Multi-relaxation time lattice Boltzmann simulations of oscillatory instability in lid-driven flows of 2D semi-elliptical cavity

Feng, Zhe; Lim, Hee-Chang

doi:10.1007/s12650-019-00590-5

Cited by 4 publications

(2 citation statements)

References 31 publications

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“…The continuous Boltzmann equation has been proved to be able to simulate gas flows with any Knudsen number, and the lattice Boltzmann method (LBM) derived from the continuous Boltzmann equation has been considered as a powerful tool for simulating many complex flows such as steady semi-elliptical cavity flow [11], oscillator semi-elliptical cavity flow [12], bubble dynamics in a bifurcated micro-channel [13], viscous fingering in anisotropic porous media [14], transitional gas flows [15], and so on. Gradually, the LBM becomes an efficient method to simulate microscale gas flows [16].…”

Section: Introductionmentioning

confidence: 99%

Kinetic boundary schemes of axisymmetric multi-relaxation-time lattice Boltzmann model for microscale gas flows in microtube

Ren¹,

Liu²,

Wu³

2021

Phys. Scr.

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Because of its mesoscopic nature and distinctive computing features, lattice Boltzmann method (LBM) is shown as a promising tool to simulate microscale gas flows. However, studies on the microtube flows are rare, and some fundamental problems for LBM to such flows still remain unsolved. In this work, three widely used kinetic boundary schemes, i.e., combined bounce-back and specular-reflection scheme, combined Maxwell-diffusion and specular-reflection scheme, and combined Maxwell-diffusion and bounce-back scheme, for the axisymmetric lattice Boltzmann equation (LBE) with multi-relaxation-time (MRT) are investigated. The discrete effects of the three boundary schemes in the axisymmetric MRT-LBE are observed by analyzing the micro-scale Hagen-Poiseuille flow, and the strategies of adjusting the parameters in the boundary schemes are put forward to implement the no-slip boundary condition and the second-order slip boundary condition. Some numerical tests are implemented to validate the proposed correction strategies for kinetic boundary schemes. Our analysis also shows that the kinetic boundary schemes of the axisymmetric Bhatnagar-Gross-Krook (BGK) LBE cannot realize the no-slip boundary condition and are also inapplicable to microscale gas flows with even some moderate Knudsen numbers (  Kn 0.25). Therefore, the axisymmetric MRT-LBE is superior to the axisymmetric BGK-LBE in realizing both the no-slip and slip boundary conditions.

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Section: Introductionmentioning

confidence: 99%

Kinetic boundary schemes of axisymmetric multi-relaxation-time lattice Boltzmann model for microscale gas flows in microtube

Ren¹,

Liu²,

Wu³

2021

Phys. Scr.

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“…Very complex and interesting vortical flows are observed including a series of Moffatt vortices. Several other geometries including arcsin cavity and a semi-circular cavity have also been computed [33][34][35][36][37][38][39][40]. Ozalp et al [41] conducted measurements of flows in cavities of different shapes in a water tunnel with flow parallel to the flat surface.…”

Section: Introductionmentioning

confidence: 99%

Shear-Driven Flow in an Elliptical Enclosure Generated by an Inner Rotating Circular Cylinder

Unnikrishnan,

Shahane,

Narayan

et al. 2021

Preprint

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Shear-driven flow between a rotating cylinder and a stationary elliptical enclosure is studied in this paper. The two-dimensional time-dependent Navier Stokes equations are solved using a meshless method where interpolations are done with Polyharmonic Spline Radial Basis Functions (PHS-RBF). The fluid flow is analyzed for various aspect ratios of the ellipse and eccentric placements of the inner cylinder. Contour plots of vorticity with streamlines, plots of non-dimensional torque, and the angle of eye of the primary vortex are presented in the paper for Reynolds numbers between 200 to 2000.Formation of Moffat like vortices in the wide-gap region of the model is observed and some benchmark data are provided for various cases that are simulated.

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Transport phenomena in a differentially heated lid-driven cavity: A study using multi-relaxation-time thermal lattice Boltzmann modeling

2020

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In this study, investigation of mixed convection phenomena in a lid driven square cavity with heated side walls is carried out. The left and right walls are maintained at different constant temperatures, while the upper and bottom walls are thermally insulated. The left wall temperature is higher than the cavity fluid temperature, and the right wall is maintained at the initial fluid temperature. Transport phenomena inside the cavity within a wide parametric range are investigated. The parameters include the Reynolds number (10 ≤ Re ≤ 1000), the Prandtl number (0.01 ≤ Pr ≤ 50), and the Richardson number (0.01 ≤ Ri ≤ 10). It was observed that the flow is induced in the cavity by a shear force resulting from the motion of the upper lid combined with the buoyancy force due to the temperature difference in the cavity. The effects of Re, Pr, and Ri within the cavity were observed simultaneously. The numerical simulations were carried out using the thermal lattice Boltzmann method with multi-relaxation time collision model. The present investigation generates a benchmark dataset for the average Nusselt number (Nuavg) with varying Re, Pr, and Ri within the laminar flow regime. Results show that heat transfer from the side wall is not affected significantly by change in Pr in low levels of Ri, but as Ri increases, average Nu increases significantly. It is also observed that the average value of Nu increases with Pr and Re at a particular value of Ri. However, at a given Ri, for Re above 500 and Pr over 10, the Nu value remains unaffected by change in Re and Pr, which defines the limiting heat transfer in the laminar regime.

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Multi-relaxation time lattice Boltzmann simulations of oscillatory instability in lid-driven flows of 2D semi-elliptical cavity

Cited by 4 publications

References 31 publications

Kinetic boundary schemes of axisymmetric multi-relaxation-time lattice Boltzmann model for microscale gas flows in microtube

Kinetic boundary schemes of axisymmetric multi-relaxation-time lattice Boltzmann model for microscale gas flows in microtube

Shear-Driven Flow in an Elliptical Enclosure Generated by an Inner Rotating Circular Cylinder

Transport phenomena in a differentially heated lid-driven cavity: A study using multi-relaxation-time thermal lattice Boltzmann modeling

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