Flowfield measurements in supersonic film cooling including the effect of shock-wave interaction

A study has been made to investigate the flowfield of supersonic slot injection and its interaction with a two- dimensional shock wave. Air and helium were injected at Mach numbers of approximately 1.3 and 2.2 into an airstream of Mach 2.4. Measurements of the total pressure profiles perpendicular to the wall were made at sev- eral axial locations, the farthest being at 90 slot heights. The profiles provided details of the structure of the flow for the different injection conditions. With heated gas injection, experiments were conducted to determine the adiabatic wall temperatures and the wall static pressures. These measurements were then repeated with the impingement of two-dimensional shock waves at 60 slot heights downstream of the slot. The shock strengths were chosen to illustrate the differences between separated and attached flows. The shock strength that produced incipient separation was found to be smaller when helium was injected than when no film coolant was present. Conversely, the shock strength that produced incipient separation with air injection was slightly larger than that obtained without film cooling. develop relations for effectiveness as a function of downstream position divided by slot height x/s and the ratio of mass flux for the injected flow to that in the freestream, A, = (pw)//( pu)^. The phys- ical basis for these relations has also been motivated from simple integral analysis of the flowfield.5 The variation in the effectiveness with downstream position is accompanied by changes in flowfield structure. Some subsonic film-cooling experiments6 and other subsonic experiments involv- ing wall jets with moving freestream7 have shown that the flow- field can be divided into three regions: a potential core region, a wall-jet region, and a boundary-layer region. The potential core region, like a freejet, contains a viscous layer that emanates from the lip and ends when it meets the slot-flow boundary layer. In this region the wall temperature remains at a constant value equal to that of the injected fluid (in the case of subsonic injection) or equal to the recovery value (in the case of supersonic injection). Thus, the effectiveness in the potential core region is unity. The wall-jet region starts when the viscous layer emanating from the lip merges with the injectant boundary layer. In this region intense mixing takes place, and the wall temperature increases toward the freestream value. In the boundary-layer region, the flow then relaxes to that of a boundary layer. Consequently, the effectiveness decreases from unity near the injector and approaches zero far downstream. Thus, film-cooling flows combine different types of familiar flows: a freejet flow, a wake, a shear layer, and a bound- ary layer. The different hydrodynamic features of the flow in each region suggest using different scaling laws to predict effectiveness. This approach was attempted with some success in low-speed flow,8 where empirical data from jet flows and boundary-layer flows were applied for near and far regions, respectively. These approxi- mate flowfields were used in the energy equation to solve for the distribution in wall temperature and the film-cooling effectiveness. In these incompressible analyses, the thermodynamic properties were considered invariant within the flowfield.5 The film-cooling effectiveness in high-speed flow is often defined as T| = T -T (2)