The paper presents modeling and simulation results of the operation of a three-phase fluidized bed bioreactorwith partial recirculation of biomass. The proposed quantitative description of the bioreactor takes into account biomass growth on inert carriers, microorganisms decay and interphase biomass transfer. Stationary characteristics of the bioreactor and local stability of steady-stateswere determined. The influence of microbiological growth kinetics on the multiplicity of steady-states was discussed. The relationship between biofilm growth and boundaries of fluidized bed existence was shown.
This paper aims at providing a framework for comprehensive steady-state time-domain analysis of rotating machines considering motion. The steady-state waveforms of electromagnetic and circuit quantities are computed via iterative solution of the nonlinear field-circuit-and-motion problem with constraints of time periodicity. The cases with forced speed and forced load torque are considered. A comparison of execution times with a conventional time-stepping transient model is carried out for two different machines. The numerical stability of a time-periodic model with forced speed is shown to be worse than that of traditional transient time-stepping one, although the model converges within a reasonable number of iterations. This is not the case if forced load via equation of mechanical balance is accounted for. To ensure convergence of the iterative process the physical equation of motion is replaced by the fixed-point equation. In this way the model delivers time-periodic solutions regarding not only the electromagnetic quantities but also the rotational speed.
The focus of research works on cavitation has changed since the 1960s; the behaviour of a single bubble is no more the area of interest for most scientists. Its place was taken by the cavitating flow considered as a whole. Many numerical models of cavitating flows came into being within the space of the last fifty years. They can be divided into two groups: multifluid and homogeneous (i.e., single-fluid) models. The group of homogenous models contains two subgroups: models based on transport equation and pressure based models. Several works tried to order particular approaches and presented short reviews of selected studies. However, these classifications are too rough to be treated as sufficiently accurate. The aim of this paper is to present the development paths of numerical investigations of cavitating flows with the use of homogeneous approach in order of publication year and with relatively detailed description. Each of the presented model is accompanied by examples of the application area. This review focuses not only on the list of the most significant existing models to predict sheet and cloud cavitation, but also on presenting their advantages and disadvantages. Moreover, it shows the reasons which inspired present authors to look for new ways of more accurate numerical predictions and dimensions of cavitation. The article includes also the division of source terms of presented models based on the transport equation with the use of standardized symbols.
In this paper, the computer modelling application based on the modal expansion method is developed to study the influence of a sound source location on a steady-state response of coupled rooms. In the research, an eigenvalue problem is solved numerically for a room system consisting of two rectangular spaces connected to one another. A numerical procedure enables the computation of shape and frequency of eigenmodes, and allows one to predict the potential and kinetic energy densities in a steady-state. In the first stage, a frequency room response for several source positions is investigated, demonstrating large deformations of this response for strong and weak modal excitations. Next, a particular attention is given to studying how the changes in a source position influence the room response when a source frequency is tuned to a resonant frequency of a strongly localized mode.
Airborne acoustic properties of composite structural insulated panels CSIPs composed of fibre-magnesium-cement facesheets and expanded polystyrene core were studied. The sound reduction ratings were measured experimentally in an acoustic test laboratory composed of two reverberation chambers. The numerical finite element (FEM) model of an acoustic laboratory available in ABAQUS was used and verified with experimental results. Steady-state and transient FE analyses were performed. The 2D and 3D modelling FE results were compared. Different panel core modifications were numerically tested in order to improve the airborne sound insulation of CSIPs.
This paper presents the improved methodology for the direct calculation of steady-state periodic solutions for electromagnetic devices, as described by nonlinear differential equations, in the time domain. A novel differential operator is developed for periodic functions and the iterative algorithm determining periodic steady-state solutions in a selected set of time instants is identified. Its application to steady-state analysis is verified by an elementary example. The modified algorithm reduces the complexity of steady-state analysis, particularly for electromagnetic devices described by high-dimensional nonlinear differential equations.
This paper presents a set of concepts aiming at the reconstruction of mechanisms of the development of economic space. These concepts are ordered in the way that consecutive concepts add new pieces of knowledge increasing the degree of cognition of the mechanisms of economic space. This set includes among others: shift from one steady-state to the next steady-states, selforganization and the development out of equilibrium, multiple equilibrium, punctuated equilibrium, innovation in the phase transition, pulsative course of development process, emergence of complex spatial systems, development code of the system of regions.
A two-parameter continuation method was developed and shown in the form of an example, allowing determination of Hopf bifurcation sets in a chemical reactor model. Exemplary calculations were made for the continuous stirred tank reactor model (CSTR). The set of HB points limiting the range of oscillation in the reactor was determined. The results were confirmed on the bifurcation diagram of steady states and on time charts. The method is universal and can be used for various models of chemical reactors.
The zero attraction affine projection algorithm (ZA-APA) achieves better performance in terms of convergence rate and steady state error than standard APA when the system is sparse. It uses l1 norm penalty to exploit sparsity of the channel. The performance of ZA-APA depends on the value of zero attractor controller. Moreover a fixed attractor controller is not suitable for varying sparsity environment. This paper proposes an optimal adaptive zero attractor controller based on Mean Square Deviation (MSD) error to work in variable sparsity environment. Experiments were conducted to prove the suitability of the proposed algorithm for identification of unknown variable sparse system.
Suitable and complete sets of stress-strain curves significantly affected by dynamic recrystallization were analyzed for 11 different iron, copper, magnesium, titanium or nickel based alloys. Using the same methodology, apparent hot deformation activation energy Qp and Qss values were calculated for each alloy based on peak stress and steady-state stress values. Linear dependence between quantities Qp and Qss was found, while Qp values are on average only about 6% higher. This should not be essential in predicting true stress of a specific material depending on the temperature-compensated strain rate and strain.
This paper describes an algorithm for finding steady states in AC machines for the cases of their two-periodic nature. The algorithm enables to specify the steady-state solution identified directly in time domain despite of the fact that two-periodic waveforms are not repeated in any finite time interval. The basis for such an algorithm is a discrete differential operator that specifies the temporary values of the derivative of the twoperiodic function in the selected set of points on the basis of the values of that function in the same set of points. It allows to develop algebraic equations defining the steady state solution reached in a chosen point set for the nonlinear differential equations describing the AC machines when electrical and mechanical equations should be solved together. That set of those values allows determining the steady state solution at any time instant up to infinity. The algorithm described in this paper is competitive with respect to the one known in literature an approach based on the harmonic balance method operated in frequency domain.