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.

Analysis of mixing in three-dimensional time-periodic cavity flows

1999 ◽  
Vol 386 ◽  
pp. 149-166 ◽  
Author(s):  
P. D. ANDERSON ◽  
O. S. GALAKTIONOV ◽  
G. W. M. PETERS ◽  
F. N. VAN DE VOSSE ◽  
H. E. H. MEIJER
Keyword(s):  
Periodic Structures ◽  
Three Dimensional ◽  
Periodic Points ◽  
Velocity Fields ◽  
Test Case ◽  
Cavity Flows ◽  
Mixing Process ◽  
Mixing Processes ◽  
Time Periodic

A method to locate periodic structures in general three-dimensional Stokes flows with time-periodic boundary conditions is presented and applied to mixing cavity flows. Numerically obtained velocity fields and particle tracking schemes are used to provide displacement and stretching fields. From these the location and identification of periodic points can be derived. The presence or absence of these periodic points allows a judgement on the quality of the mixing process. The technique is general and efficient, and applicable to mixing flows for which no analytical velocity field is available (the case for all three-dimensional flows considered in this paper). Results are presented for three different mixing protocols in a three-dimensional time-periodic cavity flow, serving as an accessible test case for the methods developed. A major result is that periodic lines are obtained for these three-dimensional flows. These lines can be complex in geometry and their nature can change along a line from hyperbolic to elliptic. They can serve as practical criteria in the optimization of three-dimensional mixing processes.

An Efficient Finite Element Procedure for the Analysis of Cross-Flow Micro Heat Exchangers

2010 ◽  
Author(s):  
C. Nonino ◽  
S. Savino ◽  
S. Del Giudice
Keyword(s):  
Heat Exchangers ◽  
Three Dimensional ◽  
Cross Flow ◽  
Computational Effort ◽  
Velocity Fields ◽  
Hybrid Technique ◽  
Number Of Layers ◽  
Micro Heat Exchanger ◽  
Finite Element Procedure ◽  
Transfer Problems

As an alternative to massive CFD, a hybrid technique, which has the advantage of accounting for all of the three-dimensional features of the flow field, but with a limited computational effort, is used for the solution of conjugate convection-conduction heat transfer problems in cross-flow micro heat exchangers. The key feature of the proposed method is represented by the separate computation of the velocity fields in single microchannels and on the subsequent mapping of such velocity fields onto the three-dimensional grid used to solve the thermal problem. The cross-flow micro heat exchangers considered in the paper consist of a number of layers of rectangular microchannels. A parametric study is carried out on the combined effect on cross-flow micro heat exchanger thermal performances due to the variation of the microchannel cross-section and of the ratio of solid to fluid thermal conductivity.

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.

Thermal Math Modeling and Analysis of an Electronic Assembly

2000 ◽  
Vol 123 (4) ◽  
pp. 372-378 ◽  
Author(s):  
K. N. Shukla
Keyword(s):  
Temperature Distribution ◽  
Integral Transform ◽  
Three Dimensional ◽  
Thermal Characteristics ◽  
Circuit Board ◽  
Heat Sources ◽  
The Finite Element Method ◽  
Modeling And Analysis ◽  
Discrete Surface ◽  
Integral Transform Technique

This paper presents a mathematical model for a three-dimensional thermal analysis of a circuit board with multiple heat dissipating sources. The model considers the three-dimensional flat plate with discrete surface heat sources and integral transform technique is employed to determine the temperature distribution. The calculation procedure for the thermal characteristics of a circuit board, with surface mounted components, is presented and the solution is compared with those obtained from the finite element method. Also, the temperature distribution of a two-layered circuit board is presented in terms of Green’s function.

Analytical Solution for Solute Transport in Semi-Infinite Heterogeneous Porous Media

2011 ◽  
Vol 312-315 ◽  
pp. 495-499
Author(s):  
B.Q. Deng ◽  
Y.F. Qiu ◽  
C.N. Kim
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
Solute Transport ◽  
Integral Transform ◽  
Integral Transforms ◽  
Heterogeneous Porous Media ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Integral Transform Technique ◽  
Linear Decay

Solute transport in porous media concerns advection, dispersion, sorption, and reaction. Since porous media is commonly heterogeneous, the properties of porous media are spatially and temporally variable. In this paper, one dimensional unsteady solute transport in semi-infinite heterogeneous porous media is investigated. Both linear and nonlinear decay is considered. Analytical solution is obtained for linear decay with spatially and temporally diffusion coefficient and velocity by using generalized integral transform technique. The inverse integral transforms are developed for the problems in semi-infinite space based on some weighted functions. Some examples are given to show the application of the method and analytical solutions.

Three-dimensional viscous wakes

1962 ◽  
Vol 14 (2) ◽  
pp. 233-240 ◽  
Author(s):  
Martin H. Steiger ◽  
Martin H. Bloom
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Axial Symmetry ◽  
Constant Velocity ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Axial Velocity Distribution ◽  
Fluid Properties ◽  
Laminar And Turbulent Flows

The velocity fields of three-dimensional viscous wakes are examined with the use of the boundary-layer approximations, Oseen's linearization of the convective terms, and the assumption of constant fluid properties. Transform methods yield solutions for general types of initial conditions. As an illustration, the axial velocity distribution of a wake whose initial isovels (lines of constant velocity) are of elliptic shape and their decay to axial symmetry are demonstrated. Both laminar and turbulent flows are considered.

scholarly journals Integral transforms for three-dimensional pumping in confined, leaky, and unconfined aquifers

2021 ◽  
Vol 69 (3) ◽  
pp. 319-331
Author(s):  
Elizeu Melo da Silva ◽  
João N. N. Quaresma ◽  
Emanuel N. Macêdo ◽  
Renato M. Cotta
Keyword(s):  
Analytical Solutions ◽  
Integral Transform ◽  
Three Dimensional ◽  
Integral Transforms ◽  
Problem Formulation ◽  
Unconfined Aquifer ◽  
Physical Parameters ◽  
Unconfined Aquifers ◽  
Solution Verification ◽  
Pumping Rates

Abstract Analytical or hybrid numerical-analytical solutions based on the Generalized Integral Transform Technique (GITT) are obtained for the transient three-dimensional pumping problem of aquifers with a fully penetrating vertical well between two parallel streams. The problem formulation for confined and leaky aquifers allows for achieving exact analytical solutions through integral transforms, while the unconfined aquifer case introduces a fourth kind boundary condition which leads to a coupled transformed head ordinary differential system, that can be solved either analytically or numerically. A convergence analysis is performed to illustrate the consistency of the numerical results achieved for the head distribution, as well as for the related pumping rates. Results are obtained for selected cases and comparisons with literature results are performed. A solution verification confirms the agreement of the integral transform solutions with available simulations and provides additional confidence for the analysis of a few physical parameters that influence the hydrological behavior.

scholarly journals Three-Dimensional Unsteady State Temperature Distribution of Thin Rectangular Plate with Moving Point Heat Source

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yogita M. Ahire ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Heat Source ◽  
Rectangular Plate ◽  
Thermal Stresses ◽  
Integral Transform ◽  
Three Dimensional ◽  
Unsteady State ◽  
Point Heat Source ◽  
Thin Rectangular Plate ◽  
Special Case ◽  
Integral Transform Technique

This paper deals with the study of thermal stresses in thin rectangular plate subjected to point heat source which changes its place along x-axis. Governing heat conduction equation has been solved by using integral transform technique. Results are obtained in the form of infinite series. As a special case, aluminum plate has been considered and results for thermal stresses have been computed numerically and graphically.

Three-Dimensional Analysis of Axisymmetric Transient Waves in Hollow Elastic Cylinders

1984 ◽  
Vol 51 (4) ◽  
pp. 792-797 ◽  
Author(s):  
P.-A. Sva¨rdh
Keyword(s):  
Integral Transform ◽  
Three Dimensional ◽  
Step Function ◽  
Necessary Condition ◽  
Asymptotic Result ◽  
Axially Symmetric ◽  
Transient Waves ◽  
Linear Elastic ◽  
Elastic Cylinders ◽  
Integral Transform Technique

The axially symmetric problem of a semi-infinite, hollow, linear-elastic circular cylinder with traction-free lateral surfaces initially at rest and subjected to transient end loadings is solved using three-dimensional theory. Two cases are treated: an axial pressure applied to a radially clamped end and a prescribed axial velocity applied to an end that is free from shear stress. A double integral transform technique is used, and asymptotic solutions valid at large distances from the end are given for two types of time variation of the end loadings: step function and finite rise time function. A necessary condition for the validity of the asymptotic result is given.

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