# Volume 8, number 2 (2014)

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Item Estimation of the nuclear fuel assembly eigenfrequencies in the probability sense(University of West Bohemia, 2014) Zeman, Vladimír; Hlaváč, ZdeněkShow more The paper deals with upper and lower limits estimation of the nuclear fuel assembly eigenfrequencies, whose design and operation parameters are random variables. Each parameter is defined by its mean value and standard deviation or by a range of values. The gradient and three sigma criterion approach is applied to the calculation of the upper and lower limits of fuel assembly eigenfrequencies in the probability sense. Presented analytical approach used for the calculation of eigenfrequencies sensitivity is based on the modal synthesis method and the fuel assembly decomposition into six identical revolved fuel rod segments, centre tube and load-bearing skeleton linked by spacer grids. The method is applied for the Russian TVSA-T fuel assembly in the WWER1000/320 type reactor core in the Czech nuclear power plant Temelín.Show more Item Analytic solution of simplified Cardan’s shaft model(University of West Bohemia, 2014) Zajíček, Martin; Dupal, JanShow more Torsional oscillations and stability assessment of the homokinetic Cardan shaft with a small misalignment angle is described in this paper. The simplified mathematical model of this system leads to the linearized equation of the Mathieu’s type. This equation with and without a stationary damping parameter is considered. The solution of the original differential equation is identical with those one of the Fredholm’s integral equation with degenerated kernel assembled by means of a periodic Green’s function. The conditions of solvability of such problem enable the identification of the borders between stability and instability regions. These results are presented in the form of stability charts and they are verified using the Floquet theory. The correctness of oscillation results for the system with periodic stiffness is then validated by means of the Runge-Kutta integration method.Show more Item Three-scale model of single bone osteon modelled as double-porous fluid saturated body: Study of influence of micro/meso-structure(University of West Bohemia, 2014) Turjanicová, Jana; Rohan, Eduard; Naili, SalahShow more This paper deals with the multiscale description of a single osteon of cortical bones. The cortical bone tissue is modeled as a double-porous medium decomposed into the solid matrix and the fluid saturated canals. The resulting homogenized model describes deformation of such medium in response to a static loading by external forces and to an injection of slightly compressible fluid. Three numerical examples are presented, showing the influence of selected lower-scales geometrical features on the macroscopic body behavior.Show more Item Modal parameters of a rotating multiple-disk-shaft system from simulated frequency response data(University of West Bohemia, 2014) Khader, NaimShow more Modal parameters of a rotating multiple disk-shaft system are estimated in Multiple Input/Multiple Output (MIMO) scheme. The response at multiple output degrees of freedom (dofs) and excitations at multiple input (reference) dofs are related through the Frequency Response Function (FRF) matrix. The corresponding Impulse Response Function (IRF) matrix is obtained by Inverse Fast Fourier Transform (IFFT) of the FRF matrix. The resulting FRF matrix is not symmetric due to the gyroscopic effects introduced by rotation. The Eigensystem Realization Algorithm (ERA) and its equivalent low order time domain algorithm, based on the Unified Matrix Polynomial Approach (UMPA) are employed to estimate the desired modal parameters, i.e., system eigenvalues and the asso- ciated right hand and left hand eigenvectors. The right hand vectors are estimated from multiple columns of the FRF matrix with the structure rotating in one direction, and the left hand vectors are estimated from the multiple rows of the FRF matrix, which are calculated as the transpose of the same multiple columns of the FRF matrix, estimated with rotation in the opposite direction. The obtained results are found to be in excellent agreement with results obtained from Theoretical Modal Analysis (TMA).Show more Item A comparative study of 1D and 3D hemodynamics in patient-specific hepatic portal vein networks(University of West Bohemia, 2014) Jonášová, Alena; Bublík, Ondřej; Vimmr, JanShow more The development of software for use in clinical practice is often associated with many requirements and restrictions set not only by the medical doctors, but also by the hospital’s budget. To meet the requirement of reliable software, which is able to provide results within a short time period and with minimal computational demand, a certain measure of modelling simplification is usually inevitable. In case of blood flow simulations carried out in large vascular networks such as the one created by the hepatic portal vein, simplifications are made by necessity. The most often employed simplification includes the approach in the form of dimensional reduction, when the 3D model of a large vascular network is substituted with its 1D counterpart. In this context, a question naturally arises, how this reduction can affect the simulation accuracy and its outcome. In this paper, we try to answer this question by performing a quantitative comparison of 3D and 1D flow models in two patient-specific hepatic portal vein networks. The numerical simulations are carried out under average flow conditions and with the application of the three-element Windkessel model, which is able to approximate the downstream flow resistance of real hepatic tissue. The obtained results show that, although the 1D model can never truly substitute the 3D model, its easy implementation, time-saving model preparation and almost no demands on computer technology dominate as advantages over obvious but moderate modelling errors arising from the performed dimensional reduction.Show more Item Wall effects on Reiner-Rivlin liquid spheroid(University of West Bohemia, 2014) Jaiswal, Bharat Raj; Gupta, B. R.Show more An analysis is carried out to study the flow characteristics of creeping motion of an inner non-Newtonian Reiner-Rivlin liquid spheroid r = 1+ ∑k=2∞αkGk(cos θ), here αk is very small shape factor and Gk is Gegenbauer function of first kind of order k, at the instant it passes the centre of a rigid spherical container filled with a Newtonian fluid. The shape of the liquid spheroid is assumed to depart a bit at its surface from the shape a sphere. The analytical expression for stream function solution for the flow in spherical container is obtained by using Stokes equation. While for the flow inside the Reiner-Rivlin liquid spheroid, the expression for stream function is obtained by expressing it in a power series of S, characterizing the cross-viscosity of Reiner-Rivlin fluid. Both the flow fields are then determined explicitly by matching the boundary conditions at the interface of Newtonian fluid and non-Newtonian fluid and also the condition of impenetrability and no-slip on the outer surface to the first order in the small parameter ε, characterizing the deformation of the liquid sphere. As an application, we consider an oblate liquid spheroid r = 1+2εG2(cos θ) and the drag and wall effects on the body are evaluated. Their variations with regard to separation parameter, viscosity ratio λ, cross-viscosity, i.e., S and deformation parameter are studied and demonstrated graphically. Several well-noted cases of interest are derived from the present analysis. Attempts are made to compare between Newtonian and Reiner-Rivlin fluids which yield that the cross-viscosity μc is to decrease the wall effects K and to increase the drag DN when deformation is comparatively small. It is observed that drag not only varies with λ, but as η increases, the rate of change in behavior of drag force increases also.Show more Item The role of vortices in animal locomotion in fluids(University of West Bohemia, 2014) Dvořák, RudolfShow more The aim of this paper is to show the significance of vortices in animal locomotion in fluids on two deliberately chosen examples. The first example concerns lift generation by bird and insect wings, the second example briefly mentiones swimming and walking on water. In all the examples, the vortices generated by the moving animal impart the necessary momentum to the surrounding fluid, the reaction to which is the force moving or lifting the animal.Show more