한국수자원학회논문집 (Journal of Korea Water Resources Association)

  • 제44권3호
  • /
  • Pages.189-198
  • /
  • 2011
  • /
  • 2799-8746(pISSN)
  • /
  • 2799-8754(eISSN)
한국수자원학회 (Korea Water Resources Association)
권호 표지
DOI QR코드

DOI QR Code

높은 레이놀즈수를 가진 난류 진동 경계층에서의 k-ε과 k-ω 난류모형의 비교

Comparative Study on k-ε and k-ω Closures under the Condition of Turbulent Oscillatory Boundary Layer Flow at High Reynolds Number

  • 손민우 (인하대학교 해양과학기술연구소) ;
  • 이관홍 (인하대학교 자연과학대학 해양과학과) ;
  • 이길성 (서울대학교 공과대학 건설환경공학부) ;
  • 이두한 (한국건설기술연구원 하천해안항만연구실)
  • 투고 : 2011.01.12
  • 심사 : 2011.02.25
  • 발행 : 2011.03.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 연구는 난류현상의 모형화를 위해 널리 이용되는 k-$\varepsilon$과 k-$\omega$ 난류모형을 비교하는 것이 목적으로, 횡방향 흐름이 무시될 수 있는 U-튜브 모양의 터널형 수로 내 높은 레이놀즈수를 가진 진동 경계층 흐름에 두 난류해석방법을 적용하였다. 난류모형의 적용은 1차원 연직 모형을 통해 이루어지며, 수치 모의 결과, 유속의 분포와 난류운동에너지 (turbulent kinetic energy) 모두에서 두 모형이 매우 유사한 결과를 나타낸다. 이를 통하여, 횡방향 압력경사가 무시될 수 있는 조건에서는 k-$\varepsilon$과 k-$\omega$ 난류모형이 큰 차이를 보이지 않고, 우수한 결과를 나타냄을 알 수 있다. 따라서 직선형 하천 및 하구부, 해안에서의 파랑 흐름 등과 같이 횡방향의 압력경사가 미미한 지역에서의 난류를 수치적으로 해석할 경우, 기존의 풍부한 연구를 통해 매개변수의 검보증이 장기간 이루어진 k-$\varepsilon$ 모형을 이용하는 것이 추천된다.

The aim of this study is to compare k-$\varepsilon$ and k-$\omega$ closures under the condition of oscillatory layer flow at high Reynolds number. A one dimensional vertical model incorporated with flow momentum equations and turbulence models (k-$\varepsilon$ and k-$\omega$) is applied to the laboratory measurements in the turbulent oscillatory boundary layer. The numerical simulation reveals that both turbulence models calculate similar velocity profiles and turbulent kinetic energy (TKE). In addition, both deliver high accuracy under the condition of negligible spanwise pressure gradient. Therefore, it is recommended in this study to use k-$\varepsilon$ closure, of which numerical coefficients have been calibrated from many studies, for the cases of straight channel, estuary, and coastal environment where the spanwise pressure gradient is not significant.

키워드

참고문헌

  1. 강형식, 최성욱 (2000). “식생된 개수로에서 난류 구조와 부유사 이동 현상의 수치해석.” 한국수자원학회논문집, 한국수자원학회, 제33권, 제5호, pp. 581-592.
  2. 곽승현 (2006). “난류모형을 적용한 엔진 연료실의 유동 해석.” 한국항해항만학회지, 한국항해항만학회, 제30권, 제5호, pp. 369-374.
  3. 양원준, 최성욱 (2002). “LES를 이용한 교각주위 국부세굴의 3차원 수치모의.” 대한토목학회논문집, 대한토목학회, 제22권, 제4-B호, pp. 437-446.
  4. 이남주, 최홍식, 이길성 (1994). “가로흐름 수역으로 방출되는 2차원 표면온배수 수치모형 비교 연구.” 한국해안해양공학회지, 한국해안해양공학회, 제6권, 제1호, pp. 40-50.
  5. Davidov, B.I. (1961). “On the statistical dynamics of an incompressible turbulent fluid.” Dokl. Akad. Nauk S.S.S.R., Vol. 303, pp. 47-50.
  6. Elghobashi, S.E., and Abou-Arab, T.W. (1983). “A two-equation turbulence model for two-phase flows.” Physics of Fluids, Vol. 26, No. 4, pp. 931-938. https://doi.org/10.1063/1.864243
  7. Harlow, F.H., and Nakayama, P.I. (1968). Transport of turbulence energy decay rate. University of California Report LA-3854, Los Alamos Science Laboratory.
  8. Henderson, S.M., Allen, J.S., and Newberger, P.A. (2004). “Nearshore sandbar migration by an eddy diffusive boundary layer model.” J. Geophysical Research, Vol. 109, No. C06024, doi:10.1029/2003 JC002137.
  9. Hsu, T.-J., Traykovski, P.A., and Kineke, G.C. (2007). “On modeling boundary layer and gravity driven fluid mud transport.” J. Geophysical Research, Vol. 112, No. C04011, doi:10.1029/2006JC003719.
  10. Huang, P.G., Coleman, G.N., and Bradshaw, P. (1995). “Compressible turbulent channel flows: DNS results and modelling.” J. Fluid Mech., Vol. 305, pp. 185-218. https://doi.org/10.1017/S0022112095004599
  11. Jones, W.P., and Launder, B.E. (1972). “The prediction of laminarization with a two-equation model of turbulence.” Int. J. Heat Mass Transfer, Vol. 15, pp. 301-314. https://doi.org/10.1016/0017-9310(72)90076-2
  12. Joung, J., Choi, S.-U., and Choi, J.-I. (2007). “Direct numerical simulation of turbulent flow in a square duct: Analysis of secondary flows.” J. Engineering Mechanics, Vol. 133, No. 2, pp. 213-221. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:2(213)
  13. Kang, H., and Choi, S.-U. (2006). “Turbulence modeling of compound open-channel flows with and without vegetation on the floodplain using the Reynoldsstress model.” Advances in Water Resources, Vol. 29, pp. 1650-1664. https://doi.org/10.1016/j.advwatres.2005.12.004
  14. Menter, F.R. (1994). “Two-equation eddy-viscosity turbulence models for engineering applications.” AIAA Journal, Vol. 32, No. 8, pp. 1598-1605. https://doi.org/10.2514/3.12149
  15. Nagaosa, R. (1999). “Direct numerical simulation of vortex structures and turbulent scalar transfer across a free surface in a fully developed turbulence.”Physics of Fluids, Vol. 11, No. 6, pp. 1581-1595. https://doi.org/10.1063/1.870020
  16. Nezu, I., and Nakagawa, H. (1993). Turbulence in open-channel flows. IAHR-Monograph, Balkema, Rotterdam, The Netherlands.
  17. Olsen, N.R.B. (2003). “Three-dimensional CFD modeling of self-forming meandering channel.” J. Hydraulic Engineering, Vol. 129, No. 5, pp. 366-372. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:5(366)
  18. Orlandi, P., Leonardi, S., Tuzi, R., and Antonia, R.A. (2003). “Direct numerical simulation of turbulent channel flow with wall velocity disturbances.” Physics of Fluids, Vol. 15, No. 12, pp. 3587-3601. https://doi.org/10.1063/1.1619137
  19. Pope, S.B. (2000). Turbulent flows. Cambridge University Press, Cambridge, UK.
  20. Puleo, J.A., Mouraenko, O., and Hanes, D.M. (2004). “One-dimensional wave bottom boundary layer model comparison: Specific eddy viscoisity and turbulence closure models.” J. Waterway, Port, Coastal and Ocean Engineering, Vol. 130, No. 6, pp. 322-325. https://doi.org/10.1061/(ASCE)0733-950X(2004)130:6(322)
  21. Rameshwaran, P, and Naden, P.S. (2003). “Threedimensional numerical simulation of compound channel flows.” J. Hydraulic Engineering, Vol. 129,No. 8, pp. 645-652. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:8(645)
  22. Rodi, W. (1993). Turbulence models and their application in hydraulics-A state-of-the-art review, IAHR, Delft, The Netherlands.
  23. Shih, T.-H., Liou, W. W., Shabbir, A., Yang, Z., and Zhu, J (1995). “A new k-$\varepsilon$ eddy viscosity model for high Reynolds number turbulent flows.” Computers Fluids, Vol. 24, No. 3, pp. 227-238. https://doi.org/10.1016/0045-7930(94)00032-T
  24. Sumer, B.M., Jensen, B.L., and Fredsoe, J. (1987). “Turbulence in oscillatory boundary layers.” In Advances in Turbulence, Edited by Gt. Comte-Bellot & J. Mathieu, Springer, pp. 556-567.
  25. Umlauf, L., Burchard, H., and Hutter, K. (2003). “Extending the k-ω turbulence model towards oceanic applications.” Ocean Modelling, Vol. 5, pp. 195-218. https://doi.org/10.1016/S1463-5003(02)00039-2
  26. Violeau, D., Bourban, S., Cheviet, C., Markofsky, M., Petersen, O., Roberts, W., Spearman, J., Toorman, E., Vested, H.J., and Weilbeer, H. (2002). “Numericalsimulation of cohesive sediment transport: Intercomparision of several numerical models.” Proceedings in Marine Science, Vol. 5, pp. 75-89. https://doi.org/10.1016/S1568-2692(02)80009-2
  27. Wilcox, D.C. (1993). Turbulence modeling for CFD. La Canada, CA: DCW Industries.
  28. Zedler, E.A., and Street, R.L. (2001). “Large-eddy simulation of sediment transport: Currents over ripples.” J. Hydraulic Engineering, Vol. 127, No. 6, pp. 444-452. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:6(444)

피인용 문헌

  1. A Numerical Study on Behavior of Fresh Water Body between Injection and Production Wells with Variation of Fresh Water Injection Rate in a Saline Aquifer vol.48, pp.1, 2015, https://doi.org/10.3741/JKWRA.2015.48.1.23
  2. On effects of skewed and asymmetric oscillatory flows on cohesive sediment flux: Numerical study vol.49, pp.7, 2013, https://doi.org/10.1002/wrcr.20365