Thermoacoustics in random fibrous

materials

Seminar

Carl JensenTuesday, March 25 2008

Outline

Thermoacoustics

Computational fluid dynamics

High performance computing

Thermoacoustics

Discovery and early designs such as Sondhauss tube (right) and Rijke tube

Developed into more efficient designs Stacks Gas mixtures High pressure Traveling wave devices

Engine Cycle

A conceptual ‘parcel’ of gas in the stack moves back and forth in the acoustic wave

The changing pressure causes the temperature of the parcel to vary with position in the acoustic cycle

The parcel is warmer on the left, but cooler than the stack so it absorbs heat

The parcel is cooler on the right, but warmer than the stack so it rejects heat

Tem

pera

ture

Position

Stack temperature gradient

Gas parcel temperature

QH

QC

TP<TS TP=TS TP>TS

Sound

QH QC

Stack types

Parallel pore Ceramics Stainless steel plates

Irregular materials Wools (Steel, glass, etc.) Foams

RVC Aluminum

Porous media theory Material approximated as rigid framework of tubes Roh and Raspet extended thermoacoustic solution for propagation in a tube to

capillary framework of porous media to create a thermoacoustic theory for porous media

Empirical model based on measured parameters: Tortuosity, q Thermal and viscous shape factors, nμ and nκ

Porosity, Ω

cos

1q

θ

Computational fluid dynamics

Based on kinetic theory Solves for particle distributions in discretized phase

space

Simple dynamics: particles move across lattice links and collide

)(),()1,( ftftf jj xexe1

e5e2e6

e3

e7 e4 e8

e0

Collision models In reality, the collisions represented by Ω are very

complicated Conservation laws and assumption of velocity independent

collision time gives the BGK collision operator

Same dynamics as Navier-Stokes equations for low Mach number with sound speed , and viscosity

Single relaxation time means Pr=1

)(1 eqff

22)(

2

3)(

2

9)(31 uueue wf eq

31sc 6/)12(

Collision models

Multiple relaxation time Same principle but different moments of the distribution are

relaxed differently

Sound speed, bulk/kinematic viscosity, and Pr are all adjustable parameters

Enhanced stability

Txyxxyxyx ppqqejjf ,,,,,,,, M

)(1 eq SM

Hybrid thermal model

Energy conserving LB hampered by spurious mode coupling

Dodge by using athermal LB and finite difference for temperature

Breaks kinetic nature of simulation but enhances stability

uu 2

02 )1( scTT

t

T

Validation

First test is sound propagation in 2 dimensional pore Infinite parallel plates

2R

Analytical solution

)),(ˆ1(

)),(ˆ1(

),(ˆ

0

0

ti

ti

ti

erxTTT

erxppp

erxucu

)()(ˆ

),(ˆ

Fdx

xpdicxu

)()(ˆ1

),(ˆ TT FxpxT

r

x, u

Rr

0ˆ

0ˆ

T

u

pT

cR

R

Computational setup

Temperature set to ambient at each wall No slip on top/bottom walls Driving wave at left Non-reflecting at right

p(t)

T=1

T=1, u=0

T=1, u=0

T=1

ResultsF(λ)

ResultsF(λT)

High Performance Computing

CPU (Athlon X2 4800+) 2 cores 9.6 Gflops 6.4 GB/s memory

bandwidth 2 GB RAM

GPU (GeForce 8800 GTX) 128 stream processors 345.6 Gflops 86.4 GB/s 768 MB RAM

Control Arithmetic

Cache

Block 0

……

Thread 0 Thread 1

Reg. Reg.

GPU Programming

Massive threading Up to 12,288 threads in flight at once Threads batched into blocks Each multiprocessor block runs one block of threads

Many threads per block Many blocks per process

Shared Mem.

Main Memory

Block 1

…Thread 0 Thread 1

Reg. Reg.

Shared Mem.

Results

Compute time Matlab: ~5 hours CUDA: 25 seconds

Other GPGPU issues Constrained memory Single precision Complex programming

Supercomputer

Host

Nodes

Image from: http://www.olympusmicro.com/micd/galleries/oblique/glasswool.html

Supercomputer

Much larger memory Less strict synchronization More flexible programming Double precision

Non-local – job queues, remote debugging, etc.

Lower overall throughput without using a lot of processors

Current Work

Sound impulse over 3D sphere

Conclusions

Hybrid thermal lattice Boltzmann method contains proper physics to simulate thermoacoustic phenomena

A lot of increasingly accessible options for high performance computing