Circular Cylinder Drag Reduction By Three-Electrode Plasma Symmetric Forcing

Different implementations of plasma discharge devices: (a) sliding discharge, (b) DBD, (c) serial DBD, and (d) three electrode discharge

Scheme of the region analyzed with PIV

(a) Schematic and detail of the electrohydrodynamic (EHD) actuator, electric circuit with the electrodes flush-mounted and (b) typical burst input waveform applied to the electrodes

Electrical power consumption for TED actuator (squares). Dotted line represents DBD actuator consumption.

(a) Wake velocity profiles for nonforced and forced flow at x = 4 and (b) normalized momentum flux produced by TED actuators

Contour levels for the time-averaged y-component of pressure gradient 〈∂p/∂y〉 for nonforced flow (a) and under TED VDC= −11 kV, f+=1 (b). Dashed lines show control volume boundaries.

Drag coefficient estimation for the unforced case (solid line), DBD and TED enhanced through stationary forcing mode. Electrode A DC voltage is decreased from 0 to −11 kV so nondimensional momentum Cμ increases monotonically with respect to V_DC.

Drag coefficient estimation for nonforced case, DBD and TED enhanced (−11 kV)) through harmonic forcing at DC = 50%. Forcing frequencies f+=ff/f0 are from 0.2 up to 5.0, measurements have been refined around the minimum at f+=1.

(a) Electric power P_TED, drag dissipated power P_D and total lost power PTED+PD as duty cycle D_C rises. Values are normalized with the power associated to drag forces when no actuation is imposed PD0. A maximum 27% net energy saving can be achieved for a 19% duty cycle, still corresponding to a 40% drag reduction. (b) Energy efficiency versus duty cycle for TED actuation. In both figures Re = 5500 and f+=1.

(a) Mean flow streamlines and velocity modulus contours for Re = 5500, (b) DBD forcing at f+=1, DC=50%, and (c) TED forcing at f+=1, DC=50%

Time-averaged velocity moments profiles: (a) 〈ux〉, (b) 〈u′y2〉1/2, (c) 〈u′x2〉1/2, and (d) 〈u′xu′y〉. The profiles are taken at positions x/D∈[1,2,3,4,5].

Global mode shape modification under TED actuation for different forcing frequencies. The black thick line stands for global mode of the nonforced case.

For the nonforced flow, clusters portrait the vortex shedding dynamics from vorticity contour lines (solid for positive values and dashed for negative values) within one period. The number of snapshots involved is shown in each subplot; initial clusters are placed after the last one to complete the loop.

(a) Phase portrait from singular value decomposition of the vorticity clusters, three modes are enough to describe the dynamics of vortex shedding. A limit cycle attractor is emphasized by a minimum distance plane to the data, and a close curve that connects the centroids. (b) The result is clearer after a 2D projection onto the plane.

Eleven clusters portrait the vortex shedding dynamics from vorticity contour lines within one period. The number of snapshots involved is shown in each subplot; initial clusters are placed after the last one to complete a loop. We observe two distinct regimes which correspond with BvK-like vortex shedding and two vortex sheets produced by DBD momentum injection.

Idem Fig. 15 for TED momentum injection

Phase portrait from singular value decomposition of the vorticity clusters, three modes are enough to describe the dynamics of vortex shedding modified by actuation. Regimes identified in Fig. 16 correspond to the outer (BvK-like regime) or inner (TED momentum injection) phase space regions.