scholarly journals Integral transforms for three-dimensional steady turbulent dispersion in rivers and channels

2007 ◽  
Vol 31 (12) ◽  
pp. 2719-2732 ◽  
Author(s):  
Felipe P.J. de Barros ◽  
Renato M. Cotta
Keyword(s):  
Three Dimensional ◽  
Integral Transforms ◽  
Turbulent Dispersion

Integral Transforms for Three-Dimensional Steady Turbulent Dispersion in Rivers and Channels

2005 ◽  
Author(s):  
Felipe P. J. de Barros ◽  
Renato M. Cotta
Keyword(s):  
Turbulent Flows ◽  
Integral Transform ◽  
Three Dimensional ◽  
Integral Transforms ◽  
Computational Effort ◽  
Velocity Fields ◽  
Turbulent Dispersion ◽  
Test Case ◽  
Solution Convergence ◽  
Integral Transform Technique

A three-dimensional steady-state mathematical model is considered for predicting the fate of dissolved contaminants in rivers and channels under turbulent flows. The model allows for variable velocity fields and non-uniform turbulent diffusivities. Making use of the Generalized Integral Transform Technique (GITT), a hybrid numerical-analytical solution is then obtained. The solution convergence behavior is investigated and the criterion for reordering the terms in the infinite series is discussed, with the aim of reducing the computational effort associated with the double eigenfunction expansion. A test case is presented to illustrate the proposed approach.

CFD Simulation of Particle Transport and Dispersion in Indoor Environment by Human Walking

2012 ◽  
Author(s):  
Iman Goldasteh ◽  
Goodarz Ahmadi ◽  
Andrea Ferro
Keyword(s):  
Particulate Matter ◽  
High Speed ◽  
Cfd Simulation ◽  
Three Dimensional ◽  
Study Data ◽  
Turbulent Dispersion ◽  
Experimental Chamber ◽  
Indoor Environments ◽  
Three Dimensional Model ◽  
Particle Resuspension

Particle resuspension is an important source of particulate matter in indoor environments that significantly affects the indoor air quality and could potentially have adverse effect on human health. Earlier efforts to investigate indoor particle resuspension hypothesized that high speed airflow generated at the floor level during the gate cycle is the main cause of particle resuspension. The resuspended particles are then assumed to be dispersed by the airflow in the room, which is impacted by both the ventilation and the occupant movement, leading to increased PM concentration. In this study, a three dimensional model of a room was developed using FLUENT™ CFD package. A RANS approach with the RNG k-ε turbulence model was used for simulating the airflow field in the room for different ventilation conditions. The trajectories of resuspended particulate matter were computed with a Lagrangian method by solving the equations of particle motion. The effect of turbulent dispersion was included with the use of the eddy lifetime model. The resuspension of particles due to gait cycle was estimated and included in the computational model. The dispersion and transport of particles resuspended from flooring as well as particle re-deposition on flooring and walls were simulated. Particle concentrations in the room generated by the resuspension process were evaluated and the results were compared with experimental chamber study data as well as simplified model predictions, and good agreement was found.

Transient interior analytical solutions of Lamb’s problem

2019 ◽  
Vol 24 (11) ◽  
pp. 3485-3513 ◽  
Author(s):  
Mohamad Emami ◽  
Morteza Eskandari-Ghadi
Keyword(s):  
Analytical Solutions ◽  
Three Dimensional ◽  
Time History ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Point Load ◽  
Lamb’S Problem ◽  
Interior Points

The classical three-dimensional Lamb’s problem is considered for an inclined surface point load of Heaviside time dependence. Attention is focused upon the acquisition of the transient elastodynamic analytical solutions for interior points through a unified method of analysis that is valid for arbitrary Lamé constants. The method of elastodynamic potentials is employed jointly with integral transforms to treat the corresponding initial boundary value problem. To derive the time-domain solutions, some integral equations are encountered, the solutions of which are found via a modified version of the Cagniard–Pekeris method. The final solutions are obtained as finite integrals that are amenable to numerical calculations. They are also expressed in the form of Green’s functions. The limit case of infinite time is investigated analytically to derive the closed-form expressions for the limits of the solutions as the temporal variable tends to infinity. As expected, the results are found to be equivalent to Boussinesq–Cerruti solutions in elastostatics. The elastodynamic solutions are also evaluated numerically to plot several time-history diagrams, depicting the transient motions of the interior points, especially of the points close to the boundary so as to illustrate the formation of forced Rayleigh waves at shallow depths within the elastic half-space.

scholarly journals On the modeling of droplet transport, dispersion and evaporation in turbulent flows

2005 ◽  
Vol 122 (3) ◽  
pp. 42-55
Author(s):  
Jorge BARATA
Keyword(s):  
Turbulent Flows ◽  
Gas Turbines ◽  
Numerical Study ◽  
Droplet Diameter ◽  
Turbulent Transport ◽  
Three Dimensional ◽  
Turbulent Dispersion ◽  
Droplet Transport ◽  
New Formulation ◽  
Evaporation Models

The present paper presents a numerical study on evaporating droplets injected through a turbulent cross-stream. Several models have been used with more or less success to describe similar phenomena, but much of the reported work deals only with sprays in stagnant surroundings. The ultimate goal of this study is to develop an Eulerian/Lagragian approach to account for turbulent transport, dispersion, evaporation and coupling between both processes in practical spray injection systems, which usually include air flows in the combustion chamber like swirl, tumble and squish in I.C. engines or crossflow in gas turbines. In this work a method developed to study isothermal turbulent dispersion is extended to the case of an array of evaporating droplets through a crossflow, and the performance of two different evaporation models widely used is investigated. The convection terms were evaluated using the hybrid or the higher order QUICK scheme. The dispersed phase was treated using a Lagrangian reference frame. The differences between the two evaporation models and its applicability to the present flow are analysed in detail. During the preheating period of the Chen and Pereira [1] model the droplets are transported far away from the injector by the crossflow, while with the Sommerfeld [2] formulation for evaporation the droplet has a continuous variation of the diameter. This result has profound implications on the results because the subsequent heat transfer and turbulent dispersion is extremely affected by the size of the particles (or droplets). As a consequence, droplet diameter, temperature and mass fraction distributions were found to be strongly dependent on the evaporation model used. So, a new formulation that takes into account also the transport of the evaporating droplets needs to be developed if practical injection systems are to be simulated. Also, in order to better evaluate and to improve the vaporization models more detailed measurements of three-dimensional configurations are required.

scholarly journals Horizontal Dispersion of Buoyant Materials in the Ocean Surface Boundary Layer

2018 ◽  
Vol 48 (9) ◽  
pp. 2103-2125 ◽  
Author(s):  
Jun-Hong Liang ◽  
Xiaoliang Wan ◽  
Kenneth A. Rose ◽  
Peter P. Sullivan ◽  
James C. McWilliams
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Ocean Surface ◽  
Turbulent Dispersion ◽  
Surface Boundary ◽  
Particle Trajectories ◽  
Stokes Flows ◽  
Surface Boundary Layer ◽  
Horizontal Dispersion ◽  
Shear Dispersion

ABSTRACTThe horizontal dispersion of materials with a constant rising speed under the exclusive influence of ocean surface boundary layer (OSBL) flows is investigated using both three-dimensional turbulence-resolving Lagrangian particle trajectories and the classical theory of dispersion in bounded shear currents generalized for buoyant materials. Dispersion in the OSBL is caused by the vertical shear of mean horizontal currents and by the turbulent velocity fluctuations. It reaches a diffusive regime when the equilibrium vertical material distribution is established. Diffusivity from the classical shear dispersion theory agrees reasonably well with that diagnosed using three-dimensional particle trajectories. For weakly buoyant materials that can be mixed into the boundary layer, shear dispersion dominates turbulent dispersion. For strongly buoyant materials that stay at the ocean surface, shear dispersion is negligible compared to turbulent dispersion. The effective horizontal diffusivity due to shear dispersion is controlled by multiple factors, including wind speed, wave conditions, vertical diffusivity, mixed layer depth, latitude, and buoyant rising speed. With all other meteorological and hydrographic conditions being equal, the effective horizontal diffusivity is larger in wind-driven Ekman flows than in wave-driven Ekman–Stokes flows for weakly buoyant materials and is smaller in Ekman flows than in Ekman–Stokes flows for strongly buoyant materials. The effective horizontal diffusivity is further reduced when enhanced mixing by breaking waves is included. Dispersion by OSBL flows is weaker than that by submesoscale currents at a scale larger than 100 m. The analytic framework will improve subgrid-scale modeling in realistic particle trajectory models using currents from operational ocean models.

A Numerical Study of Turbulent Flow in Helical Static Mixers

2006 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Anahita Ayasoufi ◽  
Theo G. Keith
Keyword(s):  
Turbulent Flow ◽  
Molecular Diffusion ◽  
Stokes Equations ◽  
Numerical Study ◽  
Critical Role ◽  
Three Dimensional ◽  
Turbulent Dispersion ◽  
Working Fluid ◽  
Static Mixer ◽  
Static Mixers

Many processing applications call for the addition of small quantities of chemicals to working fluid. Hence, fluid mixing plays a critical role in the success or failure of these processes. An optimal combination of turbulent dispersion down to eddies of the Kolmogoroff scale and molecular diffusion would yield fast mixing on a molecular scale which in turn favors the desired reactions. Helical static mixers can be used for those applications. The range of practical flow Reynolds numbers for these mixers in industry is usually from very small (Re ∼ 0) to moderate values (Re ∼ 5000). In this study, a helical static mixer is investigated numerically using Lagrangian methods to characterize mixer performance under turbulent flow regime conditions. A numerical simulation of turbulent flows in helical static mixers is employed. The model solves the three-dimensional, Reynolds-averaged Navier-Stokes equations, closed with the Spalart-Allmaras turbulence model, using a second-order-accurate finite-volume numerical method. Numerical simulations are carried out for a six-element mixer, and the computed results are analyzed to elucidate the complex, three-dimensional features of the flow. Using a variety of predictive tools, mixing results are obtained and the performance of static mixer under turbulent flow condition is studied.

INTEGRAL TRANSFORMS FOR HEAT AND FLUID FLOW IN TWO- AND THREE-DIMENSIONAL POROUS MEDIA

2001 ◽  
Vol 3 (4) ◽  
pp. 14 ◽  
Author(s):  
Renato M. Cotta ◽  
H. Luz Neto ◽  
L. S. de B. Alves ◽  
Joao N. N. Quaresma
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Three Dimensional ◽  
Integral Transforms ◽  
Heat And Fluid Flow
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