Numerical simulation of three-dimensional flow structure in a driven cavity

Abstract

Investigations have been made of three-dimensional flows of an incompressible viscous fluid in a square cubic cavity. The flows are driven by the sliding upper surface of the cavity. Numerical solutions are obtained by directly integrating the full, three-dimensional, time-dependent Navier-Stokes equations. The three-dimensional flow structure is examined in detail over a wide range of the Reynolds number Re. One primary finding of these three-dimensional numerical simulations indicates that steady solutions are attained at lower values of Re, but the flow becomes unsteady at higher values, say, when Re exceeds approximately 2000. Due to the profound influence of the endwall effects, three-dimensional flows show substantial differences from two-dimensional solutions: for two-dimensional flow situations, steady solutions are known to exist for up to Re ~10000. The three-dimensional flow structure displays qualitatively distinct features in the low-Re and high-Re regimes. The demarcation separating these two regimes appears to lie in the neighborhood of Re = 2000-3000. One principal characteristic is that the Taylor-Gortler-hkc vortices are discernible for the high-Re regimes, although these have not been clearly captured in the numerical results for the low-Re regimes. Critical assessments of the present numerical results have been made by cross-checking the data with the available experimental measurements for three-dimensional cavity flows. The comparisons demonstrate broad qualitative agreement between the present numerical computational results and the laboratory measurement data.

Transient solutions for three‐dimensional lid‐driven cavity flows by a least‐squares finite element method

“…They show that the velocity components change with time and no steady state solution appears to be possible at Re = 3200. This is consistent with the numerical result of Iwatsu et al 9 The LSFEM is able to simulate the unsteady Taylor-Gortler-like vortices. It is worth mentioning that even though our simulation represents one of the largest finite element simulations using the implicit and fully coupled equations approach, we observe slight oscillations along the downstream wall (x = 1 .O).…”

“…Iwatsu et al 9 used a timemarching MAC method for unsteady state flows at Re = 2000 and 4000. The time step was taken as At = 1 Or' and the number of grid points was 8 1 x 8 1 x 8 1.…”

Characteristic finite analytic method (CFAM) for incompressible Navier-Stokes equations

“…One goes through the eddy center towards the central plane, while the other lies surrounding the first one towards the end plane y = 1. Figure 12 shows the velocity profile along two central axes, which still coincide well with the results of Iwatsu et al [14].…”

Numerical solution of incompressible flows by discrete singular convolution

“…By taking divergence over Equation (37), one attains the following Poisson equation for the ÿrst-step potential function…”