使用平行化直接模擬蒙地卡羅法初步模擬在稀薄流體範圍時瞬間啟動的空穴超音速流場

Abstract

摘要

空穴流場是ㄧ個很基本的流體力學問題，在過去也有很多人做過相關的研究。但是大多數人都是討論連續及不可壓縮流流場，較少數人針對連續流到稀薄流體區的流場作研究。因此我們對此做ㄧ有系列的探討。 本文的目的為使用直接模擬蒙地卡羅法及非結構性網格來模擬從自由分子流到接近連體流體範圍瞬間啟動的空穴超音速流場。傳統上在模擬稀薄區中，非穩態流場較少人研究，也較困難。我們先運用非穩態的時間平均取樣方法來模擬，但發現有大量scatter現象。因而我們運用DSMC-DREAM (Rapid Ensembled Average Method) [Cave et al., 2007] 可運用在減少統計時產生的scatter時間平均的DSMC資料，也為了確保能在較鄰近的分子發生碰撞，運用transient sub-cells在非結構性網格功能，使得同時降低計算負荷及記憶體使用量。 模擬且比較在quasi-1D 不可壓縮 Couette 流體分析資料來驗證程式。結果發現DREAM能夠大量地減低在使用非穩態DSMC技術時產生的統計scatter。最後，模擬非穩態驅動空穴流場條件包含上板驅動速度馬赫數4和Knudsen數(與平均自由路徑和空穴大小有關)由10到0.0033。 結果顯示其速度滑動現象會在Knudsen 數的影響中表現的很明顯。在Knudsen 數0.1， 0.01和0.0033的渦流幾何中心隨時間改變後會朝向幾何中心; 但Knudsen 數10和1則往上板移動。而由於本文為初步模擬在非穩態的流場現象，所以先模擬在高馬赫4的流體。然而模擬此空穴超音速流場仍然有些統計樣本造成的scatter誤差現象。所以在未來會使用temporal variable time step來減少計算時間，及同時增加DSMC-DREAM (Rapid Ensembled Average Method) [Cave et al., 2007] 循環次數，來大大減低此scatter誤差現象。

Abstract

The driven cavity flow is one of the fundamental problems in the fluid dynamics. The kind of topic establishes the foundation in computational fluid dynamics and its simple geometry. However they have been completely studied in the literature, most of researches focused on incompressible or continuum compressible regime. Very few researches have been done in the rarefied and near continuum regimes. It may serve as the benchmarking problem in these regimes. Therefore, this thesis reports the simulation of instantaneously started supersonic driven cavity flows from the free-molecular to near-continuum regime using the parallel direct Monte Carlo method using unstructured grids. A special technique called DSMC-DREAM (Rapid Ensembled Average Method) was applied to reduce the statistical scatter of time-averaging DSMC data. To ensure nearest-neighbor collision, transient sub-cells are also implemented on an unstructured grid. Implementation was verified by comparing the simulation results of a quasi-1D incompressible Couette flow with the analytical data. Result shows that the DREAM can greatly reduce the statistical scatter with an acceptable runtime for unsteady flow simulation using DSMC technique. Simulation conditions for the unsteady top driven cavity flows include Ma=4 of the speed of top driven plate and Kn=10-0.0033 based on the mean free path of wall temperature and size of the cavity. Results show that the velocity slips along the solid walls increase with increase Knudsen number at the same Mach number (M=4). Center of the primary vortex during one time moves towards the geometric center with Knudsen number is 0.1, 0.01 and 0.0033. Other cases move toward the upper wall with Knudsen number is 10 and 1.Because the thesis is preliminary study on unsteady flow, thus we focus on supersonic flow (M=4). There are scatter on simulation supersonic cavity flow; hence it will use temporal variable time step to induce computational cost and increase DSMC-DREAM (Rapid Ensembled Average Method) run times. Further, the imperfection of results are on Knudsen number 10 (free molecular flow), 1 and 0.1 because of the mean free path larger than characteristic length. Thus, particles could collisionless of a square driven cavity.