第五章 結論與建議
5.2 建議
1. 本研究選用之次網格模式為等向性假設,大渦模擬係數Cs設為定值,未來 可對其作敏感度分析,或考慮選用其他之次網格模式(如 Mix scale model, MSM 或 dynamic sub-grid model, DSM),並對這些模式進行適用性分析。
2. 本研究在網格加密的配置上係依人為給定,未來可將網格之配置方法依循 函數自動分布之機制,使網格切法更為精確。
3. 數值模式基本假設為垂向靜水壓分佈,建議可以考量垂直方向動量方程 式,建構為非靜水壓(non-hydrostatic)模式:
(1) 可進一步更合理的探討結構物局部流場、水位變化劇烈流場,例如橋墩、
丁壩周圍流場等。
(2) 對於寬深比較小的明渠水流案例,結合適用的紊流模式作進一步之探討。
參考文獻
Babarutsi, S., Ganoulis, J., and Chu, V.H. (1989), “Experimental investigation of shallow recirculating flows” J. Hydr. Engrg., 115(7):906-924
Balen, W.V., Uilttewaal, W.S.J., and Blanckaert, K. (2009), “Large-eddy simulation of a mildly curved open-channel flow” J. Fluid Mech., 630, 413-442.
Basara, B., and Cokljat, D. (1995), “Reynolds stress modeling of turbulent flows in meandering open-channel” Industrial and Environmental Applications of Fluid Mechanics, 221:27-32
Blumberg, A.F., and Mellor, G.L. (1983), “Diagnostic and prognostic numerical circulation studies of the South Atlantic Bight” Journal of Geophysics Research, 88(C8):4579-4592
Boussinesq, J. (1877), “Essai sur la theorie des eaux courantes” Sci., 23:1-680
Calhoun, R.J., and Street, R.L. (2001), “Turbulent flow over a wavy surface : neutral case” J. Geoph. Res., 103, 9277-9293
Chen, N.C. (1983), “Prediction of turbulent flows” Central Res. Inst. Of Electric Power Industry Tech.Rep.17, Abiko,Japan(in Japanese)
Chung, D., and Pullin, D.I. (2009), “Large-eddy simulation and wall modeling of turbulent channel flow” J. Fluid Mech., 631, 281-309
Cokljat, D., and Younis, B.A. (1995), “Second-order closure study of open channel flows” J. Hydr. Engrg., 121(2):94-107
Deardorff, J.W. (1970), “A Numerical study of three-dimensional channel flow at large Reynolds numbers” J. Fluid Mech., 41: 453-480
Dommermuth, D.G., and Novikov, E.A. (1993), “Direct-numerical and large-eddy
simulations of turbulent free-surface flows” Sixth Intl conf. on Numerical Ship Hydrodynamics, Iowa City
Elder, J.W. (1959) “The dispersion of marked fluid in turbulent shear flow” Journal of Fluid Mech., 5:544-560
Fisher, A.T., Stoesser, T., Bates, P.,and Olsen, N.R.B. (2000), “3D numerical modeling of open channel flow with submerged vegetation” J. Hydr.
Engrg.(IAHR), 39(3), 303-310
Flokstra, C. (1977), “The closure problem for depth-averaged two-dimensional flows” Proc., 18th Congr. Of the Int. Assn. For Hydr. Res., 247-256.
Falcomer, L. and Armenio, F. (2002), “Large-eddy simulation of secondary flow over longitudinally ridged walls”, Journal of Turbulence, 3, N8
French, R.H. (1986), Open Channel Hydraulics. Water Resources Publications, LLC Gonzalez-Silvia, G., Matos, E.M., Martignoni, W.P.,and Mori, M. (2012), “The
importance of 3D mesh generation for large eddy simulation of gas-liquid turbulent flows in a fluidized beds”World Academy of science,Engineering and Technology 68
Hanjalic, K., and Launder, B.E. (1972), “A Reynolds stress model of turbulence and its application to thin shear. Part 4” J Fluid Mech., 74, 593–610
Harlow, F.H., and Nakayama, P.I. (1967), “Turbulence transport equations” Phys. of Fluids, 10 (11),2323
Hinterberger, C., Frohlich, J., and Rodi, W. (2008), “2D and 3D turbulent fluctuations in open channel flow with Re 590 studied by large eddy simulation” Flow Turbulence Combust, 80: 225-253
Hyeongsik Kang and Sung-Uk Choi (2006), “Reynolds stress modeling of rectangular open channel flow” Int. J. Numer. Fluids, 51:1319-1334
Isabelle Calmet, and Jacques, Magnaudet (2003), “Statistical structure of high-Reynolds-number turbulence close to the free surface of an open-channel flow” J. Fluid Mech., vol.474, 335-378
Jobson, H.E., and Sayre, W.W. (1970), “Vertical transfer in open channel flow”
Journal of the Hydraulics Division 96
simulation of stably stratified open channel flow” Phys. Fluids 17, 116602
Kim, J., Moin, P., and Moser, R. (1987), “Turbulence statistics in fully developed channel flow at low Reynolds number” J. Fluid Mech., Vol. 177, 133-166
Koken, M., and Constantinescu, G. (2008), “An investigation of the flow and scour mechanisms around isolated spur dikes in a shallow open channel : 2.Conditions corresponding to the final stages of the erosion abd deposition process” Water Resour. Res. 44, W08407
Kolmogorov, A.N. (1942), “Equations of turbulent motion of an incompressible fluid” IZV Akad. Nauk. USSR, Ser. Phys., 6, pp. 56-58 (in Russian)
Komori, S., Nagaosa, R., and Murakami, Y. (1990), “Mass transfer into a turbulent liquid across the zero-shear gas-liquid interface” AICHE J. 36, pp. 57-960
Komori, S., Ueda, H., Ogino, F., and Mizushina, T. (1982), “Turbulence structure and transport mechanism at the free surface of an open channel flow” Intl J. Heat Mass Transfer, 25, 513-521
Launder, B.E., Reece, G.J., and Rodi, W. (1975), “Progress in the developed of a Reynolds-stress turbulence closure. Part 3.” J. Fluid Mech., 68, 537-566
Launder, B.E., and Spalding, D.B. (1974), “The numerical computation of turbulent flows” Comp. Methods in Appl. Mech. and Engrg., 3, 269-289
Lesieur, M., and Metais, O. (1996), “New trends in large-eddy simulations of turbulence” Ann. Rev. Fluid Mech., 28, pp.45-82
Lian Shen, and Dick, K.P. Yue (2001), “Large-eddy simulation of free-surface turbulence” J. Fluid of Mech., vol.440, 75-116
Lindsey Ann Larocque, Jasim Imran and M. Hanif Chaudhry (2013), “3D numerical simulation of partial breach dam-break flow using the LES and k turbulence models” J. Hydr., 51:2, 145-157
Luca Falcomer and Vincenzo Armenio (2002), “Large-eddy simulation of secondary flow over longitudinally ridged walls” Journal of Turbulence, 3, N8
Lumley, J.L. (1975), “Prediction methods for turbulent flows” Lect. Ser. 76, von Karman Inst. for Fluid Dyn., Pennsylvania State Univ., University Park, Pa.
1097-1103
Markatos, N.C. (1986), “The mathematical modeling of turbulent flows” Appl. Math Modelling, 10(June), pp. 190-220
Mansour, N.N., Kim, J., and Moin, P. (1988), “Reynolds-stress and dissipation rate budgets in a turbulent channel flow” J. Fluid Mech., 194(September), 15-44 McCoy, A., Constantinescu, G., and Weber, L.J. (2008), “Numerical investigation of
flow hydrodynamics in a channel with a series of groynes” J. Hydr. Engng., 134, 157-172
Meneveau, C. and Katz, J. (2000), “Scale-invariance and turbulence models for large-eddy simulations” Ann. Rev. Fluid Mech., 32, 1-32
Moin, P., and Kim, J. (1981), “Numerical investigation of turbulent channel flow” J.
Fluid Mech., 118, 341-377
Moser, R.D., Moin, P. (1984), “Direct numerical simulation of curved channel flow”
NASA TM 85974, Ames RES. Ctr., Moffett, calif
Nagakawa, H. Nezu, I. (1981), “Structure of space-time correlations of bursting phenomena in open-channel flows” J. of Fluid Mechanics, 104, 1-43
Nezu, I., and Rodi, W. (1986), “Open-channel flow measurements with a laser Doppler anemometer” J. of Fluid Mechanics, 112 : 335–355
Nisizima, S., and Yoshizawa, A. (1987), “Turbulent channel and Couette flows using an anisotropic k model” AIAA J., 25(3), 414-420
Pope, S. B. (1975), “A more general effective-viscosity hypothesis” J. Fluid. Mech., 72, 331–340
Prandtl, L. (1925), “Bericht uber untersuchungen zur ausgebildeten turbulenz”
ZAMM, 5, 136 (in German)
Prandtl, L. (1945), “uber ein neues formel system fur die ausgebildete turbulenz”
Nachr. Akad, Wiss. Gottingen. Math Phys. Klasse, 6 (in German)
Rameshwaran, P., and Naden, P.S. (2003), “Three dimensional numerical simulation of compound channel flows” J. Hydr. Engrg., 129(8), 645-652
Rashidi, M., Banerjee, S. (1988), “Turbulent structure in free-surface channel flows”
Reece, R.J. (1977), “A generalized Reynolds stress of turbulence” Ph.D. Thesis, Imperial College, University of London,London,England
Reynolds, O. (1895), “On the dynamical theory of incompressible viscous fluids and the determination of criterion” Philosophical Transactions of Royal Society of London, A174, 935-982
Riccardo Broglia, Andrea Pascarelli, and Ugo Piomelli (2003), “Large-eddy simulation of ducts with a free surface” J. Fluid. Mech., 484, 223–253
Rodi, W., and Spalding, D.B. (1970), “A two-parameter model of turbulence and its application to free surface jets” Warme-und Stoffubertragung, 3(2), 85-95
Rodi, W. (1980), “Turbulence models and their application in hydraulics”
IAHR-Monograph, Balkema, Rotterdam, The Netherlands
Rodi, W. (1981), “Examples of turbulence models for incompressible flows” AIAA J., 20(7), 872-879
Rogallo, R.S., and Moin, P. (1984), “Numerical simulation of turbulent flows” Ann.
Rev. Fluid Mech., 16, 99-137
Rubinstein, R., and Barton, J.M. (1990), “Nonlinear Reynolds stress models and the renormalization group” Phys. Fluids A., 2(8), 1472–1476
Schumann, P.G. (1970), “A model of inhomogeneous turbulent flow” Proc., Royal Soc., London, A317, 417-433
Schumann, U. (1975), “Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli” J. Computational Phys., 18, 376-404
Shi, J., Thomas, T.G., and Williams, J.J.R. (1999), “Large-eddy simulation of flow in a rectangular open channel” J. Hydraulic Research, 37:3, 345-361
Smagorinsky, J. (1963), “General circulation experiments with the primitive equation” Month Weather Review, Vol.93, No.99, 99-164
Spalart, P.R. (1986), “Numerical study of sink-flow boundary layers” J. Fluid Mech., 172, 307-328
Speziale, C.G. (1987), “On linear k-l and k models of turbulence” J. Fluid
Stoesser, T., Ruether, N., and Olsen, N.R.B. (2008), “Near-bed flow behavior in a meandering channel” In. Proc Riverflow, 793-799
Takemitsu, N. (1986), “A revised k models” Proc., JSME, Japan Soc. Of Mech.
Engrs., 53(494), 2928-2936
Tominaga, A., Nezu, I., Ezakl, K., and Nakagawa, H. (1989), “Three-dimensional turbulent structure in straight open channel flows” J. Hydr. Res. Vol.27, No1, 149-173
Von Karman, T. (1931), NACA Tech. Mem. 611
Wusi Yue, Ching-Long Lin, and Virendra C. Patel (2005), “Large eddy simulation of turbulent open-channel flow with free surface simulated by level set method”
Phys. Fluids 17, 025108
附錄 A 大渦紊流模擬控制方程式之推導
考慮三維不可壓縮流之那威爾-史托克司(Navier-Stokes)方程式:
連續方程式
i ( i j i j i j) 1 2 i
附錄 B 水深平均動量方程式之推導
12 2 11 1
1 2 2
將(B.2)、(B.3)等式右邊應用萊布尼茲法則對深度方向積分,加上動力邊界條
11 2 12 1 22 2 12 11 1 1