Взаимодействие двух противоположно вращающихся сверхзвуковых вихрей




A numerical investigation of two counter-rotating wingtip vortices propagation in a supersonic flow was performed in this paper. A straight coaxial wings with sharp leading and trailing edges at an attack angle of 10 degrees were considered as wingtip vortices generators at Mach number of incoming flow M∞ = 3. Numerical simulations were carried out on the supercomputing system K-60 at the Keldysh Institute of Applied Mathematics RAS using the parallel algorithm for turbulent flow simulation. An approach based on the URANS method with using the SA turbulence model was applied. Numerical data were obtained in the domain of 10 wing chords downstream from a wings axis. A numerical data on the flow parameters in the vortex wake was obtained, in particular, data on the wingtip vortices axis and in the cross-sections. The data was investigated depending on a distance from the wings - vortex generators.

supersonic flow, turbulent flow, counter-rotating vortices, wingtip vortex

Interaction of two counter-rotating supersonic vortices

В работе представлено численное исследование двух противоположно вращающихся сверхзвуковых вихрей. Два соосных прямых полукрыла с острыми передней и задней кромками рассматривались в качестве вихре-генераторов при числе Маха набегающего потока M∞ = 3. Численные расчеты были проведены на суперкомпьютерной системе
К-60 в Институте Прикладной Математики им. М.В. Келдыша РАН с использованием параллельного алгоритма для моделирования турбулентных течений. Был применен подход, основанный на методе URANS с моделью турбулентности SA. Численные результаты были получены в области равной 10 хордам крыльев от оси крыльев вниз по потоку. В вихревом следе были численно получены параметры течения, в частности, данные на осях концевых вихрей и в поперечных сечениях. Был проведен анализ данных в зависимости от расстояния от крыльев-генераторов.

сверхзвуковые течения, турбулентные течения, противоположно вращающиеся вихри, концевой вихрь


1. Borovoy V. Y., Skuratov A. S., Stolyarov E. P. 2001 Pressure fluctuations in short-duration and in long-duration supersonic wind tunnels Uchenye zapiski TsAGI 32 3 4 pp 3-16 (in Russian).
2. Zinoviev V. N., Lebiga V. A. 2010 Investigation of acoustic fluctuations in a flow with permeable boundaries using hot-wire anemometry TsAGI Science J. 41 2 pp 133-145.
3. Leweke T., le Dizès S., Williamson C. H. K. 2016 Dynamics and instabilities of vortex pairs Annu. Rev. Fluid Mech. 48 pp 507-541.
4. Lucca-Negro O., O’Doherty T. 2001 Vortex breakdown: a review Progr. In Energy and Combustion Sc. 27 4 pp 431-481.
5. Borisov V. E., Davydov A. A., Konstantinovskaya T. V., Lutsky A. E., Shevchenko A. M., Shmakov A. S. 2018 Numerical and experimental investigation of a supersonic vortex wake at a wide distance from the wing AIP Conf. Proc. (19 Int. Conf. on the Methods of Aerophysical Research (ICMAR 2018)) 2027 030120.
6. Borisov V. E., Davydov A. A., Konstantinovskaya T. V., Lutsky A. E., Shevchenko A. M., Shmakov A. S. 2019 Influence of acoustic type waves on the vortex wake behind a wing in the supersonic flow J. of Physics: Conf. Series, IOP Publishing Ltd 1250 012003 DOI: 10.1088/1742-6596/1250/1/012003.
7. Borisov V. E., Davydov A. A., Konstantinovskaya T. V., Lutsky A. E., Shevchenko A. M., Shmakov A. S. 2019 Supersonic vortex wake at a wide distance from the wing and influence of acoustic type waves Proc. of 8th Europeen Conf. for Aeronautics and Space Sciences (EUCASS) DOI: 10.13009/EUCASS2019-869.
8. Borisov V. E., Davydov A. A., Konstantinovskaya T. V., Lutsky A. E. 2019 Influence of acoustic type disturbances on the tip vortex behind a wing in the supersonic flow Proc. of XII All-Russia Congress on fundamental problems of theoretical and applied mechanics 2 pp 369-372
ISBN 978-5-7477-4952-8 DOI: 10.22226/2410-3535-2019-congress-v2.
9. Allmaras S. R., Johnson F. T., Spalart P. R. 2012 Modifications and Clarifications for the Implementation of the Spalart-Allmaras Turbulence Model 7th Int. Conf. on CFD (ICCFD7), Big Island, Hawaii (9-13 July 2012).
10. Edwards J. R., Chandra S., 1996 Comparison of eddy viscosity-transport turbulence models for three-dimensional, shock-separated flowfields AIAA J. 34 4 pp 756-763.
11. Borisov V. E., Lutsky A. E. 2016 Simulation of transition between regular and Mach shock waves reflections by an implicit scheme based on the LU-SGS and BiCGStab methods KIAM Preprint № 68 (2016) DOI:10.20948/prepr-2016-68.
12. www.kiam.ru
13. Maslov A. A., Kudryavtsev A. N., Mironov S. G., Poplavskaya T. V., Tsyryul'nikov I. S. 2007 Numerical simulation of receptivity of a hypersonic boundary layer to acoustic disturbances J. of Applied Mechanics and Technical Physics 48 3 pp 368-374.
14. Landau L. D., Lifshitz E. M. 1987 Course of Theoretical Physics, Fluid Mechanics vol 6 (2nd ed.) (Butterworth–Heinemann) ISBN 978-0-08-033933-7.
15. Marks R. J. II 2006 The Joy of Fourier: Analysis, Sampling Theory, Systems, Multidimentions, Stochastic Processes, Random Variables, Signal Recovery, POCS, Time Scales, & Applications (Baylor University).
16. Seregin N. I. 2006 Special Aspects of the Use of Discrete Fourier Transform in Spectral Analysis (Ekaterinburg: Ural State Technical University manual) (in Russian).
17. Lyons R. G. 2004 Understanding Digital Signal Processing (Prentice Hall) ISBN 0131089897.
18. Lamb H. 1932 Hydrodynamics Cambridge UK (Cambridge Univ. Press.) 6th ed.
19. Forster K. J., Barber T. J., Diasinos S., Doig G. 2017 Interaction of a counter-rotating vortex pair at multiple offsets Experimental Thermal and Fluid Science J. 86 pp 63-74.