Three-dimensional plasma actuation for faster transition to turbulence

Abstract

We demonstrate that a three-dimensional non-linear plasma actuation method creates secondary instabilities by forming lambda vortices for a spatially developing turbulent boundary layer flow over a flat plate. Both bypass transition and controlled transition processes are numerically investigated using wall resolved modal discontinuous Galerkin based implicit large eddy simulation. The largest momentum thickness based Reynolds numbers   Re  tested are 1250 and 1100 for the bypass transition and the controlled transition, respectively. The three-dimensional actuation method is based on a square serpentine plasma actuator [1]. The transition is achieved via oblique wave transition by perturbing the flow at a frequency of 1 kHz with amplitude of 10% of the freestream velocity. Although the flow is perturbed at a single frequency, the instabilities arising due to the nonlinear interaction between the consecutive lambda vortices, creates subharmonic lambda vortices (half of the fundamental frequency), which finally break down into fully turbulent flow. These interactions have been thoroughly studied and discussed. Since the actuation creates oblique wave transition it will allow faster transition compared to the standard secondary instability mechanism with similar disturbance amplitude reducing the amount of energy input required for flow control.

Effect of plasma actuator control parameters on a transitional flow

“…The current study numerically investigates the impact of geometry, frequency, and amplitude of plasma actuation as a tripping device on a zero-pressure gradient laminar boundary layer flow over a flat plate by approximating the actuator as a distributed forcing function. This study provides an extension to the previous work [13] where a square serpentine actuator was numerically investigated to understand the transition mechanism. A wall resolved implicit large eddy simulation (ILES) is conducted to investigate the effect of plasma actuation as a tripping mechanism to generate fully developed turbulent flow field.…”

“…In figure 13 it can be seen that the quasi-streamwise vortical structures for γ = 0.05 decay in size and strength, downstream of the actuator, compared to the γ = 0.1 and 0.14 cases. The lambda shaped structures for the γ = 0.05 case do not create the subharmonic structures [13] (appearing in between two lambda structures) resulting in a longer transitional region. The wall pressure contours become almost 2D in nature after Re x ≈ 6 × 10 5 for γ = 0.05.…”

“…However, the linear actuator has an order of magnitude lower growth parameter. This is due to the formation of lifted lambda structures [13] generated by the serpentine and spanwise actuators which causes faster growth [29] in comparison to the 2D structures generated by the linear actuator. The growth of the fluctuations changes slope at Re x ≈ 6 × 10 5 for the square and spanwise actuator and at Re x ≈ 7 × 10 5 for the circular actuator due to the onset of highly nonlinear structures with higher spanwise wavenumber.…”

“…Depending on the input signal waveform or geometry of the electrodes, all SDBD actuators can be categorized as standard linear SDBD actuators [3,4], nanosecond pulsed discharge (NPD) actuators [5,6], sliding discharge actuators [7,8], serpentine plasma actuator [9][10][11][12][13][14] and plasma synthetic jet actuators [15,16]. Numerical and experimental studies have shown SDBD plasma actuators can be used to either suppress [17][18][19][20] or enhance [21,22] the growth of Tollmien-Schlichting (TS) waves and thereby delaying or advancing the transition to turbulence.…”

“…Schematic of the different electrode geometries and electrical configuration of SDBD plasma actuator. (a) and (e) Standard linear, (b) and (f) circular serpentine, (c) and (g) spanwise array, and (d) and (f) square serpentine SDBD actuator designs based on the shape of the line of actuation[13] (continuous black solid line). The arrows indicate the actuator forcing direction which is normal to the line of actuation.…”