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.
In this paper, numerical results of modeling of acoustic waves propagation are presented. For calculation of the acoustic fluctuations, a solution of the full non-linear Euler equation is used. The Euler equations are solved with the use of a numerical scheme of third-order accuracy in space and time. The paper shows a validation process of the described method. This method is suitable also for an aerodynamic noise assessment on the basis of unsteady mean flow field data obtained from a CFD calculations. In such case this method is called a hybrid CFD/CAA method. The proposed method is numerically decoupled with CFD solution, therefore the information about the mean unsteady flow field can be obtained using an arbitrary CFD method (solver). The accuracy of the acoustic field assessment depends on the quality of the CFD solutions. This decomposition reduces considerably the computational cost in comparison with direct noise calculations. The presented Euler acoustic postprocessor (EAP) has been used for modeling of the acoustic waves propagation in a cavity and in the flow field around a cylinder and an aerodynamic profile.
Periodic adsorption in a perfect mixing tank of a limited volume was considered. It was assumed that the adsorption rate is limited by diffusion resistance in a pellet. The approximate model of diffusion kinetics based on a continued fraction approximation was compared with the exact analytical solution. For the approximate model an algorithm was developed to determine a temporal variation of the adsorbate concentration in the pellet. The comparison was made for different values of the adsorbent load factor. In the numerical tests different shapes of pellets were considered. Both the numerical tests as well as our own experimental results showed that the approximate model provides results that are in good agreement with the exact solution. In the experimental part of this work adsorption of p-nitrophenol and acetic acid from aqueous solutions on cylindrical pellets of activated carbon was conducted.
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.
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.
The sound speed and parameters of nonlinearity B/A, C/A in a fluid are expressed in terms of coefficients in the Taylor series expansion of an excess internal energy, in powers of excess pressure and density. That allows to conclude about features of the sound propagation in fluids, the internal energy of which is known as a function of pressure and density. The sound speed and parameters of nonlinearity in the mixture consisting of boiling water and its vapor under different temperatures, are evaluated as functions of mass concentration of the vapor. The relations analogous to that in the Riemann wave in an ideal gas are obtained in a fluid obeying an arbitrary equation of state. An example concerns the van der Waals gases. An excess pressure in the reflected wave, which appears when standard or nonlinear absorption in a fluid takes place, is evaluated in an arbitrary fluid.
The majority of publications and monographs present investigations which concern exclusively twophase flows and particulary dispersed flows. However, in the chemical and petrochemical industries as well as in refineries or bioengineering, besides the apparatuses of two-phase flows there is an extremely broad region of three-phase systems, where the third phase constitutes the catalyst in form of solid particles (Duduković et al., 2002; Martinez et al., 1999) in either fixed bed or slurry reactors. Therefore, the goal of this study is to develop macroscopic, averaged balances of mass, momentum and energy for systems with three-phase flow. Local instantaneous conservation equations are derived, which constitute the basis of the method applied, and are averaged by means of Euler’s volumetric averaging procedure. In order to obtain the final balance equations which define the averaged variables of the system, the weighted averaging connected with Reynolds decomposition is used. The derived conservation equations of the trickle-bed reactor (mass, momentum and energy balance) and especially the interphase effects appearing in these equations are discussed in detail.
The considerations presented in this paper include a computer analysis of slide bearing wear prognosis using the solutions of recurrence equations complemented with the experimental data values. On the ground of the results obtained from analytical and computational numerical calculations, and taking into account the experimental parameters of bearing material and operation boundary conditions, the control problems of slide bearing wear surfaces have been presented. The obtained results allow us to see a connection between roughness, material properties, the amplitude of vibrations, the kind of the friction forces, the hardness of materials, the sliding speed in one side and the wear increments in succeeding time units of the exploitation process in other side.
In this paper, Lagrange’s equations along with the Ritz method are used to obtain the equation of motion for a flexible, slender cylinder subjected to axial flow. The cylinder is supported only by a translational and a rotational spring at the upstream end, and at the free end, it is terminated by a tapering end-piece. The equation of motion is solved numerically for a system in which the translational spring is infinitely stiff, thus acting as a pin, while the stiffness of the rotational spring is generally non-zero. The dynamics of such a system with the rotational spring of an average stiffness is described briefly. Moreover, the effects of the length of the cylinder and the shape of the end-piece on the critical flow velocities and the modal shapes of the unstable modes are investigated.
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 the presented paper, a problem of nonholonomic constrained mechanical systems is treated. New methods in nonholonomic mechanics are applied to a problem of a Forklift-truck robot motion. This method of the geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces. The relevance of this theory for general types of nonholonomic constraints, not only linear or affine ones, was then verified on appropriate models. On the other hand, the equations of motion of a Forklift-truck robot are highly nonlinear and rolling without slipping condition can only be expressed by nonholonomic constraint equations. In this paper, the geometrical theory is applied to the above mentioned mechanical problem. The results of numerical solutions of constrained equations of motion, derived within the theory, are presented.
This paper presents a study of the Fourier transform method for parameter identification of a linear dynamic system in the frequency domain using fractional differential equations. Fundamental definitions of fractional differential equations are briefly outlined. The Fourier transform method of identification and their algorithms are generalized so that they include fractional derivatives and integrals.
In this article we construct a finite-difference scheme for the three-dimensional equations of the atmospheric boundary layer. The solvability of the mathematical model is proved and quality properties of the solutions are studied. A priori estimates are derived for the solution of the differential equations. The mathematical questions of the difference schemes for the equations of the atmospheric boundary layer are studied. Nonlinear terms are approximated such that the integral term of the identity vanishes when it is scalar multiplied. This property of the difference scheme is formulated as a lemma. Main a priori estimates for the solution of the difference problem are derived. Approximation properties are investigated and the theorem of convergence of the difference solution to the solution of the differential problem is proved.
A complete parametric approach is proposed for the design of the Luenberger type function Kx observers for descriptor linear systems. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, parametric expressions for all the coefficient matrices of the observer are derived. The approach provides all the degrees of design freedom, which can be utilized to achieve some additional design requirements. An illustrative example shows the effect of the proposed approach.
In the paper an approach to design of multipurpose control systems is considered. It is presented an universal and efficient algorithm for synthesis of multipurpose control system for proper, invertible and right-invertible multi-input multi-output dynamic (MIMO) plants which can be both unstable and/or non-minimumphase. The developed control systems feature both dynamic (either block or row-by-row) decoupling and arbitrary closed-loop pole placement and zero steady-state errors for regulation or tracking processes in presence of (non-diminishing) disturbances.
This study is concerned with liquid flow induced by a disk which rotates steadily around its axis and touches the free surface of liquid contained in a cylindrical vessel. It is a simplified model of the flow in the inlet part of a vertical cooling crystallizer where a rotary distributor of inflowing solution is situated above the free surface of solution contained in the crystalliser. Numerical simulations of flow phenomena were conducted and the simulation results were interpreted assuming an analogy with Kármán’s theoretical equations. In a cylindrical coordinate system, the components of flow velocity were identified as functions of distance from the surface of the rotating disk. The experimental setup was developed to measure velocity fields, using digital particle velocimetry and optical flow. Conclusions concerning the influence of disc rotation on liquid velocity fields were presented and the experimental results were found to confirm the results of numerical simulation. On the basis of simulation data, an approximation function was determined to describe the relationship between the circumferential component of flow velocity and the distance from the disk.
The paper presents equations of a mathematical model to calculate flow parameters in characteristic cross-sections in the steam-water injector. In the model, component parts of the injector (steam nozzle, water nozzle, mixing chamber, condensation wave region, diffuser) are treated as a series of connected control volumes. At first, equations for the steam nozzle and water nozzle are written and solved for known flow parameters at the injector inlet. Next, the flow properties in two-phase flow comprising mixing chamber and condensation wave region are determined from mass, momentum and energy balance equations. Then, water compression in diffuser is taken into account to evaluate the flow parameters at the injector outlet. Irreversible losses due to friction, condensation and shock wave formation are taken into account for the flow in the steam nozzle. In two-phase flow domain, thermal and mechanical nonequilibrium between vapour and liquid is modelled. For diffuser, frictional pressure loss is considered. Comparison of the model predictions with experimental data shows good agreement, with an error not exceeding 15% for discharge (outlet) pressure and 1 K for outlet temperature.
The paper presents the results of numerical analysis of the SAW gas sensor in the steady and non-steady states. The effect of SAW velocity changes vs surface electrical conductivity of the sensing layer is predicted. The conductivity of the porous sensing layer above the piezoelectric waveguide depends on the profile of the diffused gas molecule concentration inside the layer. The Knudsen’s model of gas diffusion was used. Numerical results for the effect of gas CH4 on layers: WO3, TiO2, NiO, SnO2 in the steady state and CH4 in the non-steady state in recovery step in the WO3 sensing layer have been shown. The main aim of the investigation was to study thin film interaction with target gases in the SAW sensor configuration based on simple reaction-diffusion equation. The results of the numerical analysis allow to select the sensor design conditions, including the morphology of the sensor layer, its thickness, operating temperature, and layer type. The numerical results basing on the code elaborated numerical system (written in Python language), were analysed. The theoretical results were verified and confirmed experimentally.
The primary goal of the study is to diagnose satisfaction and loyalty drivers in Polish retail banking sector. The problem is approached with Customer Satisfaction Index (CSI) models, which were developed for national satisfaction studies in the United States and European countries. These are multiequation path models with latent variables. The data come from a survey on Poles’ usage and attitude towards retail banks, conducted quarterly on a representative sample. The model used in the study is a compromise between author’s synthesis of national CSI models and the data constraints. There are two approaches to the estimation of the CSI models: Partial Least Squares – used in national satisfaction studies and Covariance Based Methods (SEM, Lisrel). A discussion is held on which of those two methods is better and in what circumstances. In this study both methods are used. Comparison of their performance is the secondary goal of the study.