Report

Aerospace Plasmas Alexandre Likhanskii, Kris Beckwith Tech-X Corporation Tech-X Workshop / ICOPS 2012, Edinburgh, UK 8-12 July, 2012 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 Aerospace Energy Plasma Processing Plasma Medicine Why does one need modeling? Applications Why does one need modeling? Applications Aerospace: DBDs …. rest Why does one need modeling? Applications Aerospace: DBDs Power Supply …. rest geometry, materials, … Why does one need modeling? Applications Aerospace: DBDs geometry, materials, … Power Supply AC, DC, RF..? …. rest 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? Complete, comprehensive plasma model requires: • 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 The model needs to include complex plasma processes • Ionization • Recombination • Attachment • Detachment • Photoionization • Detailed air chemistry? • Excitation? • Fast heating? Plasma model requirements: • 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 The model needs to resolve plasma/system spatial scales 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 106-107 grid points for just 2D The model needs to resolve plasma/system time scales Time scales: Electron drift velocity ~ 106 m/s picosecond time step due to CFL The cycle of device operation ~ ms millisecond time interval should be computed 109 time points Need to use state-of-the-art numerical techniques The model needs both to solve appropriate equations and to be computationally efficient Model Complexity Drift-diffusion approximation 2-moment model • “Easy” to implement • Best for relatively low E/n • High pressures • 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 Code Performance Kinetic approach – Particle in Cell • Detailed plasma description • non-local effects • Low to high E/n • Low to high pressures 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 potential Charge Electric field Quasi-neutral body photoionization What physics are we interested in? Sheath Conductive channel Strong Efield near head Y, m PIC model provides correct electric potential evolution during streamer propagation X, m 0.3 ns X, m 2.1 ns X, m 3.0 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 Y, m PIC model provides correct electron distribution within streamer body X, m •High density of electrons in streamer body •Low density of electrons ahead of streamer head •Almost no electrons anywhere else Particle weight Y, m Concept of variable-weight particles allows accurate and efficient streamer simulation in VORPAL X, m •Electrons are combined in the region of high electron density (streamer body) •Electrons are not combined (accurate resolution) around streamer head Perform validation study of the particle combining algorithm 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 Horizontal component of Efield for the developed streamer is the same for both cases 1D Ex, V/m 2D Ex, V/m Set 1 Set 2 3.3 ns 3.3 ns • Changes in threshold for combining macroparticles do not change results • Efield is lower than in fluid modeling VORPAL can perform 3D DBD simulations and resolve 3D filamentary structure 3D DBD simulation - Electrons Z-component of Efield, top view z z x x Why can PIC be efficient at high pressures? When to use PIC: • Efficient in parallel •Streamer resolution • Using particle combination during breakdown and splitting during plasma decay avoid overand under-resolution • Simulations from first principles, detailed physics • Fluid models are generally more efficient • Validate fluid models • Resolve physics which fluid codes cannot handle Fluid DBD model in Vorpal SpeedUp • 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 64 resolved for accurate plasma modeling 32 • Background plasma density 16 • Plasma model provides force and 8 heating terms for Navier-Stokes solver 4 2 1 1 2 4 8 16 32 Number of Processors 64 VORPAL can reproduce major physical phenomena for streamer propagation potential Positive ions 20*log(Np) Electric field • Plasma is in streamer form • Potential is quasi-uniform within streamer body • Electric field is strong at the streamer head VORPAL is quantitatively validated against experimental data DBD Property Plasma length Experimental Results (3kV, 5ns) (Princeton) ~ 2 mm 150-200 microns Plasma thickness Consumed Energy per plasma volume ~20 kJ/m3 Numerical Qualitative Results Comparison (3kV, 4ns) Result ~ 0.5 mm Fair agreement 100 microns for fluid approach Good agreement 250 microns for kinetic approach ~18 kJ/m3 Excellent agreement VORPAL output can later be coupled with CFD tools 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 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 Coarse resolution 96 x 36 dx = 2.38125 mm dymin = 198.4375 μm Medium resolution 192 x 72 dx = 1.19062 mm dymin = 99.21875 μm Fine resolution 384 x 144 dx = 0.79375 mm dymin = 49.609375 μm Grid resolution study / no plasma case Fine Medium Coarse Schlieren Image Horizontal 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: Case A (realistic) Plasma is OFF No energy deposition (base line) Case B Plasma is ON 20 mJ (per pulse) is deposited within 5ns each 1 microsecond (100% instant heat deposition) Case C (realistic) Plasma is ON 8 mJ (from DBD simulations): • 3 mJ (~35%) is deposited within 5ns each 1 microsend • 5 mJ is deposited uniformly in time between pulses Case C Plasma ON Realistic heat deposition Case B Plasma ON Instantaneous heat deposition Case A Plasma OFF Baseline Schlieren: SWBLI control with pulsed DBDs Case C Plasma ON Realistic heat deposition Case B Plasma ON Instantaneous heat deposition Case A Plasma OFF Baseline Vx: SWBLI control with pulsed DBDs 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)