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Large eddy simulation of transient upstream/downstream vortex interactions

  • Kyle J. Forster (a1), Sammy Diasinos (a2), Graham Doig (a1) (a3) and Tracie J. Barber (a1)


Experimentally validated large eddy simulations were performed on two NACA0012 vanes at various lateral offsets to observe the transient effects of the near field interactions between two streamwise vortices. The vanes were separated in the streamwise direction, allowing the upstream vortex to impact on the downstream geometry. These vanes were evaluated at an angle of incidence of $8^{\circ }$ and a Reynolds number of 70 000, with rear vane angle reversed to create a co-rotating or counter-rotating vortex pair. The downstream vortex merged with the upstream in the co-rotating condition, driven by the suppression of one of the tip vortices of the downstream vane. At close proximity to the pressure side, the vane elongated the upstream vortex, resulting in it being the weakened and merging into the downstream vortex. This produced a transient production of bifurcated vortices in the wake region. The downstream vortex of the co-rotating pair experienced faster meandering growth, with position oscillations equalising between the vortices. The position oscillation was determined to be responsible for statistical variance in the merging location, with variation in vortex separation causing the vortices at a single plane to merge and separate in a time-dependent manner. In the counter-rotating condition position oscillations were found to be larger, with higher growth, but less uniform periodicity. It was found that the circulation transfer between the vortices was linked to the magnitude of their separation, with high separation fluctuations weakening the upstream vortex and strengthening the downstream vortex. In the case of upstream vortex impingement on the downstream vane, the upstream vortex was found to bifurcate, with a four vortex system being formed by interactions with the shear layer. This eventually resulted in a single dominant vortex, which did not magnify its oscillation amplitudes as it travelled downstream due to the destruction of the interacting vortices.


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Brandt, L. K. & Nomura, K. K. 2010 Characterization of the interactions of two unequal co-rotating vortices. J. Fluid Mech. 646, 233253.
Chatelain, P., Curioni, A., Bergdorf, M., Rossinelli, D., Andreoni, W. & Koumoutsakos, P. 2008 Billion vortex particle direct numerical simulations of aircraft wakes. Comput. Meth. Appl. Mech. Engng 197, 12961304.
Courant, R., Friedrichs, K. O. & Lewy, H. 1967 On the partial difference equation of mathematical physics. IBM J. 11 (March), 3274.
Crow, S. C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8 (12), 21722179.
Dacles-Mariani, J., Zilliac, G. G., Chow, J. S. & Bradshaw, P. 1995 Numerical/experimental study of a wingtip vortex in the near field. AIAA J. 33 (9), 15611568.
Devenport, W. J., Zsoldos, J. S. & Vogel, C. M. 1997 The structure and development of a counter-rotating wing-tip vortex pair. J. Fluid Mech. 332, 71104.
Dritschel, D. G. 1985 The stability and energetics of corotating uniform vortices. J. Fluid Mech. 157, 95134.
Dritschel, D. G. & Waugh, D. W. 1992 Quantification of the inelastic interaction of unequal vortices in two-dimensional vortex dynamics. Phys. Fluids A 4, 1737.
Fabre, D., Jacquin, L. & Loof, A. 2002 Optimal perturbations in a four-vortex aircraft wake in counter-rotating configuration. J. Fluid Mech. 451, 319328.
Folz, P. J. R. & Nomura, K. K. 2017 A quantitative assessment of viscous asymmetric vortex pair interactions. J. Fluid Mech. 829, 130.
Forster, K. J., Barber, T., Diasinos, S. & Doig, G.2015 Numerical investigation of streamwise vortex interaction. SAE Technical Paper. SAE International.
Forster, K. J., Barber, T., Diasinos, S. & Doig, G. 2017a The variation in co and counter-rotating upstream-downstream vortex interactions. In 47th AIAA Fluid Dynamics Conference (June), pp. 113.
Forster, K. J., Barber, T. J., Diasinos, S. & Doig, G. 2017b Interactions of a co-rotating vortex pair at multiple offsets. Phys. Fluids 29, 057102.
Forster, K. J., Barber, T. J., Diasinos, S. & Doig, G. 2017c Interactions of a counter-rotating vortex pair at multiple offsets. Exp. Therm. Fluid Sci. 86, 6374.
Forster, K. J. & White, T. R. 2014 Numerical investigation into vortex generators on heavily cambered wings. AIAA J. 52 (5), 10591071.
Garmann, D. J. & Visbal, M. R. 2015 Interactions of a streamwise-oriented vortex with a finite wing. J. Fluid Mech. 767, 782810.
Giuni, M. & Green, R. B. 2013 Vortex formation on squared and rounded tip. Aerosp. Sci. Technol. 29 (1), 191199.
Gordnier, R. E. & Visbal, M. R. 1999 Numerical simulation of the impingement of a streamwise vortex on a plate. Intl J. Comput. Fluid Dyn. 12 (1), 4966.
Huang, R. F. & Lin, C. L. 1995 Vortex shedding and shear-layer instability of wing at low-Reynolds numbers. AIAA J. 33 (8), 13981403.
Hummel, D. 1995 Formation flight as an energy-saving mechanism. Israel J. Zoology 41 (3), 261278.
Inasawa, A., Mori, F. & Asai, M. 2012 Detailed observations of interactions of wingtip vortices in close-formation flight. J. Aircraft 49 (1), 206213.
Kaya, F. & Karagoz, I. 2008 Performance analysis of numerical schemes in highly swirling turbulent flows in cyclones. Curr. Sci. 94 (10), 12731278.
Klein, R. 1995 Simplified equations for the interaction of nearly parallel vortex filaments. J. Fluid Mech. 288, 201248.
Legras, B. & Dritschel, D. 1993 Vortex stripping and the generation of high vorticity gradients in two-dimensional flows. Appl. Sci. Res. 51, 445455.
Lehmkuhl, O., Rodríguez, I., Baez, A., Oliva, A. & Pérez-Segarra, C. D. 2013 On the large-Eddy simulations for the flow around aerodynamic profiles using unstructured grids. Comput. Fluids 84, 176189.
Leweke, T., Le Dizès, S. & Williamson, C. H. K. 2016 Dynamics and instabilities of vortex pairs. Annu. Rev. Fluid Mech. 48, 507541.
Ma, J., Wang, F. & Tang, X. 2009 Comparison of Several Subgrid-Scale Models for Large-Eddy Simulation of Turbulent Flows in Water Turbine. pp. 328334. Springer.
Manolesos, M. & Voutsinas, S. G. 2015 Experimental investigation of the flow past passive vortex generators on an airfoil experiencing three-dimensional separation. J. Wind Engng Ind. Aerodyn. 142, 130148.
Meunier, P. & Leweke, T. 2005 Elliptic instability of a co-rotating vortex pair. J. Fluid Mech. 533, 125159.
Nicoud, F. & Ducros, F. 1999 Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 62, 183200.
Overman, E. A. 1982 Evolution and merger of isolated vortex structures. Phys. Fluids 25, 1297.
Patankar, S. V. 1971 Numerical Heat Transfer and Fluid Flow. McGraw-Hill Book Company.
Pereira, L. A. A., Hirata, M. H. & Filho, N. M. 2004 Wake and aerodynamics loads in multiple bodies-application to turbomachinery blade rows. J. Wind Engng Ind. Aerodyn. 92, 477491.
Peyret, R. 1996 Handbook of Computational Fluid Mechanics. Academic Press.
Probst, A. & Reuß, S. 2015 Scale-Resolving Simulations of Wall-Bounded Flows with an Unstructured Compressible Flow Solver. pp. 481491. Springer International Publishing.
Roberts, K. V. & Christiansen, J. P. 1972 Topics in computational fluid dynamics. Comput. Phys. Commun. 3 (I 972), 1432.
Rokhsaz, K. & Kliment, L. K. 2002 Experimental investigation of co-rotating vortex filaments in a water tunnel. In 32nd AIAA Fluid Dynamics Conference and Exhibit, vol. 40, pp. 11151122.
Safdari, A. & Kim, K. C. 2015 Aerodynamic and structural evaluation of horizontal archimedes spiral wind turbine. J. Clean Energy Technol. 3 (1), 3438.
Toloui, M., Chamorro, L. P. & Hong, J. 2015 Detection of tip-vortex signatures behind a 2.5 MW wind turbine. J. Wind Engng Ind. Aerodyn. 143, 105112.
Trieling, R. R. & Van Heijst, G. J. F. 1998 Kinematic properties of monopolar vortices in a strain flow. Fluid Dyn. Res. 23, 319341.
Tsai, C.-Y. & Widnall, S. E. 1976 The stability of short waves on a straight vortex filament in a weak externally imposed strain field. J. Fluid Mech. 73, 721733.
Uzun, A. & Hussaini, M. Y. 2010 Simulations of vortex formation around a blunt wing tip. AIAA J. 48 (6), 12211234.
Van Driest, E. R. 1956 On turbulent flow near a wall. J. Aero. Sci. 23 (4), 10071011.
Widnall, S. E. 1975 The structure and dynamics of vortex filaments. Annu. Rev. Fluid Mech. 7, 141165.
Yilmaz, I. & Davidson, L. 2015 Comparison of SGS models in Large-Eddy Simulation for transition to turbulence in Taylor–Green flow. In The 16th International Conference on Fluid Flow Technologies CMFF 2015, Budapest, Hungary.
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