I. Supersonic Laminar Boundary Layer Along a Two-Dimensional Adiabatic Curved Ramp. II. Non-Linear Stability Theory for a Laminar, Incompressible Wake

Citation

Ko, Denny Ru-sue (1969) I. Supersonic Laminar Boundary Layer Along a Two-Dimensional Adiabatic Curved Ramp. II. Non-Linear Stability Theory for a Laminar, Incompressible Wake. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/DM2V-N712. https://resolver.caltech.edu/CaltechETD:etd-11102003-093156

Abstract

In Part I, the integral method of Lees and Reeves is applied to study a supersonic laminar boundary layer along a two-dimensional adiabatic curved ramp. The present method of solution requires no prior knowledge of the separation point and can be used to treat relatively weak interaction, including a fully attached flow. It starts with small perturbations of the self-induced interaction on a flat plate; consequently, it can be applied to flows with the hypersonic interaction parameter Χ̅, based on the distance of the beginning station of interaction to the leading edge, of the order 1. The effect of the radius of curvature on the separation phenomena is then investigated using this method. The effect of finite ramp length on the interaction is examined by making use of the characteristics of the singularities associated with the set of moment equations. Satisfactory agreement with the theory is obtained for the corresponding experiments conducted in the Mach 6 wind tunnel at the Graduate Aeronautical Laboratories of the California Institute of Technology.

In Part II, a non-linear theory for the stability of the laminar wake behind a flat plate in an incompressible flow is presented. An integral method is used to investigate the effects of a finite amplitude disturbance on the flow. The flow is decomposed into a mean part, which is independent of time and a fluctuating part, which has a zero time average. The mean flow is assumed to be characterized by two parameters: the centerline velocity defect w[subscript c] and the wake half-width b. By using a two-length expansion procedure, the assumption of local, parallel mean flow is justified for the solution of the fluctuating component to the order considered in the present study. The fluctuation is assumed to be represented by an ascending power series of the amplitude A. The coefficients of the power series, as functions of the radial distance y, are then obtained in terms of the two mean flow parameters w_c and b. The three unknowns b, w_c and A are then obtained by solving the integral conservation equations of mean momentum, mean energy and fluctuation energy. In this integral method, the higher-order effects are introduced systematically by truncating the expansion for the fluctuation at various orders. The coupling between the mean flow and the fluctuation is found to be the most important mechanism in limiting the fluctuation amplitude and determining the mean flow. Satisfactory agreements with the experiment of Sato-Kuriki in the mean flow quantities and the relative development of the fluctuations are obtained, including the observed effect of free-stream Reynolds number.

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