Prandtl–Meyer function - Alchetron, The Free Social Encyclopedia

Prandtl–Meyer function describes the angle through which a flow can turn isentropically for the given initial and final Mach number. It is the maximum angle through which a sonic (M = 1) flow can be turned around a convex corner. For an ideal gas, it is expressed as follows,

ν ( M ) = ∫ M 2 − 1 1 + γ − 1 2 M 2 d M M = γ + 1 γ − 1 ⋅ arctan ⁡ γ − 1 γ + 1 ( M 2 − 1 ) − arctan ⁡ M 2 − 1

where ν is the Prandtl–Meyer function, M is the Mach number of the flow and γ is the ratio of the specific heat capacities.

By convention, the constant of integration is selected such that ν ( 1 ) = 0.

As Mach number varies from 1 to ∞ , ν takes values from 0 to ν max , where

ν max = π 2 ( γ + 1 γ − 1 − 1 )

where, θ is the absolute value of the angle through which the flow turns, M is the flow Mach number and the suffixes "1" and "2" denote the initial and final conditions respectively.

References

Prandtl–Meyer function Wikipedia

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