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RESEARCH PAPERS: Model Development

# A New Low Reynolds Stress Transport Model for Heat Transfer and Fluid in Engineering Applications

[+] Author and Article Information
Rongguang Jia

Fluent Inc., Lebanon, NH

Bengt Sundén1

Division of Heat Transfer, Lund Institute of Technology, Lund 22100, SwedenBengt.Sunden@vok.lth.se

Department of Mechanical Engineering and Applied Mechanics, University of Rhode Island, Kingston, RI

1

Corresponding author.

J. Heat Transfer 129(4), 434-440 (Aug 09, 2006) (7 pages) doi:10.1115/1.2709957 History: Received March 01, 2006; Revised August 09, 2006

## Abstract

A new Reynolds stress transport model (RSTM) aimed for engineering applications is proposed with consideration of near-wall turbulence. This model employs the Speziale, Sarkar, and Gatski (SSG) pressure strain term, the $ω$ equation, and the shear stress transport (SST) model for the shear stresses at the near-wall region (say, $y+<30$). The models are selected based on the following merits: The SSG RSTM model performs well in the fully turbulent region and does not need the wall normal vectors; the $ω$ equation can be integrated down to the wall without damping functions. The SST model is a proper two-equation model that performs well for flows with adverse pressure gradient, while most two-equation models can have a good prediction of the shear stresses. A function is selected for the blending of the RSTM and SST. Three cases are presented to show the performance of the present model: (i) fully developed channel flow with $Reτ$=395, (ii) backward-facing step with an expansion ratio of 1.2 and Re=5200 base on the step height, and (iii) circular impingement with the nozzle-to-wall distance H=4D and Re=20,000. It is believed that the new model has good applicability for complex flow fields.

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## Figures

Figure 1

Predicted streamlines by the SSG-W model for the backward-facing-step case

Figure 11

u′u′¯ comparison between experiments and the present simulations: (a) V2F and (b) SSG-SST

Figure 12

Line plot comparisons between experiments and the present simulations (legend as in Fig. 1): (a) u′u′¯ and (b) v′v′¯

Figure 13

Predicted Nusselt number in comparison to experiments

Figure 2

Plot of the blending function Fb

Figure 3

Computational geometry: (a) topology and (b) grid around the step

Figure 4

Streamlines for the backward-facing-step case: (a) DNS and (b) SSG-SST note: (a) and (b) are scaled the same

Figure 5

Friction coefficient of the backward-facing-step case

Figure 6

U-velocity profile of the channel flow case

Figure 7

Reynolds stresses of the channel flow case: (a) normal stresses and (b) shear stress

Figure 8

Inlet profiles of the impingement jet case: (a) geometry, (b) grid and TKE contours around the jet inlet, and (c) inlet profiles

Figure 9

Comparison between the present solver and FLUENT with the V2F model for the impingement jet case: (a) TKE contours and (b) Nusselt number

Figure 10

V-velocity comparison between experiments and present simulations (circle: PIV experiments, solid line: SSG-SST model, dashed line: V2F model, and dashed-dotted line: SST model): (a) V contours and (b) V line plots (note: the strictly horizontal lines are axes)

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