Passive Scalar Research Articles

Mixing mechanisms in a low-sheared inhomogeneous bubble column

This paper reports an experimental study of the mixing of a passive scalar in a bubble column at high Reynolds number and average gas volume fractions ranging from 2.0% to 7.5%. Starting from a homogeneous bubble column, the bubbly flow is progressively destabilized by imposing a gradient of gas volume fraction at the bottom of the tank. In that way, a single recirculation is produced, which allows to investigate the impact of a large-scale buoyancy-driven flow on the mixing of a passive scalar. It is shown that, as long as the shear-induced turbulence generated by the recirculation is negligible, mixing results from two main mixing mechanisms: the transport by the mean liquid velocity and the mixing induced by the bubbles. While the transport by the liquid recirculation can be accounted for by an advection term, the mixing induced by the bubbles is a diffusive process, the effective diffusivity of which has been measured in a homogeneous bubble column by Alméras et al. (2015). However, once the shear-induced turbulence produced by the shear develops, its role upon the mixing has to be taken into account too.

Filtered Rayleigh scattering mixing measurements of merging and non-merging streamwise vortex interactions in supersonic flow

By introducing large-scale streamwise vortices into a supersonic flow it is possible to enhance the rate of mixing between two fluid streams. However, increased vorticity content alone does not explicitly serve as a predictor of mixing enhancement. Additional factors, particularly the mutual interactions occurring between neighboring vortical structures, affect the underlying fundamental physics that influence the rate at which the fluids mix. As part of a larger systematic study on supersonic streamwise vortex interactions, this work experimentally quantifies the average rate of mixing of helium and air in the presence of two separate modes of vortex interaction, the merging and non-merging of a pair of co-rotating vortices. In these experiments vortex-generating expansion ramps are placed on a strut injector. The freestream Mach number is set at 2.5 and helium is injected as a passive scalar. Average injectant mole fractions at selected flow planes downstream of the injector are measured utilizing the filtered Rayleigh scattering technique. The filtered Rayleigh scattering measurements reveal that, in the domain surveyed, the merging vortex interaction strongly displaces the plume from its initial horizontal orientation while the non-merging vortex interaction more rapidly mixes the helium and air. The results of the current experiments are consistent with associated knowledge derived from previous analyses of the two studied configurations which have included the detailed experimental characterization of entrainment, turbulent kinetic energy, and vorticity of both modes of vortex interaction.

A hierarchical random additive model for passive scalars in wall-bounded flows at high Reynolds numbers.

The kinematics of a fully developed passive scalar is modelled using the hierarchical random additive process (HRAP) formalism. Here, 'a fully developed passive scalar' refers to a scalar field whose instantaneous fluctuations are statistically stationary, and the 'HRAP formalism' is a recently proposed interpretation of the Townsend attached eddy hypothesis. The HRAP model was previously used to model the kinematics of velocity fluctuations in wall turbulence: , where the instantaneous streamwise velocity fluctuation at a generic wall-normal location z is modelled as a sum of additive contributions from wall-attached eddies (a i ) and the number of addends is N z ~ log(δ/z). The HRAP model admits generalized logarithmic scalings including 〈ϕ 2〉~log(δ/z), 〈ϕ(x)ϕ(x+r x )〉 ~ log(δ/r x ), 〈(ϕ(x) - ϕ(x+r x ))2〉 ~ log(r x /z), where ϕ is the streamwise velocity fluctuation, δ is an outer length scale, r x is the two-point displacement in the streamwise direction and 〈·〉 denotes ensemble averaging. If the statistical behaviours of the streamwise velocity fluctuation and the fluctuation of a passive scalar are similar, we can expect first that the above mentioned scalings also exist for passive scalars (i.e. for ϕ being fluctuations of scalar concentration) and second that the instantaneous fluctuations of a passive scalar can be modelled using the HRAP model as well. Such expectations are confirmed using large-eddy simulations. Hence the work here presents a framework for modelling scalar turbulence in high Reynolds number wall-bounded flows.

Local invariants in non-ideal flows of neutral fluids and two-fluid plasmas

The main objective is the locally invariant geometric object of any (magneto-)fluid dynamics with forcing and damping (nonideal), while more attention is paid to the untouched dynamical properties of two-fluid fashion. Specifically, local structures, beyond the well-known “frozen-in” to the barotropic flows of the generalized vorticities, of the two-fluid model of plasma flows are presented. More general non-barotropic situations are also considered. A modified Euler equation [T. Tao, “Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation,” Ann. PDE 2, 9 (2016)] is also accordingly analyzed and remarked from the angle of view of the two-fluid model, with emphasis on the local structures. The local constraints of high-order differential forms such as helicity, among others, find simple formulation for possible practices in modeling the dynamics. Thus, the Cauchy invariants equation [N. Besse and U. Frisch, “Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces,” J. Fluid Mech. 825, 412 (2017)] may be enabled to find applications in non-ideal flows. Some formal examples are offered to demonstrate the calculations, and particularly interestingly the two-dimensional-three-component (2D3C) or the 2D passive scalar problem presents that a locally invariant Θ = 2θζ, with θ and ζ being, respectively, the scalar value of the “vertical velocity” (or the passive scalar) and the “vertical vorticity,” may be used as if it were the spatial density of the globally invariant helicity, providing a Lagrangian prescription to control the latter in some situations of studying its physical effects in rapidly rotating flows (ubiquitous in atmosphere of astrophysical objects) with marked 2D3C vortical modes or in purely 2D passive scalars.

Turbulent/non-turbulent interfaces detected in DNS of incompressible turbulent boundary layers

The turbulent/non-turbulent interface (TNTI) detected in direct numerical simulations is studied for incompressible, temporally developing turbulent boundary layers at momentum thickness Reynolds number Reθ ≈ 2000. The outer edge of the TNTI layer is detected as an isosurface of the vorticity magnitude with the threshold determined with the dependence of the turbulent volume on a threshold level. The spanwise vorticity magnitude and passive scalar are shown to be good markers of turbulent fluids, where the conditional statistics on a distance from the outer edge of the TNTI layer are almost identical to the ones obtained with the vorticity magnitude. Significant differences are observed for the conditional statistics between the TNTI detected by the kinetic energy and vorticity magnitude. A widely used grid setting determined solely from the wall unit results in an insufficient resolution in a streamwise direction in the outer region, whose influence is found for the geometry of the TNTI and vorticity jum...

A Way Out of the Bubble Trouble?—Upon Reconstructing the Origin of the Local Bubble and Loop I via Radioisotopic Signatures on Earth

Deep-sea archives all over the world show an enhanced concentration of the radionuclide 60Fe, isolated in layers dating from about 2.2 Myr ago. Since this comparatively long-lived isotope is not naturally produced on Earth, such an enhancement can only be attributed to extraterrestrial sources, particularly one or several nearby supernovae in the recent past. It has been speculated that these supernovae might have been involved in the formation of the Local Superbubble, our Galactic habitat. Here, we summarize our efforts in giving a quantitative evidence for this scenario. Besides analytical calculations, we present results from high-resolution hydrodynamical simulations of the Local Superbubble and its presumptive neighbor Loop I in different environments, including a self-consistently evolved supernova-driven interstellar medium. For the superbubble modeling, the time sequence and locations of the generating core-collapse supernova explosions are taken into account, which are derived from the mass spectrum of the perished members of certain, carefully preselected stellar moving groups. The release and turbulent mixing of 60Fe is followed via passive scalars, where the yields of the decaying radioisotope were adjusted according to recent stellar evolution calculations. The models are able to reproduce both the timing and the intensity of the 60Fe excess observed with rather high precision. We close with a discussion of recent developments and give future perspectives.

Advection of passive scalars induced by a bay-trapped nonstationary vortex

A simple model of fluid particle advection induced by the interaction of a point vortex and incident plane flow occurring near a curved boundary is analyzed. The use of the curved boundary in this case is aimed at mimicking the geometry of an isolated bay of a circular shape. An introduction of such a boundary to the model results in the appearance of retention zones, where the vortex can be permanently trapped being either stationary or periodically oscillating. When stationary, it induces a steady velocity field that in turn ensures regular advection of nearby fluid particles. When the vortex oscillates periodically, the induced velocity field turns unsteady leading to the manifestation of chaotic advection of fluid particles. We show that the size of the fluid region engaged into chaotic advection increases almost monotonically with the increased magnitude of the vortex oscillations provided the magnitude remains relatively small. The monotonicity is accounted for the fact that the frequency of the vortex oscillations incommensurable with the proper frequency of fluid particle rotations in the steady state. Another point of interest is that it is demonstrated that bounded regions, in which the vortex may be trapped, can appear even at a significant distance from the bay. Making use of a Lagrangian indicator, examples of fluid particle advection induced by the periodic motion of the vortex inside the bay are adduced.

Comparison of passive scalar transport models coupled with the Lattice Boltzmann method

A complex fluid flow often involves passive scalars that are transported with the flow field but can be neglected regarding the fluid motion, such as concentration distributions, markers, or temperature fields. Using the Lattice Boltzmann (LB) method for fluid dynamic simulations, different approaches for coupling advection solvers to the fluid motion exist. The aim of this work is to give an overview of four different methods used for solving the advection equation. Two of these solvers are based on finite differences, namely the Lax–Wendroff method (Lax and Wendroff, 1960) and an extension from Succi et al. (1999) that artificially reduces numerical diffusion. The other two methods Onishi et al. (2005) and Osmanlic and Körner (2016) take advantage of the already available LB distribution functions, instead of depending on macroscopic quantities only. In the ansatz of Onishi et al. (2005) the local concentration flux is calculated from distribution functions directly, while in a similar approach used by Osmanlic and Körner (2016) an additional case distinction is made between incoming and outgoing flux.Besides investigating the order of accuracy and grid dependency, numerical diffusion is examined closely with the objective to simulate fluid flow that is solely determined by advection and contains no physical diffusion.

A novel method for chemistry tabulation of strained premixed/stratified flames based on principal component analysis

The principal component analysis (PCA) is used to analyze the high dimensional chemistry data of laminar premixed/stratified flames under strain effects. The first few principal components (PCs) with larger contribution ratios are chosen as the tabulated scalars to build the look-up chemistry table. Prior tests show that strained premixed flame structure can be well reconstructed. To highlight the physical meanings of the tabulated scalars in stratified flames, a modified PCA method is developed, where the mixture fraction is used to replace one of the PCs with the highest correlation coefficient. The other two tabulated scalars are then modified with the Schmidt orthogonalization. The modified tabulated scalars not only have clear physical meanings, but also contain passive scalars. The PCA method has good commonality, and can be extended for building the thermo-chemistry table including strain rate effects when different fuels are used.

Persistence of local anisotropy of passive scalars in wall-bounded flows

A persistent small-scale anisotropy of turbulent passive scalar fields, which is independent of the scalar field initial conditions, is observed in direct numerical simulations of fully developed channel flow, even after the flow has undergone substantial mixing, and is attributed to the mean velocity gradient.

WRF modeling of PM2.5 remediation by SALSCS and its clean air flow over Beijing terrain

Atmospheric simulations were carried out over the terrain of entire Beijing, China, to investigate the effectiveness of an air-pollution cleaning system named Solar-Assisted Large-Scale Cleaning System (SALSCS) for PM2.5 mitigation by using the Weather Research and Forecasting (WRF) model. SALSCS was proposed to utilize solar energy to generate airflow therefrom the airborne particulate pollution of atmosphere was separated by filtration elements. Our model used a derived tendency term in the potential temperature equation to simulate the buoyancy effect of SALSCS created with solar radiation on its nearby atmosphere. PM2.5 pollutant and SALSCS clean air were simulated in the model domain by passive tracer scalars. Simulation conditions with two system flow rates of 2.64 × 105 m3/s and 3.80 × 105 m3/s were tested for seven air pollution episodes of Beijing during the winters of 2015–2017. The numerical results showed that with eight SALSCSs installed along the 6th Ring Road of the city, 11.2% and 14.6% of PM2.5 concentrations were reduced under the two flow-rate simulation conditions, respectively.

A priori analysis of differential diffusion for model development for scale-resolving simulations

Direct numerical simulation data of a jet with two passive scalars is compared to explicitly filtered data of the same case with regard to the influence of the turbulent/nonturbulent interface (TNTI) on differential diffusion. Filtering is found to affect differential diffusion differently at the TNTI and in the jet core.

Hydrodynamic dispersion in a tube with diffusive losses through its walls

Advective–diffusive transport of passive or reactive scalars in confined environments (e.g. tubes and channels) is often accompanied by diffusive losses/gains through the confining walls. We present analytical solutions for transport of a reactive solute in a tube, whose walls are impermeable to flow but allow for solute diffusion into the surrounding medium. The solute undergoes advection, diffusion and first-order chemical reaction inside the tube, while diffusing and being consumed in the surrounding medium. These solutions represent a leading-order (in the radius-to-length ratio) approximation, which neglects the longitudinal variability of solute concentration in the surrounding medium. A numerical solution of the full problem is used to demonstrate the accuracy of this approximation for a physically relevant range of model parameters. Our analysis indicates that the solute delivery rate can be quantified by a dimensionless parameter, the ratio of a solute’s residence time in a tube to the rate of diffusive losses through the tube’s wall.

Numerical simulations on mixing of passive scalars in river confluences

The study deals with the mixing of passive scalars (such as pollutants) in open-channel confluences when the two inflows exhibit different concentrations. The dispersion of such passive scalars is investigated through the analysis of the processes enhancing the mixing in the confluence in order to estimate the length for complete mixing Lm in the downstream branch. The aim of this study is then to establish a correlation between this length for complete mixing Lm and characteristics of the confluence, namely its angle and two hydrodynamic parameters that are the momentum ratio M* of the inflows and the width-to-depth ratio of the downstream branch b/h. In this work, the flow in the confluence is numerically simulated by RANS calculation coupled with the advection-diffusion equation at field scale, i.e. with Reynolds and Froude numbers corresponding to real rivers (Re = 107 and Fr=0.1). The role of other parameters such as bed discordance or bed forms... is not addressed here. The numerical results highlight that the mixing in the confluence and its downstream branch, is enhanced by the presence of secondary currents that are themselves strongly affected by the characteristics of the confluence. The results aim at getting an operative empirical law linking the geometric and hydrodynamic parameters of the confluence with Lm.

Simulation of Turbulent Wake at Mixing of Two Confined Horizontal Flows

The development of a turbulent mixing layer at mixing of two horizontal water streams with slightly different densities is studied by the means of numerical simulation. The mixing of such flows can be modelled as the flow of two components, where the concentration of one component in the mixing region is described as a passive scalar. The velocity field remains common over the entire computational domain, where the density and viscosity difference due to the concentration mainly affects the turbulent fluctuations in the mixing region. The numerical simulations are performed with the open source code OpenFOAM using two different approaches for turbulence modelling, Reynolds Averaged Navier Stokes equations (RANS) and Large Eddy Simulation (LES). The simulation results are discussed and compared with the benchmark experiment obtained within the frame of OECD/NEA benchmark test. A good agreement with experimental results is obtained in the case of the single liquid experiment. A high discrepancy between the simulated and the experimental velocity fluctuations in the case of mixing of the flows with the slightly different densities and viscosities triggered a systematic investigation of the modelling approaches that helped us to find out and interpret the main reasons for the disagreement.

Lateral transport of traffic pollutants in complex urban area

Owing to the spatial variability of an urban area, even the transport of passive scalar is complex. The examination of the pollutant transport in such turbulent flow as occur within the urban canopy requires the measurements not only the advective but also the turbulent part of this transport. However, recent measurement techniques for the turbulent transport have their limitations. In particular, these measurements are very demanding if one needs to analyze the ventilation processes of the street through the entire streetcanyon openings and which needs to be performed also in the positions where the handling with the measurement instruments might comprise a complex issue or is even impossible. Thus we present a comparison of two methods for the assessment of turbulent and advective pollution fluxes through the lateral openings of two different street canyons with respect to the wind direction and the roof-height nonuniformity to evaluate the importance of the measurement of these fluxes nearby the street-canyon walls. Both of them are based on the simultaneous point measurement of concentration and lateral velocity component and the interpolation between the last measured point and the street-canyon borders, but in the second method the measured area is extended from 77% to 84% of the total area of the lateral openings.

Coherent Structures in Large-Eddy Simulations of a Nonprecipitating Stratocumulus-Topped Boundary Layer

Abstract The properties of coherent convective structures are analyzed in a nonprecipitating marine nocturnal stratocumulus-topped boundary layer (STBL) with a series of high-resolution large-eddy simulations (LESs). A new classification method based on octant analysis—using vertical velocity and two passive scalars—is introduced to systematically define convective structures in both the cloudy and the cloud-free regions. It is therefore possible to detect and track updrafts, downdrafts, and their turbulent shells (both ascending and subsiding), together with the entraining air from the inversion layer or the free troposphere. The geometrical and thermodynamical characteristics (e.g., areal fraction, temperature, liquid and total water mixing ratio, buoyancy) of those structures are then accurately described, and particular attention is given to their respective contributions to the turbulent transport of mass, heat, and moisture. It is shown that updrafts, downdrafts, and entrainment are equally important to describe the STBL dynamics. Conversely, it is found that shells, although they partially contribute to the mass transport, have a negligible contribution to the turbulent fluxes of heat and moisture.

Logarithmic scaling for fluctuations of a scalar concentration in wall turbulence.

Within wall turbulence, there is a sublayer where the mean velocity and the variance of velocity fluctuations vary logarithmically with the height from the wall. This logarithmic scaling is also known for the mean concentration of a passive scalar. By using heat as such a scalar in a laboratory experiment of a turbulent boundary layer, the existence of the logarithmic scaling is shown here for the variance of fluctuations of the scalar concentration. It is reproduced by a model of energy-containing eddies that are attached to the wall.

Dispersion of a Passive Scalar Within and Above an Urban Street Network

The transport of a passive scalar from a continuous point-source release in an urban street network is studied using direct numerical simulation (DNS). Dispersion through the network is characterized by evaluating horizontal fluxes of scalar within and above the urban canopy and vertical exchange fluxes through the canopy top. The relative magnitude and balance of these fluxes are used to distinguish three different regions relative to the source location: a near-field region, a transition region and a far-field region. The partitioning of each of these fluxes into mean and turbulent parts is computed. It is shown that within the canopy the horizontal turbulent flux in the street network is small, whereas above the canopy it comprises a significant fraction of the total flux. Vertical fluxes through the canopy top are predominantly turbulent. The mean and turbulent fluxes are respectively parametrized in terms of an advection velocity and a detrainment velocity and the parametrization incorporated into a simple box-network model. The model treats the coupled dispersion problem within and above the street network in a unified way and predictions of mean concentrations compare well with the DNS data. This demonstrates the usefulness of the box-network approach for process studies and interpretation of results from more detailed numerical simulations.

Two-Dimensional Finite-Volume Eulerian-Lagrangian Method on Unstructured Grid for Solving Advective Transport of Passive Scalars in Free-Surface Flows

AbstractA two-dimensional (2D) finite-volume Eulerian-Lagrangian method (FVELM) on unstructured grid is proposed for solving the advection equation in free-surface scalar transport models. A backtr...