Turbulent energy redistribution in spanwise rotating channel flows

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

Research output: Contribution to journalArticle

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Abstract

For fully developed turbulent flows of a Newtonian fluid in a nonrotating channel with a large aspect ratio (i.e., spanwise length scale ≫ transverse length scale), the longitudinal component of the mean velocity and the mean pressure are symmetrical functions of the transverse coordinate. The three unequal normal components of the Reynolds stress are also symmetrical functions about the midplane whereas the shear component of the Reynolds stress is spatially antisymmetric. However, if the channel rotates around the spanwise axis, the Coriolis acceleration breaks the spatial symmetry of the flow field. This phenomenon occurs because the angular velocity of the frame directly couples with the linear momentum of the flow field to redistribute the turbulent kinetic energy. Consequently, rotating channel flows are ideal for testing the efficacy of closure models for the Reynolds averaged Navier-Stokes (RANS) equation. It is noteworthy that none of the classical "eddy" viscosity models are able to predict the Coriolis symmetry breaking phenomenon in spanwise rotating fully developed channel flows. This fundamental deficiency occurs because the "eddy" viscosity hypothesis assumes that the Reynolds stress is a frame-indifferent dyadic-valued operator (i.e., objective). Unlike the viscous transport of momentum, the transport of momentum by turbulent fluctuations is directly influenced by the angular velocity of the reference frame. In this paper, a recently developed algebraic closure for the Reynolds stress [see Koppula, K.; Bénard, A.; Petty, C. Realizable Algebraic Reynolds Stress Closure. Chem. Eng. Sci.2009, 64, 4611], referred to hereinafter as the universal realizable anisotropic prestress (URAPS) closure, is used to predict the spatial distribution of the normalized Reynolds (NR) stress (i.e., R≡ /tr() for rotating and for nonrotating fully developed channel flows. The new closure is formulated as an algebraic mapping of the NR stress into itself and is, thereby, realizable for all turbulent flows regardless of the specific benchmark flows used to estimate model parameters. The fixed points of the non-negative mapping depend explicitly on three specific time scales associated with the local statistical state of turbulence. The a priori predictions of the NR stress are consistent with previously published direct numerical simulations of the Navier-Stokes equation.

LanguageEnglish (US)
Pages8905-8916
Number of pages12
JournalIndustrial and Engineering Chemistry Research
Volume50
Issue number15
DOIs
StatePublished - Aug 3 2011

Profile

Channel flow
Momentum
Angular velocity
Navier Stokes equations
Turbulent flow
Flow fields
Viscosity
Direct numerical simulation
Kinetic energy
Spatial distribution
Aspect ratio
Turbulence
Fluids
Testing

ASJC Scopus subject areas

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

Cite this

Turbulent energy redistribution in spanwise rotating channel flows. / Koppula, Karuna S.; Bénard, André; Petty, Charles A.

In: Industrial and Engineering Chemistry Research, Vol. 50, No. 15, 03.08.2011, p. 8905-8916.

Research output: Contribution to journalArticle

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