工学的な設計のための流れと熱の数値シミュレーション
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1 247 Introduction of Computational Simulation Methods of Flow and Heat Transfer for Engineering Design Minoru SHIRAZAKI Masako IWATA Ryutaro HIMENO PC CAD CAD
2 248 Voxel CAD Navier-Stokes v 1 + ( v ) v = p + v t Re v = 0
3 249 T 1 + ( v )T = T t RePr v p T Re Pr Reynolds Prandtl RePr METIS MPI Message Passing Interface Poisson CG B Fractional Step
4 250 Pentium4 Gigabit Ethernet Pentium GHz, RD- RAM 2 GB, Score T = T = Reynolds 120 Prandtl , ,000
5 251 T = t = Nusselt Eckert 12 Eckert et al. Present 10 er 8 Nusselt Numb θ (degree) θ Nusselt t = CAD CAD T = T = t = y = Reynolds 100 Prandtl 0.71 Prandtl , ,574 y = 0 t = 8.75 T = T = L/D = D L Reynolds Prandtl
6 252 t = z = z Reynolds 120 Prandtl 0.71 Prandtl ,740 1,207,136 y=-7.5 z=1.0 z=-1.0 x=-8.0 y x y=7.5 u=1, v=w=0, T= u=v=0, w=1, T= p=0 w= v=0 v=0 x=22.0 w=0 p=0 t = z = y = L/D = Karman t = θ =± θ = θ = Pr = Prandtl Pr = y = t = Prandtl z = 0.5 t = 120 y = 0 z = 1.0 t = 120
7 253 Temperature t = Tube Wall x Tube Wall Upstream Pr=0.71, z=-1.0 Pr=0.71, z=-0.0 Pr=0.71, z=1.0 Pr=0.14, z=-1.0 Pr=0.14, z=0.0 Pr=0.14, z=1.0 Downstream y = 0 t = Peskin Goldstein Immersed Boundary Saiki CIP Hirt VOF Quirk Berger LeVeque Forrer Berger AMR Refining Zeeuw Refining
8 254 Voxel CAE V-CAD VOF Refining Coarsening V-CAD n n = Smoothing = = 3 4 Refining Coarsening Refining Coarsening Refining Coarsening Smoothing Refining Coarsening Refining Refining Coarsening Coarsening
9 255 Re = u = v = = Refining Refining Coarsening Refining Coarsening Karman t = 5 t = 5 t = 20 t = 20 t = 80 t = 80 Refining. Refining & Coarsening.
10 256 Navier-Stokes v = + 1 ( vv) v t p Re v = 0 T ( Vf + ρcvs) Vf ( T ) t = v Vf Vs + + λ T + VQ f f + ρvq s s RePr V f V s V f Re Reynolds Pr Prandtl ρ c λ VOF A Refining [Mesh(R)] B Refining & Coarsening [Mesh A: Mesh(R) * C D in different mesh systems and experiments B: Mesh(R&C ) * C: Voxel Mesh * experiments ** Re = ± ± ± Re = ± ± ± *: Values are average of t = for Re = 200, t = for Re = 40. **: (R&C )] C [Voxel Mesh] (C D ) (C L ) Re = C D C D Refining Refining & Coarsening Voxel Mesh Re = Refining Refining & Coarsening Voxel Mesh Refining & Coarsening Re = t = Refining Refining & Coarsening Voxel Mesh A:Mesh (R) B:Mesh (R&C) C:Voxel Mesh CD CL time t = 100 Re = 200 C D C L Re = 200
11 257 Number of Cells Calculated A:Mesh (R) 2500 B:Mesh (R & C) time Re = B (1998) B (1995) B (2002) (1991) (1998) B (1998) B (1999) Trans. JSCES 1, Paper No (1999). Donea, J., Giuliani, S. & Laval, H.: Finite Element Solution of the Unsteady Navier- Stokes Equations by a Fractional Step Method, Comput. Meths. Appl. Mech. Engrg. 30 (1982)
12 A (2001) PC (2002) Eckert, E.R.G. & Soehngen, E.: Distribution of Heat-Transfer Coefficients around Circular Cylinders in Crossflow at Reynolds Numbers from 20 to 500, Trans. ASME 74 (1952) (2002) Zdravkovich, M.M.: The Effects of Interference between Circular Cylinders in Cross Flow, J. Fluids and Structures 1 (1987) Peskin, C. S.: Numerical Analysis of Blood Flow in the Heart, J. Comput. Phys. 25 (1977) Goldstein, D., Handler, R. & Sirovish, L.: Modeling a Non-Slip Flow Boundary with an External Force Field, J. Comput. Phys. 105 (1993) Saiki, E. M. & Biringene, S.: Numerical Simulation of a Cylinder in Uniform Flow: Application of a Virtual Boundary Method, J. Comput. Phys. 123 (1996) CIP (2), 7 (1999) Hirt, C. W. & Nichols, B. D.: Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comput. Phys. 39 (1981) Quirk, J. J.: An Alternative to Unstructured Grids for Computing Gas Dynamic Flows around Arbitrarily Complex Two-Dimensional Bodies, Computer Fluids 23 (1994) Berger, M. J. & LeVeque, R. J.: Stable Boundary Conditions for Cartesian Grid Calculations, J. Comput. Phys. 120 (1995) LeVeque, R. J. et al.: Two-Dimensional Front Tracking Based on High Resolution Wave Propagation Methods, J. Comput. Phys. 123 (1996) Forrer, H. & Jeltsch, R.: A Higher-Order Boundary Treatment for Cartesian-Grid Methods, J. Comput. Phys. 140 (1998) , B (1995) , B (2002) Matsunaga, N., Liu, H. & Himeno, R.: Numerical Analysis of Two-Dimensional Incompressible Viscous Flow in Orthogonal Coordinates, Information 5 (2002) , 19 (2000) Kuwahara, K. et al.: Simulation of High Reynolds Number Flows Using Multidirectional Upwind Scheme, AIAA Paper , 40 th AIAA Aerospace Sciences Meeting & Exhibit (2002). Ono, K., Tomita, N., Fujitani, K. & Himeno, R.: An Application of Voxel Modeling Approach to Prediction of Engine Cooling Flow, Society of Automotive Engineers of Japan, Spring Convention, No. 984 (1998) Berger, M. J. & Colella, P.: Local Adaptive Mesh Refinement for Shock Hydrodynamics,
13 259 J. Comput. Phys. 82 (1989) (1992) Nakahashi, K.: An Automatic Grid Generator for the Unstructured Upwind Method, AIAA 9 th Computational Fluid Dynamics Conference CP (1989) Zeeuw, D. D. & Powell, K. G.: An Adaptively Refined Cartesian Mesh Solver for the Euler Equations, J. Comput. Phys. 104 (1993) 56. Ogawa, T.: An Efficient Numerical Algorithm for the Tree-Data Based Flow Solver, Computational Fluid Dynamics 2000 (2000) V-CAD B No Refining Coarsening A No A5 (2000) 99. (2003) ,
133 1.,,, [1] [2],,,,, $[3],[4]$,,,,,,,,, [5] [6],,,,,, [7], interface,,,, Navier-Stokes, $Petr\dot{o}$v-Galerkin [8], $(,)$ $()$,,
836 1993 132-146 132 Navier-Stokes Numerical Simulations for the Navier-Stokes Equations in Incompressible Viscous Fluid Flows (Nobuyoshi Tosaka) (Kazuhiko Kakuda) SUMMARY A coupling approach of the boundary
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