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Transport of Momentum, Energy, and Mass
Fluid flow is characterized by transport of mass, momentum and energy. In this chapter we treat the transport of these three entities and its mathematical description in a basic way. Similarity parameters and, in particular, surface boundary conditions will be discussed in detail.
Similarity parameters enable us to distinguish and choose between phenomenological models and the respective mathematical models. The Knudsen number, which we met in Chapter 2.3, is an example. It is used in order to distinguish flow regimes. As we will see, for the transport of the three entities different phenomenological models exist, which we characterize with the aid of appropriate similarity parameters.
Surface boundary conditions receive special attention because they govern, together with the free-stream conditions and the flight-vehicle geometry, the flow and thermo-chemical phenomena in the flow-regime of interest. In addition, they govern aerodynamic forces and moments as well as mechanical and thermal loads on the flight vehicle.
After a general introduction, which also shows how to distinguish between steady and unsteady flows, we look briefly at the transport properties of air. Then we treat in detail the continuum-regime equations of motion—for convenience, although with some exceptions, in two dimensions and Cartesian coordinates (the formulations of the governing equations in general coordinates are given in Appendix A)—, as well as the similarity parameters, and surface boundary conditions. We treat first momentum transport, because here the boundary-layer concept plays the major role. The transport of the two other entities is treated in an analogous way.
Far-field or external boundary conditions as well as initial conditions are in general not considered in detail in this book. In a flight situation these are the free-stream conditions. With internal flows, also wind-tunnel flows, as well as with special phenomenological models like the boundary-layer, however special considerations become necessary. They will be discussed in the respective sections.
(C Springer International Publishing Switzerland 2015 E. H. Hirschel, Basics of Aerothermodynamics,
DOI: 10.1007/978-3-319-14373-6 _4
