Excitation Of Instability Waves Research Articles

On the Excitation of Instability Waves in Plane Poisuille Flow by a Concentrated Source at the Wall

The paper addresses the excitation of instability waves in plane Poiseuille flow by means of a concentrated source at the wall. The aim of this paper is to investigate the relation between the source amplitude and the excited wave amplitude for various flow and source parameters .The source is modeled by a time harmonic Dnae function and the generated disturbance is investigated By applying Founrier transform on the resulting linearized Navier-Stokes equation in the streamwise direction, the problem is resolved using inverse Fourier transform and the residue theorem. The theoretical formulation explains some observations by previous experiments on similar cases of excitation. Moreover, the calculations demonstrate that the disturbance amplitude increases as the excitation frequency decreases for a fixed Reynolds number, while, on the other hand, it increases as Reynolds number decreases for a fixed frequency.

Excitation of instability waves in wall boundary layers with adverse pressure gradients by various types of Dirac sources

The receptivity of plane, incompressible wall boundary layers close to separation is investigated for the time-harmonic excitation by Dirac sources at the wall and within the shear layer. The basic flow is treated as parallel and modelled by a hyperbolic-tangent velocity profile with an adjustable inflexion point. The receptivity is measured by a ‘production integral’ which describes the initial energy transfer from the basic flow to the unstable part of the excited disturbances. The growing instability of the velocity profiles with growing wall-distance of the inflexion point is not completely reflected by a likewise enhanced receptivity. The influence of the Reynolds number depends strongly on the position of the inflexion point. The excitation by a Dirac source in the shear layer results in a considerably higher receptivity than the excitation by a Dirac source at the wall, if the sources is placed near the critical layer.

Excitation of instability waves in free shear layers. Part 1. Theory

The generation of instability waves in free shear layers is investigated theoretically. The model assumes an infinitesimally thin shear layer shed from a semi-infinite plate which is exposed to sound excitation. For this model the forced instability waves are calculated. The shear-layer excitation by a source farther away from the plate edge in the downstream direction is very weak while upstream from the plate edge the excitation is relatively efficient. A special solution is given for the source at the plate edge. Any type of source farther away from the plate edge produces a parabolic pressure field near the edge. For this latter, fairly general case, a reference quantity is found for the magnitude of the excited instability waves. The theory is then extended to two streams, one on each side of the shear layer, having different velocities and densities. Furthermore, the excitation of a shear layer in a channel is calculated. The limitations to the theory and some aspects related to experiments are discussed. In particular, for a comparison with measurements, numerical computations of the velocity field outside the shear layer have been carried out.

Excitation of instability waves in free shear layers Part 2. Experiments

The acoustical excitation of shear layers is investigated experimentally. Acoustical excitation causes, for example, the so-called ‘orderly structures’ in shear layers and jets. Also, the deviations in the spreading rate between different turbulent-shear-layer experiments are due to the same excitation mechanism. The present investigations focus on measurements in the linear interaction region close to the edge from which the shear layer is shed. We report on two sets of experiments (Houston 1981 and Berlin 1983/84). The measurements have been carried out with laminar shear layers in air using hot-wire anemometers and microphones. The agreement between these measurements and the theory is good. Even details of the fluctuating flow field correspond to theoretical predictions, such as the local occurrence of negative phase speeds.

Excitation of instability waves in a two-dimensional shear layer by sound

The excitation of instability waves in a plane compressible shear layer by sound waves is studied. The problem is formulated mathematically as an inhomogeneous boundary-value problem. A general solution for arbitrary incident sound wave is found by first constructing the Green's function of the problem. Numerical values of the coupling constants between incident sound waves and excited instability waves for a range of flow Mach numbers are calculated. The effect of the angle of incidence in the case of a beam of acoustic waves is analysed. It is found that for moderate subsonic Mach numbers a narrow beam aiming at an angle between 50 to 80° to the flow direction is most effective in exciting instability waves.