Variance Of Concentration Fluctuations Research Articles

A Simple Parametrization for the Concentration Variance Dissipation in a Lagrangian Single-Particle Model

A model for the evaluation of the concentration fluctuation variance is coupled with a one-particle Lagrangian stochastic model and results compared to a wind-tunnel simulation experiment. In this model the concentration variance evolves along the particle trajectories according to the same Langevin equation used for the simulation of the velocity field, and its dissipation is taken into account through a decay term with a finite time scale. Indeed, while the mean concentration is conserved, the concentration variance is not and our model takes into account its dissipation. A simple parametrization for the dissipation time scale is proposed and it is found that it depends linearly on time and on the ratio between the size and the height of the source through a scaling factor of 1 / 3.

Study of the interference of plumes released from two near-ground point sources in an open channel

The dispersion and mixing of passive scalars released from two near-ground point sources into an open-channel flow are studied using direct numerical simulation. A comparative study based on eight test cases has been conducted to investigate the effects of Reynolds number and source separation distance on the dispersion and interference of the two plumes. In order to determine the nonlinear relationship between the variance of concentration fluctuations of the total plume and those produced by each of the two plumes, the covariance of the two concentration fields is studied in both physical and spectral spaces. The results show that at the source height, the streamwise evolution of the cross correlation between the fluctuating components of the two concentration fields can be classified into four stages, which feature zero, destructive and constructive interferences and a complete mixing state. The characteristics of these four stages of plume mixing are further confirmed through an analysis of the pre-multiplied co-spectra and coherency spectra. From the coherency spectrum, it is observed that there exists a range of ‘leading scales’, which are several times larger than the Kolmogorov scale but are smaller than or comparable to the scale of the most energetic eddies of turbulence. At the leading scales, the mixing between the two interfering plumes is the fastest and the coherency spectrum associated with these scales can quickly approach its asymptotic value of unity.

Reduced graphene oxide induced phase miscibility in polystyrene–poly(vinyl methyl ether) blends

Graphene oxide and reduced graphene oxide (r-GO) were synthesized by wet chemistry and the effect of r-GO in PS–PVME blends was investigated here with respect to phase miscibility, intermolecular cooperativity in the glass transition region and concentration fluctuation variance by shear rheology and dielectric spectroscopy. The spinodal decomposition temperature (Ts) and correlation length were evaluated from isochronal temperature scans in shear rheology. The r-GO is shown to induce miscibility in the blends, which may lead to increased local heterogeneity in the blends, though the length of cooperatively re-arranged regions (ξ) at Tg is more or less unaltered. The evolution of the phase morphology as a function of temperature was assessed using polarized optical microscopy (POM). In the case of the 60/40 PS–PVME blends with 0.25 wt% r-GO, apart from significant refinement in the morphology, retention of the interconnected ligaments of PVME was observed, even in the late stages of phase separation suggesting that the coarsening of the phase morphology has been slowed down in the presence of r-GO. This phenomenon was also supported by AFM. Surface enrichment of PVME, owing to its lower surface tension, in the demixed samples was supported by XPS scans. The interconnected network of PVME has resulted in significantly higher permittivity in the bi-phasic blends, although the concentration of r-GO is below the percolation threshold.

Multiwalled-Carbon-Nanotube-Induced Miscibility in Near-Critical PS/PVME Blends: Assessment through Concentration Fluctuations and Segmental Relaxation

The effects of multiwalled carbon nanotubes (MWNTs) on the concentration fluctuations, interfacial driven elasticity, phase morphology, and local segmental dynamics of chains for near-critical compositions of polystyrene/poly(vinyl methyl ether) (PS/PVME) blends were systematically investigated using dynamic shear rheology and dielectric spectroscopy. The contribution of the correlation length (ξ) of the concentration fluctuations to the evolving stresses was monitored in situ to probe the different stages of demixing in the blends. The classical upturn in the dynamic moduli was taken as the rheological demixing temperature (T(rheo)), which was also observed to be in close agreement with those obtained using concentration fluctuation variance, <(δϕ)(2)>, versus temperature curves. Further, Fredrickson and Larson's approach involving the mean-field approximation and the double-reptation self-concentration (DRSC) model was employed to evaluate the spinodal decomposition temperature (T(s)). Interestingly, the values of both T(rheo) and T(s) shifted upward in the blends in the presence of MWNTs, manifesting in molecular-level miscibility. These phenomenal changes were further observed to be a function of the concentration of MWNTs. The evolution of morphology as a function of temperature was studied using polarized optical microscopy (POM). It was observed that PVME, which evolved as an interconnected network during the early stages of demixing, coarsened into a matrix-droplet morphology in the late stages. The preferential wetting of PVME onto MWNTs as a result of physicochemical interactions retained the interconnected network of PVME for longer time scales, as supported by POM and atomic force microscopy (AFM) images. Microscopic heterogeneity in macroscopically miscible systems was studied by dielectric relaxation spectroscopy. The slowing of segmental relaxations in PVME was observed in the presence of both "frozen" PS and MWNTs interestingly at temperatures much below the calorimetric glass transition temperature (T(g)). This phenomenon was observed to be local rather than global and was addressed by monitoring the evolution of the relaxation spectra near and above the demixing temperature.

A numerical investigation of lutocline dynamics and saturation of fine sediment in the oscillatory boundary layer

[1] Understanding the state of the muddy seabed is critical to sediment transport, hydrodynamic dissipation and seabed properties. However, this endeavor is challenging because the availability and settling velocity of sediment in muddy environments are highly variable. For a given Reynolds number, typical of fine sediment settling in a moderately energetic muddy shelf, recent 3D numerical simulations have revealed four distinct regimes of wave-induced fine sediment transport. These regimes depend on the availability (or concentration) of sediment and range from well-mixed condition to the formation of lutocline, and eventually a complete flow laminarization. By keeping the sediment availability unchanged, this study further demonstrates the existence of these flow regimes for a range of sediment settling velocities. Simulation results suggest that when settling velocity is larger, the location of the lutocline becomes lower (closer to the bed) and the flow eventually laminarizes when there is further increase in the settling velocity. Hence, the dynamics of lutocline is clearly related to the transition between these flow regimes. The vertical flow structure in the presence of lutocline is revealed through the budgets of sediment flux and turbulent kinetic energy. The suppressed mixing in the lutocline layer is further illustrated from a new perspective, i.e., the budgets of turbulent suspension and concentration fluctuation variance. The concept of saturation, commonly used for tidal boundary layer, is extended here for wave boundary layer.

Computational Fluid Dynamical Modelling of Concentration Fluctuations in an Idealized Urban Area

Turbulent mixing induces variability in concentration that is important in many applications, such as reactive plumes, risk assessments or odour impact analyses (when the effects can have time scales on the order of a second). In urban canopies, the variability may be modified by the presence of buildings. Our purpose is to study concentration fluctuation variance in built-up areas using an Eulerian approach. We performed numerical simulations with the computational fluid dynamics model Mercure_Saturne, which is a three-dimensional model adapted to atmospheric flow and pollutant dispersion. We use a k − ϵ turbulence closure and predict the concentration variance with a transport equation model. The model performance is evaluated with the near-full scale experiment MUST (Mock Urban Setting Test), a field experiment conducted in Utah’s West Desert Test Center. The modelled root-mean-square of the concentration fluctuations is compared to measurements for 20 of the MUST trials. The model shows good agreement with the measurements, with the fraction of predictions within a factor of two of observations of 60.1%, with better results for horizontal lines of detectors than for the detectors on vertical masts (with fractions of predictions within a factor of two of observations of respectively 66.4% and 52.6%). The influence of different parameters on the fluctuation variance is also studied and we show the importance of taking into account the stability of the stratification when modelling the turbulent kinetic energy.

Comparison of Continuous Blend Time and Residence Time Distribution Models for a Stirred Tank

In continuous operation, mixing in a stirred tank is often characterized by the residence time distribution (RTD) curves and the mean residence time (V/Q). The RTD is a measure of the history of the fluid element flowing through the reactor rather than a measure of the local mixing conditions inside the vessel. In this study, additional information about local mixing is obtained by taking measurements inside the vessel. The variance of concentration fluctuations from three probes (two located inside the tank and one at the outlet) is used to determine the continuous blend time (θcnts). At the limiting condition of a slow feed rate relative to the batch blend time, the CSTR is ideal, but at high flow rates the mixing inside the vessel deviates by up to 50% from the ideal case. Three design guidelines are recommended for designs where ideal mixing conditions are required. First, a line from the inlet to the outlet should pass through the impeller. Second, the feed velocity should decay to the mean impeller suction velocity by the time the feed reaches the impeller for the case of surface feed above a downpumping impeller. Third, the ratio of the mean residence time (V/Q) to the batch blend time (θb) should be at least 10. Additional guidelines will be needed for tank configurations where the feed(s) and/or outlet(s) are located on the side of the vessel.

Reacting flow of hydrogen chloride and ammonia in experimental and numerical modelling

The experimental and numerical investigations of the flow with reaction of two gases: hydrogen chloride HCl and ammonia NH3 were performed. The article contains description of the visualisation method of the formation and flow of particles of ammonia chloride NH4Cl. Analyses of mean concentration and variance of concentration fluctuations of dispersed phase were performed for different outputs of gases. Numerical calculations were performed for analysed phenomenon. Both numerical and visualisation results were matched and compared.

Predicting concentration fluctuations with a puff-particle model

This paper demonstrates that the puff-particle model (PPM) allows for the prediction of concentration fluctuations (in addition to the estimation of the concentration itself). Several models have been developed based on Gifford's meandering plume concept to separate the dispersing effect of instantaneous plume (or puff) growth, and of meandering. They all have in common the assumption of a certain shape of the probability density function of concentration, and that the variance of concentration fluctuations is derived from the properties of turbulence. In contrast, the PPM aims at simulating a realistic 3-D meandering of the puffs, which allows for direct determination of the higher moments of concentration, whilst enabling the individual puffs to account for inhomogeneous conditions.

Wind tunnel measurements of concentration fluctuations in an urban street canyon

A wind tunnel study was performed to examine some turbulent characteristics and statistical properties of the concentration field developing from the steady release of a tracer gas at street level in a canyon amidst urban roughness. The experiment was conducted with the approaching wind direction perpendicular to the street axis and, with a street width to building height aspect ratio equal to one. Concentration time series were recorded at 70 points within the test street cross-section and above. Mean concentrations, variances and related turbulent quantities, as well as other statistical quantities including quantiles were computed. Concentration spectra and autocorrelation functions were also examined. The emphasis is put here on the results concerning mean concentrations and the variance of concentration fluctuations. The main objective of this paper is to put forward potential benefits of the experimental approach taken in this study. Through a simple and already widely studied configuration it is aimed to show how, for modelling purposes, this approach can help improving our understanding of the mechanisms of dipersion of pollution from car exhausts in built-up areas and, with further measurements, how it could assist in drawing specifications for siting monitoring networks.

Large-eddy simulation of high-Schmidt number mass transfer in a turbulent channel flow

Mass transfer through the solid boundary of a turbulent channel flow is analyzed by means of large-eddy simulation (LES) for Schmidt numbers Sc=1, 100, and 200. For that purpose the subgrid stresses and fluxes are closed using the Dynamic Mixed Model proposed by Zang et al. [Phys. Fluids A 5, 3186 (1993)]. At each Schmidt number the mass transfer coefficient given by the LES is found to be in very good quantitative agreement with that measured in the experiments. At high Schmidt number this coefficient behaves like Sc−2/3, as predicted by standard theory and observed in most experiments. The main statistical characteristics of the fluctuating concentration field are analyzed in connection with the well-documented statistics of the turbulent motions. It is observed that concentration fluctuations have a significant intensity throughout the channel at Sc=1 while they are negligible out of the wall region at Sc=200. The maximum intensity of these fluctuations depends on both the Schmidt and Reynolds numbers and is especially influenced by the intensity of the velocity fluctuations present in the buffer layer of the concentration field. At Sc=1, strong similarities are observed between the various terms contributing to the turbulent kinetic energy budget and their counterpart in the budget of the variance of concentration fluctuations. At high Schmidt number, the latter budget is much more influenced by the small turbulent structures subsisting in the viscous sublayer. The instantaneous correlation between the spatial characteristics of the concentration field and those of the velocity field is clearly demonstrated by the presence of low- and high-concentration streaks close to the wall. The geometrical characteristics of these structures are found to be highly Sc dependent. In particular their spanwise wavelength is identical to that of the streamwise velocity streaks at Sc=1 while it is reduced by half at Sc=200. Analysis of the co-spectra between concentration and normal velocity fluctuations emphasizes the fact that the large-scale structures play an essential role in the turbulent mass transfer process at high Schmidt number. Overall the picture that emerges from this investigation fully confirms the conclusions of Campbell and Hanratty [AIChE J. 29, 221 (1983)]: high-Schmidt-number mass transfer at a solid wall is governed by the low-frequency part of the normal velocity fluctuation gradient at the wall, i.e., by the large-scale structures observed in planes parallel to the wall in the viscous sublayer.

The effect of line averaging on concentration fluctuations

The reduction in variance of concentration fluctuations due to line averaging is estimated assuming that the process is influenced by the integral distance scale, y I , of ambient turbulence and the scaling width, W, of the time-averaged plume. An analytical formula is derived for the line-averaged variance for situations where the autocorrelogram is exponential and the point variance decreases exponentially with distance from plume centerline. Predictions of concentration fluctuation variance are compared with water tank and field data, with the result that the decrease of variance with averaging distance is well-simulated if the model parameters y I and W are carefully chosen.

A Gaussian Plume Model of Atmospheric Dispersion Based on Second-Order Closure

A practical model of atmospheric dispersion of a passive tracer based on systematic reduction of the second-order closure transport equations using Gaussian shape assumptions is presented. The model is comparable with conventional Gaussian plume models in complexity, but still maintains the capability to also predict concentration fluctuation variance and to utilize direct measurements of turbulent velocity variances in a consistent manner. Comparison with laboratory data demonstrates the model's ability to produce reasonable predictions for the concentration field.

Spectra of concentration fluctuations: The two time scales of a meandering plume

The integral time scale, T C , of the concentration fluctuations in a narrow, meandering (intermittent) plume can be much less than the time scale, T E , of the turbulence in which the plume is immersed, and is generally of the same order of magnitude as the time required for the plume to pass once over a receptor. However the total concentration fluctuation variance is equally strongly influenced by the larger time scale, T E , associated with meandering caused by ambient turbulence. It is shown that observed energy spectra of concentration fluctuations can be fitted by a linear combination of two Markov spectra, one with the time scale of the meandering motions and another with the time scale of the small scale plume motions. The two components are weighted by I and 1 − I, respectively, where I is the intermittency or fraction of time that non-zero concentrations occur.

Intermittency and conditionally-averaged concentration fluctuation statistics in plumes

A semi-empirical Gaussian plume model is developed which predicts the intermittency factor, and the mean and variance of the non-zero time varying concentration in the plume from a point source. Wind tunnel data are used to verify the theory and to set the empirical constants. Conditionally averaged concentration fluctuation variance, which has zero concentrations removed, is only weakly dependent on source size, while intermittency caused by plume meandering is shown to be strongly dependent on source size. The resulting closed form predictions are presented in a form suitable for estimating risk of exposure to peak concentrations.

Uncertainty in Air Quality Modeling

Under the direction of the AMS Steering Committee for the EPA Cooperative Agreement on Air Quality Modeling, a small group of scientists convened to consider the question of uncertainty in air quality modeling. Because the group was particularly concerned with the regulatory use of models, its discussion focused on modeling tall stack, point source emissions. The group agreed that air quality model results should be viewed as containing both reducible error and inherent uncertainty. Reducible error results from improper or inadequate meteorological and air quality data inputs, and from inadequacies in the models. Inherent uncertainty results from the basic stochastic nature of the turbulent atmospheric motions that are responsible for transport and diffusion of released materials. Modelers should acknowledge that all their predictions to date contain some associated uncertainty and strive also to quantify uncertainty. How can the uncertainty be quantified? There was no consensus from the group as to precisely how uncertainty should be calculated. One subgroup, which addressed statistical procedures, suggested that uncertainty information could be obtained from comparisons of observations and predictions. Following recommendations from a previous AMS workshop on performance evaluation (Fox, 1981), the subgroup suggested construction of probability distribution functions from the differences between observations and predictions. Further, they recommended that relatively new computer-intensive statistical procedures be considered to improve the quality of uncertainty estimates for the extreme value statistics of interest in regulatory applications. A second subgroup, which addressed the basic nature of uncertainty in a stochastic system, also recommended that uncertainty be quantified by consideration of the differences between observations and predictions. They suggested that the average of the difference squared was appropriate to isolate the inherent uncertainty that arises because individual realizations of the concentrations are different from the average concentrations. The average square difference allows quantification of this fact. Viewed in this framework, uncertainty is related to the variance of concentration fluctuations and the integral time scale of the turbulent flow. How can the uncertainty be communicated to decision makers? There was concern expressed by a third subgroup that non-technical people would have little understanding of quantified uncertainty. This places an increased burden on modelers to ensure that their efforts are useful. Similarly, decision makers will need to educate themselves and accept the challenge of decision making with quantified uncertainty.