caused by product entrainment accelerates the evaporation process of fuel droplets. After considering the test results obtained by previous investigators as well as the conditions inthis

investigation, a value of 0.35 is used for a. The computed results show that this value is

ap-propriate.

The zone of combustion products is diluted and cooled by mixing with air. The mixing process of combustion products and air changes both the composition and the temperature of the combustion products. The value of coefficient fl in equation (4) can be used to evaluate the quantity of air mixed with combustion products. For aD.I. diesel engine, the fuel injection ends at about 2 ° CA ATDC, whilst the end of combustion is at about 40 ° CA ATDC. There-fore, the mixing of air and products occurs mainly in the period of diffusion combustion after the end of fuel injection, The mixing energy required comes from the dissipation of the turbu-lent kinetic energy. In the initial period of combustion, the quantity of products mp is small and in the later period, the quantity of air ma is small. In both cases the mixing rate of air and products dmap / dO is low. It is obvious that the mixing takes place mainly in the major part of the diffusion combustion period. The mixing process between air and products results in a

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duction of temperature Tp of the combustion product zone or shortening the high

tempera-ture period and eventually a reduction of NOx formation. Fig. 10 shows the calculated tem-perature of products Tp, the rate of NOx formation and the NOx concentration in the cylinder versus crank angle for cases 1 and 2 respectively. From the experimental results for NOx

emis-sions, it was found that = 0 . 2 in case 1, and 0.06 in case 2. The higher value of fl indi-cates higher rate of mixing between combustion products and air. This means that the mixing

rate in case I is higher.

A study of the correlation of mixing coefficient and the parameters injection pressure,

swirl ratio f2 , pump plunger diameter, engine speed etc. was made. A part of the results is giv-en in Fig.11 and 12 which show the relationship betwegiv-en # and, ,piand that between # and f2 respectively. It can be seen that an increase in increases the turbulent mixing rate between

air and products, whilst an increase in injection pressure results in a rapid reduction of the

value of fi. This probably due to the fact that although the injection pressure is higher and the turbulence induced is therefore stronger as in case 2, the intensity of air swirl is lower. In this case the mixing energy may be rapidly reduced at the end of fuel injection. On the contrary, in

case 1 the rate of air swirl is higher, the mixing energy can be kept for a longer period,

re-sulting in a higher mixing rate. This argument is supported by the experimental results that the temperature Tp in case I drops more rapidly than in case 2, as shown in Fig.10. This is also the reason why the NOx emission in case 1 is lower as compared with that incase 2.

IV. CONCLUSION

By inputting the basic engine experimental data such as the cylinder pressure, the fuel injection pressure etc., the present combustion model can be used to compute the combustion parameters including spray penetration, spray mixing rate, ROHR, rate of heat transfer and rate of NOx formation etc., and thereby to make quantitative analysis of the effects of engine design parameters on the combustion process. The model can be considered as an effective tool for analyzing the combustion process of a D. I. diesel engine.

The model of heat and mass transfer given in this paper proposes a new method for studying the incylinder heat and mass transfer problems in a D.I. diesel engine by using basic test data.

REFERENCE

G.A.Szekely, Jr. and A.C.Alkidas,

_{A TwoStage HeatRelease Model for Diesel}

Engines'

H.Hiroyasu, 'Diesel Combustion and Its Modeling' Proc. of International

Sympo-sium on D & M of Combustion in Reciprocating Engines. 1985.

13 -0

2.

I[1]

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F.P.Ricou and D.B.Spalding, 'Measurements of Entrainment by Axisymmerical

Turnbulent Jets', J.Fluid Mechanics, Vol.11.1961.

H.Hertel,"Stromungsvorgange beim Freien Hubstrahler", Luft Farttechnik, Vol. 8,1962.

Sitkei G. "Beitrag Zur Theorie des Warmeuberganges in Motor," Konstruk tion,

14(1962).

K.T. Rhee and S.L. Chang, 'Empirical Equations For Adiabatic Temperatures For

Some FuelAir Combustion System,' Combust. Sci & Tech, V44(1985), pp.75-88.

Air Zone (a)

14

fr7

Burning Zone (b)

Product Zone (p)

Fig. 1 Schematic diagram of thermodynamic zones

Air Zone

dm,

dO

Fig. 2 Schematic diagram of heat and mass transfer between zones

dm r

II! h

dm b din b

dO dO

dO

Mixing Zone Burning Zonc Products Zone

Spray dm hp dO dm II( dO

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100.0 , 0.04 0.02 500.0 400.0 ;-) 300.0 200.0 0.00 0.06 --20.0 0.0 New model

Single zone

model 10.o o(tA) 0.0

Fig. 4 Calculated accumulated ROHR for case 1 and 2

Fig. 5 Calculated spray

penetration s in cases 1 and 2

15-20.0

0.0 20.0 40.0 60.0 O(CA)

Fig. 3 Rate of heat release for case 2

-20.0 0.0 20.0 40.0 O(C A) 1 0 0.8 0.6 0.4 0.2 0.0

(17)

-16

0.80 -0.40 s. 8.0' 00 30.0 15.0

Fig. 7 Average equivalent ratio in spray mixing zone in case 1 and 2

115 0 300 45.0 -OR Al Surface - 2000r / min 1200r / min a(ms)

Fig. 8 Spray penetration s at differentengine speeds

Li 0160 it) "a 0.20 20.0 40.0 0 00 40 0 20.0 0.0 O(CA)

Fig. 6 Calculated rate of air entrainment in cases 1 and 2

00 1.0 2.0 4 0 0.60 0.40 0.00 4 12.00.20

(18)

0,1 2H00 0400 ',000 1600 1 20.00 0.00 20.00 40.00 60.00 .2 02 1 0.00 1600 12 00

two

4011 11 20.00 0.00 a=0 so(*CA)

Fig. 9 Effects of a on calculated Ti and Tp a = 0.5 a .= 20.00 40.00 60.00 00 1 1 0 20 30 40 50 GO p _Pa.)

Fig.10 Temperature of combustion, rate of NOx formation and NOx concentration versus crank angle

2. 9 3.3

Fig. 11 The relationship between turbulent mixing coefficient /3 and

equivalent pressure difference Lip;

(19)

-18

S-) 80 60 40 20 0 2000 1600 1200 800 400 -0 -40 -20 0 20 40 60 DR A)

Fig. 12 The relationship between turbulent mixing coefficient # and air swirl ratio

2800

2400