해양환경안전학회지 (Journal of the Korean Society of Marine Environment & Safety)

  • 제20권3호
  • /
  • Pages.323-333
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  • 2014
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  • 1229-3431(pISSN)
  • /
  • 2287-3341(eISSN)
해양환경안전학회 (The Korean Society of Marine Environment and safety)
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Analysis of Empirical Constant of Eddy Viscosity by Zero- and One-Equation Turbulence Model in Wake Simulation

  • Park, Il Heum (School of Marine Technology, Chonnam National University) ;
  • Cho, Young Jun (School of Marine Technology, Chonnam National University) ;
  • Kim, Tae Yun (Office of Environment Assessment, Korea Environment Institute) ;
  • Lee, Moon Ock (School of Marine Technology, Chonnam National University) ;
  • Hwang, Sung Su (School of Marine Technology, Chonnam National University)
  • 투고 : 2014.05.02
  • 심사 : 2014.06.25
  • 발행 : 2014.06.30
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초록

In this paper, the wakes behind a square cylinder were simulated using two kinds of different turbulence models for the eddy viscosity concept such as the zero- and the one-equation model in which the former is the mixing length model and the latter is the k-equation model. For comparison between numerical and analytical solutions, we employed three skill assessments: the correlation coefficient(r) for the similarity of the wake shape, the error of maximum velocity difference(EMVD) for the accuracy of wake velocity and the ratio of drag coefficient(RDC) for the pressure distribution around the structure. On the basis of the numerical results, the feasibility of each model for wake simulation was discussed and a suitable value for the empirical constant was suggested in these turbulence models. The zero-equation model, known as the simplest turbulence model, overestimated the EMVD and its absolute mean error(AME) for r, EMVD and RDC was ranging from 20.3 % to 56.3 % for all test. But the AME by the one-equation model was ranging from 3.4 % to 19.9 %. The predicted values of the one-equation model substantially agreed with the analytical solutions at the empirical mixing length scale $L=0.6b_{1/2}$ with the AME of 3.4 %. Therefore it was concluded that the one-equation model was suitable for the wake simulation behind a square cylinder when the empirical constant for eddy viscosity would be properly chosen.

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참고문헌

  1. Blevins, R. D.(1984), Applied Fluid Dynamics Handbook, van Nostrand Reinhold Company, pp. 279-311.
  2. Bosch, G. and W. Rodi(1998), Simulation of Vortex Shedding Past a Square cylinder with Different Turbulence Models, International Journal for Numerical Methods in Fluids, Vol. 28, pp. 601-616. https://doi.org/10.1002/(SICI)1097-0363(19980930)28:4<601::AID-FLD732>3.0.CO;2-F
  3. Chen, L., J. Y. Tub and G. H. Yeohc(2003), Numerical Simulation of Turbulent Wake Flows behind Two Side-by-Side cylinders, Journal of Fluids and Structures, Vol. 18, pp. 387-403. https://doi.org/10.1016/j.jfluidstructs.2003.08.005
  4. Ettema, R., B. Yoon, T. Nakato and M. Muste(2004), A Review of Scour Conditions and Scour-Estimation Difficulties for Bridge Abutments, KSCE Journal of Civil Engineering, Vol. 8, No. 6, pp. 643-650. https://doi.org/10.1007/BF02823555
  5. Flow Science(1999), FLOW-3D User's Manual, Chapter 3 Theory, Los Alamos, NM, USA, pp. 1-164.
  6. Gortler, H.(1942), Berechnung von Aufgaben der Freien Turbulenz auf Grund eines neuen Naherungsa-Ansatzes, ZAMM, Vol. 22, pp. 244-245. https://doi.org/10.1002/zamm.19420220503
  7. Hirt, C. W. and B. D. Nichols(1981), Volume of Fluid Method for the Dynamics of Free Boundaries, J. Comp. Phys., Vol. 39, pp. 201-225. https://doi.org/10.1016/0021-9991(81)90145-5
  8. Honzejk, V. and K. Frana(2008), A Turbulent Flow Past a cylinder, Journal of Applied Science in the Thermo Dynamics and Fluid Mechanics, Vol. 2, No. 22, pp. 1-6.
  9. Ishino, K., H. Otani, R. Okada and Y. Nakagawa(1993), The Flow Structure around a Cylindrical Pier for the Flow of Transcritical Reynolds number, Proc. of XXV Congress of IAHR, Vol. 5, pp. 417-424.
  10. Kang, K. S., S. C. Kim, J. H. Kim, Y. H. Lee, J. J. Lee, and C. S. Lee(1993), PC Statistics. Jayoo Academy Press, South Korea, pp. 219-223.
  11. Kolmogorov, A. N.(1942), Equation of Turbulent Motion in an Incompressible Fluid, Izv. Akad Nauk. SSSR, Seria Fizicheska, Vol. 1, No. 1-2, pp. 56-58 (English Translation;Imperial College, Mech. Eng., Report ON /6, 1968).
  12. Olsen, N. R. B. and M. C. Melaaen(1993), Three-dimensional calculation of scour around cylinders, Journal of Hydraulic Engineering, ASCE, Vol. 119, No. 9, pp. 1048-1054. https://doi.org/10.1061/(ASCE)0733-9429(1993)119:9(1048)
  13. Park, I. H., G. H. Lee and Y. J. Cho(2009), Drag Coefficient Estimation of Pile Type Structures by Numerical Water Basin Experiments, Journal of Korean Society of Coastal and Ocean Engineering, Vol. 21, No. 1, pp. 45-53.
  14. Park, I. H., J. S. Lee and M. O. Lee(1998), A Numerical Model of Large Scale Grid for Two-Dimensional Wake behind Bodies, Journal of Korean Society of Coastal and Ocean Engineering, Vol. 10, No. 2, pp. 83-92.
  15. Prandtl, L.(1945), Uber ein Neues Formel-System fur die Ausgebildete Turbulenz, Nachr Akad Wiss, Gottingen, Math.-Phys. KL 1945, p. 6.
  16. Reichardt, H.(1951), Gesetzmassigkeiten der Freien Turbulenz, VDI-Forschung-Sheft, 414(1942), 2nd Ed., p. 1951.
  17. Richardson, J. E. and V. G. Panchang(1998), Three-Dimensional Simulation of Scour-Inducing Flow at Bridge Pipers, Journal of Hydraulic Engineering, ASCE, Vol. 124, No. 9, pp. 530-540. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:5(530)
  18. Rodi, W.(1972), The Prediction of Free Turbulent Boundary Layers by Use of a Two-Equation Model of Turbulence, Thesis Submitted for the Degree of Doctor of Philosophy in the Faculty of Engineering, University of London and for the Diploma of Membership of Imperial College. p. 310.
  19. Schlichting, H.(1930), Uber das Ebene Windschatten Problem, Diss Gottingen, Ing.-Arch., Vol. 1, pp. 533-571. https://doi.org/10.1007/BF02079870
  20. Schlichting, H.(1979), Boundary Layer Theory, 7th Ed., Mc-Graw-Hill, New York(Translated by J. Kestin), p. 817.
  21. Wilcox, D. C.(1993), Turbulence Modeling for CFD, DCW Industries Inc., La Canada CA, p. 460.
  22. Yang, W. and S. U. Choi(2002), Three-Dimensional Numerical Simulation of Local Scour around the Bridge Pier Using Large Eddy Simulation, Journal of Korean Society of Civil Engineering, Vol. 22(4-B), pp. 437-446.

피인용 문헌

  1. Analysis of Empirical Constant of Eddy Viscosity by k-ε and RNG k-ε Turbulence Model in Wake Simulation vol.25, pp.3, 2014, https://doi.org/10.7837/kosomes.2019.25.3.344