aerodynamic heating

heating of a body which moves through air or another gas at a high velocity. Aerodynamic heating results from the fact that air molecules flying against the body cause localized braking of the body. If a flight proceeds at a supersonic velocity, the effect of braking is primarily that of a shock wave, which is produced in front of the body. Further deceleration of air molecules occurs at the very surface of the body, in the so-called boundary layer. As a result of deceleration, the thermal energy of air molecules increases; that is, the temperature of the gas near the surface of the moving body increases. The maximum temperature to which a gas in the vicinity of the moving body can be heated is close to the so-called stagnation temperature:

T_o = T_n + v²/2C_p

where T_n is the temperature of the impacting air, ν is the velocity of the body in flight, and C_n is the specific heat capacity of the gas at constant pressure. Thus, for example, in the flight of a supersonic aircraft at three times the speed of sound (about 1 km/sec), the stagnation temperature amounts to about 400°C, whereas in the reentry of a spacecraft into the earth’s atmosphere at the first cosmic velocity (8.1 km/sec), the stagnation temperature reaches 8000°C. If in the first case for a sufficiently extended flight the temperature of the shell of the aircraft reaches such a temperature, then in the second case the surface of the spacecraft will surely disintegrate as a result of the inability of the material to withstand such high temperatures.

Heat is transferred to the moving aircraft from the region of superheated gas, resulting in aerodynamic heating. Two forms of aerodynamic heating exist—convective and radiative. Convective heating is a consequence of heat transfer from the outer “hot” part of the border layer to the surface of the body. Quantitatively, convective heat flow is defined by the equation

q_k = ∝(T_e − T)

where T_e is the equilibrium temperature (the limiting temperature to which the surface of the body would be heated if there were no energy outflow), T_w is the actual temperature of the surface, and a is the coefficient of convective heat exchange, which depends on the velocity and altitude of the aircraft, on the shape and dimensions of the body, and on other factors. The equilibrium temperature is close to the stagnation temperature. The type of dependence of the coefficient a on the enumerated parameters is determined by the conditions of flow in the boundary layer (laminar or turbulent). In the case of turbulent flow, convective heating becomes more intensive. This is bound up with the fact that besides molecular heat conduction, an essential role in the transfer of energy is played by turbulent velocity pulsations in the boundary layer.

As the aircraft velocity increases, the temperature behind the shock wave and in the boundary layer grows, as a result of which dissociation and ionization of molecules occur. This produces atoms, ions, and electrons which are diffused into a colder region—against the surface of the aircraft. At that point, the reverse reaction occurs (recombination), proceeding with the liberation of heat. This also contributes to the process of convective aerodynamic heating.

At aircraft velocities on the order of 5,000 m/sec, the temperature behind the shock wave becomes significant, and the gas begins to radiate. As a consequence of the transfer of radiant energy from the area of superheated temperatures to the surface of the aircraft, radiative heating occurs. Radiation in the ultraviolet regions of the spectrum plays an important role in radiative heating. For an aircraft in the earth’s atmosphere at a velocity below the first cosmic velocity (8.1 km/sec), radiative heating is small as compared with convective. At the second cosmic velocity (11.2 km/sec), their values become close, and at aircraft velocities of 13–15 km/sec and higher, corresponding to the speed of return to earth after flights to other planets, radiative heating makes the major contribution.

A special case of aerodynamic heating pertains to the heating of a body moving in the upper layers of the atmosphere, where the streamline condition involves free molecules; that is, the length of the free path of air molecules is commensurate with and even exceeds the dimensions of the body.

A particularly important role is played by aerodynamic heating in the entry of spaceships into the earth’s atmosphere (for example, Vostok, Voskhod, Soiuz). Spaceships neutralize aerodynamic heating through the installation of special heat-shielding systems.