Anoop K. Dass

Analysis of Non-Darcy Models for Mixed Convection in a Porous Cavity Using a Multigrid Approach

This article investigates the performance of two models; namely the Brinkman-Forchheimer Darcy model (BFDM) and the Brinkman-extended Darcy model (BDM), in a problem involving mixed convection in a square cavity filled with a porous medium using the multigrid method. The left and right walls, moving in opposite directions, are maintained at different constant temperatures, while the top and bottom walls are thermally insulated. The transport equations were solved numerically by the finite-volume method on a colocated grid arrangement using a quadratic upwind interpolation for convective kinematics (QUICK) scheme. The influence of the key parameters, namely the Darcy number (Da) and Grashof number (Gr) on the flow and heat transfer pattern is examined. Further, the issue of reliability of the results is addressed. The results demonstrate that BDM over-predicts the momentum and heat transfer rates compared with BFDM, which is in conformity with the fact that the additional term present in the BFDM hinders convective effects. The full approximation storage (FAS) multigrid method achieves considerable acceleration of convergence for the present relatively unexplored problem.

Multiplicity of steady solutions in two-dimensional lid-driven cavity flows by Lattice Boltzmann Method

This work is concerned with the computation of two- and four-sided lid-driven square cavity flows and also two-sided rectangular cavity flows with parallel wall motion by the Lattice Boltzmann Method (LBM) to obtain multiple stable solutions. In the two-sided square cavity two of the adjacent walls move with equal velocity and in the four-sided square cavity all the four walls move in such a way that parallel walls move in opposite directions with the same velocity; in the two-sided rectangular lid-driven cavity flow the longer facing walls move in the same direction with equal velocity. Conventional numerical solutions show that the symmetric solutions exist for all Reynolds numbers for all the geometries, whereas multiplicity of stable states exist only above certain critical Reynolds numbers. Here we demonstrate that Lattice Boltzmann method can be effectively used to capture multiple steady solutions for all the aforesaid geometries. The strategy employed to obtain these solutions is also described.

Prediction of turbulent plane jet in crossflow

In this article numerical predictions of turbulent plane jets discharged normal to a weak or moderate cross stream are presented. The Reynolds-averaged Navier-Stokes equations with the standard k- k turbulence model have been used to formulate the flow problem. The governing equations that are elliptic in nature are solved using the finite volume method. The predictions are presented to illustrate the flow pattern involved and to assess the performance of the standard k- k model by comparison with available experimental data for three different jet to cross stream velocity ratios (six, nine, and ten) and the agreement is found to be satisfactory.

Higher Order Compact Simulation of Double-Diffusive Natural Convection in A Vertical Porous Annulus

Abstract In the last few decades, the Higher Order Compact (HOC) finite difference schemes are gaining momentum in the fluid dynamics community because of their high accuracy and advantages associated with compact difference stencils. However, in most of the cases, their application is seen to be limited solely to the computation of fluid flows and in some cases to problems of heat transfer only. The present work is perhaps first in the direction where an HOC algorithm has been extended to a problem of combined heat and mass transfer. A recently developed higher-order compact (HOC) scheme of fourth order spatial and second order temporal accuracy is employed to carry out simulation of double-diffusive natural convection in a vertical porous annulus between two concentric cylinders maintained at constant temperatures and concentrations. Flow is investigated in the regime -50≤N≤50, 1 ≤A≤10, 1≤κ≤50, 0≤Ra≤1000 and 1≤Le≤500, where N, A, κ, Ra and Le are the buoyancy ratio, aspect ratio, radius ratio, thermal Rayleigh number and the Lewis number respectively. Comparison is made with established numerical results and very good comparison is obtained on relatively coarser grids.

Computation of the turbulent plane plume using the k–ϵ–t′2–γ model

Abstract The k–ϵ– t ′2 –γ turbulence model is used to predict the self-similar plane plume in a quiescent environment. This model has been recently used to predict the turbulent axisymmetric plume. Modelled transport equations for the turbulent kinetic energy (k), its dissipation (ϵ), mean square temperature fluctuations ( t ′2 ) and intermittency factor (γ) have been solved numerically along with the equations for the mean quantities. A small change in one of the model constants, incorporation of the dissipation term in the intermittency transport equation and withdrawal of the intermittency interaction invariant term from the dissipation equation yield predictions of mean and turbulent quantities including intermittency that are in good agreement with the experimental data.

Simulation Of Flow In Two-sidedLid-driven Square Cavities By TheLattice Boltzmann Method

Due to the presence of corner eddies that change in number and pattern, the classical one-sided lid-driven cavity problem has been found to be particularly suitable to study various aspects of the performance of solution algorithms for incompressible viscous flows. More recently, the flow induced by the motion of two facing walls (two-sided lid-driven cavity) has also been investigated by Kuhlmann et al. For some aspect ratios this study demonstrates the existence of a multiplicity of solutions. However, for the aspect ratio of unity no multiplicity of solutions has been observed. Also it is found that for parallel motion of the walls, there appears a pair of counter-rotating secondary vortices of equal size near the centre of a wall. Because of symmetry, this pair of counter-rotating vortices has similar shapes and their detailed study as to how they grow with increasing Reynolds number has not yet been made. Such a study is attempted in this paper through the lattice Boltzmann method (LBM), as the problem has the potential of being used for testing various solution methods for incompressible viscous flows. The results for the antiparallel motion of the walls are also presented in detail. As the problem has not been investigated before, to lend credibility to the results they are further compared with those obtained from a finite difference method (FDM) code developed for this purpose.

Numerical Simulation of Viscous Flow over a Square Cylinder Using Lattice Boltzmann Method

This work is concerned with the lattice Boltzmann computation of two-dimensional incompressible viscous flow past a square cylinder confined in a channel. It is known that the nature of the flow past cylindrical obstacles is very complex. In the present work, computations are carried out both for steady and unsteady flows using lattice Boltzmann method. Effects of Reynolds number, blockage ratio, and channel length are studied in detail. As good care has been taken to include appropriate measures in the computational method, these results enjoy good credibility. To sum up, the present study reveals many interesting features of square cylinder problem and demonstrates the capability of the lattice Boltzmann method to capture these features.

Lattice Boltzmann Simulation of Two- and Three-Dimensional Incompressible Thermal Flows

This work is concerned with the application of the thermal lattice Boltzmann method (TLBM) to compute incompressible two- and three-dimensional flows in cavities. Two convection test cases, namely, the laminar flow in a differentially heated square cavity and a cubic cavity, are numerically analyzed through TLBM. The internal energy density distribution function approach with two three-dimensional particle velocity models, namely, the 15-velocity and the 19-velocity, and a two-dimensional model, namely, the nine-velocity, have been used in the present work. Computations are carried out for laminar flows in a differentially heated square cavity and a cubical cavity (Rayleigh numbers = 103 to 105). The boundary conditions used are stable and of good accuracy. To lend credibility to the thermal lattice Boltzmann model square cavity results, they are further compared with those obtained from a finite-difference-based code developed for this purpose.

Distribution of Temperature as a Passive Scalar in the Flow Field of a Heated Turbulent Jet in a Crossflow

This article presents a computational investigation of the mean flow field of heated turbulent rectangular jets in a crossflow. The jet is discharged with a slightly higher temperature (about 6°C) than the crossflow. The computations are carried out for two values of jet-to-crossflow velocity ratio, 6 and 9. The commercial code FLUENT 6.2.16, employing the Reynolds stress transport model, is used to predict the mean flow field. The influence of the velocity field on the temperature distributions is discussed. A comparison of the predicted results is made with the available experimental data, and reasonably good agreement is observed.

A Multigrid-Accelerated Code on Graded Cartesian Meshes for 2D Time-Dependent Incompressible Viscous Flows

Abstract The present work deals with the development of a multigrid-assisted solver for the 2D time-dependent incompressible Navier-Stokes equations on graded Cartesian meshes. As finite difference method is used to discretize the governing equations on nonuniform staggered grids, a transformation of the governing equations from the physical space to the computational space is performed. To obtain second-order time accuracy a fractional-step method is employed. The convective terms are discretized using a third-order accurate upwind scheme and the viscous terms are centrally differenced to fourth-order accuracy. To improve the time-wise efficiency of the code a multigrid technique is employed to solve the pressure-Poisson equation that is required to be solved at every time-step. To establish the accuracy and performance of the code the standard 2D lid-driven cavity flow is computed for unsteady, periodic and asymptotically obtained steady solution for a wide range of Reynolds numbers (Re). The code is then used to compute the transient and asymptotically approached steady flows in a hitherto unexamined problem of two-sided lid-driven square cavity, which involves gradual development of a free shear layer and accompanying off-corner vortices. The computations also show that for this configuration, at Re=2000, there exists a steady solution, about which there was some doubt earlier. The reliability of all known and unknown results in the paper is carefully established and efficiency of the method in respect of grid economy is demonstrated.