ABSTRACT
The fundamental equations of fluid dynamics are developed in this chapter. Beginning with the Navier–Stokes equations, reduced forms for different applications which include the boundary layer, Euler, and the small disturbance equations are derived. Models for chemically reacting flows and real gas behavior are discussed and flow regimes where these effects must be considered are examined. The Reynolds averaged Navier–Stokes and boundary layer equations are derived along with a detailed treatment of turbulence modeling including large eddy simulation (LES) and direct numerical simulation (DNS). Turbulence models such as one, one and one half, two equation and simple algebraic models are also given. Equations governing magnetohydrodynamic flows are included, and a discussion of reduced equations and their applicability is shown. The equations of heat transfer are studied and include applications involving phase change and also the Boussinesq approximation for free and mixed convection. Techniques for front tracing in multiphase flows including the volume of fluid and level set methods are introduced. Examples of these flows are computed, and the results are shown. The finite-volume form of the equations governing fluid flow are examined for both two dimensions and three dimensions. Computing numerical solutions in native coordinates or transformed coordinates are options, and several coordinate transformations are given as examples when the transformed coordinate approach is advantageous. Finally, governing equations are derived in generalized coordinates.
