BİR SİLİNDİRDEN ZORLANMIŞ TÜRBÜLANSLI TAŞINIM ISI GEÇİŞİNDE RANS VE LES MODELLERİNİN KIYASLAMALI BİR DEĞERLENDİRMESİ

Öz

Geçici rejimde çapraz hava (Pr=0.7) akışına maruz izotermal yatay bir silindirin 2B ve 3B türbülanslı akış ve ısı geçiş karakteristikleri halihazırda yaygın olarak kullanılan türbülans modellerinin sayısal performansı bağlamında araştırılmıştır. 2B simülasyonlar için Standard k− (SKE), Re-Normalizasyon Grup k− (RNG), Realizable k− (RKE), Standard k- (SKW), Shear Stress Transport (SST) k- and Reynolds Stress Modeli (RSM) türbülans modelleri iki-tabaka duvar (veya Gelişmiş Duvar Uygulaması) modeli ile birlikte kullanılmıştır. 3B simülasyonlar için, RNG, SKW, SST, RSM ve dinamik gerilme modeli içeren ve içermeyen Smagorinsky-Lilly algoritması kullanan LES modeli kullanılmıştır. Bu çalışmada, türbülans modeleri için performans kriteri 2B ve 3B akış ile ısı geçişi sayısal tahminlerin doğruluğuna (CD, CL, CL,rms, St ve Nu sayıları) dayanmaktadır. FLUENT 6.3.26® CFD yazılımının kullanıldığı sayısal simülasyonlar, Reynolds sayılarının 1000, 3900 ve 10000 değerleri için gerçekleştirilmiştir. Kaldırma/sürünme katsayıları ve Strouhal sayıları gibi akış karakteristikleri hesaplanarak mevcut deneysel ve sayısal verilerle karşılaştırmalı olarak kıyaslanmıştır. 2B RANS modelleri, akışın doğası gereği üç boyutlu olması nedeniyle akış karakteristiklerinin tahmininde tutarlı değildir, ancak RANS modellerine nazaran RSM biraz daha iyi bir performans göstermiştir. 2B RANS modellerinde Re=1000 ve 3900 için ortalama Nusselt sayısı makul bir doğrulukla tahmin edilmiştir. RNG modeli tutarlı bir şekilde ortalama Nusselt sayısını yüksek tahmin etmekte iken, diğer 3B-RANS modelleri mevcut Nusselt korrelasyonlarının tahmin aralığında sayısal sonuçlar vermiştir. LES modelinin, bu çalışmada göz önüne alınan akış koşullarında, makul akış ve ısı geçişi karakteristikleri ile sonuçlanmasına rağmen LES'in performansı giriş koşullarına da bağlı olduğu gösterilmiştir.

Anahtar Kelimeler

• LES simulasyonu
• türbülans modelleri
• iki-boyutlu
• üç-boyutlu
• RANS model

A COMPARATIVE ASSESSMENT OF TURBULENT FORCED CONVECTION HEAT TRANSFER FROM A SINGLE CYLINDER USING RANS AND LES MODELS

Öz

Unsteady 2D and 3D turbulent flow and heat transfer characteristics of a single isothermal horizontal cylinder in crossflow of air (Pr=0.7) is investigated to assess the numerical performance of the common turbulence models currently in use. For 2D simulations, Standard k− (SKE), Re-Normalization Group k− (RNG), Realizable k− (RKE), Standard k- (SKW), Shear Stress Transport (SST) k- and Reynolds Stress Model (RSM) turbulence models are used in conjunction with the two-layer wall (or Enhanced Wall Treatment, EWT) model. For 3D simulations, RNG, SKW, SST, RSM and Large Eddy Simulation (LES) using Smagorinsky-Lilly with and without dynamic stress models are used. In this study, the performance criterion of the turbulence models is based on the accuracy of the computational predictions of 2D and 3D flow as well as heat transfer (CD, CL, CL,rms, St and Nu numbers) characteristics. Numerical simulations are carried out for Reynolds numbers of 1000, 3900 and 10000 using FLUENT 6.3.26® CFD software. The flow characteristics, such as the lift/drag coefficients and Strouhal numbers, are computed and tabulated comparatively with available experimental and numerical data. The 2D RANS models are not consistent in predicting the flow characteristics due to three-dimensionality nature of the fluid flow, but RSM performs slightly better than RANS models. The mean Nusselt number for Re=1000 and 3900 is predicted with reasonable accuracy with 2D-RANS models. While the RNG model consistently over estimates the mean Nusselt number, other 3D-RANS models yield values within the ranges predicted by the Nusselt number correlations. It is shown that although LES models yields reasonable flow and heat transfer characteristics for flow conditions considered here, the performance of LES is also dependent on the inlet condition.

Anahtar Kelimeler

• Large eddy simulation
• turbulence models
• two-dimensional
• three-dimensional
• RANS models

Kaynakça

1. Achenbach E., 1968, Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to Re=5×106, Journal of Fluid Mechanics, 34, 625-639.
2. Ahmed G. R. and Yonanovich M. M., 1997, Experimental Study of Forced Convection From Isothermal Circular and Square Cylinders and Toroid, Journal of Heat Transfer, 119, 70-79.
3. Beaudan P. and Moin P., 1994, Numerical experiments on the flow past a circular cylinder at sub–critical Reynolds number, Technical Report TF-62, Stanford University.
4. Benim A. C., Pasqualotto E. and Suh S. G., 2008, Modelling turbulent flow past a circular cylinder by RANS, URANS, LES and DES, Progress in Computational Fluid Dynamics, 8, 299-307.
5. Breuer M., 1998, Large Eddy Simulations of the subcritical flow past a circular cylinder: numerical and modeling aspects, International Journal of Numerical Methods in Fluids, 28, 1281-1302.
6. Bose S. T., Wang B. C. and Saeedi M. D., 2012, Prediction of unsteady heat transfer from a cylinder in crossflow, Center for Turbulent Research Proceedings, Summer Prog, 107-116. Boulos M. I. and Pei D. C., 1973, Heat and mass transfer from cylinders to a turbulent fluid stream—a critical review, Canadian Journal of Chemical Engineering, 51, 673-679.
7. Cardell G. S., 1993, Flow past a circular cylinder with a permeable splitter plate, PhD Thesis, Graduate Aeronautical Lab., California Inst. of Tech, USA.
8. Celik I. and Shaffer F. D., 1995, Long time averaged solutions of turbulent flow past a circular cylinder, Journal of Wind Engineering and Industrial Aerodynamics, 56, 185-212. Churchill S. W. and Bernstein N. M., 1977, A Correlating Equation for Forced Convection From Gases and Liquids to a Circular Cylinder in Crossflow, Journal of Heat Transfer, 99, 300-306.

9. Dong S., Karniadakis G. E., Ekmekci A. and Rockwell D., 2006, A combined direct numerical simulation–particle image velocimetry study of the turbulent near wake, Journal of Fluid Mechanics, 569, 185-207.
10. Douglas W. J. M. and Churchill S. W., 1956, Recorrelation of Data for Convective Heat Transfer Between Gases and Single Cylinders With Large Temperature Differences, Chemical Engineering Progress Symposium Series, 52, 23-28.
11. Fand R. M., 1965, Heat transfer by forced convection from a cylinder to water in crossflow, International Journal of Heat Mass Transfer, 8, 995-1010. Fluent Inc., 2006, Fluent 6.3 User’s Guide, Lebanon, USA.
12. Franke J. and Frank W., 2002, Large eddy simulation of the flow past a circular cylinder at ReD=3900, Journal of Wind Engineering and Industrial Aerodynamics, 90, 1191-1206.
13. Fröhlich J., Rodi W., Kessler Ph., Parpais S., Bertoglio J. P. and Laurence, D, 1998, Large Eddy Simulation of Flow around Circular Cylinders on Structured and Unstructured Grids Numerical Flow Simulation I, Notes on Numerical Fluid Mechanics, 66, 319-338.
14. Gerrard J. H., 1961, An experimental investigation of the oscillating lift and drag of a circular cylinder shedding turbulent vortices, Journal of Fluid Mechanics, 11, 244-256.
15. Gopalkrishnan R., 1993, Vortex-induced Forces on Oscillating Bluff Cylinders, PhD Thesis, MIT, USA.
16. Henderson R. D. and Karniadakis G. E., 1995, Unstructured spectral element methods for simulation of turbulent flows, Journal of Computational Physics, 122, 191-217.
17. Hilpert R., 1933, Heat Transfer from Cylinders, Forsch. Geb. Ingenieurwes, 4, 215-220.
18. Kacker S. C., Pennington B. and Hill R. S., 1974, Fluctuating Lift Coefficient for a Circular Cylinder in Cross Flows, Journal of Mechanical Engineering Science, 16, 215-224.
19. Kalro V. and Tezduyar T., 1997, Parallel 3D computation of unsteady flows around circular cylinders, Parallel Computing, 23, 1235-1248. Kim S., Wilson P. A. and Chen Z., 2012, Effect of spanwise discretisation on turbulent flow past a circular cylinder, International Journal of Maritime Engineering, 158, 69-76.
20. Kim S., Wilson P. A. and Chen Z., 2015, Large-eddy simulation of the turbulent near wake behind a circular cylinder, International Journal of Maritime Engineering, 158, 69-76.
21. Kim S., Wilson P. A. and Chen Z., 2015, Large-eddy simulation of the turbulent near wake behind a circular cylinder: Reynolds number effect, Applied Ocean Research, 49, 1-8.
22. Kravchenkoa A. G. and Moin P, 2000, Numerical studies of flow over a circular cylinder at ReD=3900, Physics of Fluids, 12, 403-417.
23. Launder B. E. and Spalding D. B, 1972, Lectures in Mathematical Models of Turbulence, London, England.
24. Lu X., Dalton C. and Zhang J., 1997, Application of large eddy simulation to an oscillating flow past a circular cylinder, Journal of Fluids Engineering, 119, 519-525.
25. Lysenko D. A., Ertesvag I. S. and Rian K. E., 2012, Large-Eddy Simulation of the Flow Over a Circular Cylinder at Reynolds Number 3900 Using the OpenFOAM Toolbox, Flow Turbulence and Combustion, 89, 491-518.
26. McAdams W. H., 1954, Heat Transmission, McGraw-Hill, New York, USA.
27. Menter F. R., 1994, Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications, American Institute Aeronatics and Austronatics Journal, 32, 1598-1605.
28. Morgan V. T., 1975, The Overall Convective Heat Transfer from Smooth Circular Cylinders, In: Thomas F. Irvine and James P. Hartnett, Editor(s), Advances in Heat Transfer, 11, 199-264.
29. Mustto A. A. and Bodstein G. C. R., 2011, Subgrid-Scale Modeling of Turbulent Flow Around Circular Cylinder by Mesh-Free Vortex Method, Engineering Applied Computational Fluid Mechanics, 5, 259-275.
30. Nakamura H. and Igarashi T., 2004, Unsteady heat transfer from a circular cylinder for Reynolds numbers from 3000 to 15,000, Internationa Journal of Heat and Fluid Flow, 25, 741-748.
31. Niemann H. J. and Hölscher N., 1990, A review of recent experiments on the flow of past circular cylinders, Journal of Wind Engineering and Industrial Aerodynamics, 33, 197-209.
32. Norberg C. and Sunden B., 1987, Turbulence and Reynolds number effects on the flow and fluid forces on a single cylinder in cross flow, Journal of Fluids and Structures, 1, 337-357.
33. Norberg C, 1994, An experimental investigation of the flow around a circular cylinder: influence of aspect ratio, Journal of Fluid Mechanics, 258, 287-316.
34. Norberg C., 2003, Fluctuating lift on a circular cylinder: review and new measurements, Journal of Fluids and Structures, 17, 57-96.
35. Ong M. C., Utnes T., Holmedal L. E., Myrhaug D. and Pettersen B., 2009, Numerical simulation of flow around a smooth circular cylinder at very high Reynolds numbers, Marine Structures, 22, 142-153.
36. Ouvrard H., Koobus B., Dervieux A. and Salvetti M. V., 2010, Classical and variational multiscale LES of the flow around a circular cylinder on unstructured grids, Computers and Fluids, 39, 1083-1094.
37. Parnaudeau P., Carlier J., Heitz D. and Lamballais E., 2008, Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900, Physics of Fluids, 20, 085101.
38. Pasinato H. D., 2008, Large-Eddy Simulation of the Flow and Thermal Fields Past a Circular Cylinder, Mecánica, Comput XXVII, Numerical Simulation of Turbulent Flows, 249-264.
39. Patel Y., 2010, Numerical Investigation of Flow Past a Circular Cylinder and in a Staggered Tube Bundle Using Various Turbulence Models, MS Thesis, Lappeenranta University of Technology.
40. Rahman M., Karim M. and Alim A., 2007, Numerical investigation of unsteady flow past a circular cylinder using 2-D finite volume method, Journal of Naval Architecture and Marine Engineering, 4, 27-42.
41. Reiher H., 1925, Der warmeubergang von stromender luft an rohrbundel in kreuzstrom, VDI Forschungsheft, 269 (1925) 47-51.
42. Roshko A., 1961, Experiments on the flow past a circular cylinder at very high Reynolds number, Journal of Fluid Mechanics, 10, 345-356.
43. Saghafian M., Stansby P. K., Saidi M. S. and Apsley D. D., 2003, Simulation of turbulent flows around a circular cylinder using nonlinear eddy-viscosity modelling: steady and oscillatory ambient flows, Journal of Fluids and Structures, 17, 1213-1236.
44. Scholten J. W. and Murray D. B., 1998, Unsteady heat transfer and velocity of a cylinder in cross flow—I. Low freestream turbulence, International Journal of Heat Mass Transfer, 41, 1139-1148.
45. Scholten J. W. and Murray D. B., 1998, Unsteady heat transfer and velocity of a cylinder in cross flow—II. High freestream turbulence, International Journal of Heat Mass Transfer, 41, 1149-1156.
46. Selvam R. P., 1997, Finite element modeling of flow around a circular cylinder using LES, Journal of Wind Engineering and Industrial Aerodynamics, 67, 129-139.
47. Shih T. H., Liou W. W., Shabbir A., Yang Z. and Zhu, J., 1995, A New k-ε Eddy-Viscosity Model for High Reynolds Number Turbulent Flows, Compututers and Fluids, 24, 227-238.
48. Shim Y. M., Sharma R. N. and Richards P. J., 2009, Numerical study of the flow over a circular cylinder in the near wake at Reynolds number 3900, 39th AIAA Fluid Dynamics Conference 22 - 25 June 2009, AIAA 2009-4160, San Antonio, Texas, TX, 1-13.
49. Sidebottom W., Ooi A. and Jones D., 2015, A Parametric Study of Turbulent Flow Past a Circular Cylinder Using Large Eddy Simulation, Journal of Fluids Engineering, 137, 091202.
50. Tremblay F., Manhart M. and Friedrich R., 2000, DNS of flow around a circular cylinder at a subcritical Reynolds number with cartesian grids. In: Proceedings of the 8th European Turbulence Conference, Barcelona, Spain, EUROMECH, CIMNE, 27–30 June, 659–662.
51. Ünal U. O., Atlar M. and Gören Ö., 2010, Effect of turbulence modelling on the computation of the near-wake flow of a circular cylinder, Ocean Engineering, 37, 387-399.
52. Virk P. S., 1970, Heat Transfer From the Rear of a Cylinder in Transverse Flow, Journal of Heat Transfer, 92, 206-207. Wilcox D. C., 1998, Turbulence Modeling for CFD, DCW Industries Inc., La Canada, California, 73-163.
53. Williamson C. H. K. and Govardhan R., 2004, Vortex-induced vibrations, Annual Review of Fluid Mechanics, 36, 413-455.
54. Wornom S., Ouvrard H., Salvetti M. V., Koobus B. and Dervieux A., 2011, Variational multiscale large-eddy simulations of the flow past a circular cylinder: Reynolds number effects, Computers and Fluids, 47, 44-50.
55. Yakhot V. and Orszag, S. A., 1986, Renormalization Group Analysis of Turbulence: I. Basic Theory, Journal of Scientific Computing, 1, 3-51.
56. Young M. E. and Ooi A., 2007, Comparative assessment of LES and URANS for flow over a cylinder at a Reynolds number of 3900, 15th Australasian Fluid Mechanics. Conf. The University of Sydney, 2-7 December, Sydney, Australia.
57. Zhukauskas A. and Ziugzda J., 1985, Heat Transfer of a Cylinder in Crossflow, Hemisphere Publishing Corporation, New York, USA.