Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-29T02:29:47.706Z Has data issue: false hasContentIssue false
  • English
  • Français

Remeshing Strategy of the Supersonic 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 63201, R.O.C.
*
* Associate Professor
Get access

Abstract

A modified error indicator and an extended locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh are developed to study the supersonic flow over a backward-facing step. In the Cartesian coordinate system, the unsteady Euler equations are solved. The modified error indicator, in which the unified magnitude of density gradient and unified magnitude of gradient of vorticity magnitude are incorporated, is utilized to treat the new node spacing of mesh remeshing. To assess the accuracy of the extended locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh, two flow calculations which include the oblique-shock reflection at a wall and transonic flow around an NACA 0012 airfoil are performed. Based on the comparison with the related numerical and 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

remeshingerror indicatorbackward-facing step
Type
Articles
Information
Journal of Mechanics , Volume 18 , Issue 3 , September 2002 , pp. 127 - 138
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1McDonald, H., “Turbulent Shear Layer Reattachment with Special Emphasis on the Base Pressure Problem,” The Aeronautical Quarterly, 15, pp. 247–279 (1964).CrossRefGoogle Scholar
2Rom, 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).CrossRefGoogle Scholar
3Samimy, M., Petrie, 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
4Abu-Hijleh, B. and Samimi, M., “An Experimental Study of a Reattaching Supersonic Shear Layer,” AIAA Paper 89-1801 (1989).Google Scholar
5Arai, 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
6Hartfield, R. J., 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).CrossRefGoogle Scholar
7Loth, 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
8Kuruvila, 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).CrossRefGoogle Scholar
9Lombard, 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).CrossRefGoogle Scholar
10Yang, 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).CrossRefGoogle Scholar
11Tucker, P. K. and Shyy, W., “A Numerical Analysis of Supersonic Flow over an Axisymmetric Afterbody,” AIAA Paper 93-2347 (1993).CrossRefGoogle Scholar
12Halupovich, Y., Natan, B. and Rom, J., “Numerical Solution of the Turbulent Supersonic Flow over a Backward Facing Step,” Fluid Dynamics Research, 24, pp. 251–273 (1999).CrossRefGoogle Scholar
13Chen, Y. S., “Compressible and Incompressible Flow Computational with a Pressure Based Method,” AIAA Paper 89-0286 (1989).CrossRefGoogle Scholar
14Sheng, 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).CrossRefGoogle Scholar
15Rausch, 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
16Hwang, C. J. and Wu, S. J., “Global and Local Remeshing Algorithms for Compressible Flows,” Journal of Computational Physics, 102(1), pp. 98–113 (1992).CrossRefGoogle Scholar
17Webster, 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).CrossRefGoogle Scholar
18Braaten, M. E. and Connell, S. D., “Three-Dimensional Unstructured Adaptive Multigrid Scheme for the Navier-Stokes Equations,” AIAA Journal, 34(2), pp. 281–290 (1996).CrossRefGoogle Scholar
19Delanaye, M. and Essers, J. A., “Quadratic-Reconsturction Finite Volume Scheme for Compressible Flows on Unstructured Adaptive Grids,” AIAA Journal, 35(4), pp. 631–639 (1997).CrossRefGoogle Scholar
20Parthasarathy, V. and Kallinderis, Y., “Adaptive Prismatic-Tetrahedral Grid Refinement and Redistribution for Viscous Flows,” AIAA Journal, 34(4), pp. 707–716 (1996).CrossRefGoogle Scholar
21Pirzadeh, S. Z., “A Solution-Adaptive Unstructured Grid Method by Grid Subdivision and Local Remeshing,” AIAA Journal, 37(5), pp. 818–824 (2000).Google Scholar
22Walsh, P. C. and Zingg, D. W., “Solution Adaptation of Unstructured Grids for Two-Dimensional Aerodynamic Computations,” AIAA Journal, 39(5), pp. 831–837 (2001).CrossRefGoogle Scholar
23Reddy, K. C. and Jacock, J. L., “A Locally Implicit Scheme for the Euler Equations,” AIAA Paper 87-1144 (1987).CrossRefGoogle Scholar
24Hwang, 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
25Jameson, A., Schmidt, W. and Turkel, E., “Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes,” AIAA Paper 81-1259 (1981).CrossRefGoogle Scholar
26Mavriplis, D. J., “Accurate Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes,” AIAA Journal, 28(2), pp. 213–221 (1990).CrossRefGoogle Scholar
27Nayani, S. N., “A Locally Implicit Scheme for Navier-Stokes Equations,” Ph.D. Dissertation, The University of Tennessee, Knoxville, Tennessee (1988).Google Scholar
28Hwang, C. J. and Yang, S. Y., “Locally Implicit Total Variation Diminishing Schemes on Mixed Quadrilateral-Triangular Meshes,” AIAA Journal, 31(11), pp. 2008–2015 (1993).CrossRefGoogle Scholar