A Unified Asymptotic Theory of Supersonic, Transonic, and Hypersonic Far Fields
學年 111
學期 1
出版(發表)日期 2022-11-19
作品名稱 A Unified Asymptotic Theory of Supersonic, Transonic, and Hypersonic Far Fields
著者 Lung-Jieh Yang; Chao-Kang Feng
著錄名稱、卷期、頁數 Axioms 11(11), 656
摘要 The problems of steady, inviscid, isentropic, irrotational supersonic plane flow passing a body with a small thickness ratio was solved by the linearized theory, which is a first approximation at and near the surface but fails at far fields from the body. Such a problem with far fields was solved by W.D. Hayes’ “pseudo-transonic” nonlinear theory in 1954. This far field small disturbance theory is reexamined in this study first by using asymptotic expansion theory. A systematic approach is adopted to obtain the nonlinear Burgers’ equation for supersonic far fields. We also use the similarity method to solve this boundary value problem (BVP) of the inviscid Burgers’ equation and obtain the nonlinear flow patterns, including the jump condition for the shock wave. Secondly, the transonic and hypersonic far field equations were obtained from the supersonic Burgers’ equation by stretching the coordinate in the y direction and considering an expansion of the freestream Mach number in terms of the transonic and hypersonic similarity parameters. The mathematical structures of the far fields of the supersonic, transonic, and hypersonic flows are unified to be the same. The similar far field flow patterns including the shock positions of a parabolic airfoil for the supersonic, transonic, and hypersonic flow regimes are exemplified and discussed.
關鍵字 supersonic;far field;Burgers' equation;asymptotic expansion
語言 en
ISSN 2075-1680
期刊性質 國外
收錄於 SCI Scopus
通訊作者 Lung-Jieh Yang
國別 CHE
出版型式 ,電子版

機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/123246 )