Turbulent Diffusion Model Research Articles

МОНИТОРИНГ КАЧЕСТВА АТМОСФЕРНОГО ВОЗДУХА ЗАПАДНО-КАЗАХСТАНСКОГО РЕГИОНА: ПРИНЦИПЫ, МЕТОДЫ, ПОДХОДЫ

The main approaches and methods of studying the characteristics and conditions of atmospheric pollution on the example of Western Kazakhstan are considered. The classification and grouping of applied approaches by topics, methods, time intervals and other relevant criteria was conducted. An analysis of the available information on the sources and volumes of emissions into the atmosphere, as well as on the systems for monitoring the pollution of the air basin, was carried out. It is shown that to increase the effectiveness of the atmospheric air quality management system, it is expedient to use a complex approach taking into account the influence of meteorological factors and synoptic conditions that determine different levels of pollution. An analytical review of modern methods of modeling the spread of pollutants in atmospheric air showed the feasibility of using statistical methods integrated with deep machine learning and the Eulerian continuum model of turbulent diffusion. The obtained conclusions will allow further use of an integrated approach to improve the atmospheric air quality management system of the studied region.

A turbulent mass diffusivity model for analyzing the mixing characteristics in an impinging stream-rotating packed bed

In this study, the fluid flow and mixing process in an impinging stream-rotating packed bed (IS-RPB) is simulated by using a new three-dimensional computational fluid dynamics model. Specifically, the gas–liquid flow is simulated by the Euler–Euler model, the hydrodynamics of the reactor is predicted by the RNG k–ε method, and the high gravity environment is simulated by the sliding mesh model. The turbulent mass transfer process is characterized by the concentration variance and its dissipation rate εc formulations, and therefore the turbulent mass diffusivity can be directly obtained. The simulated segregation index Xs are in agreement with our previous experimental results. The simulated results reveal that the fringe effect of IS can be offset by the end effect at the inner radius of RPB, so the investigation for the coupling mechanism between IS and RPB is critical to intensify the mixing process in IS-RPB.

Three-dimensional hydrodynamic modelling of saltwater ingression and circulation in a Brackish Lake Shinji, Japan

Lake Shinji is a mesohaline lake that has intermittent saline water intrusion from its east coast connection of Ohashi River. This intrusion is often in the shape of a very thin layer that moves along the Lake bottom and stayed at the center due to bowl shape bathymetry of the Lake having maximum depth at the center. To elucidate the intrusion mechanism a 3-D hydrodynamic model (EcoPARI) was employed in a hindcast mode covering the year 2012 from the beginning of January to the end of September. Initially, the core emphasis was given to the vertical turbulence diffusion model and optimum model parameters were determined to accurately simulate the hydrodynamics. It was highlighted by the numerical simulations that alteration of one model constant, which is the multiplying coefficient of Richardson number, “α”, is influential instead of altering all the constants to tune the turbulence model. The possibility of using differential model constants for temperature and salinity was also tested and it helped in the improvement of simulations. Finally, the performance of the model was also assessed under extreme weather conditions and a historical upwelling event was simulated. The model was able to reproduce the intrusion in the summer months as well as the upwelling event in September due to strong westerly winds caused by a nearby passing typhoon.

Effect of turbulent diffusion in modeling anaerobic digestion

In this study, the impact of turbulent diffusion on mixing of biochemical reaction models is explored by implementing and validating different models. An original codebase called CHAD (Coupled Hydrodynamics and Anaerobic Digestion) is extended to incorporate turbulent diffusion and validate it against results from OpenFOAM with 2D Rayleigh-Taylor Instability and lid-driven cavity simulations. The models are then tested for the applications with Anaerobic Digestion - a widely used wastewater treatment method. The findings demonstrate that the implemented models accurately capture turbulent diffusion when provided with an accurate flow field. Specifically, a minor effect of chemical turbulent diffusion on biochemical reactions within the anaerobic digestion tank is observed, while thermal turbulent diffusion significantly influences mixing. By successfully implementing turbulent diffusion models in CHAD, its capabilities for more accurate anaerobic digestion simulations are enhanced, aiding in optimizing the design and operation of anaerobic digestion reactors in real-world wastewater treatment applications.

Challenges and Progress in Computational Geophysical Fluid Dynamics in Recent Decades

Here we present the numerical methods, applications, and comparisons with observations and previous studies. It includes numerical analyses of shallow water equations, Sun’s scheme, and nonlinear model simulations of a dam break, solitary Rossby wave, and hydraulic jump without smoothing. We reproduce the longitude and transverse cloud bands in the Equator; two-day mesoscale waves in Brazil; Ekman spirals in the atmosphere and oceans, and a resonance instability at 30° from the linearized equations. The Purdue Regional Climate Model (PRCM) reproduces the explosive severe winter storms in the Western USA; lee-vortices in Taiwan; deformation of the cold front by mountains in Taiwan; flooding and drought in the USA; flooding in Asia; and the Southeast Asia monsoons. The model can correct the small-scale errors if the synoptic systems are correct. Usually, large-scale systems are more important than small-scale disturbances, and the predictability of NWP is better than the simplified dynamics models. We discuss the difference between Boussinesq fluid and the compressible fluid. The Bernoulli function in compressible atmosphere conserving the total energy, is better than the convective available potential energy (CAPE) or the Froude number, because storms can develop without CAPE, and downslope wind can form against a positive buoyancy. We also present a new terrain following coordinate, a turbulence-diffusion model in the convective boundary layer (CBL), and a new backward-integration model including turbulence mixing in the atmosphere.

Beyond diffusion: a generalized mean-field theory of turbulent dust transport in protoplanetary discs

ABSTRACT Turbulence in protoplanetary discs, when present, plays a critical role in transporting dust particles embedded in the gaseous disc component. When using a field description of dust dynamics, a diffusion approach is traditionally used to model this turbulent dust transport. However, it has been shown that classical turbulent diffusion models are not fully self-consistent. Several shortcomings exist, including the ambiguous nature of the diffused quantity and the non-conservation of angular momentum. Orbital effects are also neglected without an explicit prescription. In response to these inconsistencies, we present a novel Eulerian turbulent dust transport model for isotropic and homogeneous turbulence on the basis of a mean-field theory. Our model is based on density-weighted averaging applied to the pressureless fluid equations and uses appropriate turbulence closures. Our model yields novel dynamic equations for the turbulent dust mass flux and recovers existing turbulent transport models in special limiting cases, thus providing a more general and self-consistent description of turbulent particle transport. Importantly, our model ensures the conservation of global angular and linear momentum unconditionally and implicitly accounts for the effects of orbital dynamics in protoplanetary discs. Furthermore, our model correctly describes the vertical settling–diffusion equilibrium solutions for both small and large particles. Hence, this work presents a generalized Eulerian turbulent dust transport model, establishing a comprehensive framework for more detailed studies of turbulent dust transport in protoplanetary discs.

Turbulent Diffusion of the Particles within Pulsar Wind Nebulae

A turbulent diffusion model is presented to account for the energy and spatial diffusion of the particles within pulsar wind nebulae (PWNe), with the assumption that the energy injected from the pulsar into the nebula is split between the turbulence waves and electrons/positrons. In the model, the mutual interactions between the turbulence waves and particles are taken into account, representing the damping effect of the turbulence waves and the stochastic acceleration and spatial diffusion of the particles, respectively. The evolutions of the turbulence waves and particles are described with the coupled kinetic equations, in which the Kolmogorov- and Kraichnan-type turbulence are, respectively, considered. The model is applied to the Crab Nebula and shows that the spectral energy distribution of the PWN can be naturally explained. Our modeling results indicate that, for the Crab Nebula, the stochastic acceleration and spatial diffusion processes play a role in modifying the electron spectrum at the low energies of E e ≲ 1 TeV. The damping process seems more effective for modulating the turbulent spectrum in the Kraichnan-type turbulence, resulting in the nonlinear variations of the current energy and spatial diffusion coefficients with energy generated in the wave–particle systems. In the Kolmogorov-type turbulence, the diffusion coefficients are more consistent with the quasi-linear distributions, due to the energy cascade dominating over the damping effect.

Dispersion and Radiation Modelling in ESTE System Using Urban LPM

In cases of accidental or deliberate incidents involving a harmful agent in urban areas, a detailed modelling approach is required to include the building shapes and spatial locations. Simultaneously, when applied to crisis management, a simulation tool must meet strict time constraints. This work presents a Lagrangian particle model (LPM) for computing atmospheric dispersion. The model is implemented in the nuclear decision support system ESTE CBRN, a software tool developed to calculate the atmospheric dispersion of airborne hazardous materials and radiological impacts in the built-up area. The implemented LPM is based on Thomson’s solution for the nonstationary, three-dimensional Langevin equation model for turbulent diffusion. The simulation results are successfully analyzed by testing compatibility with Briggs sigma functions in the case of continuous release. The implemented LPM is compared with the Joint Urban 2003 Street Canyon Experiment for instantaneous puff releases. We compare the maximum concentrations and peak times measured during two intensive operational periods. The modeled peak times are mostly 10–20% smaller than the measured. Except for a few detector locations, the maximum concentrations are reproduced consistently. In the end, we demonstrate via calculation on single computers utilizing general-purpose computing on graphics processing units (GPGPU) that the implementation is well suited for an actual emergency response since the computational times (including dispersion and dose calculation) for an acceptable level of result accuracy are similar to the modeled event duration itself.

Three-dimensional dust stirring by a giant planet embedded in a protoplanetary disc

ABSTRACT The motion of solid particles embedded in gaseous protoplanetary discs is influenced by turbulent fluctuations. Consequently, the dynamics of moderately to weakly coupled solids can be distinctly different from the dynamics of the gas. Additionally, gravitational perturbations from an embedded planet can further impact the dynamics of solids. In this work, we investigate the combined effects of turbulent fluctuations and planetary dust stirring in a protoplanetary disc on three-dimensional dust morphology and on synthetic ALMA continuum observations. We carry out 3D radiative two-fluid (gas + 1-mm-dust) hydrodynamic simulations in which we explicitly model the gravitational perturbation of a Jupiter-mass planet. We derived a new momentum-conserving turbulent diffusion model that introduces a turbulent pressure to the pressureless dust fluid to capture the turbulent transport of dust. The model implicitly captures the effects of orbital oscillations and reproduces the theoretically predicted vertical settling-diffusion equilibrium. We find a Jupiter-mass planet to produce distinct and large-scale three-dimensional flow structures in the mm-sized dust, which vary strongly in space. We quantify these effects by locally measuring an effective vertical diffusivity (equivalent alpha) and find azimuthally averaged values in a range δeff ∼ 5 × 10−3–2 × 10−2 and local peaks at values of up to δeff ∼ 3 × 10−1. In synthetic ALMA continuum observations of inclined discs, we find effects of turbulent diffusion to be observable, especially at disc edges, and effects of planetary dust stirring in edge-on observations.

An entropy viscosity method for large eddy simulation of turbulent thermal flow in a rotor–stator cavity

Turbulent flow and heat transfer in a rotor–stator cavity have fundamental importance in both academia of turbulence research and the industry of rotating turbomachinery. The main characteristic of the flow is that there is the centrifugal Ekman layer on the rotor and the centripetal Bödewadt layer on the stator, which are separated by a central rotating core. In this paper, an entropy viscosity subgrid model based on the large eddy simulation (LES) method is proposed to solve the complex flow with heat transfer in a rotating frame at high Reynolds numbers. The method is fully validated by the simulation of turbulent thermal flow in a closed stator–rotor cavity up to Re=106. By performing 12 simulations, the sensitivity of the simulation results to mesh resolution and the free parameters of entropy viscosity are systematically studied, and the proper range for the parameters is determined. In particular, it is found that the prediction on the mean flow and fluctuation from the simple turbulent diffusivity model, which scales linearly with the eddy viscosity, is as accurate as that from the alternative model that is a more computationally complex model. Despite the comparable accuracy, the entropy viscosity-based LES uses the mesh resolution two-order lower than that of direct numerical simulation; therefore, it is feasible to apply the LES to the flow at the practical Reynolds number in an aircraft engine, that is, Re≥107.

A Turbulent Mass Diffusivity Model for Predicting Species Concentration Distribution in the Biodegradation of Phenol Wastewater in an Airlift Reactor

In this study, a three-dimensional CFD transient model is established for predicting species concentration distribution in the biodegradation of phenol in an airlift reactor (ALR). The gas–liquid flow in the ALR is determined by the Euler–Euler method coupled with the standard k-ε model, and the bubble size is predicted by the population balance model (PBM). A turbulent mass diffusivity model is developed to simulate the turbulent mass transfer process and to predict the species concentration distribution. No empirical methods are needed as the turbulent mass diffusivity can be expressed by the concentration variance c2¯ and its dissipation rate εc. A good agreement is found between simulated and experimental results in the literature. It is not reasonable to assume a constant turbulent Schmidt number because the calculated distribution of turbulent mass diffusivity is not identical to that of turbulent viscosity. Finally, the hydrodynamic characteristics and biodegradation performance of the proposed model in a novel ALR are compared with that in the original ALR.

Development of the Turbulent Diffusion Model of Fine Suspended Substances in the Lower Atmosphere Layer

A promising direction for solving the problem of air pollution by fine substances is the use of numerical modeling in the development of mathematical models of the transport of pollutants in the atmosphere. An urgent problem in applying mathematical models with numerical algorithms and software is constructing a qualitative model that would meet both the physical parameters and fulfill all the optimal conditions of numerical analysis. The main objective of this study was to develop an algorithm of a mathematical model based on the equation of distribution of impurities in a turbulent medium. That allows considering the simultaneous influence of wind speed, turbulence of atmospheric air, pollution parameters, direction, and wind force on the size of scattering zones. The unique feature of the study is the use of the coordinate splitting equation of impurities distribution in a turbulent environment with subsequent normalization and parameterization of conditions. Finding integrands functions in the calculation algorithm allows obtaining a stable computational algorithm of the proposed propagation model of fine suspended particles. The solution of the function implemented in the Mathcad Prime 7 software. Distributions of concentrations and their levels for various values of turbulence of atmospheric air and dangerous wind speed are received. The most significant number of fine particles is at a distance of up to 4 km from the emission source. Still, there is also the transfer of contaminants at more than 5 km (up to 57 % of the initial emission concentration). The model has convenient software and algorithmic software, the time of calculation of graphic visualizations up to 20 minutes on medium-power computers. The obtained mathematical model can use in systems of forecasting man-caused load on the environment for the prompt solution of environmental problems.

Система моніторингу забруднення повітря автотранспортом на базі автономного аеромобільного вимірювального комплексу

The article proposes an approach to constructing a system of complex and uninterrupted monitoring of harmful emissions of motor vehicles into the air. The architecture of the environmental monitoring system for measuring and forecasting the distribution of pollutant concentrations in motor vehicle exhaust gases, among which mainly CO, SO₂, NO₂, and СО₂, is presented. The mobile information and measurement complex Sniffer4D Hyper-local Air Quality Analyzer and a charging station based on solar batteries are used as the hardware. For modeling and forecasting the distribution of concentrations of harmful emissions, mathematical models of the dynamics of the distribution of concentrations of pollutants due to harmful emissions in the exhaust gases of motor vehicles are proposed in the form of differential equations that are analogs of differential equations in partial derivatives, as models of turbulent diffusion and interval models of the distribution of the background level of pollution concentration in the form of nonlinear algebraic equations. Implemented software for data collection, processing (model learning and prediction), and visualization.

Система моніторингу забруднення повітря автотранспортом на базі автономного аеромобільного вимірювального комплексу

The article proposes an approach to constructing a system of complex and uninterrupted monitoring of harmful emissions of motor vehicles into the air. The architecture of the environmental monitoring system for measuring and forecasting the distribution of pollutant concentrations in motor vehicle exhaust gases, among which mainly CO, SO₂, NO₂, and СО₂, is presented. The mobile information and measurement complex Sniffer4D Hyper-local Air Quality Analyzer and a charging station based on solar batteries are used as the hardware. For modeling and forecasting the distribution of concentrations of harmful emissions, mathematical models of the dynamics of the distribution of concentrations of pollutants due to harmful emissions in the exhaust gases of motor vehicles are proposed in the form of differential equations that are analogs of differential equations in partial derivatives, as models of turbulent diffusion and interval models of the distribution of the background level of pollution concentration in the form of nonlinear algebraic equations. Implemented software for data collection, processing (model learning and prediction), and visualization.

A turbulent mass diffusivity model for the simulation of the biodegradation of toluene in an internal loop airlift reactor

In this study, a three-dimensional computational fluid dynamics model is established in Ansys Fluent to describe the biodegradation of toluene in an internal loop airlift reactor (IALR). The Euler-Euler approach is used with the standard k-ε method to predict the hydrodynamics of the reactor, and the population balance model is used to describe the bubble size distribution in the reactor. The recently developed concentration variance c2¯ and its dissipation rate εc formulations are adopted to close the turbulent mass transfer differential equations, so that the turbulent mass diffusivity can be determined without using empirical methods. There is a good agreement between the simulated dissolved oxygen concentrations obtained by the proposed model and the experimental data reported in the literature. As the predicted turbulent mass diffusivity is found to be unevenly distributed and the calculated turbulent Schmidt number Sct is not a constant but varies, it may not be appropriate to use a constant Sct or an experimentally determined dispersion coefficient. In addition, the maximal shear stress is found in the top region of the IALR and the liquid flow are very uniform in the riser and downcomer.

Modeling particulate pollutants dispersed in the atmosphere using fractional turbulent diffusion

Dispersion of particulate matter from natural or anthropogenic sources into the atmosphere, such as that produced by volcanoes, fires, or industries, often causes severe damages. In particular, fine-sized particles are a serious threat to human health. Therefore, it is important to identify them and evaluate their concentration. This paper aims to quantify the finest-grained ash concentration of a volcanic eruption using a turbulent diffusion model. A stationary regime at some distance from the eruption is considered and axial symmetry is assumed, with the axis in the direction of the wind, neglecting gravitational effects. To account for anomalous diffusion phenomena due to heterogeneities and/or turbulence in the medium where fine particles are dispersed, one of the derivatives in the radial direction is replaced by a fractional derivative of Caputo type. We find approximate analytical solutions in cylindrical coordinates by the Adomian Decomposition Method and compare them with solutions obtained using a numerical scheme. The analytical concentration profiles obtained are successfully compared with satellite images of a real plume originating in an explosive volcanic eruption. We have found that the concentration components depend on a parameter that seems to be directly related to particle size.

Solute Dispersion From a Continuous Release Source in a Vegetated Flow: An Analytical Study

AbstractSteady dispersion of solute in flows with submerged vegetation due to a continuous release source is a focus in water resources research. This paper presents a fully analytical effort for a complete description of the steady‐state concentration field. The analytically predicted vertical concentration profiles agree well with both experimental measurements and numerical simulation results. Relations between the steady dispersion for a continuous release source and the transient dispersion due to an instantaneous release source are also discussed. Results show that the mean concentration in the canopy layer is higher than that in the upper water layer and the steady concentration distribution approaches relative uniformity at a dimensionless downstream distance x = 0.5. The solute release position is shown highly remarkably affecting the way in which the downstream state is approached. Moreover, the vertical concentration profiles predicted by a spatially dependent four‐zone turbulent diffusivity model are better than those predicted by a constant single‐zone model. The obtained analytical results contribute essentially to our understanding of solute transport in water flows with submerged vegetation.

Physics-informed neural network method for solving one-dimensional advection equation using PyTorch

Numerical solutions to the equation for advection are determined using different finite-difference approximations and physics-informed neural networks (PINNs) under conditions that allow an analytical solution. Their accuracy is examined by comparing them to the analytical solution. We used a machine learning framework like PyTorch to implement PINNs. PINNs approach allows training neural networks while respecting the Partially differential equations (PDEs) as a strong constraint in the optimization as apposed to making them part of the loss function. In standard small-scale circulation simulations, it is shown that the conventional approach incorporates a pseudo diffusive effect that is almost as large as the effect of the turbulent diffusion model; hence the numerical solution is rendered inconsistent with the PDEs. This oscillation causes inaccuracy and computational uncertainty. Of all the schemes tested, only the PINNs approximation accurately predicted the outcome. We assume that the PINNs approach can transform the physics simulation area by allowing real-time physics simulation and geometry optimization without costly and time-consuming simulations on large supercomputers.

Sediment suspension affected by submerged rigid vegetation under waves, currents and combined wave–current flows

Laboratory experiments and mathematical analyses were carried out to investigate and quantify the impacts of submerged rigid vegetation on sediment suspension under waves, currents and combined wave–current flows. Mimic canopies constructed from wooden cylinders were used in the experiments with three configurations (sparse, dense and vertically varying density). It was found that more sediment was suspended within the vegetation canopies, where smaller velocities and higher turbulence were observed, indicating that vegetation-induced turbulence rather than mean flow was the main driver of sediment suspension over vegetated beds. Meanwhile, higher sediment concentration near the bed was observed within a denser canopy, especially in the case of vertically varying vegetation density. The near-bed suspended sediment concentration could be described by an exponential formulation using an effective bed shear velocity considering different turbulence components (i.e. vegetation wake turbulence, bed shear turbulence and near-bed coherent structures). The formula was applicable in both vegetated and bare beds with different hydrodynamic conditions. To predict the vertical distributions of sediment suspension, two theoretical models of turbulent diffusion were improved by incorporating the vertically varying turbulent intensity in the water column.

Methane leakage source location based on a near-infrared off-axis integrated cavity output spectroscopic ppbv-level sensor and an optimized inverse model

Accurate location of methane (CH4) leakage source is essential for reducing air pollution and implementing effective countermeasures. A leakage source location method was proposed based on a near-infrared off-axis integrated cavity output spectroscopic parts-per-billion in volume (ppbv)-level CH4 sensor and an optimized inverse model. The CH4 sensor was developed for real-time, in-situ atmospheric CH4 monitoring in mobile measurement, which reveals an Allan variance of ∼7.99 ppbv and a response time of ∼8 s. The inverse model combines an improved particle swarm optimization (IPSO) algorithm with a gas turbulent diffusion model. To better solve the local optimal solution and premature convergence problems, optimizing the velocity of particle was presented in the IPSO algorithm. Through comparison, simulation results show that the location precision was increased by 69.14%, 61.43%, 36.61% and 69.81% under different source locations, wind speed, wind direction and moving speed, respectively. Also, five sets of field experiments were conducted to verify the performance of the IPSO, and the location precision was improved by 73.20%, 81.73%, 77.27%, 76.57% and 91.18%, respectively. Both simulation and field experiment results show that the IPSO algorithm has high precision and good robustness in source location. The proposed optimized inversion model provides a reference for the formulation or adjustment of emergency response strategies for gas leakage accidents.