The nonlinear interaction of wave and non-wave modes in a gas planar flow are considered. Attention is mainly paid to the case when one sound mode is dominant and excites the counter-propagating sound mode and the entropy mode. The modes are determined by links between perturbations of pressure, density, and fluid velocity. This definition follows from the linear conservation equations in the differential form and thermodynamic equations of state. The leading order system of coupling equations for interacting modes is derived. It consists of diffusion inhomogeneous equations. The main aim of this study is to identify the principle features of the interaction and to establish individual contributions of attenuation (mechanical and thermal attenuation) in the solution to the system.
The effects of friction were observed in electric guitar strings passing over an electric guitar saddle. The effects of changing the ratio of the diameter of the winding to the diameter of the core of the string, the angle through which the string is bent, and the length on either side of the saddle were measured. Relative tensions were deduced by plucking and measuring the frequencies of vibration of the two portions of string. Coefficients of friction consistent with the capstan equation were calculated and were found to be lower than 0.26 for wound strings (nickel plated steel windings on steel cores) and lower than 0.17 for unwound (tin plated steel) strings. The largest values of friction were associated with strings of narrower windings and wider cores and this may be due to the uneven nature of the contact between the string and saddle for wound strings or due the surface of the windings deforming more, encouraging fresh (and therefore higher friction) metal to metal contact. It is advised to apply lubrication under the saddle to string contact point after first bringing the string up to pitch rather than before in order to prevent this fresh metal to metal contact.
The research was focused on the selection of the best conditions for the lactic acid production. As the organic source diluted waste whey was used. Two facultative anaerobic bacteria strains were examined: Lactobacillus rhamnosus and Lactococcus lactis. The neeed of anaerobic conditions as well as mineral supplementation of cultivationwere investigated. It turned out that the oxidationwas not the key parameter, but cultivationmediumneeded a supplementation for higher process efficiency. Finally, Lactobacillus rhamnosus strain was selected, for which LA production was app. 45% higher than for Lc. lactis. On the other hand, Lactobacillus rhamnosus was active at higher lactose concentration, thus waste whey needed to be less diluted. Additionally, high values of product/substrate yield coefficient make the process very efficient.
In this paper, effects of non-Fourier thermal wave interactions in a thin film have been investigated. The non-Fourier, hyperbolic heat conduction equation is solved, using finite difference method with an implicit scheme. Calculations have been carried out for three geometrical configurations with various film thicknesses. The boundary condition of a symmetrical temperature step-change on both sides has been used. Time history for the temperature distribution for each investigated case is presented. Processes of thermal wave propagation, temperature peak build-up and reverse wave front creation have been described. It has been shown that (i) significant temperature overshoot can appear in the film subjected to symmetric thermal load (which can be potentially dangerous for reallife application), and (ii) effect of temperature amplification decreases with increased film thickness.
Discontinuous coefficients in the Poisson equation lead to the weak discontinuity in the solution, e.g. the gradient in the field quantity exhibits a rapid change across an interface. In the real world, discontinuities are frequently found (cracks, material interfaces, voids, phase-change phenomena) and their mathematical model can be represented by Poisson type equation. In this study, the extended finite element method (XFEM) is used to solve the formulated discontinuous problem. The XFEM solution introduce the discontinuity through nodal enrichment function, and controls it by additional degrees of freedom. This allows one to make the finite element mesh independent of discontinuity location. The quality of the solution depends mainly on the assumed enrichment basis functions. In the paper, a new set of enrichments are proposed in the solution of the Poisson equation with discontinuous coefficients. The global and local error estimates are used in order to assess the quality of the solution. The stability of the solution is investigated using the condition number of the stiffness matrix. The solutions obtained with standard and new enrichment functions are compared and discussed.
In this paper we study the dynamical behavior of linear discrete-time fractional systems. The first main result is that the norm of the difference of two different solutions of a time-varying discrete-time Caputo equation tends to zero not faster than polynomially. The second main result is a complete description of the decay to zero of the trajectories of one-dimensional time-invariant stable Caputo and Riemann-Liouville equations. Moreover, we present Volterra convolution equations, that are equivalent to Caputo and Riemann-Liouvile equations and we also show an explicit formula for the solution of systems of time-invariant Caputo equations.
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.
Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second requirement for the commutativity of non-relaxed systems plays an important role on the commutativity conditions when non-zero initial conditions exist. Another highlight is that the commutativity of switched systems is considered and spoiling of commutativity at the switching instants is illustrated for the first time. The simulation results support the theory developed in the paper.
In the paper, the extended finite element method (XFEM) is combined with a recovery procedure in the analysis of the discontinuous Poisson problem. The model considers the weak as well as the strong discontinuity. Computationally efficient low-order finite elements provided good convergence are used. The combination of the XFEM with a recovery procedure allows for optimal convergence rates in the gradient i.e. as the same order as the primary solution. The discontinuity is modelled independently of the finite element mesh using a step-enrichment and level set approach. The results show improved gradient prediction locally for the interface element and globally for the entire domain.
Thrust bearing model is developed for fluid flow calculation and for determination of bearing integral characteristics in the presence of sliding surfaces closure and shaft angular displacements. The model is based on the coupled solution of the problem of incompressible fluid flow between the sliding surfaces and the problem of bearing and shaft elements deformation under the action of the fluid film pressure. Verification of the bearing model results is carried out by the comparison versus the fluid flow calculation results obtained by STAR-CD software and the experimental and theoretical results represented in the certain literature. Thrust bearing characteristics are determined versus sliding surfaces closure and rotating disk (runner) angular displacements. The contribution of the sliding surfaces deformations into bearing integral characteristics is estimated.
We propose a numerical surface integral method to study complex acoustic systems, for interior and exterior problems. The method is based on a parametric representation in terms of the arc’s lengths in curvilinear orthogonal coordinates. With this method, any geometry that involves quadric or higher order surfaces, irregular objects or even randomly rough surfaces can be considered. In order to validate the method, the modes in cubic, spherical and cylindrical cavities are calculated and compared to analytical results, which produced very good agreement. In addition, as examples, we calculated the scattering in the far field and the near field by an acoustic sphere and a cylindrical structure with a rough cross-section.
We derive exact and approximate controllability conditions for the linear one-dimensional heat equation in an infinite and a semi-infinite domains. The control is carried out by means of the time-dependent intensity of a point heat source localized at an internal (finite) point of the domain. By the Green’s function approach and the method of heuristic determination of resolving controls, exact controllability analysis is reduced to an infinite system of linear algebraic equations, the regularity of which is sufficient for the existence of exactly resolvable controls. In the case of a semi-infinite domain, as the source approaches the boundary, a lack of L2-null-controllability occurs, which is observed earlier by Micu and Zuazua. On the other hand, in the case of infinite domain, sufficient conditions for the regularity of the reduced infinite system of equations are derived in terms of control time, initial and terminal temperatures. A sufficient condition on the control time, heat source concentration point and initial and terminal temperatures is derived for the existence of approximately resolving controls. In the particular case of a semi-infinite domain when the heat source approaches the boundary, a sufficient condition on the control time and initial temperature providing approximate controllability with required precision is derived.
In this paper, we establish variation of constant formulas for both Caputo and Riemann- Liouville fractional difference equations. The main technique is the Z -transform. As an application, we prove a lower bound on the separation between two different solutions of a class of nonlinear scalar fractional difference equations.
In this paper, two techniques for calculating the geoid-to-quasigeoid separation are employed. One of them is GPS/Levelling customary method as a criterion where the geoid undulation and height anomaly are computed by subtracting the ellipsoid height attained via GPS from the orthometric height and normal height, respectively. Another approach is Sjöberg’s equation. We have used of the ICGEM website for definition of the variables of the Sjöberg’s equation, as the applied reference model is the EGM2008 global geopotential model and WGS84 reference ellipsoid. The investigations are performed over the stations of the GPS/Leveling network related to three selected areas in desert, mountain and flatland namely the Lout, Zagros and Khuzestan in Iran and afterward the correlation coefficient between the geoid-to-quasigeoid separation calculated using the satellite data in Sjöberg’s equation and GPS/Levelling method is estimated. The results indicate a straight correlation between the estimated separations from the two methods as its value for the Lout is 0.754, for the Zagros is 0.497 and for the Khuzestan is 0.659. consequently, using the satellite data in Sjöberg’s equation for the regions where there are not the GPS/Levelling and land gravity data, specially for the even areas, yield a satisfactory response of the geoidto-quasigeoid separation.
Room-temperature ionic liquids (RTILs) are a moderately new class of liquid substances that are characterized by a great variety of possible anion-cation combinations giving each of them different properties. For this reason, they have been termed as designer solvents and, as such, they are particularly promising for liquid-liquid extraction, which has been quite intensely studied over the last decade. This paper concentrates on the recent liquid-liquid extraction studies involving ionic liquids, yet focusing strictly on the separation of n-butanol from model aqueous solutions. Such research is undertaken mainly with the intention of facilitating biological butanol production, which is usually carried out through the ABE fermentation process. So far, various sorts of RTILs have been tested for this purpose while mostly ternary liquid-liquid systems have been investigated. The industrial design of liquid-liquid extraction requires prior knowledge of the state of thermodynamic equilibrium and its relation to the process parameters. Such knowledge can be obtained by performing a series of extraction experiments and employing a certain mathematical model to approximate the equilibrium. There are at least a few models available but this paper concentrates primarily on the NRTL equation, which has proven to be one of the most accurate tools for correlating experimental equilibrium data. Thus, all the presented studies have been selected based on the accepted modeling method. The reader is also shown how the NRTL equation can be used to model liquid-liquid systems containing more than three components as it has been the authors’ recent area of expertise.
problem of sound radiation from an unflanged duct with mean flow of the medium taking into account existence of all allowable wave modes and, in particular, occurrence of the so-called unstable wave, which results in decay of radiation on and in vicinity of the duct axis. The flow is assumed to be uniform with the source of flow located inside the duct, which is the case frequently occurring in industrial systems. Mathematical considerations, accounting for multimodal and multifrequency excitation and diffraction at the duct outlet, are based on the model of the semi-infinite unflanged hard duct with flow. In the experimental set-up a fan, mounted inside the duct served as the source of flow and noise at the same time modelled as an array of uncorrelated sources of broadband noise, what led to the axisymmetrical shape of the sound pressure directivity characteristics. The theoretical analysis was carried out for the root mean square acoustic pressure in the far-field conditions. Experimental results are presented in the form of the measured pressure directivity characteristics obtained for uniform flow directed inwards and outwards the duct compared to this observed for the zero-flow case. The directivity was measured in one-third octave bands throughout five octaves (500 Hz - 16 kHz) which, for a duct with radius of 0.08 m, corresponds to the range 0.74-23.65 in the reduced frequency ka (Helmholtz number) domain. The results obtained are consistent with theoretical solutions presented by Munt and Savkar, according to whom the weakening of the on-axis and close-to-axis radiation should take place in the presence of medium flow. Experimental results of the present paper indicate that this effect is observed even for the Mach number as low as 0.036.
The paper presents investigations related to solving of a direct and inverse problem of a non-stationary heat conduction equation for a cylinder. The solution of the inverse problem in the form of temperature distributions has been obtained through minimization of a functional being the measure of the difference between the values of measured and calculated temperatures in M points of the heated cylinder. The solution of the conduction equation was presented in the convolutional form and then numerically integrated approximating one of the integrand with a step function described with parameter Θ ∈ (0, 1]. The influence of the integration parameter Θ on the obtained solution of the inverse problem (including a number of temperature measurement points inside the heated body) has been analyzed. The influence of the parameter Θ on the sensitivity of the obtained temperature distributions has been investigated.
The paper presents numerical simulation of two-phase flow in a heated capillary with evaporation on the meniscus. To solve the problem, a model of evaporation from meniscus was developed in which the dynamics of liquid-vapour interface is described by the Cahn-Hilliard equation. The numerical simulations were performed using commercial software for 2D axially symmetric case. The flow evolution was analysed for different values of heat transfer coefficient at the capillary wall and inlet liquid mass flow rate.
The paper deals with pool boiling of water-Al2O3and water-Cu nanofluids on rough and porous coated horizontal tubes. Commercially available stainless steel tubes having 10 mm outside diameter and 0.6 mm wall thickness were used to fabricate the test heater. The tube surface was roughed with emery paper 360 or polished with abrasive compound. Aluminium porous coatings of 0.15 mm thick with porosity of about 40% were produced by plasma spraying. The experiments were conducted under different absolute operating pressures, i.e., 200, 100, and 10 kPa. Nanoparticles were tested at the concentration of 0.01, 0.1, and 1% by weight. Ultrasonic vibration was used in order to stabilize the dispersion of the nanoparticles. It was observed that independent of operating pressure and roughness of the stainless steel tubes addition of even small amount of nanoparticles augments heat transfer in comparison to boiling of distilled water. Contrary to rough tubes boiling heat transfer coefficient of tested nanofluids on porous coated tubes was lower compared to that for distilled water while boiling on porous coated tubes. A correlation equation for prediction of the average heat transfer coefficient during boiling of nanofluids on smooth, rough and porous coated tubes is proposed. The correlation includes all tested variables in dimensionless form and is valid for low heat flux, i.e., below 100 kW/m2.
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.
A role of radial corona current in a lightning discharge is discussed in the paper. It is shown that the corona current concept previously introduced by Cooray for lightning return stroke models of distributed-current-source (DCS) type, and later, by Maslowski and Rakov for lumped-current-source (LCS) type models enables to show duality between these two types of models. Further, it is demonstrated that the corona current is useful during consideration of dynamics of the lightning-channel corona sheath. As an example of application of presented approach a relaxation model of charge motion in the corona sheath is analysed together with plots which show the rate of expansion and shrinkage of the lightning corona sheath on both microsecond and millisecond time scales.
In Poland, according to the statistical data, about 40% of sewage sludges originating from wastewater treatment plants are applied in the agriculture. The mentioned way of application of sewage sludges causes the hazard of contamination of environment with carcinogenic compounds due to the presence of some organic micropollutants, such as polycyclic aromatic hydrocarbons (PAHs). The proposal of changing UE Directive obligates control of organic pollutants (PAHs and others) in sewage sludges applied in the agriculture. The aim of the investigations was to estimate the persistence of PAHs under stored conditions by determining half-life of their decomposition. Eight carcinogenic PAHs, among 16 compounds, listed by EPA were determined. In this study, the quantity changes in the concentration of PAHs in stored sewage sludges were investigated. Sewage sludges were stored under aerobic conditions for 16 weeks. At the same time the sewage sludges with sodium azide added, in order to deactivate the microorganisms (abiotic samples), were also stored. Gas chromatography-mass spectrometry was used to qualify and quantify PAHs in 2- and 4-week intervals. Sewage sludges were taken two fold from a municipal wastewater treatment plant. In practice, the sewage sludges are directed to the disposal site. The initial concentration of 16 PAHs in sewage sludge was equal to 582 μg/kg.d.m. The changes in the concentration of PAHs corresponded to exponential function. Values of correlation coefficients indicate a significant dependence of PAHs persistence and concentration on time exposition. Under experimental conditions the half-lives of individual compounds were diversed. In biotic samples half-life of hydrocarbons was in the range of 17 to 126 days. Half-life of PAHs in abiotic sewage sludges was in the range of 32 to 2048 days. The most persistent were benzo(a)pyrene and benzo(b) fluoranthene, respectively. A significant dependence of PAHs' decrease on the presence of microorganisms in sewage sludges after 10 weeks of storage was found.