The Extended Görtler-Hämmerlin Model For Linear Instability of Three-Dimensional Incompressible Swept Attachment-Line Boundary Layer Flow

Theofilis, Vassilios and Fedorov, Alexander and Obrist, Dominik and Dallmann, Uwe Ch. (2003). The Extended Görtler-Hämmerlin Model For Linear Instability of Three-Dimensional Incompressible Swept Attachment-Line Boundary Layer Flow. "Journal of Fluid Mechanics", v. 487 ; pp. 271-313. ISSN 0022-1120. https://doi.org/10.1017/S0022112003004762.

Description

Title: The Extended Görtler-Hämmerlin Model For Linear Instability of Three-Dimensional Incompressible Swept Attachment-Line Boundary Layer Flow
Author/s:
  • Theofilis, Vassilios
  • Fedorov, Alexander
  • Obrist, Dominik
  • Dallmann, Uwe Ch.
Item Type: Article
Título de Revista/Publicación: Journal of Fluid Mechanics
Date: 2003
ISSN: 0022-1120
Volume: 487
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 simple extension of the classic Görtler–Hämmerlin (1955) (GH) model, essential for three-dimensional linear instability analysis, is presented. The extended Görtler–Hämmerlin model classifies all three-dimensional disturbances in this flow by means of symmetric and antisymmetric polynomials of the chordwise coordinate. It results in one-dimensional linear eigenvalue problems, a temporal or spatial solution of which, presented herein, is demonstrated to recover results otherwise only accessible to the temporal or spatial partial-derivative eigenvalue problem (the former also solved here) or to spatial direct numerical simulation (DNS). From a numerical point of view, the significance of the extended GH model is that it delivers the three-dimensional linear instability characteristics of this flow, discovered by solution of the partial-derivative eigenvalue problem by Lin & Malik (1996a), at a negligible fraction of the computing effort required by either of the aforementioned alternative numerical methodologies. More significant, however, is the physical insight which the model offers into the stability of this technologically interesting flow. On the one hand, the dependence of three-dimensional linear disturbances on the chordwise spatial direction is unravelled analytically. On the other hand, numerical results obtained demonstrate that all linear three-dimensional instability modes possess the same (scaled) dependence on the wall-normal coordinate, that of the well-known GH mode. The latter result may explain why the three-dimensional linear modes have not been detected in past experiments; criteria for experimental identification of three-dimensional disturbances are discussed. Asymptotic analysis based on a multiple-scales method confirms the results of the extended GH model and provides an alternative algorithm for the recovery of three-dimensional linear instability characteristics, also based on solution of one-dimensional eigenvalue problems. Finally, the polynomial structure of individual three-dimensional extended GH eigenmodes is demonstrated using three-dimensional DNS, performed here under linear conditions.

More information

Item ID: 10446
DC Identifier: http://oa.upm.es/10446/
OAI Identifier: oai:oa.upm.es:10446
DOI: 10.1017/S0022112003004762
Official URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=162943
Deposited by: Memoria Investigacion
Deposited on: 05 Mar 2012 12:16
Last Modified: 20 Apr 2016 18:39
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