The High Speed Flexible Throat Supersonic Wind Tunnel

The importance assumed in recent times by experimental supersonic wind tunnels, as well as the power required, has brought about the need for a study which would permit a comparison of the types tested and the principal theoretical plans.

In the wind tunnel arrangement under consideration, the air leaves the Laval nozzle as a free jet and is recaptured by the diffuser, which is of the convergent-divergent design. A theoretical analysis of the flow process through this type of supersonic wind tunnel is presented and the diffuser efficiency is calculated for the case of equilibrium between test chamber pressure and pressure in the nozzle exit, assuming one-dimensional, in viscous, steady flow. Using the basic equations of continuity, energy and momentum flux through a bounding surface, an exact solution of the problem is obtained, which is applicable up to Mach number infinite. One of the basic results is, that in the recapturing zone of the diffuser a transition occurs from supersonic to subsonic flow, which is followed by an acceleration in the convergent portion up to sonic velocity at the second throat. The transition is not a normal shock and involves a total pressure loss greater than that of a normal shock at the test section Mach number. A mathematical solution with supersonic velocity after the transition process has no physical existence. A comprehensive comparison of the analytical results with available experiments in supersonic wind tunnels up to Mach number 4.4 regarding diffuser efficiency and second throat area shows good agreement.

The one-dimensional flow equation for mass flow through the throat of a supersonic nozzle has been modified for use with real gas values of gamma and compressibility. Curve fits for gamma and Z and a simple iteration scheme have been developed for use with air and nitrogen over a temperature range of 300 to 6000 deg. K and a pressure of 10 to 100 atm. With this approach the sonic throat method can be used with the most recent gas tables to determine high temperature wind tunnel supply temperatures or enthalpies. (Author).