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Research Papers: Flows in Complex Systems

A Representation Theory-Based Model for the Rapid Pressure Strain Correlation of Turbulence

[+] Author and Article Information
J. P. Panda

Department of Ocean Engineering and
Naval Architecture,
IIT Kharagpur,
Kharagpur 721302, India
e-mail: jppanda@iitkgp.ac.in

H. V. Warrior

Department of Ocean Engineering and
Naval Architecture,
IIT Kharagpur,
Kharagpur 721302, India
e-mail: warrior@naval.iitkgp.ernet.in

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 29, 2017; final manuscript received February 19, 2018; published online March 27, 2018. Assoc. Editor: Daniel Livescu.

J. Fluids Eng 140(8), 081101 (Mar 27, 2018) (8 pages) Paper No: FE-17-1541; doi: 10.1115/1.4039510 History: Received August 29, 2017; Revised February 19, 2018

In the presence of mean strain or rotation, the anisotropy of turbulence increases due to the rapid pressure strain term. In this paper, we consider the modeling of the rapid pressure strain correlation of turbulence. The anisotropy of turbulence in the presence of mean strain is studied and a new model is formulated by calibrating the model constants at the rapid distortion limit. This model is tested for a range of plane strain and elliptic flows and compared to direct numerical simulation (DNS) results. The present model shows agreement with DNS and improvements over the earlier models like those by Launder et al. (1975, “Progress in the Development of a Reynolds-Stress Turbulence Closure,” J. Fluid Mech., 68(3), pp. 537–566.) and Speziale et al. (1991, “Modelling the Pressure–Strain Correlation of Turbulence: An Invariant Dynamical Systems Approach,” J. Fluid Mech., 227(1), pp. 245–272.) that have been reported to give satisfactory performance for hyperbolic flows but not satisfactory for elliptic flows.

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Figures

Grahic Jump Location
Fig. 1

Anisotropy evolution to a stationary state for plane strain mean flow, elliptic mean flow, axisymmetric expansion mean flow at the rapid distortion limit: (a) plane strain mean flow, (b) elliptic mean flow, and (c) axisymmetric expansion mean flow

Grahic Jump Location
Fig. 2

Identification of stationary states for elliptic flows: (a) schematic outlining the methodology and (b) Comparison of methodology with DNS data from Ref. [28]: (a) b22 evolution at β = 0.9: instantaneous values (solid line) and mean values (dashed line) and (b) instantaneous (solid line) and mean (dashed line) values of R13 from the data of Ref. [28]

Grahic Jump Location
Fig. 3

Calculated values of the model coefficients L2, L3, and L4 as functions of β: (a) L2, (b) L3, and (c) L4

Grahic Jump Location
Fig. 4

Evolution of the bij in homogeneous shear mean flow. RDT evolution is shown by the solid line, new model predictions by the dashed line. LRR and SSG are shown by the dotted and dash-dot lines: (a) b11, (b) b22, and (c) b12.

Grahic Jump Location
Fig. 5

Evolution of b22 in elliptic mean flows at β=0.6,0.7 and 0.8. RDT evolution is shown by the solid line, new model predictions by the dashed line. LRR and SSG are shown by the dotted and dash-dot lines: (a) b22, β = 0.6, (b) b22, β = 0.7, and (c) b22, β = 0.8.

Grahic Jump Location
Fig. 6

Evolution of turbulent kinetic energy k in elliptic mean flows at β=0.6,0.7 and 0.8. RDT evolution is shown by the solid line, new model predictions by the dashed line. LRR and SSG are shown by the dotted and dash-dot lines: (a) log(k), β = 0.6, (b) log(k), β = 0.7, and (c) log(k), β = 0.8.

Grahic Jump Location
Fig. 7

Evolution of (a) the Reynolds stress anisotropy b11 and (b) turbulent kinetic energy for plane strain mean flow. The predictions of the present model are shown by the solid line. LRR and SSG are shown by the dotted and dash-dot lines. The data from the direct numerical simulation of [32] are included for comparison: (a) b11 and (b) turbulent kinetic energy.

Grahic Jump Location
Fig. 8

Predictions for homogeneous shear flow (a) b12 evolution for the LES of Ref. [34] with (Sk/ε)=27, (b) tke evolution for the LES of Ref. [34] with (Sk/ε)=27, and (c) tke evolution for the DNS of Ref. [35]: (a) b12, (b) k, and (c) k

Grahic Jump Location
Fig. 9

Turbulent kinetic energy evolution for elliptic flows (a) E = 1.5, (b) E = 2, and (c) E = 3. The present model predictions are in the solid line, the SSG and the LRR model are shown in dash-dot and dotted lines. The data from the direct numerical simulation of [28] are included for comparison.

Grahic Jump Location
Fig. 10

Reynolds stress anisotropy b13 evolution for elliptic flows (a) E = 1.5, (b) E = 2, and (c) E = 3. The present model predictions are in the solid line, the SSG and the LRR model are shown in dash-dot and dotted lines. The data from the direct numerical simulation of Ref. [28] are included for comparison.

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