Oliver V. Atassi

Using Reynolds-Averaged Navier-Stokes Calculations to Predict Trailing-Edge Noise

This paper describes a method for using Reynolds-averaged Navier―Stokes calculations of the flow over an airfoil to calculate far-field sound spectra generated by boundary-layer turbulence interacting with the airfoil trailing edge. It is shown that a model of the spatial distribution of turbulent kinetic energy in a boundary-layer flow can be related to an integral of the local turbulence spectrum multiplied by a function of the mean flow velocity distribution. Inverting this relationship gives the turbulence spectrum required for calculations of the pressure on the surface beneath the boundary layer, hence the far-field sound radiated from a turbulent boundary layer interacting with a sharp trailing edge. Results are presented showing estimates of surface pressure spectra and radiated sound from a turbulent boundary layer flowing over the sharp trailing edge of a NACA 0012 airfoil, and they are compared with measurements of airfoils with different chord and Reynolds numbers. Also shown are predictions based on this approach for the self-noise from a 22 in. fan. The measured and predicted far-field sound spectra were found to show the same dependence on flow speed and close agreement in absolute level.

Effect of Leading-Edge Thickness on High-Speed Airfoil-Turbulence Interaction Noise

Airfoil-turbulence interaction noise is studied to understand how thickness changes in the neighborhood of an airfoil leading edge can modify noise generation. The broadband interaction noise is generated by placing an airfoil in the turbulent boundary layer of a wind tunnel’s rectangular duct test section. Four airfoil leading edge configurations are tested at four different airfoil positions, relative to the duct exit plane. Local changes in mean flow properties are produced by both modifying leading edge thickness, and translating the airfoil axially to positions internal and external to the duct. In each configuration, the maximum airfoil thickness, camber distribution, and aerodynamic suction surface are unchanged. Leading edge thickness changes are confined to nearly the first ten percent of the airfoil chord, along the airfoil pressure surface only. Numerical results for the mean flow show that when the airfoil is internal to the duct, changes in thickness result in small changes in incidence between the flow and airfoil leading edge. However, with changes in the airfoil axial position, more significant changes in incidence occur, with large flow angles exhibited at the furthest external position. Measurements show that noise is reduced by several decibels as leading edge thickness increases, over a frequency range of 2-4 kHz when the airfoil lies within the duct, and 1-4 kHz when the airfoil lies external to the duct. The maximum noise reduction occurs at frequencies where the reduced frequency, based on leading edge thickness, is order one. The difference in the spectral noise reduction when the airfoil is translated internal versus external to the duct, suggests that changes in leading edge flow incidence may contribute to the noise reduction observed, and that the mechanism for noise reduction is not purely controlled by the relative turbulence scale to leading edge thickness relationship. To examine this hypothesis a simple model for turbulence-airfoil interaction noise that includes thickness effects is compared with data. Results show that agreement between the theory and the measurements are quite good when the airfoil lies within the duct and the incidence is small. When the airfoil lies external to the duct, significant variation between the theoretical model, which does not account for incidence, and measurements exists.

A model of flapping motion in a plane jet

Abstract Flow visualization near the exit of a plane jet shows a small-amplitude disturbance whose wavelength is large relative to the jet shear layer thickness. Further downstream, in the transition region, concentrated regions of vorticity are observed which drive the flapping motion of the jet. These observations motivate an inviscid, two-dimensional model for the transitional region of the jet. Linear stability analysis of a piecewise-uniform shear layer model indicates that small-amplitude, long wavelength disturbances are unstable. Long wave theory shows that regions of high circulation convect downstream faster than regions of low circulation resulting in nonlinear steepening and that the rate of the steepening is directly proportional to the strength of the local shear. The long wave theory also shows that finite-amplitude sinuous disturbances at the jet centerline will grow linearly as they convect downstream. The results predict the steepening and growth of the jet centerline observed in the flow visualization.

Analytical and numerical study of the nonlinear interaction between a point vortex and a wall-bounded shear layer

The unsteady interaction between a vortex and a wall-bounded vorticity layer is studied as a model for transport and mixing between rotational and irrotational flows. The problem is formulated in terms of contour integrals and a kinematic condition along the interface which demarcates the vortical and potential regions. Asymptotic solutions are derived for linear, weakly nonlinear and nonlinear long-wave approximations. The solutions show that the initial process of ejection of vorticity into the irrotational flow occurs at a stationary point along the interface. A nonlinear model is derived and shows that such a stationary point is more likely to exist when the circulation of the vortex is counter to the vorticity in the layer. A Lagrangian numerical method based on contour dynamics is then developed for the general nonlinear problem. Two sets of results are presented where for every initial height of the vortex its magnitude and sign are varied. In both sets, it is observed that when the magnitude of the vortex is held constant a much stronger interaction occurs when the sign of the vortex circulation is opposite to that of the vorticity in the layer

The interaction of a point vortex with a wall-bounded vortex layer

The interaction of a point vortex with a layer of constant vorticity, bounded below by a wall and above by an irrotational flow, is investigated as a model of vortex-boundary layer interaction. This model calculates both the evolution of the interface which separates the vortex layer from the irrotational flow and the trajectory of the vortex. In order to determine the conditions which lead to sustained unsteady interaction, three cases are investigated where the mutual interaction between the vortex and interface is initially assumed to be weak. (i) When a weak point vortex lies outside the layer, the vortex moves with a horizontal speed that is small relative to the long-wave phase speed of interfacial waves. (ii) When a weak vortex lies inside the layer, the vortex is convected by the mean flow and moves with a horizontal speed which matches the phase speed of an interfacial wave. (iii) When the point vortex lies close to the wall and it is sufficiently strong it propagates downstream with a large horizontal velocity.

Interacting Vortex and Vortex Layer: How Length Scale Affects Entrainment and Ejection

A contour dynamics model of the interaction between a point vortex and a layer of constant vorticity, bounded below by a slip wall and above by irrotational e ow, isstudied. Theheight of thevortex above the layerestablishes a length scale that is found to have a strong ine uence on both the evolution of the layer and the vertical displacement of the vortex. A vortex far above the boundary layer generates long-wavelength disturbances. These exhibit earlytime growth, which saturates, taking on the shape of a vortex-like structure, suggesting that a vortex far above a boundary layer can create another one within the layer. Concurrently, entrainment of irrotational e ow deep into the layer occurs within a narrow crevice. Alternatively, for a vortex initially placed close to the layer, a short-scale disturbance occurs that exhibits rapid, continuous growth that eventually rolls up around the vortex. Here, accounting for the vertical displacement of the vortex is necessary to accurately determine the interface evolution. The results support the contention that a vortex can induce ejection and roll up of the boundary layer and entrainment of irrotational e ow into the layer.