**Abstract**

The paper presents the calculated results obtained by the author for critical Mach numbers of the flow around two-dimensional and axisymmetric bodies. Although the previously proposed method was applied by the author for two media, air and water, this chapter is devoted only to air. The main goal of the work is to show the high accuracy of the method. For this purpose, the work presents numerous comparisons with the data of other authors. This method showed acceptable accuracy in comparison with the Dorodnitsyn method of integral relations and other methods. In the method under consideration, the parameters of the compressible flow are calculated from the parameters of the flow of an incompressible fluid up to the Mach number of the incoming flow equal to the critical Mach number. This method does not depend on the means determination parameters of the incompressible flow. The calculation in software Flow Simulation was shown that the viscosity factor does not affect the value critical Mach number. It was found that with an increase in the relative thickness of the body, the value of the critical Mach number decreases. It was also found that the value of the critical Mach number for the two-dimensional case is always less than for the axisymmetric case for bodies with the same cross-section.

**Keywords:** compressibility, critical Mach number, air, two-dimensional case, axisymmetric case

## **1. Introduction**

This chapter provides an overview of the results obtained by the author by an approximate method for determining the critical Mach numbers for flows in twodimensional and axisymmetric cases [1–3].

The high subsonic flow velocities in aerodynamics are a common case since most modern passenger and cargo planes fly at Mach numbers exceeding the critical Mach numbers. The compressibility effect increases with an increase in the freestream Mach number and with an increase in the perturbations created by the flying body at low Mach numbers. Compressibility problems have been considered by many scientists by various methods [4–20]. Knowing the free-stream Mach number, at which the local velocity somewhere on the surface of the body becomes equal to the local sound velocity, makes it possible to correctly choose the basic aerodynamic equations for a body moving at high speed. It is well known that when the local flow velocity becomes equal to the speed of sound, the aerodynamic equations change their own type from elliptic to hyperbolic. The value of the critical Mach number is the transition from one type of equation to another.
