Flow In Two-sided Lid-driven Cavity Research Articles

Motion of a two-dimensional neutrally buoyant circular particle in two-sided lid-driven cavity flow with thermal convection

Understanding the interaction between a cold particle and confined fluid flow is of practical importance in many industrial applications. In this work, the motion of a two-dimensional circular neutrally buoyant particle in thermal flows in the two-sided lid-driven cavity has been numerically investigated by the lattice Boltzmann model with immersed boundary method. We examined the effects of Grashof number (Gr) and Reynolds number (Re) of cavity on the motion of particle in the range of 104 ≤ Gr ≤ 107 and 500 ≤ Re ≤ 3000. It is found that the motion of the cold particle in the cavity flow manifests four different modes, driven by the competition between buoyancy-driven natural convection and lid-driven forced convection. With the increase in Gr or the decrease in Re, the motion of the cold particle would evolve from modes I to IV. We further obtained the diagram of motion modes of the cold particle with regard to Gr and Re. And a power law correlation that relates the critical Gr to Re of the cavity is proposed and capable of well predicting the transition of particle motion modes.

Combined effects of the velocity and the aspect ratios on the bifurcation phenomena in a two-sided lid-driven cavity flow

PurposeThis paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume method (FVM) and multigrid acceleration. This study has been performed for certain pertinent parameters; a wide range of the Reynolds number values has been adopted, and aspect ratios ranging from 0.25 to 1 and various velocity ratios from 0.25 to 0.825 have been considered in this investigation. Results show that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Velocity profile for special case of a square cavity (A = 1) was found to be in good agreement between current numerical results and published ones. Flow characteristics inside the cavity have been presented and discussed in terms of streamlines and vorticity contours at a fixed Reynolds number (Re = 5,000) for various aspect ratios (a = 0).Design/methodology/approachThe numerical method is based on the FVM and multigrid acceleration.FindingsComputations have been investigated for several Reynolds numbers and aspect ratios A (0.25, 0.5, 0.75, 0.825 and 1). Besides, various velocity ratios (a = 0.25, 0.5, 0.75 and 0.825) at fixed aspect ratios (A = 0.25, 0.5 and 0.75) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity is verified through time history plots for velocity components and phase-space trajectories.Originality/valueThe bifurcations between steady and unsteady states are investigated.

A global Stokes method of approximated particular solutions for unsteady two-dimensional Navier–Stokes system of equations

ABSTRACTThe unsteady two-dimensional Navier–Stokes system of equations, for viscous incompressible fluids are solved using a global method of approximated particular solutions (MAPS) in terms of a Stokes formulation, where the velocity and pressure fields are approximated from a linear superposition of particular solutions of a non-homogeneous Stokes system of equations, with a multiquadric (MQ) radial basis function (RBF) as non-homogeneous term. Steady-state solution of the flow problems considered in this work can be unstable at high Reynolds numbers (Re), corresponding to bifurcation of solutions that result in the appearance of new stable steady-state or periodic solutions. The main objective of this work is to present a global meshless numerical scheme able to predict these bifurcation points and concurrent new stable or periodic solutions. This is well known to be a very difficult task for any numerical scheme. An implicit first-order time-stepping scheme is used to approximate the transient term and the obtained nonlinear system of algebraic equations is solved by a Newton–Raphson method with variable step. Two steady-state and two transient problems are considered to validate the numerical scheme: the lid-driven cavity and backward-facing step (BFS) flows (steady-state problems) and the decaying Taylor–Green vortex and two-sided lid-driven cavity flows (transient problems). The first two problems are solved up to Re=10,000 and 2300, respectively. Results obtained are compared with corresponding benchmark numerical solutions, showing excellent agreement. Obtained numerical solutions for the decaying vortices at Re=100 shown excellent agreement with the corresponding analytical results. The transient problem of a rectangular two-sided lid-driven cavity flow is solved at Re=700. The influence of the cavity length, l, in determining the different structures of the flow pattern is studied for values of , showing that the scheme is able to reproduce the previously reported change in the flow pattern when l=2. Finally, the global Stokes MAPS are used to carry out nonlinear stability analyses of three steady-state problems: the sudden expansion, lid-driven cavity and BFS flows. Stable and unstable steady-state solutions at Re values greater than critical are predicted with the proposed numerical scheme. Our numerical results are consistent with previously stability analysis reported in the literature.

On the Importance of the Influence of both Velocity and Aspect Ratios on the Occurrence of Bifurcation Phenomena within a Two-Sided Lid-Driven Enclosure

This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. The stability analysis depending on the aspect ratio, velocity ratios α and the Reynolds number when transition phenomenon occurs is considered in this paper.

On the Importance of the Influence of both Velocity and Aspect Ratios on the Occurrence of Bifurcation Phenomena within a Two-Sided Lid-Driven Enclosure

This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. The stability analysis depending on the aspect ratio, velocity ratios α and the Reynolds number when transition phenomenon occurs is considered in this paper.

On the Importance of the Influence of both Velocity and Aspect Ratios on the Occurrence of Bifurcation Phenomena within a Two-Sided Lid-Driven Enclosure

This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. The stability analysis depending on the aspect ratio, velocity ratios α and the Reynolds number when transition phenomenon occurs is considered in this paper.

Two-Sided Lid-Driven Cavity Flow at Different Speed Ratio by Lattice Boltzmann Method

In this study, the Lattice Boltzmann method has been used to investigate flow configuration of the two-sided lid driven cavity. The top and bottom lid were moved at the same direction but with different speed ratio which varies from 0 to 1. The range of Reynolds number is 100,400 and 1000. The results show that the increase in both speed ratio and Reynolds number give an effect on flow configuration of the cavity.

Subsonic compressible flow in two-sided lid-driven cavity. Part I: Equal walls temperatures

This paper presents a numerical study of the laminar, viscous, subsonic compressible flow in a two-dimensional, two-sided, lid-driven cavity using a multi-domain spectral element method. The flow is driven by steadily moving two opposite walls vertically in opposite directions. All the bounding walls have equal temperatures. The results of the simulations are used to investigate the effects of the cavity aspect ratio, the Reynolds number and the Mach number on the flow. At lower Reynolds numbers, the flow pattern consists of two separate co-rotating vortices contiguous to the moving walls. For higher Reynolds numbers, initially a two-vortex flow is formed, which eventually turns into a single elliptical vortex occupying most of the cavity. For a higher aspect ratio, the flow patterns are dissimilar in that the streamlines become more and more elliptic. For aspect ratios as high as 2.5, at high Reynolds numbers, a three-vortex stage is formed. It is found that the compressibility effects are not very significant for Mach numbers less than 0.4. Dissipation of kinetic energy into internal energy changes the temperature field especially near the boundaries. Boundary layer studies suggest that the velocity and temperature boundary layer thicknesses are lower for higher Reynolds numbers. For engineering purposes, these thicknesses can be approximated by the existing flat-plate solutions.

Subsonic compressible flow in two-sided lid-driven cavity. Part II: Unequal walls temperatures

This paper studies the effect of unequal walls temperatures for a two-dimensional, two-sided, lid-driven cavity via numerical simulations using a multi-domain, spectral element method. The flow is driven by steadily moving the two opposite walls vertically in opposite directions. Different temperatures are applied on the two moving walls and the effect of the resulting heat transfer on the two-dimensional flow is studied. An analysis of the flow evolution shows that, with increasing the temperature difference between the opposite moving walls, the steady state flow changes from a single-vortex to a two-vortex pattern. Energy balance studies are conducted at steady state and during flow evolution. The evolution and distribution of heat transfer at all walls and work done at the moving walls are studied.

Elliptic instability in two-sided lid-driven cavity flow

The recently discovered concentration of vorticity in slender vortex tubes in turbulent flow fields has motivated the investigation of a class of vortices with elliptical streamlines. As a prototype of this flow, long vortices confined in a rectangular cavity and driven by tangentially moting walls are studied. These vortices are characterized by a large rate of plane strain at the core. The quasi-two-dimensional flow is found to be unstable at small Reynolds numbers, if the eccentricity of the streamlines, i.e. the strain rate, is sufficiently large. The three-dimensional supercritical flow is found to be steady with a wavelength of the order of the vortex core diameter. The flow pattern appears in the form of rectangular cells that are very robust. Good agreement between experiment and numerical calculations is obtained. It is argued that the instability found is due to the elliptic instability mechanism.