http://ieeexplore.ieee.org/iel5/5/31047/01444179.pdf

Fundamentals of acoustics

Various ways of implementing boundary conditions for the numerical solution of the Navier-Stokes equations by a lattice Boltzmann method are discussed. Five commonly adopted approaches are reviewed, analyzed, and compared, including local and nonlocal methods. The discussion is restricted to velocity Dirichlet boundary conditions, and to straight on-lattice boundaries which are aligned with the horizontal and vertical lattice directions. The boundary conditions are first inspected analytically by applying systematically the results of a multiscale analysis to boundary nodes. This procedure makes it possible to compare boundary conditions on an equal footing, although they were originally derived from very different principles. It is concluded that all five boundary conditions exhibit second-order accuracy, consistent with the accuracy of the lattice Boltzmann method. The five methods are then compared numerically for accuracy and stability through benchmarks of two-dimensional and three-dimensional flows. None of the methods is found to be throughout superior to the others. Instead, the choice of a best boundary condition depends on the flow geometry, and on the desired trade-off between accuracy and stability. From the findings of the benchmarks, the boundary conditions can be classified into two major groups. The first group comprehends boundary conditions that preserve the information streaming from the bulk into boundary nodes and complete the missing information through closure relations. Boundary conditions in this group are found to be exceptionally accurate at low Reynolds number. Boundary conditions of the second group replace all variables on boundary nodes by new values. They exhibit generally much better numerical stability and are therefore dedicated for use in high Reynolds number flows.

Straight velocity boundaries in the lattice Boltzmann method

The lattice Boltzmann method is modified to allow the simulation of non-Newtonian shear-dependent viscosity models. Casson and Carreau-Yasuda non-Newtonian blood viscosity models are implemented and are used to compare two-dimensional Newtonian and non-Newtonian flows in the context of simple steady flow and oscillatory flow in straight and curved pipe geometries. It is found that compared to analogous Newtonian flows, both the Casson and Carreau-Yasuda flows exhibit significant differences in the steady flow situation. In the straight pipe oscillatory flows, both models exhibit differences in velocity and shear, with the largest differences occurring at low Reynolds and Womersley numbers. Larger differences occur for the Casson model. In the curved pipe Carreau-Yasuda model, moderate differences are observed in the velocities in the central regions of the geometries, and the largest shear rate differences are observed near the geometry walls. These differences may be important for the study of atherosclerotic progression.

/pdf/analysis-of-the-casson-and-carreau-yasuda-non-newtonian-34odefqzw5.pdf

Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method

http://www.heclectics-pictures.com/Perso/Articles/mariejcp2009.pdf

Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics

Numerical simulations are performed to investigate the fundamental acoustics properties of the Lattice–Boltzmann method. The propagation of planar acoustic waves is studied to determine the resolution dependence of numerical dissipation and dispersion. The two setups considered correspond to the temporal decay of a standing plane wave in a periodic domain, and the spatial decay of a propagating planar acoustic pulse of Gaussian shape. Theoretical dispersion relations are obtained from the corresponding temporal and spatial analyses of the linearized Navier–Stokes equations. Comparison of theoretical and numerical predictions show good agreement and demonstrate the low dispersive and dissipative capabilities the Lattice–Boltzmann method. The analysis is performed with and without turbulence modeling, and the changes in dissipation and dispersion are discussed. Overall, the results show that the Lattice–Boltzmann method can accurately reproduce time-explicit acoustic phenomena.

Properties of the Lattice-Boltzmann Method for Acoustics

We consider the application of the lattice Boltzmann BGK model to simulate sound waves in situations where the density variation is small compared to the mean density. Linear sound waves are simulated in two different situations: a plane wave propagating in an unbound region; and a wave in a tube. For both cases the behaviour of the simulated waves is found to be in good agreement with analytic expressions. Non-linear sound waves are also simulated and are seen to display the expected features.

https://iopscience.iop.org/article/10.1209/epl/i1998-00346-7/pdf

Lattice BGK simulation of sound waves

In this study the applicability of the lattice Boltzmann method to oscillatory channel flow with a zero mean velocity has been evaluated. The model has been compared to exact analytical solutions in the laminar case (Reδ < 100, where Reδ is the Reynolds number based on the Stokes layer) for the Womersley parameter 1 < α < 31. In this regime, there was good agreement between numerical and exact analytical solutions. The model was then applied to study the primary instability of oscillatory channel flow with a zero mean velocity. For these transitionary flows the parameters were varied in the range 400 < Reδ < 1000 and 4 < α < 16. Disturbances superimposed on the numerical solution triggered the two-dimensional primary instability. This phenomenon has not been numerically evaluated over the range of α or Reδ currently investigated. The results are consistent with quasi-steady linear stability theories and previous numerical investigations.

/pdf/application-of-the-lattice-boltzmann-method-to-transition-in-151s7iqiqj.pdf

Application of the lattice Boltzmann method to transition in oscillatory channel flow

Silo honking is an acoustical emission with a fundamental frequency of several hundred Hertz and an intensity often greater than 100 dB . It occurs when a silo is discharging and is similar to the “honk” of a lorry horn. The high amplitude of the honk makes it a significant noise pollution issue for workers at the site and for neighboring businesses and residents. This paper considers some possible excitation mechanisms that may be responsible for honking and presents measurements obtained from a full scale honking silo detailing the acoustic emissions and the associated vibration of the silo walls. Experimental results are presented which are comprised of simultaneous measurements of the three components of the wall vibrations and the acoustic pressure. The wall vibrations have an initial impulse response with a high amplitude O (100g) and subsequent oscillatory accelerations with amplitude O (10g) . The frequency spectra of the acceleration and acoustic pressure measurements comprises a sharp peak at th...

/pdf/investigation-of-silo-honking-slip-stick-excitation-and-wall-4e2p49g5w2.pdf

Investigation of silo honking: slip-stick excitation and wall vibration

https://researchportal.port.ac.uk/portal/files/1670246/039m.pdf

Numerical simulation of particle motion in an ultrasound field using the lattice Boltzmann model.

This paper considers the measurement of the internal radius of a number of similar, short, tubular leadpipes using pulse reflectometry. Pulse reflectometry is an acoustical technique for measuring the internal bore of a tubular object by analysing the reflections which occur when an acoustical pulse is directed into the object. The leadpipes are designed to form the initial, or lead, part of a trumpet or cornet and their internal radii differ by less than 0.1 mm between similar pipes. The ability of the reflectometer to detect these small differences, which are considered by players to produce a noticeable difference in the sound of an instrument, are investigated. It is seen that the pulse reflectometer is able to distinguish between leadpipes with different nominal radii varying by as little as 0.03 mm, demonstrating its potential in the study of musical instruments and showing that it can be used as a diagnostic tool by the instrument manufacturer to detect defects which are significant enough to acoustically alter performance. The absolute accuracy of the radius measurements is also considered at the end of the leadpipe, where the uncertainty is ±0.05 mm.

/pdf/distinguishing-between-similar-tubular-objects-using-pulse-2k85c35z7g.pdf

D. M. Campbell

Papers

Lattice BGK simulation of sound waves

Application of the lattice Boltzmann method to transition in oscillatory channel flow

Investigation of silo honking: slip-stick excitation and wall vibration

Numerical simulation of particle motion in an ultrasound field using the lattice Boltzmann model.

Distinguishing between similar tubular objects using pulse reflectometry: a study of trumpet and cornet leadpipes