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Technical Brief

Turbulent Flows Over a Backward Facing Step Simulated Using a Modified Partially Averaged Navier–Stokes Model

[+] Author and Article Information
Renfang Huang

State Key Laboratory of Hydroscience and Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: hrenfang@gmail.com

Xianwu Luo

State Key Laboratory of Hydroscience and Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: luoxw@tsinghua.edu.cn

Bin Ji

School of Power and Mechanical Engineering,
Wuhan University,
Wuhan 430072, China

Qingfeng Ji

Institute of Water Resources and
Hydro-Electric Engineering,
Xi'an University of Technology,
Xi'an 710048, China

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 21, 2016; final manuscript received October 14, 2016; published online January 20, 2017. Assoc. Editor: Moran Wang.

J. Fluids Eng 139(4), 044501 (Jan 20, 2017) (7 pages) Paper No: FE-16-1185; doi: 10.1115/1.4035114 History: Received March 21, 2016; Revised October 14, 2016

A modified partially averaged Navier–Stokes model (MPANS) is proposed by treating the standard k–ε model as the parent model and formulating the unresolved-to-total kinetic energy ratio fk as a function of the local grid size and turbulence length scale. Flows over a backward facing step are used to evaluate the performance of MPANS mode. Computations of the standard k–ε model, the constant fk partially averaged Navier–Stokes (PANS) models (fk = 0.6, 0.7), and the two-stage PANS model are carried out for comparisons. Based on the detailed analyses of calculated results and experimental data, the MPANS model performs better to predict the reattachment length together with the corner vortex and provides overall improved statistics of skin frictions, pressures, velocity profiles, and Reynolds stresses, demonstrating its promising applications in industrial turbomachines that often encounter with flow separations.

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Figures

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Fig. 1

(a) The computational domain together with boundary conditions and (b) computational grid for the backward facing step

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Fig. 2

Streamlines over the backward facing step: (a) standard k–ε model, (b) MPANS, (c) fk = 0.7, (d) fk = 0.6, and (e) two-stage PANS

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Fig. 3

Skin friction distributions along the streamwise centerline

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Fig. 4

Static pressure distributions along the streamwise centerline

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Fig. 5

Profiles of streamwise velocity at stations of x/H = 2, 6, 8, 10, and 12

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Fig. 6

Profiles of averages of two normal stresses at stations of x/H = 2, 6, 8, 10, and 12

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Fig. 7

Profiles of shear stress at stations of x/H = 2, 6, 8, 10, and 12

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Fig. 8

fk distributions for the MPANS simulation

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Fig. 9

Vorticity distributions over the backward facing step (a) standard k–ε model, (b) MPANS, (c) fk = 0.7, and (d) fk = 0.6

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