The laminar-turbulent transition of a rotating-disk flow dominated by global instability is studied by solving the full Navier-Stokes equations in direct numerical simulations. A flow field in the 2π/32 region is computed using a periodic boundary condition. The flow field is disturbed in two ways. In the first case, a disturbance is introduced at the Reynolds number, Re≈ 600, while in the second case, a disturbance is introduced at Re≈ 650. In both cases, wall-normal short-duration suction and blowing are used to disturb the flow field. When a disturbance is added upstream at Re≈ 600, the wavenumber 64 component becomes dominant when the flow reaches a steady state, whereas when a disturbance is added downstream at Re≈ 650, the wavenumber 96 component becomes prominent. The transition points are different between the two cases. In addition, in both cases, the distances between neighboring spiral vortices are quite the same when measured at the locations where the turbulence begins.

The control mechanism of a dielectric barrier discharge plasma actuator is investigated via direct numerical simulations in the flow field around a square cylinder. The Reynolds number is 33000. Conditions for the burst frequency of the actuator are explored in terms of the reduction rate of drag and root mean square (RMS) lift coefficients. A good control effect is achieved, and vortex shedding is fairy repressed at Stb (Strouhal number for the burst frequency) = 0.50. The flow induced by the actuator generates two vortices: the first and second vortices. Until the next actuator on-time, the second vortex grows on the upper or lower side of the cylinder. The second vortex collides with the first vortex, and both vortices flow downstream in a straight line. This situation happens almost simultaneously on the upper and lower sides of the cylinder; thus, a high reduction rate of RMS lift and drag coefficients can be obtained. A control effect is obtained at Stb = 2.00, which is lower than that at Stb = 0.50, where a tiny vortex is raised by the flow induced by the small actuator on-time and flows downstream at a small distance away from the cylinder. The least control effect is achieved at Stb = 0.25 because the collision between the first and second vortices does not occur due to a large actuator off-time. The duration of on-time and off-time is important for determining the burst frequency for the most effective control.

This study investigates the flow control of backward-facing step flow by a dielectric barrier discharge (DBD) plasma actuator. The DBD plasma actuator is mounted onto the edge of the backward-facing step, and is driven by burst modulation. Velocity measurements, flow visualization, and pressure measurements were carried out.The results demonstrated that the reattachment point is dependent on the burst modulation frequency. When the reattachment point is moved upstream, the vortex frequency in the downstream shear layer becomes to equal the burst modulation frequency. When the reattachment point is moved downstream, the fluctuation of the shear layer weakens, and the shear layer narrows to a width that is less than that of downstream non-control. When the duty ratio of the burst modulation drive is outside of a certain range, the effect of control is reduced. In the case that the reattachment point moves upstream, the upper limit of the duty ratio at which the control effect does not change is determined by the off-time length of burst modulation, whereas the lower limit of the duty ratio is determined by the on-time length of burst modulation. In the case that the reattachment point moves downstream, the upper limit of the duty ratio at which the control effect does not change is independent of the modulation frequency.

The surface velocity model is proposed for modelling the flow caused by a DBD plasma actuator. While numerical model presented up to now for the DBD plasma actuator, i.e. Suzen's model, needs to calibrate the five parameters that must be determined by comparison with the experimental results, the surface velocity model presented here requires calibrating three parameters only. The flow by the surface velocity model is compared with the experimental results and that of Suzen's model. When DBD plasma actuators are activated on the surface of the flat plate or on that of the circular cylinder, the induced flow appears near the electrode. And then the temporal and spatial development of the flow by the surface velocity model is consistent with the results from the experiment and the Suzen's model. The surface velocity model is very easy to use compared with the Suzen's model, and it can well simulate the induced flow caused by the plasma actuator.

Background: Instabilities on a rotating disk flow can be classified into two distinct groups, convective instability and global instability. Contrary to the convective instability, many characteristics of the global instability are left unknown despite of a lot of researches. Objective: The study investigates the characteristics of the globally unstable mode. Method: Numerical simulation is carried out by a finite difference method. The simulation code solves the full Navier-Stokes perturbation equations and the continuity equation. Results: Four cases with azimuthal domain sizes of 2π/10, 2π/70, 2π/80 and 2π/90 are compared. In all cases, a short-duration wall-normal random suction and blowing is introduced from the wall at the beginning of the computation. In the computation for the wider size 2π/10 domain, wavenumber components of 70, 80 and 90 are all found to co-exist in the flow field, with the wavenumber 80 component being much stronger than the other two components. The strength of the wavenumber 80 component is equivalent to the narrower domain case. For the other two wavenumber components of 70 and 90, the strengths in the wider domain case are much lower compared to the corresponding narrower domain cases. When the same wavenumber components are compared between the wider and narrower domain computations, no difference can be found, indicating that each wavenumber component grows by the global instability. Conclusion: The results imply that the amplitude saturation levels of wavenumber components 70 and 90 are suppressed by the wavenumber 80 component through the nonlinear effect.