CFD / SPACS / COS George Mason University Fluid-Structure Interaction Calculations With Breakage and Dust Rainald Löhner, Joseph D. Baum, Orlando A. Soto

CFD / SPACS / COS George Mason University

Fluid-Structure Interaction Calculations With Breakage and Dust

Rainald Löhner, Joseph D. Baum, Orlando A. Soto and Fumiya Togashi

Center for Computational Fluid DynamicsSPACS, George Mason University, Fairfax, VA, USA

SAIC, McLean, VA, USA

cfd.gmu.edu/~rlohnerwww.scs.gmu


Overview

• Motivation / Applications Targeted• Particle/Flow Interaction• Examples• Shock/Dust Interaction• Conclusions and Outlook


Motivation/Applications Targeted


Motivation/Applications Targeted

• Fine Particles• Suspensions• Dust• Mist/Droplets

• Enhancement of Combustion• Aluminum in Solid Rocket Motors

• Shock/Dust Interaction


Cased Weapons

Adapted CFD mesh and Pressure Contours at 125 ms

Pressure Contours, t=244 ms

CSD Velocity, t=244 ms


Basic Phenomena

a) Detonation/Fragmentation b) Fragment Transport

c) Frags Hit/Pulverize Walls d) Dust/Shock Interaction


Physics


Physics

• Eulerian• Treat As Dilute Phase• Concentration: Transport (Advection, Diffusion, Reaction) Eqns.

• Lagrangian• Treat As `Particle in Fluid’• Individual (or Group): Movement, Evaporation, Heat, …Eqs.

• Focus Here: Lagrangian Treatment


Flow: Euler/Navier-Stokes Equations

jjij

ji

ijij

jijjij

jijjij

i

kTqvv

eρpp

qv

p)ρevpvρvρv

ρeρvρ

,

jv

ja

vat,

;)(

...] JWL, Table, Gas, Ideal[),(

;;0F

(;;F

;;u

SFFu


Momentum Transfer

• Drag Force of Each Particle

• Drag Coefficient and Reynolds-Number

piip

2

vv2

1

4 vv

di cd

D

dcd

p687.0 Re;Re15.01Re

24,1.0max

vv


Heat Transfer

• Heat Flux For Each Particle

• Film Coefficient, Nusselt- and Prandtl-Number

442pp TTTThdQ

kc

Nud

Nukh p

Pr;RePr459.02; 55.0333.0


Numerics


Conservation Laws…

• Conservation Law:

• Galerkin FEM:

• Consistent Numerical Flux:

• k-Step Runge-Kutta Scheme:

SFu t ,

1

1

iki

iij

ijijt

ij sfCruM ,

1innin ur)uM(u ti

)CUSP,...Osher,vanLeer,Roe,Godunov,(~~

ijijij fff


Particle Motion and Temperature (1)

• Velocity and Position

• Temperature

• Integrated Explicitly; 4th Order Runge-Kutta

ppp

3

;6

vx

Dv

dt

d

dt

ddp

Qdt

dTdcppp p

3

6


Particle Motion and Temperature (2)

• Position, Velocity and Temperature:

• Integrated Explicitly; Typically: 4th Order Runge-Kutta

),,,( turdt

dufux

1

1

iki

),,,( 111 ininfi

inin turtuu ux


Particle Tracking

• Need: Flow Variables At Location of Particle Need Host Element for Each Particle

• Initialization: Bins + Near-Neighbour Search• Incremental: Near-Neighbour Search

• Vectorized and Parallelized for OMP• Also Running in MPI


Walls: Boundary Conditions

• Walls: Bouncing, Sticking, Gliding, …

• Embedded Surfaces

Bouncing Sticking Gliding


Numerical Issues (1)

• Suppose: Very Small Particle• Low Re-Nr High Relative Drag • Drag: ~ r2

• Mass: ~ r3

• Large CFD Timestep In One Timestep, Velocity Can Exceed Flow Veloc Physically Wrong (!)• Solutions:

• Substepping (Expensive, Load Balance Issues)• Limiting



• Suppose: Very Small Particle• Low Nu-Nr High Relative Heating• Heat Flux: ~ r2

• Heat Capacity: ~ r3

• Large CFD Timestep In One Timestep, Temperature Can Exceed Flow Temp Physically Wrong (!)• Solutions:

• Substepping (Expensive, Load Balance Issues)• Limiting



• Assume 1-D: Difference in Velocities at tn: Δvn = vf - vnp

• If Δvn > 0 : Δvn+1 ≥ 0• If Δvn < 0 : Δvn+1 ≤ 0

• Same Applies to Temperatures

• Imposed at Every Runge-Kutta Stage


Particle-Flow Interaction

• Change in Momentum for 1 Particle

• Change in Energy for 1 Particle

• Multiply By Number of (True) Particles in Packet

t

d nn

pp

)(

6pp

13 vvF

t

TTdcq

nn

pppp

)(

6pp

13


Particle-Flow Interaction

• Need:• Conservative Transfer of Mass, Momentum and Energy Use Shape-Functions to Project Mass, Momentum and

Energy Increments to Flow Grid

Ni


Accurate Flow Particle ; Particle Flow

• Need Sufficient Particles Per Element

Split Up Particles If Too Few/Element Size Increases

Agglomerate Particles If Too Many in One Element

Refine Mesh If Too Many Particles in One Element



• Suppose: Very Heavy / Large / Many Particles• Outside Limits of Theory, But Sometimes Encountered In Runs

• Large CFD Timestep In One Timestep, Force Exerted By Particles May Lead

To Flow Velocity That Exceeds Particle Velocity Physically Wrong (!)• Solutions:

• Substepping Expensive, Reduction of Timestep• Limiting Non-Conservative



• Suppose: Very Heavy / Large / Many Particles• Outside Limits of Theory, But Sometimes Encountered In Runs

• Large CFD Timestep In One Timestep, Energy Flux From Particles May

Lead To Flow Temperatures That Exceeds Particle Temperature

Physically Wrong (!)• Solutions:

• Substepping Expensive, Reduction of Timestep• Limiting Non-Conservative



• Add Momentum/Energy From Particles• Compare Velocities/Temperatures• Limit to Physically Reasonable Values• Add to Source-Terms


Particle Contact (1)

• Volume of np Particles:

Equivalent Radius:

• Overlap Distance:

• Average Overlap Distance of Particles:

6

3p

K

p dnV

pK

pa dn

Vr3/13/1

84

3

jiijijaj

aiij ddrrdo xx ;

ji ppijij

s

nndodo

11

2

1



• Define Unit Normal:

• Define Tangential Direction from Velocity:

ji

jiij

xx

xxn

ijijn

ijijt

ijijijn

ijij vv nvvnvvvv ;;

tij

tij

ijv

vt



• Normal and Tangential Forces

• Limit Tangential Force to Avoid Reversal of Velocities• Add Velocity-Based Damping Force in Normal Direction

• Limit:

nijji

tij

sijji

nij fhhfdokkf

2

1;

2

1

ji

jijinijij

nd

mm

kkhhvf

ijnd

ijn

ijnd fff ,max



• Complete Force:

• Estimation of Contact Stiffness:• Assume Particle At Rest in Incoming Flow• Another Particle Behind• Penetration Factor ξ

ijt

ijijnd

ijn

ijij fff tnf

8

v1.0;

v3 2

1Re1Re

dkk



• Spatial Neighbour Information Options:• Bins• Octrees• Element Neighbour Lists

• Used Here: Bins


Particles and MPI


Particles and MPI (1)

• Approach Based on Passing Particle Info Across Overlapping Elements

• If Mesh Is Changed/Read In:

• Obtain All Elements That Overlap Domains• Order Border Elements According to Communication

Schedule

1 Layer ofOverlap

Ω1 Ω2



• For Each Timestep:• Obtain Particles in Each Element• For Each Exchange Pass:

• From List of Border Elements: Get Particles That Need to be Sent to Neighbouring Domain

• Exchange Info Of How Many Parts Sent/Received• Exchange (Send/Receive) Particles



• Duplicate Particles:• Reason: CFL < 1• Best Solution: Universal Unique Number• Integer Filter of Duplicate Particles

• Particles With Same Location• Reason: Flow Physics, Geometric Singularities (e.g. Corners)• Best Solution: Traverse Elements, Remove/Separate Particles

With Same Location



• Further Improvements:• Extensive OMP Parallelization of Particle Subs/Modules• Extensive Timing/Optimization of All Particle Subs/Modules• Improvements in MPI Send/Receive Modules

• Before Improvements: 2-3 Min/Timestep• After Improvements: 2-3 Seconds/Timestep


Link to CSD


CSD to Particles (1)

CSD

CFD

Faces Passed to CFD

CFD

CSD

Before Failure After Failure


CSD to Particles (2)

• Model Pulverization• Main Steps

• Take Failed CSD Element (Hexahedron, Tetrahedron)• Pass These to CFD via FEMAP• User Specifies Particle Size/Density/… Distribution• Initial Velocity of Particles

• From CSD• From Experimental Evidence [Can Be O(400-100 m/sec)]

• CFD Updates Flowfield and Particles


Examples


WEPACT-4


WEPACT-4 Initial Conditions

60 cmz

high p low p

250 cm

dust+airNOT TO SCALE

air only

250 cm

Closed end for variants B&C

Z>250cm: filled with air and dust (0.1g/cc)Dust particle: 2.3g/cc, D=100m

The air in z >0: p = 1.01E6 dynes/cm2 and T = 15.15 °C = 288.3 °K. The air in z < 0: p = 4000 psi = 2.7579E8 dyne/cm2 and T = 1430.6 °K.


Computed Gas Density & Velocity


Computed Gas Pressure & Mach-Nr.


Computed Gas Energy & Temperature


Computed Dust Density & Velocity


3D Plot of Dust Density Profile

Dust Density

x

Time


Movies – Gas Velocity & Dust Velocity


WEPACT-5


WEPACT-5 Initial condition

60 cmz

high p low p

250 cm

dust+air

NOT TO SCALE

air only

250 cm 180 cm

air only

430cm > Z >250cm: filled with air and dust (0.1g/cc)Dust particle: 2.3g/cc, D=100m


Computed Gas & Dust Density


Computed Gas Velocity


Computed Mach-Nr.


Computed Gas Pressure


Computed Gas Energy


Computed Gas Temperature


Computed Dust Velocity


Computed Dust Temperature


Movies


Effect of Dust on Blasts in Tunnels

• Experimental Observation: Damping Due to Dust• Step 1: Simplify in Order to Understand No CSD CFD:

• Simple EOS• Particles

• Study the Effects of Dust on:• Shock Waves• Overall Flowfield

• Solver: FEM-FCT + Particles


Blast in Tunnel


Blast in Tunnel


Station Placement


Station 8


Station 13


Generic Production Runs


Blast In Room With Particles


Blast In Room With Particles


Fluid and Particle Velocities at 2.5msρ=2.0gr/cc, d=0.1cm

ρ=2.0gr/cc, d=0.0464cm

ρ=0.4gr/cc, d=0.1cm




ρ=2.0gr/cc, d=0.0464cm





ρ=2.0gr/cc, d=0.0464cm




Conclusions and Outlook


Particle / Flow Capability

• Important In Order to Model Complex Phenomena

• Significant Effects Due To:• Momentum Loss / Transfer [Particle Acceleration]• Energy Loss / Transfer [Particle Heating]

• Have Helped to Explain Puzzling Experimental Results


Future Work

• Contact Between Particles• Contact Stiffness ?• Stability ?

• Burn With Oxygen Deficiency• Link to Chemical Reactions

• Volume Blockage Effect of Particles• For High Densities

Documents

CFD / SPACS / COS George Mason University Fluid-Structure Interaction Calculations With Breakage and Dust Rainald Löhner, Joseph D. Baum, Orlando A. Soto