List of Symbols


low frequency


high frequency


airfoil pressure side


airfoil suction side






parallel to airfoil chord


normal to airfoil chord


blade spanwise direction


angle of attack



Prandtl-Glauert correction factor



airfoil boundary layer thickness



airfoil boundary layer displacement thickness



airfoil boundary layer momentum thickness


\(\Theta_{e},\ \Phi_{e}\)

angles between emitter and observer



air density



radial frequency






speed of sound



chord at blade spanwise position i



blade span at station i



directivity function






empirical function



height of the trailing edge thickness



airfoil kinematic shape factor



turbulence intensity



wave number


\(\overline{k},\ \widehat{k}\)

nondimensional wave number


\({\mathrm{\Delta}K_{1},\ K}_{1}\),\(\ K_{2}\)

empirical parameters of the BPM model



spanwise extent of the separation zone from blade tip



lift force



length scale



Mach number



Mach number past the trailing edge



effective observer distance



Reynolds number



Sears function



Strouhal number



relative thickness of the airfoil at chordwise position x



local inflow velocity



blade spanwise position



height above the ground



ground surface roughness