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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Prandtl-Glauert method ： ウィキペディア英語版 Prandtl–Glauert transformation The Prandtl–Glauert transformation is a mathematical technique which allows solving certain compressible flow problems by incompressible-flow calculation methods. It also allows applying incompressible-flow data to compressible-flow cases. == Mathematical formulation == Inviscid compressible flow over slender bodies is governed by linearized compressible small-disturbance potential equation:〔Kuethe, A.M. and Chow, C.Y., Foundations of Aerodynamics, Wiley, 1976〕 $$ \phi_ \,+\, \phi_ \,+\, \phi_ \;=\; M_\infty^2 \phi_ \;\;\;\; \mbox together with the small-disturbance flow-tangency boundary condition. $$ V_\infty \, n_x \,+\, \phi_y \, n_y \,+\, \phi_z \, n_z \;=\; 0 \;\;\;\; \mbox $M\_\backslash infty$ is the freestream Mach number, and $n\_x,\; n\_y,\; n\_z$ are the surface-normal vector components. The unknown variable is the perturbation potential $\backslash phi(x,y,z)$, and the total velocity is given by its gradient plus the freestream velocity $V\_\backslash infty$ which is assumed here to be along $x$. $$ \vec \;=\; \nabla \phi + V_\infty \hat \;=\; (V_\infty + \phi_x) \,\hat \,+\, \phi_y \,\hat \,+\, \phi_z \,\hat The above formulation is valid only if the small-disturbance approximation applies ,〔Shapiro, A.H., Compressible Fluid Flow I, Wiley, 1953〕 $$ | \nabla \phi | \ll V_\infty and in addition that there is no transonic flow, approximately stated by the requirement that the local Mach number not exceed unity. $$ \left(+ (\gamma+1) \frac \right ) M_\infty^2 \;<\; 1 The Prandtl-Glauert (PG) transformation uses the Prandtl-Glauert Factor $\backslash beta\; \backslash equiv\; \backslash sqrt$. It consists of scaling down all y and z dimensions and angle of attack by the factor of $\backslash beta$, and the potential by $\backslash beta^2$. $$ \begin \bar &=& x \\ \bar &=& \beta y \\ \bar &=& \beta z \\ \bar &=& \beta \alpha \\ \bar &=& \beta^2 \phi \end The small-disturbance potential equation then transforms to the Laplace equation, $$ \bar_} \,+\, \bar_} \,+\, \bar_} \;=\; 0 \;\;\;\; \mbox and the flow-tangency boundary condition retains the same form. $$ V_\infty \, \bar_____ This is the incompressible potential-flow problem about the transformed geometry with surface normal vector components $\backslash bar\_\_\_$ or its gradient components $\backslash bar\_\_\_\; \backslash ;=\backslash ;$ -\frac \frac}} which is known as Göthert's Rule 〔Göthert, B.H. Plane and Three-Dimensional Flow at High Subsonic Speeds (Extension of the Prandtl Rule). NACA TM 1105, 1946.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Prandtl–Glauert transformation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.