THE IMPACT OF SELECTED PARAMETERS ON PRESSURE DISTRIBUTION IN THE FACE THROTTLE OF A CENTRIFUGAL PUMP AUTOMATIC BALANCING DEVICE

Face throttles are a necessary functional element of non-contact face seals and automatic balancing devices of centrifugal pumps of different constructions. To calculate the hydrodynamic forces and moments acting on the rotor and fluid flow through the automatic balancing device, it is necessary to know the pressure distribution in the cylindrical and face throttle when considering all important factors which predetermine fluid flow. The face throttle surfaces are moving, which leads to unsteady fluid flow. The movement of the walls of the face throttle causes an additional circumferential and radial flow, which subsequently leads to the additional hydrodynamic pressure components. The paper analyses viscous incompressible fluid flow in the face throttle of an automatic balancing device taking into account the axial and angular displacements of throttle’s surfaces and the inertia component of the fluid. The effect of local hydraulic losses as well as random changes in the coefficients of local hydraulic resistance at the inlet and outlet of the throttle is analysed.

Parametric Study of Unsteady Flow and Heat Transfer of Compressible Helium–Xenon Binary Gas through a Porous Channel Subjected to a Magnetic Field

A numerical analysis of unsteady fluid and heat transport of compressible Helium–Xenon binary gas through a rectangular porous channel subjected to a transverse magnetic field is herein presented. The binary gas mixture consists of Helium (He) and Xenon (Xe). In addition, the compressible gas properties are temperature-dependent. The set of governing equations are nondimensionalized via appropriate dimensionless parameters. The dimensionless equations involve a number of dimensionless groups employed for detailed parametric study. Consequently, the set of equations is discretized using a compact finite difference scheme and solved by using the 3rd-order Runge–Kutta method. The model’s computed results are compared with data from past literature, and very favorable agreement is achieved. The results show that the magnetic field, compressibility and variable fluid properties profoundly affect heat and fluid transport. Variations of density with temperature as well as pressure result in an asymmetric mass flow profile. Furthermore, the friction coefficient is greater for the upper wall than for the lower wall due to larger velocity gradients along the top wall.

Flow-Induced Vibration of a Candu Fuel String

A comprehensive vibration model is developed in this thesis to simulate the dynamical behaviour of a string of CANDU fuel bundles subjected to unsteady flow of coolant inside a pressure tube. The large-scale dynamical system of interest consists of several hundreds of solid and deformable components interacting with the coolant flow, with each other and with the pressure tube through frictional contact at various interfaces. In the first stage of this thesis, the three-node higher-order mixed beam finite elements and the nine-node thick plate finite elements are employed to model the fuel bundles. The equations of motion of the fuel string system are discretised in the time domain using the Newmark integration scheme. The CANDU fuel string behaviour is highly nonlinear and the total number of potential frictional contact exceeds thousand sets. In the second stage, a numerical scheme for efficiently handling three-dimensional friction and contact is developed. The incremental displacement is used to relate gaps with contact forces and the problem is formulated to be a linear complementarity problem (LCP). The accuracy and robustness of the presented method is tested against several numerical simulations and experimental results available in the literature. To find the unsteady fluid forces acting on the fuel string two comprehensive computational fluid dynamic (CFD) models that include endcaps and spacer pads are developed. The models are solved using the large eddy simulation (LES) scheme. The coolant unsteady pressure is integrated over fuel rods surfaces and unsteady fluid forces are found and used as the excitation sources for fuel string vibration. The power spectral density (PSD) of unsteady fluid forces are obtained and peak frequencies are identified. A FORTRAN code consisting of approximately 13000 lines is developed and validated at different stages for use in Canadian nuclear industry to simulate the vibrational behaviour of a 12-bundle fuel string and the material loss during reactor normal operations. Free vibration analyses of a CANDU fuel string are also performed and natural frequencies of the system are obtained.

Flow-Induced Vibration of a Candu Fuel String

A comprehensive vibration model is developed in this thesis to simulate the dynamical behaviour of a string of CANDU fuel bundles subjected to unsteady flow of coolant inside a pressure tube. The large-scale dynamical system of interest consists of several hundreds of solid and deformable components interacting with the coolant flow, with each other and with the pressure tube through frictional contact at various interfaces. In the first stage of this thesis, the three-node higher-order mixed beam finite elements and the nine-node thick plate finite elements are employed to model the fuel bundles. The equations of motion of the fuel string system are discretised in the time domain using the Newmark integration scheme. The CANDU fuel string behaviour is highly nonlinear and the total number of potential frictional contact exceeds thousand sets. In the second stage, a numerical scheme for efficiently handling three-dimensional friction and contact is developed. The incremental displacement is used to relate gaps with contact forces and the problem is formulated to be a linear complementarity problem (LCP). The accuracy and robustness of the presented method is tested against several numerical simulations and experimental results available in the literature. To find the unsteady fluid forces acting on the fuel string two comprehensive computational fluid dynamic (CFD) models that include endcaps and spacer pads are developed. The models are solved using the large eddy simulation (LES) scheme. The coolant unsteady pressure is integrated over fuel rods surfaces and unsteady fluid forces are found and used as the excitation sources for fuel string vibration. The power spectral density (PSD) of unsteady fluid forces are obtained and peak frequencies are identified. A FORTRAN code consisting of approximately 13000 lines is developed and validated at different stages for use in Canadian nuclear industry to simulate the vibrational behaviour of a 12-bundle fuel string and the material loss during reactor normal operations. Free vibration analyses of a CANDU fuel string are also performed and natural frequencies of the system are obtained.

Factorization à la Dirac Applied to Some Equations of Classical Physics

In this paper, we present an application of Dirac’s factorization method to three types of the partial differential equations, i.e., the wave equation, the scattering equation, and the telegrapher’s equation. This method gives results that contribute to a better understanding of physical phenomena by generalizing the Euler and constituent equations. Its application to the wave equation shows that it is indeed a factorization method, since it gives d’Alembert’s solutions in a more general framework. In the case of the diffusion equation, a fractional differential equation has been established that has already been highlighted by other authors in particular cases, but by indirect methods. Dirac’s method brings several new results in the case of the telegraphers’ equation corresponding to the propagation of an acoustic wave in a dissipative fluid. On the one hand, its formalism facilitates the temporal interpretation of phenomena, in particular the density and compressibility of the fluid become temporal operators, which can be “seen” as susceptibilities of the fluid. On the other hand, a consequence of this temporal modeling is the highlighting in Euler’s equation of a term similar to the one that was introduced by Boussinesq and Basset in the equation of the motion of a solid sphere in a unsteady fluid.