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1. INTRODUCTION

The two-stroke engine has fascinated the engineering world to a great

extent because of its potential advantage of higher power to weight ratio, small

package size and fewer parts. This has made it an attractive proposition for

future automobile engine. In order to reduce the fuel consumption and hydrocarbon

emissions associated with the two-stroke engine, the recent years have witnessed

an extensive effort to model the engine cycle. Mathematical modelling of

engine cycle is expected to indicate the effects of various parameters on engine

performance and emissions and thus reduces the development time and cost.

1.1 Engine Simulation

In order to develop a prediction procedure for performance characteristics

of a two stroke engine, two aspects of the engine are to be simulated, namely

wave action in engine piping system and in-cylinder processes, i.e., scavenging

and charging of the cylinder and combustion of the charge. The interaction

of the above mentioned two aspects need special attention as the wave action

in engine piping system of a two stroke engine directly influences and is

influenced by the in-cylinder processes. The combustion process in engine

cylinder depends strongly on the scavenging gas flow during the open period

via the trapped conditions and unless the exhaust system is carefully designed

the gas exchange process in the cylinder will be adversely affected. Therefore

the accurate simulation of in-cylinder processes during both the open period

and the closed period and their interaction with the wave action in engine

piping system is essential in order to validate the predictions at the design

stage.

A typical small two stroke crankcase scavenged spark ignition (s.i.)

engine has a single exhaust port and two transfer ports in the cylinder and

an inlet port in the crankcase as shown in Fig. (1.1a). The timing diagram

of the ports is displayed in Fig. (1.1b). The cycle in a two stroke engine begins

as the piston travels up towards the top dead centre (tdc) and the inlet port

is open. Fresh charge enters into the crankcase through the inlet manifold while

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the cylinder charge is compressed. Near the top dead centre, combustion

occurs, the piston travels towards the bottom dead centre (bdc), the crankcase

volume decreases and some of the fresh charge may escape to the atmosphere

in a backward flow. After this period the inlet port closes and the fresh charge

is compressed in the crankcase. The gas exchange begins as the exhaust port

is opened. In the period in which both the transfer and exhaust ports are open

the cylinder is subjected to a pressure gradient which governs simultaneously

the inflow and the outflow streams through the open ports. In this period, the

compressed fresh charge in the crankcase flows through the transfer ducts into

the cylinder and scavenges the products of combustion through the exhaust

port. In the second half of this period, the piston travels upward, the crankcase

volume increases and a backflow from the cylinder to the crankcase through

the transfer ports may occur. The gas exchange process is completed at the

moment when the piston covers up the exhaust port. The engine cycle therefore,

can be divided into two distinct periods:

1. The closed period is related to the processes occurring when both

the scavenge and exhaust ports are closed, that is, compression,

combustion and expansion.

2. The open period is related to the gas exchange processes occurring

when the ports are open, that is, blowdown, scavenging and charging.

In two stroke engine cycle, the exhaust and intake processes take place simultaneously

which allows more residual gases to remain in the cylinder and more fresh

charge to escape from the exhaust port during the scavenging process and thus

leads to a reduction in the fuel efficiency of the engine as well as an increase

in the unburned hydrocarbons in the exhaust. This problem essentially minimized

the use of two stroke cycle engines in automotive applications as environmental

concerns grew.

At present, there are two approaches for modelling engine processes

1. Thermodynamic models : the gas properties are considered to be uniformly

distributed in space and the system can be described in a global sense.

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these models are also referred to as phenomenological or zero-dimensional

models.

2. Multi-dimensional models : with a distribution of properties in space,

the analysis can be carried out with spatial information retained in 1,

2 or 3 dimensions.

For formulation of the thermodynamic models, the partial differential equations

are integrated over space such that the resulting equations are first order

ordinary differential equations. In the multidimensional models, the integration

is carried out over one or more spatial directions giving second order partial

differential equations in one or more spatial variables. It is the difficulty

associated with the solution of these equations that makes multidimensional

models more time consuming and thus expensive to use.

In the present work, the engine simulation model follows a thermodynamic

formulation. Thephysics of various aspects of the engine operation are characterised

by separate models so that the complete engine model is divided in number

of physical submodels. The flow in the pipes is analysed by one dimensional

unsteady gas dynamic equations with variable area, friction, heat transfer and

the boundary equations at the pipe ends are represented by quasi-steady flow

relations. The combustion chamber is treated as a control volume with transfer

of mass during the gas exchange process and transfer of heat to the chamber

wall and the combustion process is modelled with a mass burn rate through

a flame propagation model. The scavenging characteristics are determined

based on a semi-empirical relationship which calculates the fraction of fresh

charge escaping the exhaust port during the scavenging process. Therefore,

simulation of engine cycle consists mainly of modelling the following two

parts :

1 . Wave action in engine piping system

2. In cylinder processes

A brief survey of the available literature on the above two aspects is given

below.

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1.1.1 Wave Action in Piping System

It is conventionally assumed that engine flow is one dimensional and

the equations which describe such a flow are quasi-linear hyperbolic partial

differential equations. These equations can be solved using the method of

characteristics and thus the hyperbolic equations are reduced to a set of

simultaneous ordinary differential equations which define the characteristic

curves, see for example Benson (1982). The velocity and thermodynamic

variables are continuous along the characteristic lines while across the characteristics

they may be discontinuous. The basic hyperbolic partial differential equations

when solved using finite difference methods produce solutions automatically

satisfying the Rankine-Hogoniot relations across a shock. However, real pressure

shocks seldom occur in engine flow while temperature discontinuities are

common in the exhaust pipes of internal combustion engines. Therefore, the

method of characteristics have been commonly used for the simulation of

engine flow problems. De Haller (1945) was the first to solve the characteristic

equations graphically and Jenny (1950) was first to apply the graphical

solution to the internal combustion engines. Benson et al (1964) was the first

to solve the characteristic equations using computational techniques. Benson

(1982) solved the homentropic as well as the non-homentropic flow equations.

For non-homentropic flow the effects of entropy, friction, heat transfer, area

change and variable specific heats were taken into account. The method was

successfully applied to single and multi-cylinder engines. However, in the

above work simulation of engine with an expansion chamber was not carried

out. Blair (1990) contributed significantly to the theoretical and experimental

analysis of the unsteady flow in two stroke engines, particularly with expansion

chamber. However, only homentropic calculations were carried out and the

analysis was confined to the open period for known release conditions at the

time of exhaust port opening.

Payri et al (1986) noted that Benson algorithm (Benson et al, 1964)

resulted into some parasitic discontinuities in pressure for the exhaust and inlet

pipes. They suggested modifications to Benson algorithm which eliminated

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these discontinuities. This was achieved by interpolating pressure p, velocity

u and non-dimensional speed of sound A^ during the integration procedure

instead of interpolating the usual variables used in Benson algorithm, i.e.,

Riemann variables (A, and p) and A^. Payri et al (1986) algorithm (the Modified

algorithm) was not validated so far for complete engine simulation of a two

stroke engine fitted with an expansion chamber.

Zucrow and Hoffman (1977) expressed the characteristic and compatibility

equations which correspond to one dimensional unsteady flow in terms of

pressure p, velocity u, and density p. They reported a complete numerical

procedure (Zucrow and Hoffman algorithm) for integration of the characteristic

^nd compatibility equations in terms of the said variables for internal flow

and for simple boundary conditions. The numerical procedure is based on a

mesh method for integrating the equations of the two characteristics as well

as the pathline equations. Therefore, the mesh points in Zucrow and Hoffman

algorithm represent the solution points where the three characteristic curves

pass.

Benson and Modified algorithms referred above employ mesh method

for integrating both the right and the left running characteristic equations while

non-mesh method is employed for integrating the pathline equations. However,

the calculation procedure of the non-mesh method for integrating the pathline

equations in case of both Benson and the Modified algorithms is more complicated

as compared with the mesh method employed in Zucrow and Hoffman algorithm.

The solution technique of the Modified algorithm is further complicated for

the following two reasons :

1. The procedure requires locating the intersection of the rearward running

characteristics with the previous solution points using the characteristics

passing in the surrounding path points rather than the surrounding mesh

points as it is the case with Benson algorithm. This makes the procedure

an iterative one since the locations of path points vary and an accuracy

limit is to be set for the convergence of the solution.

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2. The Modified algorithm requires tracing the history of the pathlines

leaving one pipe and entering the next. While in Benson algorithm the

history of pathlines is lost.

The above two factors result into more CPU time and thus high computing

cost for the Modified algorithm. Brief descriptions of Benson algorithm as

well as the Modified algorithm along with some boundary equations are given

in Appendix-A. It is worth noting here that the boundary equations used with

Benson algorithm and with the Modified algorithm remain the same since the

basic difference between the two algorithms for solving any problem lies in

the solution for the internal flow.

1.1.2 In-Cyl inder Processes

In-cylinder fluid motion plays significant role in determining the

combustion characteristics which in turn determines engine performance and

emission characteristics. Simulation of in-cylinder phenomena includes modelling

of the scavenging and charging processes during the open period and modelling

of compression, combustion and expansion processes during the closed period.

A brief review of available models of the above processes is described below:

1.1.2a Scavenging and Charging Processes

The early models to simulate the scavenging process were based on the

assumptions of constant volume, constant pressure and temperature (Hopkinson

1914). These models are known as perfect displacement or perfect mixing

models and did not compare well with the experimental results since the actual

scavenging process is neither perfect mixing nor perfect displacement process.

Based on experimental observations, for example (Dedeoglu 1971), zonal

models were developed (Streit and Boreman 1971, Benson 1977, Chen and

Wallace 1987a. Chen and Wallace 1987b). In these models, the combustion

chamber was divided into zones including a burned gas zone, a fresh charge

zone and a mixing zone. In some of these models, a short circuit passage for

the fresh charge to flow directly to the exhaust port was included. The scavenging

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process was divided into several phases with specific assumptions for each

phase. In most of the zonal models numerical solution of each zone is based

on the conservation of mass and energy of the individual zones and the fluid

motion is neglected. However, Chen and Wallace (1987b) included the conservation

of momentum of the individual zones. Sher (1985) proposed a scavenging

model based on the exhaust gas purity. It is assumed that the time variation

of the mass fraction of the fresh air content in the gas passing through the

exhaust port exhibitan 's' type curve and is related to the scavenging efficiency.

The disadvantage of the above models is that they are unable to predict

the scavenging efficiency or charging efficiency of a particular engine without

resorting to experiments on combustion chamber and ports geometry. The

recent trend in scavenging simulation is to use multi-dimensional models of

in-cylinder flow and obtain numerical solution of the conservation equations

with appropriate boundary conditions. However, for the present work, Sher

model (Sher 1985) is used in view of its simplicity and ability to evaluate

important engine parameters such as charging efficiency and scavenging efficiency.

The values of the empirical constants (the form factor and the shape factor)

involved in the scavenging model of Sher are not known for the engine under

investigation and therefore to determine their proper values, the effects of the

above constants on the predicted scavenging characteristics have been investigated.

1.1.2b Combustion Process

Turbulence which plays a major role in the combustion process is

generated during the intake stroke by the high shear flow produced by the inlet

jet. However, the mixture motion and turbulence characteristics are largely

governed by the engine geometry such as the intake port, piston and cylinder

head designs. These characteristics in turn affect the turbulent flame propagation

and the heat release process. Thus it is necessary to understand the structure

of the flame as it develops from the spark discharge position and the speed

at which it propagates across the combustion chamber and only multi-dimensional

models can predict these effects. However, thermodynamic models have been

successful in describing the effects of thermodynamic changes on engine

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performance and emissions and most of the engine models which are at present

in use, are of the thermodynamic type.

Blizard and Keck (1974) proposed a quasi-dimensional entrainment

burn-up model in which the flame propagation was modelled as the entrainment

and subsequent burning of discrete, coherent eddies. The entrainment front

was considered to propagate across the chamber with an entrainment speed

that depends on the turbulent intensity and the laminar burning velocity.

Tabaczynski (1980) improved Blizard and Keck (1974) model by incorporating

detailed small scale eddy structure proposed by Tennekes (1968) and a burn

up model based on fast flame propagation along vortex tubes proposed by

Chomiak (1970). The turbulence intensity during combustion was modelled

by using the rapid distortion theory of Wong and Hoult (1979).

Chen et al (1992) have further improved the model of Tabaczynski

et al (1980) by including the history of entrainment in the burning rate equation

and thus correcting the slow burning rates which were predicted by Tabaczynski

et al (1980). The eddy entrainment model of Tabaczynski (1980) without the

modifications of Chen et al (1992) was validated for a two stroke engine by

Reid and Douglas (1994) using k-E turbulence model for predicting the turbulent

burning velocity.

In the present work, Tabaczynski model including the modifications of

Chen et al (1992) to the burning equation is used for simulating the combustion

process. Rapid distortion theory (Wong & Hoult, 1979) is used to evaluate

the turbulence intensity during the combustion process and the results are

compared with the results of the eddy entrainment model of Tabaczynski (1980)

without the modifications of Chen et al (1992).

1.2 Present Contribution

The present work is directed towards the simulation of various processes

governing the operation of a small two stroke crankcase scavenged spark

ignition engine in order to predict its performance characteristics. The emphasis

in this work is on wave action predictions in engine piping system, particularly

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in the exhaust system which includes convergent-divergent parts with the

possibility of shock formation. The numerical procedure of Zucrow-Hoffman

(1977) which is based on the method of characteristics is employed for analysing

the flow in simple systems as well as in engine piping system. Predictions

of this procedure has been compared with the predictions of existing procedures

based on the method of characteristics such as Benson algorithm and the

Modified algorithm. The numerical procedure was validated against the experimental

data whenever available. The work therefore, is divided into two main parts,

namely the numerical evaluation of Zucrow-Hoffman algorithm for simple flow

problems and for engine flow.

1.2.1 Numerical Evaluation of Zucrow-Hoffman algorithm

The first part of the present study deals with evaluation of Zucrow-

Hoffman algorithm predictions as compared to the other two algorithms, i.e.,

Benson algorithm and the Modified algorithm. The predictions of the three

algorithms are validated against experimental data whenever available or

against available theoretical solutions. The flow problems considered are

briefly described below. The details for this part of study is available in Section

(5.1).

1. Shock wave in a straight pipe with a closed end (Benson et al, 1964)

A pressure pulse of an amplitude of 1.68 atm was applied at the open

end of a straight pipe which propagated to the closed end and is reflected

back to the open end. The predicted pressure diagrams using the three

algorithms are compared with the results of the non mesh method of

solution by Benson et al (1964). Effects of mesh size and number of

applications of the modified Euler predictor-corrector integration procedure

employed in case of Zucrow-Hoffman algorithm are also examined.

2. Wave action in a straight pipe fitted with a nozzle (Benson, 1982)

A pressure-crankangle diagram representing the blowdown pulse in

a two stroke-engine is applied at one end of a straight pipe terminated

by a nozzle at the other end. The predicted pressure at nozzle end using

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the three algorithms is compared with the experimental measurements.

The effect of number of applications of the modified Euler predictor-

corrector integration procedure employed in case of Zucrow-Hoffman

algorithm is also examined.

3 . Wave action in a straight pipe with a diffuser (Wallace and Boxer,

1956)

A flow system is considered which consists of a straight pipe joined

to four lengths of diffuser cones having the same angle of divergence.

A pressure-crankangle diagram which represents the blowdown pulse

of a two stroke engine is applied at the entrance to the straight pipe

and the predicted pressure diagrams at diffuser entry section for the three

algorithms are compared with the experimental measurements of Wallace

and Boxer (1956). Effect of mesh size on the pressure developed at

diffuser entry is also examined.

4. Discharge from Cylinder into a straight pipe (Benson, 1982)

A flow system consisting of a single cylinder four-stroke engine with

a straight exhaust pipe terminated by a nozzle is considered. Cylinder

pressure-crankangle diagram and valve area-crankangle diagram are

given and the pressure-crankangle diagrams in the exhaust pipe at both

ends are calculated using the three algorithms and compared with the

results of the graphical method of characteristics by Benson (1982). The

effects of the initial exhaust pipe temperature and the mesh size on the

predicted pressure diagrams are examined.

Once the capability of Zucrow-Hoffman algorithm for wave action

predictions was established, the algorithm was applied with confidence to

simulating the wave action in engine piping system under firing conditions

as described below :

1.2.2 Engine Simulat ion

The second part of the study is concerned with the simulation of a small

two-stroke spark ignition engine and the development of a prediction procedure

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for engine performance characteristics, taking into account the various processes

governing engine operation. The engine data considered is that of Husqvarna-

250 with MKl exhaust system described by Blair and Ashe (1976). The

simulation includes wave action in engine piping system along with in-cylinder

processes such as scavenging and combustion described in Section (1.1.2).

For wave action analysis in inlet, transfer and exhaust systems, the

effects of friction, heat transfer, variable specific heats and area changes are

considered in the solution of one dimensional unsteady flow equations. The

following boundary conditions are encountered in engine simulation:

1. Closed end

2. Fully open end

3. Partially open end (nozzle)

4. Cylinder boundary

5. Carburettor boundary

6. A joint of two pipes

The equations which satisfy the above boundary conditions in terms of pressure

p, velocity u and density p are derived, and the unit processes for various

solution points based on Zucrow-Hoffman algorithm (1977) are developed.

Modified Euler predictor-corrector method is employed for integrating the

characteristic and the compatibility equations. Further, the numerical procedures

are developed for employing Benson algorithm and the Modified algorithm

for wave action analysis. Tabaczynski et al model (1980) as modified by Chen

et al (1992) is employed for simulating the combustion process and Sher model

(1985) is employed for simulating the scavenging and charging processes.

Finally, a predictive procedure is developed based on Zucrow-Hoffman algorithm

which successfully predicts pressure history at various locations of engine

system and gives the correct trend of engine performance characteristics.

The work in this section consists of the following three parts :

1. Wave action analysis in engine piping system, i.e., inlet, transfer and

exhaust systems for the engine Husqvarna-250 at 6500 RPM. Two

exhaust systems are considered :

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I. A straight pipe

II. MKl-standard expansion chamber described by Blair and Ashe

(1976).

Pressure-crankangle diagrams and temperature-crankangle diagrams are

predicted at various locations of engine piping system and compared

critically for the three algorithms. The wave action predictions for

engine with straight exhaust pipe are given in Section (5.2.1) and for

engine with expansion chamber in Section (5.2.2).

2. The second part deals with the study of scavenging characteristics

predicted by Sher model (1985), see Section (5.2.3) for details.

3. In the third part the effects of two burn rate equations by Tabaczynski

et al (1980) and Chen et al (1992) on the predicted mass burned, pressure

and temperature in the cylinder during the combustion process are

examined. Also, the effects of two different turbulent flame speed

expressions by Hires etal (1978) and Chenet al (1991) are also examined,

see Section (5.2.4).

1.2.3 Experimental Data and Validation Studies

The engine Husqvarna-250 with MKl exhaust system described by Blair

and Ashe (1976) is simulated in this work. The experimental data reported

in the above work are pressure-crankangle diagrams in inlet and exhaust pipes

and the pressure-crankangle diagrams in the cylinder and crankcase, the

characteristics of these diagrams are described in Section (5.2.2.1). The performance

characteristics of the engine such as delivery ratio, charging efficiency, scavenging

efficiency and brake mean effective pressure for a range of engine speeds are

also available in this work. The wave action results of Zucrow-Hoffman

algorithm for the above engine are validated against the experimental results

in Section (5.2.2.2) for the two engine speeds, 6500 RPM and 4000 RPM. The

performance characteristics are validated in Sections (5.2.3) and (5.2.4).

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The computer programs are written in Fortran-77 and are run on DEC

ALPHA-3000/400 computer system. The flow chart for the engine simulation

model employing Zucrow-Hoffman algorithm for wave action analysis is given

in Fig. (D. l ) , Appendix-D.

1.3 Layout of the Thesis

The present thesis is divided into six chapters and four appendices.

Chapter 1 gives brief description of various aspects of engine processes

and modelling of these processes. The survey of the previous work in this area

is described briefly. The contribution of the present study is also mentioned.

Chapter 2 gives a detailed review of the available literature on modelling

of the various processes of two stroke engine and the deficiencies of the

available models are highlighted.

Chapter 3 describes the unsteady one dimensional flow equations. The

characteristics and compatibility equations in terms of pressure, velocity and

density are presented. Derivations of the equations which describe the various

boundary conditions encountered in engine simulation in terms of pressure,

velocity and density are also included. Formulations of the scavenging and

combustion models adopted in the present study are given.

Chapter 4 describes the integration procedure of the characteristic and

the compatibility equations using Modified Euler predictor-corrector algorithm.

The derived finite difference equations are also presented. Unit processes for

various solution points in the flow are described along with the corresponding

computer flow charts.

Chapter 5 presents detailed discussion on the results of wave action

predictions obtained using the three algorithms for the selected flow problems

and for the engine Husqvarna-250 with different exhaust systems. Predictions

of scavenging and combustion models are also presented. Validations of the

predicted results of pressure-crankangle diagrams and performance characteristics

of the above engine are given.

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Chapter 6 presents general concluding remarks about the comparative

studies carried out for several problems using the three algorithms and the

capability of Zucrow-Hoffman algorithm to deal with problems associated with

engine flow.

The references are available at the end of Chapter 6. At the end of the

thesis the following four Appendices are provided :

Appendix-A:

Appendix-B:

Describes briefly Benson algorithm and the Modified

algorithm along with the boundary equations for these

algorithms.

Contains the procedure for the initiation of combustion

process as well as the calculations of the volumes of

both burned and unburned zones. It also includes areas

of burned and unburned gases exposed to the cylinder

and areas of the flame front.

Contains the procedure for calculations of the number

of moles of various products at particular pressure and

temperature and the calculations of viscosity and thermal

conductivity of various products and of the fuel (iso-

otane).

Appendix-D: Contains the following computer flow charts :

Fig. D.l Flow chart for the engine simulation programme

Fig. D.2 Flow chart for crankcase calculations

Fig. D.3 Flow chart for cylinder calculations

Appendix-C:

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Scavenge Port

Exhaust Port

Scavenge Port

Inlet Port

Fig. (1.1a) A Typical Two-stroke Crankcase Scavenged Engine.

ec Y

sc

i o ^ itdc

ic

7 eo

/so

tdc : Top Dead Centre bdc : Bottom Dead Centre ic : Inlet Port Closes io : Inlet Port Opens eo : Exhaust Port Opens ec : Exhaust Port Closes so : Scavenge (Transfer) Port Opens sc : Scavenge (Transfer) Port Closes

Fig (1.1b) Port Timing Diagram