^{1}and Koji Fukagata

^{1,a)}

### Abstract

Two-dimensional numerical simulation of ion transport and flow around a single dielectric barrier discharge plasma actuator (PA) is performed. Spatial distributions of ions and electrons as well as their time evolution are obtained by solving the transport equations of monovalent positive ions, monovalent negative ions, and electrons. Voltage and frequency of the driving alternating-current signal are assumed to be 8 kV and 5 kHz, respectively. Special focus is laid upon the effect of voltage gradient dV/dt on the magnitude of the body force. The validity of steady force models often used in flow simulation is also examined. The simulation results show that the magnitude of the body force induced by the PA increases as the voltage gradient dV/dt increases and its increase rate becomes milder at higher voltage. The mechanism of body force generation is explained from the time evolution of number density fields of ions and electrons. A comparison between flow simulations using a time-resolved body force and its time-averaged counterpart demonstrates that the time-averaged model gives sufficiently accurate results when the time scale of the flow is more than 30 times greater than that of the PA.

We are grateful to Dr. Shinnosuke Obi (Keio University) and Dr. Takehiko Segawa (AIST) for valuable comments, Dr. Simon Illingworth (The University of Melbourne) for advice on language improvement, and Ms. Arisa Chuma (Keio University) for assistance on artwork. This work was supported through Keio Gijuku Academic Development Funds.

I. INTRODUCTION

II. NUMERICAL PROCEDURE

A. Numerical simulation of a plasma actuator

B. Numerical simulation of fluid flow

III. RESULTS AND DISCUSSION

A. Body force field induced by a plasma actuator

B. Fluid velocity field induced by a plasma actuator

IV. CONCLUSIONS

### Key Topics

- Electrodes
- 34.0
- Electric fields
- 10.0
- Plasma flows
- 10.0
- Flow simulations
- 9.0
- Photon density
- 8.0

## Figures

Structure of a SDBD-PA.

Structure of a SDBD-PA.

Photograph of the plasma discharge. 2

Difference in dV/dt among different sinusoidal signals.

Difference in dV/dt among different sinusoidal signals.

Computational domain used in the simulation of ion transport.

Computational domain used in the simulation of ion transport.

Voltage signals V(t) applied over one period T (see Table I for descriptions of cases 1-6).

Computational domain for flow simulation.

Computational domain for flow simulation.

Streamlines and velocity profile of cavity flow at Re = 1000.

Streamlines and velocity profile of cavity flow at Re = 1000.

Instantaneous snapshots at t/T = 0.10: (a) voltage signal (marker indicates t/T = 0.10); (b) body force vectors ; (c) profiles of body force components and at different locations; (d) number density distribution .

Instantaneous snapshots at t/T = 0.10: (a) voltage signal (marker indicates t/T = 0.10); (b) body force vectors ; (c) profiles of body force components and at different locations; (d) number density distribution .

Instantaneous snapshots at t/T = 0.40: (a) voltage signal (marker indicates t/T = 0.40); (b) body force vector ; (c) profiles of body force components and at different locations; (d) number density distribution .

Instantaneous snapshots at t/T = 0.40: (a) voltage signal (marker indicates t/T = 0.40); (b) body force vector ; (c) profiles of body force components and at different locations; (d) number density distribution .

Instantaneous snapshots at t/T = 0.80: (a) voltage signal (marker indicates t/T = 0.80); (b) body force vector ; (c) profiles of body force components and at different locations; (d) number density distribution .

Instantaneous snapshots at t/T = 0.80: (a) voltage signal (marker indicates t/T = 0.80); (b) body force vector ; (c) profiles of body force components and at different locations; (d) number density distribution .

Time-averaged body force field in case 3 (dV/dt = 320 V/μs).

Time-averaged body force field in case 3 (dV/dt = 320 V/μs).

Domain-averaged body force, Fx , as functions of time (see Table I for descriptions of cases 1-6).

Domain-averaged body force, Fx , as functions of time (see Table I for descriptions of cases 1-6).

Relationship between dV/dt and time-averaged domain-averaged body force (per unit volume), .

Relationship between dV/dt and time-averaged domain-averaged body force (per unit volume), .

Typical instantaneous streamlines and location of check points.

Typical instantaneous streamlines and location of check points.

Time trace of U 1 obtained with the time-averaged model at f = 5000 Hz.

Time trace of U 1 obtained with the time-averaged model at f = 5000 Hz.

Comparison of U 1 between the time-averaged model and the time-resolved model at f = 5000 Hz: (b) is a zoom-up view in the time period circled in (a).

Comparison of U 1 between the time-averaged model and the time-resolved model at f = 5000 Hz: (b) is a zoom-up view in the time period circled in (a).

Comparison of U 3 between the time-averaged model and the time-resolved model at f = 5000 Hz: (b) is a zoom-up view in the time period circled in (a).

Comparison of U 3 between the time-averaged model and the time-resolved model at f = 5000 Hz: (b) is a zoom-up view in the time period circled in (a).

Comparisons of PSD between the time-averaged model and the time-resolved model at f = 5000 Hz: (a) U 1; (b) U 3.

Comparisons of PSD between the time-averaged model and the time-resolved model at f = 5000 Hz: (a) U 1; (b) U 3.

Vorticity distributions obtained in numerical experiments assuming different driving frequencies f: (a) f = 50 Hz; (b) f = 100 Hz; (c) f = 200 Hz; (d)f = 500 Hz; (e) f = 5000 Hz; (f) the time-averaged model.

Vorticity distributions obtained in numerical experiments assuming different driving frequencies f: (a) f = 50 Hz; (b) f = 100 Hz; (c) f = 200 Hz; (d)f = 500 Hz; (e) f = 5000 Hz; (f) the time-averaged model.

Comparisons of PSD of wall-normal velocity at check point 5 (V 5) between the time-averaged model and the time-resolved model: (a) f = 200 Hz; (b)f = 500 Hz.

Comparisons of PSD of wall-normal velocity at check point 5 (V 5) between the time-averaged model and the time-resolved model: (a) f = 200 Hz; (b)f = 500 Hz.

## Tables

Test cases.

Test cases.

Constants (for air) used in the present simulations.

Constants (for air) used in the present simulations.

Location of check point.

Location of check point.

Ratio of powers at the driving frequency (f = 5000 Hz) and the flow oscillation frequency (f = 15 Hz), B/A, and relative difference of powers at f = 15 Hz between the time-averaged and time-resolved models, , at different check points.

Ratio of powers at the driving frequency (f = 5000 Hz) and the flow oscillation frequency (f = 15 Hz), B/A, and relative difference of powers at f = 15 Hz between the time-averaged and time-resolved models, , at different check points.

Ratio of powers at the driving frequency (f = 200 Hz) and the flow oscillation frequency (f = 15 Hz), B/A, and relative difference of powers at f = 15 Hz between the time-averaged and time-resolved models, , at different check points.

Ratio of powers at the driving frequency (f = 200 Hz) and the flow oscillation frequency (f = 15 Hz), B/A, and relative difference of powers at f = 15 Hz between the time-averaged and time-resolved models, , at different check points.

Ratio of powers at the driving frequency (f = 500 Hz) and the flow oscillation frequency (f = 15 Hz), B/A, and relative difference of powers at f = 15 Hz between the time-averaged and time-resolved models, , at different check points.

Ratio of powers at the driving frequency (f = 500 Hz) and the flow oscillation frequency (f = 15 Hz), B/A, and relative difference of powers at f = 15 Hz between the time-averaged and time-resolved models, , at different check points.

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