Scalar Dispersion Research Articles

Turbulent scalar fluxes from a generalized Langevin model: Implications on mean scalar mixing and tracer particle dispersion

A Generalized Langevin Model (GLM) formulation to be used in transported joint velocity-scalar probability density function methods is recalled in order to imply a turbulent scalar-flux model where the pressure-scrambling term is in correspondence with standard Monin's return-to-isotropy term. The proposed non-constant C0 formulation is extended to seen-velocity models for particle dispersion modeling in dispersed two-phase flows. This allows us to correct the wrong turbulent scalar-flux modeling in the limit of tracer particles. Moreover, this allows us to have a more general formulation in order to consider advanced Reynolds-stress models. The cubic model of Fu, Launder, and Tselepidakis is considered, together with the model of Merci and Dick for turbulent dissipation. Results are presented for different swirling and recirculating single-phase and two-phase flows, showing the capabilities of the proposed non-constant C0 GLM formulations compared to the standard GLM.

Analysis of Pollutant Entrainment from Localized Sources in a Street Network

The propagation of a pollutant emitted from localized sources both within and above a regular street network is studied by analyzing data from direct numerical simulations of passive scalar dispersion. Two wind directions are considered, corresponding to aligned and oblique flow with respect to the street axes. Particular attention is paid to the role of entrainment of the scalar into the urban canopy from an elevated source and re-entrainment of material originally released further upstream from a ground source. The variation of concentration differences and vertical fluxes between the streets and the air above as a function of distance reveals important differences between the rate of lateral and vertical mixing for the two sources. Detrainment and entrainment need a longer fetch to equilibrate for the elevated source than for the ground source. There are large differences between the advection and detrainment velocities for the aligned and oblique cases, so that a change in wind direction could affect ventilation efficiency considerably. Time scales associated with different dispersion processes are computed and the time of first appearance of the scalar from the onset of release in different streets is mapped. It is shown that re-entrainment can provide a shortcut dispersion pathway for reaching certain parts of the network. This is particularly striking in the case of oblique flow, when material can be transferred by entrainment up to twice as rapidly as by advection. Taken together, these results highlight the overall message that vertical exchange is a two-way process and that entrainment needs to be considered in the context of emergency response as well as urban ventilation.

Construction of urban turbulent flow database with wavelet-based compression: A study with large-eddy simulation of flow and dispersion in block-arrayed building group model

Urban Turbulent flow database, which includes accurately simulated velocity field with full spatial distribution and time-dependent dynamics, is beneficial for fast analysis of pollutant dispersion and comprehensive validation. However, the enormous data volume makes storage and sharing difficult. This research investigated the feasibility of constructing a small-sized database by compression. A wavelet-based compression method was selected because of its light calculation burden and independence of time series data. The database of the flow field in urban-like arrayed blocks was obtained by large-eddy simulation, and then the velocity and diffusion coefficient fields were compressed with different error controls to construct databases. The compression ability of the wavelet-based method was evaluated, and it was found that the maximum compression ratio is reached when most information in the wavelet coefficients is discarded. The effects of compression error on both the single snapshot and the time-series results were studied. The applicability of the compressed database was verified by the resimulation of passive scalar dispersion in the flow. According to results, the database with approximately 100-times compression is suitable for such applications as the visualization and dispersion simulation of passive scalars with sufficient accuracy.

High-frequency simultaneous measurements of velocity and concentration within turbulent flows in wind-tunnel experiments

We analyse the metrological aspect related to systems devoted to the simultaneous measurements of (one point) velocity and scalar concentration statistics. We consider systems based on the coupling of an anemometer (laser Doppler or hot wire) with a flame ionization detector. In particular, we focus on the estimate of the cross-correlation velocity-concentration. Key aspects in the reliability of such measurements are related to the identification of an optimal distance between the two probes, the time lag with which the velocity and concentration signals are acquired, and, eventually, the influence of seeding particles (when using a laser Doppler anemometer) on the concentration measurements. We investigate these aspects by performing wind-tunnel experiments on the scalar dispersion downwind a ground-level source in a turbulent boundary layer. This analysis allowed us to identify a time delay and a convenient distance between the signals provided by the anemometer and the concentration detector. Results also show that the seeding used for the laser Doppler anemometer measurements modifies the cut-off frequency in the concentration spectra and induces a slightly larger uncertainty on the statistics of scalar field. The results show the reliability of both systems in estimating (horizontal and vertical) turbulent mass fluxes.

A mathematical framework for estimating risk of airborne transmission of COVID-19 with application to face mask use and social distancing.

A mathematical model for estimating the risk of airborne transmission of a respiratory infection such as COVID-19 is presented. The model employs basic concepts from fluid dynamics and incorporates the known scope of factors involved in the airborne transmission of such diseases. Simplicity in the mathematical form of the model is by design so that it can serve not only as a common basis for scientific inquiry across disciplinary boundaries but it can also be understandable by a broad audience outside science and academia. The caveats and limitations of the model are discussed in detail. The model is used to assess the protection from transmission afforded by face coverings made from a variety of fabrics. The reduction in the transmission risk associated with increased physical distance between the host and susceptible is also quantified by coupling the model with available and new large eddy simulation data on scalar dispersion in canonical flows. Finally, the effect of the level of physical activity (or exercise intensity) of the host and the susceptible in enhancing the transmission risk is also assessed.

The impact of stretching-enhanced mixing and coalescence on reactivity in mixing-limited reactive flows

We analyze the dynamics of solute mixing and reaction in a mixing-limited reactive flow by considering the transport of a tracer in a linear shear flow and in a Rankine vortex. The action of a shear flow, in general, achieves stretching of fluid elements due to the heterogeneous nature of the flow. A vortex flow exhibits not only stretching but also folding of fluid elements in a way that brings adjacent fluid elements closer at every turn. A strong stretching along the tangential direction is accompanied by a concomitant thinning in the radial direction leading to a strong diffusive flux, which may cause the material from neighboring regions of the mixing interface to aggregate. Through a Lagrangian concentration evolution technique, the diffusive strip method, we obtain the concentration field and pinpoint the signature of coalescence of two neighboring concentration regions by analyzing the concentration distribution profiles. The role of substrate deformation on the reaction kinetics of a classical heterogeneous chemical reaction is also studied where we derive analytical expressions for the coupling between the rate of product formation and the Péclet number in different time limits. Finally, the impact of coalescence on reaction rates is studied for a Rankine vortex, a result that holds important implications for simple bimolecular reactions. This analysis is useful to understand scalar dispersion in vortical flow structures and the consequences of stretching-enhanced diffusion in mixing-limited reactive flows.

Isothermal and non-isothermal flow in street canyons: A review from theoretical, experimental and numerical perspectives

Urban street canyon flows play a central role in microclimate control, from street canyon to neighbourhood and city scale, which affect pollutant dispersion, thermal comfort of residents and building energy consumption for various indoor and outdoor flow conditioning systems. Extensive studies have been devoted to this field, from theoretical modelling to experimental measurements and numerical simulations. While some important characteristics of street canyon flows, such as the presence of a primary standing vortex and the mechanism for its establishment, have been well revealed, a holistic understanding consolidating theoretical, experimental and numerical research has not been achieved. This review is therefore aimed to holistically articulate these approaches and research outcomes in the field. Some critical points overlooked in the literature are identified and commented on. These are: distinguishing gradient and bulk Richardson numbers; identifying dominant similarity characteristic numbers for scaling down models; predicting the condition in which thermal effects come into play; modelling the convective heat transfer in non-equilibrium mixed convection conditions using wall functions; and exploring the influence of neutral and non-neutral urban boundary layers on street canyon flows and associated passive scalar dispersion. The review is concluded with an outlook to most challenging research questions towards understanding of microclimate of full-scale realistic street canyons.

Using helicity to investigate scalar transport in wall turbulence

Since flow regions of high helicity are associated with low dissipation of kinetic energy, helicity can be used to mark the flow structures that are major contributors to turbulent scalar dispersion. Employing a Lagrangian approach to compare the helicity between scalar tracers and fluid particles in the same flow field shows that flow structures that contribute to the transport of low Schmidt number markers are different than those for fluid particles. This is quite important in anisotropic wall turbulence, where the interplay between molecular and turbulent transport is critical.

Influence of submeso motions on scalar oscillations and surface energy balance

AbstractThe presence of wave‐like structures in the planetary boundary layer and their influence on the scalar fluxes and on the surface energy balance were investigated analyzing one year of continuous measurements collected in southern Brazil. Submeso oscillating patterns in the wind velocity components, temperature and scalar (CO, HO) concentrations were isolated using their auto‐correlation functions. The analysis showed that low wind speeds are necessary to trigger wavy motions. During night‐time, in the presence of large vertical temperature gradients, horizontal meandering and internal gravity waves are dominant features of the stable boundary layer. Furthermore, a significant number of meandering cases were identified also during daytime in neutral conditions associated with low values of net radiation. One case‐study showed how, during daytime, the wave‐like patterns may be triggered by variations in the net radiation. Spectral analysis on the whole dataset showed that oscillations in the wind velocity and temperature field are frequently associated with CO and HO wavy patterns with similar time‐scales. These non‐turbulent oscillations produce unpredictable large‐scale contributions to vertical fluxes of temperature and scalar concentrations. The energy budget analysis showed how the choice of a proper averaging time filters out these contributions and improves the energy budget closure, as well as the estimation of the net ecosystem exchange. The results confirm the influence of submeso motions in scalar dispersion, flux patterns and surface energy balance during low wind speed conditions and stable stratification.

Detailed magnetic resonance imaging measurements of a contaminant dispersed in an Oklahoma City model

Magnetic resonance imaging techniques were used to collect time-averaged three-component velocity and concentration data across a scaled model of 2003 Oklahoma City. The experiments included the release of a passive scalar designed to mimic the field tests of the Joint Urban 2003 (JU03) study conducted at the same site and provide measurements throughout the entire three-dimensional domain in nearly 10 million locations. The flow was in a fully turbulent water channel with a Reynolds number of 36,000 based on the channel hydraulic diameter. The geometrically similar cityscape was on the bottom wall of the channel. A low-momentum injector was designed to release the contaminant at the intersection of Broadway and Main street – a location that closely matches the Intense Observation Period 8 of JU03, which has been previously examined in several studies. Magnetic Resonance Velocimetry (MRV) and Magnetic Resonance Concentration (MRC) techniques measured the time averaged field with experimental uncertainties of 5.5% and 4% respectively, providing a candidate validation data set for atmospheric flow models. The inflow velocity boundary condition was measured at the inlet plane of the test section. Detailed analysis is provided of the flow field and concentration distribution, focusing on major features in the downtown area. In addition, a comparison with the available field test data near surface locations is conducted. The measurements are believed to be amongst the first of their kind and suggest that MRV/MRC techniques may be an effective means to study the flow and scalar dispersion within urban environments.

Spatial reconstruction of steady scalar sources from remote measurements in turbulent flow

Identifying the source of passive scalar transported in a turbulent environment from remote measurements is an ill-posed problem due to the irreversibility of diffusive processes. A significant difficulty of the source reconstruction is due to different potential source locations generating very highly correlated signals at the sensor. A variational algorithm is formulated, which utilizes high-fidelity simulations to reconstruct the spatial distribution of the source. A cost functional is defined based on the difference between the true measurements and their prediction from the simulations with the estimated source. Using forward–adjoint looping, the gradient of the cost functional with respect to the source distribution is evaluated, and the estimate of the source is updated. The adjoint-variational approach naturally accommodates measurements from multiple sensors, with essentially the same computational cost. The algorithm is evaluated for scalar dispersion in turbulent channel flow. When a single sensor is placed directly downstream of the source, the reconstruction is accurate in the cross-stream directions and is elongated in the streamwise direction. The estimated source, however, can reproduce the measurements and the scalar plume downstream of the sensor location. In the channel centre and log layer, the scalar fields are dominated by dispersion, and therefore the reconstruction is better than in the near-wall regions, where the scalar fields are dominated by diffusion. When a sensor is placed near the wall, the accuracy of the source recovery deteriorates due to diffusive effects. By using more sensors that span the plume cross-section, improvement of performance can be demonstrated despite an enlarged domain of dependence.

Quantification of Vegetation Arrangement and Its Effects on Longitudinal Dispersion in a Channel

AbstractIn nature, aquatic vegetation is one of the important factors—along with hydraulic characteristics and geometric configuration—determining the dispersion of scalars. Previous research has studied the effects of vegetation on longitudinal dispersion, varying plant population with uniform arrangement. However, since vegetation grows more often in clumped and heterogeneous rather than uniform patterns, the present work investigates the effects of the vegetation arrangement on the flows characteristics such as longitudinal dispersion, mean velocities, and drag coefficients. Several types of vegetation arrangement are described with the isometric and allometric concept and quantified with the standardized Morisita index. Laboratory experiments were performed to investigate variations of hydraulic parameters and longitudinal dispersion coefficients according to vegetation arrangements, which were quantified with the standardized Morisita index. The hydraulic parameters of mean velocity, turbulent kinetic energy, and drag depend on the vegetation arrangements, and in particular, the longitudinal dispersion coefficient varies with these arrangements by a factor of 4 or more.

Impact of Along-Valley Orographic Variations on the Dispersion of Passive Tracers in a Stable Atmosphere

A numerical model is used to investigate the transport of passive tracers in an idealized Alpine valley during stable wintertime conditions after the evening transition. The valley is composed of an upstream-valley section, which opens on a narrower downstream valley section, which opens onto a plain. The ratio between the valley-floor widths of the upstream and downstream sections is either 4 (simulation P1) or 11.5 (P2). The change in the thermal structure of the atmosphere in the along-valley direction and over the plain leads to the development of an along-valley flow. This flow is up-valley in the upstream section during the first three hours of the P1 simulation, reversing to the down-valley direction afterwards, but remains up-valley during the six hours of the P2 simulation. The effect of wind dynamics on the dispersion of passive scalars is identified by tracking areas prone to stagnation, recirculation, and ventilation using the methodology developed by Allwine and Whiteman (1994). Zones identified as prone to stagnation are consistent with those of high tracer concentration in both simulations. The narrowing of the valley is found to significantly reduce ventilation in the upstream section, an observation quantified by a ventilation efficiency.

Passive scalar dispersion in the near wake of a multi-scale array of rectangular cylinders

The near wakes of flows past single- and multi-scale arrays of bars are studied by means of planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV). The aim of this research is to better understand dispersion of passive scalar downstream of the multi-scale turbulence generator. In particular, the focus is on plausible manifestations of the space-scale unfolding (SSU) mechanism, which is often considered in the literature as the reason for the enhancement of the turbulent scalar flux in flows past fractal grids (i.e. specific multi-scale turbulence generators). The analysis of qualitative and quantitative PLIF results, as well as the simultaneously acquired PIV results, confirms the appearance of a physical scenario resembling the SSU mechanism. Unlike the anticipation of the literature, however, this scenario applies to some extent also to the flow past the single-scale obstacle. Application of a triple decomposition technique (which splits the acquired fields into their means, a number of coherent fluctuations and their stochastic parts) and a conditional-averaging technique reveals that the SSU mechanism is active in the vicinity of an intersection point between two adjacent wakes and is driven almost exclusively by coherent fluctuations associated with the larger of the intersecting wakes. This suggests that the SSU mechanism is related to the coherent fluctuations embedded in the flow rather than to the fine-scale turbulence and its underlying integral length scale, as proposed in previous works.

Discussion of “Tang, H., Zhang, H., & Yuan, S. (2018). Hydrodynamics and contaminant transport on a degraded bed at a 90-degree channel confluence. Environmental Fluid Mechanics, 18(2), 443–463”

The authors measured and computed the hydrodynamics and passive scalar dispersion in 90-degree open channel confluences over flat and degraded beds with a dominant upstream or tributary inflow. The present discussion essentially deals with the direction of rotation of the secondary currents, reported for the flat bed configuration with dominant tributary inflow. This rotation direction is indeed surprisingly opposite to the ones reported in the literature, both from calculations and measurements, even if present geometry slightly differs from literature geometries.

A Semi-analytical Model for Short-Range Near-Ground Continuous Dispersion

We present a semi-analytical model for the dispersion of passive scalars from continuous ground sources up to distances of a few hundred metres. We attempt to cope with problems typical of analytical models, such as the correct representation of the near-ground concentration and lateral dispersion, while avoiding the use of any empirical parameters. A previous analysis of Prairie Grass Project (PGP) data has shown that the near-ground, cross-wind integrated concentration decreases as some power of the distance from the source that is, itself, distance dependent. As the conventional power-law model is incapable of reproducing this behaviour, we propose a model in which the vertical diffusivity depends on both the height as a power law, and on the distance from the source. For this equation, we construct an infinite-series formal solution, with the first term used as an approximation. A set of equations based on this approximation and on Monin–Obukhov similarity theory is proposed for the the vertical diffusivity, from which the cross-wind integrated concentration is derived analytically. We further construct a simple empirical model for the distance-dependent vertical diffusivity. For the plume lateral width, a Langevin stochastic model depending on the plume height is proposed, whose formal analytical solution is used to derive a set of equations for the cloud width, which are easily solved numerically, with the results validated against PGP data. We apply four statistical measures to evaluate the performance of the model, including the computation of the 95% confidence intervals, for which we find very good agreement. Implementation of this model is extremely simple and computationally efficient.

A Simple Physically-Based Model for Wind-Turbine Wake Growth in a Turbulent Boundary Layer

The growth rate of wind-turbine wakes in the atmospheric boundary layer is a key parameter in analytical models used to predict wind-turbine wakes and their effects in wind farms. To date, the turbine-wake growth rate is determined empirically, owing to our limited understanding of the physical mechanisms leading to the recovery of the wakes in turbulent flows. Here, a simple physically-based model for wind-turbine wake growth is proposed based on the analogy with scalar dispersion in turbulent flows. The model is developed based on Taylor’s diffusion theory and intrinsically accounts for the effect of ambient turbulence intensity. In validations against large-eddy simulations of the wake flow of a turbine under different inflow turbulence conditions, it is found that the model yields good predictions of the growth of the turbine wakes. A slight underestimation of the wake growth rate is found only in the lowest ambient turbulence case, due to the non-negligible contribution of the turbine-induced turbulence in that case.

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.

Development of an analytical Lagrangian model for passive scalar dispersion in low-wind speed meandering conditions

Describing the effects of wind meandering motions on the dispersion of scalars is a challenging task, since this type of flow represents a physical state characterized by multiple scales. In this study, a Lagrangian stochastic diffusion model is derived to describe scalar transport during the horizontal wind meandering phenomenon that occurs within a planetary boundary layer. The model is derived from the linearization of the Langevin equation, and it employs a heuristic functional form that represents the autocorrelation function of meandering motion. The new solutions, which describe the longitudinal and lateral wind components, were used to simulate tracer experiments that were performed in low-wind speed conditions. The results of the comparison indicate that the new model can effectively reproduce the observed concentrations of the contaminants, and therefore, it can satisfactorily describe enhanced dispersion effects due to the presence of meandering.

Scalar Fluxes Near a Tall Building in an Aligned Array of Rectangular Buildings

Scalar dispersion from ground-level sources in arrays of buildings is investigated using wind-tunnel measurements and large-eddy simulation (LES). An array of uniform-height buildings of equal dimensions and an array with an additional single tall building (wind tunnel) or a periodically repeated tall building (LES) are considered. The buildings in the array are aligned and form long streets. The sensitivity of the dispersion pattern to small changes in wind direction is demonstrated. Vertical scalar fluxes are decomposed into the advective and turbulent parts and the influences of wind direction and of the presence of the tall building on the scalar flux components are evaluated. In the uniform-height array turbulent scalar fluxes are dominant, whereas the tall building produces an increase of the magnitude of advective scalar fluxes that yields the largest component. The presence of the tall building causes either an increase or a decrease to the total vertical scalar flux depending on the position of the source with respect to the tall building. The results of the simulations can be used to develop parametrizations for street-canyon dispersion models and enhance their capabilities in areas with tall buildings.