Theoretical and Experimental Modeling of Real Projectile Flight Heating

Abstract

A projectile with a conical nose e ying at Mach number M1 >1 in the atmosphere develops a bow shock around its nose by which the incoming aire ow is turned parallel to the projectile surface. Across the shock wave, the air is compressed,heated,andacceleratedfromupstreamairpressure p1 ,upstreamairtemperature T1 ,andu1 ,which is equal to the projectile e ight velocity up, to the downstream parameters pe, Te, and ue. Consequently, a heat e ux develops from the hot aire ow along the projectile surface which is directed into the projectile material. This heat e ux causes a temperature increasethat depends on the projectile speed, the e ight time, thestructure of the surface material, and its geometry. A boundary-layer model is applied, and the gas heat e ux into the projectile nose cone is analytically determined. To predict the heating of the solid projectile cone, an analytical solution, coming from the heat conduction equation, is used to obtain thesurface temperature distribution. Experimentally theprojectile e ight in the atmosphere is modeled in a worldwide unique aerothermoballistic high-pressure facility built at the French‐German Research Instituteof Saint-Louis, where the heating during several seconds of atmospheric e ight is duplicated with a e ight in compressed gas resulting in the same heat e ux for a e ight time of some milliseconds. In this facility the cone surface temperature is measured by detecting the intensity of the infrared emission coming from the cone surface.