Unsteady Friction Fundamentals And Pressure Controlling Approaches Of Transient Flow In Water Pipeline Systems

Water hammer events can severely impact pipeline systems,such as pipe bursts,control valve failure,cyclic stress-induced fatigue failure,pump malfunction,vibration,contamination due to leakage,and infiltration of pathogens in potable water distribution networks.These effects emphasize the significance of modeling transient flow to reduce the risk of water hammer incidents.Myriad research on transient flow modeling currently relies on classical steady-state friction models.Method of Characteristics(MOC)is employed in these models to convert the governing equations of water hammer flows into elementary finite differential equations.Afterward,these equations are deployed to develop a numerical algorithm and computer programs.However,the steady-state friction formulation approach used in the classical water hammer models is better for calculating energy losses in slow transient flows(i.e.,low-frequency flow oscillations).When these approaches are applied to rapid transient flow,the computational results differ significantly from the experimental results regarding the pressure waves’ damping,form,and frequency.However,the accurate prediction of transient pressure signals is crucial for designing protection devices,monitoring transient flows for the system recovery time,and conducting inverse transient analysis for leakage detection.In order to address the issue of classical steady-state friction models’ inability to predict the attenuation process of pressure fluctuation accurately,several unsteady friction models,such as,weighting function-based(WFB)and instantaneous acceleration-based(IAB)models,were established by past researchers.However,their real-world applicability remains uncertain to a large extent.Most recent unsteady friction-based transient flow modeling investigations focus on a simple reservoir-pipe-valve system.They seldom evaluate the response of a pumping system under transient loads using various unsteady friction models.Given the significance of unsteady models in precisely simulating a transient event,this study assesses the effectiveness of different unsteady friction models in predicting the transient response of a pumping and gravity-based pipeline system,with or without a protection device.Besides,the past literature did not adequately address the overall transient behavior of complex pumping pipelines.Therefore,this study comprehensively addresses this gap by utilizing energy-based expressions to summarize the system’s behavior.In addition,the impact of entrapped air,fluid inertia,and unsteady friction is generally ignored in existing numerical models for transient cavitating flow;thus,it is necessary to conduct a study by integrating the WFB unsteady friction model and momentum correction factor into the discrete gas cavity model(DGYM).Prior research suggests that increasing the rotational inertia of the pumping system and integrating it with appropriate valve-closing schemes can improve surge protection.However,these studies did not account for unsteady frictional effects and additional power requirements for pump restart.Similarly,pressure vessels are effective in alleviating negative and positive overpressures,but scarce literature exists on optimizing pressure vessel connection configurations.To fill these research gaps,this study proposes a novel technique that uses a porous flow throttling connector to optimize the size of a pressure vessel.This study’s adopted research methods,major findings,and unique contributions are summarized below,and arranged in accordance with the study’s chapters and objectives:(1)The adjustment of rotational inertia of a pumping system alongside various valve closing operations was investigated here to determine its efficacy in controlling water hammer flows.One-dimensional IAB unsteady friction models were also improved by investigating the response of elastic pipes under transient events.The advanced version of IAB unsteady friction models was used to explore the complexities of transient energy dissipation.Mathematical expressions were derived for boundary conditions defining the behavior of different elements in the pumping pipeline system,including centrifugal pumps,check valves,flywheels,and reservoirs.After that,novel modifications were introduced into the newly proposed numerical models to better represent internal conditions during a transient event,such as unsteady friction,reservoir entrance/exit losses,and instantaneous decay coefficients.These expressions and internal conditions were then combined with water hammer governing equations via the MOC.As a result,a final system of equations was attained and implemented into Fortran script,which was capable of predicting the transient pressure and flow variations.The numerical results of the two IAB unsteady friction models were compared with experimental data to verify the proposed numerical algorithm.The results indicate that the oneand the two-coefficient IAB unsteady friction models yield almost similar results that match the experimental outcomes.However,the latter model is comparatively more complex in terms of formulation.Furthermore,a parametric study shows that increasing the moment of inertia of the pump and integrating it with the optimal operation of the valve helps in significantly controlling the transient pressure.This helps in reducing the check-valve slam and controls the water hammer with no need for additional protection devices.Also,the total frictional dissipation rate prediction using the unsteady IAB models approaches the quasi-steady model prediction for slow valve closures and larger moment of inertia values.Consequently,the unsteady friction effect becomes less important for the aforementioned conditions of the pumping system.The current research provides valuable tools(i.e.,numerical algorithm and water hammer protection strategy)for designing pipeline protection strategies against hazardous water hammer effects.(2)An iterative algorithm for applying various boundary expressions into transient flow models of pumping pipelines comprising a pressure vessel was developed to investigate the influence of system parameters on transient pressure.Moreover,an innovative approach was devised for modifying the connection configuration with the main pipeline for improved pressure vessel design.To this end,an integrated numerical model of the pressure vessel,connection pipe,and pumping system was established based on the MOC and IAB unsteady friction model.The simulation results were compared with relevant experimental results to verify the proposed numerical algorithm with two decay coefficients.Based on the proposed numerical model and computational algorithms,a novel approach was also explored to increase the working efficiency of the pressure vessel during transient events.Moreover,a parametric study was conducted to determine the impact of the pressure vessel’s numerous parameters(i.e.,discharge coefficient of perforated plates,initial air volume,polytropic exponent,and installation location)on transient pressure signals.According to the simulation results,the IAB unsteady friction model with two decay parameters can accurately replicate the form of transient waves caused by a power failure in a pumping system comprising a pressure vessel,with almost no deviations between numerical and experimental results.Furthermore,the numerical study shows that the initial air volume,polytropic exponent,installation location,pressure vessel size,and connection arrangement of the pressure vessel with the pump-rising pipeline significantly affect the performance of water hammer protection.However,the flow resistance of connecting pipes containing perforated plates in a separate bypass line reduces the desired vessel volume from the standpoint of economy.The redesigned connection configuration decreases the required pressure vessel volume by up to 70%,leading to costeffectiveness.The findings of this study can guide practitioners working on designing pipeline systems under severe hydraulic transient conditions.(3)An energy-based technique was utilized to obtain a holistic overview of the transient condition in a pump-rising pipeline integrated with a pressure vessel.To this end,this study identifies various energy forms to understand the energy transfer during transient flow triggered by a pump failure and valve closure and compares the hydraulic performance of different protective devices.The system for this study comprised two centrifugal pumps,a pressure vessel,a check valve,and a linearly ascending pipeline that connects two reservoirs.The governing equations for water hammer flow and their accompanying boundary conditions equations were mathematically manipulated to formulate an integrated numerical model for energy analysis.Moreover,the absolute instantaneous value of local attenuation parameters was considered to ensure that friction is always associated with dissipation.According to numerical results,the energy supplied by the vessel leads to negative pressure control at the onset of transient flow,after which energy dissipation occurs due to the energy exchange mechanisms.Also,the relative significance of unsteady friction is heavily dependent on system parameters(i.e.,pressure vessel size,the rotational inertia of the pumping system,valve closing time,and connection arrangement of the pressure vessel).However,the inclusion of unsteady friction is imperative for accurately simulating transient flow in relatively large-scale pipe systems with high-frequency wave behaviors.Hence,the application of the unsteady friction models is preferable in contrast to a quasi-friction model in the design of pipeline systems.In addition,the energy analysis of the pumping system aids in determining the role of compressibility under transient conditions.This analysis permits the evaluation of the impact of changes in the compressibility index and the categorization of various flow conditions,which can aid in the model selection process.These findings have numerous applications while designing and operating pumping systems in various industries.(4)A discrete cavity model considering unsteady frictional effects was developed to produce accurate predictions of the transient cavitating flow in pipelines.This novel approach combined the advantages of the unsteady friction model,momentum correction factor,and the DGYM.In order to verify the proposed numerical algorithm,different numerical analyses of transient cavitating flow in a simple reservoir-pipeline-valve setup are presented.Whereas for simulation analysis,the MOC was used to develop a hydraulic transient solver by combining the DGYM with the WFB unsteady friction model.The Vardy-Brown weighting function for turbulent flow in rough pipes was approximated using a scaling approach,yielding exponential coefficients used in any WFB model.Also,the flow scenarios tested for the comparative analysis of unsteady flow include a water hammer flow without cavitation,active as well as passive column separation flow regimes,and a transient flow with entrapped air.Results reveal that the damping and dispersion recorded in non-cavitating flow experiments can be accurately predicted using the WFB unsteady friction models.For cavitating flows,the commonly used DGYM with quasi-steady friction provides workable results;however,introducing WFB unsteady friction and momentum correction factor to this model further improves the results.The DGYM that incorporates the WFB unsteady friction not only modifies the shape of the pressure wave but also dampens the intensity of the short-duration pressure pulses.Note that these pulses originate from the collapse of the first cavity and the reflection of pressure waves.Unlike traditional quasi-steady state friction models,the estimation of the time required for the formation and collapse of gas cavities in the model proposed here is more consistent with experimental results.Also,merging the momentum correction factor in the proposed unsteady friction-based DGYM makes it possible to further improve the agreement between the simulated results and experimental data from the standpoint of the phase of transient waves.Finally,the results of this study have significant implications for pipeline design,and they can be applied to a range of engineering applications.