e. Low-Density Flow
Hypersonic flights at higher altitudes experience very low density flows. The governing non-dimensional parameter for these regimes is called as Knudsen number which is defined as the ratio of mean free path to the characteristic length of the object. Here mean free path is termed as the mean distance traveled by the fluid molecule between two successive collisions with other molecules. Since density of air is very high on the earth's surface, therefore Knudsen number is close to zero for standard dimensions of hypersonic flights. However if we consider any standard hypersonic flight taking off from earth surface, it becomes clear that, the flight vehicle is going to encounter change in density with increase in altitude. Validation of continuum assumption and in turn the usage of usual governing equations remains intact till the altitude of around 90 km from earth surface where Knudsen number is below 0.3. Above this altitude, till 150 km from earth surface, density becomes lower as a effect of which fluid velocity and temperature at the surface do not remain in equilibrium with the surface. Therefore flow for Knudsen number in range 0.3 to 1 is treated in the transitional regime where slip wall boundary conditions should be used along with the usual governing equations based on continuum assumption. However above 150 km from earth's surface, density of air becomes very low therefore this region is called as free molecular flow where Knudsen number becomes more than or equal to unity. Thus need for change in governing equations arise in this regime. Hence kinetic theory of gases finds its application for hypersonic flights at such altitudes.

From these specifications of hypersonic flow regime, it is clear that Mach number to be very much greater than one is the formal definition of hypersonic flow. Higher density ratio is also one of the definitions of hypersonic flow. Density ratio across normal shock would reach 6 for calorically perfect gas (air or diatomic gas) at very high Mach numbers. If concerned fluid is chemically reacting mixture or even thermally perfect then this ratio increases to value more than 20, which was reached in Apollo flight. For density ratio to reach more than 20, the specific heat ratio should decrease and reach a value close to one for air. In actual flight conditions, hypersonic flow field can be reached with increasing the flight velocity without altering thermal properties of surrounding fluid. However, it is difficult to achieve this flow in ground testing with very high kinetic energy and high Mach number without change in thermal properties the fluid. Therefore there are many challenges for experimental simulation of hypersonic flow. One solution for this problem is the use of different gases to simulate the low specific heat ratio condition. Tetrafluoroethane is used for specific heat ratio of 1.2 and hexafluoroethane for 1.1. Understanding the challenges faced by hypersonic flight and derived solutions for some of those problems are the themes of this subject.