On Problems in 2D Viscous Flows Simulation at Higher Values of the Reynolds Numbers by Vortex Methods Using the VM2D Code
https://doi.org/10.15514/ISPRAS-2023-35(2)-14
Abstract
Vortex methods of computational fluid dynamics are an efficient tool in engineering practice for estimating hydrodynamic loads acting on bodies placed in a flow. Their usage allows for solving of coupled hydroelastic problems with relatively small computational cost. In many applications, the cross flow around structural elements with large elongation is considered, that allows one to use the flat cross-sections method providing the acceptable accuracy. Thus, flat flows simulation around airfoils is required. Modern modifications of vortex particle methods make it possible to simulate flows of a viscous incompressible medium. Based on the method of viscous vortex domains in 2017-2022 the VM2D code have been developed in Bauman University and Ivannikov Institute for System Programming. This code allows for flow simulating around airfoils with acceptable accuracy at low Reynolds numbers, while for higher Reynolds numbers, correct results are observed only for airfoils with sharp edges and corner points, and only in regimes where the most intensive flow separation takes place at these points. The reason for the error in the results for other regimes is seen in incorrect modeling of the flow separation on smooth airfoil surface line at high Reynolds numbers, which, in turn, is a consequence of incorrect modeling of vorticity evolution in the vicinity of separation points (zones). Some results of flow simulations around different airfoils at different values of the Reynolds number are presented and a hypothesis explaining the reason for the discrepancy between numerical results and experimental data is proposed. It is shown that the kinetic energy spectrum of turbulence corresponds to “two-dimensional turbulence”.
About the Authors
Irina Aleksandrovna KOROBOVA
Bauman Moscow State Technical University
Russian Federation
Russian Federation
2nd year post-graduate student and an assistant of the Applied Mathematics Department
Evgeniya Pavlovna RYATINA
Bauman Moscow State Technical University
Russian Federation
Russian Federation
3rd year PhD student of the Applied Mathematics Departmen
Anna Aleksandrovna KHOROSHEVA
Bauman Moscow State Technical University
Russian Federation
Russian Federation
4th year student of the Department of Mathematical Modeling
References
1. . Cottet G.-H., Koumoutsakos P.D. Vortex methods: theory and practice. Cambridge: Cambridge University Press, 2000. 328 p.
2. . Андронов П.Р., Гувернюк С.В., Дынникова Г.Я. Вихревые методы расчета нестационарных гидродинамических нагрузок. М.: Изд-во МГУ, 2006. 184 с. / Andronov, P.R., Guvernyuk, S.V., Dynnikova, G.Y. Vortex methods for non-stationary hydrodynamic loads estimation. Moscow, Moscow State University, 2006. 184 p. (in Russian).
3. . Mimeau C., Mortazavi I. A review of vortex methods and their applications: from creation to recent advances // Fluids. 2021. V. 6. Art. 68. DOI: 10.3390/fluids6020068
4. . Kempka S.N., Glass M.W., Peery J.S., Strickland J.H., Ingber M.S. Accuracy considerations for implementing velocity boundary conditions in vorticity formulations // SANDIA report. SAND96-0583, UC-700, 1996. 52 p. DOI: 10.2172/242701
5. . Дынникова Г.Я. Аналог интегралов Бернулли и Коши — Лагранжа для нестационарного вихревого течения идеальной несжимаемой жидкости // Изв. РАН. Механика жидкости и газа. 2000. № 1. С. 31– 41. / Dynnikova, G.Y. An analog of the Bernoulli and Cauchy—Lagrange integrals for a time dependent vortex flow of an ideal incompressible fluid // Fluid Dynamic. 2000. V. 35. No. 1. Pp. 31– 41. DOI: 10.1007/BF02698782
6. . Девнин С.И. Гидроупругость конструкций при отрывном обтекании. Л.: Судостроение, 1975. / Devnin S.I. Hydroelasticity of Structures under Separated Flow. Leningrad: Sudostroenie (in Russian.)
7. . Marchevsky I., Sokol K., Ryatina E., Izmailova Y. The VM2D open source code for two-dimensional incompressible flow simulation by using fully Lagrangian vortex particle methods // Axioms. 2023. V. 12. Art. 248. DOI: 10.3390/axioms12030248
8. . Дынникова Г.Я. Лагранжев подход к решению нестационарных уравнений Навье – Стокса // Доклады Академии наук. 2004. Т. 399, № 1. С. 42–46. / Dynnikova G.Ya. The Lagrangian approach to solving the time-dependent Navier-Stokes equations // Doklady Physics. 2004. V. 49. Pp. 648–652.
9. . Марчевский И.К., Сокол К.С., Измайлова Ю.А. Т-схемы для математического моделирования генерации завихренности на гладких профилях в вихревых методах // Вестник МГТУ им. Н.Э. Баумана. Естественные науки. 2022. № 6. C. 33–59. DOI: 10.18698/1812-3368-2022-6-33-59 59 / Marchevskii I.K., Sokol K.S., Izmailova Yu.A. T-schemes for mathematical modelling of vorticity generation on smooths airfoils in vortex particle methods // Herald of the Bauman Moscow State Technical University, Series Natural Sciences. 2022. No. 6. Pp. 33–59 (in Russian). DOI: 10.18698/1812-3368-2022-6-33-59
10. . Kuzmina K., Marchevsky I., Soldatova I., Izmailova Y. On the scope of Lagrangian vortex methods for two-dimensional flow simulations and the POD technique application for data storing and analyzing // Entropy. 2021. V. 23. Art. 118. DOI: 10.3390/e23010118
11. . Belotserkovsky S.M., Lifanov I.K. Method of Discrete Vortices. CRC Press, 1992. 464 p.
12. . Лифанов И.К. Метод сингулярных интегральных уравнений и численный эксперимент (в математической физике, аэродинамике, теории упругости и дифракции волн). М.: ТОО «Янус», 1995. 520 с. / Lifanov, I.K. Singular Integral Equations and Discrete Vortices; VSP: Utrecht, The Netherlands, 1996; 475p.
13. . Katz J., Plotkin A. Low-speed aerodynamics. From wing theory to panel methods. Singapore: McGraw-Hill Book Co., 1991. 632 p.
14. . McBain G.D. Theory of Lift: Introductory Computational Aerodynamics in MATLAB/Octave. New-York: Wiley, 2012. 342 p.
15. . Chorin A.J. Numerical study of slightly viscous flow // Journal of Fluid Mechanics. 1973. V. 57, No. 4. P. 785–796. DOI: 10.1017/S0022112073002016
16. . Degond P., Mas-Gallic S. The weighted particle method for convection-diffusion equations. I. The case of an isotropic viscosity // Mathematics of Computation. 1989. V. 53, No. 188. P. 485 –507. DOI: 10.2307/2008716
17. . Kuwahara K., Takami H. Numerical studies of two-dimensional vortex motion by a system of point vortices // Journal of the Physical Society of Japan. 1973. V. 34, No. 1. P. 247–253. DOI: 10.1143/JPSJ.34.247
18. . Rossi L.F. Resurrecting core spreading vortex methods: A new scheme that is both deterministic and convergent // SIAM Journal on Scientific Computing. 1996. V. 17, No. 2. P. 370–397. 10.1137/S1064827593254397
19. . Bar-Lev M., Yang H.T. Initial flow over an impulsively started circular cylinder // Journal of Fluid Mechanics. 1975. V. 72. P. 625–647. DOI: 10.1017/S0022112075003199
20. . Collins W.M., Dennis S.C.R. The initial flow past an impulsively started circular cylinder // Quarterly Journal of Mechanics and Applied Mathematics. 1973. V. 26. P. 53–75. DOI: 10.1093/qjmam/26.1.53
21. . Koumoutsakos P., Leonard A. High-resolution simulations of the flow around an impulsively started cylinder using vortex methods // Journal of Fluid Mechanics. 1995. V. 296. P. 1–38. DOI: 10.1017/S0022112095002059
22. . Pepin F.M. Simulation of the flow past an impulsively started cylinder using a discrete vortex method. Ph.D. Thesis, California Institute of Technology, Pasadena, CA, USA, 1990.
23. . Shankar S. A new mesh-free vortex method. Ph.D. Thesis, FAMU-FSU College of Engineering, Tallahassee, FL, USA, 1996.
24. . Anderson C.B., Reider M.B. A high order explicit method for the computation of flow about a circular cylinder // Journal of Computational Physics. 1996, V. 125. P. 207–224. DOI: 10.1006/jcph.1996.0089
25. . Ploumhans P., Winckelmans G.S. Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry // Journal of Computational Physics. 2000. V. 165. P. 354–406. DOI: 10.1006/jcph.2000.6614
26. . Lakkis I., Ghoniem A. A high resolution spatially adaptive vortex method for separating flows. Part I: Two-dimensional domains // Journal of Computational Physics. 2009. V. 228. P. 491–515. DOI: 10.1016/j.jcp.2008.09.025
27. . Liu Z., Kopp G.A. High-resolution vortex particle simulations of flows around rectangular cylinders // Computers & Fluids. 2011. V. 40. P. 2–11. DOI: j.compfluid.2010.07.011
28. . Zahm A.F. Flow and drag formulas for simple quadrics // NACA Technical Report No. 253. 1927. 23 p.
29. . Дынникова Г.Я. Использование быстрого метода решения задачи N тел при вихревом моделировании течений // Журнал вычислительной математики и математической физики. 2009. Т. 49, № 8. C. 1458–1465. / Dynnikova G.Y. Fast technique for solving the N-body problem in flow simulation by vortex methods. // Computational Mathematics and Mathematical Physics. 2009. V. 49. Pp. 1389–1396. DOI: 10.1134/S0965542509080090
30. . Pereira L.A.A., Hirata H., Silveira Neto A. Vortex method with turbulence sub-grid scale modelling // Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2003, V. 25, No. 2. DOI: 10.1590/S1678-58782003000200005
31. . Yokota R., Shinnosuke O. Vortex methods for the simulation of turbulent flows: review // Journal of Fluid Science and Technology. 2011. V. 6, No. 1. P. 14–29. DOI: 10.1299/jfst.6.14
32. . Branlard E., Papadakis G., Gaunaa M., Winckelmans G., Larsen T. Aeroelastic large eddy simulations using vortex methods: unfrozen turbulent and sheared inflow // Journal of Physics: Conference Series. 2015, V. 625. Art. 012019. DOI: 10.1088/1742-6596/625/1/012019
33. . Alvarez E. J.; Ning A. Reviving the vortex particle method: A stable formulation for meshless large eddy simulation. 2022. arXiv preprint arXiv:2206.03658.
Review
For citations:
KOROBOVA I.A., RYATINA E.P., KHOROSHEVA A.A. On Problems in 2D Viscous Flows Simulation at Higher Values of the Reynolds Numbers by Vortex Methods Using the VM2D Code. Proceedings of the Institute for System Programming of the RAS (Proceedings of ISP RAS). 2023;35(2):201-214. (In Russ.) https://doi.org/10.15514/ISPRAS-2023-35(2)-14
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