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)