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##### Thermoacoustics in random fibrous materials

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**Thermoacoustics in random fibrous materials**Seminar Carl Jensen Tuesday, 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**Stack temperature gradient • 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 Gas parcel temperature Temperature Sound Position QH QC QH QC TP<TS TP=TS TP>TS**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, nμand nκ • Porosity, Ω θ**e6**e2 e5 e3 e1 e0 e7 e4 e8 Computational fluid dynamics • Based on kinetic theory • Solves for particle distributions in discretized phase space • Simple dynamics: particles move across lattice links and collide**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**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**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**Validation**• First test is sound propagation in 2 dimensional pore • Infinite parallel plates 2R**r**x, u Analytical solution**Computational setup**• Temperature set to ambient at each wall • No slip on top/bottom walls • Driving wave at left • Non-reflecting at right T=1, u=0 p(t) T=1 T=1 T=1, u=0**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**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 Block 0 Block 1 Reg. Reg. Reg. Reg. … … Thread 0 Thread 1 Thread 0 Thread 1 … Shared Mem. Shared Mem. Main Memory**Results**• Compute time • Matlab: ~5 hours • CUDA: 25 seconds • Other GPGPU issues • Constrained memory • Single precision • Complex programming**Supercomputer**Nodes Host 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