engleski

An Approximate Closed-Form Solution for the Airfoil Critical Mach Number

The airfoil critical Mach number is usually determined by equalizing the Prandtl-Glauert correction for the pressure coefficient and the isentropic critical pressure coefficient. The resulting equation is solved for the critical Mach number either graphically or numerically. In this paper the expression for the isentropic critical pressure coefficient is replaced with its binomial approximation. The resulting equation is transformed into a cubic equation. The cubic equation has been solved for the airfoil critical Mach number M_(inf cr) as a function of the pressure coefficient for the incompressible flow C_(p inc min) and the adiabatic coefficient k. The effects of the pressure coefficient C_(p inc min) and the adiabatic coefficient k are lumped to a single variable C*_p=C_(p inc min)(k+1). In the most interesting range, 0.5<M_(inf cr)<0.95, the difference between the cubical approximation and the numerical solution is 5.3% (at M_(inf cr)=0.5) and 0.07% (at M_(inf cr)=0.95). The obtained closed-form solution for M_(inf cr) is a good approximation for the preliminary design and as the initial guess for the numerical iterative procedure. The proposed solution is applicable not only to airflow but for other fluids including cryogenic gasses.

critical Mach number; subsonic flow; airfoil; compressible flow

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