Nonstationary aspects of passive scalar gradient behaviour

The dynamics of a passive scalar gradient experiencing fluctuating velocity gradient through the Lagrangian variations of strain persistence is studied. To this end, a systematic, numerical analysis based on the equation for the orientation of the gradient of a nondiffusive scalar in two-dimensional flow is performed. When the gradient responds weakly its orientation properties are determined by the mean value of strain persistence. Statistical alignment of the scalar gradient with the direction defined by the opposed actions of strain and rotation, by contrast, requires the gradient to keep up with strain persistence fluctuations. These results have been obtained for both strain- and effective-rotation-dominated regimes and are supported by relevant experimental data. Consequences of the unsteady behaviour of the scalar gradient on mixing properties are also analysed.     

Large eddy simulation (2D) of spatially developing mixing layer using vortex‐in‐cell for flow field and filtered probability density function for scalar field

A large eddy simulation based on filtered vorticity transport equation has been coupled with filtered probability density function transport equation for scalar field, to predict the velocity and passive scalar fields. The filtered vorticity transport has been formulated using diffusion‐velocity method and then solved using the vortex method. The methodology has been tested on a spatially growing mixing layer using the two‐dimensional vortex‐in‐cell method in conjunction with both Smagorinsky and dynamic eddy viscosity subgrid scale models for an anisotropic flow. The transport equation for filtered probability density function is solved using the Lagrangian Monte‐Carlo method. The unresolved subgrid scale convective term in filtered density function transport is modelled using the gradient diffusion model. The unresolved subgrid scale mixing term is modelled using the modified Curl model. The effects of subgrid scale models on the vorticity contours, mean streamwise velocity profiles, root‐mean‐square velocity and vorticity fluctuations profiles and negative cross‐stream correlations are discussed. Also the characteristics of the passive scalar, i.e. mean concentration profiles, root‐mean‐square concentration fluctuations profiles and filtered probability density function are presented and compared with previous experimental and numerical works. The sensitivity of the results to the Schmidt number, constant in mixing frequency and inflow boundary conditions are discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

Vortex-In-Cell and Probability Density Function Approach for a Passive Scalar Field in a Mixing Layer

A Reynolds-averaged simulation based on the vortex-in-cell (VIC) and the transport equation for the probability density function (PDF) of a scalar has been developed to predict the passive scalar field in a two-dimensional spatially growing mixing layer. The VIC computes the instantaneous velocity and vorticity fields. Then the mean-flow properties, i.e. the mean velocity, the root-mean-square (rms) longitudinal and lateral velocity fluctuations, the Reynolds shear stress, and the rms vorticity fluctuations are computed and used as input to the PDF equation. The PDF transport equation is solved using the Monte Carlo technique. The convection term uses the mean velocities from the VIC. The turbulent diffusion term is modeled using the gradient transport model, in which the eddy diffusivity, computed via the Boussinesq's postulate, uses the Reynolds shear stress and gradients of mean velocities from the VIC. The molecular mixing term is closed by the modified Curl model.

The computational results were compared with two-dimensional experimental results for passive scalar. The predicted turbulent flow characteristics, i.e. mean velocity and rms longitudinal fluctuations in the self-preserving region, show good agreement with the experimental measurements. The profiles of the mean scalar and the rms scalar fluctuations are also in reasonable agreement with the experimental measurements. Comparison between the mean scalar and the mean velocity profiles shows that the scalar mixing region extends further into the free stream than does the momentum mixing region, indicating enhanced transport of scalar over momentum. The rms scalar profiles exhibit an asymmetry relative to the concentration centerline, and indicate that the fluid on the high-speed side mixes at a faster rate than the fluid on the low-speed side. The asymmetry is due to the asymmetry in the mixing frequency cross-stream profiles. Also, the PDFs have peaks biased toward the high-speed side.     

Schlieren measurement of turbulent structure in a diffusion flame

The regular and random mixing structures in a turbulent diffusion flame were investigated using the quantitative, dynamic crossed-beam schlieren method. Evidence was found close to the nozzle relating to the vortexlike structure of eddies surrounding the central fuel jet flow. The observations also make possible resolution of turbulent intensity, scales, convection, and spectra within the diffusion flame without the use of seeding or intrusion of measuring probes. It is found that length scales and other turbulence parameters in the diffusion flame progressively revert to values similar to those expected and observed in scalar passive mixing as the combustion reaction intensity reduces with axial distance from the nozzle system.     

Velocity and Passive Scalar Characteristics in a Round Jet with Grids at the Nozzle Exit

Velocity and passive scalar (temperature) measurements have been made in the near field of a round jet with and without obstructing grids placed at the jet exit. The Reynolds number Re _D (based on the exit centreline velocity and nozzle diameter) is 4.9 × 10⁴ and the flow is incompressible, while the temperature rise does not affect the velocity behaviour. The streamwise development and radial spreading of the passive scalar are attenuated, relative to the unobstructed jet. Close to the jet outlet, the spatial similarity of the moments (up to the third-order) of velocity fluctuations is improved, when the jet is perturbed. An explanation, based on the reduced effect of the large coherent structures in the developing region, is provided.     

Direct numerical simulation of turbulent mixing of a passive scalar in pipe flow

Turbulent mixing of a passive scalar in fully developed turbulent pipe flow has been investigated by means of a Direct Numerical Simulation (DNS). The scalar is released from a point source located on the centreline of the pipe. The domain size of the concentration field has been chosen large enough to capture the different stages of turbulent mixing. Results are presented for mean concentration profiles, turbulent fluxes, concentration fluctuations, probability density functions and higher-order moments. To validate the numerical simulations the results are compared with experimental data on mixing in grid-turbulence that have been reported in the literature. The agreement between the experimental measurements and the computations is satisfactory. We have also considered the Probability Density Function (PDF). For small diffusion times and positions not on the plume centreline, our results lead to a PDF of an exponential form with a large peak at zero concentration. When the diffusion time increases, the PDF shifts from a exponential to a more Gaussian form.     

Passive Scalar Transport in a Turbulent Mixing Layer

This paper describes a combined experimental and numerical study of scalar transport in spatially developing, two-stream, turbulent mixing layers with velocity ratios of approximately 2:1. The experimental mixing layer was created by an S-shaped splitter plate mounted in a wind tunnel, and the concentration field was realized by releasing incense smoke into the high-speed side boundary layer above the splitter plate. Simultaneous measurements of the velocity and concentration fields were performed. A 12-sensor hot-wire probe was used to measure the velocity field and its gradients, while the concentration field was recorded with digital photographs of the laser-illuminated smoke. In parallel, a large-eddy simulation (LES) of the spatially developing mixing layer was carried out. Auxiliary turbulent boundary layer LES were used to provide high quality inflow boundary conditions for the velocity and concentration fields. By synchronizing the velocity and concentration measurements, concentration fluxes were also determined. Octant analysis based on the sign combinations of the velocity and concentration fuctuations was performed on the flux data to investigate the scalar transport processes. It was found that octants compatible with mean gradient transport of the scalar contribute most to the scalar fluxes. Conditional planar averages of scalar and momentum fluxes were obtained to determine their spatial distribution with respect to the organized roller and rib vortices of the mixing layer, and distinct patterns were observed. The simulation provided additional insight about the flow and scalar flux distribution topology. This topology was found to be partially compatible with simple models of roller and rib vortices that transport the scalar in a mean gradient sense.     

Turbulence and transport of passive scalar in magnetohydrodynamic channel flows with different orientations of magnetic field

DNS of turbulent flow and passive scalar transport in a channel are conducted for the situation when the fluid is electrically conducting (for example, a liquid metal) and the flow is affected by an imposed magnetic field. The cases of wall-normal, spanwise, and streamwise orientation of the magnetic field are considered. As main results, we find that the magnetic fields, especially those in the wall-normal and spanwise directions, significantly reduce the turbulent scalar transport and modify the properties of the scalar distribution.     

最小均方差条件和非线性IEM模型的分析

对最小均方差估计条件在构造混合模型中的应用作了进一步的讨论，证明了最小均方差条件可以代替工方程作为推导混合模型的约束条件，同时得到了混合项的一个严格的展开式。作为一般情况的一个特例，重新得到了NLIME模型，最后利用NLIEM模型计算了两个基本流场，并和IEM模型的计算结果作了比较。进一步表明了NLIEM模型的优越性。     

Analysis of small-scale scalar mixing processes in highly under-expanded jets

In the present study, we numerically investigate turbulent scalar mixing taking place downstream of highly under-expanded jets. The focus is placed on two inter-related issues: (i) the closure of the mean scalar dissipation rate (SDR) and (ii) the turbulence–scalar interaction (TSI) term. It is indeed commonly admitted that the former, i.e., the SDR, which is defined as the product of the scalar diffusivity with the squared scalar gradient, provides a good measure of the mixing efficiency. In turbulent flows, the mean (turbulent) SDR requires a specific closure to be settled. It is generally obtained within the approximation of a linear relaxation of scalar fluctuations or linear relaxation model. We will first evaluate herein the performance of this widely used closure. The analysis is further developed by means of the consideration of the mean SDR transport equation which shows that, in gaseous conditions, the SDR is mainly driven by two terms: (i) a dissipation contribution and (ii) the third-order correlation between the velocity gradient tensor and small-scale scalar anisotropy tensor. The scalar mixing efficiency thus appears to be controlled by the latter quantity, which is often denoted as the TSI term. It can be shown that only the symmetric part (rate of strain) of the velocity gradient tensor contributes to this term; the anti-symmetric part modifies, indeed, the orientation of the scalar gradient but not its magnitude. The classical approach is to analyze this contribution in the eigenframe of the rate of strain tensor. Such analyses show that, in homogeneous isotropic turbulence, the scalar gradient tends to align with the most compressive direction, thus leading to SDR production. However, the present conditions, which are far from homogeneity and involve strong density variations, may modify this classical picture. The present study analyzes this possible influence.     

Scalar transport from a point source in flows over wavy walls

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re _b = 5,600, Re _b = 11,200 and Re _b = 22,400, respectively, based on the bulk velocity u _b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.     

Numerical study on the performance of nozzle flow for supersonic chemical oxygen–iodine lasers

Laser performance is greatly dependent on its operating conditions due to the strong coupling among multi- physics such as gas-dynamics, chemical reaction kinetics and optics in the mixing nozzle of COIL. In this paper, 3D CFD technology is used to simulate the mixing and reactive flow of subsonic cross jet scheme at different conditions. Results obtained show that the jet penetration depth plays a dominant role in the spatial distribution of small signal gains. In the case of over-penetration, unsteady flow structures are induced by impinging between the opposing jets. The optimum spatial distribution of the chemical performance cannot be obtained even if the full penetration condition is achieved through the subsonic transverse jet mixing scheme in the COIL nozzle flow.     

PIV Measurements in the Near and Intermediate Field Regions of Jets Issuing from Eight Different Nozzle Geometries

An experimental study was conducted to investigate the effect of nozzle geometry on the mixing characteristics and turbulent transport phenomena in turbulent jets. The nozzle geometry examined were round, square, cross, eight-corner star, six-lobe daisy, equilateral triangle as well as ellipse and rectangle each with aspect ratio of 2. The jets were produced from sharp linear contoured nozzles which may be considered intermediate to the more widely studied smooth contraction and orifice nozzles. A high resolution particle image velocimetry was used to conduct detailed velocity measurements in the near and intermediate regions. It was observed that the lengths of the potential cores and the growth rates of turbulence intensities on the jet centerline are comparable with those of the orifice jets. The results indicate that the decay and spreading rates are lower than reported for orifice jets but higher than results for smooth contoured jets. The jets issuing from the elliptic and rectangular nozzles have the best mixing performance while the least effective mixing was observed in the star jet. The distributions of the Reynolds stresses and turbulent diffusion clearly showed that turbulent transport phenomena are quite sensitive to nozzle geometry. Due to the specific shape of triangular and daisy jets, the profiles of mean velocity and turbulent quantities are close to each other in their minor and major planes while in the elliptic and rectangular jets are considerably different. They also exhibit more isotropic behavior compared to the elliptic and rectangular jets. In spite of significant effects of nozzle geometry on mean velocity and turbulent quantities, the integral length scales are independent of changes in nozzle geometry.     

Scalar Mixing and Large-Scale Coherent Structures in a Turbulent Swirling Jet

The paper presents large eddy simulations of co-annular swirling jets into an open domain. In each of the annuli a passive scalar is introduced and its transport is computed. If the exit of the pilot jet is retracted strong coherent flow structures are generated which substantially impact on the transport and mixing of the scalars. Average and instantaneous fields are discussed to address this issue. A conditional averaging technique is devised and applied to velocity and scalars. This allows to quantify the impact of the coherent structures on the mixing process.     

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.     

Comparison of magnetic resonance concentration measurements in water to temperature measurements in compressible air flows

Magnetic resonance imaging (MRI) measurements in liquid flows provide highly detailed 3D mean velocity and concentration data in complex turbulent mixing flow applications. The scalar transport analogy is applied to infer the mean temperature distribution in high speed gas flows directly from the MRI concentration measurements in liquid. Compressibility effects on turbulent mixing are known to be weak for simple flows at high subsonic Mach number, and it was not known if this would hold in more complex flows characteristic of practical applications. Furthermore, the MRI measurements are often done at lower Reynolds number than the compressible application, although both are generally done in fully turbulent flows. The hypothesis is that the conclusions from MRI measurements performed in water are transferable to high subsonic Mach number applications. The present experiment is designed to compare stagnation temperature measurements in high speed airflow (M = 0.7) to concentration measurements in an identical water flow apparatus. The flow configuration was a low aspect ratio wall jet with a thick splitter plate producing a 3D complex downstream flow mixing the wall-jet fluid with the mainstream flow. The three-dimensional velocity field is documented using magnetic resonance velocimetry in the water experiment, and the mixing is quantified by measuring the mean concentration distribution of wall-jet fluid marked with dissolved copper sulfate. The airflow experiments are operated with a temperature difference between the main stream and the wall jet. Profiles of the stagnation temperature are measured with a shielded thermocouple probe. The results show excellent agreement between normalized temperature and concentration profiles after correction of the temperature measurements for the effects of energy separation. The agreement is within 1 % near the edges of the mixing layer, which suggests that the mixing characteristics of the large scale turbulence structures are the same in the two flows.     

Computational Modelling of Turbulent Mixing in Confined Swirling Environment Under Constant and Variable Density Conditions

A high-intensity swirling flow in a model combustor subjected to large density variations has been examined computationally. The focus is on the Favre-averaged Navier–Stokes computations of the momentum and scalar transport employing turbulence models based on the differential second-moment closure (SMC) strategy. An updated version of the basic, high-Reynolds number SMC model accounting for a quadratic expansion of both the pressure–strain and dissipation tensors and a near-wall SMC model were used for predicting the mean velocity and turbulence fields. The accompanied mixing between the annular swirling air flow and the central non-swirling helium jet was studied by applying three scalar flux models differing mainly in the model formulation for the pressure-scalar gradient correlation. The computed axial and circumferential velocities agree fairly well with the reference experiment [So et al., NASA Contractor Report 3832, 1984; Ahmed and So, Exp. Fluids 4 (1986) 107], reproducing important features of such a weakly supercritical flow configuration (tendency of the flow core to separate). Although the length at which the mixing was completed was reproduced in reasonable agreement with the experimental results, the mixing activity in terms of the spreading rate of the shear/mixing layer, that is its thickness, was somewhat more intensive. Prior to these investigations, the model applied was validated by computing the transport of the passive scalar in the non-swirling (Johnson and Bennet, Report NASA CR-165574, UTRC Report R81-915540-9, 1981) and swirling (Roback and Johnson, NASA Contractor Report 168252, 1983) flow in a model combustor.     

Passive heat transfer in a turbulent channel flow simulation using large eddy simulation based on the lattice Boltzmann method framework

In this paper, a large eddy simulation based on the lattice Boltzmann framework is carried out to simulate the heat transfer in a turbulent channel flow, in which the temperature can be regarded as a passive scalar. A double multiple relaxation time (DMRT) thermal lattice Boltzmann model is employed. While applying DMRT, a multiple relaxation time D3Q19 model is used to simulate the flow field, and a multiple relaxation time D3Q7 model is used to simulate the temperature field. The dynamic subgrid stress model, in which the turbulent eddy viscosity and the turbulent Prandtl number are dynamically computed, is integrated to describe the subgrid effect. Not only the strain rate but also the temperature gradient is calculated locally by the non-equilibrium moments. The Reynolds number based on the shear velocity and channel half height is 180. The molecular Prandtl numbers are set to be 0.025 and 0.71. Statistical quantities, such as the average velocity, average temperature, Reynolds stress, root mean square (RMS) velocity fluctuations, RMS temperature and turbulent heat flux are obtained and compared with the available data. The results demonstrate great reliability of DMRT–LES in studying turbulence.     

Passive heat transfer in a turbulent channel flow simulation using large eddy simulation based on the lattice Boltzmann method framework

In this paper, a large eddy simulation based on the lattice Boltzmann framework is carried out to simulate the heat transfer in a turbulent channel flow, in which the temperature can be regarded as a passive scalar. A double multiple relaxation time (DMRT) thermal lattice Boltzmann model is employed. While applying DMRT, a multiple relaxation time D3Q19 model is used to simulate the flow field, and a multiple relaxation time D3Q7 model is used to simulate the temperature field. The dynamic subgrid stress model, in which the turbulent eddy viscosity and the turbulent Prandtl number are dynamically computed, is integrated to describe the subgrid effect. Not only the strain rate but also the temperature gradient is calculated locally by the non-equilibrium moments. The Reynolds number based on the shear velocity and channel half height is 180. The molecular Prandtl numbers are set to be 0.025 and 0.71. Statistical quantities, such as the average velocity, average temperature, Reynolds stress, root mean square (RMS) velocity fluctuations, RMS temperature and turbulent heat flux are obtained and compared with the available data. The results demonstrate great reliability of DMRT–LES in studying turbulence.