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 OJFD  Vol.6 No.4 , December 2016
Tracking a Tip Vortex with Adaptive Vorticity Confinement and Hybrid RANS-LES
Abstract: The prediction of coherent vortices with standard RANS solvers suffers especially from discretisation and modelling errors which both introduce numerical diffusion. The adaptive Vorticity Confinement (VC) method targets to counteract one part of the discretisation error: the one due to the discretisation of the convection term. This method is applied in conjunction with a hybrid RANS-LES turbulence model to overcome the overprediction of turbulence intensity inside vortex cores which is a typical deficiency of common RANS solvers. The third main source for numerical diffusion originates from the spatial discretisation of the solution domain in the vicinity of the vortex core. The corresponding error is analysed within a grid convergence study. A modification of the adaptive VC method used in conjunction with a high-order discretisation of the convection term is presented and proves to be superior. The simulations of a wing tip vortex flow are validated in terms of vortex velocity profiles using the results of a wind tunnel experiment performed by Devenport and colleagues (1996). Besides, the results are compared with another numerical study by Wells (2009) who uses a Reynolds Stress turbulence model. It turns out that the application of the modified adaptive VC method on the one hand reinforces the tip vortex, and on the other hand accelerates the axial flow which leads to a slight degradation compared to the experimental results. The result of Wells is more accurate close to the wing, but the result obtained here is superior further downstream as no excessive diffusion of the tip vortex occurs.
Cite this paper: Feder, D. and Abdel-Maksoud, M. (2016) Tracking a Tip Vortex with Adaptive Vorticity Confinement and Hybrid RANS-LES. Open Journal of Fluid Dynamics, 6, 406-429. doi: 10.4236/ojfd.2016.64030.
References

[1]   Devenport, W.J., Rife, M.C., Liapis, S.I. and Follin, G.J. (1996) The Structure and Development of a Wing-Tip Vortex. Journal of Fluid Mechanics, 312, 67-106.
https://doi.org/10.1017/S0022112096001929

[2]   Hahn, S. and Iaccarino, G. (2008) Simulations of Vortex-Dominated Flows: Adaptive Vorticity Confinement vs. Rotational-Form Upwinding. Center for Turbulence Research, Annual Research Briefs, 359-368.

[3]   Spalart, P.R. and Shur, M. (1997) On the Sensitization of Turbulence Models to Rotation and Curvature. Aerospace Science and Technology, 1, 297-302.
https://doi.org/10.1016/S1270-9638(97)90051-1

[4]   Wallin, S. and Girimaji, S.S. (2000) Evolution of an Isolated Turbulent Trailing Vortex. AIAA Journal, 38, 657-665. https://doi.org/10.2514/2.1007

[5]   Mishra, A.A. and Girimaji, S.S. (2013) Intercomponent Energy Transfer in Incompressible Homogeneous Turbulence: Multi-Point Physics and Amenability to One-Point Closures. Journal of Fluid Mechanics, 731, 639-681. https://doi.org/10.1017/jfm.2013.343

[6]   Stephan, A., Holzäpfela, F. and Misaka, T. (2014) Hybrid Simulation of Wake-Vortex Evolution during Landing on at Terrain and with Plate Line. International Journal of Heat and Fluid Flow, 49, 18-27. https://doi.org/10.1016/j.ijheatfluidflow.2014.05.004

[7]   Feder, D.-F. and Abdel-Maksoud, M. (2016) Potential of the Adaptive Vorticity Confinement Method for RANS Simulations and Hybrid RANS-LES. Proceedings of the 7th International Conference on Vortex Flows and Vortex Models, Rostock, 19-22 September 2016, 23-32.

[8]   Pierson, K. and Povitsky, A. (2013) Vorticity Confinement Technique for Preservation of Tip Vortex of Rotating Blade. 31st AIAA Applied Aerodynamics Conference, Fluid Dynamics and Collocated Conferences, San Diego, 24-27 June 2013, 260-270.
https://doi.org/10.2514/6.2013-2420

[9]   Jeong, J. and Hussain, F. (1995) On the Identification of a Vortex. Journal of Fluid Mechanics, 285, 69-94.

[10]   Lilek, Z. and Perić, M. (1995) A Fourth-Order Finite Volume Method with Collocated Variable Arrangement. Computers & Fluids, 24, 239-252. https://doi.org/10.1016/0045-7930(94)00030-3

[11]   Jasak, H. (1996) Error Analysis and Estimation for the Finite Volume Method with Applications to Fluid Flows. PhD Thesis, Imperial College London, London.

[12]   Spalart, P.R. and Allmaras, S.R. (1994) A One-Equation Turbulence Model for Aerodynamic Flows. Recherche Aerospatiale, No. 1, 5-21.

[13]   Steinhoff, J., Yonghu, W., Mersch, T. and Senge, H. (1992) Computational Vorticity Capturing: Application to Helicopter Rotor Flow. 30th Aerospace Sciences Meeting and Exhibit, Aerospace Sciences Meetings, Reno, 6-9 January 1992, 92-112.

[14]   Steinhoff, J. and Underhill, D. (1994) Modification of the Euler Equations for ‘‘Vorticity Confinement’’: Application to the Computation of Interacting Vortex Rings. Physics of Fluids, 6, 2738-2744. https://doi.org/10.1063/1.868164

[15]   Steinhoff, J., Lynn, N. and Wang, L. (2005) Computation of High Reynolds Number Flows Using Vorticity Confinement: I. Formulation. University of Tennessee Space Institute, Tullahoma.

[16]   Costes, M. and Kowani, G. (2003) An Automatic Anti-Diffusion Method for Vortical Flows Based on Vorticity Confinement. Aerospace Science and Technology, 7, 11-21.
https://doi.org/10.1016/S1270-9638(02)01180-X

[17]   Costes, M. (2008) Analysis of the Second Vorticity Confinement Scheme. Aerospace Science and Technology, 12, 203-213. https://doi.org/10.1016/j.ast.2007.06.004

[18]   Choi, K. and Simpson, R.L. (1987) Some Mean Velocity, Turbulence and Unsteadiness Characteristics of the VPI & SU Stability Wind Tunnel. Report VPIAOE-161, Virginia Tech, Blacksburg.

[19]   Spalart, P.R., Deck, S., Shur, M.L., Squires, K.D., Strelets, M.K. and Travin, A. (2006) A New Version of Detached-Eddy Simulation, Resistant to Ambiguous Grid Densities. Theoretical and Computational Fluid Dynamics, 20, 181-195. https://doi.org/10.1007/s00162-006-0015-0

[20]   Ferziger, J.H. and Perić, M. (2002) Computational Methods for Fluid Dynamics. Vol. 3, Springer, Berlin.

[21]   Wells, J. (2009) Effects of Turbulence Modeling on RANS Simulations of Tip Vortices. Master’s Thesis, Virginia Polytechnic Institute and State University, Blacksburg.

[22]   Launder, B.E., Reece, G.J. and Rodi, W. (1975) Progress in the Development of a Reynolds-Stress Turbulence Closure. Journal of Fluid Mechanics, 68, 537-566.

 
 
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