1. introduction -...
TRANSCRIPT
- 1 -
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
- 2 -
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.
- 3 -
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.
- 4 -
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
- 5 -
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.
- 6 -
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
- 7 -
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
- 8 -
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
- 9 -
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
- 1 0 -
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
- 1 1 -
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 :
- 1 2 -
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).
- 1 3 -
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.
- 1 4 -
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:
- 1 5 -
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