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FREE PISTON GASIFIER STUDIES:

FURTHER DEVELOPMENT AND USE OF THE HYBRID SIMULATION

by

A. SWIDERSKI, F. RUETER AND R.E. GAGNE

E. P. Cockshutt, Head Engine Section

D. C. MacPhail Director

SUMMARY

Previous work on the modelling of the free piston gasifier has been extended to include refined models of the combustion process and of engine friction. The model was used to study the sensitivity 'Jf the engine performance to envi­ronmental and design paramders.

(iii)

TABLE OF CONTENTS

Page

SUMMARY. . . . . • . . . . . . . • . . • . . . . . . . • . . • . • . . • . • . . . . . • . . . . • . . • . • • . . . . . . (iii)

SYMBOLS ....... . . . . . . . . . • . • . • . . • . . . . . . . • . . • . . . . . . . . . . . . . . . . . . . . . • . (v)

1.0 lNTRODUCTION. . . . . . . . . . . . • . . . . . . . . . . . . . . • . . . . . . . • . . . . . . . • . . . . • . . . 1

2.0 THE ENGINE .... . . .. .. •. .. . . . ... . . . •..•.•. . . . . . . •. . . . .. ...•. .•. .•. . 1

3.0 THE MODEL AND lTS lMPLEMENTATION .....•..........•........... 2

3. 1 Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . 2

3. 1. 1 Combustion Model I . • . . . . • . . . . . . . • . . . . • . . . . . . . . . . • . . • . • . . . 2 3. 1. 2 Combustion Model II .•....•..........•.••.•....••.•....•.. 4

3. 2 Friction........................................................ 8 3.3 Effect of Small Changes . ...............................•.....•. • 9 3.4 Stability and Receiver Volume ..........................•....•... 10

4.0 CONCLUSIONS. . . . . . . . . . . . . . . . . . . . • . . . . • . . • . . . . • . . • . . . . . . . . . . . . • . . . . 10

5.0 REFERENCES... . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . • . . . . • . . • . . . 10

TABLES

Table Page

1 Engine Data . .. .•....•....................•.......•..........•.. 1

2 Effect of Small Changes .....•..•..........•...•..........•..•.•. 13

lLLUSTRA TIONS

Figure Page

1 Longitudinal Section of Engine ...........•.••.•... . ••.•........••. 15

2 Information Flow Diagram ................. . •.................... 16

3 Diesel Engine Cycle with Model I Combustion ..... . ............... . 17

4 Diesel Engine Cycle with Model II Combustion 18

(iv)

Figure

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

Symbol

Ad

C

ILLUSTRATIONS (Cont'd)

Injection Timing ...................................•...........

Comparison of Combustion Models land 11 ....................... .

Performance With and Without Viscous Friction .................. .

Viscous Friction Coefficient ................................... .

Effect of Small Changes: Ambient Pressure ..................... .

Effect of Small Changes: Ambient Temperature . ~ . . . . . . . . . . . . . . . .

Effect of Small Changes: Diesel Efficiency ...................... .

Effect of Small Changes: Leakage Factor ....................... .

Effect of Sm all Changes: Compressor Polytropic Exponent

Effect of Small Changes: Combustion Exponent .................. .

Effect of Small Changes: Timing ............................... .

Effect of Small Changes: Bounce Reference Pressure

Effect of Small Changes: Compressor Delivery Valve Loss

Effect of Small Changes: Compressor Inlet Valve Loss ........... .

Effect of SmaU Changes: Coulomb Friction ....•........... . ...•..

Effect of Small Changes: Viscous Friction Coefficient ............. .

Stability ............................•.........................

SYMBOLS

Definition

double area of diesel cylinder

viscous friction coefficient

specific heat at constant pressure

(v)

Page

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Symbol

HV

F

FLEAK

ghp

IML

J

m f56

ODP

P

P omb

Q

R

SFC

SYMBOLS (Cont'd)

Definition

specific heat at constant volume

lower heating value of the fuel

total friction force

Coulomb friction force

gasifier leakage factor

gas horsepower

inner mechanical limit

mechanical equivalent of heat

mass of air trapped in the diesel cylinder

mass of fuel injected per stroke

mass of fuel burned between beginning of combustion and IDP

combustion exponent

outer dead point

pressure

atmospheric pressure

bounce reference pressure

pressure in diesel cylinder at closing of intake ports

compression pressure in diesel cylinder

maximum pressure in diesel cylinder

amount of heat

gas constant

specific fuel consumption

(vi)

Symbol

T

T omb

u

v

Vr

x

y

~5 DoT

1]

SYMBOLS (Cont'd)

Definition

temperature

atmospheric temperature

temperature in diesel cylinder at closing of intake ports

compression temperature in diesel cylinder

temperature in diesel cylinder at the start of constant volume combustion

temperature in diesel cylinder at the end of combustion

internal energy

volume

gas receiver volume

volume of diesel cylinder at end of compression

diesel cylinder volume at IDP

diesel cylinder volume at E. '1d of combustion

piston speed

position of diesel exhaust ports

diesel piston position at IDP

diesel piston position at end of combustion

isentropic exponent (ratio of specific heat of constant pressure to that at constant volume)

compressor polytropic exponent

isentropic exponent during diesel compression process

temperature difference

start of combustion measured from IDP

assumed efficiency factor assigned to the combustion process, but includ­ing heat losses and gas leakage for the entire cycle and excluding friction

(vii)

- 1 -

FREE PISTON GASIFIER STUDIES:

FURTHER DEVELOPMENT AND USE OF THE HYBRID SIMULATION

1. 0 INTRODUCTION

Reference 1 describes the development of a hybrid computer simulation of a free piston gasifier, and compares the gasifier performance with the output of the simu­lation under similar running conditions . One of the observations made in this reference was that, although gene rally good agreement was obtained, there were discrepancies in the shapes of some of the curves from the engine tests and the simulation. The most ob­vious of these was in the plot of inner dead point versus load, which was almost flat for the simulation, but increased sharply with load in the engine. The explanation offered for this was that in the engine, injection begins earlier with increasirig fuel, thus causing a greater piston deceleration at higher load and moving the IDP outward. In the model this effect was absent because with the simple heat release model chosen (constant volume followed by constant pressure) no heat release could take place until IDP was reached.

It was thus argued that a modified heat release model, in which some of the heat was released before IDP, might give a more realistic variation of IDP with load. The present report describes this change in the model and its effect upon predicted per­formanee. Also studied was an experimental change in the modelling of friction, and the effe cts on performance of small changes in environmental and design parameters.

2.0 THE ENGINE

The engine studied is a small free-piston gasifier of the outward-compressing type, and is described in some detail in Reference 1. Figure 1 shows a longitudinal sec­tion of the engine in diagrammatic form, and the principal dimensions and masses are given in Table 1. It will be appreciated that the simulation is by no means restricted to these values.

TABLE 1

ENGINE DATA

Maximum stroke between mechanical limits Piston mass (2 piston ~semblies) Compressor piston area (2 pistons) Diesel piston area (2 pistons) Negative bounce piston area (2 pistons) Bounce piston area (2 pistons) Compressor cylinder volume at IML (2 cylinders) * Negative bounce volume at IML (2 cylinders) * Bounce cylinder volume at IML (2 cylinders)* Gas receiver volume

5.20 in 58.00 Ibm

127.60 in 2

19.24 in2

123.31 in2

15.04 in2

746.90 in3

181. 45 in3

90.86 in3

4.70ft 3

*The volume of a cylinder at IML (inner mechanical limit) is its volume when the two diesel piston crowns are in contact.

- 2 -

3.0 THE MODEL AND lTS IMPLEMENTATION

A detailed description of the basic model and of its implementation on the EAI 690 hybrid computer is given in Reference 1 and will not be repeated here. An informa­tion flow chart for the simulation is, however, reproduced in Figure 2.

The sections that follow describe the changes introduced into the model.

3. 1 Combustion

The combustion process is probably the least understood of all the processes occurring in reciprocating engines. This is supported by Streit and Borman 2 ) and Borman, Myers and Uyehara 3) in their development of engine models for simulation. The design and development of an actual combustion system is usually done experimentally and on the basis of past experience rather than from theoretical treatment.

The work described in Reference 1 embodies a simple combustion model that assumes constant volume heat release up to a previously selected maximum pressure, followed by constant pressure heat release for any remaining fuel. The oversimplifica­tion implied by this model was at first considered acceptable hecause the resulting pressure-volume diagram bore a close resemblance to the realone, and its area was correct. However, it made no provision for variable injection timing and its effect on piston dynamics, nor for the effect on the inner dead point position of variations in the amount of fuel injected per stroke.

In the real engine, the fuel for combustion is delivered by a jerk-type fuel pump actuated by a cam driven by the pistons themselves. Since the cam comt::s to rest at Inp, the pump delivery stroke must be completed at or before IDP. Some measure of controlled injection delay is introduced by the compressibility of the fuel trapped in the lines between the pump and the injection nozzles, so that the actual injection will occur later and may, in fact, continue beyond inner dead point. In addition, there is an un­controlled ignition delay before the actual beginning of heat release.

It was therefore considered not unreasonable to postulate a heat release model in which heat release would begin at a selected point near IDP on the compression stroke and proceed while the piston continued moving toward IDP. Any remaining energy would then be released at constant pressure as before.

The simulation was so arranged that either combustion model could he used. The two scheme s are hereafter referred to as Combustion Model land Combustion Model 11 respectively, and are defined in some detail below.

3. 1. 1 Combustion Model I

The constant volume followed by constant pressure heat release model is shown in Figure 3, and is described fully in Reference 1. For the sake of completeness, the derivations of the equations are repeated here, in a simplified form consistent with the second combustion model.

- 3 -

The heat released by the combustion of a mass mf of fuel,

where the numbered subscripts refer to the states indicated in Figure 3, and

HV = lower heating value of the fuel,

TI an assumed efficiency factor assigned to the combustion process, but including heat losses and gas leakage for the entire cyc1e, and excluding friction,

ma mass of gas trapped in the cylinder,

Cv and cp specific heats at constant volume and constant pressure, respectively,

and T temperature.

Equation (1) ignores the heat absorbed by the mass of fuel mf' Since

p·V = mo·R·T

Vs Tó-Ts -- (Pó-Ps)

mo·R

Pó and T7-Tó

mo'R (V7 -v ó)

where Pand V refer to pressure and volume, respectively, and R is the gas constant. Substituting these values in (1) gives

+ mO'R mo'R

cp

R . xdó'Ad'(PÓ-Ps) + R 'Ad'(Xd7-Xdó)'Pó

(1)

-4-

Substituting Cv = cp / l' gives

(2)

If the quantity of fuel injected is insufficient to raise the pressure to the pre­selected maximum value of P6' all combustion will take place at constant volume, and

and

Combining, and again substituting Cv

(3)

If, on the other hand, the compression pressure at IDP reaches or exceeds the assumed maximum value, all heat release will take place at the maximum compression pressure, and the constant volume portion of the process disappears. In this case,

Hence, (4)

3. 1. 2 Combustion Model II

The new combustion model, shown in Figure 4, postulates that heat release begin at a selected point 5 near the end of the compression stroke. This is mode lIed by switching from the isentropic exponent 1'45 when the piston reach Xd5 to an arbitrarily

- 5 -

chosen polytropic exponent nc having a value much in excess of Y45 (typically 2.5). In other respects, the solution of the equation for compression,

proceeds normally until the piston reaches IDP at 6.

For polytropic compression with heat addition, the heat added,

dQ = dU + P·dV

where dU is the change in internal energy.

Hence,

dQ dT R . T . dV ma· cv· + ma . J V

For adiabatic compression, dQ 0,

and dT c .­

v T

dT T

dV V

Similarly, for the polytropic case,

dV V

dT T

dT T

c -c p v

-1 y-1

dV V

(5)

- 6 -

Substituting this in (5), putting cp -c v = cv' (1' - 1), and integrating, gives

(6)

Also, 1 + ~~ ~ (::) (n,-l)

Substituting in (6),

Substituting Cv = cp/'}' and Q mf 56 . HV ,1], where m f 56 is the fuel burned from 5 to 6,

mf56' HV·1] m . Q

and

HV·1]· l' [(

XXdd

6

5 .) (ne-1) ] ) -1 '(1-~

Any remaining fuel, mf67 = mf-mf56' is burned at a constant pressure P6 P 7 ·

m f67 . HV'Tj

But T 7

and T6

Therefore

Substituting, mf67 ·HV·Y}

and

The temperature at the end of combustion,

But

- 7 -

P6·Ad,X d7

mo·R

P6·Ad,X d 6 mo·R

m f67 'HV'Y} ·R

P6 ·A d ·c P

Hence, P·A·x ·R 4 d d 4

P ,xd 4 4

(7)

(8)

For a given setting of the injection pump timing, the pump delivery will begin at a fixed distance before IML, in terms of piston travel. However, a study of indicator cards taken during test runs on the engine suggests that, regardless of load, the distance from the beginning of heat release to IDP is nearly constant for a given setting of injec­tion timing. This phenomenon has not been fully explained, but is presumably connected with the variations in injection and ignition delay with variations in speed and load. See also Reference 4.

In the model, therefore, it has been decided to select the point at which heat release begins on the basis of IDP rather than of IML. Timing is therefore set by se-

- 8 -

lecting a distance ~X5 (typically 0.1 in) from the beginning of heat release to IDP. Since the next IDP is not known at the time the value of xd 5 is required and the variations in IDP from one cycle to the next are small, the current value of Xd 5 is obtained by adding ~x 5 to the previous IDP. In order to avoid hunting, it was found necessary in practice to allow a small tolerance so that a new value of x 5 would be generated only if the change in IDP exceeded a preset small amount, typically 0.003 in.

It is thus possible to study the effect of timing by varying ~X5 and of the rate of heat release before IDP by varying nco The results of this study are illustrated in Figure 5, which also gives a comparison between the two combustion modeis, since Combustion Model I is in force when the abscissa is zero (beginning of heat release at IDP). Exam­ination of Figure 5 suggests that an optimum timing position exists with the beginning of heat release about 0.07 inches before IDP, or 0.32 inches before IML. Unfortunately, only a limited study of the effect of timing in the real engine was made, since the begin­ning of the pump delivery stroke could not be advanced beyond 1. 2 inches before IML. At this point, the specific fuel consumption appeared to have levelled off, although horse­power was still increasing with advancing timing. Because of the unknown injection and ignition delays, it is not possible to make a direct comparison of timing figures for the engine and the simulation.

Simulation performance with the two combustion models is compared in Figure 6. The dependence of IDP on load is only very slightly greater with Model 11 than Model I, and the new model, at least with constant values of ~X5 and n c, cannot be said to be sig­nificantly superior to the old. It may be inferred from Figure 5 that even with varying ~X5 and nt> the effect on IDP is not likely to be strong.

Aside from the absence of any clear superiority of Model 11 combustion over Model I, an additional argument against its adoption lies in the tendency toward instability exhibited in a hybrid simulation of another free piston engine concept using the same combustion model. In this case, the power take-off from the engine was by means of a mechanically coupled hydraulic pump, and this, together with the externalload assumed, produced an inherently unstable system. It was almost impossible to run this model until the Model 11 combustion was replaced by Model I.

3. 2 Friction

Experimental data on friction in diesel engines are singularly scarce (Refer­ence 5), and for free piston engines appear to be totally lacking. In the case of the crankshaft engine, one can gain some insight into the magnitude of friction by means of a motoring test, but with the free piston machine this is not possible. The results of motoring tests must, in any case, by applied with extreme caution because the conditions during such a test are quite different from those that apply in a running engine .

Probably the best that one can do in the case of the free piston engine is to estimate the friction forces. Most of these are caused by ring friction in the diesel, compressor and bounce cylinders, with some additional losses in the synchronising mechanism and fuel pump drive. The sliding friction of rings against cylinder walls is affected by such operating conditions as temperature, pressure, and lubrication, and may vary considerably during any one cycle, as well as over the engine operating range.

- 9 -

In the earlier work (References 1 and 6) Coulomb friction only was modelled; piston motion was opposed by a friction force of constant magnitude but with its sign changing each time the piston assembly reversed direction. This oversimplification is now refined following Millington et al. 5) by the addition of a viscous friction term propor­tional to piston velocity .

The equation for friction force then assumes the form:

(9)

where Fe is the assumed Coulomb friction force,

c is an assumed factor for viscous friction,

and x is the instantaneous piston speed.

A comparison of engine performance with and without viscous friction is given in Figure 7. Based on a typical mean piston speed of 1500 ft/min, the mean viscous fric­tion force here amounts to about one -sixth of the total. Figure 8 shows performance as a function of the viscous friction factor c.

A study of Figures 7 and 20 suggests that the effect of viscous friction is nearly identical to that of Coulomb friction. This result is not entirely unexpected, since the frequency dependence of the viscous friction loss is largely nullified by the narrow fre­quency range of the free piston engine.

3. 3 Effect of Small Changes

It is of interest to know the effects on engine performance of small changes in the operating conditions, such as ambient temperature and pressure, and in such esti­mated quantities as friction and leakage factors.

These influences were studied by the method used in Reference 6, varying each of the selected quantities in turn, and noting the effect on engine performance. The re­sults of this study are given in Table 2. A number in the main body of the table gives the percentage change in the selected performance criterion for a one percent change in the engine variable in question. Thus, for example, a one percent increase in bounce ref­erence pressure is seen to cause a decrease of almost 0.2% in gas horsepower and an increase of nearly 0.4% in freq~ncy; and a small change in ambient pressure has no measurable effect at all on üDP or specific fuel consumption. The same results are presented in graphic form in Figures 9 to 20. In each of these figures, the standard value is indicated by a vertical line.

The strongest interactions are found between ambient pressure and IDP, gas horsepower, mass flow and fuel flow, and between bounce reference pressure and IDP. The assumed polytropic exponent for expansion in the compressor cylinder also has a strong effect on IDP, but the position of the beginning of heat release (injection timing in the real engine) has almost no influence. This bears out the observation made in 3.2 above, and suggests that improvement in the simulation of IDP must be sought elsewhere

- 10 -

than in the combustion model. Decreasing the bounce reference pressure with increasing load may be justified on physical grounds, but can be applied only to a very limited extent because of the fairly strong dependence of frequency on bounce pressure level.

3.4 Stability and Receiver Volume

There is always a time lag of a number of cycles between a change in running conditions and the attainment of a new equilibrium running point. This is particularly evident each time the simulation is started.

Figure 21 presents the results of an experiment in which readings were taken at intervals after simulation starts with various receiver volumes, but with the engine controls and ambient conditions held constant. As expected, stabie running was achieved in fewer cycles with the smaller receiver volumes . It is noteworthy, however, that the same equilibrium point was reached in each case, regardless of receiver volume. This suggests that an economy in simulation running time may be effected by reducing, the re­ceiver volume to a value lower than that used in the real engine, if the interest is only in steady-state results .

A receiver volume of 2.0 ft 3 was selected as the standard value for subsequent tests, and a stabilization period of 100 cycles provided an adequate margin of error for the attainment of repeatable readings.

4.0 CONCLUSIONS

1. A combustion model has been produced that permits the evaluation of combustion effects prior to IDP. However, performance is not strongly affected by a con­siderable simulated advance in injection timing.

2. Further experimental data would be essential for a detailed assessment of com­bustion modelling.

3. An improved piston friction model has been produced that permits the incorpo­ration of viscous components along with Coulomb friction.

4. A study of the effects of small changes indicates that it is possible to predict the trend and character of variations in performance as the result of small changes in operating conditions .

5 . Stability tests indicate that simulation performance is not affected by reasonable reductions in the receiver volume in order to avoid excessive running times.

5.0 REFERENCES

1. Rueter, F. Swiderski, A.

Free Piston Gasifier Studies: Development of a Hybrid Simulation. NRC, DME Mech. Eng. Report ME-230, National Research Council of Canada, Ottawa, Ontario, April 1969.

2.

3.

4.

5.

6.

Streit, E. E. Borman, G. L.

Borman, G. L. Myers, P.S. Uyehara, O.A.

Samolewicz, J.J.

Millington, B. W. Hartless, E.R.

Rueter, F. Swiderski, A. Samolewicz, J. J.

-11-

Mathematical Simulation of a Large Turbo Charged Two­Stroke Diesel Engine. S.A.E. Paper No. 710176, January 1971.

Some Problem Areas in Engine Simulation. S.A.E. Paper No. 710172, January 1971.

Experimental and Analytical Study of a Small Free-Piston Gasifier . ASME Paper No. 71-DGP-5, April 1971.

Frictional Losses in Diesel Engines. S.A.E. Paper No. 68059, September 1968.

Hybrid Computer Study of a Free Piston Engine with a Hydraulic Pump. NRC, DME Mech. Eng. Report ME-236, National Research Council of Canada, Ottawa, Ontario, July 1970.

ttl ll"" IIIU111"rq =11'_'''''111''''''''",,''',,''

TABLE 2

EFFECTS OF SMALL CHANGES

._---- ----- --

~ ~ ~ ~

~ ~ :><~ ~ ~ 0 ~~ 0 ....:l m Po. :>< ~~

~ ~ H

<C! t-< ~ U ~~ ~

>- H

~ Z 0 0 PARAMETER QO

Z ~ ....:l~ ....:l ....:l m ~ 0 ~ ~~ ~ ~ ....:l

~~

-+-::c ry QPo. m ....:l <C!

<C!t-< Po. Po. m ~ U m::8 m ~ ~ Q~ 8

Q <C! ~ ~ <C!~ <C! ~ ~ z~ 0 0 ~ m ot-< ::8 ~ m <C!Po. ~O in in hp min-' Ibm /ghph OK Ibm /s Ibm/h No.

Ambient Pressure 14.70 IbJin2 1.1l -0.01 1.00 0.20 0.00 0.02 1. 00 1. 02 9

Ambient Temperature 288 OK -0.28 0.08 0.49 0.02 0.02 0.91 -0.48 0.53 10

Diesel Efficiency 0.75 - 0.00 0.00 0.00 0.00 -1. 12 0.00 -0.0 3 -1. 09 1l

Leakage Factor 0.77 - 0.27 -0.15 -0.22 -0.01 -0.32 -0.48 0.27 -0.56 12

compressor, Compr. 1. 27 - 0.00 -0.06 0.43 0.04 0.47 0.63 -0.30 0.78 13

Polytropic E 1. 27 - 0.99 -0.16 -0.08 -0.19 -0.15 -0.12 0.12 -0.27 13 Exponent xp .

Diesel Combustion 2.50 -0.22 -0.03 -0.08 0.03 0.07 0.06 -0.06 0.04 14 -

Exponent

Beginning of Heat 0.10

in from 0.09 -0.00 -0.00 0.00 0.01 0.01 -0.02 0.01 15

Release IDP

Bounce Reference Pressure

60 IbJin2 -1. 33 -0.08 -0.07 0.36 -0.09 -0.09 0.07 -0.15 16

Compressor l Deliv. 15 % -0.09 0.00 0.02 0.04 0.03 0.04 -0.02 0.05 17

Valve Loss Inlet 5 % 0.00 0.01 -0.04 -0.01 0.03 0.02 -0.04 -0.01 18

Coulomb Friction 160 lb l 0.15 -0.01 0.0 7 -0.02 0.08 0.1l -0.06 0.13 19

Viscous Friction 30* IbIS/ in 0.13 -0.01 -0.05

Coefficient -0.01 0.02 0.02 -0.04 -0.01 20

* Although the simulation was normally run without viscous friction, values in the table are based on a datum of 30 IbIS/in.

I

I

REMARKS I

I

I Constant delivery pressure ratio I

Constant delivery pressure = 46 IbJin2

Constant delivery pressure = 46 IbJin2

Constant delivery pressure = 46 IbJin2

I

Constant delivery pressure = 46 Ib / in2 ,

Constant delivery pressure = 46 Ib/in2 I

I I

Constant fuel per cycle

Constant fuel per cycle

Constant delivery pressure = 46 lb/in2

I

Constant fuel per cycle

Constant fuel per cycle I

Constant fuel per cycle

Constant fuel per cycle I

I

I-' W

I

L I LUlUlHlIIlIUUllIIIIIU__ __'''''I!'''IIjW ,,''l .... u'''l'!'l'll* '11111111"'1"1 I 1'11" " '""!U"'lll''''!l'l! HU'"

DISCHARGE

COMPRESSOR

DELIVERY VALVES

COMPRESSOR

INLET VALVES

EXHAUST RECEIVER

FUEL INJECTION NOZZLE

TRANSFER DueT

INLET PORTS NEGATIVE BOUNCE DOOR

EXHAUST PORTS

FIG.I : LONGITUDINAL SECTION OF ENGINE

...... C1J

I

/ u "W - - -

~ f\

F. ~ ~ BLOW 7)

~ +l Fr DOWN X port MODEL eONS!

1 X Pc Xporl

BOUNCE NEGAT)VE ~

DIESEL X7 DIESEL

CYLINDER BOUNCE

~ CYLINDER PdG COMBUSTION X CYLINDER ~

P Pnb Pd rT9 A) tx I Pd b

r:-- ~ (

( r ( (

r. [ TIME

x. (

~ X x1 w Pe

::'<

~ PISTON ~ 1-, T9 1 Mfuel

1. DYNAMICS Ff

~ COMPRESSOR

Me Tree Pc GAS

NOZZLE RECEIVER Pree

~~~ r-- ~ Î tM noz Po ~

l [ Vlo) LEAKAGE c \..J \

FIG.2: INFORMATION FLOW DIAGRAM

I ~ """"'""'" • • • • or •• u_a: _ •• 6 ___ • .". '. lrij . . E .i.. . u __ •• _= _=

Mfuel Flo) e C

~ FRICTION

r--

TIM~

X

Pree Tree.. w

U Mfu.1 Z

<l ::'<

Mnoz cr 0 lL. cr w a.

AnCl,L

Po

-

o V D

DESIGN PARAMETERS

ENVI RONME NTAL PARAMETERS

ASSUMPTIONS

Po

I-' cr:.

Pmax.

w 0:: ::J Cf) Cf)

W 0:: Cl.

5

- 17 -

CONSTANT PRESSURE HEAT RELEASE

CONSTANT VOLUME HEAT RELEASE

COMPRESSION

EXPANSION

2 8

~~~-=i.3 Pree -- ------------------------------- 4 3'(9)

COMPRESSOR

Po -----------I'

PISTON POSITION

FIG.3: DIESEL ENGINE CYCLE WITH MODEL I COMBUSTION

w cr => Cf) Cl)

w cr a..

- 18 -

rCONSTANT PRESSURE HEAT RELEASE

6; 7

HEAT RELEASE DURING COMPRESSION

EXPANSION

COMPRESSION

2 --;::.====~8 _----.3

- - - - - - - - - - - - - - - - - -- - - - - - - - - ----::-:-:-:-:-:-:-=-:-=-:-*-=----~.---à::::.....-_t. 3' (9)

COMPRESSOR

Po -- --------------I'

PISTON POSITION

FIG. 4 : DIESEL ENGINE CYCLE WITH MODEL TI COMBUSTION

2 ~ Cl:: 2 .85 Cf) Cf)

w 2.80 Cl:: 0-

>- 2.75 Cl:: w > 2.70 --l w o

. ~ 030r

~ 0 .25[

0.20

~ 0.48

r .oE 0.46

u ~ 0.44

'" "-E

:e 0 .31

~ 03+ <l 0 .29 :::E

COMBUSTION MODEL!

- 19 -

;:- 760 ~ • COMBUSTION MODELlI ----------------0-:::E ~ 740

>-ffi 720 > ~ 700 o

4.60~ ~ 4.55

o 4.50

4.45L

IE

~1860r ~1840 CJ

~1820 LL

Cl:: w 3: 0 36

t 0-

w Cf)

34 Cl:: 0 :r: Cf) 32 <l (9

~ 16 .2 E

.0

; 16.0 o --l LL 15 .8 --l w

------- ----- --- ---==~~~~~----o

o

o

.... .... "-

" "-"-

"-" " "

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

.... .... .... "-

"-"

--- ne = 2.0

--- ne = 2 .5

------- ne = 3 .0

--

-------o ~=_=_=_=~___=_=__=~---~~-

-- - - -----=--- - - -- ---.,,/ -- -----------------..:..--

o~

-------- --0

0 ...--:::- - -.-.=--

o

--------

---

"- .... " "

---

------

---------------o __ - _____

-----

--

--

--

2. 15. 6 L.-~0-::-0.-=0-=2-:0::-c.0=-4:-:::0~.0:-:::6-:0=-:.0=-=8::-c-:0:-':.1:-:::0:---::-0.-'-:12::-c-:0::-'.1:-:4----:::0-7-.16=--0::;-.~18:-:::0-:!:. 2:::::0-:0::-.2!-:2;:--::0:-:!. 2:-:4:-:::0-=.2-=6-:0~. 2 8 BEGINNING OF HEAT RELEASE 6. x 5 in. BEFORE IOP

FIG. 5: INJECTION TIMING

800 790 780 770

;' 760 a. 750 ~ w 740 f- 730 >-[5720 > 7 10 :J 700 w 0690

680 670

~ 0 .35[

- 0 .25

1820

-;- 1800 E

~17eO z w &1760 w Cl: l1.1740

1720

0.38

",0.36 ..... E

:e 0.34 ~ g l1. 0 .32 IJ)

~ 0 .30 ~

0 .28

0 .26

5.0

4 .9

4 .8

.~ 4 .7 a. 0 04.6

4 .5

4.4

4 .3

0 .50

.s:0.48 a. .s: ~0.46

E .0

~0 . 44 l1. IJ)

0.42

0 .40

~ 65 Ct

Cl: 60 ~ 55 0 50 a. I 45 w

IJ) 40 Cl: 0 35 :I: IJ) 30 « 25 C)

24

22 .s: ..... ,OE 20

~ 0 18 ...J l1. ...J 16 w ::::> l1.

14

12

- 20 -

-------

-- - MODEL 1

MODEL n

--

2.6 2.7 2.8 2 .9 3.0 3 .1 3 .2 3 .3 3.4 DELIVERY PRESSURE RATIO

---

b.x 5 = O. 10 in.

n c =2.50

---

-­...----------

FIG.6: COMPARISON OF COMBUSTION MODELS lAND n

720 710 700 690 680

~ 670 0 660 Cl. :2 650 w

640 l-

r 630 0:: w 620 > -.J

610 w 600 0

590 580 570 560

Q.o~ 0.30[

- 0 .20

0 .64 0.62 0 .60

.r: 0.58 ~ 0.56 0>

...... 0 .54 E

:!:? 0.52 ü 0.50 ~ 0.48

en ......

E

0.46 0.44 0.42

0.36

0 .34

:!:? 0 .32 3: o ~ 0 .30 en ~ 0 .2 8 :2

0.26

0 .2 4

4 .8

4.7

4.6

4.5

~4.4 o

4 .3

4.2

4.1

4 .0 ,

;

1800

l 11700

~ 1600 LL

~50 0>

0:: 45 ~ 40 ~ 35 W 30 ~ 25 ~ 20 en 15 « l') 22

.r: ...... 20

.J 18

3: gl6 LL

t;:j14 ~ LL

12

10

- 21 -

....-.....- ...-.....- .....----- /' ---- /' .....- /' .....- /'

.....-""'- /' .....- .,/

.....- .,/ .....-""'- .,/

.....- .,/ ....---- .,/

--- ../ --- ../

FRICTION FACTOR "c"

----glo [lbfXSecl ../ ../

../ ../

. In. J ../

/' /'

-----------

2.0 2 .1 2 .2 2 .3 2.4 2 .5 2 .6 2.7 2 .8 2 .9 3.0 3 . 1 3.2 3 .3 3.4 DELIVERY PRESSURE RATIO

FIG.7 : PERFORMANCE WITH AND WITHOUT VISCOUS FRICTION

~ 0..30.[

- 0..20.

I

E

~190.0.t ~180.0. o ~170.0. u.

70.0. ~ o

0.. 680. :2' w ..... >- 660. a:: w > 640. ---.l w Cl 620.

4 . 9

4.8

~ 4.7 o

4 . 6

4.5

.c

~0. . 60.t .<> 0. .50. <..>

~ 0..40.

a. L

"'40. a:: w

~38 0..

I

w (/)36 a:: o I34 (/)

<:t

0..38 <.!) 32

~ 0..34 ---.l u. (/) 0. .32 (f)

<:t :2' 0..30.

0. .28 L ......

~EI 8l 017 ...J u.

Ldl6 :::> u.

- 22 -

----

0. 0.0.2 0..0.4 0. .0.6 0. .0.8 0. .10. 0. .12 0.. 14 0..16 "e " Ib f x sec/in.

FIG.8 : VISCOUS FRICTION COEFFICIENT

- 23 -

~ 0 780 a.. ~ 770 w ~ 760 >-0: 750 w > 740 -l

~ 49[ w 0

o 4.8

C O.30[ a.. 0

0.20 I

~ 1800[ ~ ~1700 a. .r; Ol O.45[ ....... E a. .D ~

U 0.40 Ol

l.J... 0: Cf) w

3: r5[

0: 35 0

0 .36 I

0.3 5 Cf)

<I (.9

(/) 0.34 ....... E 0.33

..0

3: 0.32 0 0.31 -I l.J... Cf) 0 .30 Cf)

0.29 <I ~ 0.28

0.27

0.26 ~ 21

,520

3: 19 g 18 l.J...

-117 w ::J16 l.J...

15 12 13 14 16 2 18

Pamb I b f / in.

FIG .9 : EFFECT OF SMALL CHANGES AMBIENT PRESSURE

r - 24 -

840 820 800

~ 780 0

a.. 760 ~ w 740 r >- 720 0:: w 700 > ..J 680 w 660 0

640 620

4.9

c

a.. 4 .8 0 0

4.7-

C O.30[ a.. 0 0.20

I

~ 1900[ .c ~ 1800 a. .c j OA5[ a.

.s::. 0-0::

U 0.40 w u. ~ Cf) f5[ f/) 0.37 Cf) 40

0:: '- 0 E 0 .36 I .D

0 .35 Cf)

~ <l

9 0 .34 C!>

u. Cf) 0 .33 Cf)

0.32 <l .s::. ~ '-0 .31 E20

.0

- 19 ~ 9 18 LL 17 ..J w 16 ::> LL

240 260 280 300 320 T amb oK

FIG.IO :EFFECT OF SMALL CHANGES: AMBIENT TEMPERATURE

~ o a.. ~ w f- 760

t ~ 740

~ 720 -1 w o

~ 0 .30[

~ 0 .20

0 .60

0.55 ..s:: 0.

..s::

.!? 0 .50 E

.0

0 0.45 l1... Cf)

0.40

0 .35 en

" E .0

~ 034

t ~ 0 .33 (j') 0 .32 (j')

<f ~

-~1900[ fi: 1800

a. ~ Ol

Cl:: w 3:

r 5

[ ~40 0 I (j')

<f <.:)

24

..s:: 23 ....... E22

.0

3: 2 I g 20 l..1... -1 19

~ 18 l..1...

17

- 25 -

16~------~--------~------~------~

0 .55 0.65 0.75 0 .85 ?)

FIG.II : EFFECT OF SMALL CHANGES : DIESEL EFFICIENCY

- 26 -

880

~ 860 0

Cl.. 840 :!E 820 w ~ 800 >-cr 780 5.0 w > 760 -.J w 740 4 .9 0 C 720

Cl.. o 4.8 0

0.50 4 .7

c 0 .40 4 .6

Cl..

~ 0 .30 1820

-I

E 18 10 0

-w Cl::: ll... 1800

L:- 0.50 a. 1790

L:-Ol "-

E 0.45 a. .D L:-

Ol U cr ~ 0.40 w50 s:

0 Cl..

w45 Cf)

en cr "- ~40 E 0 .34 .D

Cf)

3: <t

g 0 .32 (!)

l.L Cf)

<j] 0.30 L:-

~ '- 22 E

.:e 2 I

~ 20 ..J

19 l.L ..J

18 w :::>

17 l.L 0.60 0.70 0 .80 0 .90

FLEAK

FIG.12 : EFFECT OF SMALL CHANGES : LEAKAGE FACTOR

- 27 -

::s: 800 0 780 Cl.

-- EXPANSION t __ COMPRESSION ~ STROKE

~ 760 w I- 740 >-0:: 720 w > 700 ..J 680 w 0 660

~ 030[ e 0 .20

.c. 0.

ï E 0 w 0:: l.l...

r45

[ ü 0.40 l.l... Cf)

<f) ......

E 0 .36 .D

$ :3 0.34 l.l... Cf)

~ 0 .32 ~

5.0

c4.9 Cl. o 04.8

4.7

2000

1900

1800 -

1700

0. .c. 0>

0:: W ~ r 5

[ ~ 40 o I Cf)

<l: {.:;)

.c. ...... E 20

.D

$ 19 :3 18 ~ 17 w 16 ::> l.l...

- ,.-- -"" ,.,. -----"./ ----

----------~~~~~-

---------~-=--r==-.:==-=::.:::=-==_=_=

----- --

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

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

1.0 1.1 1.2 1.3 IA yc

FIG.13 : EFFECT OF SMALL CHANGES : COMPRESSOR POLYTROPIC EXPONENT

~ o Cl..

~ 750

t ~ 740

~ 730 w 720 > -..J W o

<f) 0 .32 "-EO .31

.D

~ 0 .30

~ 0 .29 LL Cf) 0.28 Cf) <{ 0.27 ~ 0 .26

~ 1900[ E 18QO

a. .c. Ol

a::: w ~40 o Cl..

I

~35 a::: o I

30 Cf) <{ t::>

.c. "-

E

~ 18~ ~ 17 ..J LLI6 ..J w 15 :::J LL

- 28 -

f). x = 0 .10 in.

n 3 .5 c

FIG.14: EFFECT OF SMALL CHANGES: COMBUSTION EXPONENT

- 29 -

nc = 2 .50

~ 0

a.. 760 ~ w 750 I->- 740 n:

730 w >

720 -.J w 0

f6[ o 4 .5

~ 030[ e 0 .20

I

~1900[

~1800 L:-050 0. . L:-Ol

....... EO .45

.D

U a. LL L:-

Cf) 0.40 Ol 0:: w40 ~ 0 a.. w35 Cf)

In 0:: .......

~30 E .D

15 031 t Cf)

<t

--10.30 (.:>

LL Cf) 0 .29 L:-Cf) "-<t E ~ .D

~17t g 16 LL 15 --1 w ::J LL

I I I

0 .025 0.05 0.10 0.15 0 .20 0.25 b. x5 in .

FIG.15: EFFECT OF SMALL CHANGES: TIMING

~ 820 0

800 Cl. ~ 780 w I-

760 >-0:: 740 w > 720 -' w 0

OAO

c

Cl. 0.30 0

0 .20

L; 0 .50 Cl. .c Ol ....... E 0 .45

.D

u ~ OAO

(f) .......

E 0 .34 .0

~ o -' 0 .32 lL (j) (j)

<I 0 .30 ~

5.0

c 4 .9

Cl. 0 o 4 .8

4 .7

2000

1900 ï E 01800 w 0:: LL

1700

1600

Cl. .c 0'1

0::

~50 o Cl.

I

w45 Cf)

0:: o I40 (j) <I ~

.c

....... E

.D

3: 20

gl9 lL 18 -'

- 30 -

~ 1 7 L--___ --L ____ --L. ____ ....I..-____ L--___ --'

lL 40 50 60 70 80 Pb ref Ib f / in .2

FI G.16 : EFFECT OF SMALL CHANGES : BOUNCE REFERENCE PRESSURE

- 31 -

~ 800 0

Cl. 790 ~ w 780 f-

>- 770 0:::

760 w > 750 --1 w 740 0

4.9 c .-~ 4 .8 °

~ OAO[ 4 .7

- 0.30 1900-

I

E 1800 a w 0::: u... 1700

L 0. rA5

[ 0 0 .40 0. u... ..c. Cf) cr>

0::: w50 ~ ° Cl. 145

w Cf)

0:::

°40 I Cf)

<t rJ) t9 "-E

.D0 .35

~ 034[ u... 0 .33

~ 0 .32 L

<t "-E

~ .D

;< 20t gl9 u... --118 -W ::> u...

0 5 10 15 20 25 30%

FIG.17 : EFFECT OF SMALL CHANGES: COMPRESSOR DELIVERY VALVE LOSS

- 32 -

~ 820 0

0... 810 :2: w 800 r >- 790 0::: w 780 > -l 770 w

760 0 4 .9 c .-

0... 0 4 .8 0

c O.40[ 4 .7 .-0... 0

0 .30

-á 0 .50

~1850[ e:1750

.L: 0> "-

,DE 0.4 5

u 0. u.. .r;

en 0.4 0 ~50 w ~ 045 0... I

W Cf) 40 0::: 0 I

~ 35 <..?

lil 0.35 "-.E 0 .34

,D

~ 0 .33 g 0 . 32 u.. en 0 . 31 Cf)

0 . 30 <I .r; :2: 0 . 29 "-

E

~ ~~.~ ~18 dl7 ::::> u..

0 5 10 15 20 25 %

FIG.18: EFFECT OF SMALL CHANGES : COMPRESSOR INLET VALVE LOSS

860 :::.:: 840 0

a.. 820 ~ w 800 f-

>- 780 a:: w 760 > :J 740 w 0 720

700

0.40

c: .-a.. 0 30 o .

0 .20

~ 0.50 .c. Ol '-E0.45

.0

U l.L Cf) 0.40

~ .oE 0.35

~ 0 .34

~ 0 .33 Cf) 0.32 Cf)

<{ 0.31 ~

4.9 c:

a.. o 4.8 0

4.7

1900 ï

E ~1800 a:: l.L

1700

a. ~ 0"1

a:: w 3: o r 5

[ a:: 40 o I Cf) <{

<.9

.c. '-E21

.0

~20 g19-

~18

- 33 -

~ 17~------~~------~------~------~ l.L 100 200 300 400

Fe Ibf

FIG.19: EFFECT OF SMALL CHANGES: COULOMB FRICTION

- 34 -

~ 0

a.. 680 ~ w 670 f-

T 660 Cl:: w 650 > Fe = 180lbf ::i 640 w 0

4.9

c

a.. 4 .8 0 0

4.7

~ 030[ - 0.20

-I

819OO

[ fîl800

~0 . 50 ..c Ol

........

. l0.4 5 u l.L (/)0.40 0-

..c Ol

Cl:: W ~ 0.4 5 0 a.. ~0.40 (/)

Cl:: 0

CIl I 0 .3 5 ........

.oE O.37 (/)

<t - ~ ~ 0.36

~ 0 .35 ..c ........

(/) 0 .34 E (/) .0 <t 0 .33 -19 ~ ~ 18t

l.L 17 -1 w ::J

0 10 20 30 40 50 60 l.L

"e" Ibf' sec/in.

FIG .20: EFFECT OF SMALL CHANGES: VISCOUS FRICTION COEFFICIENT .

.r: a. .r:

0 .55

0.50

~ EOA5

.0

U IJ.. Cf)

OAO

a. D o

. ~ 0 ' 35

t a. 0 .30 D

0 .25 "É. 52

50 0>

Cl:: W ~ o a.

I

w Cf)

Cl:: o I Cf)

<t (.!)

45

40

T~ 1900r_

1800l

0 .50

<J) 0 .45 '-

E .0

~ g IJ.. 0.40 Cf) Cf)

<t :!!'

0.35

- 35 -

A

\ \

\ \ \ \ .

\ I

\

\ / \ I 'v , I j: \ ' I I" .)(,' ,/

1/ '. "\ _-< V ~" " y--'

RECEIVER VOLUME FT 3

--0-- 0 .3 --0----

--+--

----x----

1.0 2.0 4 ·7

- -IA-- 10.0

/ / ~----

%~BO~-iII--m----i!J~--+.)( +--+ .)(-+-o~.tSOo-.)(-~x----IA----~

, /

.: / ; ;'

I!i

'\ n, I \

\ \ I • \ \ \ ' I \ I I

X \ \ \

\ IA \

\

I I I I + \ \. \ " \ \ , ' .

\... ~ \ x, " \ ', .. +', '" '\ , 'IA _ _

.... ... :~x~-~'I--I-x-+-~=ó---X- - - - -I!>- - - - - - - IA

0 . 30L-0L------10~0~--~2~O~0~--~3~0~0~--~4~0~0----~5~O~O~--~6700~--~700 CYCLES SINCE START

FI G. 21: STABILITY