静止系射流与旋转系移动水膜流间时空相互干涉
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摘要
为了进行冲击式水轮机水斗的优化设计,提高冲击式水轮机整体水力性能,本研究开发了可计算静止系射流与旋转系移动水膜流之间的时空同期干涉的流体解析软件。利用该解析软件得到冲击式式水轮机各个时空同期非定常流动解析,实现了水斗内不可见流的可视化,为冲击式水轮机水斗优化设计提供理论依据和技术支持。
本文首先定义了描述水斗形状的直角水斗坐标系,用于分析射流的静止坐标系及转动的旋转坐标系,说明了不同坐标系之间的坐标变换。利用边界贴体网格描述水斗复杂的三维形状,计算了局部非正交曲线坐标系下贴体网格点的自然基本矢量及偏微分。基于微分几何,提出利用边界贴体网格点来进行空间局部自由曲面的创建理论,为流动数值解析作准备。
利用不同坐标系下的位移、速度、加速度三角形理论来进行静止系射流与旋转系移动水膜流间时空同期干涉的矢量分析。在静止坐标系下,利用微分几何阐述了自由射流与水斗内移动水膜流之间的时空同期相互干涉,成功开发了自由射流时空同期着陆于水斗三维曲面的计算软件。在旋转坐标系下,利用微分几何阐述了着陆于水斗的新水膜流与水斗上已存在的旧水膜流之间的时空同期相互干涉,成功完成了新旧水膜流动及水斗中部分不可见流可视化的计算软件。
本研究利用边界贴体网格描述了冲击式水轮机水斗复杂的三维几何形状,基于微分几何创建了空间局部三维自由曲面,进而进行了流动数值解析,根据流动解析结果对水斗进行优化设计。依照水斗在旋转坐标系下的安装进行了比转速的定义,对于任何比转速的冲击式水轮机都可以进行静止系射流与旋转系移动水膜之间时空同期干涉的流动解析及预测。完成了射入水斗的入射面和被水斗缺口分离的偏流射流的后缘面计算,使流入水斗两分支自由射流三维形状的时空同期可视化成为可能。分析射入水斗的新水膜流与已存在的旧水膜流之时空干涉流动,使新旧水膜流时空同期干涉的三维可视化成为可能。本论文提出的时空同期干涉计算软件,不需要使用高价服务器,也不需要长时间的计算,只要在普通的计算机上在非常短的时间内即可完成时空同期的有效流量、无效流量、欧拉能量、转轮力矩、水力效率预测等的计算,可以进行水斗的优化设计。
In order to maximize the hydraulic performance of Pelton turbines by an innovative optimum design criteria based on the visualization of invisible flow in the Peloton buckets, the research developed the basis theory and algorithm for the flow analysis software to simulate the space-time synchronous interaction between the free jet in stationary frame and the moving water sheet in rotating runner frame. The space-time synchronous hydraulic performance based on the unsteady flow interaction was numerically computed and visualized in every space-time step. According to the acquired flow visualization, the innovative optimum design criterion is established.
An isolated coordinate system of bucket frame is used for the design of bucket geometry. The boundary-fitted grids (BFG) of non-orthogonal curvilinear frame were applied to discretize the geometry of bucket with the natural basis vectors in differential geometry math. After mounting the bucket frame onto the rotating runner frame of Cartesian based on the standardization of specific speed, the unsteady flow interaction of a free water jet in the stationary frame with the free moving sheet on the bucket in the rotating runner frame was discretized in space-time synchronously. The frame transformations among the three frames on the isolated bucket with BFG, on the moving sheet in rotating runner, and on the free jet flow in stationary were theoretically described and computed.
An unique space-time synchronous theory of displacement, velocity and acceleration triangle was used to connect the two frames of stationary jet and of rotating moving sheet flow. This theory is used for the vector analysis to the space-time synchronous interactions between free jet in stationary frame and moving water sheet in rotating runner frame. Under the world of stationary frame, the space-time synchronous interaction between the stationary free jet and the moving water sheet flow in rotating frame was elaborated to the innovative software of the free jet landing on the 3D curved surface of rotating buckets successfully. On the other hand, under the world of rotating runner frame, the space-time synchronous interaction between the new water sheet landing on a bucket and the existing old water sheet in the bucket was creatively solved by differential geometry, and completed the innovative software for the flow analysis of free water sheet moving in a bucket with the visualization of invisible flow successfully.
Since the complicated 3D geometric free-surface of Pelton bucket has exactly been described by the local curved surface based on differential geometry, an innovative design is possible by optimizing any local curved surface of Pelton buckets according to the results of flow analysis. Any specific speed of Peloton turbine can be analyzed by the software, as the mounting of bucket onto the runner frame was standardized by the specific speed. It is possible to visualize the landing surface of impinging jet branch on the relevant bucket and the trailing edge surface of deflected jet branch toward the preceding bucket, as well as the flow interaction between newcomer and old-timer of flow water sheet in a bucket. The numerical software to compute the space-time synchronous interaction presented in the research doesn’t require expensive engineering workstation with long computing hours. This software can predict the effective discharge and invalid discharge, Euler energy, stress on bucket, torque of runner and hydraulic efficiency within a short minute in a personal computer. It supplies the efficient design-tool to optimize the design of Pelton buckets quickly.
本文首先定义了描述水斗形状的直角水斗坐标系,用于分析射流的静止坐标系及转动的旋转坐标系,说明了不同坐标系之间的坐标变换。利用边界贴体网格描述水斗复杂的三维形状,计算了局部非正交曲线坐标系下贴体网格点的自然基本矢量及偏微分。基于微分几何,提出利用边界贴体网格点来进行空间局部自由曲面的创建理论,为流动数值解析作准备。
利用不同坐标系下的位移、速度、加速度三角形理论来进行静止系射流与旋转系移动水膜流间时空同期干涉的矢量分析。在静止坐标系下,利用微分几何阐述了自由射流与水斗内移动水膜流之间的时空同期相互干涉,成功开发了自由射流时空同期着陆于水斗三维曲面的计算软件。在旋转坐标系下,利用微分几何阐述了着陆于水斗的新水膜流与水斗上已存在的旧水膜流之间的时空同期相互干涉,成功完成了新旧水膜流动及水斗中部分不可见流可视化的计算软件。
本研究利用边界贴体网格描述了冲击式水轮机水斗复杂的三维几何形状,基于微分几何创建了空间局部三维自由曲面,进而进行了流动数值解析,根据流动解析结果对水斗进行优化设计。依照水斗在旋转坐标系下的安装进行了比转速的定义,对于任何比转速的冲击式水轮机都可以进行静止系射流与旋转系移动水膜之间时空同期干涉的流动解析及预测。完成了射入水斗的入射面和被水斗缺口分离的偏流射流的后缘面计算,使流入水斗两分支自由射流三维形状的时空同期可视化成为可能。分析射入水斗的新水膜流与已存在的旧水膜流之时空干涉流动,使新旧水膜流时空同期干涉的三维可视化成为可能。本论文提出的时空同期干涉计算软件,不需要使用高价服务器,也不需要长时间的计算,只要在普通的计算机上在非常短的时间内即可完成时空同期的有效流量、无效流量、欧拉能量、转轮力矩、水力效率预测等的计算,可以进行水斗的优化设计。
In order to maximize the hydraulic performance of Pelton turbines by an innovative optimum design criteria based on the visualization of invisible flow in the Peloton buckets, the research developed the basis theory and algorithm for the flow analysis software to simulate the space-time synchronous interaction between the free jet in stationary frame and the moving water sheet in rotating runner frame. The space-time synchronous hydraulic performance based on the unsteady flow interaction was numerically computed and visualized in every space-time step. According to the acquired flow visualization, the innovative optimum design criterion is established.
An isolated coordinate system of bucket frame is used for the design of bucket geometry. The boundary-fitted grids (BFG) of non-orthogonal curvilinear frame were applied to discretize the geometry of bucket with the natural basis vectors in differential geometry math. After mounting the bucket frame onto the rotating runner frame of Cartesian based on the standardization of specific speed, the unsteady flow interaction of a free water jet in the stationary frame with the free moving sheet on the bucket in the rotating runner frame was discretized in space-time synchronously. The frame transformations among the three frames on the isolated bucket with BFG, on the moving sheet in rotating runner, and on the free jet flow in stationary were theoretically described and computed.
An unique space-time synchronous theory of displacement, velocity and acceleration triangle was used to connect the two frames of stationary jet and of rotating moving sheet flow. This theory is used for the vector analysis to the space-time synchronous interactions between free jet in stationary frame and moving water sheet in rotating runner frame. Under the world of stationary frame, the space-time synchronous interaction between the stationary free jet and the moving water sheet flow in rotating frame was elaborated to the innovative software of the free jet landing on the 3D curved surface of rotating buckets successfully. On the other hand, under the world of rotating runner frame, the space-time synchronous interaction between the new water sheet landing on a bucket and the existing old water sheet in the bucket was creatively solved by differential geometry, and completed the innovative software for the flow analysis of free water sheet moving in a bucket with the visualization of invisible flow successfully.
Since the complicated 3D geometric free-surface of Pelton bucket has exactly been described by the local curved surface based on differential geometry, an innovative design is possible by optimizing any local curved surface of Pelton buckets according to the results of flow analysis. Any specific speed of Peloton turbine can be analyzed by the software, as the mounting of bucket onto the runner frame was standardized by the specific speed. It is possible to visualize the landing surface of impinging jet branch on the relevant bucket and the trailing edge surface of deflected jet branch toward the preceding bucket, as well as the flow interaction between newcomer and old-timer of flow water sheet in a bucket. The numerical software to compute the space-time synchronous interaction presented in the research doesn’t require expensive engineering workstation with long computing hours. This software can predict the effective discharge and invalid discharge, Euler energy, stress on bucket, torque of runner and hydraulic efficiency within a short minute in a personal computer. It supplies the efficient design-tool to optimize the design of Pelton buckets quickly.
引文
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