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The turbulent flow through a 90o pipe bend is complex with secondary flow that can affect pressure drop and heat/mass transfer. The mean and unsteady flow is studied using refractive index matched two-dimensional two-component (2D2C) Particle Image Velocimetry in a single 90o bend with Rc/D = 1.5 and at Re = 34800. The measurements were performed in a closed loop using a 1-inch diameter test section that was machined out of acrylic. The flow is imaged in the symmetric plane parallel to the axial flow and at different cross sectional planes including 0.25D and 1D upstream, 10o, 20o, 70o, 80o from the bend inlet and 0.25D and 1D downstream of the bend. The axial flow accelerates on the inner wall at the inlet and then moves towards the outer wall at 40o-50o. A shear layer is formed between high velocity fluid near the outer wall and the slower moving fluid at the inner wall side in the second half of the bend. The axial turbulent kinetic energy ((u^2 ) ̅+(v^2 ) ̅) is found to be high in regions corresponding to high velocity gradient regions: (i) at the outer wall near the inlet that extends up to the outlet, (ii) near the inner wall at 40o-50o, and (iii) at the shear layer formed near the inner wall. In the cross sectional planes, two vortices are formed and have a maximum strength at 80o from the bend inlet. The cross sectional turbulent kinetic energy ((v^2 ) ̅+(w^2 ) ̅) is found to be highest on the inner wall at the 80o plane. The snapshot Proper Orthogonal Decomposition (POD) technique is used to study the unsteady flow structures within the flow. There are long and short flow structures in the upstream pipe which can be related to Very Large Scale and Large Scale Motions. The secondary flow at 20o and further downstream cross sectional planes show evidence of unsteadiness as two vortices oscillate about the symmetry axis with low frequencies of St ~ 0.07, 0.13 and higher frequency at St ~ 0.3-0.6. The low frequency oscillations can be related to Very Large Scale Motions while high frequency oscillations are related to separation of the flow on the inner wall side. Evidence of swirl switching in the high frequency range (St ~ 0.3-0.5) is found at cross sectional plane 1D downstream. / Thesis / Master of Applied Science (MASc)

Starting with tensor calculus and the variational form of the Hamiltonian functional, a generalized theory is formulated for doubly curved thin shells. The formulation avoids geometric approximations commonly adopted in other formulations. The theory is then specialized for cylindrical and toroidal shells as special cases, both of interest in the modeling of straight and elbow segments of pipeline systems. Since the treatment avoids geometric approximations, the cylindrical shell theory is believed to be more accurate than others reported in the literature. By adopting a set of consistent geometric approximations, the present theory is shown to revert to the well known Flugge shell theory. Another set of consistent geometric approximations is shown to lead to the Donnell-Mushtari-Vlasov (DMV) theory. A general closed form solution of the theory is developed for cylinders under general harmonic loads. The solution is then used to formulate a family of exact shape functions which are subsequently used to formulate a super-convergent finite element. The formulation efficiently and accurately captures ovalization, warping, radial expansion, and other shell behavioural modes under general static or harmonic forces either in-phase or out-of-phase. Comparisons with shell solutions available in Abaqus demonstrate the validity of the formulation and the accuracy of its predictions. The generalized thin shell theory is then specialized for toroidal shells. Consistent sets of approximations lead to three simplified theories for toroidal shells. The first set of approximations has lead to a theory comparable to that of Sanders while the second set of approximation has lead to a theory nearly identical to the DMV theory for toroidal shells. A closed form solution is then obtained for the governing equation. Exact shape functions are then developed and subsequently used to formulate a finite element. Comparisons with Abaqus solutions show the validity of the formulation for short elbow segments under a variety of loading conditions. Because of their efficiency, the finite elements developed are particularly suited for the analysis of long pipeline systems.

Starting with tensor calculus and the variational form of the Hamiltonian functional, a generalized theory is formulated for doubly curved thin shells. The formulation avoids geometric approximations commonly adopted in other formulations. The theory is then specialized for cylindrical and toroidal shells as special cases, both of interest in the modeling of straight and elbow segments of pipeline systems. Since the treatment avoids geometric approximations, the cylindrical shell theory is believed to be more accurate than others reported in the literature. By adopting a set of consistent geometric approximations, the present theory is shown to revert to the well known Flugge shell theory. Another set of consistent geometric approximations is shown to lead to the Donnell-Mushtari-Vlasov (DMV) theory. A general closed form solution of the theory is developed for cylinders under general harmonic loads. The solution is then used to formulate a family of exact shape functions which are subsequently used to formulate a super-convergent finite element. The formulation efficiently and accurately captures ovalization, warping, radial expansion, and other shell behavioural modes under general static or harmonic forces either in-phase or out-of-phase. Comparisons with shell solutions available in Abaqus demonstrate the validity of the formulation and the accuracy of its predictions. The generalized thin shell theory is then specialized for toroidal shells. Consistent sets of approximations lead to three simplified theories for toroidal shells. The first set of approximations has lead to a theory comparable to that of Sanders while the second set of approximation has lead to a theory nearly identical to the DMV theory for toroidal shells. A closed form solution is then obtained for the governing equation. Exact shape functions are then developed and subsequently used to formulate a finite element. Comparisons with Abaqus solutions show the validity of the formulation for short elbow segments under a variety of loading conditions. Because of their efficiency, the finite elements developed are particularly suited for the analysis of long pipeline systems.

Starting with tensor calculus and the variational form of the Hamiltonian functional, a generalized theory is formulated for doubly curved thin shells. The formulation avoids geometric approximations commonly adopted in other formulations. The theory is then specialized for cylindrical and toroidal shells as special cases, both of interest in the modeling of straight and elbow segments of pipeline systems. Since the treatment avoids geometric approximations, the cylindrical shell theory is believed to be more accurate than others reported in the literature. By adopting a set of consistent geometric approximations, the present theory is shown to revert to the well known Flugge shell theory. Another set of consistent geometric approximations is shown to lead to the Donnell-Mushtari-Vlasov (DMV) theory. A general closed form solution of the theory is developed for cylinders under general harmonic loads. The solution is then used to formulate a family of exact shape functions which are subsequently used to formulate a super-convergent finite element. The formulation efficiently and accurately captures ovalization, warping, radial expansion, and other shell behavioural modes under general static or harmonic forces either in-phase or out-of-phase. Comparisons with shell solutions available in Abaqus demonstrate the validity of the formulation and the accuracy of its predictions. The generalized thin shell theory is then specialized for toroidal shells. Consistent sets of approximations lead to three simplified theories for toroidal shells. The first set of approximations has lead to a theory comparable to that of Sanders while the second set of approximation has lead to a theory nearly identical to the DMV theory for toroidal shells. A closed form solution is then obtained for the governing equation. Exact shape functions are then developed and subsequently used to formulate a finite element. Comparisons with Abaqus solutions show the validity of the formulation for short elbow segments under a variety of loading conditions. Because of their efficiency, the finite elements developed are particularly suited for the analysis of long pipeline systems.

The thesis aim is an evaluation of achieved results coming from the analysis of pipe bend 180° for the critical bending / bend 1D and supercritical bending / bend 0,7D. The theoretical part is focused on material property of a bimetallic pipe and on methods applied to work out the analysis. The definition of critical points at a considered segment and possible defects arisen while bending is embodied in the thesis. The practical part of the thesis is based on presenting dimensional and proportional analysis based on using optical microscopes and 3D scanner GOM ATOS. The material analysis was aimed at macrostructure as well as microstructure of the bimetallic pipe material, at chemical composition and at the hardness when low-loaded. The analysis achieved results are assessed at the end of the thesis.

This thesis deals with turbulent flows in 90 degree curved pipes of circular cross-section. The flow cases investigated experimentally are turbulent flow with and without an additional motion, swirling or pulsating, superposed on the primary flow. The aim is to investigate these complex flows in detail both in terms of statistical quantities as well as vortical structures that are apparent when curvature is present. Such a flow field can contain strong secondary flow in a plane normal to the main flow direction as well as reverse flow. The motivation of the study has mainly been the presence of highly pulsating turbulent flow through complex geometries, including sharp bends, in the gas exchange system of Internal Combustion Engines (ICE). On the other hand, the industrial relevance and importance of the other type of flows were not underestimated. The geometry used was curved pipes of different curvature ratios, mounted at the exit of straight pipe sections which constituted the inflow conditions. Two experimental set ups have been used. In the first one, fully developed turbulent flow with a well defined inflow condition was fed into the pipe bend. A swirling motion could be applied in order to study the interaction between the swirl and the secondary flow induced by the bend itself. In the second set up a highly pulsating flow (up to 40 Hz) was achieved by rotating a valve located at a short distance upstream from the measurement site. In this case engine-like conditions were examined, where the turbulent flow into the bend is non-developed and the pipe bend is sharp. In addition to flow measurements, the effect of non-ideal flow conditions on the performance of a turbocharger was investigated. Three different experimental techniques were employed to study the flow field. Time-resolved stereoscopic particle image velocimetry was used in order to visualize but also quantify the secondary motions at different downstream stations from the pipe bend while combined hot-/cold-wire anemometry was used for statistical analysis. Laser Doppler velocimetry was mainly employed for validation of the aforementioned experimental methods. The three-dimensional flow field depicting varying vortical patterns has been captured under turbulent steady, swirling and pulsating flow conditions, for parameter values for which experimental evidence has been missing in literature. / QC 20120425

Starting with tensor calculus and the variational form of the Hamiltonian functional, a generalized theory is formulated for doubly curved thin shells. The formulation avoids geometric approximations commonly adopted in other formulations. The theory is then specialized for cylindrical and toroidal shells as special cases, both of interest in the modeling of straight and elbow segments of pipeline systems. Since the treatment avoids geometric approximations, the cylindrical shell theory is believed to be more accurate than others reported in the literature. By adopting a set of consistent geometric approximations, the present theory is shown to revert to the well known Flugge shell theory. Another set of consistent geometric approximations is shown to lead to the Donnell-Mushtari-Vlasov (DMV) theory. A general closed form solution of the theory is developed for cylinders under general harmonic loads. The solution is then used to formulate a family of exact shape functions which are subsequently used to formulate a super-convergent finite element. The formulation efficiently and accurately captures ovalization, warping, radial expansion, and other shell behavioural modes under general static or harmonic forces either in-phase or out-of-phase. Comparisons with shell solutions available in Abaqus demonstrate the validity of the formulation and the accuracy of its predictions. The generalized thin shell theory is then specialized for toroidal shells. Consistent sets of approximations lead to three simplified theories for toroidal shells. The first set of approximations has lead to a theory comparable to that of Sanders while the second set of approximation has lead to a theory nearly identical to the DMV theory for toroidal shells. A closed form solution is then obtained for the governing equation. Exact shape functions are then developed and subsequently used to formulate a finite element. Comparisons with Abaqus solutions show the validity of the formulation for short elbow segments under a variety of loading conditions. Because of their efficiency, the finite elements developed are particularly suited for the analysis of long pipeline systems.

The production and transportation of hydrocarbon fluids in multiphase pipelines could be severely hindered by particulate solids deposit such as produced sand particles which accompany hydrocarbon production. Knowledge of the flow characteristics of solid particles in fluids transported in pipelines is important in order to accurately predict solid particles deposition in pipelines. This research thesis presents the development of a three-dimensional (3D) Computational Fluids Dynamics (CFD) modelling technique for the prediction of liquid-solids multiphase flow in pipes, with special emphasis on the flow in V-inclined pipe bends. The Euler-Euler (two-fluid) multiphase modelling methodology has been adopted and the multiphase model equations and closure models describing the liquid-solids flow have been implemented and calculated using the finite volume method in a CFD code software. The liquid phase turbulence has been modelled using a two-equation k−ε turbulence model which contains additional terms to account for the effects of the solid-particles phase on the multiphase turbulence structure. The developed CFD numerical framework has been verified for the relevant forces and all the possible interaction mechanisms of the liquid-solids multiphase flow by investigating four different numerical frameworks, in order to determine the optimum numerical framework that captures the underlying physics and covers the interaction mechanisms that lead to sand deposition and the range of sand transport flow regimes in pipes. The flow of liquid-sand in pipe has been studied extensively and the numerical results of sand concentration distribution across pipe and other flow properties are in good agreement with published experimental data on validation. The numerical framework has been employed to investigate the multiphase flow in V-inclined pipe bends of ±4o−6o, seemingly small inclined bend angles. The predicted results which include the sand segregation, deposition velocity and flow turbulence modulation in the pipe bend show that the seemingly small pipe bends have significant effect on the flow differently from that of horizontal pipes. The pipe bend causes abrupt local change in the multiphase flow characteristic and formation of stationary sand deposit in the pipe at a relatively high flow velocity. The threshold velocity to keep sand entrained in liquid in pipe bends is significantly higher than that required for flow horizontal pipes. A critical implication of this is that the correlations for predicting sand deposition in pipelines must account for the effect of pipe bend on flow characteristics in order to provide accurate predictions of the critical sand transport velocity (MTV) in subsea petroleum flowlines, which V-inclined pipe bends are inevitable due to seabed topology.