Michal Bednařík

Nonlinear waves in resonators

The purpose of this paper is to find a suitable model equation for the description of finite amplitude standing waves in resonators of arbitrary axisymmetric shape filled with gas.

Optimal shaping of acoustic resonators for the generation of high-amplitude standing waves.

Within this paper, optimal shaping of acoustic resonators for the generation of high-amplitude standing waves through the use of evolutionary algorithms is discussed. The resonator shapes are described using sets of control points interconnected with cubic-splines. Positions of the control points are calculated by means of an evolutionary algorithm in order to maximize acoustic pressure amplitude at a given point of the resonator cavity. As an objective function for the optimization procedure, numerical solution of one-dimensional linear wave equation taking into account boundary-layer dissipation is used. Resonator shapes maximizing acoustic pressure amplitude are found in case of a piston, shaker, or loudspeaker driving. It is shown that the optimum resonator shapes depend on the method of driving. In all the cases, acoustic field attains higher amplitude in the optimized resonators than in simple-shaped non-optimized resonators of similar dimensions. Theoretical results are compared with experimental data in the case of a loudspeaker driving, good agreement of which is achieved.

Calculation of an axial temperature distribution using the reflection coefficient of an acoustic wave

This work verifies the idea that in principle it is possible to reconstruct axial temperature distribution of fluid employing reflection or transmission of acoustic waves. It is assumed that the fluid is dissipationless and its density and speed of sound vary along the wave propagation direction because of the fluid temperature distribution. A numerical algorithm is proposed allowing for calculation of the temperature distribution on the basis of known frequency characteristics of reflection coefficient modulus. Functionality of the algorithm is illustrated on a few examples, its properties are discussed.

Comparison of various strategies for colorectal cancer screening tests.

Introduction Colorectal cancer (CRC) is one of the most serious health problems worldwide and thus it is important to assess health and economic impacts of preventative CRC screening strategies. Methods For this reason, a theoretical model based on Markov chains is proposed to compare these strategies: fecal occult blood test, capsule endoscopy, once-life and twice-life colonoscopy, and no screening. The model predicts the health state of a population of individuals aged from 50 to 75 years. Results The numerical results show that the optimal timing for a once-lifetime colonoscopy screening method is before the age of 50 and that the twice-lifetime colonoscopy is the best screening strategy with respect to CRC incidence. In contrast, it is the most expensive one if the CRC treatment costs are not included. The model predicts that there is a minimal CRC incidence in the population when the second colonoscopy is appropriately timed. By using specific data, this age was found to be 59 years. Conclusion The screening strategies probably save expenses on the treatment of the population and at the same time decreases mortality. Optimized twice-lifetime colonoscopy seems to be the most efficient strategy with respect to mortality and overall costs including subsequent treatment.

Numerical study of the influence of the convective heat transport on acoustic streaming in a standing wave

Within this work, acoustic streaming in an air-filled cylindrical resonator with walls supporting a temperature gradient is studied by means of numerical simulations. A set of equations based on successive approximations is derived from the Navier-Stokes equations. The equations take into account the acoustic-streaming-driven convective heat transport; as time-averaged secondary-field quantities are directly calculated, the equations are much easier to integrate than the original fluid-dynamics equations. The model equations are implemented and integrated employing commercial software COMSOL Multiphysics. Numerical calculations are conducted for the case of a resonator with a wall-temperature gradient corresponding to the action of a thermoacoustic effect. It is shown that due to the convective heat transport, the streaming profile is considerably distorted even in the case of weak wall-temperature gradients. The numerical results are consistent with available experimental data.

Optimized reactive silencers with narrow side-branch tubes

This paper presents a theoretical study of the sound propagation in a waveguide loaded by an array of flush-mounted narrow side-branch tubes, forming a simple low-frequency reactive silencer. The individual tube-lengths and the distances between the adjacent tubes are optimized in order to maximize the minimum transmission loss over a given frequency range. The transmission properties of the silencer are calculated using the transfer matrix method, heuristic evolutionary approach is employed for the determination of the optimal parameters. The numerical results are validated against the finite element method simulation. A comprehensive parametric study is performed to demonstrate the optimized silencer performance as a function of the number of side-branch tubes, and the frequency range. It is shown that for the given frequency range, the minimum transmission loss of the optimized silencer increases linearly with the number of the side-branch tubes.

Effect of inhomogeneous temperature fields on acoustic streaming structures in resonators

Acoustic streaming in 2D rectangular resonant channels filled with a fluid with a spatial temperature distribution is studied within this work. An inertial force is assumed for driving the acoustic field; the temperature inhomogeneity is introduced by resonator walls with prescribed temperature distribution. The method of successive approximations is employed to derive linear equations for calculation of primary acoustic and time-averaged secondary fields including the streaming velocity. The model equations have a standard form which allows their numerical integration using a universal solver; in this case, COMSOL Multiphysics was employed. The numerical results show that fluid temperature variations in the direction perpendicular to the resonator axis influence strongly the streaming field if the ratio of the channel width and the viscous boundary layer thickness is big enough; the streaming in the Rayleigh vortices can be supported as well as opposed, which can ultimately lead to the appearance of additional vortices.

Numerical study of low-frequency sound beams

This paper is concerned with study of low-frequency sound beams generated as difference-frequency secondary field in parametric array. As model equations for theoretical investigation, KZK equation and Higher-order parabolic equation (HOPE) [Kamakura, T., Masahiko, A., Kenicii, A, Acoust. Sci. & Tech. 25, 2, (2004)] were used. Efficient numerical algorithm capable of massive parallelization was proposed for numerical integration of the model equations. Numerical results obtained using KZK equation and HOPE show that the KZK equation overestimates amplitude of the difference-frequency secondary wave in the near-field of the primary wave at the axis of symmetry. Both the equations provide the same results in the far-field and at the off-axis for both low- and high-frequency secondary fields.

Nonlinear waves in closed tubes

The purpose of this investigation was to choose a suitable model equation for description of finite amplitude waves in closed tubes filled with air. The boundary layer effects were also taken into account. Unfortunately, a general analytic solution of the used model equations has not been known, consequently it was necessary to find a numerical method for solution of these equations. When a standing wave is driven to high amplitude in an acoustic resonator, nonlinear effects couple energy from low‐ to high‐frequency modes, ultimately resulting in shock wave formation and heightened dissipation. Therefore this work was focused on study of suppressing the energy transfer into harmonics that represents a parasitic loss. This suppressing of the energy transfer enables store energy in the form of an acoustic standing wave in a resonant cavity more effectively.