scholarly journals Study of Pollutant Transport in Environmental Flows Using Depth-Averaged Random Walk Method

10.29007/gd96 ◽  
2018 ◽  
Author(s):  
Xuefei Wu ◽  
Fan Yang ◽  
Dongfang Liang
Keyword(s):  
Random Walk ◽  
Solute Transport ◽  
Analytical Solutions ◽  
Environmental Flows ◽  
Concentration Gradients ◽  
Bed Elevation ◽  
Numerical Predictions ◽  
Parametric Studies ◽  
Transport Problems ◽  
Sharp Concentration

A depth-averaged random walk scheme is applied to investigate the process of solute transport, including advection, diffusions and reaction. Firstly, the model is used to solve an instantaneous release problem in a uniform flow, for which analytical solutions exist. Its performance is examined by comparing numerical predictions with analytical solutions. The advantage of the random walk model includes high accuracy and small numerical diffusion. Extensive parametric studies are carried out to investigate the sensitivity of the predictions to the number of particles. The result reveals that the particle number influences the accuracy of the model significantly. Finally, the model is applied to track a pollutant cloud in the Thames Estuary, where the domain geometry and bed elevation are complex. The present model is free of fictitious oscillations close to sharp concentration gradients and displays encouraging efficiency and accuracy in solving the solute transport problems in a natural aquatic environment.

scholarly journals On the application of the depth-averaged random walk method to solute transport simulations

2019 ◽  
Vol 22 (1) ◽  
pp. 33-45 ◽  
Author(s):  
Fan Yang ◽  
Dongfang Liang ◽  
Xuefei Wu ◽  
Yang Xiao
Keyword(s):  
Random Walk ◽  
Solute Transport ◽  
Sampling Technique ◽  
Meshfree Method ◽  
Chaotic Mixing ◽  
Random Walk Method ◽  
Parametric Studies ◽  
Artificial Diffusion ◽  
Shallow Basin ◽  
Number Of Particles

Abstract Most numerical studies on solute mixing rely on mesh-based methods, and complicated schemes have been developed to enhance numerical stability and reduce artificial diffusion. This paper systematically studies the depth-averaged random walk scheme, which is a meshfree method with the merits of being highly robust and free of numerical diffusion. First, the model is used to solve instantaneous release problems in uniform flows. Extensive parametric studies are carried out to investigate the influences of the number of particles and the size of time steps. The predictions are shown to be independent of time steps but are sensitive to the particle numbers. Second, the model is applied to the solute transport problem along an estuary subject to extensive wetting and drying during tidal oscillations. Finally, the model is used to investigate the wind-induced chaotic mixing in a shallow basin. The effect of diffusion on the chaotic mixing is investigated. This study proposes a generic sampling method to interpret the output of the random walk method and highlights the importance of accurately taking diffusion into account in analysing the transport phenomena. The sampling technique also offers a guideline for estimating the total number of particles needed in the application.

The Effectiveness of the Unit Cell Method in Numerically Modeling and Designing Liquid Cooled Heatsinks

2019 ◽  
Vol 11 (6) ◽  
Author(s):  
Ali C. Kheirabadi ◽  
Dominic Groulx
Keyword(s):  
Heat Transfer ◽  
Wall Temperature ◽  
Parametric Design ◽  
Unit Cell ◽  
Liquid Cooling ◽  
Cell Method ◽  
Numerical Predictions ◽  
Finite Element Package ◽  
Parametric Studies ◽  
Relative Differences

This study compares two numerical strategies for modeling flow and heat transfer through mini- and microchannel heatsinks, the unit cell approximation, and the full 3D model, with the objective of validating the former approach. Conjugate heat transfer and laminar flow through a 2 × 2 cm2 copper–water heatsink are modeled using the finite element package COMSOL Multiphysics 5.0. Parametric studies showed that as the heatsink channels’ widths were reduced, and the total number of channels increased, temperature and pressure predictions from both models converged to similar values. Relative differences as low as 5.4% and 1.6% were attained at a channel width of 0.25 mm for maximum wall temperature and channel pressure drop, respectively. Due to its computational efficiency and tendency to conservatively overpredict temperatures relative to the full 3D method, the unit cell approximation is recommended for parametric design of heatsinks with channels’ widths smaller than 0.5 mm, although this condition only holds for the given heatsink design. The unit cell method is then used to design an optimal heatsink for server liquid cooling applications. The heatsink has been fabricated and tested experimentally, and its thermal performance is compared with numerical predictions. The unit cell method underestimated the maximum wall temperature relative to experimental results by 3.0–14.5% as the flowrate rose from 0.3 to 1.5 gal/min (1.1–5.7 l/min).

scholarly journals Development of An Integrated Numerical Model for Simulating Wave Interaction with Permeable Submerged Breakwaters Using Extended Navier–Stokes Equations

2020 ◽  
Vol 8 (2) ◽  
pp. 87 ◽  
Author(s):  
Paran Pourteimouri ◽  
Kourosh Hejazi
Keyword(s):  
Porous Medium ◽  
Wave Propagation ◽  
Numerical Model ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stokes Wave ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
The Impact

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.

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