Computational Modelling of Shock Waves in Transsonic Flow Regime

Stephan Reichel

When developing machines and facilities with optimization regarding fluid dynamic behavior, the form of the optimization tools results from the operating conditions of the studied flow (laminar, turbulent, incompressible, trans-sonic, hyper-sonic, molecular, continuous etc.). If mixed conditions are present, the interactions between the sub-models has to be investigated and modeled through coupled transport equations.

The modeling of the behavior of thermo-fluid dynamic systems is achieved through computational methods. For this, the fluid domain of a complex technical flow is discretized in single cells. Furthermore, previously developed transport equations are discretized into a system of discrete differential equations. After linearization large sparse systems of linear equations are the result. The fluid and thermodynamic properties for each single cell of the discretized volume are then computed using modern solving algorithms. The computational engineering tool for the study and analysis of these problems is called CFD (Computational Fluid Dynamics).

Further technical applications such as sprays and reacting flows are characterized by their time-dependent behavior. In order to describe them, macro-scale laws are developed based on micro-scale investigations and the continuum hypothesis (usually used for rheological modeling). This way, properties associated with molecular motion are transformed into models of reactive flows or continuum mechanics. The description of molecular flows through continuous models do not satisfy the diffusive and convective behavior of dilute gas flows in micro-channels. In this case, the non-continuous motion of the dilute gas flow is characterized by the very high values of the Knudsen number.