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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

Power Supply

geometry, materials, …

- AC, DC, RF..?

- 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

Code Performance

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)

What physics are we interested in?

photoionization

Electrons

Positive ions

potential

Electric field

Charge

Quasi-neutral body

Sheath

Conductive channel

Strong Efield near head

PIC model provides correct electric potential evolution during streamer propagation

Y, m

X, m

X, m

X, m

0.3 ns

2.1 ns

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

PIC model provides correct electron distribution within streamer body

Y, m

X, m

- High density of electrons in streamer body
- Low density of electrons ahead of streamer head
- Almost no electrons anywhere else

Concept of variable-weight particles allows accurate and efficient streamer simulation in VORPAL

Y, m

Particle weight

X, m

- Electrons are combined in the region of high electron density (streamer body)
- Electrons are not combined (accurate resolution) around streamer head

Horizontal component of Efield for the developed streamer is the same for both cases

Set 1

Set 2

2D Ex, V/m

1D Ex, V/m

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?

- 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

- When to use PIC:
- Validate fluid models
- Resolve physics which fluid codes cannot handle

- 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

VORPAL can reproduce major physical phenomena for streamer propagation

20*log(Np)

Positive ions

potential

- Plasma is in streamer form
- Potential is quasi-uniform within streamer body
- Electric field is strong at the streamer head

Electric field

VORPAL output can later be coupled with CFD tools

Obtain spatial and temporal distribution of force and heating terms from VORPAL

Insert them as RHS into Navier-Stokes equations

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?

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
- Bodyfittedand 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

Grid resolution study / no plasma case

Schlieren Image

Horizontal component of velocity

Coarse

Medium

Fine

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

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 freeflow / 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)

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