LOW-REYNOLDS-NUMBER INSTABILITY OF THE LAMINAR FLOW BETWEEN WAVY WALLS
Instability of a viscous incompressible flow in a channel with wavy walls is investigated theoretically, numerically and experimentally. Linear stability analysis shows that appropriately chosen wall waviness leads to flow destabilization at surprisingly low Reynolds numbers. The unstable mode of disturbances forms a vortex array, which travels downstream. The remarkable feature is that the most destabilizing waviness does not introduce any additional flow resistance. The outcome of the stability analysis are consistent with the result of direct numerical simulation obtained using CFD finite volume package FLUENT (Ansys Inc.). Preliminary experimental data gained for a channel with appropriately corrugated wall seem to confirm these predictions.
On the linear stability of channel flow over riblets
In the present study channel flow with the lower wall mounted with streamwise riblets is considered. The laminar flow state is computed and its stability is investigated by superimposing infinitesimal perturbations, which leads to a hydrodynamic stability problem in a complex geometry. Linear stability characteristics for riblets with several scalloped cross sections are computed. The computations show that at the primary instability level the laminar flow in the presence of riblets is more unstable than channel flow with smooth walls.
Analysis of convective hydrodynamic instabilities in a symmetric wavy channel
The dynamic development of a laminar flow in a two-dimensional symmetric wavy channel is studied numerically by numerical integration of the unsteady Navier–Stokes equations. It is shown that beyond a critical Reynolds number the flow is convectively unstable and exhibits an exponential spatial growth of the velocity fluctuations. The amplification factor for these “natural instabilities” increases with Reynolds number. It is characteristic of the geometry but independent of the number of the periods chosen for the simulation and other numerical parameters. The amplitude of velocity fluctuations saturates at a distance from the entry that decreases with increasing Reynolds number. The structure of the developing unsteady flow is compared with the most unstable modes of the fully developed laminar steady flow obtained by linear stability analysis. Although visual inspection would tend to favor the assumption of a single mode disturbance, it is found that the disturbances are wave packets centered around a ...