異重流於下坡加速運動之高解析度模擬

High-resolution simulation of downslope gravity currents in the acceleration phase

黃友麟(Yu-Lin Huang)

指導教授 ： 許中杰

淡江大學/工學院/水資源及環境工程學系碩士班/碩士(2015年)

https://doi.org/10.6846/TKU.2015.00278

摘要

本研究為數值模擬二維性異重流於不同角度下加速段之流況，並且在Boussinesq假設下，以數值方法解不可壓縮的 Navier-Stokes 方程式。在不受到實驗條件限制的情況下，能夠自由選取斜板角度0°≤θ≤90°，也能控制其它變因並且比較其中差異，如:雷諾數、水深比。在先前研究中Beghin et al.(1981)，他們無法準確找出最大的速度U_(f,max)發生的角度，透過數值運算，我們能準確分析在θ=40°的時候，U_(f,max)最大值會在此發生。

關鍵字

異重流 ； 密度流 ； 浮力

並列摘要

This paper is a two-dimensional numerical simulation of gravity current in the acceleration phase at different angles, and the problem have been solved by numerical methods of the incompressible Navier-Stokes equation with the Boussinesq approximation. Without the limited of experimental condition, can freely selected the plate angle 0°≤θ≤90°, and control other factor (Reynolds number, depth ratio) which can compare the difference. In a previous study (Beghin et al 1981), they can not accurately indentify the maximum U_(f,max) occurs angle. Though numerical computation, we can accurately find when θ=40° , the maximum U_(f,max) will occur in this.

並列關鍵字

gravity currents ； density currents ； buoyancy

參考文獻

2. C. Adduce, G. Sciortino, and S. Proietti, “Gravity currents produced by lock-exchanges: experiments and simulations with a two layer shallow-water model with entrainment,” J. Hydraul. Eng. 138, 111–121 (2012).

3. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, 1967).

4. R. E. Britter and P. F. Linden, “The motion of the front of a gravity current travelling down an incline,” J. Fluid Mech. 99, 531–543 (1980).

5. P. Beghin, E. J. Hopfinger, and R. E. Britter, “Gravitational convection from instantaneous sources on inclined boundaries,” J. Fluid Mech. 107, 407–422 (1981).

6. V. K. Birman, J. E. Martin, and E. Meiburg, “The non-boussinesq lock-exchange problem. Part 2. High-resolution simulations,” J. Fluid Mech. 537, 125–144 (2005).