Influence of mean flow profile and geometrical ratios on scattering of sound at a sudden area expansion in a duct

The scattering of sound at a sudden area expansion in a duct with subsonic mean flow has been modelled with a multimodal method. Technological applications are for instance internal combustion engine exhaust silencers and silencers in industrial duct systems. Both 2D rectangular and 2D cylindrical geometries are considered.The influence of the mean flow profile, and the—in this method—associated application of an acoustic Kutta condition at the edge of the area discontinuity, is investigated. The scattering coefficients for the plane waves are found to change smoothly as the flow profile is changed gradually from one, where the acoustic Kutta condition is applied to one where it is not applied. Furthermore, for high Strouhal numbers no difference is observed in the results for the scattering coefficients obtained for different flow profiles. Also, at low Strouhal numbers the magnitudes of the scattering coefficients are the same for different profiles.The influence of the ratio of the heights (in 2D rectangular geometry), respectively, radii (in 2D cylindrical geometry), of the ducts upstream and downstream of the area expansion on the scattering coefficients is examined. Around a certain Strouhal number, a specific feature in the scattering coefficients is observed when the ratio of the duct heights or radii is less than 0.5. This is found to be connected to a strong interaction between the first evanescent acoustic mode and the hydrodynamic instability mode. For non-uniform flow even an apparent jump between the first evanescent acoustic mode and the hydrodynamic unstable mode and a corresponding jump in scattering coefficients is observed, when employing causality analysis according to the Briggs-Bers or Crighton-Leppington procedure. This implies that in fact an absolute instability occurs.     

Simulations of whistling and the whistling potentiality of an in-duct orifice with linear aeroacoustics

This paper demonstrates a linear aeroacoustic simulation methodology to predict the whistling of an orifice plate in a flow duct. The methodology is based on a linearized Navier–Stokes solver in the frequency domain with the mean flow field taken from a Reynolds-Averaged Navier–Stokes (RANS) solution. The whistling potentiality is investigated via an acoustic energy balance for the in-duct element and good agreement with experimental data is shown. A Nyquist stability criterion based on the simulation data was applied to predict whistling of the orifice when placed in a finite sized duct and experiments were carried out to validate the predictions. The results indicate that although whistling is a nonlinear phenomena caused by an acoustic-flow instability feed-back loop, the linearized Navier–Stokes equations can be used to predict both whistling potentiality and a duct system's ability to whistle or not.     

流管实验装置中声传播计算的模态方法

流管实验装置是测量有流动情况下航空发动机消声短舱内声衬声阻抗的主要装置。本文发展了一种解析的模态匹配方法进行在平均流有声衬条件下矩形流管中声传播的计算。用同伦方法求解特征值问题,并与用环绕积分求解的结果进行比较。声场通过轴向阻抗间断面的声压和声质点速度积分相等计算。第一个算例是无流动、硬壁、有限长、考虑端口反射的情况,并与北航流管实验台测量数据进行了对比;第二个算例为有流动情况下有限长声衬管道不考虑端口反射的声场计算,它与文献中NASA流管实验结果和CAA计算结果符合得很好。     

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.     

The effect of varying the hydraulic parameters of a flow cell in a dye laser pumped by a copper vapor laser

A simple method for measuring hydrodynamic parameters that influence the copper vapor laser (CVL) pumped dye laser stability is reported. A specially designed converging diverging curved flow duct is employed. The flow gap at the laser pump region is varied from 0.4 to 0.6 mm and the Reynolds number is varied from 1000 to 20,000. As a result, the channel aspect ratio and effective curvature ratio are varied from 41.6 to 62.5, and 69 to 102, respectively, at the CVL pump region. The variation in the intensity of a He-Ne laser beam transmitted through the water flowing in the test dye cell at different flow rates correlated with the numerically estimated hydrodynamic parameters. The impacts of these hydrodynamic parameters on a 5.5 kHz CVL pumped dye laser output are discussed.     

预混气体燃烧火焰闪烁现象分析

在低速射流的预混火焰和扩散火焰中都存在火焰闪烁现象。对扩散火焰,其机理已比较明确,是由于浮力诱导引起的一种水力学不稳定性。而对预混火焰闪烁现象则存在水力学不稳定性和热驱动不稳定性两种观点。本文根据水力学不不稳定性观点,把预混火焰的闪烁现象看成是包围火焰锋面的已燃混气层中内、外区间在垂直方向上的相对脉动,应用Ｋｅｌｖｉｎ－Ｈｅｌｍｈｏｌｔｚ不稳定性机理进行了分析,获得了火焰闪烁频率与重力和压力的关系式,并与已有的结果作了对比。     

Numerical simulation of the hydrodynamic instability experiments and flow mixing

Based on the numerical methods of volume of fluid (VOF) and piecewise parabolic method (PPM) and parallel circumstance of Message Passing Interface (MPI), a parallel multi-viscosity-fluid hydrodynamic code MVPPM (Multi-Viscosity-Fluid Piecewise Parabolic Method) is developed and performed to study the hydrodynamic instability and flow mixing. Firstly, the MVPPM code is verified and validated by simulating three instability cases: The first one is a Riemann problem of viscous flow on the shock tube; the second one is the hydrodynamic instability and mixing of gaseous flows under re-shocks; the third one is a half height experiment of interfacial instability, which is conducted on the AWE’s shock tube. By comparing the numerical results with experimental data, good agreement is achieved. Then the MVPPM code is applied to simulate the two cases of the interfacial instabilities of jelly models accelerated by explosion products of a gaseous explosive mixture (GEM), which are adopted in our experiments. The first is implosive dynamic interfacial instability of cylindrical symmetry and mixing. The evolving process of inner and outer interfaces, and the late distribution of mixing mass caused by Rayleigh-Taylor (RT) instability in the center of different radius are given. The second is jelly layer experiment which is initialized with one periodic perturbation with different amplitude and wave length. It reveals the complex processes of evolution of interface, and presents the displacement of front face of jelly layer, bubble head and top of spike relative to initial equilibrium position vs. time. The numerical results are in excellent agreement with that experimental images, and show that the amplitude of initial perturbations affects the evolvement of fluid mixing zone (FMZ) growth rate extremely, especially at late times.     

Laser driven acoustic instabilities in materials with strain-dependent dielectric constants

A simple analysis of the laser driven acoustic wave instability in a material with strain-dependent dielectric constants is given. The analysis is based on the hydrodynamic model of a plasma in the collision dominated regime. Using coupled mode theory, the acoustic instability in the medium is investigated and the threshold value of the pump electric field and the conditions for the initial growth rates of unstable acoustic waves are deduced. It is found that large values of growth can be achieved for materials having an anomalously large dielectric constant, which is otherwise not achievable with piezoelectric interaction. Because of the non-availability of the relevant experimental data, we were unable to compare our theoretical case with an experimental one.     

Experimental study of pressure pulsations in the flow duct of a medium-size model hydroelectric generator with Francis turbine

In the present study, we report on the results of an experimental study of pressure pulsations in the flow duct of a medium-scale hydrodynamic bench with Francis turbine. In various regimes, integral and pulsation characteristics of the turbine were measured. With the help of high-speed filming, the structure of the flow behind the turbine runner was analyzed, and the influence of this structure on the intensity and frequency of pressure pulsations in the flow duct was demonstrated.     

Hydrodynamic instability of premixed flame propagating in narrow planar channel in the presence of gas flow

The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.     

The numerical study of shock-induced hydrodynamic instability and mixing

Based on multi-fluid volume fraction and piecewise parabolic method (PPM), a multi-viscosity-fluid hydrodynamic code MVPPM (Multi-Viscosity-Fluid Piecewise Parabolic Method) is developed and applied to the problems of shock-induced hydrodynamic interfacial instability and mixing. Simulations of gas/liquid interface instability show that the influences of initial perturbations on the fluid mixing zone (FMZ) growth are significant, especially at the late stages, while grids have only a slight effect on the FMZ width, when the interface is impulsively accelerated by a shock wave passing through it. A numerical study of the hydrodynamic interfacial instability and mixing of gaseous flows impacted by re-shocks is presented. It reveals that the numerical results are in good agreement with the experimental results and the mixing growth rate strongly depends on initial conditions. Ultimately, the jelly layer experiment relevant to the instability impacted by exploding is simulated. The shape of jelly interface, position of front face of jelly layer, crest and trough of perturbation versus time are given; their simulated results are in good agreement with experimental results.     

Numerical computation of an immiscible two-phase flow in comparison with experiment

The flow of fluids with interfaces or free surfaces is of great interest in both basic and applied research. Despite enormous efforts to develop numerical methods for solving such flow problems, no undisputed standards have emerged yet. We compare here three different approaches for the problem of a liquid film falling down along a vertical wall under the action of gravity. Due to an instability, waves form on the film surface and a nontrivial flow pattern emerges. This provides a test case for two-phase flow simulation methods under conditions of practical relevance. The methods compared are a moving boundary method and a volume of fluid method implemented in commercial software packages and a new phase field method. A set of experimental data is used as a reference for the comparison. All three methods correctly reproduce the main features of the experiment; however, none are free of quantitative deviations from the data. The text was submitted by the authors in English.     

Cooling performance of a nanofluid flow in a heat sink microchannel with axial conduction effect

In this work, the forced convection of a nanofluid flow in a microscale duct has been investigated numerically. The governing equations have been solved utilizing the finite volume method. Two different conjugated domains for both flow field and substrate have been considered in order to solve the hydrodynamic and thermal fields. The results of the present study are compared to those of analytical and experimental ones, and a good agreement has been observed. The effects of Reynolds number, thermal conductivity and thickness of substrate on the thermal and hydrodynamic indexes have been studied. In general, considering the wall affected the thermal parameter while it had no impact on the hydrodynamics behavior. The results show that the effect of nanoparticle volume fraction on the increasing of normalized local heat transfer coefficient is more efficient in thick walls. For higher Reynolds number, the effect of nanoparticle inclusion on axial distribution of heat flux at solid–fluid interface declines. Also, less end losses and further uniformity of axial heat flux lead to an increase in the local normalized heat transfer coefficient.     

Comparison of measured broadband noise attenuation spectra from circular flow ducts and from lined engine intakes with predictions

Sound propagation in lined circular ducts is investigated in the presence of uniform and sheared flow. The modal solutions are obtained by solving an eigenvalue equation which, in the case of sheared flow, is derived by using finite differences and by matching the pressure and the radial component of the particle velocity at the interface of the regions of uniform and sheared flow. For the uniform flow region, standard Bessel function solutions are used. The attenuation of acoustic energy at a given frequency and for a given liner length is computed on the assumption that at the inlet to the lined duct, the acoustic energy is equally distributed among the propagating modes. The total number of propagating modes is determined from the hard wall “cut off” condition. The failure to find some of the modal solutions on the attenuation computed in this way is discussed. It is shown that the reliability of this method of computing liner attenuation depends on the ability to successfully compute most of the modal solutions over a large range of frequencies, flow conditions and duct wall impedance values. A numerical technique is developed which uses a fraction of the total number of solutions to compute the total attenuations without appreciable loss of accuracy. Measured attenuation spectra from a flow duct facility and from lined intake ducts of the RB.211 engine are compared with predictions. In general very good agreement between predictions and measurements is obtained.     

A piecewise linear mean flow model for studying stability in a lined channel

Acoustic liners are used to reduce sound emission by turbofan engines. Under grazing flow they may sustain hydrodynamic instabilities and these are studied using a stability analysis, based on a simplified model: the liner is a mass–spring–damper system, the base channel flow is piecewise linear, and the inviscid, incompressible Rayleigh equation is used. The model is an extension to the channel case of a boundary layer model by Rienstra and Darau. The piecewise linear profile introduces a finite boundary layer thickness which ensures well-posedness, allowing an initial value problem to be conducted to investigate absolute stability. For typical values in aeronautics the flow above the liner is unstable. Absolute instability is obtained for somewhat extreme values of the mean flow (tiny boundary layer thickness), and under realistic conditions the flow is convectively unstable. The effect of finite channel height is investigated in both cases. In particular, for large boundary layer thicknesses associated with convective instability the channel height has little effect on the unstable mode. Favorable outcomes and failures of the model are shown by comparison to a published experimental work.     

Numerical investigation of the air injection effect on the cavitating flow in Francis hydro turbine

At full and over load operating points, some Francis turbines experience strong self-excited pressure and power oscillations. These oscillations are occuring due to the hydrodynamic instability of the cavitating fluid flow. In many cases, the amplitude of such pulsations may be reduced substantially during the turbine operation by the air injection/ admission below the runner. Such an effect is investigated numerically in the present work. To this end, the hybrid one-three-dimensional model of the flow of the mixture “liquid?vapor” in the duct of a hydroelectric power station, which was proposed previously by the present authors, is augmented by the second gaseous component — the noncondensable air. The boundary conditions and the numerical method for solving the equations of the model are described. To check the accuracy of computing the interface “liquid?gas”, the numerical method was applied at first for solving the dam break problem. The algorithm was then used for modeling the flow in a hydraulic turbine with air injection below the runner. It is shown that with increasing flow rate of the injected air, the amplitude of pressure pulsations decreases. The mechanism of the flow structure alteration in the draft tube cone has been elucidated, which leads to flow stabilization at air injection.     

Turbulent flame and the darrieus–landau instability in a three-dimensional flow

The velocity of a weakly turbulent flame influenced by the Darrieus–Landau (DL) instability in a three-dimensional geometry is investigated on the basis of a model nonlinear equation. The equation takes into account realistically large thermal expansion of burning matter, external turbulence and thermal conduction related to small, but finite flame thickness. An external turbulent flow is imitated by a model obeying the Kolmogorov law. The effects of the DL instability and external turbulence are studied, first separately and then as they influence the flame dynamics together for different values of the turbulent intensity, different thermal expansion of the burning matter and different length scales of the hydrodynamic motion controlled by the width of a hypothetic tube with ideally adiabatic walls. The velocity increase obtained is in a good agreement with experimental results in the case of relatively weak turbulent intensity.     

Nanoscale hydrodynamic instability in a molten thin gold film induced by femtosecond laser ablation

A mechanism of the formation of a nanotip with a nanoparticle at its top that appears in a thin metal film irradiated by a single femtosecond laser pulse has been studied experimentally and theoretically. It has been found that the nanotip appears owing to a melt flow and a nanojet formation, which is cooled and solidified. Within a proposed hydrodynamic model, the development of thermocapillary instability in the melted film is treated with the use of the Kuramoto-Sivashinsky-type hydrodynamic equation. The simulation shows that the nanojet nucleates in the form of a nanopeak in a pit on the top of a microbump (linear stage) and, then, grows in a nonlinear (explosive) regime of an increase in thermocapillary instability in good agreement with experimental data.     

Numerical investigation of low-frequency instability and frequency shifting in a scramjet combustor

The combustion instability in a laboratory-scale direct-connect hydrogen-fueled scramjet combustor is investigated numerically. The numerical simulation has been carried out using a delayed detached eddy simulation (DDES) with a detailed reaction mechanism. The computational framework has high fidelity by applying multi-dimensional high order accurate schemes for handling convective and viscous fluxes. The field data were accumulated up to 100 milliseconds on each case to capture sufficiently the repetitive behavior of low-frequency instability of order of 100 Hz. The numerical results exhibit the formation/dissipation of pressure and shock wave induced by continuous heat release in the combustor. This motion of pressure/shock wave, so-called upstream-traveling shock wave, presents repeated dynamics between isolator and combustor with a period of several milliseconds. With this periodic hydrodynamic characteristic, the upstream-traveling shock wave interacts with the boundary layer and injected fuel stream affecting fuel/air mixing and burning, and finally inducing the combustion instability in a scramjet combustor. Frequency analysis derived major instability frequencies of 190 Hz and 450 Hz in the isolator and combustor for low and high equivalence ratios, respectively. Current numerical results present the underlying flow physics on the shifting of the instability frequency by changing the equivalence ratio observed by the previous experimental studies. The fact that an instability frequency exists homogeneously from isolator to combustor informs that the combustion instability of scramjet engine is the fully coupled flow/combustion dynamics throughout the engine on a macroscopic scale.     

Fermionic renormalization group flow into phases with broken discrete symmetry: charge-density wave mean-field model

We generalize the application of the functional renormalization group (fRG) method for the fermionic flow into the symmetry-broken phase to finite temperatures. We apply the scheme to the case of a broken discrete symmetry: the charge-density wave (CDW) mean-field model at half filling. We show how an arbitrarily small initial CDW order parameter starts to grow at the CDW instability and how it flows to the correct final value, suppressing the divergence of the effective interaction in the fRG flow. The effective interaction peaks at the instability and saturates at low energy scales or temperatures. The relation to the mean-field treatment, differences compared to the flow for a broken continuous symmetry, and the prospects of the new method are discussed.