David Marx

Numerical Simulation of Stack-Heat Exchangers Coupling in a Thermoacoustic Refrigerator

The Navier‐Stokes equations for an unsteady and compressible flow are solved numerically to investigate the flow near the stack of a thermoacoustic refrigerator. The computational domain is a resonator “slice” including the resonator end but not the source. An incoming wave is introduced into the domain using the method of characteristics. Also included in the domain is a stack plate and two heat exchangers. The effects of the acoustic Mach number and geometrical parameters on refrigerator performance is investigated. Of special interest are some nonlinear temperature oscillations, which are not predicted by linear models and are due to acoustic propagation, and coupling between the stack plate and the heat exchangers. It is shown that the maximum heat pumping occurs fo ra stack/heat exchanger separation that is of the order of one particle displacement amplitude.

Experimental localization of an acoustic sound source in a wind-tunnel flow by using a numerical time-reversal technique

The possibility of using the time-reversal technique to localize acoustic sources in a wind-tunnel flow is investigated. While the technique is widespread, it has scarcely been used in aeroacoustics up to now. The proposed method consists of two steps: in a first experimental step, the acoustic pressure fluctuations are recorded over a linear array of microphones; in a second numerical step, the experimental data are time-reversed and used as input data for a numerical code solving the linearized Euler equations. The simulation achieves the back-propagation of the waves from the array to the source and takes into account the effect of the mean flow on sound propagation. The ability of the method to localize a sound source in a typical wind-tunnel flow is first demonstrated using simulated data. A generic experiment is then set up in an anechoic wind tunnel to validate the proposed method with a flow at Mach number 0.11. Monopolar sources are first considered that are either monochromatic or have a narrow or wide-band frequency content. The source position estimation is well-achieved with an error inferior to the wavelength. An application to a dipolar sound source shows that this type of source is also very satisfactorily characterized.

An introduction to synthetic aperture sonar

DTI has demonstrated that synthetic aperture sonar (SAS) can provide orders of magnitude improvement in cross-range resolution when compared to conventional sonar beamforming. Like synthetic aperture radar (SAR), SAS processing requires coherence over multiple measurements, but has long been impractical due to the nature of the ocean environment. We have extended SAR processing ideas to accommodate the issues specific to the underwater environment, and have successfully synthesized apertures extending many thousands of wavelengths. We will present an overview of the theory of SAS processing, how it differs from SAR, and will show experimental results from SAS processing of sonar data.

Computation of the temperature distortion in the stack of a standing-wave thermoacoustic refrigerator

The numerical computation of the flow and heat transfer in the vicinity of a stack plate in a standing wave refrigerator is performed. Temperature distortion is observed, which appears only in the stack region, even if the acoustic standing wave outside the stack is itself sinusoidal. The distortion takes place above the whole plate surface when the length of the plate is equal to or shorter than four times the particle displacement. This condition may occur at high drive ratios and is favored by plate positions close to the velocity antinode. The thermal distortion decreases the thermoacoustic heat pumping along the plate. At high drive ratios, if the length of the plate is not large enough, the thermal distortion can typically explain a difference of about 10% between the calculated heat flux and the heat flux predicted using linear theory.

Time-domain delay-and-sum beamforming for time-reversal detection of intermittent acoustic sources in flows

This study focuses on the identification of intermittent aeroacoustic sources in flows by using the time-domain beamforming technique. It is first shown that this technique can be seen as a time-reversal (TR) technique, working with approximate Green functions in the case of a shear flow. Some numerical experiments investigate the case of an array measurement of a generic acoustic pulse emitted in a wind-tunnel flow, with a realistic multi-arm spiral array. The results of the time-domain beamforming successfully match those given by a numerical TR technique over a wide range of flow speeds (reaching the transonic regime). It is shown how the results should be analyzed in a focusing plane parallel to the microphone array in order to estimate the location and emission time of the pulse source. An experimental application dealing with the aeroacoustic radiation of a bluff body in a wind-tunnel flow is also considered, and shows that some intermittent events can be clearly identified in the noise radiation. Time-domain beamforming is then an efficient tool for analyzing intermittent acoustic sources in flows, and is a computationally cheaper alternative to the numerical TR technique, which should be used for complex configurations where the Green function is not available.

Analysis of the Acoustic Flow at an Abrupt Change in Section of an Acoustic Waveguide Using Particle Image Velocimetry and Proper Orthogonal Decomposition

In the vicinity of an abrupt change in cross section, an acoustic wave generates a nonlinear flow. This is investigated experimentally using Particle Image Velocimetry (PIV). The effect of both the acoustic level and the radius of curvature of the abrupt change in section on the flow is studied. At sufficiently high acoustic levels, and past a value of about 0.5 for the Strouhal number, the flow separates and a vortex is formed. Its evolution with the different parameters is studied. Proper Orthogonal Decomposition (POD) is applied to the ensemble of phase-averaged flow fields in the vicinity of the abrupt change. It is used as a means to separate the global acoustic movement from the localized non linear movements induced by it. The quantity of energy flowing from the first (acoustic) mode toward the higher (nonlinear) modes is calculated and is shown to be largely governed by the Strouhal number.

Evidence of Hydrodynamic Instability over a Liner in a Duct with Flow

Lined ducts are widely used to reduce noise radiation from ducts, from air conditioning systems to turbofan engines. Liners may sustain some instabilities although there is no definite knowledge on that subject. Some analytical studies based on simple flow models have predicted the existence of unstable hydrodynamic modes, but their prediction capability for realistic conditions is difficult to assess. Experimentalevidence of the existence of instable modes in realistic flow conditions exist but is rare. While large increase in acoustic transmission across a lined part of ducts have been measured in the past, the flow itself over the liner has never been investigated. In the present paper an experimental study of the flow over a liner is made in such a configuration where the acoustic transmission is large, and evidence of an underlying hydrodynamic instability is provided, based on optical flow measurements.

Numerical Computation of a Lined Duct Instability Using the Linearized Euler Equations

The two-dimensional linearized Euler equations in the time domain are computed to obtain the sound field in a channel with a rigid upper wall and an acoustic liner on the bottom wall in the presence of a shear flow. The liner is a simple mass–spring–damper system. The shear flow has a rather thin boundary layer, and the mesh has to be refined close to the walls. The objective is to assess whether an instability can be computed and whether a computed instability is physical. The computations are backed by a linear stability analysis of the flow that is performed by solving a matrix eigenvalue problem. By comparing the results of the simulations of the linearized Euler equations with the results of the stability analysis, it is found that the computed instabilities are physical and that their characteristics can be predicted. The effect of using selective filtering on the wave-number spectrum is also discussed.

Detection of Non-Stationary Aeroacoustic Sources by Time-Domain Imaging Methods

Imaging methods such as the beamforming technique are widely used to localize and identify aeroacoustic sources. However, so far, existing applications in aeroacoustics have mostly been performed in the frequency domain. To tackle the characterization of nonstationary sources (for example, intermittent sources), time-domain imaging methods are more appropriate. Indeed, the spatio-temporal reconstruction of the acoustic fields allows studying the source structure in “real-time”. In this paper, two aeroacoustic problems are investigated with the help of time-domain inverse methods. First, numerical acoustic data obtained from the simulation of the radiation of a 2D mixing layer are studied through a numerical time-reversal method based on the Linearized Euler Equations. The spatio-temporal maxima of the acoustic energy are then detected by observing successive snapshots of the reconstructed acoustic field. These are assumed to correspond to wave focusing and, hence, to be related to the presence of a source. Finally, vorticity field snapshots are observed at the times at which spatio-temporal maxima are found. A conditional average of the flow fields, assuming large acoustic emission, is thus possible in principle. The global structure of the source is found to be quadripolar and each kind of detected maxima corresponds to a fixed vortical structure. Second, experimental data of the noise produced by a forward-facing step in a wind-tunnel flow are analysed by using the timedomain beamforming technique. The detection of spatio-temporal maxima highlights that the broadband noise source produced by the step can be seen as a succession of short duration events scattered around the step edge.

Comparison of Experiments with Stability Analysis Predictions in a Lined Flow Duct

Lined ducts are widely used to reduce noise radiation from ducts in turbofan engines. They may sustain some instabilities. Analytical studies based on simple o w models have predicted the existence of unstable hydrodynamic modes, but that point is still discussed. Here a linear local spatial stability analysis of the o w in a 2D lined channel is performed, using a numerical integration of the governing equations. A realistic mean o w prole is used that vanishes at the wall, and the Myers boundary condition is not used. The stability analysis results are compared to recent experimental results. Both the model and the experiments conclude in the existence of an unstable mode. Quantities such as the growth rate and the velocity eigenfunctions are compared and are shown to agree rather well.