## 4. The importance of the stagnation temperatureLet us now consider the heating due to the conversion of kinetic energy of the flow into thermal energy, when the gas is brought to rest (in the boundary layer). This process can be described in terms of a steady flow energy in an adiabatic process: where and
are the stagnation and free stream
enthalpy of the fluid, respectively, and
is the free stream speed. Note that
the choice of the reference frame is not important here: if we
consider a frame centered on the body, the fluid will move, and
where is the specific heat at constant pressure. During the atmospheric path, as the Mach number is large, the meteoroid's speed is close to the maximum value corresponding to the stagnation temperature. Changes in the stream properties are mainly due to changes in the stagnation temperature , which is a direct measure of the amount of heat transfer. This argument stresses the importance of the stagnation temperature in hypersonic flow, since it is related to the maximum speed of the stream, which in turn is close to the speed of the cosmic body. According to Shapiro (1954), the relationship between stagnation temperature and maximum speed of the stream can be expressed in the following way: where is the ratio of specific heats. By means of the equation of state for the air, can be expressed as a function of the stagnation pressure and density: In order to obtain a condition for the meteoroid breakup, the
stagnation pressure must be set
equal to the mechanical strength For we can use a value of about 1.7, resulting from experimental studies on plasma developed in hypervelocity impacts (Kadono & Fujiwara 1996). Comparing Eq. (6) to Eq. (1), we see an additional factor of about 1.6. This comes from the fact that Eq. (6) derives from Eq. (4), according to which the stagnation temperature depends on speed when a body is travelling at hypersonic velocity. Eq. (6) shows that the airburst occurs thanks to the combined thermal and mechanical effects acting on the meteoroid. In other words, thermodynamic processes decrease the effective pressure crushing the body in a significant way, so the same body can reach a lower altitude, or for a given airburst altitude a lower strength is required. © European Southern Observatory (ESO) 1999 Online publication: December 22, 1998 |