添加高分子聚合物的過渡和臨界紊流於管道拉板流的數值模擬

簡易檢索 / 詳目顯示

回結果列表

研究生：	林哲宇 Lin, Che-Yu
論文名稱：	添加高分子聚合物的過渡和臨界紊流於管道拉板流的數值模擬 Numerical simulation of transitional and marginally turbulent Couette duct flows with polymer additives
指導教授：	林昭安 Lin, Chao-An
口試委員:	王訓忠 Wong, Shwin-Chung 林洸銓 Lin, Kuang-C. 牛仰堯 Niu, Yang-Yao 陳慶耀 Chen, Ching-Yao 陳明志 Chern, Ming-Jyh 廖川傑 Liao, Chuan Chieh
學位類別：	博士 Doctor
系所名稱：	工學院 - 動力機械工程學系 Department of Power Mechanical Engineering
論文出版年：	2021
畢業學年度：	109
語文別：	英文
論文頁數：	98
中文關鍵詞：	臨界雷諾數、黏彈流體、減阻、直接數值模擬、拉板管流
外文關鍵詞：	Critical Reynolds number, FENE-P model, Drag reduction, Couette duct flow
相關次數：	點閱：2 下載：0
分享至:	分享至facebook 分享至twitter

查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

本論文對黏彈性流體在湍流、過渡和層流狀態下的管道流動進行了直接數值模擬，並使用FENE-P模型求解高分子聚點物的構象方程式。這項研究有兩個目的；第一個是找到合適的方法來實現構象方程式的數值邊界條件。結果表明，構象方程的邊界計算使用線性外推法，可為二階精度並提供最小的誤差。使用相同的方法模擬不同Weissenberg值對平板間紊流的影響，當Weissenberg值增加則減阻增加，當Weissenberg值增加到200時，接近最大減阻 (MDR) 的極限。
第二個目標是研究黏彈性流體在方管拉板流的自持紊流臨界雷諾數。結果發現，層流和紊流中的平均速度對摩擦速度關係式與壓力驅動方管流有著相同比例，表明了方管流場的相似性。在層流轉變到紊流的臨界雷諾數較大於牛頓流體，並隨著魏森伯格數的增加而增加。對於雷諾數相對較低的紊流，黏彈性流體也可以被觀察到在方管流中存在兩種流場狀態的交替。然而，隨著Weissenberg值的增加則二次流的強度變弱。在雷諾數為85和Weissenberg值為11時，可獲得的紊流統計數據與高減阻條件下的實驗數據一致。

This dissertation presents direct numerical simulation for the duct flow of a drag-reducing viscoelastic fluid in both turbulent, transitional and laminar regimes. The FENE-P dumbbell model was used for solving the conformation tensor. There were two aims in this study; the first one was to find the appropriate approach of implementing numerical boundary conditions for the conformation tensor and the second objective was to investigate the critical Reynolds number for self-sustaining turbulence in viscoelastic fluid of Couette duct flow. The results showed that, boundary treatments for calculation of the conformation equation based on the linear extrapolation scheme could provide more accurate results of error norms for second-order accurate numerical method. By applying the same treatment in simulation of different Weissenberg numbers in turbulent channel flow, it allowed observation of drag-reducing phenomenon. When the Weissenberg number increased to $We_\tau\approx 200$, the drag reduction would approach the limit of maximum drag reduction (MDR).

In further application on the square duct Couette flow, the relationship between the bulk velocity and friction velocity, both in laminar and turbulent flow, were found to maintain the same scaling as those in pressure-driven duct flow; thus, indicating a degree of universality in the two classes of wall-bounded flows. An investigation of the laminar-turbulent transition indicated that there was a delay, where the critical Reynolds number increased with higher Weissenberg number and was greater than that of the Newtonian case. For turbulent flows of relatively low Reynolds numbers, the alternation between two states normally observed in Newtonian duct flow persisted in the viscoelastic fluid. The two states however became increasingly similar as the Weissenberg number was increased and the secondary motion was weaker in magnitude. The statistics of turbulence obtained at a shear Reynolds number of $85$ and Weissenberg number of $11$ were consistent with the experimental data in the high drag reduction regime.

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iv
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .viii
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1 Introductions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Literature survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Drag reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 MDR Asymptote in mean velocity profiles . . . . . . . . . . . . . 3
2.3 Critical Reynolds number of turbulent duct flow . . . . . . . . . . 5
3 The numerical simulation of viscoelastic flow . . . . . . . . . . . . . . . . 6
3.1 The simplified model of long-chain polymer . . . . . . . . . . . . 7
3.2 The conformation tensor of continuous polymer model . . . . . . 10
4 Two difficulties of Numerical simulation for viscoelastic flow . . . . . . . 12
5 Case analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Mathematical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
1 Flow velocity field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 Constitutive equations of FENE-P model . . . . . . . . . . . . . . . . . . 18
3 Conformation equations of FENE-P model . . . . . . . . . . . . . . . . . 19
4 The detailed derivation of dimensionalized for the equation . . . . . . . . 21
Numerical method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
1 Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2 Discretization of the Momentum Equation . . . . . . . . . . . . . . . . . 26
2.1 Spatial discretization . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Discretization of conformation equation . . . . . . . . . . . . . . . . . . . 28
3.1 MINMOD scheme using Flux-limiter method . . . . . . . . . . . 28
4 Temporal discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Flowchart of solving procedure . . . . . . . . . . . . . . . . . . . . . . . 32
6 Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Preliminary tests of prediction procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
1 Laminar channel flow with polymer additives using FENE-P model . . . 37
2 DNS of Newtonian turbulent Poiseuille channel flow . . . . . . . . . . . . 43
2.1 Statistics of turbulent flow field . . . . . . . . . . . . . . . . . . . 44
3 The drag reduction of turbulent channel flow . . . . . . . . . . . . . . . . 49
4 Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
DNS of Turbulent Couette duct flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2 Validation for Couette duct flow . . . . . . . . . . . . . . . . . . . . . . . 61
2.1 Laminar Couette duct flow in Newtonian fluid . . . . . . . . . . . 62
2.2 Turbulent Couette duct flow in Newtonian fluid . . . . . . . . . . 63
3 Case description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.1 Couette duct flow at low Reynolds number . . . . . . . . . . . . . 69
4 Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Conclusions and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86
1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
2 The suggestions of the future work . . . . . . . . . . . . . . . . . . . . . 87
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88
                                

[1] H. Abe, H. Kawamura, and Y. Matsuo. Direct numerical simulation of a fully developed turbulent channel flow with respect to the reynolds number dependence. Journal of Fluids Engineering, 123(2):382–393, 2001.
[2] A. M. Afonso, F. T. Pinho, and M. A. Alves. The kernel-conformation constitutive laws. Journal of Non-Newtonian Fluid Mechanics, 2012.
[3] N. Balci, B. Thomases, M. Renardy, and C. R. Doering. Symmetric factorization of the conformation tensor in viscoelastic fluid models. Journal of Non-Newtonian Fluid Mechanics, 166:546–553, 2011.
[4] R. B. Bird. Dynamics of polymeric liquids, volume 2. New York: Wiley, 1987.
[5] S. Bottin and H. Chaté. Statistical analysis of the transition to turbulence in plane couette flow. The European Physical Journal B, 6:143–155, 1998.
[6] D. R. Carlson, S. E. Widnall, and M. F. Peeters. A flow-visualization study of transition in plane poiseuille flow. Journal of Fluid Mechanics, 121:487, 1982.
[7] D. Cruz, F. Pinho, and P. Oliveira. Analytical solutions for fully developed laminar flow of some viscoelastic liquids with a newtonian solvent contribution. Journal of Non-Newtonian Fluid Mechanics, 132(1-3):28–35, dec 2005.
[8] V. Dallas, J. C. Vassilicos, and G. F. Hewitt. Strong polymer-turbulence interactions in viscoelastic turbulent channel flow. Physical Review E, 82, 2010.
[9] A. Davey. On the stability of plane couette flow to infinitesimal disturbances. Journal of Fluid Mechanics, 57(2):369–380, 1973.
[10] F. Daviaud, J. Hegseth, and P. Bergé. Subcritical transition to turbulence in plane couette flow. Physical Review Letters, 69:2511–2514, 1992.
[11] J. Den Toonder, A. Draad, G. Kuiken, and F. Nieuwstadt. Degradation effects of dilute polymer solutions on turbulent drag reduction in pipe flows. Applied Scientific Research, 55(1):63–82, 1995.
[12] J. Den Toonder, M. Hulsen, G. Kuiken, and F. Nieuwstadt. Drag reduction by polymer additives in a turbulent pipe flow: numerical and laboratory experiments. Journal of Fluid Mechanics, 337:193–231, 1997.
[13] Y. Dubief, V. E. Terrapon, C. M. White, E. S. G. Shaqfeh, P. Moin, and S. K. Lele. New answers on the interaction between polymers and vortices in turbulent flows. 74:311–329, 2005.
[14] H. Faisst and B. Eckhardt. Sensitive dependence on initial conditions in transition to turbulence in pipe flow. Journal of Fluid Mechanics, 504:343–352, 2004.
[15] R. Fattal and R. Kupferman. Constitutive laws for the matrix-logarithm of the conformation tensor. Journal of Non-Newtonian Fluid Mechanics, 123:281–285, 2004.
[16] K. D. Housiadas and A. N. Beris. Polymer-induced drag reduction: Effects of the variations in elasticity and inertia in turbulent viscoelastic channel flow. Phys. Fluids, 15(8):2369–2384, 2003.
[17] H. W. Hsu, J. B. Hsu, W. Lo, and C. A. Lin. Large eddy simulations of turbulent couette–poiseuille and couette flows inside a square duct. Journal of fluid mechanics, 702:89–101, 2012.
[18] J. Jimenez and P. Moin. The minimal flow unit in near-wall turbulence. 225:213–240, 1991. [19] S. Jin and L. R. Collins. Dynamics of dissolved polymer chains in isotropic turbulence. New Journal of Physics, 9(10):360–360, oct 2007.
[20] J. Komminaho, A. Lundbladh, and A. V. Johansson. Very large structures in plane turbulent couette flow. Journal of Fluid Mechanics, 320:259–285, 1996.
[21] J. L. Lumley. Drag reduction by additives. Annual Review of Fluid Mechanics, 1(1):367–384, jan 1969.
[22] J. L. Lumley and G. R. Newman. The return to isotropy of homogeneous turbulence. Journal of Fluid Mechanics, 82(1):161–178, 1977.
[23] V. S. L’vov, A. Pomyalov, I. Procaccia, and V. Tiberkevich. Drag reduction by polymers in wall bounded turbulence. Physical Review Letters, 92(24), jun 2004.
[24] T. Min, H. Choi, and J. Y. Yoo. Maximum drag reduction in a turbulent channel flow by polymer additives. Journal of Fluid Mechanics, 492:91–100, oct 2003.
[25] T. Min, J. Y. Yoo, and H. Choi. Effect of spatial discretization schemes on numerical solutions of viscoelastic fluid flows. Journal of non-newtonian fluid mechanics, 100:27–47, 2001.
[26] T. Min, J. Y. Yoo, H. Choi, and D. D. Joseph. Drag reduction by polymer additives in a turbulent channel flow. Journal of Fluid Mechanics, 486:213–238, jun 2003.
[27] P. Moin, K. Squires, W. Cabot, and S. Lee. A dynamic subgridscale model for compressible turbulence and scalar transport. Phys. Fluids, 3:2746–2757, 1991.
[28] R. D. Moser, J. Kim, and N. N. Mansour. Direct numerical simulation of turbulent channel flow up to reτ = 590. Physics of fluids, 11(4):943–945, 1999.
[29] P. Orlandi, M. Bernardini, and S. Pirozzoli. Poiseuille and couette flows in the transitional and fully turbulent regime. Journal of Fluid Mechanics, 770:424–441, 2015.
[30] B. E. Owolabi, D. J. Dennis, and R. J. Poole. Turbulent drag reduction by polymer additives in parallel-shear flows. Journal of Fluid Mechanics, 827, 2017.
[31] B. E. Owolabi and C.-A. Lin. Marginally turbulent couette flow in a spanwise confined passage of square cross section. Physics of Fluids, 30:075102, 2018.
[32] A. S. Pereira, G. Mompean, L. Thais, and E. J. Soares. Transient aspects of drag reducing plane Couette flows. Journal of Non-Newtonian Fluid Mechanics, 241:60– 69, 2017.
[33] A. Peterlin. Streaming birefringence of soft linear macromolecules with finite chain length. Polymer, 2:257–264, 1961.
[34] A. Pinelli, M. Uhlmann, A. Sekimoto, and G. Kawahara. Reynolds number dependence of mean flow structure in square duct turbulence. Journal of Fluid Mechanics, 644:107–122, 2010.
[35] S. Pirozzoli, M. Bernardini, and P. Orlandi. Turbulence statistics in Couette flow at high Reynolds number. Journal of Fluid Mechanics, 758:327–343, 2014.
[36] V. A. Romanov. Stability of plane-parallel couette flow. Functional analysis and its applications, 7(2):137–146, 1973.
[37] G. Ryskin. Turbulent drag reduction by polymers: A quantitative theory. Physical Review Letters, 59(18):2059–2062, nov 1987.
[38] A. Shahmardi, S. Zade, M. N. Ardekani, R. J. Poole, F. Lundell, M. E. Rosti, and L. Brandt. Turbulent duct flow with polymers. 859:1057–1083, 2019.
[39] P. A. Stone, F. Waleffe, and M. D. Graham. Toward a structural understanding of turbulent drag reduction: nonlinear coherent states in viscoelastic shear flows. Physical review letters, 89(20):208301, 2002.
[40] R. Sureshkumar and A. N. Beris. 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, 60:53–80, 1995.
[41] R. Sureshkumar, A. N. Beris, and R. A. Handler. Direct numerical simulation of the turbulent channel flow of a polymer solution. Phys. Fluids, 9(3):743–755, 1997.
[42] M. Tabor and P. G. de Gennes. A cascade theory of drag reduction. Europhysics Letters (EPL), 2(7):519–522, oct 1986.
[43] H. Teng, N. Liu, X. Lu, and B. Khomami. Turbulent drag reduction in plane couette flow with polymer additives: a direct numerical simulation study. Journal of Fluid Mechanics, 846:482, 2018.
[44] B. A. Toms. Some observations on the flow of linear polymer solutions through straight tubes at large reynolds numbers. Proceedings of the 1st International Congress on Rheology, 2:135–141, 1948.
[45] M. Uhlmann, A. Pinell, G. Kawahara, and A. Sekimoto. Marginally turbulent flow in a square duct. Journal of Fluid Mechanics, 588:153–162, 2007.
[46] P. S. Virk. Drag reduction fundamentals. AIChE J., 21(4):625–656, 1975.
[47] P. S. Virk, E. W. Merrill, H. S. Mickley, K. A. Smith, and E. L. Mollo-Christensen. The Toms phenomenon: turbulent pipe flow of dilute polymer solutions. Journal of Fluid Mechanics, 30(02):305, nov 1967.
[48] M. D. Warholic, H. Massah, and T. J. Hanratty. Influence of drag-reducing polymers
on turbulence: effects of Reynolds number, concentration and mixing. Exp. Fluids, 27(5):461–472, 1999.
[59] C. M. White and M. G. Mungal. Mechanics and prediction of turbulent drag reduction with polymer additives. Annual Review of Fluid Mechanics, 40(1):235–256, jan 2008.
[50] F. M. White. Viscous fluid flow. McGraw-Hill series in mechanical engineering. McGraw-Hill, Boston, Mass. [u.a.], 3. ed edition, 2006. Includes bibliographical references (p. 590-616) and index.
[51] B. Yu and Y. Kawaguchi. Direct numerical simulation of viscoelastic drag-reducing flow: a faithful finite difference method. Journal of Non-Newtonian Fluid Mechanics, 116:431–466, 2004.
[52] M. Zhang, I. Lashgari, T. A. Zaki, and L. Brandt. Linear stability analysis of channel flow of viscoelastic oldroyd-b and FENE-p fluids. Journal of Fluid Mechanics, 737:249–279, nov 2013.

簡易檢索 / 詳目顯示

相關論文