Citation
Ko, Denny Rusue (1969) Supersonic laminar boundary layer along a twodimensional adiabatic ramp. Nonlinear stability theory for a laminar incompressible wake. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd11102003093156
Abstract
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In Part I, the integral method of Lees and Reeves is applied to study a supersonic laminar boundary layer along a twodimensional 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 selfinduced interaction on a flat plate; consequently, it can be applied to flows with the hypersonic interaction parameter [...], 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 nonlinear 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 halfwidth b. By using a twolength 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[subscript c] and b. The three unknowns b, w[subscript 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 higherorder 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 SatoKuriki in the mean flow quantities and the relative development of the fluctuations are obtained, including the observed effect of freestream Reynolds number.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Aeronautics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  4 September 1968 
Record Number:  CaltechETD:etd11102003093156 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd11102003093156 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4484 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  10 Nov 2003 
Last Modified:  26 Dec 2012 03:09 
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