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Refining Strategy of the Supersonic Turbulent Flow Over a Backward-Facing Step

Published online by Cambridge University Press:  05 May 2011

Shih-Ying Yang
Shih-Ying Yang*
Affiliation:
Department of Aeronautical Engineering, National Huwei Institute of Technology, Huwei, Yunlin, Taiwan 632, R.O.C.
*
*Associate Professor
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Abstract

A modified error indicator is developed to study the supersonic turbulent flow over a backward-facing step. In the Cartesian coordinate system, the unsteady Navier-Stokes equations with a low-Reynolds-number k−ε turbulence model are solved. The modified error indicator, in which the unified magnitude of substantial derivative of pressure and unified magnitude of substantial derivative of weighted vorticity magnitude are incorporated, is applied to treat the mesh refining. To assess the present approach, the transonic turbulent flow around an NACA 0012 airfoil is performed. Based on the comparison with the experimental data, the accuracy of the present approach is confirmed. According to the high-resolutional result on the adaptive mesh, the structure of backstep corner vortex, expansion wave and oblique shock wave is distinctly captured.

Keywords

RefiningError indicatorBackward-facing stepTurbulent.
Type
Articles
Information
Journal of Mechanics , Volume 19 , Issue 4 , December 2003 , pp. 397 - 407
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

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References

REFERENCES

1.McDonald, H., “Turbulent Shear Layer Reattachment with Special Emphasis on the Base Pressure Problem,” The Aeronautical Quarterly, 15, pp. 247–279 (1964).Google Scholar
2.Rom, J., “Analysis of the Near Wake Pressure in Supersonic Flow Using the Momentum Integral Method,” Journal of Spacecraft and Rockets, 3(10), pp. 1504–1509 (1966).Google Scholar
3.Samimy, M., Pétrie, H. L. and Addy, A. L., “A Study of Compressible Turbulent Free Shear Layers Using Laser Doppler Velocimetry,” AIAA Paper 85–0177 (1985).CrossRefGoogle Scholar
4.Abu-Hijleh, B. and Samimy, M., “An Experimental Study of a Reattaching Supersonic Shear Layer,” AIAA Paper 89–1801 (1989).Google Scholar
5.Arai, T., Sugiyama, H., Homareda, M. and Uno, N., “Turbulence Characteristics of Supersonic Boundary Layer Past a Backward Facing Step,” AIAA Paper 95–6126 (1995).Google Scholar
6.Hartfield, R. I., Hollo, S. D. and McDaniel, J. C., “Planar Measurement Technique for Compressible Flows Using Laser Induced Iodine Fluorescence,” AIAA Journal, 31(3), pp. 483–490 (1993).Google Scholar
7.Loth, E., Kailasanath, K. and Lohner, R., “Supersonic Flow over an Axisymmetric Backward-Facing Step,” Journal of Spacecraft and Rockets, 29(3), pp. 352–359(1992).CrossRefGoogle Scholar
8.Yang, S. Y., “Adaptive Analysis of the Inviscid Supersonic Flow over a Backward-Facing Step,” Journal of Propulsion and Power, 17(4), pp. 938–940 (2001).Google Scholar
9.Kuravila, G. and Anderson, J. D., “A Study on the Effects of Numerical Dissipation on the Calculations of Supersonic Separated Flow,” AIAA Paper 85–0301 (1985).Google Scholar
10.Lombard, C. K., Luh, R. C.-C., Nagaraj, N., Bardina, J. and Venkatapathy, E., “Numerical Simulation of Backward Step and Jet Exhaust Flows,” AIAA Paper 86–0432 (1986).Google Scholar
11.Yang, A. S., Hsieh, W. H. and Kuo, K. K., “Theoretical Study of Supersonic Flow Separation over a Rearward Facing Step,” AIAA Paper 91–2161 (1991).Google Scholar
12.Tucker, P. K. and Shyy, W., “A Numerical Analysis of Supersonic Flow over an Axisymmetric Afterbody,” AIAA Paper 93–2347 (1993).CrossRefGoogle Scholar
13.Halupovich, Y., Natan, B. and Rom, I., “Numerical Solution of the Turbulent Supersonic Flow over a Backward Facing Step,” Fluid Dynamics Research, 24, pp. 251–273 (1999).Google Scholar
14.Chen, Y. S. and Farmer, R. C., “CFD Analysis of Baffle Flame Stabilization,” AIAA Paper 91–1967 (1991).CrossRefGoogle Scholar
15.Sheng, C., Whitfield, D. L. and Anderson, W. K., “Multiblock Approach for Calculating Incompressible Fluid Flows on Unstructured Grids,” AIAA Journal, 37(2), pp. 169–176 (1999).Google Scholar
16.Mavriplis, D. J., “Viscous Flow Analysis Using a Parallel Unstructured Multigrid Solver,” AIAA Journal, 38(11), pp. 1243–1251 (2000).Google Scholar
17.Rausch, R. D., Batina, J. T. and Yang, H. T. Y., “Spatial Adaptation of Unstructured Meshes for Unsteady Aerodynamic Flow Computations,” AIAA Journal, 30(5), pp. 1243–1251 (1992).CrossRefGoogle Scholar
18.Hwang, C. J. and Wu, S. J., “Global and Local Remeshing Algorithms for Compressible Flows,” Journal of Computational Physics, 102(1), pp. 98–113 (1992).Google Scholar
19.Webster, B. E., Shephard, M. S., Rusak, Z. and Flaherty, J. E., “Automated Adaptive Time-Discontinuous Finite Element Method for Unsteady Compressible Airfoil Aerodynamics,” AIAA Journal, 32(4), pp. 748–757 (1994).Google Scholar
20.Parthasarathy, V. and Kallinderis, Y., “Adaptive Prismatic-Tetrahedral Grid Refinement and Redistribution for Viscous Flows,” AIAA Journal, 34(4), pp. 707–716 (1996).Google Scholar
21.Pirzadeh, S. Z., “A Solution-Adaptive Unstructured Grid Method by Grid Subdivision and Local Remeshing,” AIAA Journal, 37(5), pp. 818–824 (2000).Google Scholar
22.Walsh, P. Z., and Zingg, D. W., “Solution Adaptation of Unstructured Grids for Two-Dimensional Aerodynamic Computations,” AIAA Journal, 39(5), pp. 831–837 (2001).Google Scholar
23.Oh, W. S., Kim, J. S. and Kwon, O. J., “Numerical Simulation of Two-Dimensional Blade-Vortex Interactions Using Unstructured Adaptive Meshes,” AIAA Journal, 40(3), pp. 474–480 (2002).Google Scholar
24.Reddy, K. C. and Jacock, J. L., “A Locally Implicit Scheme for the Euler Equations,” AIAA Paper 87–1144(1987).CrossRefGoogle Scholar
25.Hwang, C. J. and Liu, J. L., “Inviscid and Viscous Solutions for Airfoil/Cascade Flows Using a Locally Implicit Algorithm on Adaptive Meshes,” Journal of Turbomachinery, 113(4), pp. 553–560 (1991).CrossRefGoogle Scholar
26.Yang, S. Y., “Remeshing Strategy of the Supersonic Flow over a Backward-Facing Step,” Chinese Journal of Mechanics, Series A, 18(3), pp. 127–138 (2002).Google Scholar
27.Abe, K. and Kondoh, T., “A New Turbulence Model for Predicting Fluid Flow and Heat Transfer in Separating and Reattaching Flows—I. Flowfield Calculations,” International Journal of Heat and Mass Transfer, 37(1), pp. 139–151 (1994).Google Scholar
28.Nagano, Y and Tagawa, M., “An Improved K-E Model for Boundary Layer Flows,” Journal of Fluids Engineering, 112(2), pp. 33–39 (1990).Google Scholar
29.Jameson, A., Schmidt, W. and Türkei, E., “Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes,” AIAA Paper 81–1259 (1981).Google Scholar
30.Mavriplis, D. J., “Accurate Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes,” AIAA Journal, 28(2), pp. 213–221 (1990).CrossRefGoogle Scholar
31.Nayani, S. N., “A Locally Implicit Scheme for Navier-Stokes Equations,” Ph.D. Dissertation, The University of Tennessee, Knoxville, Tennessee (1988).Google Scholar
32.Hwang, C. J. and Fang, J. M., “Solution-Adaptive Approach for Unsteady Flow Calculations on Quadrilateral-Triangular Meshes,” AIAA Journal, 34(4), pp. 851–853 (1996).Google Scholar
33.Thibert, J. J., Granjacques, M. and Ohman, L. H., “NACA 0012 Airfoil AGARD Advisory Report No. 138, Experimental Data Base for Computer Program Assessment,” pp. A1–9 (1979).Google Scholar