Simulating Combustion (PDF)

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.