https://www.win.tue.nl/~sjoerdr/papers/boek.pdf

An introduction to acoustics

In several papers published in the first decade of this century, Kutta and Joukowsky independently proposed that the lift on an airfoil at incidence in a steady un separated flow is given by potential-flow theory with the unique value of the circulation that removes the inverse-sQuare-root velocity singularity at the trailing edge. This proposal-tantamount to saying (cf. Batchelor 1967) that in the unsteady start-up phase the action of viscosity is such that, in the ultimate steady motion, viscosity can be explicitly ignored but implicitly incorporated in a single edge condition-is known as the Kutta-Joukowsky hypothesis. Subsequently the name "Kutta condition" (no doubt largely for brevity) has come to be used to connote the removal of a velocity singularity at some distinguished point on a body in unsteady flow. 1 The condition has recently been applied to unsteadiness in a variety of mean configurations. These include trailing-edge flows with the same and with different flows on the two sides of the body upstream of the edge, attached leading-edge flows, and grossly separated flows past bluff bodies. Imposition of a Kutta condition on unsteady perturbations to one of these mean flows has a variety of physical ramifications. It represents the mechanism by which both the lift is changed and the amplitude and directivity of a sound field are modified. It is the analytical step that in many cases describes the conversion-almost total-of acoustic energy in an incident sound wave to energy of vortical motion on a shear layer ; on

The Kutta Condition in Unsteady Flow

The propagation of plane acoustic waves in smooth pipes and their reflection at open pipe terminations have been studied experimentally. The accuracy of the measurements is determined by comparison of experimental data with results of linear theory for the propagation of acoustic waves in a pipe with a quiescent fluid. The damping and the reflection at an unflanged pipe termination are compared.In the presence of a fully developed turbulent mean flow the measurements of the damping confirm the results of Ronneberger & Ahrens (1977). In the high-frequency limit the quasi-laminar theory of Ronneberger (1975) predicts accurately the convective effects on the damping of acoustic waves. For low frequencies a simple theory combining the rigid-plate model of Ronneberger & Ahrens (1977) with the theoretical approach of Howe (1984) yields a fair prediction of the influence of turbulence on the shear stress. The finite response time of the turbulence near the wall to the acoustic perturbations has to be taken into account in order to explain the experimental data. The model yields a quasi-stationary limit of the damping which does not take into account the fundamental difference between the viscous and thermal dissipation observed for low frequencies.Measurements of the nonlinear behaviour of the reflection properties for unflanged pipe terminations with thin and thick walls in the absence of a mean flow confirm the theory of Disselhorst & van Wijngaarden (1980), for the low-frequency limit. It appears however that a two-dimensional theory such as proposed by Disselhorst & van Wijngaarden (1980) for the high-frequency limit underestimates the acoustical energy absorption by vortex shedding by a factor 2.5.The measured influence of wall thickness on the reflection properties of an open pipe end confirms the linear theory of Ando (1969). In the presence of a mean flow the end correction δ of an unflanged pipe end varies from the value at the high-Strouhal-number limit of δ/a = 0.61, with a the pipe radius, which is close to the value in the absence of a mean flow given by Levine & Schwinger (1948) of δ/a = 0.6133, to a value of δ/a = 0.19 in the low-Strouhal-number limit which is close to the value predicted by Rienstra (1983) of δ/a = 0.26.The pressure reflection coefficient is found to agree with the theoretical predictions by Munt (1977, 1990) and Cargill (1982b) in which a full Kutta condition is included. The accuracy of the theory is fascinating in view of the dramatic simplifications introduced in the theory. For a thick-walled pipe end and a pipe terminated by a horn the end correction behaviour is similar. It is surprising that the nonlinear behaviour at low frequencies and high acoustic amplitudes in the absence of mean flow does not influence the end correction significantly.The aero-acoustic behaviour of the pipe end is dramatially influenced by the presence of a horn. In the presence of a mean flow the horn is a source of sound for a critical range of the Strouhal number.The high accuracy of the experimental data suggests that acoustic measurements can be used for a systematic study of turbulence in unsteady flow and of unsteady flow separation.

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Damping and reflection coefficient measurements for an open pipe at low Mach and low Helmholtz numbers

The dissipation of sound at an edge

Self-sustained aero-acoustic pulsations in gas transport systems: Experimental study of the influence of closed side branches

Sound absorption caused by vorticity shedding, demonstrated with a jet flow☆

From previous measurements it has become evident that a low frequency sound wave can be absorbed significantly when transmitted through a nozzle and a jet flow. The basic underlying physical phenomenon is that acoustic energy is converted into energy of fluctuating vorticity, which is shed from the nozzle edge. In the meantime, different theories have become available which already yield an excellent quantitative description of this effect. These theories are discussed, and a derivation of the simplest of them, a multipolea analysis, is presented. It is demonstrated that this absorption effect is not restricted just to jet flows but occurs also in flows through apertures or through blade rows. A variety of applications is shown including a jet noise muffler and a new non-reflective termination.

D. W. Bechert

Papers

Sound absorption caused by vorticity shedding, demonstrated with a jet flow☆

Sound absorption caused by vorticity shedding, demonstrated with a jet flow