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Symmetry methods for turbulence modeling

Günther, Silke (2006):
Symmetry methods for turbulence modeling.
Darmstadt, Technische Universität, Technische Universität Darmstadt, [Online-Edition: urn:nbn:de:tuda-tuprints-6789],
[Ph.D. Thesis]

Abstract

The given thesis is based on the turbulence theory based on Lie group methods, which has been developed in the last couple of years. With this theory at hand it is possible to derive classical semi-empirical approaches, as for example the law of the wall, from "first principles". Here three different flow cases, which are the turbulent diffusion, the zero-pressure gradient turbulent boundary layer flow and the fully developed turbulent rotating pipe flow have been investigated. Using symmetry methods linear and non-linear eddy viscosity models as well as Reynolds stress models have been analyzed. Thereby it has been checked if the model equations have the same symmetry properties as the two-point correlation equations and if they are able to describe the turbulent scaling laws which have been derived for the given flow cases. Based on these investigations conditions for the model constants and the structure of the model equations have been derived.

Item Type: Ph.D. Thesis
Erschienen: 2006
Creators: Günther, Silke
Title: Symmetry methods for turbulence modeling
Language: English
Abstract:

The given thesis is based on the turbulence theory based on Lie group methods, which has been developed in the last couple of years. With this theory at hand it is possible to derive classical semi-empirical approaches, as for example the law of the wall, from "first principles". Here three different flow cases, which are the turbulent diffusion, the zero-pressure gradient turbulent boundary layer flow and the fully developed turbulent rotating pipe flow have been investigated. Using symmetry methods linear and non-linear eddy viscosity models as well as Reynolds stress models have been analyzed. Thereby it has been checked if the model equations have the same symmetry properties as the two-point correlation equations and if they are able to describe the turbulent scaling laws which have been derived for the given flow cases. Based on these investigations conditions for the model constants and the structure of the model equations have been derived.

Place of Publication: Darmstadt
Publisher: Technische Universität
Uncontrolled Keywords: Turbulenzmodellierung, Symmetriemethoden
Divisions: 13 Department of Civil and Environmental Engineering Sciences
16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
Date Deposited: 24 Aug 2011 18:24
Official URL: urn:nbn:de:tuda-tuprints-6789
License: only the rights of use according to UrhG
Referees: David, Prof. Dr. Ioan and Jakirlic, PD Dr. Suad
Refereed / Verteidigung / mdl. Prüfung: 24 November 2005
Alternative keywords:
Alternative keywordsLanguage
Turbulence modeling, Symmetry methodsEnglish
Alternative Abstract:
Alternative abstract Language
Die vorliegende Arbeit baut auf der in den letzten Jahren entwickelte Turbulenztheorie auf der Basis der Lie-Gruppen-Theorie auf. Mit dem neuen Ansatz sind eine Reihe klassischer semi-empirischer Ansätze, wie z.B. das logarithmische Wandgesetz, bestätigt und eine Vielzahl neuer Turbulenzgesetze hergeleitet worden, die sich ausschliesslich aus "First principle" ergaben. Im Speziellen werden in der vorliegenden Arbeit drei Strömungsfälle untersucht: der Strömungsfall der turbulenten Diffusion, die turbulente Grenzschichtströmung ohne Druckgradient und die voll ausgebildete, turbulente, rotierende Rohrströmung. Mit Hilfe von Symmetriemethoden werden für diese Stömungsfälle lineare und nichtlineare Wirbelviskositätsmodelle, sowie Reynolds-Spannungsmodelle analysiert. Dabei wird überprüft, ob die Modellgleichungen die gleichen Symmetrieeigenschaften wie die Zwei-Punkt-Korrelations Gleichungen haben und zusäatzlich in der Lage sind, die turbulenten Skalengesetze für die gegebenen Strömungsfälle zu beschreiben. Basierend auf diesen Untersuchungen werden dann zum Teil Bedingungen für die Modellkonstanten, sowie die Struktur der Modellgleichungen hergeleitet.German
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