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The present study deals with the computational simulation of transient events of water hammer and column separation in a water pipeline system. Three-dimensional CFD simulations based on the Finite-Volume (FV) approach are performed to predict pressure fluctuations and to visualize liquid column separation/rejoining caused by the sudden closure of a valve located at the upstream end of the pipe. Explanation of vaporous cavitation phenomena is also presented. The Volume of Fluid (VOF) model and Schnerr-Sauer cavitation model are used to describe the multiphase flow and the transient vaporous cavitation, respectively. Moreover, the shear-stress transport (SST) turbulence model is applied to model the Reynolds stresses using the Boussinesq hypothesis. Present results are compared with available experimental and numerical results from the literature. The comparisons show that the present method gives adequate results. Also, the 3D model adopted is deemed physically superior to the existing 1D models as it removes the restriction of the 1D models that vapor cavities, when formed, fill the whole cross-section of the pipe without radial variation. In addition, 1D models are not able to predict the stratification effect due to density variation of the two phases. Consequently, the 3D model can better visualize the phenomenon of liquid column separation/rejoining in pipes than 1D models.
In this study, air-water flow in a downward sloping pipe subsequent to the entrapping of an air pocket is investigated both numerically and experimentally. A transient, two-dimensional computational fluid dynamics model is applied to study the different possible flow regimes and their associated phenomena. The numerical model is based on the Reynolds averaged Navier Stokes (RANS) equations and the Volume of Fluid (VOF) method. Both numerical and experimental investigations provide visualization for the hydraulic jump, the blowback regime, and the full gas transport regime. The numerical results predict that the flow structure in the pipe downstream the toe of the hydraulic jump is subdivided into three distinct regions including the jet layer, the shear zone and the circulation region, which agrees qualitatively with the previous investigations of the hydraulic jump characteristics in open channel flow. Numerical results are in reasonable agreement with the experimental measurements of the circulation length and the hydraulic jump head loss.
Numerical simulations of transient entropy generation in a reservoir-pipe-valve system are presented. The flow transient is initiated through sudden closure of the downstream valve. An unsteady two-dimensional water hammer model is adopted. Time integration is performed using the classical fourth-order Runge–Kutta method while the spatial terms are discretized using central difference expressions. Entropy generation is shown to depend on a non-dimensional parameter representing the ratio of the viscous diffusion time scale to the pipe period. For small values of the non-dimensional parameter, entropy generation is rapidly attenuated from its steady-state value to zero while for large values, entropy generation persists for a much longer time. Moreover, for large values of the non-dimensional parameter, excessive entropy generation rates are realized during the transient which are several orders of magnitude higher than the steady-state rate. Such a behavior is attributed to elevated transient shear stress values in the near wall region which result in excessive viscous dissipation and hence higher entropy generation rates. Finally, it is shown that during the transient, the location of maximum entropy generation is no longer restricted to the pipe wall.
Modeling turbulence in two-dimensional water hammer simulations is considered in the present study. The Baldwin–Lomax turbulence model is implemented, both in quasi-steady and frozen forms. Numerical simulations using both forms agree well with experimental data for lower Reynolds numbers (Re=5600) and the attenuation of the transient is adequately captured. However, for higher Reynolds numbers (Re=15,800), the frozen form overpredicts the attenuation of the transient. Moreover, it is shown that switching the turbulence model off altogether and applying a quasi-laminar approximation results in good agreement with experimental data for the lower Reynolds number case (Re=5600) while underpredicting the attenuation of the transient for the higher Reynolds number case (Re=15,800).
In this study, a numerical model based on the Method of Characteristics (MOC) is developed for modeling pressure transients in viscoelastic pipelines in the presence of column separation. The model is capable of modeling complex phenomena, which could not be modeled by the standard MOC, such as unsteady friction and viscoelastic behavior of the pipe walls. Unsteady friction is modeled through a universal model developed by the authors. The viscoelastic behavior of the pipe walls is modeled through a one-element Kelvin-Voigt Viscoelastic Model. The column separation phenomenon is simulated through two models; namely the Discrete Vapor Cavity Model (DVCM) and the Discrete Gas Cavity Model (DGCM). In comparison with the DVCM, the DGCM was shown to enable a better prediction of the pressure transients in the system. An expression was developed for the effective wave speed in the DGCM and this expression was compared with the expression of the wave speed for twophase flow transients of low void fraction. However, the rate of gas release assumed in the DGCM, remains a highly sensitive parameter in the model. An experimental setup was constructed to provide reliable experimental data for transient flows in PVC (viscoelastic) pipes to verify the numerical model. Eventually, the numerical model was experimentally verified to be capable of dealing with all unsteady complex phenomena and efficiently simulating the pressure transients in the presence of column separation.
In this study, a numerical model based on the Method of Characteristics (MOC) is developed for modeling pressure transients in viscoelastic pipes. The model is capable of dealing with unsteady friction and viscoelastic behavior of the pipe walls. These complex phenomena cause strong distortion of the pressure waves traveling through fluids that may not be predicted by the standard MOC. A universal model, developed by the authors, for unsteady friction for both laminar and turbulent flows is used in the analysis. The viscoelastic behavior of the pipe wall is modeled through a one element Kelvin-Voigt-Viscoelastic Model that is in good agreement with the experimental data. The viscoelastic effect was shown to be the dominant damping factor of the pressure oscillations in transient flows through pipes exhibiting a viscoelastic behavior. The analysis showed also that unsteady friction has a minor effect on the damping of the pressure transient in viscoelastic pipes while it has a dominant damping effect in case of elastic pipes. An experimental setup was constructed to provide reliable experimental data for transient flows in PVC (viscoelastic) pipes to verify the numerical model. Eventually, the numerical model was experimentally verified to be capable of accurately and efficiently reproducing the experimentally measured pressure oscillations in viscoelastic pipes.