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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 EngineeringUniversity of MichiganAnn Arbor, MI 48109Support Provided By:MSI, AFOSR, DARPA, NASA

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.

Overview

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 m).

Gas dynamics:

rarefied flow (high Knudsen number);

collisions still important;

continuum equations physically inaccurate.

Modeling Considerations

Characterization ofNonequilibrium Gas Flows

Flow Regimes:

transitional

slip

free-molecular

continuum

Kn

0.1

0.01

10

DSMC

Boltzmann Equation

Control equations:

Collisionless

Boltzmann Eqn

Navier-Stokes

Euler

Burnett

- 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 Dx ~ l, time step Dt ~ t=1/n;
- 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, z

m, erot, evib

- MOVE:
- translate particles Dx = uDt;
- 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.

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).

Current DSMC-Related Projects

- 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).

- 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.

- 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.

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.

- Consists of four modular libraries:
- KERN, GEOM, PHYS, UTIL.

- 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%.

Hypersonic flow around

a planetary probe

3D Surface geometry of

TOMEX flight experiment

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.

NASA’s Hyper-X

DSMC: particle approach

high altitude

sharp edges

uses kinetic theory

CFD: continuum approach

low altitude

long length scales

solves NS equations

Hypersonic Viscous Interaction

- Flow separation configuration:
- N2 at M~10 over double cone;
- data from LENS (Holden).

- Cowl lip configuration:
- N2 at M~14;
- data from LENS (Holden).

- TRIO flight experiment:
- analysis of pressure gauges;
- external/internal flows.

Of Sharp Leading Edges

- 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.

2. Materials Processing

3M experimental chamber for YBCO deposition

Top view

Side view

- Effect of atomic collisions:
- – between the same species;
- – between different species.

- 20x60x50 cuboid cells.
- Non-uniform cell sizes.
- 2,000,000 particles.
- Overnight solution time

- Comparison of calculated and measured film deposition thickness.
- Significant effect of atomic collisions.

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).

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

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.

DSMC Applications:

3. Spacecraft Propulsion

Gridded

ion thruster

(UK-10)

Arcjet

(Stanford)

Pulsed

Plasma

Thruster

(EOS-1)

Hall:stationary

plasma thruster

(SPT-100)

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.

Express Spacecraft

- 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).

- 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 Dx ~ d, time step Dt ~ 1/w;
- self-consistent electric fields, E;
- may be combined with DSMC for collisional plasmas.

E3

E4

E2

E1

{

u’, v’, w’

x, y, z

m, q

- 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:

- Collision mechanisms:
- charge exchange;
- momentum exchange.

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.

Summary

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.

Future Directions

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