1. Time-Dependent Dielectric Barrier Discharge Plasma Actuator Modeling Ben Mertz, Thomas Corke Center for Flow Physics and Control University of Notre Dame, Notre Dame, IN

2. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Objective  Further develop simulations for Single-Dielectric Barrier Discharge (SDBD) Plasma Actuators for use in Computer Flow Simulations  Extend Orlov (Ph.D., 2006) approach for actuator body force to include arbitrary (curved) shapes  Develop single and dual potential models  Compare various dynamic models Leading-edge Profiles Turbine Blade Shapes

3. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Empirical vs. First Principle Models  First Principle Models  Accurately describes plasma discharge processes  Computationally intensive Limited to single streamer Simplified chemistry  Gibalov and Pietsch (2008), Golubovskii et al. (2002), Kozlov et al. (2001), Madani et al. (2003), and others  Empirical Models  Computationally efficient  Physics not directly modelled  Shyy et al. (2002), Singh and Roy (2008)‏ Do not model spatial-temporal dynamics accurately

4. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Models Considered  Orlov (2006) – Space-time lumped circuit element model  Voltage BC (One Phi w/ Voltage BC)‏  Negative of Voltage BC (One Phi w/ Negative Voltage BC)‏  Current used to calculate BC  Based on total plasma height (One Phi w/ Current-H BC)‏  Based on fraction of plasma height (One Phi w/ Current-h BC)‏  Suzen et al. (2005) – Two-potential model  Current used to calculate BC for charge density (Lemire and Vo, 2008)‏  Two Phi w/ Current-H BC

5. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Background: Plasma Actuators exposed electrode dielectric AC voltage source covered electrode substrate  High voltage AC causes air to ionize (plasma).  Ionized air in presence of electric field results in body force that acts on neutral air.  Body force is mechanism of flow control. Ref: Prog. in Aero. Sci., 43, 2007 The SDBD is stable at atmospheric pressure because it is self-limiting due to charge accumulation on the dielectric surface.

6. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Physics and Modelling - (Single Potential Model) ‏ D - Electric Induction Maxwell’s equationBoltzmann relation  (x,t) Electro-static body force in a charged Fluid:

7. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Physics and Modelling - (Dual Potential Model) ‏ Potential associated with external electric field Potential associated with charged particles solution of equation - electric potential  solution of equation - electric potential ɸ

8. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Computational Domains Computational domain with electrode arrangement for single potential model Computational domain with electrode arrangement for dual potential model Ref: AIAA-2005-4633

9. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Lumped Circuit Model Electric circuit with N-sub-circuits (N=100)‏ exposed electrode dielectric AC voltage source covered electrode substrate Ref: AIAA-2006-1206

10. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Lumped Circuit Model Voltage on the dielectric surface in the n-th sub-circuit Plasma current air capacitor dielectric capacitor  Light Emission

11. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Light Emission Results Ref: AIAA-2006-1206 Light emission measurements Current from lumped circuit model

12. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Light Emission Results (cont.) ‏ Ref: AIAA-2006-1206

13. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Time-Averaged Force Vectors One Phi w/ Voltage BC

14. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Time-Averaged Force Vectors One Phi w/ Negative Voltage BC

15. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Time-Averaged Force Vectors One Phi w/ Current-H BC

16. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Time-Averaged Force Vectors One Phi w/ Current-h BC

17. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Time-Averaged Force Vectors Two Phi w/ Current-H BC

18. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Force Scaling with Voltage

19. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Force Scaling with Voltage (cont.) ‏

20. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL “Starting” vortex after the impulsive start of the actuator Simulation (One Phi w/ neg volt BC)‏ experiment (Post, 2004)‏ t=10 ms t=5 ms t=2 ms t=12 ms t=35 ms t=60 ms t=20 ms t=50 ms

21. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Application: Flow over a Cylinder  4 in Diameter Cylinder  4 m/s Free-stream Speed (Re ≈ 40,000)‏  4 actuators (±90° and ±135°)‏  One Phi w/ Negative Voltage BC  V = 23 kV p-p,, f = 10 kHz, t = 2.5 mm, Glass (ε = 3.7)‏  Performed experimentally by Thomas et al. (2008)‏

22. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Stream Functions Actuators Off Actuators On

23. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Summary  Comparison of different dynamic models  Only One Phi w/ Negative Voltage BC matches all experimental evidence  Applied to shedding cylinder  Able to eliminate shedding  Validates model  Future work  Apply to other applications  Investigate time-dependent force in CFD code

24. Mertz and Corke: 47 th AIAA Aerospace Sciences Meeting, January 2009, Orlando, FL Questions?