Multiple actuators

The starting vortices by the plasma actuators play an important role in the flow evolution. Jukes and Choi (2013) studied how the three-dimensional starting vortex induced by plasma actuators was folded in a laminar boundary layer and compared it with the conventional vane-type vortex generator for the flow separation control application. For the skin-friction control, besides the folding effect of the starting vortices, another important factor is the interaction between two neighbour starting vortices. These two effects are studied in a laminar channel flow atRe= 3150. Based on the works on Lorentz force actuators in chapter 5, the geometry and strength of the plasma actuators are fixed at Af = 1, σ= 0.07 (non-dimensionalised byh) and

0 300 600 900 0 300 600 (a) (b) 0 300 600 900 0 300 600 (c) (d) 0 300 600 900 0 300 600 (e) (f)

Figure 6.5: Vorticity field (contour) and velocity vectors for the starting vortex at (a)(b) t∗ = 1620; (c)(d) t∗ = 2700; and (e)(f) t∗ = 3780. (a)(c)(e) are PIV data taken from (Whalley and Choi, 2012) and (b)(d)(f) are simulation result. The same contour levels are used everywhere.

λ= 45 (∆+ = 4.5). For the study in this section, the plasma actuators are aligned in the streamwise direction, and only cover a range of [1/3Lx,2/3Lx] (Lx= 32) in

the streamwise direction. The inflow of the channel is a parabolic velocity profile, and the outlet is a convection boundary with the convection velocity equal to the local mean velocity.

Figure 6.6(a) shows a close view of the starting vortex at the leading edge of a single DBD plasma actuator. The vortex-formation mechanism in a shear layer has been nicely explained by Jukes and Choi (2013), and this can be visualised by the two streamlines released from y = 0.2 (blue) and y = 0.1 (red). When the spanwise distance between two adjacent DBD plasma actuators is reduced to

s = 0.5, as shown in figure 6.6(b), there is a strong interaction between the two neighbour vortices. At the leading edge of the actuators, it forms complicated ‘W’ shaped vortices. The entrainment of the adjacent actuators inhabits the lift-up of the single starting vortex in figure 6.6(a). The upward and downward velocity by the starting vortices is much weaker, which can be observed from the streamwise velocity contour lines.

(a) (b)

Figure 6.6: Starting vortices at the leading edge of the plasma actuators with dif- ferent actuator gaps: (a) s= 3 and (b)s= 0.5. The vortex is shown by iso-surface ofλ2 =−0.001. Black contour lines show the streamwise velocity at several down- stream locations. The blue and red lines show the streamlines starting fromy= 0.2 andy = 0.1 respectively. Only one portion of the domain is shown.

The cores of the starting vortices are identified by the local minima of theλ2 field in eachyzplane, and the trajectory of the core is plotted against the streamwise location x in figure 6.7 to show the spatial evolution of the starting vortices. Jukes and Choi (2013) showed that the starting vortices for their DBD-VG1 and DBD-VG2 had a similar scaling at the initial stage,i.e.,y_∼x2/3 _andz∼x2/3_{. This is roughly} matched for the present starting vortex withs= 3, despite that the actuators are within very different streamwise shear layer. However, the evolution of the vortex core trajectory is significantly modified for s = 0.5. The starting vortex tends to move faster in both wall normal and spanwise directions, when the effect from the neighbour starting vortex becomes important. Especially when the starting vortex moves to above the neighbour actuator atx= 3, it suddenly drops to a much lower wall normal location due to the strong entrainment from the neighbour actuator, which is clearly shown in figure 6.6(b).

The effect of the spanwise actuator gaps can be more clearly seen in figure 6.8 for the transition to turbulence in a periodic channel. Here, seven different gaps

1 2 3 4 0.1 0.2 0.3 0.4 x y s= 3 s= 0.5 z 1 2 3 4 10-2 10-1 100 x (a) (b)

Figure 6.7: Spatial evolution of the starting vortex core in (a) wall normal direction and (b) spanwise direction for spanwise actuator gap s = 3 (closed circles) and

s= 0.5 (closed squares). The open circles and open squares are the data for DBD- VG1 and DBD-VG2 studied by Jukes and Choi (2013) in a laminar boundary layer, and the given scalingy _∼x2/3 _andz∼x2/3 _{are shown by the solid line in each plot.}

s = 0.5, 0.6, 0.75, 1, 1.5, 2, 3 are considered. For s _≥ 1, the flow ends at the turbulent state; while fors_≤0.75 the flow stays at the laminar state. Interestingly, an “increase-increase” stage and an “increase-decrease” stage for eachCf trajectory

curve are observed. The initial Cf increasing rate is inversely proportional to the

spanwise actuator gaps, because smallersmeans more starting vortices are created to generate stronger upward and downward fluid motion. If the interaction of the neighbour starting vortices is weak (s_≥1), the flow transits to turbulence quickly due to the strong disturbance growth from each individual vortex roller; while if this interaction is strong (s_≤0.75), the behaviour of the single starting vortex can be inhibited (figure 6.6(b)), resulting in the return of the flow to the laminar state. Therefore, in order to reduce the skin-friction using DBD plasma actuators, the spanwise actuator gapsshould be kept as small as possible to weaken the starting vortices. This will be confirmed in the following sections.