Experimental measurement of the Prandtl–Meyer function in non-ideal supersonic flows

This paper presents the first experimental measurement of the Prandtl–Meyer function in the non-ideal compressible flow regime. Planar contoured nozzle profiles expand the flow to the supersonic regime, providing a uniform parallel flow of siloxane MM (hexamethyldisiloxane, $\textrm{C}_{6}\textrm{H}_{18}\textrm{OSi}_{2}$ ). Prandtl–Meyer expansions are then generated at sharp convex corners, for discrete flow deflection angles from 5 $^\circ$ to 30 $^\circ$ . Stagnation pressures and temperatures are measured in the settling chamber, immediately upstream of the test section, to estimate the level of non-ideality of the investigated flows, ranging from mild non-ideal conditions to dilute ideal-gas states. Non-ideal thermodynamic effects through the expansions are characterised by means of independent measurements of Mach number by schlieren visualisations, and static pressure. Experimental comparisons across different thermodynamic states confirm the role of the compressibility factor evaluated at total conditions as a similarity parameter for moderately high non-ideal flows. To extract values of the Prandtl–Meyer function from the measurements, a simplified analytical model for the Prandtl–Meyer function dependency on the Mach number is formulated. The recovered values agree with Prandtl–Meyer theory, complemented with state-of-the-art thermodynamic models, for all the examined operating conditions.