### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 8905-8916 |

Number of pages | 12 |

Journal | Industrial and Engineering Chemistry Research |

Volume | 50 |

Issue number | 15 |

DOIs | |

State | Published - Aug 3 2011 |

### Profile

### ASJC Scopus subject areas

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

### Cite this

*Industrial and Engineering Chemistry Research*,

*50*(15), 8905-8916. DOI: 10.1021/ie1020409

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

Research output: Contribution to journal › Article

*Industrial and Engineering Chemistry Research*, vol 50, no. 15, pp. 8905-8916. DOI: 10.1021/ie1020409

}

TY - JOUR

T1 - Turbulent energy redistribution in spanwise rotating channel flows

AU - Koppula,Karuna S.

AU - Bénard,André

AU - Petty,Charles A.

PY - 2011/8/3

Y1 - 2011/8/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79960870525&partnerID=8YFLogxK

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U2 - 10.1021/ie1020409

DO - 10.1021/ie1020409

M3 - Article

VL - 50

SP - 8905

EP - 8916

JO - Industrial & Engineering Chemistry Product Research and Development

T2 - Industrial & Engineering Chemistry Product Research and Development

JF - Industrial & Engineering Chemistry Product Research and Development

SN - 0888-5885

IS - 15

ER -