A series of time-dependent three-dimensional (3D) computations of a lid-driven flow in a cube with no-slip boundaries is performed to find the critical Reynolds number corresponding to the steady-oscillatory transition. The computations are done in a fully coupled pressure-velocity formulation on ${104}^3$ , ${152}^3$ , and ${200}^3$ stretched grids. Grid-independence of the results is established. It is found that the oscillatory instability of the flow sets in via a subcritical symmetry-breaking Hopf bifurcation at ${\text{Re}}_{\text{cr}}\approx 1914$ with the nondimensional frequency $\omega =0.575$ . Three-dimensional patterns in the steady and oscillatory flow regimes are compared with the previously studied two-dimensional configuration and a three-dimensional model with periodic boundary conditions imposed in the spanwise direction.

Particle image velocimetry is applied to the lid-driven flow in a cube to validate the numerical prediction of steady-oscillatory transition at lower than ever observed Reynolds number. Experimental results agree with the numerical simulation demonstrating large amplitude oscillatory motion overlaying the base quasi-two-dimensional flow in the mid-plane. A good agreement in the values of critical Reynolds number and frequency of the appearing oscillations as well as similar spatial distributions of the oscillations amplitude are obtained.

Microdimples generated by laser surface texturing (LST) can be used to enhance performance in hydrostatic gas-lubricated tribological components with parallel surfaces. The pressure distribution and load carrying capacity for a single three-dimensional dimple, representing the LST, were obtained via two different methods of analysis: a numerical solution of the exact full Navier-Stokes equations, and an approximate solution of the much simpler Reynolds equation. Comparison between the two solution methods illustrates that, despite potential large differences in local pressures, the differences in load carrying capacity, for realistic geometrical and physical parameters, are small. Even at large clearances of 5% of the dimple diameter and pressure ratios of 2.5 the error in the load carrying capacity is only about 15%. Thus, for a wide range of practical clearances and pressures, the simpler, approximate Reynolds equation can safely be applied to yield reasonable predictions for the load carrying capacity of dimpled surfaces.

Microdimples generated by laser surface texturing (LST) can be used to enhance performance in hydrostatic gas-lubricated mechanical seals. This is achieved by applying microdimples with high area density over a certain portion of the sealing dam width adjacent to the high-pressure side, leaving the remaining portion untextured. The textured portion provides an equivalent larger gap that results in converging clearance in the direction of pressure drop and hence, hydrostatic pressure buildup, similar to that of a radial step seal. A mathematical model based on the solution of the Reynolds equation for compressible Newtonian fluid in a narrow gap between two nominally parallel stationary surfaces is developed. A detailed dimensionless analysis of the texturing parameters is performed to achieve maximum gas film stiffness with minimum gas leakage.