Date of Award
Doctor of Philosophy
Laminar boundary-layer theory has been correctly developed for streamwise corners using singular perturbation techniques. Theoretical predictions, however, do not compare well with experimental measurements due to the observed breakdown of flow stability and similarity. Both of these properties appear as basic assumptions of the boundary-layer theory, thereby providing needed simplification as well as imposing limitations upon the mathematical model.;Any theoretical investigation of similarity breakdown would require knowledge of the similar solution not only as an initial condition, but also for insight into how to proceed. Examination of the cross-flow behavior, which affects the onset of similarity breakdown, may suggest ways of formulating the problem without abandoning entirely the simplifying assumption of similarity.;The formulation of boundary-layer equations is reviewed beginning with time-independent Navier-Stokes equations. Tensor analysis is used so that the resulting equations are generally applicable to any similar flow configuration. A non-orthogonal Cartesian coordinate system is chosen to deal with streamwise concave corners (i.e. with corner angles less than 180(DEGREES)). Coordinate and flow-variable transforms are then used to define bounded quantities.;The computational procedures for obtaining the boundary conditions and solving the main equations are described briefly, noting some pitfalls that would hinder numerical computation. Results characterizing the mainstream flow and the secondary cross-flow are displayed and discussed for corners with angles of 30(DEGREES), 60(DEGREES), 90(DEGREES), 120(DEGREES) and 150(DEGREES). Ways to proceed with further investigation, while keeping the mathematical model simple, are then suggested.
Wilkinson, Steven Ray, "Boundary Layer Flow In Streamwise Concave Corners" (1983). Digitized Theses. 1248.