대한기계학회논문집B (Transactions of the Korean Society of Mechanical Engineers B)

  • 제34권8호
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  • Pages.799-807
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  • 2010
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  • 1226-4881(pISSN)
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  • 2288-5324(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
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폴리머 첨가제에 의한 항력감소 난류 채널 유동장의 직접수치모사

DNS of Drag-Reduced Turbulent Channel Flow due to Polymer Additives

  • 김경연 (한밭대학교 기계공학과)
  • 투고 : 2010.04.12
  • 심사 : 2010.06.18
  • 발행 : 2010.08.01
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초록

폴리머 첨가제에 의한 항력감소 난류 채널 유동에 대한 직접수치모사를 스펙트럴 기법을 통해 수치적으로 해석하였다. 마찰속도 및 채널 높이의 절반으로 무차원화한 레이놀즈수는 395 이며, 폴리머 첨가제에 의해 발생하는 폴리머 응력은 FENE-P 모델을 통해 고려하였다. 폴리머 분자의 이완 시간 및 최대 연신 한계와 같은 FENE-P 모델 인자는 항력감소율에 큰 영향을 끼치는 것으로 나타났다. 항력감소율이 낮은 유동과 높은 유동에 대해 항력감소에 따른 난류 통계량의 변화를 조사하였다. 또한, 동일한 항력감소율을 갖는 유동에 대해, 서로 다른 FENE-P 모델 인자가 난류 통계량의 변화에 미치는 영향도 조사하였다. 최종적으로, Li 등(2006) 이 제시한 유변학 인자들과 항력감소율과의 상관관계식을 본 수치해석 결과를 통해 확인하였다.

Direct numerical simulations (DNS) of turbulent channel flow for which the drag is reduced by using polymer additives have been performed by a pseudo-spectral method. The Reynolds number based on the friction velocity and half-channel height is 395, and the polymeric stresses due to the polymer additives are evaluated using the FENE-P (finitely extensible nonlinear elastic-Peterlin) model. The numerical results show that the drag reduction rate is significantly affected by the parameters used in the FENE-P model, such as the maximum extensibility and relaxation time of the polymer molecules. The turbulence data for both low- and high-drag reduction regimes are analyzed. In addition, the effects of FENE-P model parameters on the flow characteristics have been investigated for the same drag reduction rate due to the polymer additives. Finally, the present DNS results have been used to verify the correlation between rheological parameters and the extent of drag reduction, which was suggested by Li et al. (2006).

키워드

참고문헌

  1. Toms, B.A., 1948, "Some Observations on the Flow of Linear Polymer Solutions Through Straight Tubes at Large Reynolds Numbers," in Proc. 1st Int. Congr. Rheol. North Holland, Amsterdam.
  2. Alyeska Pipeline Service Company. [cited 2010 April 12]; Available from: http://www.alyeskapipe.com/.
  3. Virk, P.S., Merrill, E.W., Mickley, H.S., Smith, K.A. and Mollo-Christensen, E.L., 1967, "The Toms Phenomenon: Turbulent Pipe Flow of Dilute Polymer Solutions," Journal of Fluid Mechanics, Vol. 30, pp. 305-328. https://doi.org/10.1017/S0022112067001442
  4. Virk, P.S., 1971, "An Elastic Sublayer Model for Drag Reduction by Dilute Solutions of Linear Macromolecules," Journal of Fluid Mechanics, Vol. 45, pp. 417-440. https://doi.org/10.1017/S0022112071000120
  5. Warholic, M.D., Massah, H. and Hanratty, T.J., 1999, "Influence of Drag-Reducing Polymers on Turbulence: Effects of Reynolds Number, Concentration and Mixing," Experiments in Fluids, Vol. 27, No. 5, pp. 461-472. https://doi.org/10.1007/s003480050371
  6. White, C.M. and Mungal, M.G., 2008, "Mechanics and Prediction of Turbulent Drag Reduction with Polymer Additives," Annual Review of Fluid Mechanics, Vol. 40, pp. 235-256. https://doi.org/10.1146/annurev.fluid.40.111406.102156
  7. Adrian, R.J., 2007, "Hairpin Vortex Organization in Wall Turbulence," Physics of Fluids, Vol. 19, pp. 041301. https://doi.org/10.1063/1.2717527
  8. Robinson, S.K., 1991, "Coherent Motions in the Turbulent Boundary Layer," Annual Review of Fluid Mechanics, Vol. 23, No. 1, pp. 601-639. https://doi.org/10.1146/annurev.fl.23.010191.003125
  9. Kim, K., Adrian, R.J., Balachandar, S. and Sureshkumar, R., 2008, "Dynamics of Hairpin Vortices and Polymer-Induced Turbulent Drag Reduction," Physical Review Letters, Vol. 100, No. 13, pp. 134504. https://doi.org/10.1103/PhysRevLett.100.134504
  10. White, C.M., Somandepalli, V.S.R. and Mungal, M.G., 2004, "The Turbulence Structure of Drag- Reduced Boundary Layer Flow," Experiments in Fluids, Vol. 36, No. 1, pp. 62-69. https://doi.org/10.1007/s00348-003-0630-0
  11. Sureshkumar, R., Beris, A.N. and Handler, R.A., 1997, "Direct Numerical Simulation of the Turbulent Channel Flow of a Polymer Solution," Physics of Fluids, Vol. 9, p. 743. https://doi.org/10.1063/1.869229
  12. De Angelis, E., Casciola, C.M. and Piva, R., 2002, "DNS of Wall Turbulence: Dilute Polymers and Self-Sustaining Mechanisms," Computers and Fluids, Vol. 31, No. 4-7, pp. 495-507. https://doi.org/10.1016/S0045-7930(01)00069-X
  13. Housiadas, K.D. and Beris, A.N., 2003, "Polymer-Induced Drag Reduction: Effects of the Variations in Elasticity and Inertia in Turbulent Viscoelastic Channel Flow," Physics of Fluids, Vol. 15, pp. 2369-2384. https://doi.org/10.1063/1.1589484
  14. Min, T., Yoo, J.Y., Choi, H. and Joseph, D.D., 2003, "Drag Reduction by Polymer Additives in a Turbulent Channel Flow," Journal of Fluid Mechanics, Vol. 486, pp. 213-238. https://doi.org/10.1017/S0022112003004610
  15. Ptasinski, P.K., Boersma, B.J., Nieuwstadt, F.T.M., Hulsen, M.A., Van den Brule, B. and Hunt, J.C.R., 2003, "Turbulent Channel Flow Near Maximum Drag Reduction: Simulations, Experiments and Mechanisms," Journal of Fluid Mechanics, Vol. 490, pp. 251-291. https://doi.org/10.1017/S0022112003005305
  16. Dubief, Y., White, C.M., Terrapon, V.E., Shaqfeh, E.S.G., Moin, P. and Lele, S.K., 2004, "On the Coherent Drag-Reducing and Turbulence-Enhancing Behaviour of Polymers in Wall Flows," Journal of Fluid Mechanics, Vol. 514, pp. 271-280. https://doi.org/10.1017/S0022112004000291
  17. Bird, R.B., Armstrong, R.C. and Hassager, O., 1987, Dynamics of Polymeric Liquids, Vol. 2: Kinetic Theory. 2nd ed. John Wiley & Sons, New York.
  18. Li, C.F., Sureshkumar, R. and Khomami, B., 2006, "Influence of Rheological Parameters on Polymer Induced Turbulent Drag Reduction," Journal of Non-Newtonian Fluid Mechanics, Vol. 140, No. 1-3, pp. 23-40. https://doi.org/10.1016/j.jnnfm.2005.12.012
  19. Sureshkumar, R. and Beris, A.N., 1995, "Effect of Artificial Stress Diffusivity on the Stability of Numerical Calculations and the Flow Dynamics of Time-Dependent Viscoelastic Flows," Journal of Non-Newtonian Fluid Mechanics, Vol. 60, No. 1, pp. 53-80. https://doi.org/10.1016/0377-0257(95)01377-8
  20. Dimitropoulos, C.D., Sureshkumar, R. and Beris, A.N., 1998, "Direct Numerical Simulation of Viscoelastic Turbulent Channel Flow Exhibiting Drag Reduction: Effect of the Variation of Rheological Parameters," Journal of Non-Newtonian Fluid Mechanics, Vol. 79, No. 2-3, pp. 433-468. https://doi.org/10.1016/S0377-0257(98)00115-3
  21. Warholic, M.D., Heist, D.K., Katcher, M. and Hanratty, T.J., 2001, "A Study with Particle-Image Velocimetry of the Influence of Drag-Reducing Polymers on the Structure of Turbulence," Experiments in Fluids, Vol. 31, No. 5, pp. 474-483. https://doi.org/10.1007/s003480100288
  22. Housiadas, K.D. and Beris, A.N., 2004, "Characteristic Scales and Drag Reduction Evaluation in Turbulent Channel Flow of Nonconstant Viscosity Viscoelastic Fluids," Physics of Fluids, Vol. 16, pp. 1581-1586. https://doi.org/10.1063/1.1689971
  23. Dean, R.B., 1978, "Reynolds Number Dependence of Skin Friction and Other Bulk Flow Variables in Two-Dimensional Rectangular Duct Flow," Journal of Fluid Engineering, Vol. 100, pp. 215-223. https://doi.org/10.1115/1.3448633
  24. Kim, K., Li, C.F., Sureshkumar, R., Balachandar, S. and Adrian, R.J., 2007, "Effects of Polymer Stresses on Eddy Structures in Drag-Reduced Turbulent Channel Flow," Journal of Fluid Mechanics, Vol. 584, pp. 281-299. https://doi.org/10.1017/S0022112007006611