Study of the Wake of a Circular Cylinder under Spatially and Temporally Modulated Plasma Actuation

Abstract

The wake of a circular cylinder was forced with a temporally-modulated, spatiallysegmented dielectric barrier discharge (DBD) plasma actuator. The buried electrode was located at only certain spanwise locations along the cylinder such that spatially-modulated plasma was created. Along with this, the supply signal was amplitude-modulated with a square wave of twice the vortex shedding frequency. It was found that significant changes in wake properties occurred based on the modulation frequency and the power of actuation. When high-power, modulated forcing was employed with the segmented actuator, vortex shedding was significantly attenuated. A clear difference in the most prominent frequency peak was observed in the spectra between locations on the cylinder where plasma formed and where it did not. In the near-wake of the cylinder, the sub-harmonic mode was found to be stronger behind the non-plasma-forming region compared to the plasma-forming region. The high-power, modulated forcing also resulted in less drag compared to the unforced case as calculated by numerically integrating the velocity profile at a streamwise distance of x/d=40, where d is the cylinder diameter. In the case of low-power, modulated forcing, the unsteadiness in the wake increased. The unsteadiness was caused by sudden attenuation of the shedding peak caused by the emergence of a secondary peak in the spectra. The lowpower, modulated forcing also increased the velocity defect and consequently resulted in higher drag. The performance of the segmented actuator was compared with a straight actuator where the buried electrode covered the whole span of the cylinder. It was found that for the same induced velocity, a 'W'-shaped velocity profile was obtained in the cylinder wake with a straight actuator and modulated forcing at both low and high power. Modulated forcing with the straight actuator increased the drag compared to the unforced case. Nomenclature a = limits of integration in the y-direction C d = section drag coefficient d = cylinder diameter f = frequency f 0 = vortex shedding frequency f m = modulation frequency L = length along the actuator (spanwise direction) Re = Reynolds number t = time u = fluctuating component of U u f = bandpass filtered fluctuating component of U with center of the band at frequency f U = streamwise velocity component U  = freestream velocity U c = centerline velocity U j = plasma actuator jet velocity 2 U = mean of streamwise velocity component v = fluctuating component of V v f = bandpass filtered fluctuating component of V with center of the band at frequency f V = transverse velocity component V = mean of transverse velocity component V pp = peak-to-peak voltage x = streamwise direction y = transverse direction z = spanwise direction  = spanwise wavelength of actuator