Modares Mechanical Engineering

Modares Mechanical Engineering

Investigating effect of applying FCT scheme in vorticity confinement method on reducing the influence of confinement parameter on the final solution

Authors
1 Department of Mechanic Engineering, University of Birjand, phd candidate
2 Department of Mechanic Engineering, University of Birjand
Abstract
One of the most important difficulties of the vorticity confinement method is the need for manual adjustment of confinement parameter. In other word, user must adjust the parameter for each new problem. The small values deactivate this method and high values lead to non-physical results. Many attempts have been made by researchers to overcome this problem, but the dependence on manual adjustment has not been resolved. One way to conquer this problem is to reduce the effect of the confinement parameter on the final solution. At the present study, reducing the sensitivity of the vorticity confinement method to confinement parameter variations has been proposed by combining this method with FCT scheme for various limiters. In order to validate the proposed method, the problem of single vortex has been investigated. At first stage, the effect of changes in the confinement parameter on the final results has been compared for central difference scheme against the FCT scheme) using different limiters(. Then, the best way to combine the FCT scheme and the vorticity confinement method is discussed. It has been shown that, the best results were obtained using the minmod limiter at the middle step.
Keywords

[1] J. Steinhoff, Y. Wenren, D. Underhill, E. Puskas, Computation of short acoustic pulses, Proceeding of Proceedings, 6th International Symposium on CFD, Lake Tahoe Nevada, 1995.
[2] J. Steinhoff, C. Wang, D. Underhill, T. Mersch, Y. Wenren, Computational Vorticity Confinement: A Non-Diffusive Eulerian Method for VortexDominated Flows, The University of Tennessee Space Institute, Tullahoma Tennessee, 1992.
[3] J. Steinhoff, G. Raviprakash, Navier-Stokes computation of blade-vortex interaction using vorticity confinement, Proceeding of 33rd AIAA Aerospace Sciences Meeting and Exhibit, Reno Nevada, 1995.
[4] J. Steinhoff, T. Mersch, F. Decker, Computation of incompressible flow over delta wings using vorticity confinement, Proceeding of 32nd AIAA Aerospace Sciences Meeting and Exhibit, Reno Nevada, 1994.
[5] J. Steinhoff, Vorticity confinement: A new technique for computing vortex dominated flows, D.Caughey, M.Hafez (Eds.), Frontiers of Computational Fluid Dynamics, pp. 235-264, John Wiley & Sons, 1994.
[6] S. V. Pevchin, J. Steinhoff, B. Grossman, Capture of contact discontinuities and shock waves using a discontinuity confinement procedure, 35 th AIAA Aerospace Sciences Meeting and Exhibit, Reno Nevada, 1997 .
[7] K. Yee, An euler calculation for a hovering coaxial rotor flow field with new boundary condition, 24 Th European Rotorcraft Forum, Marseilles France, 1998 .
[8] G. Hu, B. Grossman, J. Steinhoff, Numerical method for vorticity confinement in compressible flow, AIAA Journal, Vol. 40, No. 10, pp. 1945- 1953, 2002 .
[9] M. Costes, G. Kowani, An automatic anti-diffusion method for vortical flows based on Vorticity Confinement, Aerospace Science and Technology, Vol. 7, No. 1, pp. 11-21, 2003 .
[10] M. Robinson, Application of vorticity confinement to inviscid missile force and moment prediction, 42 nd AIAA Aerospace Sciences Meeting and Exhibit, Reno Nevada, 2004 .
[11] M. M. Jafarian, M. P. Fard, Development and application of compressible vorticity confinement, Scientia Iranica, Vol. 14, No. 3, pp. 251-262, 2007 .
[12] N. Butsuntorn, A. Jameson, Time spectral method for rotorcraft flow, Proceeding of 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno Nevada ,2008.
[13] S. Hahn, G. Iaccarino, Towards adaptive vorticity confinement, Proceeding of 47th AIAA Aerospace Sciences Meeting and Exhibit, Reno Nevada, 2009.
[14] H. Bagheri-Esfeh, M. Malek-Jafarian, Development of artificial dissipation schemes and compressible vorticity confinement methods, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 225, No. 8, pp. 929-945, 2011 .
[15] K. Pierson, A. Povitsky, Vorticity Confinement technique for preservation of tip vortex of rotating blade, Proceeding of 31st AIAA Applied Aerodynamics Conference, Reno Nevada, 2013.
[16] M. Sadri, K. Hejranfar, M. Ebrahimi, On application of high-order compact finite-difference schemes to compressible vorticity confinement method, Aerospace Science and Technology, Vol. 46, pp. 398-411, 2015 .
[17] M. O'Regan, P. Griffin, T. Young, A vorticity confinement model applied to URANS and LES simulations of a wing-tip vortex in the near-field, International Journal of Heat and Fluid Flow, Vol. 61, pp. 355-365, 2016 .
[18] M. Costes, I. Petropoulos, P. Cinnella, Development of a third-order accurate vorticity confinement scheme, Computers & Fluids, Vol. 136, pp. 132-151, 2016 .
[19] I. Petropoulos, M. Costes, P. Cinnella ,Development and analysis of highorder vorticity confinement schemes, Computers & Fluids, Vol. 156, pp. 602-620, 2017 .
[20] A. Povftsky, D. Ofengeim, Numerical study of interaction of a vortical density inhomogeneity with shock and expansion waves, International Journal of Computational Fluid Dynamics, Vol. 12, No. 2, pp. 165-176, 1999 .