以蒙地卡羅法模擬次音速流通過垂直平板的現象

Abstract

Vortex-shedding屬於流體力學中的外流場問題，產生的原因是當流體通過不同形狀的物體時，使物體的尾流產生週期性的剝離的渦流現象，此現象就稱vortex-shedding。常發現在鳥在空中飛行、車子在路面上行走、橋的橋墩以及氣流受到島嶼影響等。在過去也有很多科學家做過相關的研究，但是大多數的研究vortex-shedding都是在連續流及不可壓縮流流場的範圍，而少數針對稀薄流體區域做研究，主要由於在稀薄流體區做實驗以及在非穩態流場模擬也較為困難。 本文的目的是使用直接模擬蒙地卡羅法及結構性格網來模擬次音速流體通過垂直平板，研究vortex-shedding現象。我們使用time-averaging with temporal variable time step平均取樣時間方法的模擬，這種方法稱為TVTS。 利用不同Unsteady time average with temporal variable time step (TVTS)、particle per cell、number of temporal node、domain size以及Reynolds number等這些參數，觀察垂直平板尾流層產生vortex-shedding的變化情形。 由結果顯示TVTS=100和150設定條件下，尾流層都會發生擺動的現象，而TVTS=100的時候，尾流層產生明顯vortex-shedding。當固定TVTS=100，模擬不同Reynolds number，則會發生Strouhal number和aerodynamics coefficient會隨著Reynolds number增加。

The phenomena of vortex shedding associated with the subsonic external flow problems in different length scales are visible everywhere in fluid dynamics. For example, aviation of fruit flies and birds, driving car in the wind, flowing river through piers under a bridge, and the air current interaction with an island and so forth. A large number of experimental and numerical studies have been reported on the vortex-shedding flows in the continuum limit, while there have been very few studies focusing on similar flows in the rarefied gas regime. Major obstacle of the investigation in rarefied regime mostly came from the difficulties of experiments and also numerical simulations for unsteady flows in this regime. In the present paper, a general-purpose Parallel Direct Simulation Monte Carlo Code, named PDSC, is used to simulate the subsonic flow pasts a 2D vertical plate for studying the vortex-shedding phenomena. An unsteady time-averaging with temporal variable time step sampling method, called TVTS. Parametric studies, including temporal variable time step (TVTS) factor, particles per cell, number of temporal nodes, domain size and Reynolds number, are conducted to obtain the Strouhal number and aerodynamics coefficients. The results are compared to experimental data in the continuum region and simulations from the literature wherever they are available. Results of TVTS=100 and 150 has oscillation phenomenon, but results of TVTS=100 has results clear vortex shedding. Both the Strouhal number (0.174, 0.188, and 0.21) and the average drag coefficients (1.05, 1.14, 1.35, and 1.4) are increased with respect to Re=73, 126, 287 and 412 respectively, expect that the Strouhal value of Re=73 case is unavailable because the vortex is steady.