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標題: | 在單軸向壓縮下降伏材料運動型態之理論推導 Methodology to Describe the Motion of a Yield-Type Material Under Uniaxial Compression |
作者: | Shan-Yu Lin 林珊羽 |
指導教授: | 楊馥菱(Fu-Ling Yang) |
關鍵字: | 單軸壓縮,賓漢流體,降伏相變,格林函數, Uni-axial compression (squeeze flow),Bingham plastic model,phase transition upon yielding,Green’s function, |
出版年 : | 2020 |
學位: | 碩士 |
摘要: | 本論文針對不可壓縮賓漢材料受單軸等速壓縮、由固態至降伏流動過程的進行理論分析,不同於純流體行為,當我們將類固態的行為代入Navier動量方程式後將得到一四階非線性偏微分方程,其解與雷諾數、賓漢數以及無因次壓縮率有關。跳脫傳統薄層流動的化簡,我們針對固轉流相變化過程小剪切率的特性,以其與觀察時間比值來之定義微擾小參數,得以線性化此四階偏微分方程式,進而得到以級數展開之動量方程式。針對第零階方程式,我們分解成stream function—vorticity function的模式,針對動邊界無速度滑移、自由液面無剪切降伏的邊界條件,搭配分離變數與格林函數求得解析解,更重要的是,此解提供我們一個手段,可反解等速壓縮過程中時變流場所發展之邊界旋度條件。 This thesis presents a theoretical framework on which an analytic solution to a Bingham material under uniaxial compression may be developed to describe how a solid bulk yields and deforms to a fluid flow. Taking into account of the solid-like behavior, the Navier momentum equation becomes a fourth-order nonlinear partial differential equation controlled by the Reynolds number, the Bingham number, and a characteristic compression time scale. We bypass the thin lubrication layer approximation but linearize the problem by stretching the time scale with respect to the small shear strain rate around the yielding point. We define a small parameter by the ratio of the shear time to the observation time scale to manipulate the momentum equation in expansion to different orders. The first order equation is solved via the stream function-vorticity formulation using the methods of separation of variables and Green’s function. Most importantly, this framework allows us to determine specifically a flow-dependent vorticity boundary condition in view of the no-slip boundary condition. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/20965 |
DOI: | 10.6342/NTU202004011 |
全文授權: | 未授權 |
顯示於系所單位: | 機械工程學系 |
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