Simulations of the scattering of sound waves at a sudden area expansion

The scattering of acoustic plane waves at a sudden area expansion in a flow duct is simulated using the linearized Navier–Stokes equations. The aim is to validate the numerical methodology for the flow duct area expansion, and to investigate the influence of the downstream mean flow on the acoustic scattering properties. A comparison of results from numerical simulations, analytical theory and experiments is presented. It is shown that the results for the acoustic scattering obtained by the different methods gives excellent agreement. For the end correction, the numerical approach is found superior to the analytical model at frequencies where coupling of acoustic and hydrodynamic waves is significant. A study with two additional flow profiles, representing a non-expanding jet with an infinitely thin shear layer, and an immediate expansion, shows that a realistic jet is needed to accurately capture the acoustic–hydrodynamic interaction. A study with several different artificial jet expansions concluded that the acoustic scattering is not significantly dependent on the mean flow profile below the area expansion. The constructed flow profiles give reasonable results although the reflection and transmission coefficients are underestimated, and this deviation seems to be rather independent of frequency for the parameter regime studied. The prediction of the end correction for the constructed mean flow profiles deviates significantly from that for the realistic profile in a Strouhal number regime representing strong coupling between acoustic and hydrodynamic waves. It is concluded that the constructed flow profiles lack the ability to predict the loss of energy to hydrodynamic waves, and that this effect increases with increasing Mach number.     

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.     

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。     

Identification of aero-acoustic scattering matrices from large eddy simulation. Application to a sudden area expansion of a duct

A methodology is presented which allows to determine the coefficients of transmission and reflection of plane acoustic waves at flow discontinuities in piping systems by combining large eddy simulation (LES) of turbulent compressible flows with system identification. The method works as follows. At first, an LES with external, broadband excitation of acoustic waves is carried out. Time series of acoustic data are extracted from the computed flow field and analyzed with system identification techniques in order to determine the acoustic scattering coefficients for a range of frequencies. The combination of broadband excitation with highly parallelized LES makes the overall approach quite efficient, despite the difficulties associated with simulation of low-Mach number compressible flows. The method is very general, here it is applied to study the scattering behavior of acoustic waves at a sudden change in cross-section in a duct system. The complex aero-acoustic interactions between acoustic waves and free shear layers are captured in detail by high resolution compressible LES, such that the scattering coefficients can be determined accurately from first principles. In order to demonstrate the reliability and accuracy of the method, the results for the scattering behavior and the acoustic impedance are presented and physically interpreted in combination with several analytical models and experimental data.     

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.     

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.     

The effect of thermal prehistory on turbulent separated flow at sudden tube expansion

Results of numerical investigation of the effect of heat boundary layer thickness in front of a sudden expansion of a round tube on turbulent transfer in the zone of flow separation, attachment, and relaxation are presented. Before separation the flow was hydrodynamically stable, and the heat layer in front of expansion could change its thickness in maximally possible limits: from zero to a half of tube diameter. The Reynolds number varied from 6.7·10³ to 1.33·10⁵. It was found that the growth of heat layer thickness leads to reduction of heat transfer intensity in the separation area and moving away of the coordinate of maximal heat transfer from the place of tube expansion. Generalizing dependence for the maximum Nusselt number is given for variation of the heat layer thickness. Comparison with experimental data of [1] proved the main behavior tendencies of heat and mass transfer processes in separation flows behind a backward-facing step with different thermal prehistory.     

On classification of flow regimes in a channel with sudden expansion

Supersonic flows of gas in the vicinity of the bottom region known as flows with sudden expansion have been considered. On the basis of extensive experimental studies, authors have proposed a complete classification of flow regimes: stationary, oscillating, and transient. Hysteresis of the regimes change at total gas pressure increasing and decreasing in front of the nozzle has been found. Typical shock-wave configurations emerging at the jet flowing in a channel at different modes have been determined. The type of shock-wave structure and the nature of interaction of the mixing layer of a jet with the wall or reverse flow flowing into the channel from ambient medium determine the appropriate mode. Combination of physical and numerical experiment with bottom pressure calculation according to the developed semi-empirical model have revealed new flow regimes that were not studied earlier.     

Bifurcation of a Newtonian-fluid flow in a planar channel with sudden contraction and expansion

The features of a Newtonian-fluid flow in a two-dimensional channel with sudden contraction and expansion are investigated by numerical modeling. The kinetics of the bifurcation transition from the symmetric mode to steady-state asymmetric flow on the outlet from the zone of contraction of the channel is analyzed. The linear dependence of the degree of asymmetry of flow on the Reynolds number is established.     

突扩燃烧室湍流预混反应流的数值模拟

对突扩燃烧室这一典型工程燃烧装置内的湍流预混反应流进行了数值模拟。时平均控制方程组的封闭采用k-ε湍流输运模型和EBU-Arhenius湍流反应模型。模拟结果给出了突扩燃烧室内湍流预混反应流的气体时均流场、组分浓度场与温度场的分布。通过数值模拟结果与实验的比较对EBU-Arhenius模型进行了讨论与评价。     

Measurement of geometrical dispersion in a sound beam

A method for measuring the geometrical dispersion caused by diffraction processes in sound beams is considered. The experimental setup is described, and the results of measuring the longitudinal distributions of both the additional shift of the phase invariant of a three-frequency wave and the dispersion parameter are presented. The local character of the geometrical dispersion, which manifests itself within the near-field zone of the beam, is revealed, and the presence of two different mechanisms underlying its nonuniform spatial distribution is pointed out.     

Turbulent gas-dispersed flow in a pipe with sudden expansion: numerical simulation

A mathematical model was developed to simulate two-phase gas-dispersed flow moving through a pipe with axisymmetric sudden expansion. In the model, the two-fluid Euler approach was used. The model is based on solving Reynolds-averaged Navier — Stokes equations for a two-phase stream. In calculating the fluctuating characteristics of the dispersed phase, equations borrowed from the models by Simonin (1991), Zaichik et al. (1994), and Derevich (2002) were used. Results of a comparative analysis with previously reported experimental and numerical data on two-phase flows with separation past sudden expansion in a plane channel and in a pipe are given. This work was supported by the President of the Russian Federation through the Foundation for Young Candidates of Sciences under Grant MK-186.2007.8 and by the Russian Foundation for Basic Research (Grants Nos. 05-08-33586 and 06-08-00967).     

Simulation of turbulent non-isothermal polydisperse bubbly flow behind a sudden tube expansion

The results of numerical simulation of the structure of non-isothermal polydisperse bubbly turbulent flow and heat transfer behind a sudden tube expansion are presented. The study was carried out at a change in the initial diameter of the air bubbles within d _m1 = 1–5 mm and their volumetric void fraction β = 0–10 %. Small bubbles are available in almost the entire cross section of the tube, while the large bubbles pass mainly through the flow core. An increase in the size of dispersed phase causes the growth of turbulence in the liquid phase due to flow turbulization, when there is a separated flow of liquid past the large bubbles. Adding the air bubbles causes a significant reduction in the length of the separation zone and heat transfer enhancement, and these effects increase with increasing bubble size and their gas volumetric flow rate ratio.     

Interaction of induced sound with flow past a square leading edged plate in a duct

The interaction of resonant sounds with the flow past a thick, blunt, flat plate in a rigid walled square duct has been examined. Sound pressure levels of up to 146 dB (re 20 μPa) have been recorded. It has been established that the resonant sound can initially be excited at a harmonic of the normal vortex shedding frequency. In some cases, the sound “feeds back” on the vortex shedding process causing a step change in the shedding frequency, increasing the Strouhal number for the plate by up to twice the normal value. This excited vortex shedding and associated resonances can be suppressed by locating the plate at incidence to the air flow direction. Complex duct modes can be generated by the vortex shedding resulting in different regions of the plate shedding at different Strouhal numbers.