2024年4月22日发(作者：)
C-Technologies
Zero-Dimensional Combustion
Simulation in Real Time
by Oliver Philipp, Robert Hoepler, Cornelius Chucholowski, Tesis Dynaware
The development and validation of engine control device functions relies more and more on
modern simulation and modelling techniques. The en-Dyna Themos models not only provide a
realistic description of the physical behaviour of the entire internal combustion engine, they
also satisfy the need for high computational efficiency mandated by the real-time application
in Software-in-the Loop and Hardware-in-the-Loop environments.
Components of
combustion
engine models
The latest engine technology has a strong impact on
the model-based development and validation of con-
trol device functions. Whereas well-known mass-flow
based models were sufficiently accurate in the past,
more detailed model approaches are required nowa-
days to consider the signals measured by new sensors
or regard the influence of new actuators. A typical
example is the introduction of cylinder pressure sen-
sors on diesel engines. The sensor signals have to be
physically consistent to pass the plausibility checks of
diagnosis functions, for example those demanded by
OBD II (Onboard-Diagnostic System) legislation.
The model presented here maps all of the main
components of modern internal combustion engines,
including the compressor, turbine, EGR valve, particu-
late filter and oxidizing catalytic converter, to form
Simulink blocks. In this paper, we focus on the simu-
lation of the combustion process within the cylinder
of a diesel engine, which is akin to the model of a
spark-ignition engine not presented here. The chosen
approach is a zero-dimensional description of the
combustion, which takes into account the inert gas
portion from the recycled exhaust gas as well as mul-
tiple injections in the cylinder pressure calculation.
It provides the required degree of physical detail
and enables simulation step sizes commonly used in
HiL applications, such as 1 ms and above, whereas
other model approaches either require smaller step
sizes in order to ensure accurate simulation or the
computational cost depends strongly on, for exam-
ple, the engine speed.
Accuracy and computational performance are
enhanced by an innovative step size control system
that maintains upper limits for the computing time
and a maximum angle increment essential for the
accuracy of the simulation independent of the step
size of the overall simulation.
Engine Modelling Framework
The modelling framework depicted in Figure 1 com-
prises two main parts:
• Simulink block libraries representing all promi-
nent parts of the engine and the vehicle, such as
the cylinder, throttle, manifold, injector and
transmission. This modular structure of fully ge-
neric model blocks enables almost all engine
model configurations to be implemented quickly.
• A data preparation tool — so-called Preprocessing
— to derive the model parameters in a fast and
reproducible process from measurements and data
sheet information. For each model block, Preproc-
essing provides appropriate methods to calculate
the required parameters.
Thermodyna-
mical engine
dynamics
simulation
paves the way
to faster ECU
function deve-
lopment.
32
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Figure 1: Process
for setting up an
HiL/SiL applica-
tion.
The intake part is composed of individual model blocks for the com-
Figure 2 shows a typical engine model with its major components.
pressor, intercooler and throttle as well as containers between the inter-
cooler and throttle and between the throttle and the engine. The ex-
haust
converter, a number of lambda sensors and a container model located
part consists of models for a turbine, an oxidising catalytic
between the engine and the turbine. The compressor and turbine are
rigidly linked by a shaft. The intake and exhaust manifolds are con-
nected by an EGR valve and an EGR cooler. Each cylinder is modelled
by an individual instance of a generic library block.
the number of blocks, for example the cylinder blocks, or rearranging
The model is adapted to specific requirements by either changing
existing model blocks. For instance, two-stage charging can be realised
by the arrangement of two compressor and turbine blocks connected by
a container block. The operating point-dependent bypass of a compres-
sor or a turbine can be modelled by throttle blocks connected to adja-
cent containers. In order to exploit the full capability and accuracy of
the model library, it is necessary to have correct model parameters, as
the overall quality of the simulation results is determined by the model
Figure 2: Schematic view of a typical model.
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Figure 3: Characteristic map of the Arrhenius coefficient K
processing.
arrh
resulting from Pre-
the combustion is
The simulation of
equations and algorithms as well as the parameteri-
sation. Preparing the parameters for a new model
laws of thermo-
based on the
can be a tedious and error-prone task. To alleviate
dynamics
this
data preparation system called Preprocessing. It cal-
work, the model library is accompanied by a
culates the model parameters from standard meas-
urements and data sheet information usually avail-
able during engine development [4].
One
characteristic map of the Arrhenius coefficient K
important step of this process calculates the
arrh
shown in Figure 3, which is required by the combus-
,
tion
coefficient for each operating point in such a way
model. An optimisation algorithm adapts the
that the sum of the mean combustion torques of the
cylinders in the simulation matches the combustion
torque calculated from the measurement data.
parameters
In the same way, heat transfer coefficients and
blocks, for example, are calculated by Preprocessing.
describing turbine and compressor
Many of these calculations are also based on results
of the engine characteristic map measurement.
Gas Dynamics and Combustion
Appropriate simulation of the processes inside the
cylinder in engine control device test applications
requires (i) treatment of the gas dynamics describing
the inflowing and outflowing gas, (ii) calculation of
the
and (iii) determination of the gas composition.
heat release and pressure during combustion,
intake and exhaust manifolds, is simulated by con-
The gas state in the manifolds, for example the
tainer models. These calculate the pressure, tempera-
ture and gas composition, presuming the gas to be
ideal.
heat loss to the surroundings of each container. The
A realistic temperature calculation considers the
following approach is used in the model to calculate
the temperature of the exhaust gas from the weight-
ed mean temperature of the inflowing mass flows T
in
,
34
where kA is the heat transfer coefficient between the
container and its surroundings. This leads to the or-
dinary differential equation (ODE):
m
Container
c
v
T
˙
Container
= kA · (T
Container
∑m˙
– T
Ambient
T
) +
in
c
p
T
in
– m˙
out
c
pContainer
p˙
m˙
m
· p
+
˙
· p
container
=
_____
____
T
T
with a fully implicit integration method in order to
This ODE is solved in the presented approach
guarantee a stable calculation of the container pres-
sure even in the case of simulation step sizes >1 ms
and small container volumes. If this problem is treat-
ed by explicit or partially implicit integration meth-
ods, the solution of the ODE may become unstable
[3].
N
The gas under consideration is composed of O
2
,
2
, CO
2
, C
x
H
y
, CO, NO
x
of the exhaust mass flow is calculated as a weighted
and particles. The composition
average of the composition of the inflowing mass
flows.
laws of thermodynamics: the gas state in the cylin-
The simulation of the combustion is based on the
der is determined by the balance of mass and energy.
It is assumed that the gas state is homogenous in the
entire cylinder, also known as a zero-dimensional
model approach. The calculation of the heat release
and heat losses forms the basis for simulating the
pressure
crank angle and the resulting cylinder torque. Syn-
inside the cylinder synchronously to the
chronous in this context denotes that the crank an-
gle is provided by an external source, for example
HiL hardware or a separate model block, to ensure
that the current model calculation uses the present
crank angle.
Using equilibrium thermodynamics, the gas temper-
ature is determined by
T
˙
=
__________________________________
Q
˙
wall
+Q
˙
combustion
–p·V
˙
+c
p
m·c
·m˙
in
·T
in
+c
p
·m˙
out
·T
out
–m˙·c
v
·T
v
. (1)
mined from the current crank angle and the kine-
The time-dependent cylinder volume is deter-
matics of the crank drive [1]. The wall heat transfer
coefficient
˙
wall
lated using various simplifying assumptions in ac-
a used in Q = a
wall
(T – T
wall
) is calcu-
cordance with the approach by Woschni [2].
The reaction kinetics of the combustion of fuel is ap-
proximated by the following chemical reaction
C
x
H
y
+
(
x +
y
_
4
O
2
)
→ xCO
y
2
+
_
2
H
2
O.
Hence, the heat release dQ
combustion
bustion can be represented by the concentration of
/dt during com-
CO
2
dQ
_
combustion
dt
=
1
_
x
·
d(c(CO
_
))
dt
2
· m
Cylinder
· H
Fuel
concentration of CO
In the approach presented here, the change in the
equation, where K
2
is determined by an Arrhenius
ent Arrhenius parameter [2]:
Arrh
is the operating point-depend-
AutoTechnology 2/2007
d(c(CO
_
dt
2
))
= K
Arrh
· exp
(
–
4650K
_
T
)
· c(O
2
) · c(C
x
H
y
)
the exhaust gas are calculated from the reaction ki-
The concentrations of O
2
, H
2
O, CO
2
and C
x
H
y
in
netics, while the concentrations of CO, NO
x
ticles are determined by characteristic maps.
and par-
considerable influence on the heat release with re-
The ignition delay time of the injected fuel has a
spect to time. The delay time between injection and
ignition is considered by [2]:
t
delay
= 4.4 · 10
– 4
· p
–1.2
· exp
(
_
4650K
T
)
release rate during combustion, as depicted in Fig-
The influence of multiple injections on the heat
ure
account by an abrupt change in the concentration of
4 for the case of a double injection, is taken into
C
x
This assumption is justified by the fact that, during
H
y
in accordance with the quantity of fuel injected.
the simulation, injection signals are evaluated dis-
cretely at each time step.
method of high order and low computational effort
Solving the differential equation (1) requires a
to calculate the crank angle-resolved values of tem-
perature,
cision.
DOPRI5, which permits a maximum angle increment
The
pressure
approach
and
presented
torque with
here
adequate
is based
pre-
on
of
maximum engine speed of 6000 rpm to achieve an
Da = 2° at a simulation step size of 1 ms and a
accuracy comparable with the explicit Runge-Kutta
method (RK 4) with an increment of Da
designed to enable real-time operation of the model
An innovative step size control system (SCS) was
=1°.
mandatory for HiL operation. During the combustion
phase, the SCS subdivides one step into several mi-
cro-steps [3]. A time-based solution ensures that the
CPU load is almost independent of the engine speed
and leads to sufficient precision of the combustion
process even for step sizes >1 ms. Values such as the
crank
mapped to mean values at each simulation step.
shaft-synchronous combustion torque are
tinuous consideration of the injection signals in HiL
An important aspect to be considered is the con-
operation. When the measurement technology used
in this scenario is able to continuously pass injection
signals to the model, alterations in the injection sig-
nal directly effect the simulation without delay.
Application Scenarios
The
process of an engine control unit (ECU) at various
presented model facilitates the development
stages. In controller design, a graphical specification
of the controller function may be interfaced to the
engine model to validate the conceptual design. Pa-
rameter studies up to pre-calibration of the controller
before it is run with the real engine can reveal sensi-
tivity to controller parameters. Tests of the ECU on an
HiL test rig take place later in the development, either
for the ECU alone or as a part of a network of con-
trollers for integration tests. In a recent application, a
car manufacturer developed controller functions with
cylinder pressure feedback. At first, it was planned to
test these functions on the real engine. However,
AutoTechnology 2/2007
C-Technologies
since an HiL test rig with the presented model was
Early optimisa-
available, the
tion of the con-
HiL. The simulation results obtained allowed for an
controller design was tested on the
troller design and
early optimisation of the controller design and its
its parameters
parameters. Thus, development results were available
much earlier than expected.
Conclusion
Real-time engine simulation including gas dynamics
and combustion is a key enabler for testing leading-
edge engine control device functions and can be ap-
plied to design control algorithms at an early stage
of the development process, with the model simulat-
ing the engine as a controlled system. The high-fi-
delity approach presented here includes a zero-di-
mensional model for the simulation of combustion
that guarantees a realistic calculation of the crank-
shaft-related combustion torque and the pressure in
the cylinder.
by treating the combustion process in detail on the
The problem of very small time scales introduced
one hand and expensive computations on the other
is solved by an innovative step size control to main-
tain real-time capability. Hence, the same model is
applicable in SiL and HiL applications for designing
and testing control device functions.
Figure 4: Heat release in the case of double injection.
[1] Pischinger, Rudolf; Kell, Manfred; Sams, Theodor: Thermo-
dynamik der Verbrennungskraftmaschine; Springer Verlag,
Berlin, 2002.
[2] Urlaub, Alfred: Verbrennungsmotoren; Springer Verlag,
Berlin,1995.
[3] Philipp, Oliver, Thalhauser, Josef: A Diesel Engine Model
with Turbocharging, EGR and Cylinder-pressure Calcula-
tion for HiL and SiL, 5th IAV Symposium, 2005.
[4] Philipp, Oliver; Röhlich, Stefan: The enDYNA Preprocess-
ing tool for model parameterisation, Simulation und Test in
der Funktions- und Softwareentwicklung für die Automo-
bilindustrie, 2005.
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