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

Perumal, D. Arumuga; Dass, Anoop K.

doi:10.1016/j.camwa.2010.03.053

Cited by 62 publications

(17 citation statements)

References 18 publications

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“…Thus, the critical Reynolds number (Re c ) for 3D FSL with K=1 is identified as 380. This result is different with that observed from the 2D FSL study (Re c =300) (Wahba 2009, Perumal andDass 2011), which may be caused by the stability effect from stationary end walls available in this 3D model. Two possible asymmetry steady solutions at Re=381 (figures 11(b) and 12) show the effect of a slight change of the relaxation time and viscosity, by slightly changing the nondimensional lid speed.…”

Section: Multiple Steady Solutionscontrasting

confidence: 99%

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Lattice Boltzmann Simulation of Mixed Convection Heat Transfer in a Driven Cavity with Non-uniform Heating of the Bottom Wall

Bettaibi¹,

Sediki²,

Kuznik³

et al. 2015

Commun. Theor. Phys.

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Numerical study on three-dimensional (3D), incompressible, four-sided lid (FSL) driven cavity flows has been conducted to show the effects of the transverse aspect ratio, K, on the flow field by using a multiple relaxation time lattice Boltzmann equation. The top wall is driven from left to right, the left wall is moved downward, whereas the right wall is driven upward, and the bottom wall is moved from right to left, all the four moving walls have the same speed and the others boundaries are fixed. Numerical computations are performed for several Reynolds numbers for laminar flows, up to 1000, with various transverse aspect ratios. The flow can reach a steady state and the flow pattern is symmetric with respect to the two cavity diagonals (i.e., the center of the cavity). At Reynolds number=300, the flow structures of the 3D FSL cavity flow at steady state with various transverse aspect ratio, i.e., 3, 2, 1, 0.75, 0.5 and 0.25 only show the unstable symmetrical flow pattern. The stable asymmetrical flow pattern could be reproduced only by increasing the Reynolds number that is above a critical value which is dependent on the aspect ratio. It is found that an aspect ratio of more than 5 is needed to reproduce flow patterns, both symmetric and asymmetric flows, simulated by using 2D numerical models.

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Section: Multiple Steady Solutionscontrasting

confidence: 99%

“…For MRT-LBM, the multiple steady solutions could be obtained by (1) changing the Reynolds number, or (2) a slight change of the relaxation time when Re is close to Re c (Perumal and Dass 2011). For the first approach calculations are performed for the Reynolds varies from 100 to 400, and using a 112 3 grid size with K=1.…”

Section: Multiple Steady Solutionsmentioning

confidence: 99%

Lattice Boltzmann Simulation of Mixed Convection Heat Transfer in a Driven Cavity with Non-uniform Heating of the Bottom Wall

Bettaibi¹,

Sediki²,

Kuznik³

et al. 2015

Commun. Theor. Phys.

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“…In the last 20 years, the LBM has appeared as a newly efficacious method of CFD and it has acquired significant progress to simulate fluid flow problems . The simplified form of lattice Boltzmann equation can be written for the Equations and , respectively, as

f_{α} (x + {bolde}_{α} Δ t, t + Δ t) = true(1 - \frac{1}{τ_{f}} true) f_{α} true(x, t true) + \frac{1}{τ_{f}} f_{α}^{(0)} true(x, t true)

and

g_{α} (x + {bolde}_{α} Δ t, t + Δ t) = true(1 - \frac{1}{τ_{g}} true) g_{α} true(x, t true) + \frac{1}{τ_{g}} g_{α}^{(0)} true(x, t true),

where

f_{α} false(boldx goodbreakinfix, t false) and f_{α}^{false(0 false)} false(boldx goodbreakinfix, t false)

are, respectively, the particle distribution function and equilibrium distribution function for the vorticity Ω at ( x , t ).…”

Section: Methods Of Solution By Lbmmentioning

confidence: 99%

LBM simulation of forced convective channel flow containing multiple obstacles: Effects of obstacles height and position

Bala

Saha

2019

Heat Trans. Asian Res.

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We examine the effects of the obstacles, height, and position on the forced convective flow in a channel having three obstacles on the lower wall of the channel. All the walls of the channel and obstacles are retained at a constant temperature while the fluid with temperature more than the walls are entered into the channel. The flow governing equations, vorticity equation, and energy equation are solved numerically by using the lattice Boltzmann method (LBM) together with the finite difference successive over relaxation method (SOR). The effects of obstacles height, h, and distance, d, between the obstacles on the streamlines and isotherms are presented. To investigate the heat transfer rate for changing the height and position of the obstacles, local Nusselt number distribution and the mean Nusselt number distribution are also presented. It is observed that vortices, produced backward to each obstacle, increase axially with increasing the height of each obstacle. Also vortices, produced between obstacles, change its shape with decreasing the distance between obstacles. It is asserted that heat transfer rate can be increased by extending only the height of first obstacle.

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“…General Navier-Stokes and continuity equations for solving a limited domain in a cavity, like the case studies in [25][26][27], is developed for the current study. When cavitation happens in the field, modeling the cavitation is essential.…”

Section: Governing Equationsmentioning

confidence: 99%

Investigation of rib’s effect in cavitation on an axisymmetric separated flow over a longitudinal blunt circular cylinder

et al. 2020

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The current investigation, determines the effects of rib shape and its parameters on an inner flow in which a circular cylinder exist in the middle. The problem is solved in 2 dimensional methods and the distance from the channel's entrance to cylinder is 125 mm. Ansys 14.5 is used for modeling the geometry and meshing of the problem and for modeling the turbulence the k − ε (realizable) is employed. In this study rib and its four parameters of pitch (p), length (h), rib's height (e) and the distance from the cylinders' head to start of rib (a) in a cavitation flow is investigated. The results show that none of rib's parameters has a direct relation with void fraction. The values for these parameters are different for the maximum or the minimum cavitation; namely if a rib's pitch increases and surpasses a specific value, it will reduce the effect of the previous rib in the flow. In fact, the turbulence eradicates before it become more turbulent by the next rib. On the other hand, if the rib's pitch is too small the flow traps between the two ribs and stagnation happens which is the key element in plummeting the pressure and forming cavity. For other parameters either no correlation with void fraction is observed.

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

Cited by 62 publications

References 18 publications

Lattice Boltzmann Simulation of Mixed Convection Heat Transfer in a Driven Cavity with Non-uniform Heating of the Bottom Wall

Lattice Boltzmann Simulation of Mixed Convection Heat Transfer in a Driven Cavity with Non-uniform Heating of the Bottom Wall

LBM simulation of forced convective channel flow containing multiple obstacles: Effects of obstacles height and position

Investigation of rib’s effect in cavitation on an axisymmetric separated flow over a longitudinal blunt circular cylinder

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