^{1}and Subrata Roy

^{1,a)}

### Abstract

In this paper, a curved class of plasma actuator geometries is presented. The intension of this paper is to extend the versatility of a dielectric barrier discharge plasma actuator by modifying the geometry of its electrodes, so that the plasma generated body force is able to excite a broader spectrum of flow physics than plasma actuators with a more standard geometry. Two examples of flow control are demonstrated numerically. An example of this class of actuators is shown to generate boundary layer streaks, which can be used to accelerate or delay the laminar to turbulent transition process, depending on how they are applied. Simulations of a low Reynolds number airfoil are also performed using additional examples of this class of actuators, where it is shown that this plasma actuator geometry is able to introduce energy into and excite a secondary instability mode and increase unsteady kinetic energy in the boundary layer. These two cases show that this general class of curved actuators possesses an increased versatility with respect to the standard geometry actuators.

This work was partially supported by AFOSR grant FA9550-09-1-0372 monitored by Dr Douglas Smith. The authors would like to thank Dr. Miguel Visbal of the Air Force Research Laboratory for the use of the code FDL3DI. The first author would also like to thank the University of Florida's Graduate School Fellowship Award, which provided partial support for this study.

I. INTRODUCTION

II. SERPENTINE GEOMETRY DBD ACTUATORS

III. ACTUATOR BEHAVIOR UNDER QUIESCENT CONDITIONS

A. Numerical details

B. Characteristic flow features

IV. APPLICATION TO A LAMINAR BOUNDARY LAYER

A. Characteristic flow features

V. APPLICATION TO A LAMINAR SEPARATED FLOW

A. Numerical details and data collection

B. Characteristics of the baseflow around and SD7003 airfoil

C. Controlling the flow

1. Application of a standard geometry actuator

2. Application of serpentine geometry actuation

VI. CONCLUSIONS

### Key Topics

- Flow control
- 38.0
- Plasma flows
- 37.0
- Flow instabilities
- 21.0
- Laminar flows
- 19.0
- Turbulent flows
- 17.0

## Figures

(a) Schematic of DBD plasma actuator and the generated body force. (b) Linear, (c) arc, (d) rectangle, (e) comb/finger, and (f) triangle geometry serpentine actuators.

(a) Schematic of DBD plasma actuator and the generated body force. (b) Linear, (c) arc, (d) rectangle, (e) comb/finger, and (f) triangle geometry serpentine actuators.

(a) Mesh, (b) two-dimensional slice of the body force (at z = 0), and (c) top view of the geometry used to simulate the serpentine geometry plasma actuation. Every other point is shown. The black lines in (b) and (c) refer to where the body force is 1% of the maximum body force.

(a) Mesh, (b) two-dimensional slice of the body force (at z = 0), and (c) top view of the geometry used to simulate the serpentine geometry plasma actuation. Every other point is shown. The black lines in (b) and (c) refer to where the body force is 1% of the maximum body force.

(a) Velocity profiles at a location downstream of the plasma actuation for various values of Dc under quiescent conditions. (b) Values of up used to calibrate Dc .

(a) Velocity profiles at a location downstream of the plasma actuation for various values of Dc under quiescent conditions. (b) Values of up used to calibrate Dc .

Velocity fields at the ((a) and (c)) pinch point (z = 0), ((b) and (d)) spreading point (z = 0.05) of the serpentine geometry actuator operated under quiescent conditions for ((a) and (b)) simulations with a prescribed induced velocity of and ((c) and (d)) experiments performed by Durcher and Roy. 14 The experimental results have been non-dimensionalized so that the relative sizes of the actuators match.

Velocity fields at the ((a) and (c)) pinch point (z = 0), ((b) and (d)) spreading point (z = 0.05) of the serpentine geometry actuator operated under quiescent conditions for ((a) and (b)) simulations with a prescribed induced velocity of and ((c) and (d)) experiments performed by Durcher and Roy. 14 The experimental results have been non-dimensionalized so that the relative sizes of the actuators match.

Streamlines in the flow fields from the (a) simulation of a serpentine actuator and (b) experiments for a curved serpentine actuator. A black line is used to indicate the location of the actuator. Experimental data from Durscher and Roy. 14

Streamlines in the flow fields from the (a) simulation of a serpentine actuator and (b) experiments for a curved serpentine actuator. A black line is used to indicate the location of the actuator. Experimental data from Durscher and Roy. 14

Streamwise vorticity at x = 1.025 of the serpentine geometry actuator operated under quiescent conditions for simulation with a prescribed induced velocity of .

Streamwise vorticity at x = 1.025 of the serpentine geometry actuator operated under quiescent conditions for simulation with a prescribed induced velocity of .

Comparisons of the velocity field near the plasma actuator for the velocity ratio in a boundary layer flow. The (a) pinching and (b) spreading points are shown, along with the (c) streamwise vorticity at x = 1.025. Note that the x and y scales are not equal in (a) and (b).

Comparisons of the velocity field near the plasma actuator for the velocity ratio in a boundary layer flow. The (a) pinching and (b) spreading points are shown, along with the (c) streamwise vorticity at x = 1.025. Note that the x and y scales are not equal in (a) and (b).

(a) Streamtraces (with a background of the u velocity at x = 1.5) and (b) Q-criteria (colored by velocity magnitude) for the case of in a boundary layer flow. The data set is repeated twice more in the z-direction, only a single wavelength was simulated.

(a) Streamtraces (with a background of the u velocity at x = 1.5) and (b) Q-criteria (colored by velocity magnitude) for the case of in a boundary layer flow. The data set is repeated twice more in the z-direction, only a single wavelength was simulated.

Angle of the vectored jet as the velocity ratio is varied. This angle was measured as the maximum flow angle at the height of downstream of the pinching point.

Angle of the vectored jet as the velocity ratio is varied. This angle was measured as the maximum flow angle at the height of downstream of the pinching point.

Streamwise variations in the (a) velocity magnitudes and (b) streamwise vorticity at x = 1.2 for the case of . The 99% boundary layer height ( ) is marked by the thick solid line.

Streamwise variations in the (a) velocity magnitudes and (b) streamwise vorticity at x = 1.2 for the case of . The 99% boundary layer height ( ) is marked by the thick solid line.

Normalized boundary layer streak profiles based on the standard deviation of the streamwise velocity across the span of the boundary layer for (a) , (b) , (c) , and (d) .

Normalized boundary layer streak profiles based on the standard deviation of the streamwise velocity across the span of the boundary layer for (a) , (b) , (c) , and (d) .

Normalized boundary layer streak (a) velocity magnitude and (b) streamwise vortex magnitude.

Normalized boundary layer streak (a) velocity magnitude and (b) streamwise vortex magnitude.

Grid used to perform simulations around an SD7003 airfoil. Every fourth grid point is shown.

Grid used to perform simulations around an SD7003 airfoil. Every fourth grid point is shown.

(a) Instantaneous velocity magnitude and (b) streamlines of the baseline separated flow. (c) Power spectral densities of the turbulent kinetic energy for the baseline separated flow at the mid chord and near the trailing edge. (d) Turbulent kinetic energy along the surface of the airfoil for varying .

(a) Instantaneous velocity magnitude and (b) streamlines of the baseline separated flow. (c) Power spectral densities of the turbulent kinetic energy for the baseline separated flow at the mid chord and near the trailing edge. (d) Turbulent kinetic energy along the surface of the airfoil for varying .

Kinetic energy contained in Fourier modes across a number of temporal and spatial frequencies for the baseline separated flow. (a) St = 5.0 and (b) St = 10.0 effects are shown. Separation and reattachment points are marked.

Kinetic energy contained in Fourier modes across a number of temporal and spatial frequencies for the baseline separated flow. (a) St = 5.0 and (b) St = 10.0 effects are shown. Separation and reattachment points are marked.

Duty cycle applied to the plasma body force over a cycle of forcing.

Duty cycle applied to the plasma body force over a cycle of forcing.

Geometries of the actuators tested. (a) Linear. (b) Quarter serpentine. (c) Half serpentine. (d) Full serpentine.

Geometries of the actuators tested. (a) Linear. (b) Quarter serpentine. (c) Half serpentine. (d) Full serpentine.

(a) Instantaneous velocity magnitude and ((b) and (c)) Q = 100 iso-surfaces (colored by the velocity magnitude) for the linear geometry actuation as viewed from the (b) top and (c) iso-metric perspectives.

(a) Instantaneous velocity magnitude and ((b) and (c)) Q = 100 iso-surfaces (colored by the velocity magnitude) for the linear geometry actuation as viewed from the (b) top and (c) iso-metric perspectives.

(a) Power spectral densities of the turbulent kinetic energy and (b) magnitudes of the fundamental frequency (St = 5.0) modes across a number spatial frequencies for the flow actuated by the linear actuator.

(a) Power spectral densities of the turbulent kinetic energy and (b) magnitudes of the fundamental frequency (St = 5.0) modes across a number spatial frequencies for the flow actuated by the linear actuator.

((a) and (d)) Instantaneous velocity magnitude and vortical structures as viewed from the ((b) and (e)) top and ((c) and (f)) iso-metric perspectives. The vortical structures are visualized through the Q-criterion, Q = 100, and colored by the velocity magnitude for the ((a)-(c)) quarter and ((d)-(f)) full serpentine geometries.

((a) and (d)) Instantaneous velocity magnitude and vortical structures as viewed from the ((b) and (e)) top and ((c) and (f)) iso-metric perspectives. The vortical structures are visualized through the Q-criterion, Q = 100, and colored by the velocity magnitude for the ((a)-(c)) quarter and ((d)-(f)) full serpentine geometries.

Magnitude of the fundamental frequency (St = 5.0) modes across a number spatial frequencies for the quarter serpentine geometry.

Magnitude of the fundamental frequency (St = 5.0) modes across a number spatial frequencies for the quarter serpentine geometry.

Magnitude of the (a) spanwise constant (0,1) and (b) fundamental spatial (1,1) Fourier modes at the fundamental temporal frequency.

Magnitude of the (a) spanwise constant (0,1) and (b) fundamental spatial (1,1) Fourier modes at the fundamental temporal frequency.

Exponential growth rates of Fourier modes for (a) spanwise constant (0,1) and (b) fundamental spatial (1,1) Fourier modes at the fundamental temporal frequency.

Exponential growth rates of Fourier modes for (a) spanwise constant (0,1) and (b) fundamental spatial (1,1) Fourier modes at the fundamental temporal frequency.

## Tables

Dimensional and non-dimensional values used to compute the base flow.

Dimensional and non-dimensional values used to compute the base flow.

Details of the plasma actuator geometries.

Details of the plasma actuator geometries.

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