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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