In this paper a three-dimensional model for determination of a microreactor's length is presented and discussed. The reaction of thermocatalytic decomposition has been implemented on the base of experimental data. Simplified Reynolds-Maxwell formula for the slip velocity boundary condition has been analysed and validated. The influence of the Knudsen diffusion on the microreactor's performance has also been verified. It was revealed that with a given operating conditions and a given geometry of the microreactor, there is no need for application of slip boundary conditions and the Knudsen diffusion in further analysis. It has also been shown that the microreactor's length could be practically estimated using standard models.

In slowly flaring horns the wave fronts can be considered approximately plane and the input impedance can be calculated with the transmission line method (short cones in series). In a rapidly flaring horn the kinetic energy of transverse flow adds to the local inertance, resulting in an effective increase in length when it is located in a pressure node. For low frequencies corrections are available. These fail at higher frequencies when cross-dimensions become comparable to the wavelength, causing resonances in the cross-direction. To investigate this, the pipe radiating in outer space is modelled with a finite difference method. The outer boundaries must be fully absorbing as the walls of an anechoic chamber. To achieve this, Berenger's perfectly matched layer technique is applied. Results are presented for conical horns, they are compared with earlier published investigations on flanges. The input impedance changes when the largest cross-dimension (outer diameter of flange or diameter of the horn end) becomes comparable to half a wavelength. This effect shifts the position of higher modes in the pipe, influencing the conditions for mode locking, important for ease of playing, dynamic range and sound quality.

The accuracy of the Moment Method for imposing no-slip boundary conditions in the lattice Boltzmann algorithm is investigated numerically using lid-driven cavity flow. Boundary conditions are imposed directly upon the hydrodynamic moments of the lattice Boltzmann equations, rather than the distribution functions, to ensure the constraints are satisfied precisely at grid points. Both single and multiple relaxation time models are applied. The results are in excellent agreement with data obtained from state-of-the-art numerical methods and are shown to converge with second order accuracy in grid spacing.

An efficiency of the nonsingular meshless method (MLM) was analyzed in an acoustic indoor problem. The solution was assumed in the form of the series of radial bases functions (RBFs). Three representative kinds of RBF were chosen: the Hardy’s multiquadratic, inverse multiquadratic, Duchon’s functions. The room acoustic field with uniform, impedance walls was considered. To achieve the goal, relationships among physical parameters of the problem and parameters of the approximate solution were first found. Physical parameters constitute the sound absorption coefficient of the boundary and the frequency of acoustic vibrations. In turn, parameters of the solution are the kind of RBFs, the number of elements in the series of the solution and the number and distribution of influence points. Next, it was shown that the approximate acoustic field can be calculated using MLM with a priori error assumed. All approximate results, averaged over representative rectangular section of the room, were calculated and then compared to the corresponding accurate results. This way, it was proved that the MLM, based on RBFs, is efficient method in description of acoustic boundary problems with impedance boundary conditions and in all acoustic frequencies.

Two optimization aspects of the meshless method (MLM) based on nonsingular radial basis functions (RBFs) are considered in an acoustic indoor problem. The former is based on the minimization of the mean value of the relative error of the solution in the domain. The letter is based on the minimization of the relative error of the solution at the selected points in the domain. In both cases the optimization leads to the finding relations between physical parameters and the approximate solution parameters. The room acoustic field with uniform, impedance walls is considered.

As results, the most effective Hardy’s Radial Basis Function (H-RBF) is pointed out and the number of elements in the series solution as a function of frequency is indicated. Next, for H-RBF and fixed n, distributions of appropriate acoustic fields in the domain are compared. It is shown that both aspects of optimization improve the description of the acoustic field in the domain in a strictly defined sense.

In this paper we present the results of simulations of the Magnetic Induction Tomography (MIT) forward problem. Two complementary calculation techniques have been implemented and coupled, namely: the finite element method (applied in commercial software Comsol Multiphysics) and the second, algebraic manipulations on basic relationships of electromagnetism in Matlab. The developed combination saves a lot of time and makes a better use of the available computer resources.

On the basis of Euler-Bernoulli beam theory, the large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The von Karman type nonlinear strain-displacement relationship is employed where the ends of the beam are constrained to move axially. The material properties are assumed to be graded in the thickness direction according to the power-law and sigmoid distributions. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law index, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible.

One of the main issues of design process of HVAC systems and ventilation ducts in particular is correct modelling of coupling of the flow field and acoustic field of the air flowing in such systems. Such a coupling can be modelled in many ways, one of them is using linearised Euler equations (LEE). In this paper, the method of solving these equations using finite element method and open source tools is decribed. Equations were transformed into functional and solved using Python language and FEniCS software. The non-reflective boundary condition called buffer layer was also implemented into equations, which allowed modelling of unbounded domains. The issue, influence of flow on wave propagation, could be adressed using LEE equations, as they take non-uniform mean flow into account. The developed tool was verified and results of simulations were compared with analytical solutions, both in one- and two-dimensional cases. The obtained numerical results are very consistent with analytical ones. Furthermore, this paper describes the use of the developed tool for analysing a more complex model. Acoustic wave propagation for the backward-facing step in the presence of flow calculated using Navier-Stokes equations was studied.

Excitation of the entropy mode in the field of intense sound, that is, acoustic heating, is theoretically considered in this work. The dynamic equation for an excess density which specifies the entropy mode, has been obtained by means of the method of projections. It takes the form of the diffusion equation with an acoustic driving force which is quadratically nonlinear in the leading order. The diffusion coefficient is proportional to the thermal conduction, and the acoustic force is proportional to the total attenuation. Theoretical description of instantaneous heating allows to take into account aperiodic and impulsive sounds. Acoustic heating in a half-space and in a planar resonator is discussed. The aim of this study is to evaluate acoustic heating and determine the contribution of thermal conduction and mechanical viscosity in different boundary problems. The conclusions are drawn for the Dirichlet and Neumann boundary conditions. The instantaneous dynamic equation for variations in temperature, which specifies the entropy mode, is solved analytically for some types of acoustic exciters. The results show variation in temperature as a function of time and distance from the boundary for different boundary conditions.

A hybrid artificial boundary condition (HABC) that combines the volume-based acoustic damping layer (ADL) and the local face-based characteristic boundary condition (CBC) is presented to enhance the absorption of acoustic waves near the computational boundaries. This method is applied to the prediction of aerodynamic noise from a circular cylinder immersed in uniform compressible viscous flow. Different ADLs are designed to assess their effectiveness whereby the effect of the mesh-stretch direction on wave absorption in the ADL is analysed. Large eddy simulation (LES) and FW-H acoustic analogy method are implemented to predict the far-field noise, and the sensitivities of each approach to the HABC are compared. In the LES computed propagation field of the fluctuation pressure and the frequency-domain results, the spurious reflections at edges are found to be significantly eliminated by the HABC through the effective dissipation of incident waves along the wave-front direction in the ADL. Thereby, the LES results are found to be in a good agreement with the acoustic pressure predicted using FW-H method, which is observed to be just affected slightly by reflected waves.