0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Bradshaw, P. , and Wong, F. Y. F. , 1972, “ The Reattachment and Relaxation of a Turbulent Shear Layer,” J. Fluid Mech., 52(01), pp. 113–135. [CrossRef]
Eaton, J. K. , and Johnston, J. P. , 1981, “ A Review of Research on Subsonic Turbulent Flow Reattachment,” AIAA J., 19(9), pp. 1093–1100. [CrossRef]
Driver, D. M. , and Seegmiller, H. L. , 1985, “ Features of a Reattaching Turbulent Shear Layer in Divergent Channel Flow,” AIAA J., 23(2), pp. 163–171. [CrossRef]
Le, H. , Moin, P. , and Kim, J. , 1997, “ Direct Numerical Simulation of Turbulent Flow Over a Backward-Facing Step,” J. Fluid Mech., 330, pp. 349–374. [CrossRef]
Kim, J. Y. , Ghajar, A. J. , Tang, C. , and Foutch, G. L. , 2005, “ Comparison of Near-Wall Treatment Methods for High Reynolds Number Backward-Facing Step Flow,” Int. J Comput. Fluid D., 19(7), pp. 493–500. [CrossRef]
Šarić, S. , Jakirlić, S. , and Tropea, C. , 2005, “ A Periodically Perturbed Backward-Facing Step Flow by Means of LES, DES and T-RANS: An Example of Flow Separation Control,” ASME J. Fluids Eng., 127(5), pp. 879–887. [CrossRef]
Yang, X. D. , Ma, H. Y. , and Huang, Y. N. , 2005, “ Prediction of Homogeneous Shear Flow and a Backward-Facing Step Flow With Some Linear and Non-Linear kε Turbulence Models,” Commun. Nonlinear Sci., 10(3), pp. 315–328. [CrossRef]
Erturk, E. , 2008, “ Numerical Solutions of 2-D Steady Incompressible Flow Over a Backward-Facing Step—Part I: High Reynolds Number Solutions,” Comput. Fluids, 37(6), pp. 633–655. [CrossRef]
Huang, B. A. , and Wang, G. Y. , 2011, “ Partially Averaged Navier-Stokes Method for Time-Dependent Turbulent Cavitating Flows,” J Hydrodyn., 23(1), pp. 26–33. [CrossRef]
Luo, X. , Huang, R. , and Ji, B. , 2016, “ Transient Cavitating Vortical Flows Around a Hydrofoil Using k-ω Partially Averaged Navier–Stokes Model,” Mod. Phys. Lett. B, 30(01), p. 1550262. [CrossRef]
Speziale, C. G. , 1997, “ Computing Non-Equilibrium Turbulent Flows With Time-Dependent RANS and VLES,” Fifteenth International Conference on Numerical Methods in Fluid Dynamics, Monterey, CA, June 24–28, pp. 123–129.
Travin, A. , Shur, M. , Strelets, M. , and Spalart, P. , 2000, “ Detached-Eddy Simulations Past a Circular Cylinder,” Flow, Turbul. Combust., 63(1–4), pp. 293–313. [CrossRef]
Girimaji, S. S. , 2006, “ Partially-Averaged Navier-Stokes Model for Turbulence: A Reynolds-Averaged Navier-Stokes to Direct Numerical Simulation Bridging Method,” ASME J. Appl. Mech., 73(3), pp. 413–421. [CrossRef]
Lakshmipathy, S. , and Girimaji, S. S. , 2010, “ Partially Averaged Navier–Stokes (PANS) Method for Turbulence Simulations: Flow Past a Circular Cylinder,” ASME J. Fluids Eng., 132(12), p. 121202. [CrossRef]
Jeong, E. , and Girimaji, S. S. , 2010, “ Partially Averaged Navier–Stokes (PANS) Method for Turbulence Simulations—Flow Past a Square Cylinder,” ASME J. Fluids Eng., 132(12), p. 121203. [CrossRef]
Song, C.-S. , and Park, S.-O. , 2009, “ Numerical Simulation of Flow Past a Square Cylinder Using Partially-Averaged Navier–Stokes Model,” J. Wind Eng. Ind. Aerodyn., 97(1), pp. 37–47. [CrossRef]
Luo, D. , Yan, C. , and Wang, X. , 2015, “ Computational Study of Supersonic Turbulent-Separated Flows Using Partially Averaged Navier-Stokes Method,” Acta Astronaut., 107, pp. 234–246. [CrossRef]
Ji, B. , Luo, X. W. , Wu, Y. L. , and Xu, H. Y. , 2012, “ Unsteady Cavitating Flow Around a Hydrofoil Simulated Using the Partially-Averaged Navier-Stokes Model,” Chin. Phys. Lett., 29(7), p. 5. [CrossRef]
Liu, J. T. , Zuo, Z. G. , Wu, Y. L. , Zhuang, B. T. , and Wang, L. Q. , 2014, “ A Nonlinear Partially-Averaged Navier-Stokes Model for Turbulence,” Comput. Fluids, 102, pp. 32–40. [CrossRef]
Frendi, A. , Tosh, A. , and Girimaji, S. , 2006, “ Flow Past a Backward-Facing Step: Comparison of PANS, DES and URANS Results With Experiments,” Int. J. Comput. Methods Eng. Sci. Mech., 8(1), pp. 23–38. [CrossRef]
Ma, J. M. , Peng, S. H. , Davidson, L. , and Wang, F. J. , 2011, “ A Low Reynolds Number Variant of Partially-Averaged Navier–Stokes Model for Turbulence,” Int. J. Heat Fluid Flow, 32(3), pp. 652–669. [CrossRef]
Davidson, L. , 2014, “ The PANS kε Model in a Zonal Hybrid RANS–LES Formulation,” Int. J. Heat Fluid Flow, 46, pp. 112–126. [CrossRef]
Foroutan, H. , and Yavuzkurt, S. , 2014, “ A Partially-Averaged Navier–Stokes Model for the Simulation of Turbulent Swirling Flow With Vortex Breakdown,” Int. J. Heat Fluid Flow, 50(0), pp. 402–416. [CrossRef]
Hu, C. L. , Wang, G. Y. , Chen, G. H. , and Huang, B. , 2014, “ A Modified PANS Model for Computations of Unsteady Turbulence Cavitating Flows,” Sci. China-Phys. Mech. Astron., 57(10), pp. 1967–1976. [CrossRef]
Girimaji, S. S. , and Abdol-Hamid, K. S. , 2005, “ Partially Averaged Navier–Stokes Model for Turbulence: Implementation and Validation,” AIAA Paper No. AIAA 2005-502.
Abdol-Hamid, K. S. , and Girimaji, S. S. , 2004, “ A Two-Stage Procedure Toward the Efficient Implementation of PANS and Other Hybrid Turbulence Models,” NASA Technical Report No. TM, 213260.

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 3

Skin friction distributions along the streamwise centerline

Grahic Jump Location
Fig. 4

Static pressure distributions along the streamwise centerline

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

fk distributions for the MPANS simulation

Grahic Jump Location
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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In