Direct numerical simulation and global stability analysis of three-dimensional instabilities in a lid-driven cavity

Abstract

The first bifurcation in a lid-driven cavity characterized by three-dimensional Taylor-Görtler-Like instabilities is investigated for a cubical cavity with spanwise periodic boundary conditions at Re = 1000. The modes predicted by a global linear stability analysis are compared to the results of a direct numerical simulation. The amplification rate, and the shape of the three-dimensional perturbation fields from the direct numerical simulation are in very good agreement with the characteristics of the steady S1 mode from the stability analysis, showing that this mode dominates the other unstable unsteady modes.

Oscillatory instability of a three-dimensional lid-driven flow in a cube

“…8, the largest amplitudes are observed near the x = −0.5 boundary. The three-dimensional amplitude patterns are similar to those reported by Theofilis et al 31 and Chicheportiche et al 35 for a 3D lid-driven box with periodic spanwise boundaries ͑cf. …”

“…Only Leiriche and Gavrilakis 33 and Bouffanias et al 34 studied strongly supercritical 3D flows at Re= 10 4 and larger. Stability of flow in a three-dimensional lid-driven cavity was studied only for spatially periodic spanwise boundary conditions, 28,35,36 for which the base flow remains twodimensional. Beya and Lili 37 investigated three-dimensional incompressible flow in a two-sided nonfacing lid-driven cubical cavity.…”

Effect of Mach number on linear stability of lid-driven cavity flows

“…Considering the differences in boundary conditions and compressibility effect, the results for critical Reynolds number Re c and critical wavenumber β c for M a = 0.1 are in good agreement with the results for the imcompressible lid-driven cavity present in literature. 2,3,15 For the modes S1, T1, T2, and T3 a significant increment in the critical Reynolds number was observed when increasing Mach number. That is, the compressibility has a stabilizing effect on the linear stability for a lid-driven cavity flow.…”

“…There is a vast literature, including experimental, theoretical and numerical results regarding this subject for incompressible flows. [1][2][3] It also has several industrial applications, like coaters and melt spinning processes. It also gives insight to understand the behavior of similar eddy structures found in other flows.…”

Velocity field and parametric analysis of a subsonic, medium-Reynolds number cavity flow

“…If all of the eigenvalues have negative real parts, the global modes will eventually decay at large times and the base flow is asymptotically stable (Sipp et al 2010). That global stability approach has been used for the study of open cavity flows (Brès and Colonius 2008;Barbagallo et al 2009;Sipp et al 2010;Meseguer-Garrido et al 2011, 2014de Vicente et al 2014;Gomez et al 2014;Yamouni et al 2013) and lid-driven cavity flows (Chicheportiche et al 2008;Merle et al 2010). That approach has demonstrated that both two-dimensional and three-dimensional cavity modes can coexist and are dependent on the cavity geometry and Reynolds number.…”