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Stability of the Compressible Laminar Boundary Layer

Reshotko, Eli (1960) Stability of the Compressible Laminar Boundary Layer. Hypersonic Research Project Memorandum, 52. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20151102-162610869

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Abstract

In previous theoretical treatments of the stability of the compressible laminar boundary layer the effect of the temperature fluctuations on the 11viscous11 (rapidly-varying) disturbances is either ignored (Lees-Lin), or is accounted for incompletely (Dunn-Lin). A thorough reexamination of this problem shows that temperature fluctuations have a profound influence on both the "inviscid" (slowly-varying) and viscous disturbances above a Mach number of about 2.0. The present analysis includes the effect of temperature fluctuations on the viscosity and thermal conductivity, and also introduces the viscous dissipation term that was dropped in the earlier theoretical treatments. Some important results of the present study are: (1), the rate of conversion of energy from the mean flow to the disturbance flow through the action of viscosity in the vicinity of the wall increases with Mach number; (2), instead of being nearly constant across the boundary layer, the amplitude of inviscid pressure fluctuations for Mach numbers greater than 3 decreases markedly with distance outward from the plate surface. This behavior means that the jump in magnitude of the Reynolds stress in the neighborhood of the critical layer is greatly reduced; (3), at Mach numbers less than about 2 dissipation effects are minor, but they become extremely important at higher Mach numbers since for neutral disturbances they must compensate for the generally destabilizing effects of items (1) and (2). Numerical examples illustrating the effects of compressibility (including neutral stability characteristics) are obtained and are compared with the experimental results of Laufer and Vrebalovich at M = 2.2, and of Demetriades at M = 5.8.


Item Type:Report or Paper (Technical Report)
Additional Information:Army Ordnance Contract No. Da-04-495-Ord-19. Army Project No. 5B0306004 Ordnance Project No. TB3-0118 OOR Project No. 1600-PE. The author acknowledges with gratitude the receipt of a Daniel and Florence Guggenheim Fellowship in Jet Propulsion for the academic years 1957-58 and 1958-59.
Group:Hypersonic Research Project
Funders:
Funding AgencyGrant Number
U.S. Army Office of OrdnanceDA-04-495-Ord-19
Daniel and Florence Guggenheim Fellowship in Jet PropulsionUNSPECIFIED
Record Number:CaltechAUTHORS:20151102-162610869
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20151102-162610869
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:61776
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:03 Nov 2015 00:35
Last Modified:03 Nov 2015 00:35

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