Numerical Analysis of Flow Around Bluff Bodies with 4th and 2nd order compact formulations

Yıl 2018, Cilt: 22 Sayı: 5, 1234 - 1252, 01.10.2018

Erman Aslan , İlker İnan İlyas Kandemir , Hasan Rıza Güven

https://doi.org/10.16984/saufenbilder.334449

Öz

In the present study, fourth-order compact
formulation has been improved for Navier-Stokes (N-S) equations, which is
expressed for two-dimensional, steady, incompressible flow problems. N-S
equation system has been expressed with Stream Function-Vorticity Approach
using Finite Difference Method (FDM) from the numerical methods. In order to test the functionality and
applicability of the improved numerical formulation, a sample for submerged
bluff bodies, flow problem around cylinder with square cross-section was chosen
as a benchmark problem. As a result of applying improved numerical formulation
with Gauss-Seidel Relaxation Method was used for this benchmark problem. The benchmark problem was also solved
with second-order accuracy and obtained numerical results were compared with
fourth-order accuracy numerical results. With the same Reynolds Number and the
same free-stream velocity values, fourth-order numerical results are more
convergent than second-order numerical results. Furthermore, in the flow field
for considered benchmark problem, separation bubble length that consisted in
the wake region is increased proportionally depending on the alteration of the
Reynolds Number values.

Anahtar Kelimeler

Akım Fonsiyonu-Vortisite Formülasyonu, Küt Cisim Etrafındaki Akış, Daimi Akış, Sıkıştırılamaz Akış

Kaynakça

• Referans1 S. C. Chapra and R. P. Canale “Numerical Methods for Engineers”, 6th edition, McGraw-Hill, Boston, 2010. Referans2 Y. Cengel and J. M. Cimbala, “Fluid Mechanics Fundamentals and Applications (In SI Units)”, McGraw-Hill, Boston, 2006. Referans3 I. Karagoz, “Sayısal Analiz ve Mühendislik Uygulamaları”, 4. Basım, Nobel Akademik Yayıncılık, 2011. Referans4 T. Breuer, J. Bernsdorf, F. Durst, “Accurate computations of the laminar flow past a square cylinder based on two different methods: Lattice-Boltzmann and Finite-Volume”, Int. J. Heat Fluid Flow, vol. 21, no. 2, pp. 186-196, 2000. Referans5 M. Ozgoren, “Flow structure in downstream of square and circular cylinders”, Flow Meas. Inst., vol. 17, no. 4, pp. 225-235, 2006. Referans6 C. A. J. Fletcher, “Computational Techniques for Fluid Dynamics I”, Second Edition, Springer-Verlag, Berlin, 1991. Referans7 C. H. K. Williamson, “Vortex dynamics in the cylinder wake”, Ann. Review Fluid Mech., vol.28, pp. 477-539, 1996. Referans8 M. M. Zdravkovich, “Flow around Circular Cylinders, vol. 1: Fundamentals”, Oxford University Press, New York, 1997. Referans9 A. C. Benim, E. Pasqualotto, S. H. Suh, “Modelling Turbulent Flow Past a Circular Cylinder by RANS, URANS, LES and DES”, Prog. Compt. Fluid Dynamics, vol. 8, pp. 299-307, 2008. Referans10 R. W. Davis, E.F. Moore, “A numerical study of vortex shedding from rectangles”, J. Fluid Mech., vol. 116, pp. 475-506, 1982. Referans11 A. Okajima, “Strouhal numbers of rectangular cylinders”, J. Fluid Mech., vol. 123, pp. 379-398, 1982. Referans12 A. Okajima, “Numerical simulation of flow around rectangular cylinders”, J. Wind Eng. Indust. Aerodynamics, vol. 33, no. 1-2, pp. 171-180, 1990. Referans13 R. W. Davis, E. F. Moore, L. P. Purtell, “A numerical-experimental study of confined flow around rectangular cylinders”, Phys. Fluids, vol. 27, no. 1, pp. 46-59, 1984. Referans14 R. Franke, W. Rodi, B. Schönung, “Numerical calculation of laminar vortex shedding past cylinders”, J. Wind Eng. Indust. Aerodynamics, vol. 35, pp. 237-257, 1990. Referans15 K. M. Klekar, S.V. Patankar, “Numerical prediction of vortex shedding behind square cylinders”, Int. J. Numer. Methods Fluids, vol. 14, no. 3, pp. 327-341, 1992. Referans16 A. Mukhopadhyay, G. Biswas, T. Sundararajan, “Numerical investigation of confined wakes behind a square cylinder in a channel”, Int. J. Numer. Methods Fluids, vol. 14, no. 12, pp. 1473-1484, 1992. Referans17 A. Sohankar, C. Norberg, L. Davidson, “Numerical Simulation of Flow Past a Square Cylinder”, in Proc. 3rd ASME/JSME, San Francisco, USA, 1999, pp. 1-6. Referans18 M. Raisee, A. Jafari, H. Babaei, H. Iacovides, “Two-dimensional prediction of time dependent, turbulent flow around a square cylinder confined in a channel”, Int. J. Numer. Methods Fluids, vol. 62, no. 11, pp. 1232-1263, 2010. Referans19 S. Sen, S. Mittal, G. Biswas, “Flow past a square cylinder at low Reynolds numbers”, Int. J. Numer. Methods Fluids, vol. 67, no. 9, pp. 1160-1174, 2010. Referans20 T. Bano, N. A. Sheikh, S. Mnazoor, S. Khushnood, “Numerical Simulation of Flow past a Square Cylinder” In Proc. 9th IBCAST, Islamabad, Pakistan, 2012. Referans21 G. Biswas, H. Laschefski, N. K. Mitra and M. Fiebig, “Numerical Investigation of mixed convection heat transfer in a horizantal channel with a built-in square cylinder”, Numer. Heat Trans. Part A, vol. 18, pp. 173-188, 1990. Referans22 D. Chakrabarty, R. Bharma, “Experimental study of fluid flow and heat transfer form a square prism approaching the wall of a wind tunnel”, J. Eng. Physc. Thermophysics, vol. 82, pp. 697-705, 2009. Referans23 Y. Yoshida, T. Nomura, “A transient solution method for the finite element method for the finite element incompressible Navier-Stokes equations”, Int. J. Numer. Methods Fluids, vol. 15, no. 10, pp. 873-890, 1985. Referans24 X. Li, L. Gao, C. Zhang, and X. Shao, “A review on integrated process planning and scheduling,” International Journal of, vol. 5, no. 2, pp. 161–180, 2010. Referans25 O. Aydın, B. Cuhadaroglu, “Numerical Investigation of Viscous Flow around a Square Obstacle”, Turkish J. Eng. Environmental Sci., vol. 21, no. 4, pp. 209-214, 1997. Referans26 E. Erturk, T. Corke, C. Gökçöl, “Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers”, Int. J. Numer. Methods Fluids, vol. 48, no. 7, pp. 747-774, 2005. Referans27 U. Ghia, and R. T. Davis, “Navier Stokes Solutions for Flow Past a Class of Two-Dimensional Semi-Infinite Bodies”, AIAA Journal, vol. 12, pp. 1659-1665, 1974. Referans28 A. C. Benim, E. Aslan, I. Taymaz, “Lattice Boltzmann Method for Laminar Forced Convection in a Channel with a Triangular Prism”, Heat Trans. Res., vol. 42, no. 4, pp. 359-377, 2011. Referans29 A. C. Benim, H. Chattopadhyay, A. Nahavandi, “Computational Analysis of Turbulent Forced Convection in a Channel with a Triangular Prism”, Int. J. Thermal Sci., vol. 50, pp. 1973-1983, 2011. Referans30 I. Inan, “Kare Silindir Etrafından Akan Daimî Sıkıştırılamaz İki-Boyutlu Akışın 4. Hata Mertebesinden Yoğun Formülasyon ile Nümerik Modellenmesi”, MSc. Thesis in Gebze Instute of Technology, 2014. Referans31 E. Erturk, C. Gökçöl, “Fourth-order compact formulation of Navier-Stokes equations and driven cavity flow at high Reynolds numbers”, Int. J. Numer. Methods Fluids, vol. 50, no. 4, pp. 421-436, 2006. Referans32 E. Erturk, “Numerical performance of compact fourth-order formulation of the Navier-Stokes equations”, Commun. Numer. Methods Eng., vol. 24, no. 12, pp. 2003-2019, 2008. Referans33 E. Erturk, “CFD Lecture Notes”, Gebze Instute of Technology, 2009. Referans34 C. Gökçöl, “Kararlı Sıkıştırılamayan Navier-Stokes Denklemlerinin Yüksek Dereceli Sıkı Formülasyon İle Çözümü İçin Bir Yöntem Geliştirme”, MSc. Thesis in Gebze Instute of Technology, 2006. Referans35 MATLAB and Statistics Toolbox Release2010a, The MathWorks Inc., Natick, Massachysetts, United States, 2010. Referans36 Ansys-Fluent, Ansys-Fluent User’s Guide, Ansys Inc., Canonsburg, PA, 2009.