Redchyts Numerical simulation of the viscous incompressible flow around of the group of two bodies
DOI:
https://doi.org/10.34185/1562-9945-3-122-2019-14Keywords:
Математическое моделирование, уравнения Навье-Стокса, обтекание двух цилиндров, обтекание двух сферAbstract
Analysis of recent research and publications. It is known that the presence near the body of another body or a solid wall in a flow can significantly change both the overall flow pattern and the aerodynamic characteristics of bodies in a group. Studies of the interaction of bodies in the flow are conducted for a long time. In [6], the results of a study of changes in the overall flow pattern and the form of interaction of vortices behind tandem-arranged circular cylinders are presented. Further, experimental studies of the flow around a group consisting of two cylinders were aimed at classifying flow patterns depending on the position of the group in the flow, the distance between the cylinders and the Reynolds number [1, 2, 9]. A rather complete identification and classification of the pattern of flow was performed in [6, 7]. Studies on the classification and analysis of flow patterns are still being conducted [1].
Studies on the classification of patterns of the flow around group of spheres are currently performed mainly with the help of numerical simulation. In [3, 4, 5], simulation of the flow around spheres on the side-by-side position was performed. In [8], the classification of typical patterns of the flow around two spheres (Re = 300) with considering of different positions of the spheres relative to the flow direction was made. The authors of [8] describe nine typical patterns of the flow around two spheres in analogy with the patterns of the flow of the two cylinders.
The purpose of the study. The main goal of this work is study the mutual influence of two bodies in a flow of a viscous incompressible fluid and a change in the flow structure with a change in the position of the bodies in the group relative to the incoming flow. Also, the aim of the work was to study the influence of the mutual arrangement of bodies in a group on the non-stationary and time-averaged aerodynamic characteristics of bodies in a group.
Modeling of the flow around groups of cylinders and spheres. Numerical simulation of the flow around the group of cylinders was carried out with the values of the angle θ = 0°, 15°, 30°, 45°, 60°, 75°, 90° and the gap between the cylinders h = 0.2D, 0.4D, 0.6D, 0.8D, 1.0D, 2.0D, 3.0D, 4.0D, 5.0D. The flow parameters was corresponded to the flow around a circular cylinder at Re = 80 and 1.66 105. Eight patterns (regimes) of flow around a group of two cylinders at Re = 80 were found. Regimes 1 and 2 are steady state flows. In regime 1, the drag coefficient is Cx2 <0, and for regime 2, Cx2> 0. Regimes 3-8 are unsteady flows. Regime 8 is an aperiodic change in Cx, Cy. Regimes 3 - 7 are periodic, characterized by different values of the coefficients Cx, Cy, as well as those oscillations of Cx and Cy that occur in phase or antiphase. Simulation of the turbulent flow around a group of two cylinders took place at the tandem and the side-by-side positions at distances between cylinders centers 1.435D and 3.7D.
Similarly, in this work, was performed the parametric study of the flow around two spheres for Reynolds number 750 with the distances between the centers of the spheres along axis Δx = 0.0, 1.0, 2.0, 3.0 and Δy = 0.0, 1.0, 2.0, 3.0. The drag and lift coefficients were obtained, as well as the patterns of flow around two spheres were analyzed.
Conclusions. Depending on the position of the group relative to the flow, the average drag coefficient of the cylinders and spheres in the group can be both smaller and larger than the drag coefficient of a single body with the same parameters of the free flow. With a tandem arrangement, the second cylinder has a stabilizing effect and with a decrease in the gap of less than three diameters, the flow becomes steady state. For all cases with staggered arrangement of spheres the symmetry restoration of vortex structures is observed. In the case of the tandem arrangement of spheres, the separation of loop-shaped vortex structures is realized as in the case of a flow around a single sphere.
References
Anderson, D. Vyichislitelnaya gidromehanika i teploobmen [Tekst]/ D. Anderson, Dzh. Tannehil, R. Pletcher. M.: Mir, 1990. - T.1. − 392 s. − T.2.−336 s.
Bogachev, K.Yu. Osnovyi parallelnogo programmirovaniya [Tekst]/ K.Yu. Bogachev // M: Binom. – 2003. – 342s.
Vovk, I.V. Obtikannia sfery viazkoiu nestyslyvoiu ridynoiu [Tekst]/ I.V.Vovk V.S.Maliuha // Visnyk Kyivskoho natsionalnoho universytetu imeni Tarasa Shevchenka – K., 2013.- №3. -C. 102-105. – (Seriia: «fizyko-matematychni nauky»).
Volkov, K.N. Vyichislitelnaya tehnologii v zadachah mehaniki zhidkosti i gaza [Tekst]/ K.N. Volkov, V.N. Emelyanov – M.: Fizmatlit, 2012. – 468 s.
Guschin, V.A. Chislennoe modelirovanie prostranstvennyih otryivnyih techeniy okolo sferyi [Tekst]/ V.A. Guschin, P.V. Matyushin // Zhurnal vyichislitelnoy matematiki i matematicheskoy fiziki, - 1997 – tom 37, #9 – C.1122-1137.
Loytsyanskiy, L.G. Mehanika zhidkosti i gaza [Tekst]/ L.G. Loytsyanskiy. –M: Drofa, 2003. – 846s.
Chzhen, P. Otryivnyie techeniya [Tekst] / P. Chzhen. – M:Mir, 1972. – 300s.
Shlihting, G. Teoriya pogranichnogo sloya [Tekst]/ G. Shlihting - M.:Nauka, 1974 – 713s.
Biermann D. The interference between struts in various combinations [Text]/ D. Biermann, W. H. Herrnstein Jr. // NACA Technical Reports. – 1933. – 468p.
Blocken, B. CFD simulations of the aerodynamic drag of two drafting cyclists [Text]/ B. Blocken, T. Defraeye, E. Koninckx, J. Carmeliet, P. Hespel // Computers & Fluids – 2013. – №71. – P. 435–445.
Carmo. B. S., On Wake Interference in the Flow around Two Circular Cylinders: Direct Stability Analysis and Flow-Induced Vibrations/ PhD thesis// Department of Aeronautics, Imperial College, London – 2009 – 262p.
Chung, T.J. Computational Fluid Dynamics (Second edition) [Text]/T.J. Chung.—New York City, USA: Cambridge University Press, 2009 – 1058p.
Chorin, A.J. A numerical Method for Solving incompressible Viscous Flow Problems [Text]/ A.J. Chorin// Journal of Computational Physics. – 1997. - №135. – P. 118-125.
Ferziger, J.H. Computational Methods for Fluid Dynamics [Text]/ J.H. Ferziger, M. Periс. – Springer, 2002. – 431p.
Greenshields C.J. OpenFOAM the open source CFD toolbox programmers guide [Text]/ C.J. Greenshields. - OpenFOAM Foundation Ltd. – 2015. –101p.
Greenshields C.J. OpenFOAM the open source CFD toolbox user guide [Text]/ C.J. Greenshields. - OpenFOAM Foundation Ltd. – 2015. –232p.
Hoffmann, K.A. Computational Fluid Dynamics [Text]/ K.A. Hoffmann, S.T. Chiang.-Wichita, Kansas, USA: Engineering Education System, 2000.- 500p.
Johnson, T.A. Flow past a sphere up to a Reynolds number of 300 [Text]// T.A. Johnson, V.C. Patel // J. Fluid Mech., –1999. –Vol. 378. –P.19-70.
Jones, D. A. Simulation of Flow Past a Sphere using the Fluent Code [Text]/ D.A. Jones, D.B. Clarke// DSTO Technical Report DSTO-TR-2232. – 2008. - 35p.
Kim H. J. Investigation of the flow between a pair of circular cylinders in the flopping regime// H. J. Kim, P. A. Durbin - J. Fluid Mech. – 1988. - vol. 196. - P.431-448
Kaneko, S. Flow-Induced Vibrations: Classifications and Lessons from Practical Experiences[Text]/ S. Kaneko. – Elsevier, 2014. – 411p.
Khorrami M. Simulations of Bluff Body Flow Interaction for Noise Source Modeling [Text]/ M. Khorrami, D. Lockard, M. Choudhari, L. Jenkins, C. McGinley, D. Neuhart // AIAA. – 2006. – 3203.
Lam K. Phenomena of vortex shedding and flow interference of three cylinders in different equilateral arrangements [Text]/ K. Lam, W.C . Cheung // J . Fluid Mech. –1988.– vol. 196. – P. 1–26
Maric, T. The OpenFOAM technology primer[Text]/ T. Maric, J. Hopken, K. Mooney // sourceflux UG. – 2014. – 458p.
Menter F.R. Two–equation eddy–viscocity turbulence models for e lications [Text] / F.R. Menter // AIAA Journal. — 1994. — 32, N 8. — P. 1598—1605.
Moukalled F. The finite volume method in computational fluid dynamics, an advanced introduction with OpenFOAM and Matlab [Text]/ F. Moukalled, L. Mangani, M. Darwish // Springer. – 2015. – 798p.
Sakamoto, H. A Study of Vortex Shedding From Spheres in a Uniform Flow [Text]/ H. Sakamoto, H. Hanui// Journal of Fluids Engeneering . – 1990. – Vol. 112. – P. 386-392.
Schouveiler, L. Interactions of the wakes of two spheres placed side by side [Text]/ L. Schouveiler, A. Brydon, T. Leweke, M.C. Thompson// European Journal of Mechanics B/Fluids. – 2014. №23 – P. 137–145.
Stein, H.N. Hydrodynamic interactions between two identical spheres held at fixed side by side against a uniform stream directed perpendicular to the line connecting the spheres' centres [Text]/ H.N. Stein, F.N. van de Vosse, R. Folkersma// International Journal of Multiphase Flow. – 2000, № 26 – P.877-887.
Strouhal V. Ueber eine besondere Art der Tonerregung [Text]/ V. Strouhal // Ann. Phys. – 1878. – 5. – N. 10. – P. 216–251.
Sumer B. M. Hydrodynamics around cylindrical structures [Text]/ B. M. Sumer, J.Fredsoe // Denmark: Technical University of Denmark. – 2006. – 550p
Thomas D.G. 1964 Interaction of vortex streets [Text]/ D. G. Thomas, K.A. Kraus //Journal of Applied Physics. – 1964. – vol. 35 (12). – P. 3458–3459.
Versteeg, H.K. An Introduction to Computational Fluid Dynamics [Text]/ H.K. Versteeg, W. Malalasekera. - England, Harlow: Pearson Education Limited, 2007. – 517p.
Yoon, D.-H. Characterization of flow pattern past two spheres in proximity [Text]/H.-D. Yoon, K.-S. Yang//Physics of Fluids. – 2009, № 21 – P 1-8.
Zdravkovich M. M. Smoke observation of the wake of a group of three cylinders at low Reynolds number [Text]/ M.M. Zdravkovich //J . Fluid Mech. – 1968. – vol. 32. – P. 339–351.
Zdravkovich, M. M. Smoke observations of wakes of tandem cylinders at low Reynolds numbers [Text]/ M.M. Zdravkovich //Aeronautical Journal. – 1972. – vol. 76. – P. 108–114.
Platooning Lets Trucks Get By With a Little Help from Their Friends [elektronnyiy resurs] - MH&L Staff, Feb 24, 2017. – rezhim dostupa: https://www.mhlnews.com/transportation-distribution/platooning-lets-trucks-get-little-help-their-friends - Zagolovok s ekrana.
