水轮机弱可压缩水体耦合水锤与空化流数值模拟研究
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摘要
本文是由包括国家自然科学基金重点项目“水电站的水机电耦合研究(50839003)”和内的多个项目的长期资助下完成的(项目编号：50079007,90210005,50579025,51279071)。从弱可压缩流体的相关理论出发建立了基于弱可压缩水体耦合水锤与空化流动的理论模型,针对理论模型开发了适用于弱可压缩问题求解的非对角占优非线性大规模并行计算求解器,并完成了一例高水头、长管线水电站耦合水锤的现场试验,获得了大量有关耦合水锤的实测数据。基于自主开发的数万条程序代码,对某高水头水电站管道竖井段的耦合水锤问题、高水头混流式水轮机以及低水头混流式水轮机的空化流动问题进行了精细数值模拟并与试验实测和文献进行了比较,结果吻合很好,验证了本文理论、方法及源程序代码的正确性,取得了具有创新性的研究成果。研究工作主要表现在以下四个方面：
1.理论建模
(1)根据相关的弱可压缩流体理论,在柱坐标下建立了适合描述水电站管道弱可压缩水体运动的控制方程,能够描述管道水锤波-流耦合、波-波耦合的水力瞬态过程。
(2)在经典压力管道壳模型的基础上将传统用势流理论描述流体的方法改用三维粘性流体来描述,在任意曲线坐标下基于ALE框架建立弱可压缩水体基于壳模型的控制方程,得到了考虑管道与水轮机波-流耦合、波-波耦合、流-固耦合的水锤模型。
(3)建立了考虑弱可压缩水体的单相空化模型和质量输运空化模型,可描述水轮机弱可压缩水体瞬态条件下的空化特性。
2.程序代码开发
(1)在OpenFoam开源C++类库之下基于提出的水轮机弱可压缩水体耦合水锤及空化模型,编写了数万条程序代码,自主开发了适用于弱可压缩水体的非对角占优三维高效并行求解器。
(2)实现了基于OpenFoam扩展版中有限元模块和本文弱可压缩水体CFD代码的耦合,建立了高精度的插值方法,使描述流体空间离散的有限体积在单元中心处的属性插值到节点上,实现了根据物面条件进行力及位移的传递。
(3)构造了弱可压缩水体CFD代码与FEAP开源有限元壳单元代码相结合的考虑弱可压缩水体与管道耦合的程序代码,并在FEAP上构造了基于正交曲线坐标的壳单元,同时利用面向对象技术调用OpenFoam类库中的k-ε湍流模型,使得代码既考虑了水体的弱可压缩性又可描述流体的湍流特性。
3.原型试验研究
结合理论研究,耗时2年完成了某高水头、长管道水电站耦合水锤的原型观测和试验分析工作,得到了大量的试验实测数据,获得了高水头电站水体弱可压缩性及甩负荷耦合水锤波动特性第一手数据,验证了本文理论模型及程序代码的正确性。
4.数值模拟及验证
(1)基于本文建立的弱可压缩水体耦合水锤理论、空化模型以及开发的求解器,对荷兰DELFT水锤基准试验装置A进行了数值模拟,数值结果清晰给出了该装置“波-流”、“波-波”及“流-固”耦合的耦合水锤波动情况,计算的相关数据与试验实测完全吻合。
(2)利用本文开发的求解器,对上述试验的高水头、长管道水电站压力管道的竖管段进行了流体-结构耦合作用分析。通过两种工况下竖管弯头处的压力及应力的比较,计算的管壁应变及压力结果与试验实测数据吻合。
(3)用本文提出的空化模型和开发的程序代码模拟了文献广泛使用的NACA0015翼型,并将计算结果与文献提供的实验和计算数据进行对比,结果表明,本文模型和代码的计算结果与文献提供的空化实验结果吻合,并能清晰的捕捉翼型前沿片状空泡初生、反向射流使空泡断裂、后部云状空泡脱落以及前沿片状空泡再生成的准周期运动规律。
(4)分别对高、低水头混流式水轮机空化流特性用本文模型及代码进行了全流道空化数值模拟,并对蜗壳-固定导叶区、活动导叶区、转轮区及尾水管区的空化特性进行了分析,得到的尾水管中的涡带形状、转轮区及尾水管锥管段内空化特性以及压力脉动等与相应机组的实际运行情况吻合。
(5)用本文开发的程序代码对上述高水头电站水轮机尾水管补入自然空气进行了考虑相变的水-气-汽多相流数值模拟,分析了空气进入尾水管后压力脉动的改善情况,计算得到的结果与实际工程运行的情况吻合。
通过以上四个方面的工作,本文将水轮机弱可压缩水体耦合水锤及空化问题从理论建模、计算方法、源程序代码开发、原型水电站水锤试验观测、水轮机空化流数值模拟等方而进行了系统的理论研究及相关技术开发,研究工作耗时近10年,取得了具有创新性的成果。
This work was financially supported by the National Natural Science Foundation of china key project "Water-electro-mechanical coupling studies of hydropower station (50839003)" and other National Natural Science Foundation of china projects (number:50079007,90210005,50579025,51279071) long-term funded. The theoretical model of weakly compressible coupling water hammer and cavitation were established based on related theories about weakly compressible fluid. A non-diagonally dominant nonlinear massively parallel computing solver was developed based on the proposed theoretical model for the weakly compressible problem. Completed a coupling water hammer field test for a high head, long pipeline hydropower station and get a lot of measured data about coupling water hammer. Based on tens of thousands of self-developed code, we completed a series of fine numerical simulation about the problem of coupling water hammer for a high head hydropower station shaft penstock and the problem of cavitation flow in high head and low head Francis turbine. The results were compared with the literature and test measured in good agreement. It proves the correctness of theories, methods and source code in this thesis. Some innovative research has been made. Research work mainly in the following four areas:
1. Theoretical modeling
(1) According to the relevant weakly compressible fluid theory, established equations suitable for describing weakly compressible water in hydropower penstock. It can describe the hydraulic transients of water hammer wave for wave-fluid coupling, wave-wave coupling.
(2) On the basis of classic penstock shell model, instead the potential flow theory traditionally with a three-dimensional viscous fluid. In any curvilinear coordinates, based on the ALE framework the shell model control equations of weakly compressible water were created. The water hammer model of the wave-fluid coupling, wave-wave coupling, fluid-structure interaction for the penstock and hydroturbine was obtained.
(3) The weakly compressible water single phase cavitation model and mass transport cavitation model was created. It can describe the cavitation of weakly compressible water for a hydroturbine under transient conditions.
2. Programming
(1) Use OpenFoam C++class library, wrote tens of thousands of program code, a non-diagonally dominant nonlinear massively parallel computing solver was developed based on the proposed theoretical model for the hydroturbin weakly compressible and cavitation.
(2) Implemented coupling the finite element module in OpenFoam extended version and self-developed weakly compressible CFD code. Precision interpolation method was completed. It enables the attributes of finite volume cell center of description fluid spatial dispersion interpolated to node. According to contact surface condition, the displacement and force transfer is implemented.
(3) A program code was developed for coupled weakly compressible water with penstock movement. It combines the weakly compressible water source CFD code and FEAP finite element shell element code. Based on orthogonal curvilinear coordinates shell element was completed in FEAP. Meanwhile, the k-ε turbulence model in OpenFoam class library was called by using object-oriented technology. This code takes into account both the weak compressibility of water and fluid turbulence characteristics.
3. Prototype test study
Combined with theoretical study, took two years to complete coupling water hammer prototype observation and test analysis for a high head, long pipeline hydropower. A large number of measured data was obtained. The first-hand data about weak compressibility of water and coupling water hammer characteristics after the load rejection were obtained too. It verifies the theoretical model and program code is correct.
4. Numerical simulation and validation
(1) Based on weakly compressible coupling water hammer theory, cavitation models and solver crated in this thesis, numerical simulation of the Netherlands DELFT water hammer benchmark test device A was completed. Numerical results clearly shows that the coupling water hammer fluctuation including:wave-flow, waves-waves and flow-structure coupled in test device. Calculations and test measured data fully consistent.
(2) Using the solver developed in this thesis, a fluid structure interation analysis to be completed for the above tests high head, long pipeline hydropower shaft of penstock segment. The pressure and the stress were calculated at the penstock elbow on tow case. The result of wall strain and stress agree with the test measured data.
(3) Using the cavitation model proposed and program code developed in this thesis, simulated a NACA0015hydrofoil widely used in the literature, and compared the calculation results with the test and calculated data by literature provided. The results show that the results calculated by the proposed model and the developed code in this thesis accord with the cavitation test results by literature. It can clearly capture the cavity quasi-periodic motion law for hydrofoil leading edge the growth of the sheet cavity, the reentrant jet breaking the cavity, rear cloud cavitation shedding while a new sheet cavity is growing.
(4) A numerical simulation of cavitation was implemented for full flow channel of a high and a low head Francis turbine with the proposed model and the code respectively. The cavitation characteristics were analyzed for spiral casing-vanes, guide vanes, runner and draft tube. The draft tube vortex shape, the cavitation characteristics and pressure pulsation for runner and draft tube cone segment are identical with an actual operation hydroturbin unit.
(5) With program code developed in this thesis, a numerical simulation of cavitating turbulent flow in a Francis turbine with draft tube natural air admission was completed. It takes into account the phase change for water-gas-vapor multiphase flow. The pressure pulsation was analyzed after air into the draft tube. The calculated results coincide with the actual operation.
Through the above four aspects of the work, In this thesis, for the problem about hydroturbin weakly compressible water coupling water hammer and cavitation, from theoretical modeling, computational methods, source code development, hydropower water hammer test prototype observations, hydroturbine cavitation flow simulation and other aspects, the theoretical research and related technology development was completed systematically. Research work took nearly10years, has made innovative achievements.
1.理论建模
(1)根据相关的弱可压缩流体理论,在柱坐标下建立了适合描述水电站管道弱可压缩水体运动的控制方程,能够描述管道水锤波-流耦合、波-波耦合的水力瞬态过程。
(2)在经典压力管道壳模型的基础上将传统用势流理论描述流体的方法改用三维粘性流体来描述,在任意曲线坐标下基于ALE框架建立弱可压缩水体基于壳模型的控制方程,得到了考虑管道与水轮机波-流耦合、波-波耦合、流-固耦合的水锤模型。
(3)建立了考虑弱可压缩水体的单相空化模型和质量输运空化模型,可描述水轮机弱可压缩水体瞬态条件下的空化特性。
2.程序代码开发
(1)在OpenFoam开源C++类库之下基于提出的水轮机弱可压缩水体耦合水锤及空化模型,编写了数万条程序代码,自主开发了适用于弱可压缩水体的非对角占优三维高效并行求解器。
(2)实现了基于OpenFoam扩展版中有限元模块和本文弱可压缩水体CFD代码的耦合,建立了高精度的插值方法,使描述流体空间离散的有限体积在单元中心处的属性插值到节点上,实现了根据物面条件进行力及位移的传递。
(3)构造了弱可压缩水体CFD代码与FEAP开源有限元壳单元代码相结合的考虑弱可压缩水体与管道耦合的程序代码,并在FEAP上构造了基于正交曲线坐标的壳单元,同时利用面向对象技术调用OpenFoam类库中的k-ε湍流模型,使得代码既考虑了水体的弱可压缩性又可描述流体的湍流特性。
3.原型试验研究
结合理论研究,耗时2年完成了某高水头、长管道水电站耦合水锤的原型观测和试验分析工作,得到了大量的试验实测数据,获得了高水头电站水体弱可压缩性及甩负荷耦合水锤波动特性第一手数据,验证了本文理论模型及程序代码的正确性。
4.数值模拟及验证
(1)基于本文建立的弱可压缩水体耦合水锤理论、空化模型以及开发的求解器,对荷兰DELFT水锤基准试验装置A进行了数值模拟,数值结果清晰给出了该装置“波-流”、“波-波”及“流-固”耦合的耦合水锤波动情况,计算的相关数据与试验实测完全吻合。
(2)利用本文开发的求解器,对上述试验的高水头、长管道水电站压力管道的竖管段进行了流体-结构耦合作用分析。通过两种工况下竖管弯头处的压力及应力的比较,计算的管壁应变及压力结果与试验实测数据吻合。
(3)用本文提出的空化模型和开发的程序代码模拟了文献广泛使用的NACA0015翼型,并将计算结果与文献提供的实验和计算数据进行对比,结果表明,本文模型和代码的计算结果与文献提供的空化实验结果吻合,并能清晰的捕捉翼型前沿片状空泡初生、反向射流使空泡断裂、后部云状空泡脱落以及前沿片状空泡再生成的准周期运动规律。
(4)分别对高、低水头混流式水轮机空化流特性用本文模型及代码进行了全流道空化数值模拟,并对蜗壳-固定导叶区、活动导叶区、转轮区及尾水管区的空化特性进行了分析,得到的尾水管中的涡带形状、转轮区及尾水管锥管段内空化特性以及压力脉动等与相应机组的实际运行情况吻合。
(5)用本文开发的程序代码对上述高水头电站水轮机尾水管补入自然空气进行了考虑相变的水-气-汽多相流数值模拟,分析了空气进入尾水管后压力脉动的改善情况,计算得到的结果与实际工程运行的情况吻合。
通过以上四个方面的工作,本文将水轮机弱可压缩水体耦合水锤及空化问题从理论建模、计算方法、源程序代码开发、原型水电站水锤试验观测、水轮机空化流数值模拟等方而进行了系统的理论研究及相关技术开发,研究工作耗时近10年,取得了具有创新性的成果。
This work was financially supported by the National Natural Science Foundation of china key project "Water-electro-mechanical coupling studies of hydropower station (50839003)" and other National Natural Science Foundation of china projects (number:50079007,90210005,50579025,51279071) long-term funded. The theoretical model of weakly compressible coupling water hammer and cavitation were established based on related theories about weakly compressible fluid. A non-diagonally dominant nonlinear massively parallel computing solver was developed based on the proposed theoretical model for the weakly compressible problem. Completed a coupling water hammer field test for a high head, long pipeline hydropower station and get a lot of measured data about coupling water hammer. Based on tens of thousands of self-developed code, we completed a series of fine numerical simulation about the problem of coupling water hammer for a high head hydropower station shaft penstock and the problem of cavitation flow in high head and low head Francis turbine. The results were compared with the literature and test measured in good agreement. It proves the correctness of theories, methods and source code in this thesis. Some innovative research has been made. Research work mainly in the following four areas:
1. Theoretical modeling
(1) According to the relevant weakly compressible fluid theory, established equations suitable for describing weakly compressible water in hydropower penstock. It can describe the hydraulic transients of water hammer wave for wave-fluid coupling, wave-wave coupling.
(2) On the basis of classic penstock shell model, instead the potential flow theory traditionally with a three-dimensional viscous fluid. In any curvilinear coordinates, based on the ALE framework the shell model control equations of weakly compressible water were created. The water hammer model of the wave-fluid coupling, wave-wave coupling, fluid-structure interaction for the penstock and hydroturbine was obtained.
(3) The weakly compressible water single phase cavitation model and mass transport cavitation model was created. It can describe the cavitation of weakly compressible water for a hydroturbine under transient conditions.
2. Programming
(1) Use OpenFoam C++class library, wrote tens of thousands of program code, a non-diagonally dominant nonlinear massively parallel computing solver was developed based on the proposed theoretical model for the hydroturbin weakly compressible and cavitation.
(2) Implemented coupling the finite element module in OpenFoam extended version and self-developed weakly compressible CFD code. Precision interpolation method was completed. It enables the attributes of finite volume cell center of description fluid spatial dispersion interpolated to node. According to contact surface condition, the displacement and force transfer is implemented.
(3) A program code was developed for coupled weakly compressible water with penstock movement. It combines the weakly compressible water source CFD code and FEAP finite element shell element code. Based on orthogonal curvilinear coordinates shell element was completed in FEAP. Meanwhile, the k-ε turbulence model in OpenFoam class library was called by using object-oriented technology. This code takes into account both the weak compressibility of water and fluid turbulence characteristics.
3. Prototype test study
Combined with theoretical study, took two years to complete coupling water hammer prototype observation and test analysis for a high head, long pipeline hydropower. A large number of measured data was obtained. The first-hand data about weak compressibility of water and coupling water hammer characteristics after the load rejection were obtained too. It verifies the theoretical model and program code is correct.
4. Numerical simulation and validation
(1) Based on weakly compressible coupling water hammer theory, cavitation models and solver crated in this thesis, numerical simulation of the Netherlands DELFT water hammer benchmark test device A was completed. Numerical results clearly shows that the coupling water hammer fluctuation including:wave-flow, waves-waves and flow-structure coupled in test device. Calculations and test measured data fully consistent.
(2) Using the solver developed in this thesis, a fluid structure interation analysis to be completed for the above tests high head, long pipeline hydropower shaft of penstock segment. The pressure and the stress were calculated at the penstock elbow on tow case. The result of wall strain and stress agree with the test measured data.
(3) Using the cavitation model proposed and program code developed in this thesis, simulated a NACA0015hydrofoil widely used in the literature, and compared the calculation results with the test and calculated data by literature provided. The results show that the results calculated by the proposed model and the developed code in this thesis accord with the cavitation test results by literature. It can clearly capture the cavity quasi-periodic motion law for hydrofoil leading edge the growth of the sheet cavity, the reentrant jet breaking the cavity, rear cloud cavitation shedding while a new sheet cavity is growing.
(4) A numerical simulation of cavitation was implemented for full flow channel of a high and a low head Francis turbine with the proposed model and the code respectively. The cavitation characteristics were analyzed for spiral casing-vanes, guide vanes, runner and draft tube. The draft tube vortex shape, the cavitation characteristics and pressure pulsation for runner and draft tube cone segment are identical with an actual operation hydroturbin unit.
(5) With program code developed in this thesis, a numerical simulation of cavitating turbulent flow in a Francis turbine with draft tube natural air admission was completed. It takes into account the phase change for water-gas-vapor multiphase flow. The pressure pulsation was analyzed after air into the draft tube. The calculated results coincide with the actual operation.
Through the above four aspects of the work, In this thesis, for the problem about hydroturbin weakly compressible water coupling water hammer and cavitation, from theoretical modeling, computational methods, source code development, hydropower water hammer test prototype observations, hydroturbine cavitation flow simulation and other aspects, the theoretical research and related technology development was completed systematically. Research work took nearly10years, has made innovative achievements.
引文
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