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.
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.
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.
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.
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.
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.
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.