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**Order of Magnitude Improvement of SDBD Actuator Effect**

T. Corke, F. Thomas, D. Orlov, M. Iqbal, A. Kozlov, H. Othman, D. Shatzman Center for Flow Physics and Control Aerospace and Mechanical Engineering University of Notre Dame Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Questions: How do we improve the performance of SDBD plasma actuators?**

What are the governing properties? What is the ultimate performance limit? Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Approach: Develop space-time model for ionization in SDBD operation.**

Include amplitude and frequency effects. Not including maximum limits. Compare to experiments. Perform experiments that investigate limiting conditions on SDBD design and operation parameters. Develop a theory to be included in space-time model. Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**SDBD Actuators: What we know**

Three time scales: Micro discharges (nsec) a.c. period (.1ms) Fluid response (10ms) Ionization space-time dependent. Static models give wrong results (e.g. fb~V2). Temporal/space-uniform models give correct V-dependence (fb~V7/2), need spatial weighting Space-time models give correct V, frequency and space dependence (Orlov, 2006). Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Steps to model actuator in flow**

Space-time electric potential, Space-time body force Flow solver with body force added Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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Space-time model Physical space over the encapsulated electrode is divided into N parallel networks. Each parallel network consists of air capacitor, dielectric capacitor, plasma resistive elements and zenor diodes. Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Model circuit elements**

air capacitor dielectric capacitor Voltage on the dielectric surface in the n-th sub-circuit Plasma current Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Model Time Series Vn (t) Ipn (t) t/Ta.c. t/Ta.c. 5 1 5 1 Nov. 8, 2006**

AF Academy Workshop on Plasma Actuators

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**Model Space-time Characteristics**

Experiment Illumination Model Ip(t) dxp/dt (xp)max Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Plasma Propagation Characteristics**

Effect of Vapp dxp/dt vs Vapp (xp)max vs Vapp Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Plasma Propagation Characteristics**

Effect of fa.c. dxp/dt vs fa.c. (xp)max vs fa.c. Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Numerical solution for (x,y,t)**

Model provides time-dependent B.C. for Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Body Force, fb(x,t) Y Normalized fb(x,t) t/Ta.c.=0.2 t/Ta.c.=0.7**

Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Frequency Dependence of fb & Wp**

Impact: Optimum frequency for body force. Depends on actuator capacitance. Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**What limits maximum body force?**

SDBD Plasma actuator is voltage driven, fb~V7/2. Not current driven like voice-coil type actuators. For fixed power (I·V), one needs to limit current to maximize voltage. What governs maximum achievable voltage for fixed power? Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Maximum Voltage Optimization**

Investigated different parameters on thrust produced by actuator Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Order of Magnitude Improvement**

Imax Imax Material Quartz 3.8 Kapton 3.4 Teflon 2.0 Imax Imax Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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Premise The maximum voltage at fixed power is limited by local electric field exceeding breakdown of air. Thicker dielectrics and/or lower dielectric constants reduce capacitance of actuator and reduce concentration of electric field lines. Other parameters? Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Effect of frequency on Vmax**

1kHz 0.25in. quartz glass 2kHz Vmax(f) 4kHz 8kHz Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Effect of dielectric thickness on Vmax**

quartz glass; 1,2,4,8kHz Tmax ~ Vmax fa.c. ~ (t/)d Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Tmax Efficiency 0.25in. quartz glass Nov. 8, 2006 AF Academy Workshop**

on Plasma Actuators

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Answers to Questions: To improve the performance of SDBD plasma actuators? Maximize V for fixed power. Minimize I by preventing formation of strong plasma filaments. Governing properties? Dielectric design (t & ) and a.c. frequency. Ultimate performance limit? Maximum local E-field for air breakdown? Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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**Further Improvements: Additive Effect**

Nov. 8, 2006 AF Academy Workshop on Plasma Actuators

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