The Discrete Temporal Eigenvalue Spectrum of the Generalised Hiemenz Boundary Layer Flow As Solution of the Orr-Sommerfeld Equation

Theofilis, Vassilios (1994). The Discrete Temporal Eigenvalue Spectrum of the Generalised Hiemenz Boundary Layer Flow As Solution of the Orr-Sommerfeld Equation. "Journal of Engineering Mathematic", v. 28 (n. 3); pp. 241-259. ISSN 0022-0833. https://doi.org/10.1007/BF00058439.

Description

Title: The Discrete Temporal Eigenvalue Spectrum of the Generalised Hiemenz Boundary Layer Flow As Solution of the Orr-Sommerfeld Equation
Author/s:
  • Theofilis, Vassilios
Item Type: Article
Título de Revista/Publicación: Journal of Engineering Mathematic
Date: 1994
ISSN: 0022-0833
Volume: 28
Subjects:
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Motopropulsión y Termofluidodinámica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

A spectral collocation method is used to obtain the solution to the Orr-Sommerfeld stability equation. The accuracy of the method is established by comparing against well documented flows, such as the plane Poiseuille and the Blasius Boundary layers. The focus is then placed on the generalised Hiemenz flow, an exact solution to the Navier-Stokes equations constituting the base flow at the leading edge of swept cylinders and aerofoils. The spanwise profile of this flow is very similar to that of Blasius but, unlike the latter case, there is no rational approximation leading to the Orr-Sommerfeld equation. We will show that if, based on experimentally obtained intuition, a nonrational reduction of the full system of linear stability equations is attempted and the resulting Orr-Sommerfeld equation is solved, the linear stability critical Reynolds number is overestimated, as has indeed been done in the past. However, as shown by recent Direct Numerical Simulation results, the frequency eigenspectrum of instability waves may still be obtained through solution of the Orr-Sommerfeld equation. This fact lends some credibility to the assumption under which the Orr-Sommerfeld equation is obtained insofar as the identification of the frequency regime responsible for linear growth is concerned. Finally, an argument is presented pointing towards potential directions in the ongoing research for explanation of subcriticality in the leading edge boundary layer.

More information

Item ID: 10438
DC Identifier: http://oa.upm.es/10438/
OAI Identifier: oai:oa.upm.es:10438
DOI: 10.1007/BF00058439
Official URL: http://www.springerlink.com/content/h4532k114617n434/
Deposited by: Memoria Investigacion
Deposited on: 05 Mar 2012 10:58
Last Modified: 20 Apr 2016 18:39
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