An analysis is made of the sound produced when a field of vorticity is cut by an airfoil in low Mach number flow. A general formula is given for the acoustic pressure when the airfoil is rigid and the chord is acoustically compact. This expresses the radiation in terms of an integral over the region occupied by the vorticity; the integrand contains factors describing the influence of the thickness, twist and camber of the airfoil. Explicit analytical results are derived for the case of a rectilinear vortex, having small core diameter and finite axial velocity defect, which is 'chopped' by an airfoil of large aspect ratio. The acoustic signature generally comprises two components associated respectively with the axial and azimuthal vorticity, the latter being determined by the velocity defect distribution within the core. Sound is generated predominantly when the core is in the neighborhoods of the leading and trailing edges. The contribution from the trailing edge is usually small, however, because of destructive interference between sound produced by edge-diffraction of near field energy of the vortex and that produced by vorticity shed into the wake of the airfoil in order to satisfy the unsteady Kutta condition that the pressure and velocity should be bounded at the edge.

Table of contents

This book provides an introductory account of the theory of sound production and propagation and its interactions with solid structures. It includes general theory, diffraction and scattering theory, aerodynamic sound and fluid-structure-acoustic interactions, and a chapter of worked examples. It is intended for a one-semester course on acoustics at the advanced undergraduate or graduate level.

The method of compact Green's functions is described for calculating the sound produced by low Mach number turbulence interacting with a surface and by surfaces in relative motion. The method is very powerful and can supply analytical predictions of complex fluid-structure interaction noise, and can also be used to make acoustic predictions by postprocessing' data obtained from a numerical simulation of a hydrodynamic interaction. The theory is illustrated by cases of sound production by a vortex interacting with a sphere, by the linear and nonlinear theories of parallel vortex-airfoil interaction noise, the trailing edge noise produced by an airfoil of finite thickness and of arbitrary chord, and by the compression wave generated when a projectile is fired into a long duct.

The book comprises of different areas in which vortex dynamics is important, its generation, evolution, interactions with other motions, and finally the ways it can be controlled. Vortex characteristics are important in many aspects of our lives, from blood circulation in the arteries to the high-speed jet. Flow control and manipulation of vortices have been used to reduce drag for large tankers resulting in billions of dollars in savings. An effective smoke management system must be put in place for critical areas to ensure the safety of people, for example in a very large shopping complex or a large airport. Advanced computational and cloud-computing facilities have contributed significantly to large-scale simulation projects. Therefore, validations could be performed for larger windows of study so that it can now cover the entire e.g. central business district (CBD) for urban heat island (UHI) study or land-ocean interactions.