Development of a fast and simple simulation model for the fuel injection system of diesel engines

Advancer

in Engineering

Sojhvare

Pnnted

Vol.

1, pp. 13-28,

Development of a fast and simple simulation model for the fuel injection system of diesel engines D. T. Hountalas

& A. D. Kouremenos

Internal Combustion Engines Laboratory, Thermal Engineering Section, Mechanical Engineering Department, National Technical University of Athens, 42 Patission Street, Athens 106 82, Greece (Received 4 April

1996; revised 9 June 1997; accepted 15 July 1997)

The fuel injection system is one of the most important parameters for the operation of diesel engines. It controls the combustion mechanism in the engine cylinder and the mechanisms that lead to the formation of pollutants. A great deal of effort has been made up to now to simulate the operation of the fuel injection system, using complicated simulation models. These models require a great deal of computational time and the knowledge of precise engine geometrical data that usually are unknown. In the present work a new and simple algorithm is proposed for the simulation of fuel injection systems that is very fast, requiring little computational time and the least possible geometrical data. The proposed model aims to overcome the difficulties during field applications where it is impossible to know details of the geometry of the system and especially about the delivery valve and the injector. The algorithm is written in FORTRAN-77 language and provides the fuel injection rate and the conditions at the nozzle exit with reasonable accuracy. The method is applied to a high speed direct injection diesel engine and the results are compared with experimental data. Furthermore, in order to validate the proposed model against other detailed models, a comparison is given between the present model and a detailed simulation model developed by the present research group. From this comparison, a good accuracy of the model is revealed when compared against experimental data and the predictions of the previous detailed model, despite its simplicity. 0 1998 Elsevier Science Ltd. Key words: diesel engine, fuel injection system, simulation.

NOTATION

k Cd D f” Kt 1’ N P

Q t u V x Z

Greek letters Area of pipe cross-section (m’) Discharge coefficient Diameter of connecting pipe (m) You&s modulus of elasticity of pipe metal (N m-‘) Friction coefficient for fuel flow Bulk modulus of compressibility of fuel (N rnm2) Connecting pipe length (m) _ Number of divisions on connecting pipe Pressure (N mb2) Volumetric flow rate (m3 s-‘) Time coordinate (s) Speed of liquid fuel (m s-‘) Volume (m ) Space coordinate along pipe (m) Frictisnal pressure in fuel flow (N m-‘)

Speed of sound (m s-l) Pressure difference across an orifice (N me2) Connecting pipe wall thickness (m) Fuel density (kg mm3) Subscripts ifi C

CYl f 13

1998

0965~9~78/98/$19.00+0.00

PIl:SO965-9978(97)00042-2

ELSEVIER

29, No.

0 1998 Elsevier Science Ltd in Great Britain. All tights reserved

Refers to point A Refers to point B Refers to point C Cylinder Fuel

14 . inj t valv

D. T. Hountalas, A. D. Kouremenos Injector Total Valve

1 INTRODUCTION Simulation models are widely used in the field of reciprocating internal combustion engines for engine development and for the understanding of the mechanisms affecting their operation and the formation of pollutants.1-9 One of the most important subsystems of the diesel engine is the fuel injection system, since its operation affects greatly the combustion mechanism and the formation of pollutants in the engine cylinder. 1,2~s*9A number of simulation models have been reported in the literature for the operation of the fuel injection system.1°-17 These models are usually complicated, require high computational time and the knowledge of geometrical details that are usually not available. The only accurate approach is to model each subsystem of the fuel injection system separately, and subsequently to combine them in a pertinent way into the entire system.17 Starting with the work of De Juhasz,” who used graphical water hammer concepts to provide a simplified linear model, a few works dealing with this subject are reported in the literature, making an effort to deal with the problem in a fairly advanced way.12-16 At first Giffen and Rowe12 theoretically solved the equations representing the operation of the injection system, taking into account the effect of pressure waves in the delivery pipeline and the capacity effects of the volumes concentrated in the pump and nozzle parts. They handled the differential equations by putting them in a finite difference form and finding an algebraic expression for the solution. This method of solution was limited to simple injection models because of the high time required for the mathematical solution. Knight13 tried to introduce the effect of viscous friction and cavitation in the delivery pipeline using a digital computer, but he made some rather unsophisticated assumptions and simplifications to reach a simple solution of differential equations describing the system operation. The work of Brown and McCallion14 moved over similar lines, with a more detailed representation of the injector and the pump. Wylie et a1.l5 have gone a step further by examining each component of the fuel injection system in detail. Also, Matsuoka et a1.16717modelled the fuel injection system by the use of a simulator for comparison between calculated and experimental results. The greatest difficulty when using advanced simulation models” exists in the description of the operation of the delivery valve and the injector needle, because details are required for their geometry and the discharge coefficients of the various passages which for practical applications are usually not available. Usually, simulation models for the operation of diesel engines avoid using fuel injection system models due to

their complexity, high calculation time and the complex geometry of the delivery valve and the nozzle. Instead, they prefer to use a constant injection pressure profile that differs seriously from reality. Because of this they are unable to take into account the effect of operating conditions such as speed and load on the injection profile, thus introducing an error that does not allow us to make accurate predictions. The method introduced in the present work offers a solution to this problem by proposing a simple fuel injection system simulation model with very low computational time. The problem of simulating the delivery valve and the injector is solved in a satisfactory way, avoiding the need for introducing their detailed geometry and data. The results obtained are satisfactory and compare quite well with experimental measurements and with the predictions of a sophisticated model”, offering to the engineer a fast and reasonably accurate tool to describe the operation of the fuel injection system.

2 DESCRIPTION

OF THE MODEL

2.1 Control volumes considered The main purpose of the proposed model is to examine the behaviour of the fuel injection system and to predict the effect of engine operation parameters (i.e. speed and load) upon it. The following control volumes are considered”, pertaining to a DI (direct injection) engine: (i) High pressure pump chamber (ii) Delivery valve chamber (iii) Delivery tube from pump to injector (iv) Injector At each instant of time the pressure (history) inside the previous control volumes is obtained. This allows the computation of the injection profile. The fuel is considered to be compressible16 with a bulk modulus of compressibility given by the following expression:10,18

(1) All elastic deformations of solid parts of the system, due to pressure changes, are neglected. The foregoing assumptions yield a pressure-dependent wave propagation velocity which is a function of fluid compressibility only. The error in wave propagation velocity, as a result of neglecting pipeline deformation, is less then 5% for the maximum pressure variation as reported by various researchers. 15-17 In Fig. 1 a schematic form of the fuel injection system layout is presented. In this figure, one can see the volumes considered 0’ = 1,2,3,4) for the system simulation, each

Simulation model for diesel engine fuel injection system

15

equation describesthe operation of the valve: 1 Pump

2 Delivery

Qvalv

Valve Fuel Pipe 4 Injector

3

one taken as a separatecontrol volume. In this figure ‘1’ standsfor the pump chamber, ‘2’ for the delivery valve, ‘3’ for the connecting pipe and ‘4’ for the injector.

valve

As mentioned above, the fuel is considered to be compressible, with a compressibility defined by the following relation:

Kf+j

Qflow

for kow > 0

CL = 0 for C?flow < 0

Fig. 1. Fuel injection system layout.

2.2 Simulation of pump chamber-delivery chamber-injector

=

(2) J

where Pj is the correspondingcontrol volume pressureand rate Vj its instantaneous volume. The volumetric flow through orifices, various openings or ports is given by the formula

where j is the corresponding volume. The simulation of each control volume is accomplished by considering eqn (2) and the incoming and outgoing volume flow rates, eqn (3), thus obtaining the following relation:

where Qtj = CQj is the total net volume flow rate into the control volume, and dV!dt is the rate of its volume change. For the estimation of Aj the corresponding geometry is taken into account, while the volume flow rate Qj is given by relation (3). For the fuel pump, the rate of volume change is obtained from the motion of the piston which is driven by the fuel injection system cam. As already stated, the modelling of the delivery valve is accomplishedin a fairly simpleway, comparedto a previous detailed model developed by the authors”, by considering it as a check valve allowing the flow to take place only from the pump ch,amberto the fuel pipeline. The following

Using this method, we avoid introducing additional data concerning the valve itself and its spring. The pressure in the valve chamber is obtained from eqn (4), where dVddt = 0 and Qt2 = Q1* + Q2sis the net volume flow rate of fuel from the valve chamber. The term Q12 is obtained from eqn (3), where AP = AP,z is the pressure difference between the pump and valve chamberswhile Q23 is the volume flow rate of fuel between the valve chamber and the connecting pipeline. As shown later on by comparing the predictions of the current model with experimental data and with the predictions of a detailed sophisticatedmodel”, the error caused by neglecting the effect of the valve motion is small andthis enablesus to make a good prediction of the pressurehistory inside the volume. In a previous, more sophisticated model developed by the authors” the fuel injector was modelled in a detailed way by considering the needle motion and two control volumes in it. In the present work a simpler method is used which requires only the injector opening pressure and the nozzle hole area. The injector is considered as a control volume at the end of the pipe, having a flow area equal to that of the nozzle holes. Fuel flows out of the control volume into the engine cylinder when the following condition is satisfied:

otherwise the flow rate of fuel is set equal to zero. The massflow rate of fuel is obtained through eqn (3) whereasthe instantaneouspressureis obtained by integrating eqn (4). As in the delivery valve, the needle motion is neglected, thus resulting in dVJdt = 0. The total volume flow rate of fuel into the injector volume is Qt4 = Q43 + Q 4,+ where Qd3 is the volume flow rate between the injector and the connecting pipe and Q+ CYlis the fuel injection rate into the cylinder obtained via relation (3), in which AP representsthe pressuredifference between the injector and the engine cylinder.

2.3 Calculation pipeline

of pressure inside the connecting

The estimation of pressurein the previous control volumes is a relatively simple task when comparedto the problem of estimating the pressurein the connecting pipeline. To solve the unsteady flow equationsinside the tube, useis made of the two basic principles of masscontinuity and momentum conservation, 60th expressedin differential form. 10*17*18 The connecting pipeline is considered to be flexible, having a deformation rate (dAldt), due to the fuel pressureforces

16

D. T. Hountalas. A. D. Kouremenos

acting upon it, given by the expression:“*”

2At

GAW at

+ GAu)

ax

dx=o

w 0

=

o

x(m)

computational grid.

mass continuity equation is obtained (where p = const. for an incompressible fluid):

aP dt+po!2~=o

takes the form

1aA lap --+--+;i;=O A at p at

au

(8)

The fluid (fuel) momentum equation, neglecting convective acceleration terms, reads (9) The frictional pressure Z is taken to be a function of speed raised to the second power”, as follows:

Z=fpC

(10)

so that eqn (9) takes the final form, with consideration of the flow direction:

au lap -$- iil*+fg=O

(11)

Taking into consideration eqns (4) and (5) and the following relation, which results from the condition of constant mass,

1av v ax

we obtain the next expression eqn (8):

(15)

Thus one ends up with a system of two partial differential equations, (11) and (15), for the pressure P and the flow velocity u inside the connecting pipe, with independent variables x, t. The problem is then converted to the integration of eqns (11) and (15) with respect to pressure P and velocity u inside the connecting pipeline, simultaneously with eqns (3) and (4), at both ends of the pipe, which constitute its boundary conditions. The hyperbolic partial differential eqns (11) and (15) are transformed, using the method of charactetistics,10,19 into two ordinary differential equations with respect to time (only), each of which is integrated along a particular characteristic line. When these equations are placed into finite difference form, by a first-order approximation of integration, they become

Ax=x,

P at

B

(7)

ax

1ap

A

Fig. 2. Spac&me

(6)

which after the appropriate simplification GA)

C

At

where E is taken from Streeter and Wylie.” The mass continuity equation reads

(12) for the mass continuity

(13) The speed of sound is given by the following

equation: “J

-xX,=craAt

~(&-&)+Axf$, A Ax=x,-x,,=c+,At

PC- =Pb+

so that, according to eqn (13), the final expression for the

(17)

where Q = Au and C(x,, tc) is the point for which the pressure and local flow velocity are determined on the basis of the known values for points A(x,, ta) and B(x~, tb) along the pipe at positions x, and xb, respectively. To solve the unsteady flow problem in the connecting pipe, a space-time grid is considered on an x-t plane, which is defined as shown in Fig. 2. Therefore the pipe is divided into N sections equal in length: N = NAx with Ax = aAt

(14)

(16)

(18)

where At is the corresponding time step used to integrate the previous finite difference equations. The number of elements N depends on the pipe length and the calculation accuracy required.”

17

Simulation model for diesel engine fuel injection system Table Il. Fuel injection systemdata Plungerdiameter Plungerstrok.e Pipeinternaldiameter Pipeexternaldiameter Pipelength Injector openingholes Numberof injectorholes Diameterof injector hole

7mm 13mm 1.5mm 6mm 0.45m 250bar 3 0.235 mm

For the solution of differential eqn (4) for the pump chamber, the delivery v,alve and the injector control volumes, a predictor-corrector method is applied.“,‘s The predictorcorrector method has been found to be suitable for such calculations, becauseit makes use of system responseat earlier times, requiring information from the pipeline during the step change. This information is available through the characteristics eqns (16) and (17). The integration procedure initiates from the pump chamber and continues with the space-time grid x-t on the connecting pipeline, terminating at the injector. The boundary conditions at both ends of the pipe are obtained by combining eqns (16) and (17) with eqns(3) and (4).

3 COMPUTER

I’ROGRAM

OUTLINE

To initiate the calc:ulations,all engine parameters,i.e. load, expressedby the effective pump stroke and speed,are fed into the program. The entire injection system geometry is supplied and the plunger displacement, as a function of crank angle, is determined from the cam geometry. The plunger geometry is precisely determined to account for its helix, which communicatesat the end of injection with the spill port located on the pump barrel. The program is written in FORTRAN-77 language and executed on an IBM-486 compatible personal computer. The time required for the calculation of an entire injection cycle is about 4 s,a very low value for this kind of problem.16 When the calculation commencesan additional unknown exists, the residual pressureinside the connecting pipeline. Its value is measuredin the presentanalysis using a piezoresistive transduce:rcapableof measuringabsolutepressure values.“*i5 The theoretical value is obtainedby assumingan initial value at the beginning of the cycle. The calculated value at the end of the cycle serves as a new guessfor the next cycle, and so on.*‘,*’ The procedure continuesuntil the two values, calculated and assumed in two successive cycles, differ by a value less than 0.5%. The measured residual pressurevalue may also serve as an initial guess for the calculation. A listing of the simulation model is given in Appendix A. The required input data are shown in Appendix B whereas the corresponding output is given in Appendix C. The fuel pump piston lift, which is determinedfrom the cam geometry, is given to the program as data.

0 0

100

25

125

Fig. 3. Measuredpressuretracescomparedto calculatedones obtained from the proposedmodel and a detailed one at 1500rpm and 100%load.

4 VALIDATION

OF THE MODEL

To validate the model, a comparisonis given in the present work between the results obtained from the simulation model and the onesobtained from an experimental investigation conducted in the R&D laboratories of Lister and Petter on an ALPHA series,direct injection diesel engine. The basic data of the fuel injection system are given in Table 1. Furthermore, in order to validate the model against existing sophisticated models, a comparison is given between the newly developed fast and simple model and a detailed one developed by the presentresearchgroup.” During the experimental investigation measurements were taken from the fuel injection system of cylinder No. 1, using a piezoresistive transducer located approximately 5 mm before the injector. The pressure diagram was obtained using a fast data sampling system,developed

400 Speed : 2000 tpm Load : 10096

0

25

loo

125

Fig. 4. Measuredpressuretracescomparedto calculatedones obtained from the proposedmodel and a detailed one at 2000rpm and 100%load.

18

D. T. Hountalas, A. D. Kouremenos Speed : 3000 pm Load : 100%

Engine Load : 50%

0

0 0

25

100 AN2LE

125

0

5

10

15

20

25

30

35

40

ANGLE (DEG)

(DZG)

Fig. 5. Measuredpressuretracescomparedto calculatedones obtained from the proposedmodel and a detailed one at 3000rpm and 100%load.

Fig. 7. Calculatedpressure tracesin the fuel pumpchamberfrom the proposedmodel and a detailed one at 1500, 2000 and 3000rpm speedat 50% load.

by the presentresearchgroup, using a time step equivalent to 1” CA. Measurements were taken at three different speedsof 1500, 2000 and 3000 rpm, and at two different loads corresponding to 100% and 50% of full load. The fuel consumption was measured using standard test bed instrumentation. Fig. 3 showsthe comparisonbetween the calculated and experimental pressure traces in the connecting pipeline, at the measuringpoint located 5 mm before the injector at 1500rpm and 100% of full load. In the samefigure is also given the comparison of the pressure trace calculated from the present simple model with the one predicted by the detailed simulation model mentioned above.” As is shown, the coincidence between calculated and measured data is very good. The pressuretrace obtained using the proposed model is close to the one obtained from the detailed one, a small difference existing only in the

prediction of the absolutevalues of the pressureoscillations in the fuel pipe. The frequency of these oscillations is predicted quite accurately by both models. Similar results were obtained at 50% of full load but, due to lack of space, only the results for 100% are given in the present case and for the other operating speedsexamined as well. Similar results are observed in Fig. 4 where the comparison between the calculated and experimental pressure traces at a speed of 2000 rpm and 100% of full load are shown. The entire pressurediagram is predicted with good accuracy for both load conditions examined but here, as mentioned above, only the results for 100% load are given. The pressuretraces predicted by the proposed model are close to the ones obtained from the detailed simulation model. The difference observed after the end of injection in the pressureoscillations insidethe connecting pipe is due to the action of the delivery valve which, in the

700 Enghe

600

Load 100%

is? Q

500 m 2; 400 Lbtaited

5v) 300

Mode/

2 w 200 a 100 0 0

5

10

15

20

25

30

35

40

ANGLE (DEG) Fig. 6. Calculatedpressure pressure tracesin the fuel pumpchamber from the proposed modelanda detailedoneat 1500,200Oand 3000rpm speedat 100%load.

7500

1750

2000

2250

2500

2750

3000

ENGINE SPEED (RPM) Fig. 8. Comparisonof measuredand calculatedpipe residual pressures obtainedfrom the proposedmodeland a detailedone asa function of enginespeedat 100%and50% load.

Simulation model for diesel engine fuel injection system 2.4 2,2 r^ 2.0 g 1.8 p 1.8 d 1.4 (3 1.2 5 7.0 d 0.8 2 0.6 0.4 0.2L--7-----~ 1500 17’50

G 4.0 aJ zm 3.5 g aY. IY z 0 t; Lu 2 irf 2000

2250

I 2500

1 27~~00

ENGINE SPEED (RPM) Fig. 9. Comparisonbetweenmeasuredand calculatedfuelling

ratesvs speedcurves obtainedfrom the proposedmodel and a detailedoneat 100%and50% load. current model, is simulatedin a very simple way. But in any case the values obtained from the proposed simple model are closeto the onesobtained from the detailed one, proving its validity. An increase of absolute pressure values and residual pressure in the pipe is revealed, compared to the corresponding 1500rpm case. In Fig. 5 are given the results obtained at 3000 rpm operating speedand 100% of full load. The absolutepressure values are increasedas well as the residual pressure. The coincidence between calculated and experimental values is good, r’evealing the accuracy of the developed simulation model. The pressuretrace predicted by the proposed model is close to the one obtained from the detailed model, especially during the main injection period. Figures 6 and 7 show the comparisonbetween the calculated pressuretraces in the pump chamber when using the proposed simple model and the detailed one at 100% and 50% load respectively for all engine speedsexamined. As is observed, the fuel pump chamber pressureincreasesconsiderably with engine speedand load. The pump chamber pressureis considerably higher then the pressureat the measuring point just before the injector. The pressurevalues obtained from thseproposed simple model compare well with those obtained from the detailed model for all test casesconsidered. The only difference observed is during the initial stageof pressurerise, where a temporary pressure drop is predicted from the detailed model. This pressure drop is due to the volume increase caused by the lift of the delivery valve but, as shown above, it does not have a strong effect on the pressurediagram inside the fuel pipe. The effect of engine speedon the residual pressurein the connecting pipeline, for both load conditions examined, is presentedin Fig. 8. The comparisonbetween the calculated and experimental values reveals a good coincidence. As is shown, there is in general an increaseof residual pressure with speed and load. The absolute values obtained from both models, the proposed simple one and the detailed

1

Load

19

100%

Prwosed Mo6e

3.0 2.5 2.0 1.5 7.0 0.5

I? 0.0 0

5

IO

15

20

25

30

35

40

ANGLE (DEG) Fig. 10. Calculatedfuel massinjection ratesobtainedfrom the

proposedmodeland a detailedone for 1500,2000and3000rpm speedand 100%load. one, are very close, verifying the validity of the newly developed model. The comparison between the calculated and experimentally determinedfuelling rate of the pump, for all engine speedsand loads examined, is given in Fig. 9. The coincidence between calculated and experimental values is good, verifying the accuracy of the simulation model. The values obtained from the proposedmodel and the detailed one are practically the samefor all test conditions examined. Finally, Fig. 10 showsthe comparisonbetween the calculated fuel massinjection rates obtained when usingthe proposedmodel and the detailed one at 100%of full load and at all engine speedsexamined. As is observed, the massflow rate expressedin mg deg-’ decreaseswith increasingengine speedsince the increasein absolute pressurevalues at the injector cannot compensatethe decreaseof available time. The injection rates obtained from the proposed model are quite similar to the onesobtained from the detailed model, even though they are somewhatsmoother.The higher oscillations in injection rate observed in the caseof the detailed model are due to the effect of the injector needle motion on the injector volume and available flow area. From the results provided in the previous graphs it is obvious that the newly proposedsimulation model is quite accurate and that its predictions are comparable to those obtained from detailed simulation models that require high computational time and a great deal of data for their operation.

5 CONCLUSIONS A simple simulation model for the fuel injection system of diesel engines has been developed that can be easily incorporated in existing engine simulation codes. The model requires the least possible geometrical data, it is simple and requires very low computational time-about

20

D. T. Hountalas.

4 s per engine stroke. It can be usedto study the effect of various parametersaffecting the fuel injection mechanism such asspeedand load. It can alsobe usedfor the development of new fuel injection systemsfor diesel enginesand for the better understandingof the fuel injection process. To validate the model, an experimental investigation has been conducted on a high speed direct injection diesel engine at various operating conditions. Comparison of the measuredpressuretraces with those calculated from the simulation model reveals a good coincidence. The model predicts with reasonableaccuracy the performance of the fuel injection systemand provides the fuel massflow rate from the injector accurately. To validate the proposedfast and simple fuel injection system simulation model against existing sophisticated models, a comparisonhas been given in the present work between values obtained from the current model and a detailed one developed by the present researchgroup. As is revealed, the values obtained from both modelsare almost the same, showing the validity of the newly proposed simple model. This is especially important if we take into account the very low computational time required by the proposedmodel, which is in the order of 4-5 s for a complete run while in the caseof the detailed model this time increasesto about 5-10 min, depending on the operating conditions (speedand load). Due to its simplicity and low computational time the proposed simulation model can be used as a design tool for the development of new fuel injection systems,offering the ability to reduce the time and thus the cost of development.

REFERENCES 1. Patterson, D. J. and Henein, N. A., Emissions from Combustion Engines and their Control. Ann Arbor Science, Ann Arbor, 1972. 2. Obert, E. F., Internal Combustion Engines-Air Pollution. Intext, New York, 1973. 3. Benson, R. S. and Whitehouse, N. D., Internal Combustion Engines. Pergamon Press, Oxford, 1979.

A. D. Kouremenos 4. Ferguson, C. R., Internal Combustion Engines. Wiley, New York, 1986. 5. Heywood, J. B., Internal Combustion Engine Fundamentals. McGraw-Hill, New York, 1988. 6. Kouremenos, D. A. and Rakopoulos, C. D. The operation of a turbulence chamber diesel engine, with LPG fumigation, for exhaust emissions control. VDI Forsch. Ing.- Wesens., 1986, 52, 185. 7. Needham, J. R., Doyle, D. M., Faulkner, S. A. and Freeman, H. D., Technology for 1994. SAE Paper 891949, 1989. 8. Stevens, J. L. and Taylor, A. J. F., The design and development of a new range of small industrial diesel engines. SAE Paper 901569, 1990. 9. Kouremenos, D. A., Rakopoulos, C. D., Yfantis, E. A. and Hountalas, D. T. An experimental investigation of fuel injection pressure and engine-speed effects on the performance and emission characteristics of a divided-chamber diesel engine. Energy Rex, 1993, 17, 315-326. 10. Kouremenos, D. A., Rakopoulos, C. D., Hountalas, D. T. and Kotsiopoulos, P. N., A simulation technique for the fuel injection system of diesel engines. Proc. ASME-WA Meeting, Atlanta, Georgia, AES, 1991, pp. 91-102. 11. De Juhasz, K. J., Phenomena in linear flow. .I. Franklin Inst., 1937, 233, 463, 643, 751. 12. Giffen, E. and Rowe, W. Pressure calculations for oil engine fuel-injection systems. Proc. Inst. Mech. Eng., 1939, 141, 519. 13. Knight, B. E., Fuel injection system calculations. Proc. Inst. Mech. Eng. (A.D.), 1960-61, 1. 14. Brown, G. W. and McCallion, H. Simulation of an injection system with delivery pipe cavitation using a digital computer. Proc. Inst. Mech. Eng., 1967, 182, 206. 15. Wylie, E. B., Bolt, J. A. and El-Erian, M. F., Diesel fuel injection system simulation and experimental correlation. SAE Paper 710569, 1976. 16. Matsuoka, S., Yokota, K., Kamimoto, T. and Igoshi, M., A study of fuel injection systems in diesel engines, Part I. SAE Paper 760 550, 1976. 17. Matsuoka, S.,Yokota, K., Kamimoto, T. and Igoshi, M., A study of fuel injection systems in diesel engines, Part II. SAE Paper 760551, 1976. 18. Streeter, V. L. and Wylie, E. B., Fluid Mechanics. McGraw-Hill, New York, 1979. 19. Watson, N. and Janota, M. S., Turbocharging the Internal Combustion Engine. MacMillan Press, London, 1982. 20. Beck, J. V. and Arnold, K. J., Parameters Estimation in Engineering and Science. Wiley, New York, 1977. 21. Sage, A. R. and Melsa, J. I., System Identijcation. Academic Press, New York, 1971.

Simulation model for diesel engine fuel injection system APPENDIX

A: PROGRAM

LISTING

c _______________-____-----..-----------PROGRAM FUEL

DIMENSION PPINJ(400),PPUMP(400),PPT~NS(400),X(36~),DM~NJ(400)~ + ANGX(400).P(400.2),Q(400,2).THETOP(2),THETBP(2), + PPINJ0(400),DMINJ0(400) c ______________-- _______-- ._ COMMON/ ARPii /PI COMMON/ SOLIJD /ASTEP,ACCUR COMMON/ WORK /X c ____________________-----.- FUEL PUMP PISTON LIFT DATA (in mm)-------DATA (X(I),I=l,360)/ +.oo. .oo, .oo, .Ol, .Ol, .02, .03, .04, .05, .07, +.08, .lO, .12, .14, .17, .19, ‘.22, .24, .27, .31, +.34, ,379 .41( .45. .49, 53. 58, .63, .67, .72, +.78, ,838 .89, .94, 1.01, 1.07, 1.13, 1.20, 1.27, 1.34, +1.41, 1.49, 1.57, 1.65, 1.73, 1.81, 1.90, 1.99, 2.08, 2.18, +2.27, 2.37, 2.48, 2.58. 2.69, 2.80, 2.92, 3.03, 3.15. 3.28, +3.40, 3.53, 3.67, 3.80, 3.94, 4.09, 4.23, 4.38.4.54, 4.69, +4.86, 5.02, 5.19, 5.37, 5.55, 5.73, 5.92,6.11,6.31, 6.51, +6.72.6.93, 7.14, 7.34, 7.54, 7.74, 7.93, 8.12, 8.30, 8.48, +8.66, 8.83, 9.00, 9.17, 9.33, 9.49, 9.64, 9.80. 9.94,10.09, +10.23,10.37,10.50,10.63,10.76,10.88,11.00,11.12,11.23,11.34, +11.44,11.55,11.64,11,74,11.83,11.92,12.00,12.09,12.16,12.24, +12.31,12.38.12.44,12.50,12.56,12.61,12.66,12.71~~2.75~~2.79, +12.83,12.86,12.89,12.92,12.94,12.96,12.97,12.98,12.99,13.00, +13.00,13.00,13.00,13.00,13.00,13.00,13.00,13.00,13.00,13.00, +13.00,13.00,13.00,13.00,13.00,13.00,13.00,13.00,13.00,13.00, +13.00,13.00,13.00,13.00,13.00,13.00,13.00,13.00,13.00,13.00, +13.00,13.00.13.00,13.00,13.00,13.00,13.00,13.00,13.00,13.00, +~3.00.~3.00.12.99,12.98,12.97,12.96,12.94,12.92,12.89,12.86, +12.83.~2.79.12.75,~2.7~,12.66,12.61,12.56,12.50,12.44,12.38, +12.3~,~2.24,12.16,12.09,12.00,11,92,11.83,11.74,11.64,11.55, +11.44,~~.34~~~.23.11.12,11.00,10.88,10.76,10.63,10.50,10.37, +10.23,10.09, 9.04, 9.80, 9.64, 9.49, 9.33, 9.17, 9.00, 8.83, +8.66, 8.48s8.30, 8.12, 7.93, 7.74, 7.54, 7.34. 7.14, 6.93, +6.72, 6.51,6.3’1.6.11, 5.92, 5.73, 5.55, 5.37, 5.19, 5.02, +4.86,4.69,4.54.4.38,4.23,4.09, 3.94, 3.80, 3.67, 3.53, +3.40, 3.28, 3.15, 3.03, 2.92, 2.80, 2.69, 2.58, 2.48, 2.37, +2.27,2.18,2.06, 1.99, 1.90, 1.81, 1.73, 1.65, 1.57, 1.49, +1.41, 1.34, 1.27, 1.20, 1.13, 1.07, 1.01. .94, .89, .83, +.78, ‘72, .67, .63, .58, .53, .49, .45, .41, .37, +.34, .31, .27, .24. .22, .19, .17, .14, .12, .10, +.08, .07, .05, .04, .03, .02, .Ol, .Ol, .OO, .OO, +.oo. .oo, .oo, .oo. .oo, .oo, .oo, .oo, .oo, .oo. +.oo, Do. .oo, .oo, .oo, .oo, .oo. .oo, .oo, .oo. +.oo. .w, .oo, .oo, .oo, .oo, .oo, .oo, .oo, .oo, +.oo, Do, .oo, .oo, .oo. .oo, .oo, .oo, .oo, .oo/ DO 1 1=1,360 X(I)=X(I)‘l .E-3 1 CONTINUE C------I-----------I________________________________ OPEN(1 ,FILE=‘FUEL.DAT’,STATUS=‘OLD’) READ(l,‘3 IREMAIN,PREM.PTANK.POPENl READ(l,‘? ASTEP,ILIM,ACCUR,ITRMAX,IPRINT,~NJRES READ(1,“) DPUMP,SVCP,S

21

D. T. Hountalas,

22

READ(l,y DHOLEP,CDHOLEP,NHOLEP,XO,VINO READ(l,*) XEFF READ(1,“) PIPEL.DPIPE,FCOEFP,XMEAS READ(l,y DINJP,CDINJP.NHOLEI READ(1 ,3 IVALV READ(l,y RPM,NTYPE,DENSF,PMIN,DVALV,CDVALV,VOLVALV,POPEV.ACCURREM CLOSE(l) C- ---- ------_----_---_---___I Pl=3.1415926 ANGBEG=60 ANGEND=l50 RELP=l CFl P=5 CF2P=-3 IF(INJRES.EQ.1) THEN OPEN(6,FILE=‘PRESDAT’) ENDIF ISTOP=O IF(IREMAIN.EQ.0) ISTOP=l RPM6=6:RPM APUMP=PI’DPUMP’-2/4. AHOLE=PI’DHOLEP”2/4. AHOLEO=AHOLE APIPE=PI’DPIPE*2/4. AVALV=PI*DVALV?!l4. C----FUEL INJECTOR FLOW AREA AREAH=PI’DINJP’-2/4.‘FLOAT(NHOLEI)

-----

C----INITIAL VALUES----VPUMPO=S*APUMP FBM=l.2’1 .E09 ITER=O ICAV=O ACURV=Pl/4. C-----ESTIMATION OF GRID POINTS ON CONNECTING SOUND=SQRT(l .BEOS/DENSF) B=SOUND*DENSF/APIPE DEGT=RPMGPIPEL/SOUND NPOlNT=lNT(DEGT/ASTEP) DIFF=DEGT/ASTEP-FLOAT(NPOlNT) IF(DIFF.GE.0.5) NP~INT=NPO~NT+I NEND=NPOINT+l DX=PlPEUFLOAT(NPOlNT) DT=DX/SOUND NMEAS=XMEAs/Dx IF(NMEAS.EQ.0) NMEAS=l lF(NMEAS.GT.NEND) NMEAS=NEND FRlCT=FCOEFP’DX*DENSF1(2.‘DPlPE*APlPE~2) ASTEP=RPMG*DT IXEFF=O IROUND=O 10 CONTINUE C---lNlTlALlZATlON ITER=ITER+l ANGRATE=O.O IBEGIN=O CORRECT=0

OF VALUES

FOR

ITERATION

PIPELINE

CYCLES

--------

A. D. Kouremenos

Simulation model for diesel engine fuel injection system DMCORR=O DMFUEL=O AMINJT=O SUM=0 ICOUNT=O ANG=O ANCAM=O QPIPE=O DO 12 I=1,400 DMINJO(I)=O.O DMINJ(I)=O.O PPTRANSIIj=O PPINJ(I)=O% PPUMP(I)=O.O ANGX(I)=O.O 12 CONTINUE IPUMP=l PREMO=PREM JO=1 J=l X1=X(l) PIN=PREM’l .EC6 PUMP=PTANK ANGX(l)=O.O PPUMP(l)=PUMP’l .E-05 PPINJ(l)=PREM PPTRANSll\=PREM PVALV=PtiiM*l .E5 DO 15 I=1 .NEND Q(l.2)=0.0 P(I.P)=PREM*‘I .EOS 15 CONTINUE C-----FUEL INJECTION SYSTEM SIMULATION DO 110 1=1,500000 ANCAM=ANCAM+ASTEP IDX=INT(ANCAM)+l DXPIST=X(IDX+l)-X(IDX) IF(X1 .LE.XO) THEN X1 =X1 +DXPIST’ASTEP GOT0110 ENDIF 20 CONTINUE ANG=ANG+ASTEP IF(IPUMP.EQ.1) THEN IF(IVALV.NE.l) THEN lF((X1/(XO+XEFF).GE.1.AND.PUMP.LE.(1.5’PTANK)).OR. + (DXPIST.LE.0)) IPUMP=O ELSE IF(XlI(XO+XEFF).GE.l.AND.PUMP.LE.2*PTANK) IF(IPUMP.EQ.0) PUMP=PTANK ENDIF ENDIF

--------------------

IPUMP=O

23

24

D. T. Hountalas,

A. D. Kouremenos

C-----SOLUTION OF DIFFERENTIAL EQUATIONS FOR PUMP CHAMBER------AHOLE=O.O CHECK1 =I .O CHECK2=1 .O PUMPO=PUMP PVALVO=PVALV DO 40 II=1 ,ILIM C _____ESTIMATION OF PORT FLOW AREA _-_____________________ IF(IPUMP.EQ.1) THEN IF(II.EQ.2) Xl=Xl+DXPIST*ASTEP IF(X1 .GE.(XO-DHOLEP).AND.Xl .LE.XO) ANGLE=2.*ACOS((XO-DHOLEP/2.+ Xl)‘P.IDHOLEP) lF((XO-DHOLEP/2.).LT.X1) ANGLE=P.‘PI-ANGLE IF(X1 .GE.(XO-DHOLEP).AND.Xl .LE.XO) AHOLE=DHOLEP*r.*(ANGLE+ SIN(ANGLE))/8. IF(X1 .LE.(XO-DHOLEP/2.)) AHOLE=AHOLEO-AHOLE IF(X1 .GT.XO.AND.Xl .LE.(XO+XEFF)) AHOLE=O.O . IF(X1 .GT.(XO+XEFF).AND.Xl .LE.(XO+XEFF+DHOLEP/COS(ACURV))) + ANGLE=2.‘ACOS((DHOLEP-2.*~l-XO-XEFF)’COS(ACURV))/DHOLEP) IF(X1 .GE.(DHOLEP/(2.‘COS(ACURV))+XEFF+XO)) ANGLE=P.‘PI-ANGLE IF(X1 .GT.(XO+XEFF).AND.Xl .LE.(XO+XEFF+DHOLEP/COS(ACURV))) + AHOLE=DHOLEP*P.*(ANGLE-SIN(ANGLE))/8. IF(X1 .GE.(DHOLEP/(2.%OS(ACURV))+XEFF+XO)) AHOLE=AHOLEO-AHOLE IF(X1 .GT.(XO+XEFF+DHOLEP/COS(ACURV))) AHOLE=AHOLEO IF(NHOLEP.EQ.0) NHOLEl=l IF(NHOLEPkT.0) NHOLEI =NHOLEP QHOLE=CDHOLEP’NHOLE~*AHOLE’SQRT(ABS(2.’(PUMP-PTANK)/ + DENSF))/RPMG IF(RELP.GT.0) CALL RELAX(QHOLE,CFIP,CFZP,PUMP,PTANK) QPIST=DXPIST*APUMP C-----PUMP

CHAMBER

PRESSURE

ESTIMATION

--______________________________

FBMl=FBM*(l .+PUMP*l .E-08) VOLPUMP=VPUMPO-Xl *APUMP DPPUMP=FBMl*(QPlST-QHOLE-QVALV)A/OLPUMP IF(II.EQ.1) DPPUMPO=DPPUMP CALL SOLU(PUMPO,PUMPl ,PUMP,DPPUMPO,DPPUMP,CHECKl PUMP=(PUMP+PUMP1)/2. IF(PUMP.LT.PTANK) PUMP=PTANK ENDIF

,II)

C-----ESTIMATION OF FUEL FLOW RATE THROUGH THE DELIVERY VALVE---------lF(lvALV.EQ.l) THEN THEN IWPUMP-PvALv).GT.o).oR.(PVALV-PuMP).GE.PoPEw APVALV=AVALV ELSE APVALV=O ENDIF QVALV=CDVALV*APVALV.SQRT(2.*ABS(PUMP-PVAL~/DENSF)/RPM6 IF(RELP.GT.0) CALL RELAX(QVALV,CFlP,CFPP,PUMP,PVALV) IF(PVALV.GT.PUMP) QVALV=-QVALV C----DELIVERY VALVE CONTROL VOLUME PRESSURE ESTIMATION-------FBMI =FBM*(l .+PVALV’l .E-08) DPPVALV=FBMl’(QVALV-QPlPE)/VOLVALV IF(II.EQ.1) DPPVALVO=DPPVALV CALL SOLU(PVALVO,PVALVl,PVALV,DPPVALVO,DPPVALV,CHECK2,II) ENDIF

Simulation model for diesel engine fuel injection system C-----BOUNDARY CONDITIONS AT THE PUMPIF(II.EQ.1) CN=P(2,1)-Q(2,l)*(B-FRICT*ABS(Q(2,1))) IF(IVALV.EQ.0) THEN Q(I ,2)=(PUMPCN)/B P(I ,2)=PUMP ELSEIF(1VALV.E:Q.I) THEN Q(1 ,P)=(PVAL’J-CN)/B P(l,2)=PVALV ENDIF QPIPE=Q(l,2)/RPM6 IF(CHECKl*CHECK2.GT.O) 40 CONTINUE 50 CONTINUE

BEGINNING

OF THE PIPE-----

GO TO 50

C-----SOLUTION OF UNSTEADY FLOW EQUATIONS IN THE PIPELINE-------DO 60 L=Z,NEND-I CN=P(L+l ,I)-Q(L+I ,I)-(B-FRICT*ABS(Q(L+I ,I))) CP=P(L-I ,I)+Q(L-I ,I)*(B-FRlCT*ABS(Q(L-I ,I))) P(L,2)=(CP+CN)/2. IF(P(L,2).LT.O.O) P(L,2)=0.0 Q(L,P)=(CP-P(L,S))/B 60 CONTINUE C-----SOLUTION PINO=PIN RATE=O.O CHECK3=1 CP=P(NEND-1 PINO=PIN

OF DIFFERENTIAL

,l)+Q(NEND-1

EQUATIONS

FOR

THE INJECTOR---------

,l)‘(B-FRICT*ABS(Q(NEND-I

,I)))

DO 80 II=1 ,ILIM C-----BOUNDARY CONDITIONS AT PIPE END ____________________------..P(NEND,2)=PIN Q(NEND,2)=(CP-PIN)/B QEND=Q(NEND ,2)IRPM6 QIN=O.O IF(IOPEN.EQ.1 .AND.PIN.LE.PMIN*l .ES) IOPEN=P IF(PlN.GT.POPE~Nl.OR.lOPEN.EQ.1) THEN IF(IOPEN.EQ.0) IOPEN=I QIN=AREAH’SQRT(2.*PlN/DENSF)IRPMG C IF(PIN.LE.PCYL) QIN=O.O ENDIF RATE=QIN”DENSF FBMl=FBM*(I .+PIN’l .E-08) DPlN=FBMl/(VlNO)*(-QIN+QEND) IF(II.EQ.1) DPINO=DPIN CALL SOLU(PINO,PINI .PIN,DPINO,DPIN,CHECK3,ll) IF(PIN.LE.0) PIN=O.O IF(PIN.LE.1 .E05) CHECKS=1 IF(CHECK2.GT.D) GO TO 90 80 CONTINUE 90 CONTINUE C--e__ FUEL

MASS

IFlJECTlON

RATE

_______-_____------

IF(RATE.GT.0) IBEGIN=l IF(IBEGIN.EQ.1) THEN ANGRATE=ANGRATE+ASTEP lF(lNT(ANGRATE).GE.J) THEN

--- --_________.

25

D. T. Hountalas,

26

A. D. Kouremenos

CORRECT=FLOAT(J)-ANGRATE DMCORR=CORRECT*RATE DMFUEL=DMFUEL+DMCORR DMINJ(J)=DMFUEL PPINJO(J)=PIN J=J+l DMFUEL=RATE*ASTEP-DMCORR ELSE DMFUEL=DMFUEL+RATE*ASTEP ENDIF AMINJT=AMINJT+RATE*ASTEP ENDIF C _____DATA SAVING ________________________________________-------IF(ANG.GT.JO) THEN JO=JO+l ANGX(JO)=ANG PPUMP(JO)=PUMP’l .E-05 IF(XMEAS.GE.0) PPTRANS(JO)=P(NMEAS,2)*1 .E-05 PPINJ(JO)=PIN*l .E-05 DMINJO(JO)=RATE’l .E6 ENDIF C _____RE,,,AlNlNG PRESSURE ESTIMATION IF(ANG.GT.ANGBEG) THEN SUM=SUM+P(NENDR,2)‘1 .E-05 ICOUNT=ICOUNT+l IF(ANG.GT.ANGEND) THEN PREM=SUM/lCOUNT GO TO 120 ENDIF ENDIF

___-_________________________

IF(IPRINT.EQ.1.) THEN WRITE(‘,lOO) ANG,PUMP*l .E-OS,P(l,2)‘1 .E-05,PIN*l Xl/(XO+XEFF),J,II IO; FORMAT(lX.F5.l.2X,F6.l,2X,F6.l,W,F6.1.2X,F7.2,W,l4,W,l3) ENDIF 110 CONTINUE 120 CONSCAL=AMINJT’RPM’l2O./FLOAT(NTYPE) C _____ DUf?ATl(-JN

OF

INJECTION

DO 130 IH=l,200 lF(DMlNJ(~Ol-lH).GT.O) NDUOI=POl-IH WRITEC,l50) NDUOI GO TO 140 ENDIF 130 CONTINUE 140 150

CONTINUE FORMAT(lX,‘lnjection

.E-5,

______--__________--------------------

THEN

Duration

: ‘,13,’ deg’)

lF(IVALV.NE.O.AND.IREMAIN.EQ.l.AND.ITER.LE.ITRMAX.AND. + ISTOP.EQ.0) THEN ERROR=ABS(pREM-PREM~)IPREM~*I~~. WRITE(‘,160) PREM,PREMO,ERROR,CONSCAL IF(I?RROR.LE.ACCURREM.OR.ITER.EQ.ITRMAX) GOT010 160 FORMAT(lX,‘Calc. Value=:FG.l ,PX,‘Previous

ISTOP=l Value=‘,

Simulation model for diesel engine fuel injection system +F6.1,2X,‘Error(%)~=‘,F5.1,2X,‘Consumption=’,F5.2) ENDIF C __I_ RESULTS

PRINTOUT

_-_____----------------------------------

IF(INJRES.EQ.l.AND.ISTOP.EQ.1) THEN DO 170 I=l,JO WRITE(8,180) ANGX(l),PPUMP(l),PPTRANS(I),PPINJ(I), + DMINJO(I) 170 CONTINUE 180 FORMAT(F5.‘l.‘,‘,F6.1,‘,‘.F6.1,‘,’,F6.1,’,’,E12.6) ENDIF IF(INJRES.EQ.l) CLOSE(8) ENDIF

THEN

RETURN END C

___________________-------

I ------

-

----

-

----------------------

SUBROUTINE RELAX(DM,CFl .CFZ,Pl RATIO=Pl/PZ IF(RATIO.LT.l) RATIO=1 ./RATIO IF(RATIO.GT.1 S) RETURN ORISMA=ABS(RATIO”CFl-1 .) COEF=l .-(EXP(ORISMA))*CF2 DM=DM%OEF RETURN END

,P2)

SUBROUTINE SOLU(FXO,FXl ,FX.ZFXO,ZFXl C- ___________________-----COMMON/ SOLUD /ASTEP,ACCUR C _-__--_----_-_ ---- -------CHECK=O.

,CHECK,I)

IF(I.EQ.l) THEN FXl=FXO+ZFXO*ASTEP FX=FXl RETURN ENDIF FX2=FXO+(ZFXO*ZFXl)*ASTEPI;!. IF(FX1 .LE.O) THEN CHECK=1 .O FXl =FX2 FX=FXl RETURN ENDIF ERROR=(FX2-FXl)/FXl’lOO. lF(ABS(ERROR).LE.ACCUR) FXl =FX2 FX=FXl RETURN END

CHECK=1

.O

21

28

D. T. Hountalas,

APPENDIX

B : PROGRAM

A. D. Kouremenos

INPUT

DATA FILE : “FUEL.DAT” 1,20.,1 .E5,250.E5 0.05,10,0.5,5,0,1 7.0E-3,6.34&3,19.34E-3 2.0E-3,0.9.2.2.5E-3,1.OE-6 1.80E-3 0.5,1.5E-3,0.15,0.45 2.35E-4,0.85,3 1 1500,4,850.,50.,2.E-3,.7,1.E-6,4O.E5,2

APPENDIX

C: PROGRAM FILE

Angle .O, 1 0, 2 0, 30, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0,

Pump 1.0, 53.0, 88.2, 118.1, 144.2, 168.0, 188.9, 207.9, 223.8, 233.3, 241 8.

IIREMAINIPREMIPTANKIPOPEI/ IASTEP/ILIM/ACCUR/ITRMAX/IPRlNT/INJRES/ IDPUMPISVCPISI lDHOLEP/CDHOLEP/NHOLEP/XO/VINO/ IXEFFI IPIPEL/DPIPE/FCOEFP/XMEAS IDINJP/CDINJP/NHOLEI/ IIVALVI /SPEED/NTYPE/DENSF/PMIN/DVALV/CDVALV/VOLVALV/

OUTPUT

: “PRES.DAT” Pmeas

19.4, 19.4, 19.4, 19.4, 43.8. 52.9, 65.2, 87.2, 114.6, 144.6, 174.9,

Rate

Pinj 19.4, 19.4, 19.4, 19.4, 19.8, 30.9, 52.8, 80.5, 111.3, 143.2, 175.3,

.000000E+00 .000000E+00 .000000E+00 .000000E+00 .000000E+00 .000000E+00 .000000E+00 .000000E+00 .000000E+OO .000000E+00 .000000E+00