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Direct Simulation Monte Carlo: A Particle Method for Nonequilibrium Gas Flows. Iain D. Boyd Department of Aerospace Engineering University of Michigan Ann Arbor, MI 48109 Support Provided By: MSI, AFOSR, DARPA, NASA. Physical characteristics of nonequilibrium gas flow.

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slide1

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

slide2
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

slide3
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

slide4

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

slide5

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 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

slide7

The DSMC Algorithm

  • 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.
slide8
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

slide9

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).
slide10

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.
slide11

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.
slide12

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.
slide14

MONACO: The Software System

  • Consists of four modular libraries:
    • KERN, GEOM, PHYS, UTIL.
slide15

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%.
slide16

MONACO: Unstructured Grids

Hypersonic flow around

a planetary probe

3D Surface geometry of

TOMEX flight experiment

slide17

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.

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

slide18

Hypersonic Viscous Interaction

  • Flow separation configuration:
    • N2 at M~10 over double cone;
    • data from LENS (Holden).
slide19

Shock-Shock Interactions

  • Cowl lip configuration:
    • N2 at M~14;
    • data from LENS (Holden).
slide20

Complex 3D Flows

  • TRIO flight experiment:
    • analysis of pressure gauges;
    • external/internal flows.
slide21

Aerothermodynamics

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.
slide22

Flow Fields

Temperature Ratio (T / T∞)

Cylinder at 7.5 km/s

n=0.7 at 7.5 km/s

slide23

Aerothermodynamic Assessment

Drag Coefficient

Shock Standoff Distance/Heat Transfer Coefficient

slide24

DSMC Applications:

2. Materials Processing

3M experimental chamber for YBCO deposition

Top view

Side view

  • Effect of atomic collisions:
  • – between the same species;
  • – between different species.
slide25

3D MONACO Modeling

  • 20x60x50 cuboid cells.
  • Non-uniform cell sizes.
  • 2,000,000 particles.
  • Overnight solution time
slide26

Yttrium Evaporation

Source flux: 9.95x10-5 moles/sec

Number density

Z-component of velocity

slide27

Yttrium Evaporation

  • Comparison of calculated and measured film deposition thickness.
  • Significant effect of atomic collisions.
slide28

Yttrium Evaporation

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).

slide29

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

slide30

Co-evaporation of Yt, Ba, and Cu

Flux (moles/cm2/s) across the substrate

Yt

Cu

Ba

slide31
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

slide32

Spacecraft Propulsion

Gridded

ion thruster

(UK-10)

Arcjet

(Stanford)

Pulsed

Plasma

Thruster

(EOS-1)

Hall:stationary

plasma thruster

(SPT-100)

slide33
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).
slide35

Particle In Cell (PIC)

  • 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

slide36

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:
  • Collision mechanisms:
    • charge exchange;
    • momentum exchange.
slide39

Ion Energy Distributions

Beam plasma (15 deg.)

CEX plasma (77 deg.)

slide40
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

slide41
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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