Determination of correlation functions of turbulent velocity and sound speed fluctuations by means of ultrasonic technique

An experimental study of the propagation of high-frequency acoustic waves through grid-generated turbulence by means of an ultrasound technique is discussed. Experimental data were obtained for ultrasonic wave propagation downstream of heated and non-heated grids in a wind tunnel. A semi-analytical acoustic propagation model that allows the determination of the spatial correlation functions of the flow field is developed based on the classical flowmeter equation and the statistics of the travel time of acoustic waves traveling through the kinematic and thermal turbulence. The basic flowmeter equation is reconsidered in order to take into account sound speed fluctuations and turbulent velocity fluctuations. It allows deriving an integral equation that relates the correlation functions of travel time, sound speed fluctuations and turbulent velocity fluctuations. Experimentally measured travel time statistics of data with and without grid heating are approximated by an exponential function and used to analytically solve the integral equation. The reconstructed correlation functions of the turbulent velocity and sound speed fluctuations are presented. The power spectral density of the turbulent velocity and sound speed fluctuations are calculated.     

Numerical prediction of turbulent boundary layer noise from a sharp-edged flat plate

An efficient hybrid uncorrelated wall plane waves–boundary element method (UWPW-BEM) technique is proposed to predict the flow-induced noise from a structure in low Mach number turbulent flow. Reynolds-averaged Navier-Stokes equations are used to estimate the turbulent boundary layer parameters such as convective velocity, boundary layer thickness, and wall shear stress over the surface of the structure. The spectrum of the wall pressure fluctuations is evaluated from the turbulent boundary layer parameters and by using semi-empirical models from literature. The wall pressure field underneath the turbulent boundary layer is synthesized by realizations of uncorrelated wall plane waves (UWPW). An acoustic BEM solver is then employed to compute the acoustic pressure scattered by the structure from the synthesized wall pressure field. Finally, the acoustic response of the structure in turbulent flow is obtained as an ensemble average of the acoustic pressures due to all realizations of uncorrelated plane waves. To demonstrate the hybrid UWPW-BEM approach, the self-noise generated by a flat plate in turbulent flow with Reynolds number based on chord Re_c = 4.9 × 10⁵ is predicted. The results are compared with those obtained from a large eddy simulation (LES)-BEM technique as well as with experimental data from literature.     

平板湍流边界层的声辐射

基于平板湍流边界层的壁压起伏波数—频率谱 ,给出了一种湍流边界层声辐射的估算方法 ,并对光滑平板湍流边界层和平板表面粗糙度引起的湍流边界层声辐射进行了分析。结果表明 :湍流边界层声辐射是一种四极子声辐射 ,且其辐射声能集中于平板表面粗糙度引起的湍流边界层声辐射 ;光滑平板湍流边界层的声辐射也不可忽略。     

Constant temperature hot-wire anemometer practice in supersonic flows

The performance of a constant-temperature normal hotwire in a supersonic flow is critically examined. It is shown that this instrument is inherently unsuitable for measuring turbulent temperature correlations because of the highly non-linear response to temperature fluctuations, particularly at low overheat ratios. The instrument is therefore limited to measurements of mean and fluctuating mass-flow rates. Suitable calibration procedures. as well as the limits on spatial and temporal resolution are discussed. and corrections for mean stagnation temperature changes are suggested. The instrument was used to measure the mass-flow fluctuations in a zero pressure gradient Mach 2.9 turbulent boundary layer. A comparison with the available data suggests good agreement.     

Finite Difference Method for the Acoustic Radiation of an Elastic Plate Excited by a Turbulent Boundary Layer: A Spectral Domain Solution

A finite difference method is developed to study, on a two-dimensional model, the acoustic pressure radiated when a thin elastic plate, clamped at its boundaries, is excited by a turbulent boundary layer. Consider a homogeneous thin elastic plate clamped at its boundaries and extended to infinity by a plane, perfectly rigid, baffle. This plate closes a rectangular cavity. Both the cavity and the outside domain contain a perfect fluid. The fluid in the cavity is at rest. The fluid in the outside domain moves in the direction parallel to the system plate/baffle with a constant speed. A turbulent boundary layer develops at the interface baffle/plate. The wall pressure fluctuations in this boundary layer generates a vibration of the plate and an acoustic radiation in the two fluid domains. Modeling the wall pressure fluctuations spectrum in a turbulent boundary layer developed over a vibrating surface is a very complex and unresolved task. Ducan and Sirkis [1] proposed a model for the two-way interactions between a membrane and a turbulent flow of fluid. The excitation of the membrane is modeled by a potential flow randomly perturbed. This potential flow is modified by the displacement of the membrane. Howe [2] proposed a model for the turbulent wall pressure fluctuations power spectrum over an elastomeric material. The model presented in this article is based on a hypothesis of one-way interaction between the flow and the structure: the flow generates wall pressure fluctuations which are at the origin of the vibration of the plate, but the vibration of the plate does not modify the characteristics of the flow. A finite difference scheme that incorporates the vibration of the plate and the acoustic pressure inside the fluid cavity has been developed and coupled with a boundary element method that ensures the outside domain coupling. In this paper, we focus on the resolution of the coupled vibration/interior acoustic problem. We compare the results obtained with three numerical methods: (a) a finite difference representation for both the plate displacement and the acoustic pressure inside the cavity; (b) a coupled method involving a finite difference representation for the displacement of the plate and a boundary element method for the interior acoustic pressure; (c) a boundary element method for both the vibration of the plate and the interior acoustic pressure. A comparison of the numerical results obtained with two models of turbulent wall pressure fluctuations spectrums - the Corcos model [3] and the Chase model [4] - is proposed. A difference of 20 dB is found in the vibro-acoustic response of the structure. In [3], this difference is explained by calculating a wavenumber transfer function of the plate. In [6], coupled beam-cavity modes for similar geometry are calculated by the finite difference method. This revised version was published online in July 2006 with corrections to the Cover Date.     

Measurements of admixture concentration fluctuations in a turbulent shear flow using an averaged Talbot image

The present study is concerned with adopting of a Talbot effect-based technique for analyzing flows with random phase inhomogeneities. It is shown that this method is a powerful tool for diagnostics of turbulent flows. The potential of the technique is illustrated by measuring mean and fluctuating values of admixture concentration of two-dimensional turbulent helium jet issuing into the ambient air. Averaged air and helium concentrations throughout the flow field are determined using local light refraction measurements with a high spatial resolution from a long-exposed Talbot image of the jet. The analysis of light intensity distributions in light spots of a Talbot-image shows that the jet turbulence is inhomogeneous and anisotropic. Quantitative information on rms fluctuations of concentration gradients throughout the flow field is obtained from local photometric measurements at the Talbot light spots.     

Electrical fluctuations in turbulent electrogasdynamic flows

Processes in turbulent flows containing charged particles are examined. It is shown that fluctuations of the electrical charge, which can be recorded by special apparatus, occur in the jets of aircraft engines in the presence of charged particles of unburned fuel in them and in turbulent jets created under laboratory conditions by blowing corona sources with air. The problem of determining the characteristics of turbulence in jets from measurements of electrical fluctuations sensed by an electrostatic probe is formulated. The electrical fluctuations generated by a submerged electrogasdynamic jet were measured under laboratory conditions and the results were compared with the data of acoustic measurements. A good correlation of the relative electrical and acoustic characteristics was found. The spectra of electrical fluctuations of a jet during its neutralization were studied by means of a special compensator and the mixing zone of opposite electrical charges was determined. The electrical fluctuations generated by the jets of aircraft were measured under airfield conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 148–159, March–April, 1977.The authors thank A. N. Sekundov for a valuable discussion and help in the work and also A. P. Strekalov and V. F. Kudryashov for participating in the experimental investigations.     

Spectral Vorticity and Lagrangian Velocity Measurements in Turbulent Jets

In this paper we report an experimental investigation of various statistical properties of the spatial Fourier modes of the vorticity field in turbulent jets for a large range of Reynolds numbers (530 ≤R _λ≤ 6100). The continuous time evolution of a spatial Fourier mode of the vorticity distribution, characterized by a well-defined wavevector, is obtained from acoustic scattering measurements. The spatial enstrophy spectrum, as a function of the spatial wave-vector, is determined by scanning the incoming sound frequencies. Time-frequency analysis of the turbulent vorticity fluctuations is also performed for different length scales of the flows. Vorticity time-correlations show that the characteristic time of a Fourier mode behaves as the sweeping time. Finally, we report preliminary Lagrangian velocity measurements obtained using acoustic scattering by soap bubbles inflated with helium. Gathering a large number of passages of isolated bubbles in the scattering volume, one is able to compute the Lagrangian velocity PDF and velocity spectrum. Despite the spatial filtering due to the finite size of the bubble, the latter exhibits a power law, with the -2 exponent predicted by the Kolmogorov theory, over one decade of frequencies.     

Holographic velocimetry for flow diagnostics

Currently, there are a number of flow diagnostic tools available for the evaluation of fluid dynamic systems. In spite of its great potential, holographic velocimetry is one technique which has not been widely used. It does, however, have great potential in this area due to its inherent three-dimensionality. As demonstrated in this study of fully developed turbulent flow in a pipe, full three-dimensional mapping can be achieved at any instant in a flow cycle. Comparisons of holographic results with analytical predictions and laser-Doppler-anemometry (LDA) measurements demonstrate the accuracy of the technique as well as some of its advantages and disadvantages relative to LDA. Although relatively poor spatial resolution is obtained, the fact that holographic velocimetry is both an instantaneous and full volume measuring tool makes it useful for a range of complex and high-speed flow-measurement applications.     

An Experimental Database for Benchmarking Simulations of Turbulent Premixed Reacting Flows: Lean Extinction Limits and Velocity Field Measurements in a Dump Combustor

This contribution is aimed at drawing the attention of the computational fluid dynamics community on the availability of an experimental database regarding turbulent lean premixed prevaporised (LPP) reacting flows stabilised behind a double symmetric, plane sudden expansion fed by two fully developed turbulent channel flows of air plus propane. This flow configuration can be thought of as a relevant benchmark for testing turbulence and/or combustion models aimed at helping for the design of reliable LPP combustion chambers. This database contains a large amount of raw and processed data regarding essentially the velocity field for one inert and three different reacting flows configurations. Additional pieces of information are available and concern the lean extinction properties and the wall static pressure evolution in the feeding channels. For the reacting flows, the presence of a large scale coherent motion is clearly visible in the velocity spectra and it is shown how a data processing based on the semi-deterministic approach that decomposes the velocity signal into the sum of its steady time average, its coherent fluctuations and its stochastic fluctuations can permit to evaluate their respective contribution to the total velocity fluctuations.     

Transition from Countergradient to Gradient Scalar Transport in Developing Premixed Turbulent Flames

A simple model of turbulent scalar flux developed recently by the present authors is applied to determine the direction of the flux in a statistically planar one-dimensional premixed flame that does not affect turbulence and has self-similar mean structure. Results obtained in the case of statistically stationary turbulence indicate that transition from countergradient to gradient turbulent scalar transport may occur during flame development, as the peak mean rate of product creation moves to the trailing edge of the flame brush. In the case of decaying turbulence, the opposite transition (from gradient to countergradient transport) was simulated in line with available DNS data. In both cases, transition instant depends strongly on turbulence and mixture characteristics. In particular, countergradient transport is suppressed by an increase in the rms turbulent velocity and by a decrease in the laminar flame speed or density ratio, in line with available experimental and DNS data. The obtained results lend qualitative support to the model of turbulent scalar flux addressed in the present work.     

Characterization of gas–solid fluidized bed hydrodynamics by vibration signature analysis

Vibration measurement, as a non-intrusive technique, was used to characterize the hydrodynamics of fluidized beds. A series of experiments were performed in a lab-scale fluidized bed using two accelerometers for measuring the vibration of the bed and a pressure probe for measuring pressure fluctuations. The output signals were analyzed by statistical methods. The results show that the vibration technique can predict transition velocities at high velocities and indicate that analyzing the vibration signals can be an effective non-intrusive technique to characterize the hydrodynamics of fluidized beds. It was shown that transition from bubbling to turbulent velocity can be determined from the variation of standard deviation and kurtosis of vibration signals against superficial gas velocity of the bed. However, this point could be determined only from standard deviation of pressure fluctuations, and not from skewness or kurtosis of pressure fluctuations.     

可压缩各向同性衰减湍流直接数值模拟研究

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性 和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等. 研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大 尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量(压缩)耗散率所占比率也显著增长. 标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高(p ≥ 5)时,纵向速度结构函数的扩展自相似性则不再成立. 对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的 间歇性要强于横向湍流脉动.     

Free-surface fluctuations in hydraulic jumps: Experimental observations

A hydraulic jump is the rapid and sudden transition from a high-velocity supercritical open channel flow to a subcritical flow. It is characterised by the dynamic interactions of the large-scale eddies with the free-surface. New series of experimental measurements were conducted in hydraulic jumps with Froude numbers between 3.1 and 8.5 to investigate these interactions. The dynamic free surface measurements were performed with a non-intrusive technique while the two-phase flow properties were recorded with a phase-detection probe. The shape of the mean free surface profile was well defined and the turbulent fluctuation profiles highlighted a distinct peak of turbulent intensity in the first part of the jump roller, with free-surface fluctuation levels increasing with increasing Froude number. The dominant free-surface fluctuation frequencies were typically between 1 and 4 Hz. A comparison between the acoustic sensor signals and conductivity probe data suggested that the air–water “free-surface” detected by the acoustic sensor corresponded to about the boundary between the turbulent shear layer and the upper free-surface layer. Simultaneous measurements of free surface and bubbly flow fluctuations for Fr = 5.1 indicated that the frequency ranges of both sensors were similar (F < 5 Hz) whatever the position downstream of the toe. The present results highlighted that the dynamic free-surface measurements can be conducted successfully using acoustic displacement meters, and the time-averaged depth measurements was a physical measure of the free-surface location in hydraulic jumps.     

Sustainment of Oscillations in Localized Turbulent Structures in Pipes

The solution of the Navier–Stokes equations which reproduces some qualitative features of localized turbulent structures developed in circular pipes at transitional Reynolds numbers is numerically investigated. In the phase space this solution corresponds to the limiting state of the solution which evolves along the separatrix dividing the regions of attraction of the solutions corresponding to the laminar and turbulent flow regimes. Relative simplicity of the spatial and temporal behavior of the limiting solution on the separatrix makes it possible to investigate it in detail. In particular, the nonlinear mechanism of the onset of streamwise vortices responsible for sustainment of near-wall streaks whose instability ensures the presence of fluctuations is revealed.     

Direct numerical simulation of the turbulent energy balance and the shear stresses in power-law fluid flows in pipes

The results of direct numerical simulation of turbulent flows of non-Newtonian pseudoplastic fluids in a straight pipe are presented. The data on the distributions of the turbulent stress tensor components and the shear stress and turbulent kinetic energy balances are obtained for steady turbulent flows at the Reynolds numbers of 10⁴ and 2×10⁴. As distinct from Newtonian fluid flows, the viscous shear stresses turn out to be significant even far from the wall. In power-law fluid flows the mechanism of the energy transport from axial to transverse component fluctuations is suppressed. It is shown that with decrease in the fluid index the turbulent transfer of the momentum and the velocity fluctuations between the wall layer and the flow core reduces, while the turbulent energy flux toward the wall increases. The earlier-proposed models for the average viscosity and the non-Newtonian one-point correlations are in good agreement with the data of direct numerical simulation.     

The Acoustic Limit for the Boltzmann Equation

The acoustic equations are the linearization of the compressible Euler equations about a spatially homogeneous fluid state. We first derive them directly from the Boltzmann equation as the formal limit of moment equations for an appropriately scaled family of Boltzmann solutions. We then establish this limit for the Boltzmann equation considered over a periodic spatial domain for bounded collision kernels. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations that converge entropically (and hence strongly in L ¹) to a unique limit governed by a solution of the acoustic equations for all time, provided that its initial fluctuations converge entropically to an appropriate limit associated to any given L ² initial data of the acoustic equations. The associated local conservation laws are recovered in the limit. Accepted: October 22, 1999     

The effect of boundary layer fluctuations on the streamwise vortex structure in simulated plane turbulent mixing layers

This paper details the influence of the magnitude of imposed inflow fluctuations on Large Eddy Simulations of a spatially developing turbulent mixing layer originating from laminar boundary layers. The fluctuations are physically-correlated, and produced by an inflow generation technique. The imposed high-speed side boundary layer fluctuation magnitude is varied from a low-level, up to a magnitude sufficiently high that the boundary layer can be considered, in a mean sense, as nominally laminar. Cross-plane flow visualisation shows that each simulation contains streamwise vortices in the laminar and turbulent regions of the mixing layer. Statistical analysis of the secondary shear stress reveals that mixing layers originating from boundary layers with low-level fluctuations contain a spatially stationary streamwise structure. Increasing the high-speed side boundary layer fluctuation magnitude leads to a weakening of this stationary streamwise structure, or its removal from the flow entirely. The mixing layer growth rate reduces with increasing initial fluctuation level. These findings are discussed in terms of the available experimental data on mixing layers, and recommendations for both future experimental and numerical research into the mixing layer are made.