Fan Noise Estimate: Method

Gutin and Vortex Noise

Rotational noise

A rotor's steady thrust and torque are carried by blades that sweep past a fixed observer B times per revolution; to the observer the pressure field is periodic at the blade-passing frequency B Ω/2π and its harmonics. Gutin (1936) derived the far-field sound pressure of each harmonic of a static propeller from the thrust and torque alone. In the engineering form of NACA TN 2968 the rms pressure of harmonic m is

p_m = (m B Ω / (2√2 π c s)) [−T cos β + c Q / (Ω R_e²)] J_mB(m B (Ω R_e / c) sin β)

with Ω the rotor speed, c the speed of sound, s the distance, β the angle from the forward thrust axis, Q the torque and R_e = 0.8 R the radius at which the loads are concentrated. J_mB is the Bessel function of order mB; its argument is the order times the Mach number of the effective radius times sin β. On the axis (β = 0 or 180°) the argument vanishes and so does the rotational noise; the maximum lies a little behind the rotor plane, near 105°, where the thrust and torque terms add. Because the Bessel order grows with the blade count, more blades push the sound into higher harmonics and cut the level sharply at low tip Mach numbers, which is why many-bladed fans are quiet. The level is 20 log₁₀(p / 20 µPa).

The tool evaluates the first four harmonics and sums them by energy. NACA TN 2968 doubled the pressures for ground reflection in its charts and tables (+6 dB); the checkbox reproduces that, and the tool's own check cases are its Table I.

Vortex noise

The broadband hiss of a rotor comes from the vortices shed by the blade sections. Yudin found its energy proportional to the blade area and to the sixth power of the section velocity; Hubbard evaluated the constant from a helicopter blade and wrote the level at 300 ft as L_v = 10 log₁₀(k A_B V_0.7⁶ / 10⁻¹⁶) with k = 3.8 × 10⁻²⁷ for A_B in square feet and the velocity at 0.7 R in feet per second. He rated the result as tentative, accurate to about ±10 dB. Other distances follow the inverse-distance law.

What is not included

Forward flight (the static formula is used; TN 1358 found flight levels about 6 dB lower), atmospheric absorption, the duct's shielding and its own inlet and tip-gap noise, unsteady loading from inflow distortion, and the thickness noise that becomes important above a tip Mach number of about 0.9. The figures are the rotor's own far-field contribution in still air and should be read as an upper bound for the rotational part of a ducted fan.