外裝型凸緣氣罩的流場與粒子軌跡模擬

A Simulation of the Flow Field and Particle Trajectories around Exterior Hoods

本文主要在於介紹 HOODTRJ 氣罩捕集模擬程式的基本功能，並探討程式對氣罩附近流場以及粒子在其中運動的計算模擬方式。此程式結合勢流理論、氣膠動力以及電腦圖學等技術，透過個人電腦以動畫形態顯示外裝型無限凸緣氣罩對給定粒子發生源的捕集模擬計算結果。程式的計算結果可以粒子軌跡、捕集區範圍、流線與風速向量等方式顯示。程式所考慮與動力相關的因素包括氣罩風量、氣罩開口形狀及大小、氣罩傾斜角、側風強度、發生源形狀及大小、發生源位置、粒子數目、粒子動力相關參數（密度、粒徑、擴散係數、釋放方向與釋放初速）等。程式對流場與粒子軌跡計算模擬的基本方法為：先計算抽氣開口所產生的風速，此風速加上給定的側風得流場風速，再配合粒子運動方程式即可得流場中給定起始位置與釋放速度的粒子軌跡。運用不同的參數設定以及假設，程式所顯示的粒子可用以模擬氣膠微粒或氣體分子。在計算抽氣風速時，程式考慮圓形與矩形兩種開口。對於矩形開口流場，使用既有的理論解直接計算；對於圓形開口流場，則以內差近似方法配合碎形積分法計算，使計算速度與準確性均得以兼顧。流場中粒子軌跡則是使用 Runge-Kutta 四階法配合以亂數模擬的擴散模式計算。此外，藉助程式的圖形顯示，本文尚對計算所使用時間間距設定進行討論。

This paper presents the basic features of the hood capture simulation program, HOODTRJ, and the simulations of the flow field and particulate motion in front of the hoods. Incorporating the potential flow theory, aerosol dynamics and computer graphics, the program shows the capture performance of the exterior infinite-flanged hood by animation. The results can be displayed in form of trajectories, capture zone, streamlines and velocity vectors. The parameters considered in the program include hood flow rate, opening geometry of the hood, hood orientation, cross-draft, particulate source geometry, source position, particulate number, and those related to the particle dynamics(density, diameter, diffusion coefficient, release velocity)., …, and so on. In order to obtain the particle trajectories, the program calculates the flow velocity generated by a sucking opening first. The flow velocity is determined by superposing the cross-draft on the flow resulting from sucking. The particle trajectory for a given initial position and release velocity then is calculated by solving the particle motion equation based on the aerosol dynamics. With appropriate parameters and assumptions, the particle trajectory displayed by the program can simulate the dispersion of either aerosol particles or gases. The program considers both rectangular and circular openings of the hoods. For the rectangular openings, the program uses the exact solution to calculate the flow velocity generated by the sucking opening. For the circular openings, the program uses a new interpolation scheme associated with the fractal integration, which results in an excellent compromise on both speed and accuracy. The particulate trajectories are computed by Runge- Kutta 4th order method associated with the diffusion model simulated by random number generation. With the help of the graphic display, the appropriate time step used by the trajectory computation is also discussed.