FIG 2 - uploaded by Paul Stansell
Content may be subject to copyright.
Graphs of typical results for a FHP-III lattice gas automaton simulation of a no-slip harmonically oscillating flat plate at y0. For these examples 0.004 with 0 1.995 broken line and 0 2.779 solid line.
Source publication
The lattice gas automaton fluid modelling technique is used to study acoustic streaming phenomena arising from the interaction of sound waves with no-slip boundaries in a two-dimensional pipe. It is demonstrated that this fluid simulation tool is able to reproduce the general form of the acoustic streaming flow field observed by Andrade [Proc. R. S...
Contexts in source publication
Context 1
... addition, a typical set of numerical results for a simu- lation over the whole range of y is shown in Fig. 2. The supercells used for averaging in this figure were 1 lattice node in the x-direction by 256 in the y-direction. A subrange of these same results, showing a region close to the bound- ary, is illustrated in Fig. 3 and compared directly with theory as predicted by equation 52. It can be seen that the agree- ment with theory is very ...
Context 2
... to carry out lattice gas automaton simulations which can be compared with Rayleigh's theory for acoustic streaming one needs to be able to set up and maintain a standing sound wave in the system. To this end an examina- tion was made of the behavior of standing and progressive sound waves when modelled by the FHP-III lattice gas au- tomaton. Fig. 2 showing direct comparison between the results of the FHP-III simulations and those of theory as pre- dicted by equation 52. For these simulations 0.004 with 0 1.995 crosses simulation, broken line theory and 0 2.779 pluses simulation, solid line theory. TABLE I. Parameter settings and results from FHP-III lattice gas automata ...
Citations
... Using (28) and α ph /α lbm = 1/ x we can write: ...
The paper presents a three-dimensional numerical study of the acoustic streaming induced by the dissipation of ultrasounds during their propagation in the air. The waves are generated by a circular acoustic source positioned at the center of the left wall of a parallelepipedic cavity. The simulations are performed with the lattice Boltzmann method associated with the D3Q19 multiple relaxation time model. A validation of this model is first performed by comparing the numerical and analytical acoustic intensities along the central axis of the acoustic source. The main objective of this study is to use two different methods to calculate the acoustic streaming flow. The first method is the direct calculation of the mean velocity fields as the mean values of the instantaneous velocities. The second method is an indirect technique, which first calculates the acoustic streaming force and then injects this force into the numerical code to produce the streaming. A comparison between the results obtained by the two methods was carried out and a good agreement was found between them. These different investigations, rather new in three-dimensional configurations, have allowed us to discuss the advantages and limitations of the lattice Boltzmann approach to simulate real situations of wave propagation and acoustic streaming.
Graphical abstract
... La méthode de Boltzmann sur réseau est utilisée depuis de nombreuses années pour étudier l'acoustic streaming. Par exemple, Stansell et Greated[75] ont étudié numériquement l'acoustic streaming résultant de l'interaction des ondes acoustiques avec les limites non glissantes dans un tuyau en 2D en utilisant la méthode de modélisation des fluides par automate à gaz sur réseau. Haydock et Yeomans[28] ont utilisé l'approche LB pour étudier les phénomènes d'acoustic streaming induits par l'interaction d'une onde sonore avec une limite. ...
The Lattice Boltzmann Method (LBM) is applied in this thesis to study acoustic waves propagation and heat transfer in fluids. The work can be summarized in five parts:
The first two sections deal with the basic mathematical formulations of the kinetic theory of gases and the numerical lattice Boltzmann approach. Numerical simulations are started in the third part. This part first presents the basic principles of acoustics and then gives a two-dimensional (2D) study of acoustic waves propagation in water. The waves are generated by a rectangular acoustic source vibrating at 200 kHz. The objective is to calculate the acoustic pressure and force produced in the near field, and then to inject the numerically calculated force into the LBM code used to produce the acoustic streaming flow.
Given the importance of numerical studies used as data to perform experiments, the simulation of physical problems in three dimensions (3D) becomes a necessity to visualize the physical phenomenon much better than in 2D. Therefore, the three-dimensional lattice Boltzmann method is used in the fourth section to study the propagation of acoustic waves in water. The main objective of this numerical study is to show how waves generated by a point source and square and circular shaped sources propagate instantaneously in 3D, to calculate the acoustic pressure and to highlight the performance of LBM simulations. A comparison of the numerical results found with the analytical data is performed to validate the numerical approach used.
The fifth part presents a 3D numerical study of the physical phenomena of ultrasound propagation in air, thermal convection and their interaction. Considering its advantages in terms of accuracy and computational efficiency over the pure LBM method, the hybrid method based on the LBM approach for the description of the hydrodynamic behavior of the fluid and the finite difference technique for the temperature calculation is introduced in this last part to investigate the improvement of the heat transfer by the ultrasound.
... The lattice Boltzmann method has been used to study acoustic streaming for many years. For example, Stansell and Greated [30] numerically studied the acoustic streaming resulting from the interaction of acoustic waves with no-slip boundaries in a 2D pipe using the lattice gas automaton fluid modeling method. Haydock and Yeomans [31] used the LB approach to study the acoustic streaming phenomena induced by the interaction of a sound wave with a boundary. ...
This paper presents a numerical investigation of the propagation of acoustic waves generated by a linear acoustic source using the lattice Boltzmann method (LBM). The main objective of this study is to compute the sound pressure and acoustic force produced by a rectangular sound source located at the center of the west wall of a rectangular cavity, filled with water. The sound source is discretized into a set of point sources emitting waves according to the acoustic point source method. The interference between the generated cylindrical waves creates an acoustic beam in the cavity. An analytical study is carried out to validate these numerical results. The error between the numerical and analytical calculations of the wave propagation is also discussed to confirm the validity of the numerical approach. In a second step, the acoustic streaming is calculated by introducing the acoustic force into the LBM code. A characteristic flow structure with two recirculating cells is thus obtained.
... The LBM code can be easily parallelized, and straight forward to implement [11]. A study of acoustic streaming produced by a standing wave between two parallel plates was reported by Stansell et al. [12]. They used lattice gas approach (considered to be a predecessor of LBM) to simulate full N-S equation and streaming appeared as a small correction to the oscillatory flow field. ...
One important factor in the efficiency of thermoacoustic engines is acoustic streaming, which causes convective heat transfer between high and low temperature reservoirs. Most experimental and numerical studies performed so far have focused on Rayleigh streaming. Less work has been done on acoustic streaming due to the stack. Most numerical studies of Rayleigh streaming were performed using Navier-Stokes based numerical methods. In this study, large eddy numerical simulations were performed using schemes based on the lattice Boltzmann method (LBM). The model considered a simplified thermoacoustic refrigerator made of a rectangular standing wave resonator with a flat plate spoiler. Low-amplitude results obtained for Rayleigh streaming velocity magnitudes were compared with linear acoustic theory for verification. High amplitude recirculated streaming flow structures around the edges of the flat plate spoiler were identified. These are likely to contribute to heat transfer much more than Rayleigh streaming. Parametric studies were performed to investigate the effects of Strouhal number and spoiler edge shape. The results confirm that vertical edge streaming flows play a significant role in thermoacoustic heat transport.
... Difficulty in simulating flows at high Reynolds number (Aaltosalmi 2005). Only applicable in the low Mach number limit to flows where there is a density variation which is much smaller compared to the mean density (Stansell & Greated, 1997; Buick et al., 1998). The cell size must be similar to the local mean free path (Prasanth & Kakkassery 2006) The number of particles per cell must be roughly constant in order to preserve collision statistics (Prasanth & Kakkassery 2006). ...
Advances in nanotechnology have provided acoustic researchers with a number of new materials with nanofibres and nanopores that can potentially be implemented as an acoustic porous absorber. The molecular behaviour of these new nanoscopic materials may have a significant influence on their sound absorption; in addition, their properties could play an important role in reducing the absorber thickness compared to the currently available materials. However, the absorption mechanisms of nanoscopic fibres are not fully understood and the application of numerical and analytical modelling methods to this problem is still at an early stage. This paper presents a review of numerical methods which have been implemented for various micro- and nano-scale analyses of relevance to the acoustics of nanofibres. The review is focused mainly on the application of non-continuum particle based approaches such as the Lattice Boltz-mann Method (LBM) and the Direct Simulation Monte Carlo (DSMC) method, since it is expected that the flow behaviour for nanoscopic fibres will be in transition regime (where molecular mean free path is comparable to characteristic dimension) due to the high Knudsen number. The acoustic absorption mechanisms are thus likely to deviate from the continuum phenomena and modelling approaches applicable to flow associated with larger scale fibres. It is intended that this review will provide an overview of the potentially applicable approaches for the exploration of acoustic absorption mechanisms of nanoscopic fibres.
... In the past few years the lattice Boltzmann model (LBM) has been used to simulate a variety of isothermal, incompressible fluid flows [1,2]. It is well established that the LBM satisfies the incompressible Navier-Stokes and continuity equation although, like its predecessor the lattice gas model (LGM), it is generally considered to be applicable in the low Mach number limit to flows where there is a density variation which is small compared to the mean density [3,4]. In this letter we consider a new class of problems, the simulation of sound waves. ...
... Here there is a clear density variation, although in many circumstances this is small compared to the mean density and an incompressible approximation can yield good results, even when non-linear sound waves are modelled. The LGM has been shown to be effective under such circumstances [3,[5][6][7] despite the inherent noise which is not present in LBM simulations. ...
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.
... Two particular problems are the statistical noise associated with the simulation due to the small number of`particlesof`particles' being considered, and the viscosity being limited to relatively high values. These both limited the range of application of the LGA, see for example 9, 15]. In an attempt to overcome these drawbacks the LGA evolved in a number of stages and developed into the LBM; details of the various steps can be found in, for example 18, 19]. ...
The application of the lattice Boltzmann model to simulating nonlinear propagative acoustic waves is considered. The lattice Boltzmann model, and its application to the study of nonlinear sound propagation, are discussed. Lattice Boltzmann simulations of the development of a shock front are performed when a sound wave is emitted from a high-amplitude sinusoidal source. For a number of parameters, representing different physical situations, the wave development is compared with inviscid shock theory and with the solution of Burgers' equation for a fully viscous fluid. The simulations show good agreement with Burgers' equation and with the inviscid theory when propagation at high Reynolds number is considered. These results suggest that the lattice Boltzmann model is a useful technique for studying a range of problems in nonlinear acoustics.
Resonance dispersion mixing technology is a new process developed in recent years. The main function of the technology is each scale vortex caused by the vibration, which is a multiscale phenomenon that includes macroscopic vortices and mesoscopic vortices. For mesoscopic vortices, due to the lack of sufficient resolution, current commercial software filter and average these vortices, so it is difficult to meet the needs of research. Based on this, the paper proposes a lattice Boltzmann Method (LBM) to simulate the mesoscopic vortices. The LBM is a mesoscale research method, so it has sufficient resolution to study mesoscopic vortices. The paper mainly simulated the process of splitting and evolution of mesoscopic vortices, studied the effects of parameters such as simulation interval, viscosity, vibration frequency on mesoscopic vortices. The results show that the selection of the simulation interval has a certain influence on the evolution of the vortices. The viscosity of the flow field plays a decisive role in the vortices, for there is no vortex generation when the viscosity exceeds a certain threshold. The excitation frequency controls the development process of the vortices, larger frequency can significantly reduce the micro-mixing characteristic time to increase mixing efficiency. Different from the previous theoretical analysis literature, this paper gives visual numerical simulation results.
This paper investigates enhancement of cooling of an IC chip by acoustic streaming induced by a PZT-covered vibrating beam, which is placed underneath the chip. Vibration of the beam induces acoustic streaming in the gap between the chip and the beam. The governing equations are asymptotically decomposed into the first order harmonic equations and second order time-independent acoustic streaming equations by the infinite small parameter defined as the ratio of characteristic beam vibration velocity and the local sound speed. The first order harmonic equations are numerically solved in the reduced wave equation form. The steady acoustic streaming equations are driven by the first order harmonic field and are solved by SIMPLER method. The cooling effect on the uniform heat flux from the chip is also analyzed and behavior of the cooling effect on the uniform heat generation within a chip with finite thickness is also estimated.
