Investigation into the flow of a viscous heat conducting compressible fluid

• Main Author: Trilling, Leon
• Format: Others
• Published: 1948
• Online Access: https://thesis.library.caltech.edu/5134/1/Trilling_l_1948.pdf; Trilling, Leon (1948) Investigation into the flow of a viscous heat conducting compressible fluid. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/14DR-5V68. https://resolver.caltech.edu/CaltechETD:etd-12242008-101248 <https://resolver.caltech.edu/CaltechETD:etd-12242008-101248>

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The present investigation is concerned with the effect of a small viscosity and heat conduction coefficient on the flow of a compressible fluid. It is well known that, in the case of an incompressible fluid, such an investigation leads to the boundary layer theory. The chief purpose of this paper is to determine whether the main result of boundary layer theory, namely, that viscosity plays a negligible part in the flow outside a very narrow region in the immediate vicinity of any solid boundary in the fluid, is still valid for a compressible fluid. To investigate that point, a very simple type of flow is selected: the flow past a semi-infinite two-dimensional flat plate parallel to the main stream direction. The problem is further simplified as follows: on the basis of experimental results, the existence of a layer influenced by viscosity is assumed, and the boundary conditions are applied near the outer edge of this layer. This allows a linearization of the equation of motion, and gives information on the interaction between the outer edge of this layer and the main field of flow. The analysis is carried out by the methods based on the theory of the Laplace Transformation. The results are essentially, that if the flow is subsonic, the boundary layer theory developed for incompressible fluids may be extended without qualitative changes. However, in a supersonic flow, one must expect two related effects: one finds the boundary layer, which, as a first approximation, in similar to the boundary layer of an incompressible fluid, and a shock-wave along the Mach line which starts at the leading edge of the flat palate, and whose strength is given by the expression: [...] where [...] is the normal velocity across the shock, M is the free stream Mach number, [...] is the distance from the leading edge of the flat plate along the shock, [...] is the distance normal to the shock, [...] is sonic velocity of the free stream and [...] is the mean effective free stream kinematic viscosity of the fluid.