本文主要針對一具壁面噴流之背向階梯高溫紊流場的暫態冷卻效應作數值模擬，並與Yang et al.(2000) 所發表的實驗結果作比較。紊流統御方程式乃是以控制體積法為基礎，配合有限差分法及冪次法則來離散成差分方程式。對於紊流的行為與結構則是以 紊流模式配合牆函數來描述。動量方程式的速度及壓力則以SIMPLE法來解出。至於格點設計，則採用不等間距的交錯式格點系統。
　　本文參數為進口速度(U0 = 10、20、30 m/s)，進口溫度(T0 = 150、200、300℃)及壁面噴流量(Q = 0.15、0.25、0.35 m3/min)。對於固定階梯高度 (H = 15mm)分別作暫態及穩態的溫度及熱傳分析。流場的數值模擬結果顯示，隨著壁面噴流量的增大，再接觸點長度Xr隨之減少，與Yang et al.(2000)所發表的實驗值誤差約在7%~10%。在迴流區內，因為垂直均勻壁面噴流的存在，使得區域內的水平速度減弱，垂直速度增加。紊流特性方面，紊流強度與雷諾剪應力在各個截面的最大值大約發生在剪流層附近或速度梯度大的位置。在迴流區內，紊流強度隨著壁面噴流量增加而減少，在再接觸點下游處，紊流強度反而隨噴流量增加而增強。
　　在暫態流場分析中，在相同的溫度下，較高的壁面噴流展現出較快且較深的暫態溫度變化曲線。在壁面噴流主導的流場區域中，不同噴流量的暫態溫度變化曲線有相似性。在暫態初期，壁面噴流冷空氣主導流場，低溫區擴展至整個下壁面，隨著時間增加，流場逐漸改變為高溫空氣主導，低溫區逐漸往階梯角落縮小，但迴流區依然由壁面噴流主導，只出現些微的變化。在穩態流場分析中，隨著壁面噴流量增加，階梯角落處的低溫區會擴大，入口溫度增加會壓抑壁面噴流對流場的冷卻範圍。

　　This study presents the numerical simulation of transient mixing process of the high temperature turbulent flow behind the backstep with low temperature wall mass injection, and compares with the experimental results of Yang et al.(2000). The turbulent governing equations are solved by a Control-Volume-based finite-difference method with power-law scheme and the well know turbulence model and its associate wall function to describe the turbulent structure. The velocity and pressure terms of momentum equations are solved by SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) method. An orthogonal non-uniform staggered grids are used for the establishment of mesh grids.
　　The parameters studied include inlet velocity (U0 = 10、20、30 m/s), inlet temperature (T0 = 150、200、300℃), and the wall injection rate(Q = 0.15、0.25、0.35 m3/min). Heat transfer and temperature analysis for steady and unsteady state with the constant height of the step. The flow field numerical calculations indicate that reattachment length Xr becomes shorter as the wall injection rate increases. The error of the reattachment length is about 7%~10% comparing with the experimental results of Yang et al.(2000). In recirculation zone, the horizontal velocity decreases and the vertical velocity increases because of the uniform wall injection. The turbulent characteristics show that the maximum turbulent intensity and Reynolds stress on any section is happened near the shear layer or the larger gradient of the velocity. In recirculaton zone, the turbulent intensity decreases as the wall injection increases. Downstream the reattachment point, the turbulent intensity increases as the wall injection increases.
　　The analysis of the unsteady flow, the larger wall injection displays the faster and deeper change of the transient temperature curve in the same temperature. In the flow zone dominating by wall injection, the change of the transient temperature curves are similar with different wall injections. The initial stage of transient state, the cold air of the wall injection dominates the flow field, and the low temperature zone spreads to the lower wall. As the time increases, the high temperature air dominates the flow field, and the low temperature area becomes small, but the wall injection also dominates the recirculation zone that appears smaller change. In the steady state, the low temperature area spreads around the corner of the step becomes larger as the wall injection increases. Increasing the mainstream inlet temperature suppresses the cooling range of the wall injection.

Abu-Hijleh, B. A/K, “Heat Transfer from a 2D Backward Facing Step with Isotropic Porous Floor Segments”, Int. J. Heat Mass Transfer, Vol.43, 2727-2737, 2000.
Abbott, D. E., and Kline, S. J., “Experimental Investigation of a Subsonic Turbulent Flow over Single and Double Backward Facing Steps”, ASME Journal of Basic Engineering, Vol.84, 317, 1962.
Baek, B. J., Armaly, B. F., and Chan, T. S., “Measurements in Buoyancy- Assisting Separated Flow Behind a Vertical Backward-Facing Step”, J. Heat Transfer, Vol.115, 403-408, 1993.
Bradshaw, P. F., and Wong, Y. F., “The Reattachment and Relaxation of a Turbulent Shear Layer”, J. Fluid Mechanics, Vol.52, 113-135, 1972.
Caton, J. A., “The Use of a Simple Heat Transfer Model for Separted Flows in Tube”, J. Heat Transfer, Vol.105, 928-931, 1983.
Chun, K. B., and Sung, H. J., “Visualization of a Locally-Forced Separated Flow over a Backward-Facing Step”, Experiments in Fluids, Vol.25, 133-142, 1998.
Cheng, Y. C., Hwang, G. J., and Ng, M. L., “Developing Laminar Flow and Heat Transfer in a Rectangular Duct with One-Walled Injection and Suction”, Int. J. Heat Mass Transfer, Vol.37, 2601-2613, 1994.
De Brederode, V., and Bradshaw, P., “Three-Dimensional Flow in Normally Two-Dimensional Separation Bubbles：I. Flow Behind a Rearward-Facing Step”, Aeronautical Report, 72-19, Imperial College, 1972.
Emery, A., “Heat Transfer Downstream of a Step in a Plate”, M. S. thesis, University of California at Berkeley, 1958.
Filetti, E. G., and Kays, W. M., “Heat Transfer in Separated, Reattached, and Redevelopment Regions Behind a Double Step at Entrance to a FLAT Duct”, J. Heat Transfer, Vol.88, 131-136, 1967.
Eaton, J. K., and Johnston, J. P., “A Review of Research on Subsonic Turbulent Flow Reattachment”, AIAAJ, Vol.19, 1093-1100, 1981.
Heenan, A. F., and Morrison, J. F., “Passive Control of Backstep Flow”, Experimental Thermal and Fluid Science, Vol.16, 122-132, 1998.
Kuehn, D. M., “Effects of Adverse Pressure Gradient on the Incom- pressible Reattaching Flow over a Rearward-Facing Step”, AIAA Joural, Vol.18, 343-344, 1980.
Kitamura, K., and Kimura, F., “Heat Transfer and Fluid Flow of Natural Convection Adjacent to Upward-facing Horizontal Plates”, Int. J. Heat Mass Transfer, Vol.38, 3149-3159, 1993.
Kondoh, T., Nagano, Y., and Tsuji, T., “Computational Study of Laminar Heat Transfer Downstream of a Backward-Facing Step”, Int. J. Heat Mass Transfer, Vol.36, 577-591, 1993.
Lin, J. T., Armaly, B. F., and Chen, T. S., “Mixed Convection in Buoyancy–Assisting, Vertical Backward-Facing Step Flow”, Int. J. Heat Transfer, Vol.33-10, 2121-2132, 1990.
Martin, A. R., Saltiel, C., and Shyy, W., “Heat Transfer Enhancement with Porous Inserts in Recirculating Flows”, J. Heat Transfer, Vol.120, 458-467, 1998.
Olson, R. M., and Eckert, E. R. G., “Experimental Studies of Turbulent Flow in a Porous Circular Tube with Uniform Fluid Injection through the Tube Wall”, J. Applied Mechanics, Vol.33, 7-17, 1966.
Papadolos, G., and Otugen, M. V., “Separating and Reattaching Flow Structure in a Sunddenly Expansion Rectangular Duct”, J. Fluids Engineering, Vol.117, 17-23, 1995.
Pitz, R. W., and Daily, W., ”Combustion in a Turbulent Mixing Layer Formed at a Rearward-Facing Step”, AIAAJ, Vol.21, 1565-1570, 1983.
Richardson, J., de Groot, W. A., Jagoda, J. I., Waiterick, R. E., Hubbartt, J. E., and Strahle, E. C., “Solid Fuel Ramjet Simulators Results：Experimental and Analysis in Cold Flow”, J. Propulsion Power, Vol.24, 1956-1963, 1985.
Soong, C. Y., and Hsueh, W. C., “ Mixed Convection in a Suddenly- Expanded Channel with Effects of Cold Fluid Injection”, Int. J. Heat Mass Transfer, Vol.36, 1477-1484, 1993.
Seki, N., Fukusako, S., and Hirate, T., “Turbulent Fluctuations and Heat Transfer for Separated Flow Associated with a Double Step at Entrance to an Enlarged Flat Duct”, J. Heat Transfer, Vol.98, 588-593, 1976.
Seban, R. A., Emery, A., and Levy, A., “Heat Transfer to Separated and Reattached Subsonic Turbulent Flows Obtained Downstream of a Surface Step”, Journal of the Aerospace Sciences, Vol.26-12, 809-814, 1959.
Vogel, J. C., and Eaton, J. K., “Combined heat Transfer and Fluid Dynamic Measurements Downstream of a Backward-Facing Step”, J. Heat Transfer, Vol.107, 922-929, 1985.
Xie, C., and Hartnett, J. P., “Influence of Variable Viscosity of mineral oil on Laminar Heat Transfer in a 2:1 Rectangular Duct”, Vol.35, 641-648, 1992.
Yang, J. T., Tsai, B. B., and Tsai, G. L., “Separated-Reattaching Flow over a Backstep with Uniform Normal Mass Bleed”, J. Fluid Eng., Vol.116, 29-35, 1994.
Yang, J. T., and Tsai, C. H., “High Temperature Heat Transfer of Separated Flow over a Sudden-Expansion with Bass Mass Injection”, Int. J. Heat Mass Transfer, Vol.39, 2293-2301, 1996.
Yang, J. T., Ma, W. J., and Tsai, C. H., “Transient Effect of Micro-Jet Cooling on a Flat in Separated Flow Field”, Proceedings of the Eleventh International Symposium on Transport Phenomena, Hsinchu, Taiwan, R.O.C., November 29-December 3, 278-282, 1998.
Yang, J. J., Gu, J. D., and Ma, W. J., “Transient Cooling Effect by Wall Mass Injection After Backstep in High Temperature Flow Field”, Int. J. Heat and Mass Transfer 00, 1-13, 2000.
Yang, J. T., Wu, Y. Y., and Din, S. J., “Ignition Transient of a Polymethylmethacrylate Slab in a Sudden-Expansion Combustor”, Combust. Flame, Vol.98, 300-308, 1994.
Yang, Y. T., and Kuo, C. L., “Numerical Study of a Backward-Facing Step with Uniform Normal Mass Bleed”, Int. J. Heat Mass Transfer, Vol.44-7, 1677-1686, 1997.
Yogesh, G. P., and Raghunandan, B. N., “Flow Structure and Heat Transfer Characteristics Behind a Diaphragm in the Presence of a Diffusion Flame”, Int. J. Heat Mass Transfer, Vol.32, 19-28, 1989.
Zvuloni, R., Levy, Y., and Gany, A., “Investigation of a Small Solid Fuel Ramjet Combustor”, J. Propulsion Power, Vol.5, 269-275, 1989.