自由表面旋涡的机理研究
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摘要
自由表面旋涡是水工建筑物进水口前常见的水力现象,在水电站引水管道、溢洪道、导流隧洞、泵站和船闸等进水口的上游表面时有发生。自由表面旋涡发展到一定程度将演化为吸气旋涡,给工程建筑物和设备带来严重危害。自由表面旋涡的生成和演化机制复杂,研究自由表面旋涡运动的现象和规律,揭示其流动机理,探求对它们实施控制的有效方法,是大量工程实践提出的迫切需要解决的问题。自由表面旋涡机理的研究还涉及到多项力学的前沿基础理论问题,具有重要的学术价值。
本文设计并建造了实验水槽来研究自由表面旋涡的生成和演化过程。采用流场染色技术对自由表面旋涡的演化过程进行显示,观测记录自由表面旋涡的旋转方向、生成位置以及不同演化阶段的形状;根据观测结果对自由表面旋涡的形成原因进行分析,定性分析了科氏力在自由表面旋涡形成和演化过程中的作用;测量了不同工况下的临界淹没深度这一反映自由表面旋涡发展程度的重要参数;考察和分析了来流速度、来流湍流度、来流预旋以及吸水口位置等对自由表面旋涡生成和演化的影响。
在实验观测的基础上,采用粒子图像测速(Particle Image Velocimetry,简称PIV),对自由表面旋涡演化不同阶段的流场结构进行了测量,通过对测量数据进行分析,得到自由表面旋涡流场随时间演化规律和随空间变化的规律。自由表面旋涡在演化过程中,切向速度在半径方向上随着半径的增大先增大后减小,在变化过程中切向速度存在最大值,并以此对应的半径定义了涡核半径。在涡核半径内外,切向速度的变化是不同的。切向速度最大值随着深度的增加先增大后逐渐减小,最大值不在自由表面处,而在自由表面下某一深度。径向速度随着半径的增大逐渐减小,由于自由表面旋涡是一种向心流动,导致越靠近涡核径向速度越大。径向速度最大值随着深度的增加逐渐减小,在靠近自由表面的地方径向速度大,这表明自由表面旋涡在演化过程中,吸水口吸入的流体大部分来自旋涡上部流体,因此发生自由表面旋涡流动后,容易将表面漂浮物吸入吸水口。
在实验研究的基础上,对自由表面旋涡流动进行理论分析,得到了科氏力作用下流动运动的控制方程。以此控制方程为基础,通过简化得到科氏力作用下平面点汇运动的规律,分析了科氏力在旋涡生成和演化过程中的作用,确定科氏力是引起旋涡流动的重要原因之一。
以圆桶底部出流装置为模型,通过自编程序,采用有限体积法对控制方程进行离散,对离散后的方程采用SIMPLE算法进行求解,获得了不同工况下圆桶内流体运动规律。数值分析表明,在科氏力作用下圆桶内流体产生了旋涡流动。旋涡流动的切向速度和径向速度在半径方向以及深度方向的变化规律和实验测量结果定性符合,并分析了产生误差的原因。用拉格朗日观点考察了迁移加速度、粘性力以及科氏力在流动中的关系,发现在涡核中心以外,流体微团在运动过程中的加速旋转是由科氏力的作用引起的。并考察了科氏力大小以及流量对旋涡运动的影响。
利用自编程序对三维圆筒模型进行计算,研究来流预旋和科氏力共同作用对自由表面旋涡流场的影响。逆时针方向来流预旋条件下,来流预旋和科氏力的双重作用使得圆桶内产生逆时针方向旋涡运动,而且来流旋涡越大,产生的旋转速度也越大。顺时针方向来流预旋条件下,来流预旋的一部分用于抵消科氏力产生的逆时针方向旋转作用,剩余部分产生了顺时针方向旋转运动。同时以商用软件FLUENT为工具,对方形水槽内不同方向来流预旋情况下的流动进行了数值解析,模拟得到的旋涡的方向和位置与实验结果符合。
The free surface vortex is a common hydraulic phenomenon in front of the intakes of hydraulic structures such as diversion pipeline of hydropower station, spillway, diversion tunnel, large scale pump station, and ship lock. The free surface vortex will evolve into air entrainment vortex when it develops to a certain extent, which may seriously endanger hydraulic structures or hydraulic equipments. The mechanism of the free surface vortex formation and evolution are greatly complex. It is an urgent problem in the practical engineering to research the vortex phenomenon and its evolution law, to reveal its flow mechanism and to seek the effective methods to control it. It also has an important academic value because many forward basic theories are involved in the study of the mechanism of the free surface vortex.
In the thesis, experimental apparatus was designed and set up to study of the mechanism of the free surface vortex. The formation and evolution of the free surface vortex were observed in detail using flow visualization. The direction of rotation, position and shape of the free surface vortex in different development stage were investigated. Based on the observation results, the effect of the Coriolis force caused by the earth rotation to the formation and evolution of the free surface vortex were analyzed qualitatively. The critical submergence, which is an important factor that refelcts the free surface vortex development stage was obtained under different experimental conditions. The effects of the flow discharge, the incoming flow turbulence intensity, the incoming prerotation and the position of the outlet to the formation and evolution of the free surface vortex were analyzed.
A particle image velocimetry(PIV) system was used to measure the whole flow field of the free surface vortex at different development stage. The evolution law and the changing law in space of the free surface vortex were obtained by analyzing the experimental data. In the evolution of the free surface vortex, with the radius increasing, the tangential velocity increases to a maximum value and then decreases. The radius corresponding to the maximum tangential velocity is defined as the vortex core radius. The maximum tangential velocity increases with the depth increasing and then decreases, and the maximum tangential velocity exists in a certain depth under the free surface. As the free surface vortex is a centripetal flow, the radial velocity increases with the radius decreasing. In the depth direction, the maximum radial velocity decreases with the depth increasing. The maximum radial velocity is in the free surface, which shows that most of the fluid sunk by the intake during the formation and evolution of the free surface vortex come from the top of it. So the free surface vortex can easily inhale floating debris on the free surface.
Based on the experimental studies, the governing equations considering the Coriolis force caused by the earth rotation were established by theoretical analysis. By simplifying the governing equations, the flow law of the point sink flow under the Coriolis force was obtained, and the effect of the Coriolis force to the free surface vortex was analyzed. The theoretical analysis indicates that the Coriolis force caused by the earth rotation is one of the major reasons that cause the free surface vortex.
A barrel with an outlet on the bottom was used as a physical model. Program was compiled to simulate the flow field in the barrel. The flow field in the barrel under different conditions were obtained by using FVM(Finite Volume Method) to discrete the governing equations and SIMPLE(Semi-Implicit Method for Pressure Linked Equation) to solve the discrete equations. The numerical simulation shows that vortex generated in the barrel under the effect of the Coriolis force. The changing law of the tangential velocity and the radial velocity in radius and depth are qualitatively consistent to that of the experiments. The errors between numerical calculation and experiment were analyzed. In the viewpoint of Lagrange, the relation of the remove acceleration, the viscosity force and the Coriolis force were analyzed. It shows that the particle acceleration was caused by the Coriolis force out of the vortex core during the vortex evolution. The effects of the magnitude of the Coriolis force and the flux to the vortex were also studied.
Based on the program, the effect of the prerotation in the incoming flow together with the Coriolis force to the free surface vortex was studied. The calculations indicate that when the prerotation in the incoming flow is counterclockwise, the vortex generated by the prerotation and the Coriolis force is counterclockwise, and the rotation speed increase with the prertotation increasing. When the prerotation in the incoming flow is clockwise, parts of the prerotation was used to counteract the effect of the Coriolis force, and the remains was used to produce the clockwise vortex. The flow fields in the flume under different incoming flow conditions were numerically simulated using commercial software Fluent. The shape and position of the vortex obtained by numerical simulation agree well with that of the experiments.
本文设计并建造了实验水槽来研究自由表面旋涡的生成和演化过程。采用流场染色技术对自由表面旋涡的演化过程进行显示,观测记录自由表面旋涡的旋转方向、生成位置以及不同演化阶段的形状;根据观测结果对自由表面旋涡的形成原因进行分析,定性分析了科氏力在自由表面旋涡形成和演化过程中的作用;测量了不同工况下的临界淹没深度这一反映自由表面旋涡发展程度的重要参数;考察和分析了来流速度、来流湍流度、来流预旋以及吸水口位置等对自由表面旋涡生成和演化的影响。
在实验观测的基础上,采用粒子图像测速(Particle Image Velocimetry,简称PIV),对自由表面旋涡演化不同阶段的流场结构进行了测量,通过对测量数据进行分析,得到自由表面旋涡流场随时间演化规律和随空间变化的规律。自由表面旋涡在演化过程中,切向速度在半径方向上随着半径的增大先增大后减小,在变化过程中切向速度存在最大值,并以此对应的半径定义了涡核半径。在涡核半径内外,切向速度的变化是不同的。切向速度最大值随着深度的增加先增大后逐渐减小,最大值不在自由表面处,而在自由表面下某一深度。径向速度随着半径的增大逐渐减小,由于自由表面旋涡是一种向心流动,导致越靠近涡核径向速度越大。径向速度最大值随着深度的增加逐渐减小,在靠近自由表面的地方径向速度大,这表明自由表面旋涡在演化过程中,吸水口吸入的流体大部分来自旋涡上部流体,因此发生自由表面旋涡流动后,容易将表面漂浮物吸入吸水口。
在实验研究的基础上,对自由表面旋涡流动进行理论分析,得到了科氏力作用下流动运动的控制方程。以此控制方程为基础,通过简化得到科氏力作用下平面点汇运动的规律,分析了科氏力在旋涡生成和演化过程中的作用,确定科氏力是引起旋涡流动的重要原因之一。
以圆桶底部出流装置为模型,通过自编程序,采用有限体积法对控制方程进行离散,对离散后的方程采用SIMPLE算法进行求解,获得了不同工况下圆桶内流体运动规律。数值分析表明,在科氏力作用下圆桶内流体产生了旋涡流动。旋涡流动的切向速度和径向速度在半径方向以及深度方向的变化规律和实验测量结果定性符合,并分析了产生误差的原因。用拉格朗日观点考察了迁移加速度、粘性力以及科氏力在流动中的关系,发现在涡核中心以外,流体微团在运动过程中的加速旋转是由科氏力的作用引起的。并考察了科氏力大小以及流量对旋涡运动的影响。
利用自编程序对三维圆筒模型进行计算,研究来流预旋和科氏力共同作用对自由表面旋涡流场的影响。逆时针方向来流预旋条件下,来流预旋和科氏力的双重作用使得圆桶内产生逆时针方向旋涡运动,而且来流旋涡越大,产生的旋转速度也越大。顺时针方向来流预旋条件下,来流预旋的一部分用于抵消科氏力产生的逆时针方向旋转作用,剩余部分产生了顺时针方向旋转运动。同时以商用软件FLUENT为工具,对方形水槽内不同方向来流预旋情况下的流动进行了数值解析,模拟得到的旋涡的方向和位置与实验结果符合。
The free surface vortex is a common hydraulic phenomenon in front of the intakes of hydraulic structures such as diversion pipeline of hydropower station, spillway, diversion tunnel, large scale pump station, and ship lock. The free surface vortex will evolve into air entrainment vortex when it develops to a certain extent, which may seriously endanger hydraulic structures or hydraulic equipments. The mechanism of the free surface vortex formation and evolution are greatly complex. It is an urgent problem in the practical engineering to research the vortex phenomenon and its evolution law, to reveal its flow mechanism and to seek the effective methods to control it. It also has an important academic value because many forward basic theories are involved in the study of the mechanism of the free surface vortex.
In the thesis, experimental apparatus was designed and set up to study of the mechanism of the free surface vortex. The formation and evolution of the free surface vortex were observed in detail using flow visualization. The direction of rotation, position and shape of the free surface vortex in different development stage were investigated. Based on the observation results, the effect of the Coriolis force caused by the earth rotation to the formation and evolution of the free surface vortex were analyzed qualitatively. The critical submergence, which is an important factor that refelcts the free surface vortex development stage was obtained under different experimental conditions. The effects of the flow discharge, the incoming flow turbulence intensity, the incoming prerotation and the position of the outlet to the formation and evolution of the free surface vortex were analyzed.
A particle image velocimetry(PIV) system was used to measure the whole flow field of the free surface vortex at different development stage. The evolution law and the changing law in space of the free surface vortex were obtained by analyzing the experimental data. In the evolution of the free surface vortex, with the radius increasing, the tangential velocity increases to a maximum value and then decreases. The radius corresponding to the maximum tangential velocity is defined as the vortex core radius. The maximum tangential velocity increases with the depth increasing and then decreases, and the maximum tangential velocity exists in a certain depth under the free surface. As the free surface vortex is a centripetal flow, the radial velocity increases with the radius decreasing. In the depth direction, the maximum radial velocity decreases with the depth increasing. The maximum radial velocity is in the free surface, which shows that most of the fluid sunk by the intake during the formation and evolution of the free surface vortex come from the top of it. So the free surface vortex can easily inhale floating debris on the free surface.
Based on the experimental studies, the governing equations considering the Coriolis force caused by the earth rotation were established by theoretical analysis. By simplifying the governing equations, the flow law of the point sink flow under the Coriolis force was obtained, and the effect of the Coriolis force to the free surface vortex was analyzed. The theoretical analysis indicates that the Coriolis force caused by the earth rotation is one of the major reasons that cause the free surface vortex.
A barrel with an outlet on the bottom was used as a physical model. Program was compiled to simulate the flow field in the barrel. The flow field in the barrel under different conditions were obtained by using FVM(Finite Volume Method) to discrete the governing equations and SIMPLE(Semi-Implicit Method for Pressure Linked Equation) to solve the discrete equations. The numerical simulation shows that vortex generated in the barrel under the effect of the Coriolis force. The changing law of the tangential velocity and the radial velocity in radius and depth are qualitatively consistent to that of the experiments. The errors between numerical calculation and experiment were analyzed. In the viewpoint of Lagrange, the relation of the remove acceleration, the viscosity force and the Coriolis force were analyzed. It shows that the particle acceleration was caused by the Coriolis force out of the vortex core during the vortex evolution. The effects of the magnitude of the Coriolis force and the flux to the vortex were also studied.
Based on the program, the effect of the prerotation in the incoming flow together with the Coriolis force to the free surface vortex was studied. The calculations indicate that when the prerotation in the incoming flow is counterclockwise, the vortex generated by the prerotation and the Coriolis force is counterclockwise, and the rotation speed increase with the prertotation increasing. When the prerotation in the incoming flow is clockwise, parts of the prerotation was used to counteract the effect of the Coriolis force, and the remains was used to produce the clockwise vortex. The flow fields in the flume under different incoming flow conditions were numerically simulated using commercial software Fluent. The shape and position of the vortex obtained by numerical simulation agree well with that of the experiments.
引文
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