Convective and absolute instability in the incompressible boundary layer on a rotating disk in the prescence of a uniform magnetic field

The stability of a conducting fluid flow over a rotating disk with a uniform magnetic field applied normal to the disk, is investigated. It is assumed that the magnetic field is unaffected by the motion of the fluid. The mean flow and linear stability equations are solved for a range of magnetic field-strength parameters and the absolute/convective nature of the stability is investigated. It is found that increasing the magnetic field parameter is in general stabilizing

Numerical Investigation of S822 Wind Turbine Airfoil

We carried out direct numerical simulations of the flow past a two-dimensional S822 wind turbine blade section at a chord Reynolds number of Re=100,000 and an angle of attack of α = 5deg. Without blade rotation the separated boundary layer “rolls up ” into spanwise vortices which then “break up ” into smaller scale structures leading to transition to turbulence. Simulation results compare favorably with XFoil predictions and wind tunnel data by the University of Illinois at Urbana Champaign. By adding volume forcing terms to the right-hand-side of the Navier-Stokes equations the effect of blade rotation can be simulated. Blade rotation is shown to result in a radial velocity component towards the blade tip in areas where the velocity is substantially different from its free stream value, such as near the stagnation point and especially in the separated flow region. The spanwise velocity component makes the flow crossflow unstable resulting in stationary and traveling crossflow vortices. A linear stability theory analysis which compares favorably with the simulation data provides proof that the primary instabilities are of mixed type, including both a two-dimensional mode (Tollmien-Schlichting and Kelvin-Helmholtz type) and a stationary and unsteady crossflow mode. The crossflow instability results in an earlier transition and a separation delay, lift increase, and drag reduction. This effect is more pronounced at 20 % than at 80 % blade radius. Because we apply periodicity conditions in the spanwise direction our results provide an explanation for rotational augmentation that is not based on the transfer of fluid from the inboard region towards the blade tips (“centrifugal pumping”). Instead, we argue that rotational augmentation, at least for low Reynolds number flows, is a direct consequence of crossflow instabilities which destabilize the flow leading to earlier transition and separation delay. I