Multipoint correlations of concentration fluctuations in a turbulent passive scalar field

This study experimentally analyzes a turbulent passive scalar field using two-point and three-point correlation functions of the concentration fluctuations. The scalar field was created by the iso-kinetic release of a high Schmidt number dye into a fully developed turbulent boundary layer of an open channel flow. Concentration data at spatially separated measurement points were collected via the planar laser induced fluorescence (PLIF) technique. The current study complements previous research efforts by examining three-point correlations for several configurations in a turbulent shear flow. In the case of two streamwise-aligned points combined with one transversely separated point, contours of the three-point correlation function exhibit the symmetric properties reported in an earlier study of non-shear flow. In a second set of three-point configurations consisting of isosceles and collinear geometries, the influence of the orientation angle between the three-point configuration and the mean concentration gradient varies depending on the specified three-point geometry. The results also suggest that the scaling exponent in the inertial-convective regime is dependent on the injection length scale with weak dependence on the Reynolds number.     

Spatial resolution effects on the measurement of scalar variance and scalar gradient in turbulent nonpremixed jet flames

The effect of spatial averaging is important for scalar gradient measurements in turbulent nonpremixed flames, especially when the local dissipation length scale is small. Line imaging of Raman, Rayleigh and CO-LIF is used to investigate the effects of experimental resolution on the scalar variance and radial gradient in the near field of turbulent nonpremixed CH₄/H₂/N₂ jet flames at Reynolds numbers of 15,200 and 22,800 (DLR-A and B) and in piloted CH₄/air jet flames at Reynolds numbers of 13,400, 22,400 and 33,600 (Sandia flames C/D/E). The finite spatial resolution effects are studied by applying the Box filter with varying filter widths. The resulting resolution curves for both scalar variance and mean squared-gradient follow nearly the same trends as theoretical curves calculated from the model turbulence kinetic energy spectrum of Pope. The observed collapse of resolution curves of mean squared-gradient for nearly all studied cases implies the shape of the dissipation spectrum is approximately universal. Fluid transport properties are shown to have no effect on the dissipation resolution curve, which implies that the dissipation length scale inferred from the square gradient is equivalent to the length scale for the scalar dissipation rate, which includes the diffusion coefficient. With the Box filter, the required spatial resolution to resolve 98% of the mean dissipation rate is about one−two times of the dissipation cutoff length scale (analogous to the Batchelor scale in turbulent isothermal flows). The effects of resolution on the variances of mixture fraction, temperature, and the inverted Rayleigh signal are also compared. The ratio of the filtered variance to the true variance is shown to depend nearly linearly on the probe resolution. The inverted Rayleigh scattering signal can be used to study the resolution effect on temperature variance even when the Rayleigh scattering cross section is not constant. The experimental results also indicate that these laboratory scale turbulent jet flames have small effective Reynolds numbers, such that there is some direct interaction of the large (energy containing) and small (dissipative) scalar length scales, especially for the near field case at x/d = 7.5 of the piloted Sandia flames C/D/E.     

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.     

On the role of the smallest scales of a passive scalar field in a near-wall turbulent flow

Role of the smallest diffusive scales of a passive scalar field in the near-wall turbulent flow was examined with pseudo-spectral numerical simulations. Temperature fields were analyzed at friction Reynolds number Re _τ=171 and at Prandtl numbers, Pr=1 and Pr=5.4. Results of direct numerical simulations (DNS) were compared with the under-resolved simulations where the velocity field was still resolved with the DNS accuracy, while a coarser grid was used to describe the temperature fields. Since the smallest temperature scales remained unresolved in these simulations, an appropriate spectral turbulent thermal diffusivity was applied to avoid pile-up at the higher wave numbers. In spite of coarser numerical grids, the temperature fields are still highly correlated with the DNS results, including instantaneous temperature fields. Results point to practically negligible role of the diffusive temperature scales on the macroscopic behavior of the turbulent heat transfer.     

High-resolution turbulent scalar field measurements in an optically accessible internal combustion engine

High-resolution planar laser-induced fluorescence (PLIF) measurements were performed in an optically accessible internal combustion engine to investigate the evolution of the turbulent mixing process during the intake and compression strokes. The PLIF measurements were used to analyze the important turbulent length scales, scalar energy and dissipation spectra, and mean scalar gradients. The fluorescence images had sufficient spatial resolution and integrity to resolve all of the fine-scale features of the flow, allowing for direct determination of the Batchelor length scale. The integral and Taylor scales were also determined from two-point spatial correlations of the fluctuating scalar field using an appropriately defined mean scalar value. The general morphology of the scalar field and the measured integral, Taylor and Batchelor length scales were found to be largely independent of engine speed and intake pressure, but increased as the engine cycle progressed through the intake and compression strokes. The measured Batchelor scales ranged from 22 to 54 μm; the integral scales ranged from 1.8 to 3.5 mm; and the Taylor microscales ranged from 0.6 to 1.2 mm. The Taylor and integral scale values were comparable to values reported in the literature from in-cylinder velocity measurements. The mean scalar gradient, a measure of the fine-scale mixing rate, monotonically decreased as the engine cycle advanced. High-resolution measurements of this type are important in the development and validation of future engine combustion models used in computer simulations.     

DNS of a spatially developing turbulent boundary layer with passive scalar transport

A direct numerical simulation (DNS) of a spatially developing turbulent boundary layer over a flat plate under zero pressure gradient (ZPG) has been carried out. The evolution of several passive scalars with both isoscalar and isoflux wall boundary condition are computed during the simulation. The Navier–Stokes equations as well as the scalar transport equation are solved using a fully spectral method. The highest Reynolds number based on the free-stream velocity U_∞ and momentum thickness θ is Re_θ=830, and the molecular Prandtl numbers are 0.2, 0.71 and 2. To the authors’ knowledge, this Reynolds number is to date the highest with such a variety of scalars. A large number of turbulence statistics for both flow and scalar fields are obtained and compared when possible to existing experimental and numerical simulations at comparable Reynolds number. The main focus of the present paper is on the statistical behaviour of the scalars in the outer region of the boundary layer, distinctly different from the channel-flow simulations. Agreements as well as discrepancies are discussed while the influence of the molecular Prandtl number and wall boundary conditions is also highlighted. A Pr scaling for various quantities is proposed in outer scalings. In addition, spanwise two-point correlation and instantaneous fields are employed to investigate the near-wall streak spacing and the coherence between the velocity and the scalar fields. Probability density functions (PDF) and joint probability density functions (JPDF) are shown to identify the intermittency both near the wall and in the outer region of the boundary layer. The present simulation data will be available online for the research community.     

DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers

We perform DNS of passive scalar transport in low Reynolds number turbulent channel flow at Schmidt numbers up to Sc = 49. The high resolutions required to resolve the scalar concentration fields at such Schmidt numbers are achieved by a hierarchical algorithm in which only the scalar fields are solved on the grid dictated by the Batchelor scale. The velocity fields are solved on coarser grids and prolonged by a conservative interpolation to the fine-grid.

The trends observed so far at lower Schmidt numbers Sc  10 are confirmed, i.e. the mean scalar gradient steepens at the wall with increasing Schmidt number, the peaks of turbulent quantities increase and move towards the wall. The instantaneous scalar fields show a dramatic change. Observable structures get longer and thinner which is connected with the occurrence of steeper gradients, but the wall concentrations penetrate less deeply into the plateau in the core of the channel.

Our data shows that the thickness of the conductive sublayer, as defined by the intersection point of the linear with the logarithmic asymptote scales with Sc^−0.29. With this information it is possible to derive an expression for the dimensionless transfer coefficient K⁺ which is only dependent on Sc and Re_τ. This expression is in full accordance to previous results which demonstrates that the thickness of the conductive sublayer is the dominating quantity for the mean scalar profile.     

Concentration flux measurements of a scalar quantity in turbulent flows

A method for determination of velocity-concentration fluxes is presented that combines two conventional imaging techniques, particle image velocimetry (P.I.V.) and planar laser-induced fluorescence (P.L.I.F.). The passive concentration jet was a perfect mixture of fluorescein dye and solid particles submerged in an isotropic homogeneous turbulent channel. The light intensity fluoresced by the dye and the light intensity scattered by the particles were recorded separately on two synchronized cameras by using appropriate high and low-pass filters. Two different sets of images were thus obtained simultaneously. Once digitized and numerically processed, they provide the space and time evolution of velocity and concentration instantaneous fields. Thus, the velocity-concentration correlations can easily be determined. The statistical results for velocity and concentration are compared with classical results in order to validate the technique. We finally report some results giving velocity-concentration fluxes.     

On high spatial resolution scalar measurement with LIF Part 2: The noise characteristic

A spatial resolution of about 4 (m)³ for scalar measurement in turbulent mixing with Laser-Induced-Fluorescence is realized in this experiment. It is shown that for the high spatial resolution the signal is weak because of the measuring volume is very fine. The corresponding main problem is that the signal to noise ratio is small, especially for the high frequency signal corresponding to small structures. It is shown that the dominating noise is the shot noise in the signal from the photomultiplier tube. The measurement results indicate that an increase of the signal level through the increase of dye concentration and/or laser power is limited, mainly due to thermal blooming and photobleaching.     

Single-shot laser Mie scattering measurements of the scalar profiles in the near field of turbulent jets with variable densities

A single-shot laser Mie scattering technique is used to measure the instantaneous radial distributions of seed particles in the early development zone of turbulent jets with various bulk densities issuing into a slow coflowing air stream. Instantaneous radial profiles of mixture fraction are derived from the measured distributions with either the jet fluid or only the coflow air seeded, depending on the investigated zone. Radial gradients and autocorrelation profiles are analyzed to study the scalar dissipation and the mixing length scale respectively. Self-similar behaviour is investigated by plotting the centreline scalar decay as a function of a reduced abscissa, which accounts for the axial variation of the jet density in its early development. As the density is simultaneously derivable from the mixture fraction data, direct comparisons between Favre and Reynolds averaged values are obtained which show very significant differences in the near field.     

Streamwise evolution of a high-Schmidt-number passive scalar in a turbulent plane wake

The concentration fluctuation c of diluted fluorescein dye, a high-Schmidt-number passive scalar (Sc=ν/D ≈ 2000, ν and D are the fluid momentum and dye diffusivities, respectively), is measured in the wake of a circular cylinder using a single-point laser-induced fluorescence (SPLIF) technique. The streamwise decay rate of the mean and rms values of c is slow in comparison to that of θ, the temperature fluctuation for which the molecular Prandtl number Pr=ν/κ is about 0.7 (κ is the thermal diffusivity). The comparison between mean and rms distributions of c and θ highlights the combined role the Reynolds and Schmidt numbers play in terms of dispersing the scalar. The streamwise evolution of the probability density functions (pdfs) of c and θ suggest that while p(θ) is approximately Gaussian in the intermediate wake (x/d ≈ 80), p(c) is strongly non-Gaussian, and depends on both x/d and Re. The skewness of c is larger than that of θ along the wake centreline. Arguably, the asymmetry of p(c) reflects the relatively strong organisation of the large-scale motion in the far-wake. Received: 27 July 2000/Accepted: 22 December 2000     

Double large field stereoscopic PIV in a high Reynolds number turbulent boundary layer

An experiment on a flat plate turbulent boundary layer at high Reynolds number has been carried out in the Laboratoire de Mecanique de Lille (LML, UMR CNRS 8107) wind tunnel. This experiment was performed jointly with LEA (UMR CNRS 6609) in Poitiers (France) and Chalmers University of Technology (Sweden), in the frame of the WALLTURB European project. The simultaneous recording of 143 hot wires in one transverse plane and of two perpendicular stereoscopic PIV fields was performed successfully. The first SPIV plane is 1?cm upstream of the hot wire rake and the second is both orthogonal to the first one and to the wall. The first PIV results show a blockage effect which based on both statistical results (i.e. mean, RMS and spatial correlation) and a potential model does not seem to affect the turbulence organization.     

On high spatial resolution scalar measurement with LIF Part 1: Photobleaching and thermal blooming

A spatial resolution of about 4 (m)³ of LIF is done in the present work. For such measurements, the photobleaching and possible thermal blooming become important because of the very high laser intensity at measuring volume. The corresponding problems for the scalar measurement, calibration, the influence of laser power and laser dye concentration on photobleaching, and the measurement of photobleaching are investigated. A simple photobleaching model is proposed. Received: 18 September 1998/Accepted: 20 October 1999     

Structure of the probability density of turbulent concentration pulsations with very large amplitudes

The structure of the probability density of very large values of the concentration of a passive admixture is considered. The solution of this problem is of importance for modeling the emission of carbon monoxide and unburnt hydrocarbons. A theoretical model is constructed on the basis of the following ideas: (1) the dimension of the zones in which the concentration pulsations with vary large amplitudes are observed is of the order of the integral turbulence scale; (2) the probability of these zones being generated is very low. It is shown that there is a certain limiting large value of the concentration in the neighborhood of which the probability density can be described by a power function. On the basis of the theory of locally uniform turbulence it is shown that, generally speaking, if certain relationships between the unknown quantities entering into the theory are not satisfied, the probability density of very large values of the concentration depends on the Reynolds number.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 39–46, September–October, 1995.     

Structural inclination angle of near-field scalar fluctuations in a turbulent boundary layer

Two-point concentration measurements are obtained in a meandering passive-scalar plume released at five different heights within the fully-turbulent region of a high-Reynolds number turbulent boundary layer (TBL). Mean statistics of two-point concentration measurements are found to agree very well with the single-point measurements previously reported in Talluru et al. (2017a). The two-point correlation results of concentration indicate strong coherence in the scalar field similar to the large-scale coherence observed in the streamwise velocity fluctuations in a TBL (Marusic and Heuer, 2007). Particularly, the isocontours in the two-dimensional correlation map of concentration fluctuations illustrate that the scalar structures are inclined at 30^∘ to the direction of the flow; such a trend is consistently observed for all the elevated plumes below z/δ ≤ 0.33. This observation of steeper inclination angle of scalar structures relative to the inclination angle of large-scale velocity fluctuations in a TBL is explained using the physical model put forth by Talluru et al. (2018). Most importantly, these results provide insights on the differences in the structural organisation of a passive scalar plume in the near- and the far-field regions.