Abstract
We reconsider the transonic controversy – whether a given airfoil can exhibit a continuous range of shock-free supersonic flow. We employ the circle as our ‘airfoil’, and examine the Janzen–Rayleigh expansion in even powers of the free-stream Mach number, which we previously carried to 29 terms. In addition to expressing doubt about our previous conclusions, we introduce a promising modification of the graphical ratio test of Domb and Sykes.
Sommario.In questo lavoro si prende nuovamente in considerazione la controversia transonica, e cioè la questione se un dato profilo alare possa presentare una sequenza continua di configurazioni di flusso localmente supersonico senza onde d'urto. Quale ‘profilo alare’ consideriamo il cerchio ed esaminiamo lo sviluppo in serie di Janzen–Rayleigh secondo le potenze pari del numero di Mach asintotico, serie di cui avevamo in precedenza considerato 29 termini. Oltre ad esprimere dubbi riguardo alle nostre precedenti conclusioni, introduciamo una promettente modifica del ‘test’ del rapporto noto come grafico di Domb e Sykes.
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van Dyke, M. Long Series in Mechanics: Janzen–Rayleigh Expansion for a Circle. Meccanica 33, 517–522 (1998). https://doi.org/10.1023/A:1004324711194
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DOI: https://doi.org/10.1023/A:1004324711194