Direct Simulation Monte Carlo: A Particle Method for Nonequilibrium Gas Flows
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Direct Simulation Monte Carlo:A Particle Method for Nonequilibrium Gas Flows
Iain D. BoydDepartment of Aerospace Engineering
University of MichiganAnn Arbor, MI 48109
Support Provided By:MSI, AFOSR, DARPA, NASA
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Overview
• Physical characteristics of nonequilibrium gas flow.
• Direct simulation Monte Carlo (DSMC) method.
• The MONACO DSMC code:
– data structure;
– scalar/parallel optimization.
• Illustrative DSMC applications:
– hypersonic aerothermodynamics;
– materials processing;
– spacecraft propulsion.
• Summary and future directions.
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Modeling Considerations
• Physical characteristics of nonequilibrium gas systems:– low density and/or small length scales;– high altitude hypersonics (n=1020 m-3, L=1 m);– space propulsion (n=1018 m-3, L=1 cm);– micro-fluidics (n=1025 m-3, L=1 ).
• Gas dynamics:– rarefied flow (high Knudsen number);– collisions still important;– continuum equations physically inaccurate.
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Characterization ofNonequilibrium Gas Flows
Kn 0.01 0.1 10
continuum slip transitional free-molecular
Euler
Navier-StokesBoltzmann EquationControl
equations:
Flow Regimes:
Collisionless Boltzmann EqnBurnett
DSMC
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Direct Simulation Monte Carlo
• Particle method for nonequilibrium gas flows:– developed by Bird (1960’s);– particles move/collide in physical space;– particles possess microscopic properties,
e.g. u’ (thermal velocity);– cell size x ~ , time step t ~ =1/;– collisions handled statistically (not MD);– ideal for supersonic/hypersonic flows;– may be combined with other methods
(CFD, PIC, MD) for complex systems.
{u’, v’, w’x, y, zm, erot, evib
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Direct Simulation Monte Carlo
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The DSMC Algorithm
• MOVE:– translate particles x = u t;– apply boundary conditions (walls, sources, sinks).
• SORT:– generate list of particles in each cell.
• COLLIDE:– statistically determine particles that collide in each cell;– apply collision dynamics.
• SAMPLE:– update sums of various particle properties in each cell.
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Current DSMC-Related Projects
• Hypersonics:– vehicle aerodynamics (NASA-URETI);– hybrid particle-continuum method (AFOSR);– TOMEX flight experiment (Aerospace Corp).
• Space propulsion:– NEXT ion thruster, FEEP (NASA);– Hall thrusters (DOE, NASA);– micro-ablation thrusters (AFOSR);– two-phase plume flows (AFRL).
• Micro-scale flows:– low-speed rarefied flow (DOE).
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The DSMC Code MONACO
• MONACO: a general purpose 2D/3D DSMC code.
• Physical models:
– Variable Soft Sphere (Koura & Matsumoto, 1992);
– rotational relaxation (Boyd, 1990);
– vibrational relaxation (Vijayakumar et al., 1999);
– chemistry (dissociation, recombination, exchange).
• Applications:
– hypersonic vehicle aerodynamics;
– spacecraft propulsion systems;
– micro-scale gas flows, space physics;
– materials processing (deposition, etching).
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MONACO: Data Structure
• Novel DSMC data structure:– basic unit of the algorithm is the cell;– all data associated with a cell are stored in cache;– particles sorted automatically.
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MONACO: Scalar Optimization
• Inexpensive cache memory system used on workstations:– data localization leads to performance enhancement.
• Optimization for specific processor:– e.g. overlap *add*, *multiply* and *logical* instructions.
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MONACO: Parallel Implementation
• Grid geometry reflected in the code data structure:– domain decomposition employed.
• When a particle crosses a cell edge:– particle pointed to new cell;– thus, particles sorted-by-cell automatically.
• When a particle crosses a domain edge:– communication link employed;– linked lists of particles sent as matrix;– inter-processor communication minimized;– no explicit synchronization required.
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MONACO: Parallel Implementation
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MONACO: The Software System
• Consists of four modular libraries:– KERN, GEOM, PHYS, UTIL.
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MONACO: Code Performance
• MONACO performance on IBM SP (Cornell, 1996):
– largest DSMC computation at the time;
– best performance with many particles/processor;
– parallel performance ~ 90%;
– serial performance 30-40%.
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MONACO: Unstructured Grids
Hypersonic flow arounda planetary probe
3D Surface geometry ofTOMEX flight experiment
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DSMC Applications:1. Hypersonic Aerothermodynamics
• Hypersonic vehicles encounter a variety of flow regimes:- flights/experiments are difficult and expensive;- continuum: modeled accurately and efficiently using CFD;- rarefied: modeled accurately and efficiently using DSMC.
DSMC: particle approachhigh altitudesharp edgesuses kinetic theory
CFD: continuum approachlow altitudelong length scalessolves NS equations
NASA’s Hyper-X
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• Flow separation configuration:
– N2 at M~10 over double cone;
– data from LENS (Holden).
Hypersonic Viscous Interaction
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• Cowl lip configuration:– N2 at M~14;– data from LENS (Holden).
Shock-Shock Interactions
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• TRIO flight experiment:– analysis of pressure gauges;– external/internal flows.
Complex 3D Flows
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• Computations of hypersonic flow around several power-law leading edge configurations performed using MONACO at high altitude.
• Advanced physical modeling:- vibrational relaxation and air chemistry;- incomplete wall accommodation.
• Effects of sharpening the leading edge:- reductions in overall drag coefficient and shock standoff distance;- increases in peak heat transfer coefficient.
AerothermodynamicsOf Sharp Leading Edges
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Flow Fields
Temperature Ratio (T / T∞)
Cylinder at 7.5 km/s n=0.7 at 7.5 km/s
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Drag Coefficient Shock Standoff Distance/
Heat Transfer Coefficient
Aerothermodynamic Assessment
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DSMC Applications:2. Materials Processing
• Effect of atomic collisions: – between the same species; – between different species.
Top view
Side view
3M experimental chamber for YBCO deposition
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3D MONACO Modeling
• 20x60x50 cuboid cells.
• Non-uniform cell sizes.
• 2,000,000 particles.
• Overnight solution time
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Yttrium Evaporation
Source flux: 9.95x10-5 moles/sec
Number density Z-component of velocity
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• Comparison of calculated and measured film deposition thickness.
• Significant effect of atomic collisions.
Yttrium Evaporation
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Calculated and measured atomic absorption spectra:
– along an aperture close to the substrate symmetry line;
– at frequencies of 668 nm (left) and 679 nm (right).
Yttrium Evaporation
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Co-evaporation of Yt, Ba, and Cu
Source fluxes (10-5 moles/cm2/sec) Y : Ba :Cu = 0.84 : 1.68 : 2.52
Total Number Density
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Ba CuYt
Flux (moles/cm2/s) across the substrate
Co-evaporation of Yt, Ba, and Cu
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DSMC Applications:3. Spacecraft Propulsion
• Tasks for spacecraft propulsion systems:– orbit transfer (e.g. planetary exploration);– orbit maintenance (e.g. station-keeping);– attitude control.
• Motivations for development of accurate models:– simulations less expensive than testing;– improve our understanding of existing systems;– optimize engine performance and lifetime;– assessment of spacecraft integration concerns.
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Spacecraft Propulsion
Griddedion thruster(UK-10)
Arcjet (Stanford)
Hall:stationaryplasma thruster(SPT-100)
PulsedPlasmaThruster(EOS-1)
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Express Spacecraft
• Two Russian GEO spacecraft launched in 2000:
– SPT-100 Hall thrusters used for station-keeping;
– in-flight characterization program managed by NASA;
– first in-flight plume data for Hall thrusters.
• Diagnostics employed on spacecraft:
– electric field sensors;
– Faraday probes (ion current density);
– retarding potential analyzers, RPA’s (ion current density, ion energy distribution function);
– pressure sensors;
– disturbance torques (from telemetry data).
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Express Spacecraft
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Particle In Cell (PIC)
{u’, v’, w’x, y, zm, q
E3
E2
E1
E4
• Particle method for nonequilibrium plasma:– developed since the 1960’s;– charged particles move in physical
space;– particles possess microscopic
properties, e.g. u’ (thermal velocity);– cell size x ~ , time step t ~ 1/;– self-consistent electric fields, E;– may be combined with DSMC for
collisional plasmas.
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Hybrid DSMC-PIC
• Particle model for ions, fluid model for electrons.
• Boltzmann relation for electrons provides potential:– currentless, isothermal, un-magnetized, collisionless;– quasi-neutrality provides potential from ion density:
φ−φ* =kTe
lnnn*
⎛ ⎝ ⎜
⎞ ⎠ ⎟
• Collision mechanisms:– charge exchange;– momentum exchange.
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Number Densities (m-3)
Xe+ ion Xe atom
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Ion Current Density
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Ion Energy Distributions
Beam plasma (15 deg.) CEX plasma (77 deg.)
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Summary
• Direct simulation Monte Carlo:– now a mature, well-established technique;– statistical simulation of particle dynamics;– applied in many areas of engineering/physics;– use growing due to improved computer power.
• Some advantages of DSMC:– accurate simulation of nonequilibrium gas;– framework for detailed physical modeling;– can handle geometric complexity;– can be combined with other methods for multi-
scale and multi-process systems.
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Future Directions
• Development of MONACO:– unsteady and 3D flows;– user help: “DSMC for dummies”;– dynamic domain decomposition;– more detailed physical models.
• Extensions of DSMC:– hybrid DSMC-CFD (using IP interface);– generalized hybrid DSMC-PIC;– 2-phase DSMC (gas and solid particles);– speedup: implicit DSMC, variance reduction.