The equations of fluid and thermodynamics

Abstract

The fundamentals for the calculation of turbulent flows are given by the basic equations of fluid and thermodynamics. There are several ways to introduce these equations. After introducing the fluid dynamic variables in section 4.1, these equations will be derived here in sections 4.2 and 4.3 on the basis of a model for the underlying molecular motion. This approach explains all the quantities involved as means over molecular quantities, and it reveals the range of applicability of the basic equations. In addition to this, the approach applied here illustrates the use of an analysis technique that will also be applied in chapter 5 to construct turbulence models. Section 4.4 deals with the generalization of these equations for the case of multi-component flows. The essential problem related to applications of the basic equations of fluid and thermodynamics is then pointed out in section 4.5. The simplest approach to overcome this problem is the use of the basic equations for the construction of transport equations for averaged variables. However, this approach is also related to significant problems, which will be described in section 4.6. The conclusion that can be drawn from these explanations is the requirement to develop stochastic methods for the simulation of turbulent reacting flows. Several ways to realize this task will be addressed in chapters 5, 6 and 7.