Theory Of Turbulent Diffusion Research Articles

Resolved and subgrid-scale crossing trajectory effects in Eulerian large eddy simulations of size-dependent droplet transport

We study the dispersion characteristics of slightly buoyant droplets in a turbulent jet using large eddy simulations (LES). The droplet number density fields are represented using an Eulerian approach, with the dispersed phase modelled using the Fast-Eulerian method (Ferry & Balachandar, Intl J. Multiphase Flow, vol. 27, issue 7, pp. 1199–1226, 2001) that includes the droplet rise velocity. Radial concentration profiles and turbulent concentration fluxes for droplets of different sizes are analysed to quantify the ‘trajectory crossing effect’, when relative motions between particles and turbulent eddies tend to reduce turbulent diffusion. For finer LES grid resolutions, the model captures the differential, size-based dispersion characteristics of the droplets with the transverse dispersion of the larger droplet sizes suppressed, since trajectory crossing effects are explicitly resolved in LES. We examine a similarity solution model for the size-dependent radial concentration profiles based on a modified Schmidt number derived from the theory of turbulent diffusion of particles in the atmosphere proposed by Csanady (J. Atmos. Sci., vol. 20, pp. 201–208, 1963). The results are validated with the high resolution LES data and show good agreement. Then the size-dependent Schmidt number model is reformulated as a model for unresolved subgrid-scale trajectory crossing effects and used to calculate the subgrid concentration flux in a coarse LES of a turbulent jet, with slightly buoyant droplets injected at the centreline in the self-similar region of the jet. The results are compared to a simulation with higher grid resolution and a coarse simulation with a constant Schmidt number subgrid-scale model. We find that the subgrid model enhances the prediction accuracy of the concentration profiles and turbulent concentration flux for the coarse LES.

Analysis of the development of the flame brush in turbulent premixed spherical flames

The thickness of the turbulent flame brush is central to the modeling of premixed turbulent combustion and the theory of turbulent diffusion is often applied to explain the growth of the brush with varying success. However, numerous studies have shown that the brush evolves differently from the dispersion of material points on the account of flame propagation, density changes across the front, and hydrodynamic instabilities. Modifications to turbulent diffusion theory to incorporate these effects are challenging since the theory is Lagrangian. In this article, we present an alternate Eulerian framework based on the surface density formalism. We employ the proposed framework to analyze a database of direct numerical simulations of spherical turbulent premixed flames in decaying isotropic turbulence and recover mechanisms for which scaling laws are proposed and assessed against data. We characterize quantitatively two mechanisms: one related to the mean velocity gradient induced by thermal expansion and the other due to flame propagation in the presence of curvature. We demonstrate that the net effect of these two processes is to hinder the growth of the turbulent flame brush in the present configuration. Our analysis supports the notion that the turbulent flame brush does not grow indefinitely, rather it attains a maximum thickness.

Dry deposition of dust particles during medium- and high-level dust storms to a forest canopy in a semi-arid region

In the present study the impact of forest canopy on the spatial distribution of PM10 concentration during dust events in a region, which is subjected to frequent occurrences such as dust storms is investigated. The developed two-dimensional model is based on the application of theory of turbulent diffusion in the forest canopy in conjunction with model of dust particles deposition to vegetation elements. The leaf area density (LAD) distribution with height as well as dust particle size distribution are taken into account. The initial wind velocity profiles on the windward side of the forest were fitted from data obtained in field measurements in the studied region. The resulted dust transport in the forest canopy was validated by comparison of theoretical results with the empirical data in the studied region. Using the suggested model, we analyzed the evolution of wind velocity profiles in and above the forest canopy as well as the process of dry deposition of PM to vegetation elements. Numerical calculations performed using the developed model showed that in dust storms, PM10 concentrations at the leeward side of the forest are reduced by ≈ 16–18% depending on dust storm level. We also found that inside the canopy the ratio of PM10 concentrations between the points along the studied transect and windward side (not affected by the forest) is higher, the higher the level of the dust storm. Our model results of the atmospheric PM distribution show fairly good agreement with the data of the field measurements.

Quantitative computational fluid dynamic analyses of oil droplets deposition on vaneless diffusor walls of a centrifugal compressor

AbstractIn the vehicle turbocharger operating process, the diffusor walls are susceptible to oil droplet deposition. This deposition may cause deterioration in the diffusor flow performance, consequently resulting in the deterioration of compressor performance. In this paper, a three‐dimensional steady computational fluid dynamic (CFD) numerical investigation was performed to study droplet deposition on the walls of a centrifugal compressor diffusor. Firstly, the theoretical basis of oil droplet distribution and formation on the diffusor were presented. On the basis of these, the distribution rules of the capture efficiency and particle concentration for the diffusor were investigated considering six different droplet diameters (0.25 μm, 0.5 μm, 0.75 μm, 1.00 μm, 1.25 μm, 1.5 μm). The results indicate that the particle mass concentration on the hub side increased gradually, and the concentration on the shroud side decreased inversely. Furthermore, the area of high particle mass concentration focused on the small radius area of the hub side or at the downstream of the channel in the direction of the streamline. And the particle mass concentration on the shroud is equally distributed. Finally, the combination of turbulent diffusion and inertial theory was proposed to analyze the mentioned phenomenon, and the droplet deposition mechanisms on the centrifugal compressor diffusor were summarized.

Effects of turbulent flow regime on perforated plate stabilized piloted lean premixed flames

An experimental study of the effects of turbulent flow regime on the flame structure is conducted by using perforated-plate-stabilized, hydrogen-piloted, lean premixed methane/air turbulent flames. The underlying turbulent flow field was investigated using two-dimensional three-component particle imaging velocimetry (2D3C-PIV) with two perforated plates of different blockage ratios. The flow data allowed a separation of the turbulent flow regime into axial velocity stream dominated and vortex dominated flows. A plate with 62% blockage ratio was used to establish the stream-dominated flow regime and another with 86% blockage ratio was used to establish the vortex-dominated flow regime. OH laser-induced fluorescence was used to study the effects of the turbulent flow regime on the mean progress variable, flame brush thickness, flame surface density, and global consumption speed. In comparison with the stream-dominated flow, the vortex-dominated flow makes a wider and shorter flame. Also, the vortex-dominated flow has a thicker horizontal flame brush and a thinner longitudinal flame brush. Especially, the spatial variation of the horizontal flame brush thickness for the vortex-dominated flow does not follow the turbulent diffusion theory. The vortex-dominated flow shows a relatively constant flame surface density and the stream-dominated flow shows a decreasing flame surface density along the streamwise direction. The flame surface density for the vortex-dominated flow is higher than the one for the stream-dominated flow. Lastly, the vortex-dominated turbulent flow shows a much higher consumption speed in comparison with that of the stream-dominated turbulent flow with identical velocity fluctuation levels.

Estimation of turbulent diffusion coefficients from decomposition of Lagrangian trajectories

A new technique is proposed for estimating turbulent diffusion coefficients (in the present paper turbulence is assumed to be homogeneous) which is based upon wavelet decomposition which separates the mean and oscillatory (random) parts of Lagrangian trajectories. A one-dimensional discrete Daubechies wavelet transform is applied to decompose Lagrangian trajectories into components, each of which corresponds to a specific time scale τ. Diagonal diffusion coefficients are calculated from equations obtained from a combination of classical mixing length theory and general ideas from a theory of turbulent diffusion. Non-diagonal diffusion coefficients are found using the classical theory of the first passage boundary. The technique is illustrated through the analysis of twelve trajectories of RAFOS floats along the California-Oregon coast, twenty surface drifters deployed in the California Current System, and forty-five surface drifters deployed in the Black Sea in 2000–2002. The approach is compared with the well-known Davis (1991) approach in applications to the Black Sea drifters and single float trajectories along the California-Oregon coast.

Self-sharpening induces jet-like structure in seafloor gravity currents

Gravity currents are the primary means by which sediments, solutes and heat are transported across the ocean-floor. Existing theory of gravity current flow employs a statistically-stable model of turbulent diffusion that has been extant since the 1960s. Here we present the first set of detailed spatial data from a gravity current over a rough seafloor that demonstrate that this existing paradigm is not universal. Specifically, in contrast to predictions from turbulent diffusion theory, self-sharpened velocity and concentration profiles and a stable barrier to mixing are observed. Our new observations are explained by statistically-unstable mixing and self-sharpening, by boundary-induced internal gravity waves; as predicted by recent advances in fluid dynamics. Self-sharpening helps explain phenomena such as ultra-long runout of gravity currents and restricted growth of bedforms, and highlights increased geohazard risk to marine infrastructure. These processes likely have broader application, for example to wave-turbulence interaction, and mixing processes in environmental flows.

Turbulent particle pair diffusion: A theory based on local and non-local diffusional processes.

A re-appraisal of the Richardson’s 1926 dataset [Richardson, L. F. Proc. Roy. Soc. Lond. A 100, 709–737, (1926)] displays an unequivocal non-local scaling for the pair diffusion coefficient, , quite different to the previously assumed locality scaling law , where σl is the pair separation. Consequently, the foundations of turbulent pair diffusion theory are re-examined here and it is shown that pair diffusion is governed by both local and non-local diffusional processess inside the inertial subrange. In the context of generalised energy spectra, E(k) ∼ k−p for 1 < p ≤ 3, the new theory predicts two non-Richardson regimes depending on the size of the inertial subrange: (1) in the limit of asymptotically infinite subrange, non-local scaling laws is obtained, , with γ intermediate between the purely local and the purely non-local scalings, i.e. (1 + p)/2 < γ ≤ 2; and (2) for finite (short) inertial subrange, local scaling laws are obtained, . The theory features a novel mathematical approach expressing the pair diffusion coefficient through a Fourier integral decomposition.

Turbulent diffusion of chemically reacting flows: Theory and numerical simulations.

The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously [T. Elperin et al., Phys. Rev. E 90, 053001 (2014)PLEEE81539-375510.1103/PhysRevE.90.053001] is generalized for large yet finite Reynolds numbers and the dependence of turbulent diffusion coefficient on two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales), is obtained. Three-dimensional direct numerical simulations (DNSs) of a finite-thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in good agreement with the developed theory.

Modeling of gas adsorption by aerosol plumes emitted from industrial sources

Abstract Adsorption of trace atmospheric gases by aerosol particles contributes to the evolution of concentration distribution of the trace constituents and can affect subsequent chemical reactions in the atmosphere. We suggest a two dimensional model of adsorption of trace atmospheric constituents by aerosol particles in air pollution plume emitted from an industrial source. The model is based on an application of theory of turbulent diffusion in the atmospheric boundary layer (ABL) in conjunction with plume dispersion model and model of gas adsorption by porous solid particles. The wind velocity profiles used in the simulations were fitted from our data previously obtained in field measurements conducted in the Northern Negev (Israel) using the experimental wind mast. The developed model allows analyzing spatial and temporal evolution of adsorbate concentration in the gaseous phase as well as in the particulate matter. The adsorbate concentration distributions are calculated for the particulate matter PM2.5–10, which is typical for industrial emissions. Analysis is performed for different meteorological conditions and atmospheric stability classes. It is shown that the concentration of gases adsorbed by aerosol plume strongly depends on the level of atmospheric turbulence. The obtained results are compared with the available experimental data.

Turbulent thermal diffusion in strongly stratified turbulence: Theory and experiments

Turbulent thermal diffusion is a combined effect of the temperature stratified turbulence and inertia of small particles. It causes the appearance of a non-diffusive turbulent flux of particles in the direction of the turbulent heat flux. This non-diffusive turbulent flux of particles is proportional to the product of the mean particle number density and the effective velocity of inertial particles. The theory of this effect has been previously developed only for small temperature gradients and small Stokes numbers (Phys. Rev. Lett. {\bf 76}, 224, 1996). In this study a generalized theory of turbulent thermal diffusion for arbitrary temperature gradients and Stokes numbers has been developed. The laboratory experiments in the oscillating grid turbulence and in the multi-fan produced turbulence have been performed to validate the theory of turbulent thermal diffusion in strongly stratified turbulent flows. It has been shown that the ratio of the effective velocity of inertial particles to the characteristic vertical turbulent velocity for large Reynolds numbers is less than 1. The effective velocity of inertial particles as well as the effective coefficient of turbulent thermal diffusion increase with Stokes numbers reaching the maximum at small Stokes numbers and decreases for larger Stokes numbers. The effective coefficient of turbulent thermal diffusion also decreases with the mean temperature gradient. It has been demonstrated that the developed theory is in a good agreement with the results of the laboratory experiments.

Simulation Study on the Desulfurization Efficiency Based on Swirl Atomizing

Based on the kinetics of chemical reaction, the theory of turbulent diffusion and the theory of mass transfer, the turbulent flow of flue gas in the desulfurization tower was described by standard k –emodel, and Lagrangian discrete phase model was employed to solve the particle momentum. The SO2 absorption model of wet flue gas desulfurization (WFGD) tower was established, and swirl atomizing layer (SAL) was installed on the tower. The concentration distribution of SO2 was simulated using CFD method. The results showed that SAL could improve the desulfurization efficiency.

Trajectory-Diffusive Mechanism of Desilt Basin Operation

Within the framework of the generalized theory of turbulent diffusion, we consider the mean velocities, times, length of alternating transverse up-and-down motion of suspended particles in sediment exhibiting different settling velocities and fluid particles in calm uniform wide open flows. Experimental data obtained by various authors are used to find the maximum heights and lengths of particle saltation in the thin near-bottom region, as well as the magnitude of the dynamic flow velocity, which triggers the motion of particles on the bottom. From the combined trajectory description of particle motion in sediments of different settling velocities over the entire depth of an open flow, the trajectory limit settling velocity of suspended sediments deposited in a rectilinear desilt basin may be determined and, within the framework of relaxation models, the length of silting and erosion at the bottom may be found.

Numerical description of a pressure-swirl nozzle spray

Abstract Pressure-swirl nozzles are widely used in both industrial and experimental processes. However, the spray flow fields are difficult to predict due to the complexities of the dense break-up region. Herein, an inflow boundary condition approach is employed whereby droplets are computationally injected at 9 mm downstream of the orifice based on experimentally derived descriptions of the mean droplet and gas velocities, combined with empirical relations for turbulent kinetic energy and dissipation. The gas flow is then predicted with a Reynolds-Averaged Navier-Stokes solution while the particle trajectories are computed with a discrete random walk model. This approach was found to reasonably describe downstream spatial distribution of gas and droplet velocity, with moderate mesh resolution and CPU time. In addition, the evolution of the droplet velocity fluctuations was found to be consistent with turbulent diffusion theory based on the local Stokes numbers and turbulent kinetic energy.

Flow imbalance and Reynolds number impact on mixing in Confined Impinging Jets

Abstract The flow in a Confined Impinging Jets (CIJs) mixer was studied with Planar Laser Induced Fluorescence. Two key aspects influencing the flow regimes and mixing quality were studied: the impact of the jets’ Reynolds number (Re) in the range 50 104 the flow evolves to a self-sustained chaotic laminar regime with strong mixing dynamics. With the increase of Re it is observed the formation of smaller mixing scales in the flow and an increase on the mixing quality. The visualized mixing scales are compared with theoretical models existing in the literature for the estimation of the striation thickness, leading to the conclusion that, in the studied flow regimes, the statistical theory of turbulent diffusion does not provide a realistic physical description of the flow. Furthermore, the jets’ mass flow imbalance is shown to always influence negatively the mixing quality. This is observed even when the flow imbalance results in the increase of the flow rate of one of the jets, increasing the amount of energy supplied to the system for dissipation. Results of this work show that the mechanism of eddy engulfment promoted by the two chaotically oscillating impinging jets, in the laminar regime, is a key aspect in mixing by CIJs.

Drift Velocity of Suspended Sediment in Turbulent Open Channel Flows

The drift velocity, at which sediment disperses relative to the motion of water-sediment mixtures, is a key variable in two-phase mixture equations. A constitutive relation for the drift velocity, expressed as a power series in the particle bulk Stokes number, was obtained by solving the momentum equation for sediment with the perturbation approach. It shows that gravity and turbulent diffusion are the primary dispersion effects on sediment, whereas flow inertia, particle-particle interactions, and other forces such as lift are the first-order particle inertial corrections that also play significant roles in sediment suspension. Analysis proves that studies based on turbulent diffusion theory are the zeroth-order approximations to the present formulation with respect to the particle inertia effect. The vertical concentration and velocity distributions of sediment in simple flows were investigated with the two-phase mixture equations closed by the drift velocity acquired in the research reported in this paper. The calculated concentration profiles agree well with measurements when the first-order particle inertial effect is considered. The calculated velocity of sediment coincides with available experiments that sediment lags behind water in open-channel flows as a result of turbulence-induced drag.

Effect of flow-geometry on turbulence-scalar interaction in premixed flames

Turbulent combustion of stoichiometric hydrogen-air mixture is simulated using direct numerical simulation methodology, employing complex chemical kinetics. Two flame configurations, freely propagating and V-flames stabilized behind a hot rod, are simulated. The results are analyzed to study the influence of flame configuration on the turbulence-scalar interaction, which is critical for the scalar gradient generation processes. The result suggests that this interaction process is not influenced by the flame configuration and the flame normal is found to align with the most extensive strain in the region of intense heat release. The combustion in the rod stabilized flame is found to be flamelet like in an average sense and the growth of flame-brush thickness with the downstream distance is represented well by Taylor theory of turbulent diffusion, when the flame-brushes are non-interacting. The thickness is observed to saturate when the flame-brushes interact, which is found to occur in the simulated rod stabilized flame with Taylor micro-scale Reynolds number of 97.

Estimating turbulent diffusion in a benthic boundary layer

In aquatic environments, the benthic boundary layer (BBL) is the transition zone for dissolved solutes that are released or consumed from the sediments. The exchange of solutes between the sediment and the overlying water column depends on the turbulent transport in the benthic boundary layer. In situ measurements of turbulent diffusion in natural benthic boundary layers are scarce and are usually derived from the logarithmic law of the wall (log‐law). Based on G. I. Taylor's turbulent diffusion theory, we derived a simple approach to estimate turbulent diffusivity from acoustic Doppler velocimeter (ADV) data. The approach was applied to ADV data collected over a period of 155 h in the BBL of Lake Constance, Germany. The calculated turbulent diffusivities agreed well with those derived in parallel from flux‐gradient measurements. In addition, turbulent diffusivities were calculated from several established approaches, including those based on the logarithmic law of the wall. The log‐law failed to predict plausible diffusivities whenever the boundary flow exhibited decreased current velocities or stable density stratification. Under these conditions, the turbulent diffusivities calculated from the flux‐gradient measurement and from Taylor's theory were as low as 10−6 m2 s−1. These decreased turbulent diffusivities have the potential to control the solute exchange between the sediment and the water column and can result in low oxygen concentrations in the bottom water. Reliable measurements of turbulent diffusivities in the BBL are therefore important to investigate and predict hypoxia in bottom waters and sulfide efflux from the sediments.

Turbulent diffusion and turbulent thermal diffusion of aerosols in stratified atmospheric flows

The paper analyzes the phenomenon of turbulent thermal diffusion in the Earth atmosphere, its relation to the turbulent diffusion, and its potential impact on aerosol distribution. This phenomenon was predicted theoretically more than 10 years ago and detected recently in the laboratory experiments. This effect causes a nondiffusive flux of aerosols in the direction of the heat flux and results in formation of long‐living aerosol layers in the vicinity of temperature inversions. We applied the theory of turbulent thermal diffusion to the Global Ozone Monitoring by Occultation of Stars (GOMOS) aerosol observations near the tropopause in order to explain the shape of aerosol vertical profiles with elevated concentrations located almost symmetrically with respect to temperature profile. We demonstrate that this theory is in good agreement with the observed profiles of aerosol concentration and temperature in the vicinity of the tropopause. In combination with the derived expression for the dependence of the turbulent thermal diffusion ratio on the turbulent diffusion, these measurements yield an independent method for determining the coefficient of turbulent diffusion at the tropopause. We also derived a practically applicable formulation for dispersion of atmospheric trace species which takes into account the phenomenon of turbulent thermal diffusion. We evaluated the impact of turbulent thermal diffusion to the lower troposphere vertical profiles of aerosol concentration by means of numerical dispersion modeling and found a regular upward forcing of aerosols with coarse particles affected more strongly than fine aerosols.

Estimation of soil boundary-layer resistance in sparse semiarid stands for evapotranspiration modelling

Summary The aim of this work was first, to compare two methods for obtaining soil boundary-layer resistance, one based on the turbulent diffusion theory (TD) and another based on the energy balance of heated and unheated sensors (EB), and secondly, to analyse how the results obtained from both methods are affected by canopy structure parameters in typical sparse vegetation. The study was carried out in stands of three different species characteristic of the semiarid South East of Spain ( Retama sphaerocarpa , Anthyllis cytisoides and Stipa tenacissima ). Comparison of the two methods showed that EB boundary-layer resistances, unlike TD, implicitly considers the peculiarities of the plant architecture and structure, as well as its distribution in the field and the presence or absence of substrate under the canopies. In contrast, for the TD method, quantitative attributes of the vegetation (average vegetation height, h , leaf area index, L , fractional vegetative cover, f , drag coefficient, c d and the eddy diffusivity decay constant, n ) are necessary, which are not only sometimes difficult to obtain in the field, but also seem to be insufficient to explain the development of the soil boundary layer in sparse semiarid vegetation. The advantages of using the EB method are both practical and theoretical. Positioning of the sensors and data storage with automatic data loggers is easy, and does not require knowledge of the aerodynamic attributes of the vegetated area. Furthermore, it allows qualitative interpretation of the effect of non-transpirable vegetative elements, as well as the architecture of the vegetation and its distribution in the field, neither of which are considered in the turbulent diffusion theory.