Simulation of steady compressible flows based on Cauchy/Riemann equations and Crocco's relation

✍ Scribed by M. Hafez; W. H. Guo

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 362 KB
• Volume: 27
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/(sici)1097-0363(199801)27:1/4<127::aid-fld654>3.0.co;2-n

✦ Synopsis

In this paper, alternative formulations of the steady Euler equations for conservation of mass, momentum and energy are adopted for the numerical simulation of compressible ¯ows with shock waves. The total enthalpy is assumed to be constant and hence an isentropic density is calculated in terms of the velocity components. Also, the x-and y-momentum equations written in conservation form are combined to yield the tangential and normal momentum equations. For smooth ¯ows the tangential momentum equation reduces to the entropy transport equation, while the normal momentum equation gives the vorticity in terms of the entropy gradient normal to the ¯ow direction (Crocco's relation). Hence the velocity components can be obtained from the continuity equation and normal momentum equation (CauchyaRiemann equations), while the entropy correction for the density is obtained from the tangential momentum equation (this correction is not needed in the isentropic ¯ow regions). The present formulation can be easily extended to handle variable total enthalpy. Preliminary results are presented for transonic and supersonic ¯ows over aerofoils and the entropy and vorticity effects are clearly identi®ed.