Yıl 2018, Cilt 22, Sayı 5, Sayfalar 1234 - 1252 2018-10-01

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

Erman Aslan [1] , İlker İnan [2] , İlyas Kandemir [3] , Hasan Rıza Güven [4]

177 194

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.


  • 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.
Birincil Dil en
Konular Makine Mühendisliği, Temel Bilimler (Genel)
Yayımlanma Tarihi October 2018
Dergi Bölümü Araştırma Makalesi
Yazarlar

Yazar: Erman Aslan
Kurum: İSTANBUL ÜNİVERSİTESİ
Ülke: Turkey


Yazar: İlker İnan
Kurum: İSTANBUL KAVRAM MESLEK YÜKSEKOKULU
Ülke: Turkey


Yazar: İlyas Kandemir
Kurum: GEBZE TEKNİK ÜNİVERSİTESİ
Ülke: Turkey


Yazar: Hasan Rıza Güven
Kurum: İSTANBUL ÜNİVERSİTESİ
Ülke: Turkey


Bibtex @araştırma makalesi { saufenbilder334449, journal = {Sakarya University Journal of Science}, issn = {1301-4048}, eissn = {2147-835X}, address = {Sakarya Üniversitesi}, year = {2018}, volume = {22}, pages = {1234 - 1252}, doi = {10.16984/saufenbilder.334449}, title = {Numerical Analysis of Flow Around Bluff Bodies with 4th and 2nd order compact formulations}, key = {cite}, author = {Kandemir, İlyas and İnan, İlker and Güven, Hasan Rıza and Aslan, Erman} }
APA Aslan, E , İnan, İ , Kandemir, İ , Güven, H . (2018). Numerical Analysis of Flow Around Bluff Bodies with 4th and 2nd order compact formulations. Sakarya University Journal of Science, 22 (5), 1234-1252. DOI: 10.16984/saufenbilder.334449
MLA Aslan, E , İnan, İ , Kandemir, İ , Güven, H . "Numerical Analysis of Flow Around Bluff Bodies with 4th and 2nd order compact formulations". Sakarya University Journal of Science 22 (2018): 1234-1252 <http://www.saujs.sakarya.edu.tr/issue/31265/334449>
Chicago Aslan, E , İnan, İ , Kandemir, İ , Güven, H . "Numerical Analysis of Flow Around Bluff Bodies with 4th and 2nd order compact formulations". Sakarya University Journal of Science 22 (2018): 1234-1252
RIS TY - JOUR T1 - Numerical Analysis of Flow Around Bluff Bodies with 4th and 2nd order compact formulations AU - Erman Aslan , İlker İnan , İlyas Kandemir , Hasan Rıza Güven Y1 - 2018 PY - 2018 N1 - doi: 10.16984/saufenbilder.334449 DO - 10.16984/saufenbilder.334449 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 1234 EP - 1252 VL - 22 IS - 5 SN - 1301-4048-2147-835X M3 - doi: 10.16984/saufenbilder.334449 UR - http://dx.doi.org/10.16984/saufenbilder.334449 Y2 - 2018 ER -
EndNote %0 Sakarya University Journal of Science Numerical Analysis of Flow Around Bluff Bodies with 4th and 2nd order compact formulations %A Erman Aslan , İlker İnan , İlyas Kandemir , Hasan Rıza Güven %T Numerical Analysis of Flow Around Bluff Bodies with 4th and 2nd order compact formulations %D 2018 %J Sakarya University Journal of Science %P 1301-4048-2147-835X %V 22 %N 5 %R doi: 10.16984/saufenbilder.334449 %U 10.16984/saufenbilder.334449
ISNAD Aslan, Erman , İnan, İlker , Kandemir, İlyas , Güven, Hasan Rıza . "Numerical Analysis of Flow Around Bluff Bodies with 4th and 2nd order compact formulations". Sakarya University Journal of Science 22 / 5 (Ekim 2018): 1234-1252. http://dx.doi.org/10.16984/saufenbilder.334449