The Application of Unsteady Potential Flow Vortex Loop/Dipole Theory to the Work and Acoustics of Low-Speed Turbomachinery
Abstract
An ideal turbomachine transfers energy from a rotating shaft to a fluid through the creation of a flow, field that is unsteady, in the absolute frame. In order to understand and control the work and acoustics of this process the basic building-block singularities of potential flow are developed in a unified manner such that both near- and far-field effects appear naturally in the formulation. It is shown how the total vector force applied to the fluid by a discrete rigid blade is related to the bound and shed vortex system and the acceleration of the displaced mass. Following Lighthill, the volume integral of the vector moment of vorticity is found to describe most fundamentally how, the unsteady fluid motions in a turbomachine are related to surface forces that do work on the fluid. Because unsteady flow is required for energy transfer, the work input of a single blade creates simultaneously in the fluid an acoustic signal that propagates to the far-field. The strength of this signal is determined by the time derivative of the instantaneous blade force component in the direction of a stationary observer, i.e., with the pattern of a rotating dipole. The summation of these tonal signals from combinations of blades and vanes is computed for free-field and cylindrical duct boundary conditions. Bessel functions are found to characterize both cases, their order being determined by specific blade/vane number differences. Rules for tonal sound control by acoustic interference or mode decay, such as those of Tyler and Sofrin, are examined. Implications for broadband acoustics are discussed.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1992
- Accession Number
- ADA251160
Entities
People
- Earl Quandt