To realize the accurate control of water hammer in pipes by valve stroking, based on basic differential equations of water hammer subjected to initial and boundary conditions, the traveling solution of wave equations ...To realize the accurate control of water hammer in pipes by valve stroking, based on basic differential equations of water hammer subjected to initial and boundary conditions, the traveling solution of wave equations in finite region was applied to the linear water hammer problem. With the given velocity function at the valve and the introduction of curve integration independent of integral path, the exact analytic solution of dimensionless water hammer pressure was obtained in the course of valve closing. Based on the definition of eigen wave height, optimal eigen wave height and observation time, the control goal of water hammer pressure and the judgment rule of the optimal eigen wave height were determined, then the optimal velocity function in the calculated example was derived, which can reduce the water hammer pressure maximally. According to this function, a valve closing program was set, and the optimal control of water hammer could be realized.展开更多
Water hammer occurs whenever the fluid velocity in vertical lifting pipe systems for deep-sea mining suddenly changes. In this work, the shock wave was proven to play an important role in changing pressures and period...Water hammer occurs whenever the fluid velocity in vertical lifting pipe systems for deep-sea mining suddenly changes. In this work, the shock wave was proven to play an important role in changing pressures and periods, and mathematical and numerical modeling technology was presented for simulated transient pressure in the abnormal pump operation. As volume concentrations were taken into account of shock wave speed, the experiment results about the pressure-time history, discharge-time history and period for the lifting pipe system showed that： as its concentrations rose up, the maximum transient pressure went down, so did its discharges; when its volume concentrations increased gradually, the period numbers of pressure decay were getting less and less, and the corresponding shock wave speed decreased. These results have highly coincided with simulation results. The conclusions are important to design lifting transporting system to prevent water hammer in order to avoid potentially devastating consequences, such as damage to components and equipment and risks to personnel.展开更多
基金Sponsored by the National Natural Science Foundation of China (Grant No. 50478025 and 50506009) the 46th China Postdoctoral Science Foundation(Grant No.20090460912)
文摘To realize the accurate control of water hammer in pipes by valve stroking, based on basic differential equations of water hammer subjected to initial and boundary conditions, the traveling solution of wave equations in finite region was applied to the linear water hammer problem. With the given velocity function at the valve and the introduction of curve integration independent of integral path, the exact analytic solution of dimensionless water hammer pressure was obtained in the course of valve closing. Based on the definition of eigen wave height, optimal eigen wave height and observation time, the control goal of water hammer pressure and the judgment rule of the optimal eigen wave height were determined, then the optimal velocity function in the calculated example was derived, which can reduce the water hammer pressure maximally. According to this function, a valve closing program was set, and the optimal control of water hammer could be realized.
基金supported by the National Natural Science Foundation of China(Grant No.50875081)China Postdoctoral Science Foundation(Grant No.20080440992)+1 种基金the Planned Science and Technology Support Project of Hunan Province(Grant No.2009SK3159)Graduate Innovation Fund of Hunan University of Science and Technology(Grant No.S100109)
文摘Water hammer occurs whenever the fluid velocity in vertical lifting pipe systems for deep-sea mining suddenly changes. In this work, the shock wave was proven to play an important role in changing pressures and periods, and mathematical and numerical modeling technology was presented for simulated transient pressure in the abnormal pump operation. As volume concentrations were taken into account of shock wave speed, the experiment results about the pressure-time history, discharge-time history and period for the lifting pipe system showed that： as its concentrations rose up, the maximum transient pressure went down, so did its discharges; when its volume concentrations increased gradually, the period numbers of pressure decay were getting less and less, and the corresponding shock wave speed decreased. These results have highly coincided with simulation results. The conclusions are important to design lifting transporting system to prevent water hammer in order to avoid potentially devastating consequences, such as damage to components and equipment and risks to personnel.
