本研究應用大尺度渦流法(LES)並結合拉氏顆粒追蹤法(Lagrangian Particle Tracking)來模擬垂直渠道紊流場，於其中分別載具質量比(mass loading)為0.2的玻璃及銅顆粒。在連續相的計算上採用Smagorinsky model來模式次格點尺度的貢獻；在顆粒運動部分，則考慮four-way coupling並在顆粒與壁面碰撞的部分加入兩種壁面粗糙度模式，分別為Tsuji et al. (1987)所提出的virtual wall model，及Sommerfeld & Huber (1999)考慮撞擊角度影響所發表之壁面粗糙度模式。此外，本文也藉由改變彈性恢復係數(coefficient of restitution)及摩擦係數(coefficient of friction)來探討對顆粒運動與紊流流場的影響。
在計算中考慮壁面粗糙度會加強垂直壁面的顆粒擾動速度，因而增進垂直壁面方向顆粒混合的能力，使得顆粒在流動方向的平均速度分佈曲線趨於平坦。由於壁面粗糙度的存在，改變了顆粒運動行為，最終也將會影響氣相紊流場。此外，較大的彈性恢復係數可以產生類似壁面粗糙度的效果。在本研究中也發現計算的結果對摩擦係數並不敏感。

Particle-laden turbulent channel flow, loaded with glass and copper particles, respectively, at a mass flow ratio of 0.2, is studied numerically by the large eddy simulation (LES) coupled with Lagrangian particle tracking (LPT) method. The Smagorinsky model is employed to account for the contribution of subgrid scales. The particle motion is calculated using the four-way coupling approach. The effects of wall roughness on particle motion and turbulence modulation are investigated by incorporating two wall roughness models into the simulation. One is the virtual wall model proposed by Tsuji et al. (1987), while the other is the model developed by Sommerfeld and Huber (1999) which takes the impact angle and the particle size into consideration. In addition, sensitivities of the solution to the coefficient of restitution and coefficient of friction are studied.
It is found that consideration of the wall roughness effect in the computations strengthens the wall-normal particle velocity fluctuations. As a result, the wall-normal particle mixing is enhanced and the profiles of the streamwise mean particle velocity becomes flattened. Due to the significant change of the particle velocity, the carrier-phase turbulence intensity is modified by the present of wall roughness. It is also shown that, use of higher value of the coefficient of restitution in the computation results in a similar effect as what wall roughness does on particle motion. Additionally, variation of the value of the coefficient of friction is found to be less significant in the investigated particle-laden flows.

Chorin, A. J. 1969 A numerical method for solving incompressible viscous flow
problems, J. Comp. Phys., 2, 12.
Crowe, C. T., Sommerfeld, M., & Tsuji, Y. 1998 Multiphase Flows with Droplets and
Particles. CRC Press.
Dennis, S. C. R. Singh, S. N. & Ingham, D. B. 1980 The steady flow due to a
rotating sphere at low and moderate Reynolds numbers. J. Fluid. Mech. 101,
257-279.Eaton, J. K. & Fessler, J. R. 1994 Preferential concentration of
particles by turbulence. Int. J. Multiphase Flow, 20, 169-209.
Fessler, J. R., Kulick J. D. & Eaton, J. K. 1994 Preferential concentration of
heavy particles in a turbulent channel flow. Phys. Fluids, 6, 3742-3749.
Fukagata, K., Zahrai, S. Kondo, S. & Bark, F. H 2001a Anomalous velocity
fluctuation in particulate turbulent channel flow. Int. J. Multiphase Flow.,
27, 701-719.
Fukagata, K. Zahrai, S. Kondo, S. & Bark, F. H., Kondo, S. 2001b Effects of wall
roughness in a gas-particle turbulent vertical channel flow. In Proceedings of
the 2nd Int. Symp. on Turbulence and Shear Flow Phenomena, KTH, Stockholm, II,
117-122.
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible
Navier-Stokes equations. J. Comp. Phys., 59, 308-323.
Kulick, J. D., Fessler, J. R. & Eaton, J. K. 1994 Particle response and
turbulence modification in fully developed channel flow. J. Fluid. Mech. 277,
109-134.
Kussin, J. & Sommerfeld, M. 2002 Experimental studies on particle behaviour and
turbulence modification in horizontal channel flow with different wall
roughness. Experiments in Fluids, 25, 143-159.
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in
non-uniform flow. Phys. Fluids, 26, 883-889.
Mei, R., 1992, An approximate expression for the shear lift force on a spherical
particle at finite Reynolds numbers, Int. J. Multiphase Flow, 18. 145-147.
Rouson, D. W. & Eaton J. K. 1994 Direct numerical simulation of turbulent channel
flow with immersed particles. In Gas-Solid Flows FED-Vol. 185, 47-57. ASME.
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid
Mech., 22, 385-400.
Saffman, P. G. 1968 Corrigendum to “The lift on a small sphere in a slow shear
flow”. J. Fluid Mech., 31, 624.
Smagorinsky, J. 1963 General circulation experiments with the primitive
equations. I. The basic experiment. Monthly Weather Review, 91, 99-164.
Sommerfeld, M. 1995 The importance of inter-particle collisions in horizontal
gas-solid channel flows. In Gas-Solid Flows. FED-Vol. 228, 335-345. ASME
Sommerfeld, M. & Huber, N. 1999 Experimental analysis and modeling of
particle-wall collisions, Int. J. Multiphase flow, 25, 1457-1489.
Takagi, H., 1977 Viscous flow induced by slow rotating of a sphere. J. Phys. Soc.
Jpn. 42, 319-325.
Tsuji, Y. 1991 Review: Turbulence modification in fluid-solid flows. In Gas-Solid
Flows (ed. D. E. Stock et al.) ASME-FED 110, 1-6.
Tsuji, Y., Morikawa, Y. Tanaka, T., Nakatsukasa, N. & Nakatani, M. 1987 Numerical
simulation of pneumatic conveying in a horizontal pipe. Int. J. Multiphase-flow, 13, 671-684.
Van Driest, E. P. 1956 On the turbulent flow near a wall. J. Aero. Sci. 23,
1007-1010.
Wang, Q. & Squreis, K. D. 1996 Large eddy simulation of particle-laden turbulent
channel flow. Phys. Fluids, 8, 1207-1223.
Yamamoto, Y., Potthoff, M., Tanaka, T., Kajishima, T. & Tsuji Y. 2001 Large-eddy
simulation of turbulent gas-particle flow in a vertical channel; effect of
considering inter-particle collisions. J. Fluid Mech., 442, 303-334.