Aerospace Plasmas Tech-X Workshop / ICOPS 2012, Edinburgh, UK 8-12 July, 2012 Alexandre Likhanskii, Kris Beckwith Tech-X Corporation

DBD Background Stall control for up to M=0.4 using AC driven DBDs Stall control for transonic flow using ns-pulse driven DBDs Bow shock control using ns-pulse driven DBDs SWBLI control using LAFPA

Atmospheric pressure plasmas have a broad range of industrial applications AerospaceEnergy Plasma Processing Plasma Medicine

Applications Why does one need modeling?

Aerospace: DBDs Applications …. rest Why does one need modeling?

Aerospace: DBDs Applications …. rest Power Supplygeometry, materials, … Why does one need modeling?

Aerospace: DBDs Applications …. rest Power Supplygeometry, materials, … Pulser What is the optimum pulse duration? What is the rise time? What is the repetition rate? What is the power consumption? How heavy is it? AC, DC, RF..? Why does one need modeling?

Solve for charged species motion coupled with Poisson Solver Include all relevant plasma processes Resolve all relevant spatial and time scales Use appropriate physical model for plasma description at particular conditions Couple with CFD code Complete, comprehensive plasma model requires:

Ionization Recombination Attachment Detachment Photoionization Detailed air chemistry? Excitation? Fast heating? The model needs to include complex plasma processes

Solve for charged species motion coupled with Poisson Solver Include all relevant plasma processes Resolve all relevant spatial and time scales Use appropriate physical model for plasma description at particular conditions Couple with CFD code Plasma model requirements:

Spatial scales:  Plasma sheath size is ~ 10 microns micron grid size  Plasma length is several millimeters millimeter numerical domain for plasma generation  Surface charge accumulation centimeter numerical domain for surface charging grid points for just 2D The model needs to resolve plasma/system spatial scales

Time scales:  Electron drift velocity ~ 10 6 m/s picosecond time step due to CFL  The cycle of device operation ~ ms millisecond time interval should be computed 10 9 time points Need to use state-of-the-art numerical techniques The model needs to resolve plasma/system time scales

Drift-diffusion approximation “Easy” to implement Best for relatively low E/n High pressures 2-moment model Drift-diffusion + electron energy equation Low to moderate E/n High pressures 5-moment model Momentum and energy equations Low to moderate E/n Low to high pressures Kinetic approach – Particle in Cell Detailed plasma description non-local effects Low to high E/n Low to high pressures Model Complexity Code Performance The model needs both to solve appropriate equations and to be computationally efficient

Options / Approaches Non-uniform (unnecessary refinement) or adaptive grids (difficult to make parallel) Variable time steps (validate physical assumptions) Implicit methods (stable, but require validation of grid size and time step choices) High-performance clusters (additional investments)

Electrons Positive ions Charge photoionization potential Electric field What physics are we interested in? Quasi-neutral bodySheathConductive channelStrong Efield near head

0.3 ns2.1 ns3.0 ns Electric potential evolution represents classical streamer propagation -> conductive plasma carries the potential of exposed electrode Streamer is higher and thicker than in the fluid models PIC model provides correct electric potential evolution during streamer propagation X, m Y, m

High density of electrons in streamer body Low density of electrons ahead of streamer head Almost no electrons anywhere else PIC model provides correct electron distribution within streamer body Y, m X, m

Electrons are combined in the region of high electron density (streamer body) Electrons are not combined (accurate resolution) around streamer head Concept of variable-weight particles allows accurate and efficient streamer simulation in VORPAL Y, m Particle weight X, m

Set 1 Grid size: 0.5x0.5 microns Threshold for combining macroparticles is 3 Set 2 Grid size: 0.5x0.5 microns Threshold for combining macroparticles is 10 Perform validation study of the particle combining algorithm

3.3 ns Changes in threshold for combining macroparticles do not change results Efield is lower than in fluid modeling Horizontal component of Efield for the developed streamer is the same for both cases 2D Ex, V/m Set 1Set 2 1D Ex, V/m

x z 3D DBD simulation - ElectronsZ-component of Efield, top view z x VORPAL can perform 3D DBD simulations and resolve 3D filamentary structure

Efficient in parallel Streamer resolution Using particle combination during breakdown and splitting during plasma decay avoid over- and under-resolution Simulations from first principles, detailed physics Fluid models are generally more efficient Why can PIC be efficient at high pressures? When to use PIC: Validate fluid models Resolve physics which fluid codes cannot handle

Fluid DBD model in Vorpal Time-dependent plasma dynamics in drift-diffusion approximation coupled with 2D Poisson solver for electric potential distribution Air: neutrals, electrons, positive and negative ions Electron temperature, ionization, recombination, attachment, detachment and transport parameters: functions of E/N Proper boundary conditions (incl. charge build-up on dielectric surface, surface recombination and secondary electron emission) Subnanosecond time scales and micron geometrical scales are properly resolved for accurate plasma modeling Background plasma density Plasma model provides force and heating terms for Navier-Stokes solver

Positive ions potential Electric field 20*log(Np) VORPAL can reproduce major physical phenomena for streamer propagation Plasma is in streamer form Potential is quasi-uniform within streamer body Electric field is strong at the streamer head

DBD Property Experimental Results (3kV, 5ns) (Princeton) Numerical Results (3kV, 4ns) Qualitative Comparison Result Plasma length~ 2 mm~ 0.5 mmFair agreement Plasma thickness microns  100 microns for fluid approach  250 microns for kinetic approach Good agreement Consumed Energy per plasma volume ~20 kJ/m 3 ~18 kJ/m 3 Excellent agreement VORPAL is quantitatively validated against experimental data

1)Obtain spatial and temporal distribution of force and heating terms from VORPAL 2)Insert them as RHS into Navier-Stokes equations 3)Study DBD-flow interaction VORPAL output can later be coupled with CFD tools airfoil Example of flow separation simulation in Nautilus, Tech-X’s CFD/MHD code on unstructured meshes

Application of DBDs to Shock-Wave Boundary Layer Interaction problem Control using snow plow arcs by momentum transfer (Princeton) Control using LAFPLA by heat deposition (Ohio State) Can we control SWBLI using pulsed DBD?

Proposed experimental setup at Princeton (M=3 wind tunnel)

What can modeling do? VORPAL has an experimentally validated capability to compute heat deposition by high-V ns pulses Need an accurate CFD tool to compute SWBLI

Fluid code Nautilus General purpose fluid plasma modeling code Supports shock capturing methods for MHD, Hall MHD, Two-Fluid plasma, Navier Stokes and Maxwell’s equations Bodyfitted and unstructured grids in 1, 2 and 3 dimensions Ability to model the plasma device as part of a circuit Massively parallel and has been run on up to 4000 processors on NERSC facilities. Recent applications of Nautilus have included modeling merging plasma jets, laboratory accretion disk experiments, weakly ionized hypersonic flow modeling, magnetic nozzles and capillary discharges. Multi-platform tool: Windows, Mac and Linux

Models for SWBLI (similar to Shneider’s model) Dimensionally unsplit MUSCL-Hancock integrator (``Van-Leer'') using second order spatial reconstruction in the primitive variables Prandtl-Boussinesq turbulence model Super time stepping method to use hyperbolic time step for CFD simulations Compute steady-state solution for SWBLI without DBD Obtain gas parameters in BL for DBD model in Vorpal Compute pulsed DBD heat deposition in Vorpal Use Vorpal data as a heat source for Nautilus CFD simulations

Numerical Grid

Grid resolution study / no plasma case Coarse Medium Fine Schlieren ImageHorizontal component of velocity

DBD simulation for the boundary layer Applied Votage :7kV, 5ns pulse Numerical domain: 2cm x 1mm Grid size: 2x2 microns Running on 64 core Typical run time: ~ ½ - 1 day Output: streamer dimensions: ~1cm x 200 microns, propagating ~500 microns above the surface Output: temporal and spatial distribution of instant and integrated energy release Output: total energy (E*J) release = 8mJ/m

DBD placement

Simulation cases – 1MHz pulses:

Schlieren: SWBLI control with pulsed DBDs Case A Plasma OFF Baseline Case B Plasma ON Instantaneous heat deposition Case C Plasma ON Realistic heat deposition

Vx: SWBLI control with pulsed DBDs Case A Plasma OFF Baseline Case B Plasma ON Instantaneous heat deposition Case C Plasma ON Realistic heat deposition

Observations: Shock wave moves upstream (similar observation to Samimy’s experiments)variables Additional mixing in boundary layer Main influence by upstream DBD - good placement is at the free flow / boundary layer interface to induce mixing DBDs deep inside BL do almost nothing, but heat the BL Overall, DBD can effect SWBLI but more optimization studies are necessary - mainly DBD placement and pulse repetition rate

Acknowledgements: NASA Glenn Research Center (Dr. David Ashpis) NASA Langley Research Center (Dr. Fang-Jenq Chen) Wright-Patterson AFRL (Dr. Jon Poggie)