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    Title: 超音速流經凹角及拋物線型翼剖面精確解之探討
    Other Titles: A study of the exact solution of supersonic flow past a corner and parabolic-shaped airfoil
    Authors: 林志文;Lin, Chih-wen
    Contributors: 淡江大學航空太空工程學系碩士班
    馮朝剛
    Keywords: 超音速線性化理論;擾動法;變形座標法;超音速遠場與全場非線性理論;Supersonic linearized theory;Perturbation method;Method of strained coordinate;Supersonic far field and whole field nonlinear theory
    Date: 2006
    Issue Date: 2010-01-11 06:51:44 (UTC+8)
    Abstract: 由於尖角流動具奇異性,超音速微小擾動線性化理論無法正確地計算出尖角流場解,故吾人利用變形座標法重新建構出超音速尖角流動微小擾動之全場非線性漸近理論。
    另為修正超音速線性化理論,吾人利用漸近展開法建構出超音速微小擾動遠場非線性理論。當超音速流經拋物線型翼剖面時,超音速線性化理論只能求出近場流場解,而本文直接在物理平面利用超音速遠場非線性理論求出拋物線型翼剖面之完整全流場精確解(含近場、遠場及其翼前、後緣曲線震波),並驗證出超音速遠場非線性理論之流場精確解包含了線性理論之近場流場解。
    此外,利用漸近展開法建構超音速與極音速凹角壓縮流動邊界值問題,並利用相似法求出其流場解及陡變條件求出其震波位置,經與斜震波理論所得之結果比較而驗證出本文結果之正確性。另將超音速全場凹角壓縮流動邊界值問題轉換至極音速流場,其所求得之結果與直接由極音速全場邊界值問題所求得之結果完全相同,換言之,超音速凹角壓縮流動全場解統合了極音速全場解。
    Due to the singularity at the corner,the supersonic linearized theory is invalid for calculating the flow field of the corner flow.By using the method of strained coordinate,the nonlinear theory of supersonic flow in whole field of the corner flow is built.
    By using the asymptotic expansion,the supersonic far field nonlinear theory can be constructed to correct the supersonic linearized theory.
    When supersonic flow past a parabolic-shaped airfoil,the supersonic linearized theory is only valid for calculating the linear solution in the near field.The exact solution of the boundary value problem in the physical plane can be obtained by using the supersonic far field nonlinear theory,including the leading and trailing curved shocks.It can also be shown that the supersonic far field nonlinear theory includes its linear solution in the near field.
    The asymptotic solution of hypersonic flow past a corner can be derived from the asymptotic solution of supersonic whole field flow. The results of this study show that the supersonic whole field nonlinear theory constructed for the corner flow is correct and the solutions for corner flow are unified for supersonic and hypersonic small disturbance theories.
    Appears in Collections:[Graduate Institute & Department of Aerospace Engineering] Thesis

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