Theoretical Efficiency of Circular Sources

Abstract

The intensity and power radiated from continuous circular sources and circular arrays of point sources are derived from first principles. For the first-mentioned source, the final analytical expressions are extremely simple—that for intensity being CJμ2(ka sinθ), where C is a constant and θ the angle between the field point and the normal to the source plane. The radiation pattern depends on the product of the source radius a and the wave number k; the direction of its maximum is determined primarily by the phase parameter μ. No minor lobes exist on the axial side of the major lobe. The expression for power predicts an anomaly wherein the power—for most ka>1.9—is greater for a source “dephased” by a small amount than for one having all elements radiating in phase. These expressions are applicable to the reduction of noise from centrifugal and axial blowers and aircraft propellers. In particular, it can be shown to be impossible to reduce the noise appreciably from a single section of an open compressor by using different numbers of blades in the rotor and stator unless the difference in number exceeds the value of ka. This is usually precluded by considerations of “solidity.”