Analytical solution of supersonic axisymmetric flow around a sharp convex corner

Abstract

Supersonic axisymmetric expansion flow is a typical and fundamental issue in gas dynamics. It plays a vital role in the high-speed external and internal flow fields regarding the contour design and performance evaluation of supersonic/hypersonic vehicles and their propulsion systems. The supersonic two-dimensional (2D) planar expansion flow is dominated by the well-known Prandtl–Meyer (P–M) theory. However, no similar explicit relation exists for the supersonic axisymmetric expansion flow, and only the computational fluid dynamics results could be employed at present. Therefore, this work focuses on developing the analytical solution of supersonic axisymmetric flow around a sharp convex corner on the basis of the generic gasdynamic functions in a newly established coordinate system for addressing the aforementioned issue. Theoretical derivations and numerical results prove that the flow deflection angle and Mach number in supersonic axisymmetric flow around a sharp convex corner obey the identical law to the 2D planar situation, that is, the P–M theory, while the local axisymmetric expansion fan is not the simple wave flow despite the conical flow. Meanwhile, the method of characteristics is employed to further explicate the intrinsic connection and difference between the 2D and axisymmetric sharp convex corner flow. The equivalence of sharp corner and curved surface flows with the identical deflection angle is discussed, and three limitations of the proposed analytical solution are clarified.

Transonic flow field in critical flow Venturi nozzle

“…The mass flow rate computed with the medium mesh differs from the one predicted by the ISO 9300 standard by 0.42 % and with the fine mesh by 3.81 %. 2 These results can be taken as satisfactory.…”

“…The Mach number increases from a value only slightly higher than unity (sonic line is positioned near the end of the throat) to a value predicted by the Prandtl-Meyer function. It was recently shown in [2] that this function is valid even for an axisymmetrical case. This value is reached only in the vicinity of the sharp corner, where the expansion can be considered as a local simple wave.…”