Turbulence microscale variation due to interaction with shock wave

A speckle photographic technique is used for visualizing the planar distribution of the refractive deflection angles of light transmitted through a compressible turbulent flow. Double exposure speckle photography is applied for the statistical analysis of such flows. Quantitative visualization of the planar distribution of the refractive deflection angles of the light transmitted through the compressible turbulent flow is performed. Turbulent structures are visible in the patterns of the deflection angles isolines. The 2-D correlation functions of these deflection angles are constructed and analyzed. A mathematical procedure for solving Erbeck-Merzkirch integral transformation is described and the 3-D density correlation functions are evaluated using 2-D correlation functions of deflection angles of the light passed through the turbulence. Received 14 November 1999 / Accepted 3 June 2000     

Investigation of the Cross-beam Correlation Algorithm to Reconstruct Local Field Statistics from Line-of-sight Measurements in Turbulent Flows

Optical techniques such as speckle photography and rainbow schlieren deflectometry yield path integrated measurements of deflection angle instead of the local field variable such as density, temperature and/or species concentration. Thus, a reconstruction algorithm is employed to obtain the local properties from the path-integrated measurements. Cross-beam correlation (CBC) algorithm provides the link between path-integrated and local field statistics in time-averaged axisymmetric turbulent flows. Path-integrated statistics are obtained using orthogonal light rays crossing within the turbulent flow. The algorithm assumes local isotropy and negligible correlation between points on orthogonal beams, which is valid strictly in fully turbulent flows. In this study, noise-free synthetic scalar turbulence data are generated and used to determine how different assumptions in the CBC algorithm affect the reconstruction accuracy. Results show that the reconstruction accuracy is excellent for a narrow correlation function (or small integral length scale), while significant errors are incurred in case of a wide correlation function. A procedure to improve the reconstruction accuracy of the CBC algorithm is proposed in this study.     

Efficient Generation of Inflow Conditions for Large Eddy Simulation of Street-Scale Flows

Using a numerical weather forecasting code to provide the dynamic large-scale inlet boundary conditions for the computation of small-scale urban canopy flows requires a continuous specification of appropriate inlet turbulence. For such computations to be practical, a very efficient method of generating such turbulence is needed. Correlation functions of typical turbulent shear flows have forms not too dissimilar to decaying exponentials. A digital-filter-based generation of turbulent inflow conditions exploiting this fact is presented as a suitable technique for large eddy simulations computation of spatially developing flows. The artificially generated turbulent inflows satisfy the prescribed integral length scales and Reynolds-stress-tensor. The method is much more efficient than, for example, Klein’s (J Comp Phys 186:652–665, 2003) or Kempf et al.’s (Flow Turbulence Combust, 74:67–84, 2005) methods because at every time step only one set of two-dimensional (rather than three-dimensional) random data is filtered to generate a set of two-dimensional data with the appropriate spatial correlations. These data are correlated with the data from the previous time step by using an exponential function based on two weight factors. The method is validated by simulating plane channel flows with smooth walls and flows over arrays of staggered cubes (a generic urban-type flow). Mean velocities, the Reynolds-stress-tensor and spectra are all shown to be comparable with those obtained using classical inlet-outlet periodic boundary conditions. Confidence has been gained in using this method to couple weather scale flows and street scale computations.     

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.

     

Density-sensitive whole-field flow measurement by optical speckle photography

An optical whole-field, line-of-sight method is surveyed that allows the measurement of the refractive deflection angles of light transmitted through a flow with density changes. The method uses the principles of speckle photography. In comparison to classical optical methods such as interferometry, a much higher number of data values can be obtained from one record without the need of interpolating between experimental data. This high signal density is particularly advantageous for analyzing turbulent flows with density fluctuations. Such an analysis is, so far, restricted to the existence of axisymmetric turbulence. A number of applications to this type of turbulent flow are reported, and proposals are made for future developments that will allow this speckle technique to be applied to the study of turbulent shear flow.     

Measurements of a supersonic turbulent boundary layer by focusing schlieren deflectometry

 Some novel, non-intrusive, high-frequency, localized optical measurements of turbulence in compressible flows are described. The technique is based upon focusing schlieren optics coupled with high-speed quantitative measurement of light intensity fluctuations in the schlieren image. Measurements of density gradient fluctuations confined to a thin slice of the flowfield are thus obtained. The new instrument was used to investigate the structure of a two-dimensional, adiabatic, wind tunnel wall boundary layer at a Mach number of 3. The measurements were compared to data obtained using hot-wire anemometry and good agreement was found between the two. Distributions of broadband convection velocity of large-scale structures through the boundary later were also measured. In marked contrast to earlier results, it is shown here that the convection velocity is essentially identical to the local mean velocity. Further, results obtained using the VITA conditional sampling technique shed new light on the turbulent boundary layer structure. Overall, the data presented herein serve to validate the new measurement technique. Received: 12 February 1997/Accepted: 31 January 1998     

Turbulent flow visualization by interferometric integral imaging and computed tomography

An experimental system using integral interferometric imaging and computer tomography for visualizing the structure of a turbulent, vertical helium jet is described. Integral images and tomographic integral data were obtained using a pulsed phase-shifted interferometer. The integral images revealed a sinuous overall jet structure and large-scale buckling motions in the far-field. Tomographic reconstruction of jet cross-sections at numerous axial locations were made for three turbulent jets at two different Reynols numbers, 2,800 and 4,300. Tomographic images revealed unmixed ambient fluid far inside the jet boundary and a bimodal concentration distribution. Image interpretation and experimental errors are discussed.     

Applications of URANS on predicting unsteady turbulent separated flows

Accurate prediction of unsteady separated turbulent flows remains one of the toughest tasks and a practi cal challenge for turbulence modeling. In this paper, a 2D flow past a circular cylinder at Reynolds number 3,900 is numerically investigated by using the technique of unsteady RANS （URANS）. Some typical linear and nonlinear eddy viscosity turbulence models （LEVM and NLEVM） and a quadratic explicit algebraic stress model （EASM） are evaluated. Numerical results have shown that a high-performance cubic NLEVM, such as CLS, are superior to the others in simulating turbulent separated flows with unsteady vortex shedding.     

Short-and resonant-range interactions between scales in turbulence and their applications

Interactions between different scales in turbulence were studied starting from the incompressible Navier-Stokes equations. The integral and differential formulae of the shortrange viscous stresses, which express the short-range interactions between contiguous scales in turbulence, were given. A concept of the resonant-range interactions between extreme contiguous scales was introduced and the differential formula of the resonant-range viscous stresses was obtained. The short- and resonant-range viscous stresses were applied to deduce the large-eddy simulation ( LES ) equations as well as the multiscale equations, which are approximately closed and do not contain any empirical constants or relations. The properties and advantages of using the multiscale equations to compute turbulent flows were discussed. The short-range character of the interactions between the scales in turbulence means that the multiscale simulation is a very valuable technique for the calculation of turbulent flows. A few numerical examples were also given.     

An investigation of forced structures in turbulent jet flows

In many cases, turbulence is superimposed on an unsteady organized motion of a mean flow. In the past, these turbulent flows have been studied by time or ensemble averaging methods and some decomposition techniques such as proper orthogonal decomposition (POD). In this study, a new decomposition technique called the turbulence filter will be used to decompose the forced turbulent jet flows. By using the turbulence filtering technique, the fluctuating (turbulent) part and the more organized (forced) part of the velocity field are analyzed. Within this context several experiments on organized turbulent jet flow have been carried out. In the experiments, variable frequency and amplitude oscillation are imposed on a 1D jet. An elliptical plate was used in order to obtain sinusoidal forcing. The axial distance, Reynolds number and the forcing frequency of the signal were varied. The multiple hot wires (six probes) were used to investigate the evolution of the signal along the radial distance. The obtained results of the turbulence filter are compared with those of phase-averaging and POD techniques. The eigenmodes of the data are also evaluated by using the POD method. Received: 31 July 1998/Accepted: 19 January 2000     

Phase-locked analysis of velocity fluctuations in a turbulent free swirling jet after vortex breakdown

Large-scale organized vortical structures were studied experimentally in a free swirling jet of air experiencing vortex precession (PVC) at ambient conditions. Detailed measurements were performed in the region near the nozzle exit using phase-locked LDV and PIV, at a Reynolds number of Re ?? 24,400 and a swirl parameter S ?? 1.0. The investigation allowed reconstruction of the time-averaged flowfield, with the associated distribution of turbulent fluctuations, the phase-locked structure of the jet and the associated precessing vortex structure. An original joint analysis of power spectra and probability density functions of velocity data led to quantification of the PVC effect on turbulent fluctuations. This analysis showed that the PVC contribution can be properly separated from the background random turbulence, reproducing the results of phase-locked measurements. It is found that the background turbulence in the near field is substantially weaker if compared to the coherent fluctuations induced by vortex precession.     

壁湍流相干结构和减阻控制机理

剪切湍流中相干结构的发现是上世纪湍流研究的重大进展之一,这些大尺度的相干运动在湍流的动力学过程中起重要作用,也为湍流的控制指出了新的方向.壁湍流高摩擦阻力的产生与近壁区流动结构密切相关,基于近壁区湍流动力学过程的减阻控制方案可以有效降低湍流的摩擦阻力,但是随着雷诺数的升高, 这些控制方案的有效性逐渐降低.近年来研究发现, 在高雷诺数情况下外区存在大尺度的相干运动,这种大尺度运动对近壁区湍流和壁面摩擦阻力的产生有重要影响,为高雷诺数湍流减阻控制策略的设计提出了新的挑战.该文将对壁湍流相干结构的研究历史加以简单的回顾,重点介绍近壁区相干结构及其控制机理、近年来高雷诺数外区大尺度运动的研究进展,在此基础上提出高雷诺数减阻控制研究的关键科学问题.      

Turbulent time and length scale measurements in high-velocity open channel flows

In high-velocity open channel flows, the measurements of air–water flow properties are complicated by the strong interactions between the flow turbulence and the entrained air. In the present study, an advanced signal processing of traditional single- and dual-tip conductivity probe signals is developed to provide further details on the air–water turbulent level, time and length scales. The technique is applied to turbulent open channel flows on a stepped chute conducted in a large-size facility with flow Reynolds numbers ranging from 3.8E+5 to 7.1E+5. The air water flow properties presented some basic characteristics that were qualitatively and quantitatively similar to previous skimming flow studies. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level at a macroscopic scale, and the auto- and cross-correlation functions at the microscopic level. New correlation analyses yielded a characterisation of the large eddies advecting the bubbles. Basic results included the integral turbulent length and time scales. The turbulent length scales characterised some measure of the size of large vortical structures advecting air bubbles in the skimming flows, and the data were closely related to the characteristic air–water depth Y ₉₀. In the spray region, present results highlighted the existence of an upper spray region for C > 0.95–0.97 in which the distributions of droplet chord sizes and integral advection scales presented some marked differences with the rest of the flow.     

Fractal-Generated Turbulence in Opposed Jet Flows

The opposed jet configuration presents a canonical geometry suitable for the evaluation of calculation methods seeking to reproduce the impact of strain and re-distribution on turbulent transport in reacting and non-reacting flows. The geometry has the advantage of good optical access and, in principle, an absence of complex boundary conditions. Disadvantages include low frequency flow motion at high nozzle separations and comparatively low turbulence levels causing bulk strain to exceed the turbulent contribution at small nozzle separations. In the current work, fractal generated turbulence has been used to increase the turbulent strain and velocity measurements for isothermal flows are reported with an emphasis on the axis, stagnation plane and the distribution of mean and instantaneous strain rates. Energy spectra were also determined. The instrumentation comprised hot-wire anemometry and particle image velocimetry with the flows to both nozzles seeded with 1  $\upmu$ m silicon oil droplets providing a relaxation time of ? 3 $\upmu$ s. It is shown that fractal grids increase the turbulent Reynolds number range from 48–125 to 109–220 for bulk velocities from 4 to 8 m/s as compared to conventional perforated plate turbulence generators. Low frequency motion of the order 10 Hz could not be completely eliminated and probability density functions were determined for the location of the stagnation plane. Results show that the fluctuation in the position of the stagnation plane is of the order of the integral length scale, which was determined to be 3.1±0.1 mm at the nozzle exits through the use of hot-wire anemometry. Flow statistics close to the fractal plate located upstream of the nozzle exit were also determined using a transparent glass nozzle.     

The numerical simulation of turbulent flows of Newtonian and a sort of non-Newtonian fluid in 180-degree square sectioned bend

Using k-εmodel of turbulence and measured wall functions.turbulent flows ofNewtonian(pure water)and a sort of non-Newtonian fluid(dilute,drag-reduction solutionof polymer in a180-degree curved bend were simulated numerically.The calculated resultsagreed well with the measured velocity profiles.On the basis of calculation andmeasurement,appropriateness of turbulence model to complicated flow in which the large-scale vortex exists was analyzed and discussed.     

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.     

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.     

PIV study of large-scale flow organisation in slot jets

The paper reports on particle image velocimetry (PIV) measurements in turbulent slot jets bounded by two solid walls with the separation distance smaller than the jet width (5–40%). In the far-field such jets are known to manifest features of quasi-two dimensional, two component turbulence. Stereoscopic and tomographic PIV systems were used to analyse local flows. Proper orthogonal decomposition (POD) was applied to extract coherent modes of the velocity fluctuations. The measurements were performed both in the initial region close to the nozzle exit and in the far fields of the developed turbulent slot jets for Re ⩾ 10,000. A POD analysis in the initial region indicates a correlation between quasi-2D vortices rolled-up in the shear layer and local flows in cross-stream planes. While the near-field turbulence shows full 3D features, the wall-normal velocity fluctuations day out gradually due to strong wall-damping resulting in an almost two-component turbulence. On the other hand, the longitudinal vortex rolls take over to act as the main agents in wall-normal and spanwise mixing and momentum transfer. The quantitative analysis indicates that the jet meandering amplitude was aperiodically modulated when arrangement of the large-scale quasi-2D vortices changed between asymmetric and symmetric pattern relatively to the jet axis. The paper shows that the dynamics of turbulent slot jets are more complex than those of 2D, plane and rectangular 3D jets. In particular, the detected secondary longitudinal vortex filaments and meandering modulation is expected to be important for turbulent transport and mixing in slot jets. This issue requires further investigations.     

Quantitative Flow Visualization

Modern developments in laser and computer technology, electronic cameras, and digital image processing techniques allow to generate planar distributions of quantitative data in turbulent flows. Large amounts of data can be processed easily and analyzed statistically. With these tools, it is possible to quantitatively visualize turbulent coherent structures, even in flows of high Reynolds number, and measure characteristic spatial quantities like vorticity, length scales, spatial correlation functions, etc. These potentials in analyzing spatial characteristics of turbulent flows are demonstrated with two different methods of quantitative flow visualization: speckle photography as a representative of the line-of-sight methods, and particle image velocimetry belonging to the methods that rely on the scattering of laser light from tracer particles.Sommario.I moderni sviluppi nelle tecnologie del laser e dei computers, delle telecamere elettroniche e le tecniche di analisi digitale delle immagini permettono di ottenere distribuzioni quantitative, in un piano, di dati relativi a flussi turbolenti. Una gran quantità di dati può essere con facilità analizzata statisticamente. Con questi mezzi è possibile visualizzare quantitativamente strutture coerenti turbolente anche in flussi da alto numero di Reynolds, e misurare caratteristiche spaziali, come vorticità scale e funzioni di correlazione. Questa potenzialità di studiare caratteristiche spaziali di flussi turbolenti viene qui mostrata per due differenti metodi di visualizzazione quantitativa: fotografia speckle e PIV (particle image velocimetry).     

An extended algebraic reconstruction technique (ART) for density-gradient projections: laser speckle photographic tomography

An extended algebraic reconstruction technique (ART) is presented for tomographic image reconstruction from the density-gradient projections, such as laser speckle photography. The essence of the extended ART is that the density-gradient projection data of speckle photography (Eq. (1)) are first numerically integrated to the algebraic representation of interferometric fringe number data (Eq. (12)), which ART can readily reconstruct into the cross-sectional field. The extended ART is numerically examined by using two computer synthesized phantom fields, and experimentally by using asymmetric single and double helium jets in air. The experimentally reconstructed images were also compared with the direct measurements of helium concentration using an oxygen analyzing probe. The extended ART method shows an improved accuracy and is proposed to use to tomographically reconstruct the density-gradient projections over the previous Fourier convolution (FC) method (Liu et al. 1989). Received: 26 June 1998/Accepted: 18 March 1999