Prandtl–Glauert singularity

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Example of a Jet producing a shockwave at transonic speeds, creating a vapor cone. The Prandtl–Glauert singularity was incorrectly predicted to occur under these conditions. Jet F/A-18.


Reasons of invalidity around Mach 1[edit]

Near the sonic speed (M=1) the transformation features a singularity, although this point is not within the area of validity. The singularity is also called the Prandtl–Glauert singularity, and the aerodynamic forces are calculated to approach infinity. In reality, the aerodynamic and thermodynamic perturbations do get amplified strongly near the sonic speed, but they remain finite and a singularity does not occur. An explanation for this is that the Prandtl–Glauert transformation is a linearized approximation of compressible, inviscid potential flow. As the flow approaches sonic speed, the nonlinear phenomena dominate within the flow, which this transformation completely ignores for the sake of singularity.

Prandtl-Glauert transformation[edit]

Plot of the Prandtl-Glauert transformation as a function of Mach number. Notice the infinite limit at Mach 1.


c_{p} = \frac {c_{p0}} {\sqrt {|1-{M_{\infty}}^2|}}



\lim_{M_{\infty} \to 1 }c_p = \infty


See also[edit]

