Analyzing the influence of compressibility on the rapid pressure–strain rate correlation in turbulent shear flows

The influence of compressibility on the rapid pressure–strain rate tensor is investigated using the Green’s function for the wave equation governing pressure fluctuations in compressible homogeneous shear flow. The solution for the Green’s function is obtained as a combination of parabolic cylinder functions; it is oscillatory with monotonically increasing frequency and decreasing amplitude at large times, and anisotropic in wave-vector space. The Green’s function depends explicitly on the turbulent Mach number M _t , given by the root mean square turbulent velocity fluctuations divided by the speed of sound, and the gradient Mach number M _g , which is the mean shear rate times the transverse integral scale of the turbulence divided by the speed of sound. Assuming a form for the temporal decorrelation of velocity fluctuations brought about by the turbulence, the rapid pressure–strain rate tensor is expressed exactly in terms of the energy (or Reynolds stress) spectrum tensor and the time integral of the Green’s function times a decaying exponential. A model for the energy spectrum tensor linear in Reynolds stress anisotropies and in mean shear is assumed for closure. The expression for the rapid pressure–strain correlation is evaluated using parameters applicable to a mixing layer and a boundary layer. It is found that for the same range of M _t there is a large reduction of the pressure–strain correlation in the mixing layer but not in the boundary layer. Implications for compressible turbulence modeling are also explored.      

Turbulence Intensity and Length Scale Effects on Premixed Turbulent Flame Propagation

The effects of varying turbulence intensity and turbulence length scale on premixed turbulent flame propagation are investigated using Direct Numerical Simulation (DNS). The DNS dataset contains the results of a set of turbulent flame simulations based on separate and systematic changes in either turbulence intensity or turbulence integral length scale while keeping all other parameters constant. All flames considered are in the thin reaction zones regime. Several aspects of flame behaviour are analysed and compared, either by varying the turbulence intensity at constant integral length scale, or by varying the integral length scale at constant turbulence intensity. The turbulent flame speed is found to increase with increasing turbulence intensity and also with increasing integral length scale. Changes in the turbulent flame speed are generally accounted for by changes in the flame surface area, but some deviation is observed at high values of turbulence intensity. The probability density functions (pdfs) of tangential strain rate and mean flame curvature are found to broaden with increasing turbulence intensity and also with decreasing integral length scale. The response of the correlation between tangential strain rate and mean flame curvature is also investigated. The statistics of displacement speed and its components are analysed, and the findings indicate that changes in response to decreasing integral length scale are broadly similar to those observed for increasing turbulence intensity, although there are some interesting differences. These findings serve to improve current understanding of the role of turbulence length scales in flame propagation.

     

Influences of acoustic instabilities on turbulent-flame propagation

Influences of acoustic instabilities on premixed turbulent-flames have been studied experimentally in a Taylor–Couette (TC) combustor for downward flame propagation in a turbulent flow-field generated in the annulus between two cylinders. Flow-field velocities were measured at a fixed location upstream of the propagating flame using laser-doppler velocimetry, while flame speeds were determined from video-recorded images. It is found that the existence of pre-ignition turbulence in the combustor (generated by rotation of the combustor-cylinder walls) does not eliminate acoustic instabilities, however as the level of pre-ignition turbulence is increased the influence of the secondary acoustic instability on the turbulent-flame speed becomes insignificant. For low intensities of pre-ignition turbulence the flame is found to accelerate during the latter stages of flame propagation, while for high levels of pre-ignition turbulence the flame propagates at a statistically constant speed, even though velocity fluctuations have been substantially amplified by the time the flame reaches the bottom end of the combustor as a result of acoustic instability.     

Dispersion de particules solides en mouvement de saltation dans un écoulement turbulentDispersion of solid saltating particles in a turbulent flow

The solid particle dispersion in saltating motion is studied in an homogeneous turbulence and in a turbulent boundary layer. The fluid velocity along the particle trajectory is estimated using a continuous stochastic differential equation in which the correlation integral time takes into account gravity and inertia effects. As far as the boundary layer is concerned, the aerodynamic entrainment of particles and the rebound are modelised as random variables with Gaussian probability density functions. Compared with experimental results, the numerical results show good agreement for dispersion, although velocity fluctuations are slightly under evaluated. To cite this article: C. Aguirre et al., C. R. Mecanique 332 (2004).     

Propagation of wall pressure perturbations in a large aspect ratio shallow cavity

Wall pressure fluctuations generated by turbulent boundary layers over a shallow cavity are studied experimentally in a low-speed wind tunnel facility. The scope of the present work is to characterize the propagation of the pressure perturbations at the wall by means of pressure cross-correlations and cross-spectra measured through a microphone pair translated along the cavity floor. It is found that the mechanism characterizing the pressure propagation close to the backward facing step and in the middle of the cavity is similar to what is commonly observed in equilibrium boundary layer being the convection velocity smaller than the external mean velocity. On the other hand, in the close vicinity of the forward-step, the hydrodynamic contribution of the pressure fluctuations is accompanied by a relevant acoustic effect characterized by a convection velocity close to the speed of sound. Furthermore, in the regions close to the two steps, the spectral decay of the coherence function, even though of exponential type, is faster than that obtained in the quasi-equilibrium region.     

Internal streamwise action of saw-tooth sound waves on turbulent jets

The results of an experimental investigation of the acoustic field produced by turbulent subsonic jets under internal acoustic excitation are presented. It is shown that under the action of saw-tooth finite-amplitude waves the turbulent jets can radiate Mach waves into the ambient medium due to compact acoustic disturbances traveling along the jet at a velocity greater than the speed of sound in the surrounding space.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 153–158. Original Russian Text Copyright © 2004 by Pimshtein.     

Large-eddy simulation of circular cylinder flow at subcritical Reynolds number: Turbulent wake and sound radiation

The flows past a circular cylinder at Reynolds number 3900 are simulated using large-eddy simulation(LES) and the far-field sound is calculated from the LES results. A low dissipation energy-conserving finite volume scheme is used to discretize the incompressible Navier–Stokes equations. The dynamic global coefficient version of the Vreman's subgrid scale(SGS) model is used to compute the sub-grid stresses. Curle's integral of Lighthill's acoustic analogy is used to extract the sound radiated from the cylinder. The profiles of mean velocity and turbulent fluctuations obtained are consistent with the previous experimental and computational results. The sound radiation at far field exhibits the characteristic of a dipole and directivity. The sound spectra display the-5/3 power law. It is shown that Vreman's SGS model in company with dynamic procedure is suitable for LES of turbulence generated noise.     

Turbulent Flame Speeds of Premixed Supersonic Flame Kernels

It is unclear whether turbulent flame speed scalings established in low speed regimes are applicable to supersonic flames. To investigate this question, the canonical flame kernel is investigated in a scramjet-like channel having a one degree wall divergence. The growth, shape and internal kernel dynamics are investigated. Results are presented for three Mach numbers, four equivalence ratios, and three turbulence generators. Schlieren photography provides flame images for growth rate statistics and particle image velocimetry (PIV) provides turbulence statistics and investigation of internal kernel dynamics. Supersonic flame kernels are self-propagating and respond to the equivalence ratio in a fashion that is similar to low speed flames. However, supersonic flame kernels have features that are not present in subsonic flame kernels. Baroclinicity, resulting from pressure-density misalignment, creates a reacting vortex ring structure. Further, the mean kernel shape has a Mach number dependence and the vortex ring enhances the turbulent flame speed through entrainment of reactants and augmented flame surface growth. Hence, the previously established (low speed) flame speed scalings are inappropriate for supersonic flame kernels. Drawing motivation from vortex ring literature, the ring propagation velocity is used as the characteristic velocity and a new flame speed scaling is proposed.     

Direct Numerical Simulation of Statistically Stationary One- and Two-Phase Turbulent Combustion: A Turbulent Injection Procedure

A new turbulent injection procedure dedicated to fully compressible direct numerical simulation (DNS) or large eddy simulation (LES) solvers is proposed. To avoid the appearance of spurious acoustic waves, this method is based on an accurate tracking of the turbulent structures crossing the boundary at the inlet of the domain. A finite difference DNS solver has been coupled with a spectral simulation in which a statistically stationary homogeneous turbulence evolves to provide fluctuating boundary conditions.A new turbulence forcing method, dedicated to spectral solvers, has been developed as well to control the major properties of the injected flow (turbulent kinetic energy, dissipation rate and integral length scale). One-dimensional Navier–Stokes characteristic boundary conditions extended to non-stationary flows are coupled with the injection procedure to evaluate is potential in four various configurations: spatially decaying turbulence, dispersion of vaporizing sprays, propagation of one- and two-phase V-shape turbulent flames.     

Effect of near-wall turbulence enhancement on the mechanisms of particle deposition

The modification of deposition mechanisms of small particles in wall turbulence due to enhanced near-wall fluctuations is presented. The direct numerical simulation database of turbulent air flow over a water surface populated by gravity-capillary waves of small wave slope was used to mimic the enhancement in fluctuation intensity. Lagrangian tracking of particles is performed under the assumption of one-way coupling between the particles and the flow. Two sets of particles have been considered with inertial response times of 5 and 15, respectively, normalized using the friction velocity at the air–water interface and the kinematic viscosity of air. Compared to wall-bounded flow, the particle deposition rates on the interface were found to be considerably higher; specifically for the low-inertia particles, an eightfold increase was observed. The deposition rate for particles of higher inertia increased by only 60%. The correlation characterizing particle deposition rates for wall-bounded flows, where the deposition rate is proportional to the square of the particle response time, was found to be invalid for the flow with enhanced near-wall turbulence. Comparison with experimental results on particle deposition onto rough walls showed better correlation. Depositing particles were divided into free-flight and diffusional deposition populations. Since the primary effect of the interfacial waves is to increase the turbulence intensity in the near-interface region with high particle concentration, a remarkable increase in diffusional deposition is observed. As in wall-bounded flows, diffusional deposition is seen to be the dominant mechanism of deposition. The free-flight mechanism, where particles acquire velocities high enough to travel directly to the interface, remains unaffected by enhanced near-wall velocity fluctuations.     

Speckle tomography of turbulent flows with density fluctuations

The speckle tomography technique is used for reconstructing both large-scale structures in turbulent flows and the microstructure of turbulence. The technique is based on multi-projectional line-of-sight speckle photography measurements with a subsequent computer-assisted tomographic reconstruction of the interior structure of the flowfield. The large-scale structure is reconstructed using the Radon integral equation, and the microstructure is analysed using a statistical approach and a novel Erbeck-Merzkirch integral transform. Digital speckle photography and speckle tomography methods are described. Numerical simulation of the optical technique is performed using digital ray tracing through a turbulent flowfield. The methods are illustrated by the 3D "averaged" temperature fields in turbulent convective flows obtained earlier and by the recent reconstruction of 3D correlation functions of density variations in turbulent flows. Local values of turbulence (Kolmogorov) microscale are evaluated using these correlation functions and the Erbeck-Merzkirch integral transform The precision of the reconstruction and the spatial resolution achieved are analysed.     

High-intensity turbulence measurements in a Taylor-Couette flow reactor

Turbulence-intensity measurements were made in a Taylor-Couette flow reactor consisting of two counter-rotating concentric cylinders designed for the purpose of studying turbulent premixed-flame propagation. In the annulus separating the two cylinders, a nearly homogeneous turbulent flow is generated. The intensities of turbulent velocity fluctuations in the annulus in both axial and circumferential directions were measured by using laser-Doppler velocimetry for a wide range of cylinder rotation rates, corresponding to low through high (120 cm/s) intensities relative to typical laminar flame speeds for lean methane-air mixtures. The experimental measurements indicate a linear relation between turbulence intensities and average cylinder surface speed and demonstrate the usefulness of the Taylor-Couette apparatus for studies of premixed-flame propagation in high-intensity turbulent flow.     

The influence of peak-locking errors on turbulence statistics computed from PIV ensembles

The influence of peak-locking errors on turbulence statistics computed from ensembles of PIV data is considered. PIV measurements are made in the streamwise–wall-normal plane of turbulent channel flow. The PIV images are interrogated in three distinct ways, generating ensembles of velocity fields with absolute, moderate, and minimal peak locking. Turbulence statistics computed for all three ensembles of data indicate a general sensitivity to peak locking in the single-point statistics, except for the mean velocity profile. Peak-locking errors propagate into the fluctuations of velocity, rendering single-point statistics inaccurate when severe peak locking is present. Multi-point correlations of both streamwise and wall-normal velocity are also found to be influenced by severe levels of peak locking. The displacement range of the measurement, defined by the PIV time delay, appears to affect the influence of peak-locking errors on turbulence statistics. Smaller displacement ranges, particularly those that produce displacement fluctuations that are less than one pixel in magnitude, yield inaccurate turbulence statistics in the presence of peak locking.     

Higher-order and length-scale statistics of velocity and temperature fluctuations in turbulent boundary layer along a heated vertical flat plate

Time-developing direct numerical simulation (DNS) was performed to clarify the higher-order turbulent behaviors in the thermally-driven boundary layers both in air and water along a heated vertical flat plate. The predicted statistics of the heat transfer rates and the higher-order turbulent behaviors such as skewness factors, flatness factors and spatial correlation coefficients of the velocity and temperature fluctuations in the natural-convection boundary layer correspond well with those obtained from experiments for space-developing flows. The numerical results reveal that the turbulent structures of the buoyancy-driven boundary layers are mainly controlled by the fluid motions in the outer region of the boundary layer, and these large-scale structures are strongly connected with the generation of turbulence in the thermally-driven boundary layers, in accordance with the actual observations for space-developing flows. Moreover, to specify the turbulence structures of the boundary layers, the cross-correlation coefficients and the characteristic length scales are examined for the velocity and thermal fields. Consequently, it is found that with a slight increase in freestream velocity, the cross-correlation coefficient for the Reynolds shear stress and turbulent heat flux increases for opposing flow and decreases for aiding flow, and the integral scales for the velocity and temperature fields become larger for opposing flow and smaller for aiding flow compared with those for the pure natural-convection boundary layer.     

On the Relation between Fronts and High-Shear Layers in Wall Turbulence

Direct numerical simulation results of turbulent channel flow are analyzed in order to examine the relation between two kinds of near-wall flow structures, namely the instantaneous shear layers and the fronts which are derived from two-point statistics of the streamwise velocity component. The near-wall shear layers are analyzed by flow visualizations and conditional sampling, while the fronts are examined by means of space-time correlations and spatial two-point correlation functions. The present study focuses on the analysis of the propagation speed and the spatial shape of the structures. Concerning the propagation speed it is shown that the results obtained from flow visualizations are in close agreement with the propagation velocities derived from space-time correlation functions. The comparison of VISA results for the instantaneous shear with spatial structures obtained from two-point correlations of the streamwise velocity and the shear gives evidence that the fronts are intimately related to the pronounced near-wall shear layers.     

Velocity statistics along the stagnation line of an axi- symmetric stagnating turbulent flow

 Velocity statistics along the stagnation line of an axi-symmetric wall stagnating turbulent flow are studied experimentally. A low turbulence, uniform air flow from a nozzle type air supply with an exit diameter of 50 mm stagnates at a wall located 50 mm downstream. A flow velocity is set to 3 m/s, 10 mm downstream from the exit of the air supply. Instantaneous values of streamwise and radial velocities are measured by laser-Doppler velocimetry. The turbulence level in the air flow is changed by use of turbulence generator. When the turbulence generator is not installed in the air supply, the mean velocity profile in the streamwise direction fits well with that of a laminar viscous flow with the rms value of velocity fluctuations low near the wall. With the turbulence generator installed, a significant turbulence structure appears near the wall. When the wall is approached, the rms value of velocity fluctuations in the streamwise direction decreases monotonically while the profile of the rms value in the radial direction reaches a maximum near the wall. The increase in the rms value of velocity fluctuations in the radial direction near the wall is attributed to the bi-modal histogram of the fluctuating velocity in the radial direction. Near the wall, the instantaneous stagnation streamline fluctuates and the probability of the mean location of the stagnation point reaches a maximum not at the stagnation line but on a circle around the stagnation line, resulting in the bi-modal histogram. Turbulence statistics, the rms value of velocity fluctuation and the turbulent kinetic energy, can be normalized successfully by similarity parameters based on the strain rate and the reference turbulent kinetic energy introduced by Champion and Libby. Received: 7 April 1995/Accepted: 27 September 1996     

An attempt to localize the sound sources in a turbulent jet using the results of the measurements of the acoustic field and the velocity fluctuation correlations

A model of noise generation in the mixing layer of a jet is proposed on the basis of the measurements of the acoustic radiation of a free jet by means of a microphone system, which makes it possible to determine the location of sources of sound at a given frequency, and hot-wire measurements of the velocity of the motion of vortices of given dimensions in the mixing layer. It is shown that the acoustic wave generation can be attributed to turbulence intermittence in the jet, that is, an unsteady motion of a region occupied by a “turbulent fluid”. As a result, an unsteady motion of the air ejected by the jet produces acoustic waves.     

Experiments on the spreading of shear-free turbulence under the influence of confinement and rotation

From Lie-group (symmetry) analysis of the multi-point correlation equation Oberlack and Günther (Fluid Dyn Res 33:453–476, 2003) found three different solutions for the behavior of shear-free turbulence: (i) a diffusion like solution, in which turbulence diffuses freely into the adjacent calm fluid, (ii) a deceleration wave like solution when there is an upper bound for the integral length scale and (iii) a finite domain solution for the case when rotation is applied to the system. This paper deals with the experimental validation of the theory. We use an oscillating grid to generate turbulence in a water tank and Particle Image Velocimetry (PIV) to determine the two-dimensional velocity and out-of-plane vorticity components. The whole setup is placed on a rotating table. After the forcing is initiated, a turbulent layer develops which is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/non-turbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid. We measure the propagation of the TNTI and find quantitative agreement with the predicted spreading laws for case one and two. For case three (system rotation), we observe that there is a sharp transition between a 3D turbulent flow close to the source of energy and a more 2D-like wavy flow further away. We measure that the separation depth becomes constant and in this sense, we confirm the theoretical finite domain solution.     

A closed model of fluctuating particle motion in a turbulent flow

Random particle motion in a turbulent and molecular velocity fluctuation field is considered. Using a spectral representation of the carrier-phase Eulerian velocity fluctuation correlations, a closed system of integral equations for calculating the carrier-phase velocity correlation along the particle trajectory and the particle Lagrangian velocity fluctuation correlation is obtained. Based on this system, the fluctuations of the particle parameters are analyzed. In the limiting case of a passive admixture, an estimate is found for the ratio of the integral Lagrangian and Eulerian time scales and the Kolmogorov constant for the Lagrangian structure function of the carrier-phase velocity fluctuations.     

Determination of turbulence properties by using empirical mode decomposition on periodic and random perturbed flows

Stationary and non-stationary grid-generated turbulence was studied using a complementary technique that combines empirical mode decomposition (EMD) and triple-decomposition. Non-stationary conditions were generated by superimposing periodic and random fluctuations on the original flow. Empirical mode decomposition (EMD) was applied as a filter to separate these fluctuations from the turbulent velocity component. Triple-decomposition was then used and the turbulent intensity, the integral length scales and the Power Spectral Density of the velocity were determined. How to use EMD in order to optimize this decomposition is discussed. Finally, the properties of the turbulence are compared to those characterized without addition of fluctuations and a good agreement is found.