Zero-Dimensional Combustion Simulation in Real Time

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.

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 FrameworkThe 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.

Components of combustion

engine models

by Oliver Philipp, Robert Hoepler, Cornelius Chucholowski, Tesis Dynaware

Thermodyna-mical engine

dynamics simulation

paves the way to faster ECU

function deve-lopment.

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32 AutoTechnology 2/2007

Figure 2 shows a typical engine model with its major components. The intake part is composed of individual model blocks for the com-pressor, intercooler and throttle as well as containers between the inter-cooler and throttle and between the throttle and the engine. The ex-haust part consists of models for a turbine, an oxidising catalytic converter, a number of lambda sensors and a container model located 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 model is adapted to specific requirements by either changing the number of blocks, for example the cylinder blocks, or rearranging 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 1: Process for setting up an HiL/SiL applica-tion.

Figure 2: Schematic view of a typical model.

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equations and algorithms as well as the parameteri-sation. Preparing the parameters for a new model can be a tedious and error-prone task. To alleviate this work, the model library is accompanied by a data preparation system called Preprocessing. It cal-culates the model parameters from standard meas-urements and data sheet information usually avail-able during engine development [4]. One important step of this process calculates the characteristic map of the Arrhenius coefficient Karrh, shown in Figure 3, which is required by the combus-tion model. An optimisation algorithm adapts the coefficient for each operating point in such a way that the sum of the mean combustion torques of the cylinders in the simulation matches the combustion torque calculated from the measurement data.

In the same way, heat transfer coefficients and parameters describing turbine and compressor blocks, for example, are calculated by Preprocessing. Many of these calculations are also based on results of the engine characteristic map measurement.

Gas Dynamics and CombustionAppropriate 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 heat release and pressure during combustion, and (iii) determination of the gas composition.

The gas state in the manifolds, for example the intake and exhaust manifolds, is simulated by con-tainer models. These calculate the pressure, tempera-ture and gas composition, presuming the gas to be ideal.

A realistic temperature calculation considers the heat loss to the surroundings of each container. 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 Tin,

where kA is the heat transfer coefficient between the container and its surroundings. This leads to the or-dinary differential equation (ODE):

mContainercvTContainer = kA (TContainer TAmbient) + mincpTin moutcpTContainer

pcontainer = m p

_____ m + T p

____ T

This ODE is solved in the presented approach with a fully implicit integration method in order to 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].

The gas under consideration is composed of O2, N2, CO2, CxHy, CO, NOx and particles. The composition of the exhaust mass flow is calculated as a weighted average of the composition of the inflowing mass flows.

The simulation of the combustion is based on the laws of thermodynamics: the gas state in the cylin-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 inside the cylinder synchronously to the crank angle and the resulting cylinder torque. Syn-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= Qwall+QcombustionpV+cpminTin+cpmoutToutmcvT

__________________________________

mcv . (1)

The time-dependent cylinder volume is deter-mined from the current crank angle and the kine-matics of the crank drive [1]. The wall heat transfer coefficient a used in Qwall = awall (T Twall) is calcu-lated using various simplifying assumptions in ac-cordance with the approach by Woschni [2].The reaction kinetics of the combustion of fuel is ap-proximated by the following chemical reaction

CxHy + (x + y _ 4 O2) xCO2 + y _ 2 H2O.

Hence, the heat release dQcombustion/dt during com-bustion can be represented by the concentration of CO2

dQcombustion _ dt

= 1 _ x d(c(CO2)) _

dt mCylinder HFuel

In the approach presented here, the change in the concentration of CO2 is determined by an Arrhenius equation, where KArrh is the operating point-depend-ent Arrhenius parameter [2]:

Figure 3: Characteristic map of the Arrhenius coefficient Karrh resulting from Pre-processing.

The simulation of the combustion is

based on the laws of thermo-

dynamics

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34 AutoTechnology 2/2007

d(c(CO2)) _ dt

= KArrh exp ( 4650K _ T ) c(O2) c(CxHy)The concentrations of O2, H2O, CO2 and CxHy in

the exhaust gas are calculated from the reaction ki-netics, while the concentrations of CO, NOx and par-ticles are determined by characteristic maps.

The ignition delay time of the injected fuel has a considerable influence on the heat release with re-spect to time. The delay time between injection and ignition is considered by [2]:

tdelay = 4.4 10 4 p1.2 exp ( 4650K _ T ) The influence of multiple injections on the heat

release rate during combustion, as depicted in Fig-ure 4 for the case of a double injection, is taken into account by an abrupt change in the concentration of CxHy in accordance with the quantity of fuel injected. This assumption is justified by the fact that, during the simulation, injection signals are evaluated dis-cretely at each time step.

Solving the differential equation (1) requires a method of high order and low computational effort to calculate the crank angle-resolved values of tem-perature, pressure and torque with adequate pre- cision. The approach presented here is based on DOPRI5, which permits a maximum angle increment of Da = 2 at a simulation step size of 1 ms and a maximum engine speed of 6000 rpm to achieve an accuracy comparable with the explicit Runge-Kutta method (RK 4) with an increment of Da=1.

An innovative step size control system (SCS) was designed to enable real-time operation of the model 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 shaft-synchronous combustion torque are mapped to mean values at each simulation step.

An important aspect to be considered is the con-tinuous consideration of the injection signals in HiL 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 ScenariosThe presented model facilitates the development process of an engine control unit (ECU) at various 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,

since an HiL test rig with the presented model was available, the controller design was tested on the HiL. The simulation results obtained allowed for an early optimisation of the controller design and its parameters. Thus, development results were available much earlier than expected.

ConclusionReal-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.

The problem of very small time scales introduced by treating the combustion process in detail on the 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.

[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; Rhlich, Stefan: The enDYNA Preprocess-ing tool for model parameterisation, Simulation und Test in der Funktions- und Softwareentwicklung fr die Automo-bilindustrie, 2005.

Early optimisa- tion of the con-troller design and its parameters

Figure 4: Heat release in the case of double injection.

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