Measured Pressure Distribution and Local Heat Transfer Rates for Flow Over Concave Hemispheres

Abstract

The use of parachutes for recovery of equipment from very high velocity vehicles, such as missiles, has directed attention to the need for aerodynamic and heat transfer information associated with such high drag bodies. With this application in mind, a solid concave hemisphere, positioned in a subsonic flow, was studied. Plexiglas models were placed in water and in air streams, and by using straightforward flow visualization techniques it was determined that the flow in the cup was, in essence, a separate flow region. Quantitative measurements were made of the pressure distribu­ tion and local heat transfer rate over a Reynolds number range of 6000 to 89,000. The pressure on the inner surface of the hemisphere was found to be equal to the total pressure from the stagnation point to an angle of 75 deg, dropping somewhat at greater angles. The heat transfer was found to increase monotonically from the stagnation point to the edge. The overall dimensionless heat transfer may be given in the form NuD/(ReD)^2 = 0.42. R ECENT interest in the use of parachutes for the re­ covery of equipment from high speed vehicles has di­ rected attention to the aerodynamics and heat transfer of extremely high drag bodies. At the time the present study of heat transfer to parachutes was initiated, only limited aerodynamic information was available, and no pertinent heat transfer information was found in the open literature. [Recently, information on the pressure distribution about a hemisphere with 20 per cent porosity (l)3 and heat transfer data for a fist-type parachute (2) has become available.] To obtain preliminary estimates of the time-temperature history of descending parachutes, the porosity was neglected and the convective heat transfer coefficients were estimated for an upstream facing hemisphere. The convective coeffi­ cient on the rear surface was assumed to be the same as on the rear surface of a sphere. For the front surface of the hemisphere, the potential flow solution of Schiffman and Spencer (3) yielded the velocity and pressure distribution, which, in turn, was used to determine the local convective heat transfer performance. The velocity and heat transfer results are shown in Fig. 1 and compared with established values for flow over the front side of a sphere; surprisingly, the predicted velocity and heat transfer coefficient distribu­ tion for the front face of the hemisphere is very similar to the distribution on the front face of a sphere. However, the validity of these results was brought sharply into question when preliminary pressure distribution measurements using a solid hemisphere gave markedly different behavior. As a consequence, a rather detailed aerodynamic and heat transfer investigation using concave hemispheres was initiated.