Realizable algebraic Reynolds stress closure

Karuna S. Koppula, André Bénard, Charles A. Petty

Research output: Contribution to journalArticle

  • 5 Citations

Abstract

The normalized Reynolds (NR-) stress is a symmetric, non-negative, dyadic-valued operator. An analysis of the hydrodynamic equation governing velocity fluctuations of a constant property Newtonian fluid shows that this operator is related to a prestress operator that is also symmetric and non-negative. The prestress operator accounts for local spatial changes in the fluctuating pressure and in the fluctuating instantaneous Reynolds stress. The Cayley-Hamilton theorem from linear algebra is used to complete the closure with a non-negative mapping of the normalized Reynolds stress into the prestress. The non-negative mapping between the prestress operator and the Reynolds stress depends on a scalar-valued turbulent transport time related to the relaxation of a Green's function associated with a convective-viscous parabolic differential operator and the relaxation of a two-point, space-time correlation related to turbulent velocity fluctuations. The preclosure equation also depends on a kinematic operator related to the average velocity gradient and a rotational operator related to the angular velocity of the frame. The resulting universal realizable anisotropic prestress (URAPS-) closure is realizable for all non-rotating and rotating turbulent flows, provided the complementary transport equations for the turbulent kinetic energy and the turbulent dissipation are formulated to yield non-negative solutions. Experimental data and DNS results previously reported in the literature for non-rotating homogeneous simple shear and for non-rotating and rotating homogeneous decay are used to determine the closure constants. For rotating homogeneous simple shear, the URAPS-closure predicts the existence of self-similar states for finite positive and negative rotation numbers. The URAPS-closure for the NR-stress predicts anisotropic states consistent with expected behavior.

LanguageEnglish (US)
Pages4611-4624
Number of pages14
JournalChemical Engineering Science
Volume64
Issue number22
DOIs
StatePublished - Nov 16 2009

Profile

Prestress
Reynolds Stress
Closure
Operator
Non-negative
Linear algebra
Rotating
Angular velocity
Cayley-Hamilton theorem
Fluctuations
Green's function
Kinetic energy
Rotating Flow
Parabolic Operator
Turbulent flow
Predict
Rotation number
Hydrodynamic Equations
Kinematics
Nonnegative Solution

Keywords

  • Fluid mechanics
  • Mathematical modeling
  • Momentum transfer
  • Reynolds stress
  • Rotating frames
  • Turbulence

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Chemistry(all)
  • Applied Mathematics
  • Industrial and Manufacturing Engineering

Cite this

Realizable algebraic Reynolds stress closure. / Koppula, Karuna S.; Bénard, André; Petty, Charles A.

In: Chemical Engineering Science, Vol. 64, No. 22, 16.11.2009, p. 4611-4624.

Research output: Contribution to journalArticle

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