Large Eddy Simulation of the Flow Over non-confined Backward Facing Step Using High Order Compact Finite Difference Schemes

Document Type : Original Article

Authors

1 Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran.

2 School of Mechanical Engineering, College of Engineering, University of Tehran, Iran

Abstract

In the present study, large eddy simulation of unsteady, three-dimensional and turbulent flow over non-confined backward facing step (BFS) is numerically conducted. Due to the capability of the compact differential scheme in high-order solution of the compressible flow, this method is used to solve the filtered Navier-Stokes equations in the generalized curvilinear coordinate using a multi-block structured grid. To study the influence of the sub-grid scale (SGS) stress model, the Smagorinsky model, the MKEV model, the dynamic Smagorinsky model (DSM), and the WALE model are considered. The numerical results include the general characteristics of the flow over BFS such as the reattachment length, friction and pressure coefficients, the mean velocity and the Reynolds stresses. Moreover, the present LES results are compared with the available experimental data and DNS, LES and RANS results and a very good agreement is achieved. Moreover, the obtained results using the DSM and WALE models give a better agreement with the DNS and experimental data than those by Smagorinsky and MKEV models.

Keywords

References

  1. Pont-Vílchez, A., Trias, F., Gorobets, A., and Oliva, A. "Direct numerical simulation of backward-facing step flow at Re= 395 and expansion ratio 2," Journal of Fluid Mechanics, 863, pp. 341-363, 2019.##
  2. Driver, D. M., Seegmiller, H. L., and Marvin, J. G. "Time-dependent behavior of a reattaching shear layer," AIAA journal, Vol. 25, pp. 914-919, 1987,.##
  3. Eaton, J., and Johnston, J. "A review of research on subsonic turbulent flow reattachment," AIAA journal, Vol. 19, No.9, pp. 1093-1100, 1981,.##
  4. Rajasekaran, J. "On the flow characteristics behind a backward-facing step and the design of a new axisymmetric model for their study," , PhD Dissertation,  University of Toronto, 2011.##
  5. Adams, E., and Johnston, J. "Effects of the separating shear layer on the reattachment flow structure part 2: Reattachment length and wall shear stress," Experiments in Fluids, Vol.6, No.7, pp. 493-499, 1988.##
  6. De Brederode, V., and Bradshaw, P., Three-dimensional Flow in Nominally Two-dimensional Separation Bubbles: Flow Behind a Rearward-facing Step. I, Department of Aeronautics, Imperial College of Science and Technology, 1972.##
  7. Isomoto, K., and Honami, S. "The effect of inlet turbulence intensity on the reattachment process over a backward-facing step," Journal of fluids engineering, Vol. 111, No.1, pp. 87-92, 1989.##
  8. Jovic, S., and Driver, D. M. "Backward-facing step measurements at low Reynolds number, Reh= 5000," NASA TM, 108807, 1994.##
  9. Kuehn, D. A. D. "Effects of adverse pressure gradient on the incompressible reattaching flow over a rearward-facing step," AIAA journal, Vol. 18, No.3, pp. 343-344, 1980.##
  10. Ötügen, M. "Expansion ratio effects on the separated shear layer and reattachment downstream of a backward-facing step," Experiments in fluids, Vol.10, No.5, pp. 273-280, 1991.##
  11. Le, H., Moin, P., and Kim, J. "Direct numerical simulation of turbulent flow over a backward-facing step," Journal of Fluid Mechanics, Vol. 330, pp. 349-374, 1997.##
  12. Aider, J.-L., Danet, A., and Lesieur, M. "Large-eddy simulation applied to study the influence of upstream conditions on the time-dependant and averaged characteristics of a backward-facing step flow," Journal of Turbulence, Vol.8 , 2007,.##
  13. Benocci, C., Giammanco, R., Manna, M., and Simons, E. "Large eddy simulation of turbulent flows via domain decomposition techniques. Part 2: applications," International journal for numerical methods in fluids, Vol. 48, No.4, pp. 397-422, 2005.##
  14. Kanchi, H., Sengupta, K., and Mashayek, F. "Effect of turbulent inflow boundary condition in LES of flow over a backward-facing step using spectral element method," International Journal of Heat and Mass Transfer, Vol. 62, pp. 782-793, 2013.##
  15. Panjwani, B., Ertesvåg, I. S., Gruber, A., and Rian, K. E. "Large eddy simulation in generalized curvilinear coordinates using conventional approach: Theory and validation," International Journal for Numerical Methods in Fluids, Vol. 9, No.3, pp. 671-690, 2012.##
  16. Patil, S., and Tafti, D. "Wall modeled large eddy simulations of complex high Reynolds number flows with synthetic inlet turbulence," International Journal of Heat and Fluid Flow, Vol. 33, No.1, pp. 9-21, 2012.##
  17. Geurts, B. J., Rouhi, A., and Piomelli, U. "Recent progress on reliability assessment of large-eddy simulation," Journal of Fluids and Structures, 2019,.##
  18. Esmaeili, M., and Afshari, A. "LES/FMDF of premixed methane/air flow in a backward-facing step combustor," Energy Equipment and Systems, Vol. 7, No.2, pp. 159-173, 2019.##
  19. Choi, S.-K., and Lin, C.-L. "A simple finite-volume formulation of the lattice Boltzmann method for laminar and turbulent flows," Numerical Heat Transfer, Part B: Fundamentals, Vol. 58, No.4, pp. 242-261, 2010.##
  20. Shih, T.-H., Liou, W. W., Shabbir, A., Yang, Z., and Zhu, J. "A new k-ϵ eddy viscosity model for high reynolds number turbulent flows," Computers & Fluids, Vol. 24, No.3, pp. 227-238, 1995.##
  21. Javadi, K., Darbandi, M., and Taeibi-Rahni, M. "Three-dimensional compressible–incompressible turbulent flow simulation using a pressure-based algorithm," Computers & fluids, Vol. 37, No.6, pp. 747-766, 2008.##
  22. Nazif, H. R., and Tabrizi, H. B. "Applying a non-equilibrium wall function in k–ε turbulent modelling of hydrodynamic circulating flow," Applied Mathematical Modelling, Vol. 38, No. 2, pp. 588-598, 2014.##
  23. Razavi, S., and Hanifi, M. "A multi-dimensional virtual characteristic scheme for laminar and turbulent incompressible flows," Journal of Applied Fluid Mechanics, Vol. 9, No.4, pp. 1579-1590, 2016.##
  24. Sheikhi, N., Najafi, M., and Enjilela, V. "Extending the Meshless Local Petrov–Galerkin Method to Solve Stabilized Turbulent Fluid Flow Problems," International Journal of Computational Methods, Vol. 16, No.1, p. 1850086, 2019.##
  25. Hasse, C., Sohm, V., Wetzel, M., and Durst, B. "Hybrid URANS/LES turbulence simulation of vortex shedding behind a triangular flameholder," Flow, turbulence and combustion, Vol. 8, No.1, pp. 1-20, 2009.##
  26. Luo, D. "Numerical simulation of turbulent flow over a backward facing step using partially averaged Navier-Stokes method," Journal of Mechanical Science and Technology, Vol. 33, No.5, pp. 2137-2148, 2019.##
  27. Esmaeili, M., Afshari, A., and Jaberi, F. A. "Turbulent mixing in non-isothermal jet in crossflow," International Journal of Heat and Mass Transfer, Vol. 89, pp. 1239-1257, 2015.##
  28. Esmaeili, M., and Afshari, A., "LES/FMDF of Mixing in Turbulent Jet in Cross-Flows,"; Proc. ASME Conf., USA, 2014.##
  29. Afshari, A., Jaberi, F. A., and Shih, T. I. "Large-eddy simulations of turbulent flows in an axisymmetric dump combustor," AIAA journal, Vol. 46, No.7, pp. 1576-1592, 2008.##
  30. Yoshizawa, A. "Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling," Physics of Fluids (1958-1988), Vol. 29, No.7, pp. 2152-2164, 1986.##
  31. Colucci, P., Jaberi, F., Givi, P., and Pope, S., 1998, "Filtered density function for large eddy simulation of turbulent reacting flows," Physics of Fluids (1994-present), Vol.10, No.2, pp. 499-515, 1998.##
  32. Germano, M., Piomelli, U., Moin, P., and Cabot, W. H. "A dynamic subgrid‐scale eddy viscosity model," Physics of Fluids A: Fluid Dynamics (1989-1993), Vol.3, No.7, pp. 1760-1765, 1991.##
  33. Moin, P. a., Squires, K., Cabot, W., and Lee, S. "A dynamic subgrid‐scale model for compressible turbulence and scalar transport," Physics of Fluids A: Fluid Dynamics (1989-1993), Vol. 3, No.11, pp. 2746-2757, 1991.##
  34. Nicoud, F., and Ducros, F. "Subgrid-scale stress modelling based on the square of the velocity gradient tensor," Flow, Turbulence and Combustion, Vol. 62, No.3, pp. 183-200, 1999.##
  35. Garnier, E., Adams, N., and Sagaut, P. Large eddy simulation for compressible flows, Springer Science & Business Media, 2009.##
  36. Suh, J., Frankel, S. H., Mongeau, L., and Plesniak, M. W. "Compressible large eddy simulations of wall-bounded turbulent flows using a semi-implicit numerical scheme for low Mach number aeroacoustics," Journal of Computational Physics, Vol. 215, No. 2, pp. 526-551, 2006.##
  37. Lele, S. K. "Compact finite difference schemes with spectral-like resolution," Journal of computational physics, Vol. 103, No.1, pp. 16-42, 1992.##
  38. Visbal, M. R., and Gaitonde, D. V. "Very high-order spatially implicit schemes for computational acoustics on curvilinear meshes," Journal of Computational Acoustics, Vol. 9, No.4, pp. 1259-1286, 2001.##
  39. Gaitonde, D. V., and Visbal, M. R. "Further filevelopment of a Navier-Stokes Solution~ Procedure Based on Higher-Order Formula, 1999."##
  40. Gaitonde, D. V., and Visbal, M. R. "Pade-plusmn;-Type Higher-Order Boundary Filters for the Navier-Stokes Equations," AIAA journal, Vol. 38, No.11, pp. 2103-2112, 2000.##
  41. Gottlieb, S., Shu, C.-W., and Tadmor, E. "Strong stability-preserving high-order time discretization methods," SIAM review, Vol. 43, No.1, pp. 89-112, 2001.##
  42. Shu, C.-W., and Osher, S. "Efficient implementation of essentially non-oscillatory shock-capturing schemes," Journal of Computational Physics, Vol. 77, No.2, pp. 439-471, 1988.##
  43. Jameson, A., and Baker, T., "Solution of the Euler equations for complex configurations," Proc. 6th Computational Fluid Dynamics Conference Danvers, 1983.##
  44. Spalart, P. R. "Direct simulation of a turbulent boundary layer up to Rθ= 1410," Journal of Fluid Mechanics, Vol. 187, pp. 61-98, 1988.##
  45. Jones, W., and Wille, M. "Large-eddy simulation of a plane jet in a cross-flow," International journal of heat and fluid flow, Vol. 17, No. 3, pp. 296-306, 1996.##
  46. You, D., Bose, S., and Moin, P., "Grid-independent large-eddy simulation of compressible turbulent flows using explicit filtering," Proc. Proceedings of the Summer Program, pp. 203-210, 2010.##
  47. Cavar, D., and Meyer, K. E. "LES of turbulent jet in cross-flow: Part 1–A numerical validation study," International Journal of Heat and Fluid Flow, Vol. 36, pp. 18-34, 2012.##
  48. Esmaeili, M., Afshari, A., and Jaberi, F. A. "Large-eddy simulation of turbulent mixing of a jet in cross-flow," Journal of Engineering for Gas Turbines and Power, Vol. 137, No.9, p. 091510, 2015.##
  49. Fröhlich, J., Mellen, C. P., Rodi, W., Temmerman, L., and Leschziner, M. A. "Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions," Journal of Fluid Mechanics, Vol. 526, pp. 19-66, 2005.##
  50. Pope, S. B. Turbulent flows, Cambridge university press, 2000.##
  51. Kolář, V. "Vortex identification: New requirements and limitations," International journal of heat and fluid flow, Vol. 28, No.4, pp. 638-652, 2007.##

Files

History

  • Receive Date: 14 August 2019
  • Revise Date: 04 May 2020
  • Accept Date: 23 June 2020
  • Publish Date: 20 February 2020

Share

How to cite

Statistics