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Proper invariant turbulence modelling within one-point statistics

Frewer, Michael (2009)
Proper invariant turbulence modelling within one-point statistics.
In: Journal of Fluid Mechanics, 639
Artikel, Bibliographie

Kurzbeschreibung (Abstract)

A new turbulence modelling approach is presented. Geometrically reformulating the averaged Navier–Stokes equations on a four-dimensional non-Riemannian manifold without changing the physical content of the theory, additional modelling restrictions which are absent in the usual Euclidean (3+1)-dimensional framework naturally emerge. The modelled equations show full form invariance for all Newtonian reference frames in that all involved quantities transform as true 4-tensors. Frame accelerations or inertial forces of any kind are universally described by the underlying four-dimensional geometry.

By constructing a nonlinear eddy viscosity model within the k−ε family for high turbulent Reynolds numbers the new invariant modelling approach demonstrates the essential advantages over current (3+1)-dimensional modelling techniques. In particular, new invariants are gained, which allow for a universal and consistent treatment of non-stationary effects within a turbulent flow. Furthermore, by consistently introducing via a Lie-group symmetry analysis a new internal modelling variable, the mean form-invariant pressure Hessian, it will be shown that already a quadratic nonlinearity is sufficient to capture secondary flow effects, for which in current nonlinear eddy viscosity models a higher nonlinearity is needed. In all, this paper develops a new unified formalism which will naturally guide the way in physical modelling whenever reasonings are based on the general concept of invariance.

Typ des Eintrags: Artikel
Erschienen: 2009
Autor(en): Frewer, Michael
Art des Eintrags: Bibliographie
Titel: Proper invariant turbulence modelling within one-point statistics
Sprache: Englisch
Publikationsjahr: 2009
Verlag: Cambridge University Press
Titel der Zeitschrift, Zeitung oder Schriftenreihe: Journal of Fluid Mechanics
Jahrgang/Volume einer Zeitschrift: 639
URL / URN: http://journals.cambridge.org/action/displayAbstract?fromPag...
Kurzbeschreibung (Abstract):

A new turbulence modelling approach is presented. Geometrically reformulating the averaged Navier–Stokes equations on a four-dimensional non-Riemannian manifold without changing the physical content of the theory, additional modelling restrictions which are absent in the usual Euclidean (3+1)-dimensional framework naturally emerge. The modelled equations show full form invariance for all Newtonian reference frames in that all involved quantities transform as true 4-tensors. Frame accelerations or inertial forces of any kind are universally described by the underlying four-dimensional geometry.

By constructing a nonlinear eddy viscosity model within the k−ε family for high turbulent Reynolds numbers the new invariant modelling approach demonstrates the essential advantages over current (3+1)-dimensional modelling techniques. In particular, new invariants are gained, which allow for a universal and consistent treatment of non-stationary effects within a turbulent flow. Furthermore, by consistently introducing via a Lie-group symmetry analysis a new internal modelling variable, the mean form-invariant pressure Hessian, it will be shown that already a quadratic nonlinearity is sufficient to capture secondary flow effects, for which in current nonlinear eddy viscosity models a higher nonlinearity is needed. In all, this paper develops a new unified formalism which will naturally guide the way in physical modelling whenever reasonings are based on the general concept of invariance.

Zusätzliche Informationen:

DOI: 10.1017/S0022112009991133

Fachbereich(e)/-gebiet(e): 16 Fachbereich Maschinenbau > Fachgebiet für Strömungsdynamik (fdy)
16 Fachbereich Maschinenbau
Hinterlegungsdatum: 24 Aug 2011 18:13
Letzte Änderung: 17 Feb 2014 07:42
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