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.

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A high-temperature effect is crucial in cold-to-hot correlation for thrust nozzles to employ experimental data of cold flow to predict the real flight performance of hot gas. The high-temperature nozzle flow behaves beyond the classical gas dynamics and restricts the feasibility of cold-flow experiments, and it becomes more severe due to the species transformation from cold air to hot gas when safety and cost are considered. For an in-depth awareness, this work refines three fundamental issues regarding the high-temperature variable specific heat effect on nozzle flow characteristics. A comprehensive analysis is performed from theory to applications. First, the flow properties of calorically perfect gas (CPG) and thermally perfect gas (TPG) are distinguished and connected via the basic flow equations. One-dimensional flow theory is extended by the generalized stagnation–static gas functions for TPG. The unanticipated intersections within pressure are discovered, which could produce substantial perplexities in nozzle performance determinations. Second, the pros and cons of two homologous nozzle thrust coefficients are clarified on application objects, definition methods, and solution manners. It is proved that temperature has no influence on thrust coefficients for CPG, while the variable specific heat effect might induce three types of false-positive thrust coefficients, to make flow state unidentified, and further shake the baseline of nozzle performance. Third, for the aggravated variable specific heat effect in cold-to-hot correlation from air to hot gas, two methods are proposed with reliable verifications to solve this issue through introducing a novel concept of relative nozzle operating conditions.

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