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New results on the realizability of Reynolds stress turbulence closuresThe realizability of Reynolds stress models in homogeneous turbulence is critically assessed from a theoretical standpoint. It is proven that a well known second-order closure formulated by Shih and Lumley using the strong realizability constraints of Schumann is, in fact, not a realizable model. The problem arises from the failure to properly satisfy the necessary positive second time derivative constraint when a principal Reynolds stress vanishes - a fatal flaw that becomes apparent when the non-analytic terms in their model are made single-valued as required on physical grounds. It is furthermore shown that the centrifugal acceleration generated by rotations of the principal axes of the Reynolds stress tensor can make the second derivative singular at the most extreme limits of realizable turbulence. This previously overlooked effect appears to make it impossible to identically satisfy the strong form of realizability in any version of the present generation of second-order closures. On the other hand, models properly formulated to satisfy the weak form of realizability - wherein states of one or two component turbulence are not accessible in finite time are found to be realizable. However, unlike the simpler and more commonly used second order closures, these models can be ill-behaved near the extreme limits of realizable turbulence due to the way that higher-degree nonlinearities are often unnecessarily introduced to satisfy realizability. Illustrative computations of homogeneous shear flows are presented to demonstrate these points which can have important implications for turbulence modeling.
Document ID
19940017402
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Speziale, Charles G.
(Boston Univ. MA., United States)
Abid, Ridha
(NASA Langley Research Center Hampton, VA., United States)
Durbin, Paul A.
(Stanford Univ. CA., United States)
Date Acquired
September 6, 2013
Publication Date
October 1, 1993
Subject Category
Fluid Mechanics And Heat Transfer
Report/Patent Number
ICASE-93-76
NASA-CR-191548
NAS 1.26:191548
AD-A274005
Accession Number
94N21875
Funding Number(s)
CONTRACT_GRANT: NAS1-19480
PROJECT: RTOP 505-90-52-01
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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