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Abstract
The present work is mainly concerned on presenting a numerical simulation of both laminar, turbulent, two dimensional axi-symmetric and three dimensional flow through Hydraulic Capsule Pipelines for not only moving concentric capsule but also stationary eccentric capsule to predict the flow performance across both single long capsule and short capsules in train. This study is presented in the following four parts.
First, an analytical analysis and a numerical model are presented to study the flow behavior in concentric annulus with moving core in pipe for laminar flow condition. The analytical analysis is presented as exact solution for steady, fully developed one dimensional flow. The numerical model is presented to study two dimensional, steady, developing and fully developed flows. The numerical model established a staggered grid for axial and radial velocities (V z and V r) and using the pressure correction technique. The analyses were used to predict not only the fully developed velocity profile for Negative, zero, and adverse pressure gradients but also the developing velocity profiles until flow reaches the fully developed. The developing length (entrance length), the boundary layer thickness and the pressure distribution along the moving core at different values of Reynolds number are also obtained by the present model. The drag coefficient relative to both the moving core wall and the pipe wall can be calculated at different values of Reynolds number and diameter ratios. The results of the laminar model were shown to be in good agreement with the analytical (exact) solution for the fully developed flow. This also gives confidence of the obtained results for the developing flow through the entrance length using the numerical model.
Second, a numerical model was developed for the equations governing the turbulent flow around single concentric long capsule in pipe. First, the turbulence modeling was established for the concentric annulus between the capsule and the pipe to simulate the flow as axi-symmetric, steady flow without edge effect. Second, the turbulence modeling was established for the same case taking into account the edge effect. Finally, the turbulence modeling was established to simulate the axi-symmetric flow as three dimensional, turbulent steady flow to verify the assumption ofaxi-symmetric. Three different turbulence models were used to simulate the flow: an algebraic model (Boldwin¬Lomax model) and two types of two equation models (lc-e and lc-m models). All of these models were verified by comparing the results of the pressure gradient along the capsule in all models and with the experimental results. In addition, other experimental data of the velocity profiles of other investigators were used in the comparison to verifY the presented models. The results predicted by the three different turbulence models were shown to be in a good agreement with the experimental data but their precisions differed trom each other.
Third, the present work in this part is primarily concerned with practical aspects of modeling the turbulent flow around concentric capsule train in pipes. A turbulence model was developed using k-& model. First, the turbulence modeling was established for the concentric capsule train without any intercapsule spaces in pipe to simulate the flow as axi-symmetric, two dimensional, steady flow with edge effects. Second, the turbulence modeling was established for the same case but with different equal and unequal intercapsu1e spaces. The main concept of this simulation is to study the effect of
intercapsule space on capsule flow perfonnance such as the total pressure drop, the friction factor, and the shape of the flow pattern. Finally, all of these models were verified not only by making a force analysis on the capsule train to check its balance but also by comparing the results of the friction factor with the experimental data. The obtained results are in good agreement with the experimental data. The capsule train would be balanced (i.e. the net propelling pressure forces equal the drag resisting shear forces), so that this balancing should be applied for all cases. The overall pressure drop across the capsule train was shown to be decreased as the intercapsule space is increased. This tends to decrease the mass of the transported cargos because of decreasing the number of capsules for the same pipeline length so that the design of capsule pipeline systems would need optimization of
this intercapsule space.
Finally, the present study is primarily concerned with modeling 3D, turbulent, steady flow over a stationary capsule in a pipeline to predict the pressure distribution around the capsule. The results were used to determine the lift and Drag on the capsule. The results were compared with the experimental data to validate the models. Two types of the two equation models (k - & and k - OJ) and a second moment closure model (Reynolds stress model RSM) were used in the numerical simulation. The experimental data which were used to determine the drag were shown to be in good agreement with the three turbulence models. Meanwhile, the experimental data related to the lift were shown to be in a good agreement with the RSM model only. This explains the limitation of using the two equation models. Consequently, the RSM can be used for performing a parametric study on the lift
and drag on the stationary capsule.