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    Please use this identifier to cite or link to this item: http://ccur.lib.ccu.edu.tw/handle/A095B0000Q/157


    Title: 初探刮刀塗佈之bow-wave分析
    Authors: 董庭維;TUNG, TING-WEI
    Contributors: 機械工程系研究所
    Keywords: 刮刀塗佈;bow-wave 流場分析;正交配置近似解;Blade coating;Bow-wave flow field analysis;Orthogonal collocation
    Date: 2018
    Issue Date: 2019-05-23 12:52:45 (UTC+8)
    Publisher: 機械工程系研究所
    Abstract: 本論文針對刮刀塗佈之刮刀前興起的bow-wave流場進行分析。在不可壓縮牛頓流體的條件下,先將Navier-Stokes equation與Continuity equation簡化為二維流場,再對其進行無因次化分析,進而提出簡化後的磨潤模型。邊界條件採用了基板不滑移邊界條件、自由面零剪應力邊界條件、自由面的表面張力之Laplace pressure、流場入口等速流條件。針對自由面隨時間變化的bow wave,則採用自由面運動學條件(kinematic moving free surface condition)。理論上,將bow wave自由面輪廓當作未知參數的情況下,對上述磨潤模型與邊界條件求解,可以將自由面下的速度場與壓力場表示為bow wave自由面輪廓的函數。再將此速度場帶入bow wave自由面運動學邊界條件,即可以得到統御bow wave自由面輪廓的偏微分方程。對此bow wave自由面輪廓的偏微分方程求解後,即完成刮刀塗佈之bow wave流場分析。實際上,我們無法將自由面下的速度場與壓力場表示為bow wave自由面輪廓的解析函數,而是必須滿足一約束方程的隱函數。因此我們利用正交配置法將此約束方程和統御bow wave自由面輪廓的偏微分方程分別降階為約束的代數方程和常微分方程。接著利用時間超前差分法(time forward difference),以疊代方式解出隨時間變化的速度場與壓力場,以及bow wave自由面輪廓。然而,根據上述刮刀塗佈的bow wave流體模型解出的理論解,在初始bow wave自由面輪廓為一斜平面時,其bow wave自由面的高度會隨著時間慢慢下降,最後降為一水平面,這與我們實驗觀察到的結果不相符。可能原因應是少了bow wave出口端與刮刀接觸的邊界條件。而此條件應由刮刀下流場來表示,因此下階段可能工作也許是將以上bow wave模型與刮刀下塗佈流體模型整合,再對所得到的聯立偏微分方程進行求解,一併求得bow wave下與刮刀下流體行為。
    In this thesis, we analyze the bow-wave flow field that arises before the blade coating. Under the condition of incompressible Newtonian fluid, the Navier-Stokes equation and Continuity equation are first simplified into a two-dimensional flow field, and then the dimensionless analysis is carried out, and then the simplified lubrication model is proposed. The boundary conditions are the substrate non-slip boundary condition, the free surface zero shear stress boundary condition, the Laplace pressure of the free surface tension, and the flow field inlet constant velocity condition. For a bow wave whose free surface changes with time, a kinematic moving free surface condition is employed.In theory, if the bow wave free surface profile is treated as an unknown parameter, the velocity field and the pressure field under the free surface can be expressed as a function of the bow wave free surface profile. Then the velocity field is brought into the bow wave free surface kinematic boundary condition, that is, the partial differential equation of the bow wave free surface contour can be obtained. After solving the partial differential equation of the bow wave free surface profile, the bow wave flow field analysis of the blade coating can be completed.In fact, we cannot express the velocity field and pressure field under the free surface as the analytic function of the bow wave free surface contour, but must satisfy the implicit function of a constraint equation. Therefore, we use the orthogonal collocation method to reduce the constraint equations and the partial differential equations of the bow wave free surface contour to the constrained algebraic equations and ordinary differential equations. Then, using the time forward difference, the velocity field and the pressure field as a function of time and the bow wave free surface profile are solved in an iterative method.However, according to the theoretical solution solved by the above-mentioned blade-coating bow wave fluid model, when the initial bow wave free surface profile is an oblique plane, the height of the bow wave free surface gradually decreases with time, and finally decreases to one horizontal plane, which is inconsistent with the results observed in our experiments. The possible reason should be that there is less boundary condition between the outlet end of the bow wave and the blade. This condition should be represented by the flow field under the blade. Therefore, the next stage may work by integrating the above bow wave model with the coating fluid model under the blade, and then solving the obtained simultaneous partial differential equation and obtaining the bow wave, fluid behavior under the wave and under the blade together.
    Appears in Collections:[機械工程學系] 學位論文

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