Flow-resonant sound interaction in a duct containing a plate,part I: Semi-circular leading edge

The interaction between flow and flow-induced acoustic resonances near rigid plates with semi-circular leading edges located in a hard-walled duct is described. These plates generate acoustic resonances over flow velocity ranges depending on thickness, chord and trailing edge geometry, together with rigidity, internal dimensions, length of the working section and shape of the terminations of the working section. A potential flow model for the plate with a smooth leading edge is developed, and the acoustic power generated by vortices growing and shedding from the trailing edge is calculated. The rate of growth of the vortices is determined by an instantaneous Kutta condition applied over part of the cycle. This technique simulates the influence of the sound field on vortex growth.     

Attenuation of sound due to vortex shedding from a splitter plate in a mean flow duct

A theoretical analysis is given of an experiment being performed at the University of Southampton [1] as part of a programme to quantify the effectiveness of perforated screens in dissipating sound in the presence of tangential mean flow. In the experiment vorticity is generated at the trailing edge of a splitter plate in a mean flow duct by a plane sound wave incident from upstream, acoustic energy being ceded to the kinetic energy of the vortex field. An expression is derived for the dissipated sound power at arbitrary subsonic mean flow Mach number and frequency. The calculation is performed both by a consideration of the net flux of acoustic energy into the trailing edge region of the splitter plate, and by evaluating the rate of working of the vortex lift forces in the field of the acoustic particle velocity. In particular, it is shown that the absorption is independent of frequency, provided the frequency does not exceed the minimum cut-on frequency of transverse acoustic modes within the duct.     

有流条件下环形管道中的声传播特性

本文从线性波动方程出发,根据界面处声压连续和质点位移连续的条件,导得有流条件下无限长环形吸声管道中声传播的特征方程,并且具体分析了管道衰减系数与气流速度、壁面特性、截面几何尺寸和声波频率等参量的相互关系。研究表明,管道衰减系数随着气流流速的增加,管壁吸声系数的减小、管道截面几何尺寸的增加而减小。同时,随着声波频率从低频到高频的变化,衰减系数从小到大,再从大到小地变化,存在一个最佳峰值。     

Reflection of sound at area expansions in a flow duct

An analytical model for scattering at area discontinuities and sharp edges in flow ducts and pipes is presented. The application we have in mind is large industrial duct systems, where sound attenuation by reactive and absorptive baffle silencers is of great importance. Such devices commonly have a rectangular cross-section, so the model is chosen as two-dimensional. Earlier solutions to this problem are reviewed in the paper. The modelling of the flow conditions downstream of the area expansion, with and without extended edges, and its implications for the resulting acoustic modes are discussed. Here, the scattering problem is solved with the Wiener-Hopf technique, and a Kutta condition is applied at the edge. The solution of the wave equation downstream of the expansion includes hydrodynamic waves, of which one is a growing wave. Theoretical results are compared with experimental data for the reflection coefficient for the plane wave, at frequencies below the cut-on for higher order modes. Influence of the interaction between the sound field and the flow field is discussed. A region where the reflection coefficient is strongly Strouhal number dependent is found.     

Visualization of flow past a square prism with cut-corners at the front-edge

Flow past a square prism with cut-corners at the front-edge is numerically and experimentally visualized to investigate a mechanism of drag reduction. An adaptive numerical scheme based on the vortex method is implemented for two values of the Reynolds number between 200 and 1,250, and the results are compared with experiments. Experimental visualization techniques include the hydrogen-bubble technique atRe=4,000 and the oil-flow technique atRe=10,000 for a global wake formation, and the aluminum-flake technique for transient flow at the early stage of motion atRe=1,250. A similar reattachment flow pattern is shown in a wide range of the Reynolds number between 200 and 10,000, which implies a possibility of the drag reduction in the Reynolds number being approximately lower than 8,000 unlike the previous findings.     

The sound generated by a square cylinder with a splitter plate at low Reynolds number

The generation of aerodynamic sound by the interaction of flow at a Reynolds number of 150 and a Mach number of 0.2 with a rigid square cylinder attached to a rigid thin flat plate is numerically investigated. When the length of the plate is varied from L=0.5D to 6D, where D is the side length of the square cylinder, the results can be grouped into three distinct regimes. For the first regime (L?D), the sound levels decrease with increasing plate length. A 3 dB sound reduction is obtained when the length of the plate is D. For the second regime (1.25D?L?4.75D), the sound levels increase with increasing plate length. For the third regime (5D?L?6D), the sound levels decrease as the length of the plate increases but the levels are higher than for the other regimes. Results also show that the lift fluctuation is the dominant sound source. These acoustic results can be explained in terms of the fluid mechanics occurring in the near wake of the cylinder.     

Scattering of sound by an elastic plate with flow

An elastic plate, set in an infinite baffle and immersed in a fluid moving with a uniform subsonic velocity, is excited by an acoustic source. The scattered sound field is analyzed when fluid-plate coupling is large, and a solution is found by the use of matched asymptotic expansions. The far field is found to approximate to the solution obtained when the elastic plate is absent. At a plate resonance, however, the outer field must include eigensolutions with singularities at the plate edges, and close to the plate the dominant terms are travelling plate waves. These plate waves are found to have a wavelength independent of the frequency of the source. It is also shown that a plate resonance corresponds to a divergence instability of aerodynamic flutter theory and that the stability results found in this paper are in agreement with those obtained by using modal expansions. The limit as the Mach number goes to zero is found to be singular, suggesting an analysis of the model for small flow velocity. This calculation is performed and the results match smoothly to the respective solutions for a stationary fluid and for a large subsonic flow.     

Acoustic excitation of a square plate by turbulent flow noise

An experiment was conducted to measure the characteristics of flow noise in a bounded system with forced circulation. The flow noise facility is described herewith. Vortex shedding in the conducting rectangular ducting was experimentally controlled by the insertion of cylinders of various diameter and pitch perpendicular to the flow. The sound pressure level exciting an instrumented square plate parallel with the flow direction was measured, as well as the plate response.     

Unsteady flow of a viscous incompressible fluid past a porous plate with constant suction

An exact solution of the flow of an incompressible viscous fluid past an infinite porous plate has been derived on taking into account a step-change in suction velocity. It has been observed that the skin-friction decreases with increasingS, the suction parameter.     

Scattering and absorption of sound at flow duct expansions

The scattering of plane acoustic waves at area expansions in flow ducts is analysed using the vortex sheet model where the flow at the expansion is modelled as a jet, with a vortex sheet emanating from the edge. Of particular interest is the influence of the flow field on acoustic scattering and absorption.First, it is demonstrated that the stability properties of the shear layer can be simulated by modifying the edge condition within the vortex sheet model. To this end the accuracy for the region where the shear layer is changing from unstable to stable is improved by introducing a gradually relaxed Kutta edge condition with empirically derived coefficients. For low Strouhal numbers the vortex sheet model applies and for higher Strouhal numbers the two models converge.Second, it is demonstrated that the acoustic transmission through the jet expansion region can be determined by neglecting the scattering there. Incorporating this assumption, the vortex sheet model reproduces well the experimental results on transmission and absorption for an area expansion. This result supports the assumption that the main part of the scattering occurs at the area expansion at least for the low-frequency range. Furthermore, the influence of the flow field is particularly strong for small Strouhal numbers.     

圆柱绕流气动声的偶极子及四极子源法定量研究

以亚临界三维圆柱绕流的气动噪声为对象,研究声类比理论中偶极子及四极子源模型在预测低Mach数流动气动声的可靠性及准确性。使用大涡模拟(LES)得到非定常流场,并依据声类比中的Curle等效偶极子面源和Lighthill四极子体源模型,提取相应的声源数据,经Fourier变换得到涡脱落频率处的声源信息,进而定量预测圆柱绕流的气动声。结果表明:Curle模型的结果与实验结果吻合良好,Lighthill体源模型预测的准确性依赖于声源区域截断,不恰当的声源截断将导致错误的声场预测。     

On the analytical solution of viscous fluid flow past a flat plate

In this Letter, we propose a simple approach using HAM to obtain accurate totally analytical solution of viscous fluid flow over a flat plate. First, we show that the solution obtained using HPM is not a reliable one; moreover, we show that HPM is only a special case of HAM and its basic assumptions are restrictive rather than useful. We set ?=−1 for the case of comparison of our results to those obtained using HPM. Afterwards, we introduce an extra auxiliary parameter and a straightforward approach to find best values of this auxiliary parameter which plays a prominent role in the frame of our solution and makes it more convergent in comparison to previous works.     

Effects of thermal radiation on the MHD flow past a vertical plate

The effects of thermal radiation on the MHD flow over a vertical and porous plate of an optically thin gray, electrically conducting, viscous and incompressible fluid are studied. The differential equations and their boundary conditions, describing the problemunder consideration, are dimensionalized and the numerical solution is obtained. The numerical results for the velocity and temperature profiles are shown for different dimensionless parameters entering the problem under consideration, such as the radiation parameter S, Grashof number G, Prandtl number P, and the magnetic parameter M.     

Vibrations of a square plate with parabolically varying thickness

Vibration results for a square plate with a parabolically varying thickness distribution and built-in edges are presented. Frequency and mode shape predictions obtained from a finite element analysis are compared with measurements made with real-time laser holography. In general, the agreement between the two is very good except for a few of the lower modes where the predicted frequencies are about 15% high. So far, a satisfactory explanation for this has not been found. The vibration mode shapes for the plate exhibit a striking blend of radial and square symmetries that results from the axisymmetric thickness distribution and the square symmetry of the boundary frame.     

Reduction of sound in a low velocity flow duct by the use of Bragg reflections

This paper presents the results of some experiments on the use of structures of aerodynamically-shaped elements as narrow-band sound reflectors in a duct. The structures are tuned to give maximum attenuation for frequencies determined by the Bragg reflection condition, and are thought to be of special value where space considerations prohibit the use of conventional acoustic wave filters.     

Blockage effects on viscous fluid flow and heat transfer past a magnetic obstacle in a duct

The effect of lateral walls on fluid flow and heat transfer is investigated when a fluid passes a magnetic obstacle. The blockage ratio β that represents the ratio between the width of external magnet M y and the spanwise width L y is employed to depict the effect. The finite volume method (FVM) based on the PISO algorithm is applied for the blockage ratios of 0.2, 0.3, and 0.4. The results show that the value of Strouhal number St increases as the blockage ratio β increases, and for small β , the variation of St is very small when the interaction parameter and Reynolds number are increasing. Moreover, the cross-stream mixing induced by the magnetic obstacle can enhance the wall-heat transfer and the maximum value of the overall heat transfer increment is about 50.5%.