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題名 | An Eulerian One-Point Velocity Probability Density Function Equation Mo del for Turbulent Flows=紊流一點速度機率密度函數模式 |
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作者 | 洪祖昌; 林青; 陳明華; | 書刊名 | 力學 |
卷期 | 9:3 1993.09[民82.09] |
頁次 | 頁167-179 |
分類號 | 440.137 |
關鍵詞 | 一點速度; 紊流; 密度函數; 機率; Prbability density function; Transport equation; Turbulent flows; |
語文 | 英文(English) |
中文摘要 | 本文提出一個紊流機率密度函數模式,此機率密度函數是以尤拉座標系統為基礎 所導出的一點速度機率密度函數,並被一傳輸方程式所統御,其推演步驟分為二部分,第一 部分是將 Navier-Stokes 方程式基於某些假設改寫其應力-應變關係式, 並由此得到一過 渡機率函數,再推導出初步的紊流模式,第二部分是藉由初步模式所推演的二階相關量方程 式, 和具可靠性的雷諾應力模式之比較, 而找出初步模式所未能包含的效應, 並從 Lundgren 機率密度函數方程式中, 將具有這些效應的項找出加回初步模式,其中對會導致 模式封閉問題的項,本文利用現象論雷諾應力模式的推導技巧,予以模式化而得到能夠合理 描述紊流內在機構之最後模式。 |
英文摘要 | A transport equation for the one-point velocity probability density function (pdf) of turbulence was developed in this paper. The new pdf equation was obtained by two modeling steps. A dynamic equation for the fluid elements was proposed in the first step by modeling the fluctuating part of Navier-Stokes Equation. A transition probability density function (tpdf) was extracted from the modeled dynamic equation. A Fokker-Planck type pdf equation was then obtained by gradually unfolding the pdf of a fluid element from one phase point to its neighboring point through the assistance of tpdf. However, the effects of fluctuating pressure and molecular viscous transport have not been considered in the Fokker-Planck type pdf equation. The pdf equation was therefore modified via the assistance of Lundgren's formal pdf model for ensuring that it could properly describe the pressure and molecular viscous effects. The final pdf model was found to be different from the earlier pdf models. Additionally, the properties of the present model, e.g. conservation of pdf, positive-definiteness and relaxation of inital pdf, were also examined in this paper. |
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