Simulating Combustion

1 Introduction (p. 1-2)

1.1 Preface

One of the central tasks of engineering sciences is the most possibly exact description of technical processes with the goal of understanding the dynamic behavior of complex systems, of recognizing regularities, and thereby of making possible reliable statements about the future behavior of these systems. With regard to combustion engines as propelling systems for land, water, and air vehicles, for permanent and emergency generating sets, as well as for air conditioning and refrigeration, the analysis of the entire process thus acquires particular importance.

In the case of model-based parameter-optimization, engine behavior is described with a mathematical model. The optimization does not occur in the real engine, but rather in a model, which takes into account all effects relevant for the concrete task of optimization. The advantages of this plan are a drastic reduction of the experimental cost and thus a clear saving of time in developmental tasks, see Kuder and Kruse (2000).

The prerequisite for simulation are mechanical, thermodynamic, and chemical models for the description of technical processes, whereby the understanding of thermodynamics and of chemical reaction kinetics are an essential requirement for the modeling of motor processes.

1.2 Model-building

The first step in numeric simulation consists in the construction of the model describing the technical process. Model-building is understood as a goal-oriented simplification of reality through abstraction. The prerequisite for this is that the real process can be divided into single processual sections and thereby broken down into partial problems. These partial problems must then be physically describable and mathematically formulatable. A number of demands must be placed upon the resulting model:

The model must be formally correct, i.e. free of inconsistencies. As regards the question of "true or false", it should be noted that models can indeed be formally correct but still not describe the process to be investigated or not be applicable to it. There are also cases in which the model is physically incorrect but nevertheless describes the process with sufficient exactness, e.g. the Ptolemaic model for the simulation of the dynamics of the solar system, i.e. the calculation of planetary and lunar movement.

The model must describe reality as exactly as possible, and, furthermore, it must also be mathematically solvable. One should always be aware that every model is an approximation to reality and can therefore never perfectly conform with it. The cost necessary for the solution of the model with respect to the calculation time must be justifiable in the context of the setting of the task.

With regard to model-depth, this demand is applicable: as simple as possible and as complex as necessary. So-called universal models are to be regarded with care.

It is only by means of the concept of model that we are in the position truly to comprehend physical processes.

In the following, we will take a somewhat closer look into the types of models with regard to the combustion engine. It must in the first place be noted that both the actual thermodynamic cycle process (particularly combustion) and the change of load of the engine are unsteady processes. Even if the engine is operated in a particular operating condition (i.e. load and rotational speed are constant), the thermodynamic cycle process runs unsteadily. With this, it becomes obvious that there are two categories of engine models, namely, such that describe the operating condition of the engine (total-process models) and such that describe the actual working process (combustion models).

With respect to types of models, one distinguishes between:

linguistic models, i.e. a rule-based method built upon empirically grounded rules, which cannot be grasped by mathematical equations, and
mathematical models, i.e. a method resting on mathematical formalism.

Linguistic models have become known in recent times under the concepts "expert systems" and "fuzzy-logic models". Yet it should thereby be noted that rule-based methods can only interpolate and not extrapolate. We will not further go into this type of model. Mathematical models can be subdivided into:

parametric, and
non-parametric

models. Parametric models are compact mathematical formalisms for the description of system behavior, which rests upon physical and chemical laws and show only relatively few parameters that are to be experimentally determined. These models are typically described by means of a set of partial or normal differential equations.

Non-parametric models are represented by tables that record the system behavior at specific test input signals. Typical representatives of this type of model are step responses or frequency responses. With the help of suitable mathematical methods, e.g. the Fourier transformation, the behavior of the system can be calculated at any input signal.

Like linguistic models, non-parametric models can only interpolate. Only mathematical models are utilized for the simulation of the motor process. But because the model parameters must be adjusted to experimental values in the case of these models as well, they are fundamentally error-prone. These errors are to be critically evaluated in the analysis of simulation results. Here too, it becomes again clear that every model represents but an approximation of the real system under observation.

1.3 Simulation

For the construction of parametric mathematical models for the simulation of temporally and spatially variable fluid, temperature, and concentration fields with chemical reactions, the knowledge of thermodynamics, fluid dynamics, and of combustion technology is an essential prerequisite, see Fig. 1.1.