1. Thermoacoustics in random fibrous materials Seminar Carl Jensen Tuesday, March 25 2008

2. Outline Thermoacoustics Computational fluid dynamics High performance computing

3. 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

4. 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 Temperature Position Stack temperature gradient Gas parcel temperature QHQH QCQC T P <T S T P =T S T P >T S Sound Q H Q C

5. Stack types Parallel pore Ceramics Stainless steel plates Irregular materials Wools (Steel, glass, etc.) Foams RVC Aluminum

6. 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, n μ and n κ Porosity, Ω θ

7. Computational fluid dynamics Based on kinetic theory Solves for particle distributions in discretized phase space Simple dynamics: particles move across lattice links and collide e1e1 e5e5 e2e2 e6e6 e3e3 e7e7 e4e4 e8e8 e0e0

8. 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

9. 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

10. 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

11. Validation First test is sound propagation in 2 dimensional pore Infinite parallel plates 2R

12. Analytical solution r x, u

13. 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

14. Results F(λ)

15. Results F(λ T )

16. 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

17. Block 0 … … Thread 0Thread 1 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 0Thread 1 Reg. Shared Mem.

18. Results Compute time Matlab: ~5 hours CUDA: 25 seconds Other GPGPU issues Constrained memory Single precision Complex programming

19. Supercomputer Host Nodes Image from: http://www.olympusmicro.com/micd/galleries/oblique/glasswool.html

20. 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

21. Current Work Sound impulse over 3D sphere

22. Conclusions Hybrid thermal lattice Boltzmann method contains proper physics to simulate thermoacoustic phenomena A lot of increasingly accessible options for high performance computing