symbols.rst

List of Symbols

+-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + _l + low frequency + + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + _h + high frequency + + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + _p + airfoil pressure side + + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + _s + airfoil suction side + + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + _t + turbulence + + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + ₀ + reference + + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + ₁ + parallel to airfoil chord + + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + ₂ + normal to airfoil chord + + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + ₃ + blade spanwise direction + + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + α + angle of attack + [rad] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + β² + Prandtl-Glauert correction factor + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + δ + airfoil boundary layer thickness + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + δ^* + airfoil boundary layer displacement thickness + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + θ + airfoil boundary layer momentum thickness + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + Θ_e, Φ_e + angles between emitter and observer + [rad] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + ρ + air density + [kg/m³] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + ω + radial frequency + [rad/s] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + A_w + A-weight + [dB] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + c + speed of sound + [m/s] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + c_i + chord at blade spanwise position i + [m] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + d + blade span at station i + [m] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + $\overline{D}$ + directivity function + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + f + frequency + [Hz] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + G + empirical function + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + h + height of the trailing edge thickness + [m] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + H + airfoil kinematic shape factor + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + I + turbulence intensity + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + k + wave number + [m^-1] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + $\overline{k},\ \widehat{k}$ + nondimensional wave number + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + ΔK₁, K₁, K₂ + empirical parameters of the BPM model + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + l + spanwise extent of the separation zone from blade tip + [m] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + L + lift force + [N] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + L_t + length scale + [m] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + M + Mach number + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + M_c + Mach number past the trailing edge + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + r_e + effective observer distance + [m] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + Re + Reynolds number + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + S² + Sears function + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + St + Strouhal number + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + t_x + relative thickness of the airfoil at chordwise position x + [-] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + U + local inflow velocity + [m/s] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + y + blade spanwise position + [m] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + z + height above the ground + [m] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+ + z₀ + ground surface roughness + [m] + +-----------------------------------------------------------+------------------------------------------------------------+-------------------+