Prandtl–Glauert transformation

The Prandtl - Glauert transformation or Prandtl - Glauert rule ( also Prandtl - Glauert rule Ackeret'sche ) describes an approximate function with the aerodynamic processes can be compared with each other, which take place at different Mach number.

Mathematical formulation

As noticeable in case of subsonic flows with increasing speed compressibility of the air, the aerodynamic characteristics are to be multiplied by a factor. The following formula illustrates this with the example of the pressure coefficient cp, depending on the pressure coefficient of an incompressible flow cp0:

Wherein Ma is the Mach number. This rule does not apply in the speed range between Ma = 0.7 and Ma = 1.3.

History

Ludwig Prandtl had indeed introduced such a correction more often in courses, but the first real release was done in 1928 by Hermann Glauert Therefore, this rule is known as the Prandtl - Glauert rule. The introduction of these equations allowed the design of aircraft, for higher velocities in the subsonic range. Later this rule by Jakob Ackeret presently being made to the form, which is also valid in the supersonic range, extended.

Uniqueness

The equation has the invalid range for the speed of sound on a singularity. This point is also referred to as a singularity Prandtl Glauert singularity, wherein the flow resistance theoretically approaches infinity. In reality, namely aerodynamic and thermal disturbances near the speed of sound are disproportionately amplified and spread across the flow direction very far, but a singularity does not occur.

Nevertheless, this theoretical singularity is erroneously used to explain real-world phenomena at the speed of sound (see clouds sheet effect ).