Characterization of oscillatory instability in lid driven cavity flows using lattice Boltzmann method

Abstract

In the present work, lattice Boltzmann method (LBM) is applied for simulating flow in a three-dimensional lid driven cubic and deep cavities. The developed code is first validated by simulating flow in a cubic lid driven cavity at 1000 and 12000 Reynolds numbers following which we study the effect of cavity depth on the steady-oscillatory transition Reynolds number in cavities with depth aspect ratio equal to 1, 2 and 3. Turbulence modeling is performed through large eddy simulation (LES) using the classical Smagorinsky sub-grid scale model to arrive at an optimum mesh size for all the simulations. The simulation results indicate that the first Hopf bifurcation Reynolds number correlates negatively with the cavity depth which is consistent with the observations from two-dimensional deep cavity flow data available in the literature. Cubic cavity displays a steady flow field up to a Reynolds number of 2100, a delayed anti-symmetry breaking oscillatory field at a Reynolds number of 2300, which further gets restored to a symmetry preserving oscillatory flow field at 2350. Deep cavities on the other hand only attain an anti-symmetry breaking flow field from a steady flow field upon increase of the Reynolds number in the range explored. As the present work involved performing a set of time-dependent calculations for several Reynolds numbers and cavity depths, the parallel performance of the code is evaluated a priori by running the code on up to 4096 cores. The computational time required for these runs shows a close to linear speed up over a wide range of processor counts depending on the problem size, which establishes the feasibility of performing a thorough search process such as the one presently undertaken.

Linear instability of the lid-driven flow in a cubic cavity

“…In the case of the supercritical Hopf bifurcation the absolute value of the components of the perturbation velocity field shows how the oscillation amplitude is distributed in the flow region. As mentioned, some previous works [10,14,15,18] concluded that the steady- Figure 5 contains also perturbation patterns of the two-dimensional lid-driven cavity flow. Note that the absolute values of the perturbation patterns are quite similar to the previously reported ones [16,17], as well as to the oscillation amplitude patterns reported in Fig.…”

“…Clearly, the grid refinement in the 3D computations is strongly restricted compared to the 2D case, by both available computer memory and affordable CPU time. At the same time, the critical Reynolds number in the 3D case [10][11][12][13][14][15][16][17][18] is approximately 4 times smaller than that of the 2D case, which allows us to expect a better convergence on coarser grids.…”

Refractive Index-Matched PIV Experiments and CFD Simulations of Mixing in a Complex Dynamic Geometry

“…This flow pattern is very similar to a lid-driven cavity flow. [32][33] The location of the vortex center and the shape of the vortex in the stator cavities depends on how exactly it is being generated by the rotor and its cavities. Also in the rotor cavities, the liquid is strongly sheared while -at the same time -it moves with the rotor in the circumferential direction.…”

High-Reynolds-number turbulent cavity flow using the lattice Boltzmann method

“…An alternative approach to computationally solve threedimensional lid-driven cavity flow is to use lattice Boltzmann methods coupled with SGS turbulence models to simulate flows up to Re = 1.2 × 10 4 [13,14]. Lattice Boltzmann methods for lid-driven cavity flow have previously used simple boundary conditions, such as bounce-back for the Dirichlet condition at the stationary cavity walls and interpolation schemes [14][15][16], as well as regularized schemes to improve stability [17]. This improvement in stability for LBM is a key issue, since the time complexity is on the order of L 4 .…”