### Abstract

The anisotropic distribution of turbulent kinetic energy in fully developed channel flows is examined by using an algebraic preclosure which relates the Reynolds stress to the mean field gradient and to a prestress correlation, (I + τ_{R}∇〈u〉)^{T} · 〈u′u′〉 · (I + τ_{R}∇〈u〉) = τ^{2}_{R}〈£′£′〉. Local fluctuations in the pressure field and in the instantaneous Reynolds stress are responsible for the prestress correlation τ^{2}_{R}〈£′£′〉. Closure requires a phenomenological model for the anisotropic prestress 2kH, defined by 2kH=τ^{2} _{R}〈£′£′〉-2αI/3. The prestress coefficient α(= τ^{2}_{R}〈£′ ·£′〉12) depends algebraically on the components of the Reynolds stress, the mean velocity gradient, the relaxation time τ_{R}, and the turbulent kinetic energy k. Previously reported direct numerical simulations (DNS) results for fully developed channel flows (δ_{+} = 395) are used to evaluate the behavior of the Reynolds stress for an Isotropic prestress (IPS) correlation (i.e., H=O). The IPS theory predicts the existence of a nonzero primary normal stress difference and shows that a significant transfer of kinetic energy occurs from the transverse and normal components of the Reynolds stress to the longitudinal component for τ_{R}∥∇〈u〉∥≫ 1. The spatial distributions of the two nontrivial invariants of the anisotropic stress predicted by the IPS theory are consistent with DNS results for 10≤ y ^{+} ≤ 395. The practical utility of the isotropic prestress theory is further demonstrated by predicting the low-order statistical properties of the turbulence in the outer region of fully developed channel flows. Transport equations for the turbulent kinetic energy and the turbulent dissipation are used to estimate the spatial distributions of the turbulent time scales k/ε and τ_{R}.

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

Pages (from-to) | 1262-1271 |

Number of pages | 10 |

Journal | Physics of Fluids |

Volume | 11 |

Issue number | 5 |

State | Published - May 1999 |

### Profile

### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes
- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*11*(5), 1262-1271.

**Isotropic prestress theory for fully developed channel flows.** / Weispfennig, K.; Parks, S. M.; Petty, C. A.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol 11, no. 5, pp. 1262-1271.

}

TY - JOUR

T1 - Isotropic prestress theory for fully developed channel flows

AU - Weispfennig,K.

AU - Parks,S. M.

AU - Petty,C. A.

PY - 1999/5

Y1 - 1999/5

N2 - The anisotropic distribution of turbulent kinetic energy in fully developed channel flows is examined by using an algebraic preclosure which relates the Reynolds stress to the mean field gradient and to a prestress correlation, (I + τR∇〈u〉)T · 〈u′u′〉 · (I + τR∇〈u〉) = τ2R〈£′£′〉. Local fluctuations in the pressure field and in the instantaneous Reynolds stress are responsible for the prestress correlation τ2R〈£′£′〉. Closure requires a phenomenological model for the anisotropic prestress 2kH, defined by 2kH=τ2 R〈£′£′〉-2αI/3. The prestress coefficient α(= τ2R〈£′ ·£′〉12) depends algebraically on the components of the Reynolds stress, the mean velocity gradient, the relaxation time τR, and the turbulent kinetic energy k. Previously reported direct numerical simulations (DNS) results for fully developed channel flows (δ+ = 395) are used to evaluate the behavior of the Reynolds stress for an Isotropic prestress (IPS) correlation (i.e., H=O). The IPS theory predicts the existence of a nonzero primary normal stress difference and shows that a significant transfer of kinetic energy occurs from the transverse and normal components of the Reynolds stress to the longitudinal component for τR∥∇〈u〉∥≫ 1. The spatial distributions of the two nontrivial invariants of the anisotropic stress predicted by the IPS theory are consistent with DNS results for 10≤ y + ≤ 395. The practical utility of the isotropic prestress theory is further demonstrated by predicting the low-order statistical properties of the turbulence in the outer region of fully developed channel flows. Transport equations for the turbulent kinetic energy and the turbulent dissipation are used to estimate the spatial distributions of the turbulent time scales k/ε and τR.

AB - The anisotropic distribution of turbulent kinetic energy in fully developed channel flows is examined by using an algebraic preclosure which relates the Reynolds stress to the mean field gradient and to a prestress correlation, (I + τR∇〈u〉)T · 〈u′u′〉 · (I + τR∇〈u〉) = τ2R〈£′£′〉. Local fluctuations in the pressure field and in the instantaneous Reynolds stress are responsible for the prestress correlation τ2R〈£′£′〉. Closure requires a phenomenological model for the anisotropic prestress 2kH, defined by 2kH=τ2 R〈£′£′〉-2αI/3. The prestress coefficient α(= τ2R〈£′ ·£′〉12) depends algebraically on the components of the Reynolds stress, the mean velocity gradient, the relaxation time τR, and the turbulent kinetic energy k. Previously reported direct numerical simulations (DNS) results for fully developed channel flows (δ+ = 395) are used to evaluate the behavior of the Reynolds stress for an Isotropic prestress (IPS) correlation (i.e., H=O). The IPS theory predicts the existence of a nonzero primary normal stress difference and shows that a significant transfer of kinetic energy occurs from the transverse and normal components of the Reynolds stress to the longitudinal component for τR∥∇〈u〉∥≫ 1. The spatial distributions of the two nontrivial invariants of the anisotropic stress predicted by the IPS theory are consistent with DNS results for 10≤ y + ≤ 395. The practical utility of the isotropic prestress theory is further demonstrated by predicting the low-order statistical properties of the turbulence in the outer region of fully developed channel flows. Transport equations for the turbulent kinetic energy and the turbulent dissipation are used to estimate the spatial distributions of the turbulent time scales k/ε and τR.

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M3 - Article

VL - 11

SP - 1262

EP - 1271

JO - Physics of Fluids

T2 - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 5

ER -