Chapter 2. Special and gas dynamic functions

The following special and gas dynamic functions have been used in the current software:

standard atmospheric conditions [6],

empirical pressure losses curves for subsonic and supersonic inlets [4],

empirical curves for enthalpies [1, 3],

gas dynamic functions , , [2].

To define the conditions at the different altitudes the standard atmospheric conditions have been used [6]. The geopotential altitude is defined as

where is a radius of earth. The temperature of air is

where is a temperature on the sea level, is a temperature at altitude and is a vertical temperature gradient. The atmospheric pressure is

where is an atmospheric pressure on the sea level, is an atmospheric pressure at altitude , is a gas constant and is an acceleration of gravity at altitude . The acceleration of gravity can be defined as

where is an acceleration of gravity on the sea level.

Empirical pressure losses curves for subsonic and supersonic inlets are extracted from Fig. 2.1 [4] by using Lagrange polynomial interpolation [5] with 7/9 points to provide smooth accurate curve approximation.

Fig. 2.1. Pressure losses in the inlets as a function of flying speed [4].

The empirical curves for enthalpies are extracted from Fig. 2.2-2.4 by using Lagrange polynomial interpolation [5] with 9 points.

Fig. 2.2. Enthalpies as a function of combustion temperature (200K-1100K) [1].

Fig. 2.3. Enthalpies as a function of combustion temperature (1100K-2000K) [1].

Fig. 2.4. Enthalpies as a function of combustion temperature (2000K-2900K) [1].

The gas dynamic function is calculated as

as

and as

where is normalized velocity. The normalized velocity is defined as

where is a speed and is a critical speed of sound:

The gas dynamic functions can be calculated by using Mach number as well

where is a speed of sound:

The relation between Mach number and normalized velocity can be written as