ME615 Project Presentation Aeroacoustic Simulations using Lattice Boltzmann Method

Transcription

1 ME615 Project Presentation Aeroacoustic Simulations using Lattice Boltzmann Method Kameswararao Anupindi Graduate Research Assistant School of Mechanical Engineering Purdue Universit December 11, 11

2 Outline Introduction 2. Numerical Method 3. Results Initial pulse Monopole Dipole Longitudinal Quadrupole Lateral Quadrupole 4. Conclusions 5. References

3 Introduction Lattice Boltzmann method (LBM) is emerging as a potential tool for simulating fluid flow LBM is a mesoscopic approach tailored to simulate incompressible or compressible flow. Navier-Stokes equations can derived from LB equations b appling Chapman-Enskog multiscale and small parameter epansion Tpes of lattice Boltzmann methods 1. Classical LBM (used in the present stud) 2. Finite Difference LBM

4 Numerical Method Lattice Boltzmann Equation f α( + c αδt,t + δt) f α(,t) = Ω α (1) Ω α = 1 τ [ fα(,t) f eq α (,t)] (2) Lattice Boltzmann equation with BGK-Single Relaation time is the governing equation fα: particle distribution function Ωα: Collision operator τ: Relaation time f eq α : Equilibrium particle distribution function Equilibrium Distribution Function [ f eq α (ρ,u) = wα ρ 1 + cα.u ] cs 2 + (cα.u)2 2cs 4 u 2 2cs 2 (3) Macroscopic Quantities ρ(,t) = f α(,t) (4) α ρ(,t)u(,t) = c αf α(,t) (5) α

5 Lattice Details D2Q9 lattice is used in all simulations Lattice speed of sound: cs = 1 3 ; weights are c1 c8 c7 given b: w k=9 = 4/9 c2 c9 c6 w k=1,2,3,4 = 1/9 w k=5,6,7,8 = 1/36 c3 c4 c5 For i = 1,9, lattice vectors are defined b Figure: D2Q9 lattice [ c i = ]

6 Streaming Operation Overall Solution Algorithm: Collision Stream Appl Periodic BC Figure: Schematic showing the streaming operation Compute macroscopic quantities Streaming operation: Solid arrows represent the lattice under consideration Respective broken line arrows show the final position after streaming

7 ρ Results - Initial Sound Pulse (a) t= (b) t=1 (c) t= t = 1 t = t = 3 t = (d) t= (e) t= (f) wave motion Figure: Propagation of densit perturbation waves for the case of pulse

8 t = t = 3 t = t = 5 t = t = 1; Eact t = 5; LBM t = 5; eact t = ; Eact Results - Monopole (a) t=1 (b) t= (c) t= (d) t=5.1.6 t = t = 1; LBM t = ; LBM (e) wave motion (f) t=1 (g) t=5 (h) t= Figure: Propagation of densit perturbation waves for the case of monopole

9 Results - Monopole, Ecitation time period stud T = 1 T = 5 T = 1 T = T = 5 T = T = 1 Figure: Propagation of densit perturbations for different time periods of ecitation Time periods of ecitation T = 1 and T = show at least two wave lengths in the densit perturbation T = 5, and T = show onl one wave length of the densit perturbation T = 1, and T = 1 were not captured b the grid solution considered Longer domain is needed to capture the waves generated b T = 1 ecitation

10 Results - Dipole (a) t=1 (b) t= (c) t= t = 1 t = t = 3 t = t = 5 t = (d) t= (e) t= 5 1 (f) wave motion Figure: Propagation of densit perturbation waves for the case of a dipole

11 d D D Results - Longitudinal Quadrupole (a) t=1 (b) t= (c) t= t = 1 t = t = 3 t = t = 5 t = -.4 (d) t= (e) t= (f) wave motion Figure: Densit perturbation waves for the case of a longitudinal quadrupole

12 d D D Results - Lateral Quadrupole (a) t=2 (b) t= (c) t= t = 1 t = t = 3 t = t = 5 t = -.4 (d) t= (e) t= = line (f) wave motion Figure: Densit perturbation waves for the case of a lateral quadrupole

13 Conclusions Developed a 2D LBM solver in Fortran 9 Applied the solver to simulating bench-mark problems in aeroacoustics such as, initial sound pulse, monopole, dipole, longitudinal and lateral quadrupole The densit perturbation field computed is compared to the analtical solution and it is seen that the wave length seems to be accuratel represented but there is some discrepanc in the amplitudes which could be because of the grid resolution or the difference in the speed of sound captured. Time period of ecitation stud on the monopole case shows that T = 1 and T = are ideal cases where as T = 1 is not captured b the current domain, and a longer domain is needed to capture this. Overall, LBM seems to be a viable approach for simulating aeroacoustics

14 References Dong, Y., and Sagaut, P., A stud of time correlations in lattice Boltzmann-based large-edd simulation of isotropic turbulence, Phsics of Fluids,, 3515 (8). Luo, L., Krafczk, M., and Sh, W., Lattice Boltzmann method for Computational Fluid Dnamics, Encclopedia of Aerospace Engineering, John Wile & Sons, Ltd. Lew, P., T., Mongeau, L., and Lrintzis, A., Noise prediction of a subsonic turbulent round jet using the lattice-boltzmann method, Journal of the Acoustical Societ of America, 128(3), (1) Chikatamarla, S., S., Frouzakis, C., E., Karlin, I., V., Tomboulides, A., G., and Boulouchos, K., B., Lattice Boltzmann method for direct numerical simulation of turbulent flows, Journal of Fluid Mechanics, 656, , (1). Bhatnagar, P. L., Gross, E., P., and Krook, M., A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Sstems, Phsical Review, 94(3), , (1954) Pierce, A. D., Acoustics, An Introduction to Its Phsical Principles and Applications, Acoustical Socient of America, (1994) Chen, S., and Doolen, G., D., Lattice Boltzmann Method for Fluid Flows, Annual Review of Fluid Mechanics, 3, , (1998) Kam, E., W., S., So, R., M., C., Fu, S., C., and Leung, R., C., K., Finite Difference Lattice Boltzmann Method Applied to Acoustic-Scattering Problems, AIAA Journal, 48(2), (1) Viggen, E., M. The Lattice Boltzmann Method with Applications in Acoustics, Masters Dissertation, Department of Phsics, NTNU (9) Malaspinas, O., and Sagaut, P., Advanced large-edd simulation for lattice Boltzmann methods: The approimate deconvolution model, Phsics of Fluids, 23, 1513,(11)

15 Acknowledgements Acknowledgements are due, to Prof. A. S. Lrintzis (for guidance through the course of the project) Prof. S. H. Frankel (for help in chosing the project topic)

16 Fini... Thank You!