基于CFD流场分析的多工况多约束条件的叶片优化设计方法与实验研究
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摘要
随着全球市场竞争日益激烈,提高性能、降低研发成本和缩短设计周期的压力迫使叶轮机械设计工作者不断改进设计方法。近年来,CFD技术被广泛地应用于叶轮机械内部的三维粘性流场的数值模拟,其有效性逐步得到了研究者的肯定。同时,多种性能优良的优化算法也不断被推出。而计算机软硬件的飞速发展使得将CFD技术与优化算法相结合进行叶轮机械优化设计成为可能。本文着眼于叶轮机械叶片及叶轮的优化设计方法的实现,对相关优化设计算法进行了较为全面深入的研究。根据不同优化对象的特点,发展了适合叶轮机械叶片及叶轮的多工况多约束条件的优化设计方法,并将其成功地应用于相应的优化算例中。
为了在计算时间与计算精度之间寻求良好的平衡,使CFD技术可以有效地应用于叶轮机械的气动优化设计,作者研究了叶轮机械定常流动数值模拟中RANS方程的空间离散形式与求解方法,阐述了代数Balding-Lomax模型、一方程Sparlart-Allmaras模型和标准k-ε模型的构造形式,并介绍了本文计算中遵循的收敛准则。以NASA Low Speed Centrifugal Compressor (LSCC)实验叶轮为研究对象,结合其试验结果,讨论了湍流模型和网格等因素对计算结果的影响,为后续优化设计中湍流模型与网格的选取提供指导。
本文发展了一套基于CFD流场分析的多工况多约束条件的叶片优化设计方法。针对优化对象计算成本和优化工况或目标多少的不同,该方法可以灵活地发展成适合其具体特征的优化设计方法,本文将该优化方法分别应用于平面叶栅的单、多工况多约束条件优化设计、带分流叶片的离心叶轮优化设计单目标多约束条件和某一工业用超低比转速离心鼓风机叶片的多工况多约束条件优化设计中。
为实现上述优化方法,根据优化对象的不同特点和要求,发展了相应的实现算法。发展了适于叶栅和离心压缩机/鼓风机叶型参数化方法,大大减少了优化的设计变量;提出了并行神经网络算法,其映射质量和训练效率较传统神经网络算法有较大的提高;为避免基本遗传算法存在的早熟或陷入停滞现象等问题,受自然界和人类社会进化现象的启发,发展了一种新的遗传算法—改进的等级公平竞争遗传算法HFCGA-DN;发展了改进的INSGA-II算法,将分布函数引入NSGA-II算法中,提高了多目标Pareto遗传算法的多样性;并将上述算法与试验设计方法和CFD技术通过发展的数据接口有机地连接起来。
针对某二维透平叶栅优化问题,以极大化其升阻比作为优化目标函数,以叶栅的几何进出口角不变,叶栅截面的面积不小于初始叶型的20%和优化叶型阻力系数不大于初始叶型为约束条件,运用本文针对平面叶栅发展的单目标优化设计方法对叶栅进行优化设计。从气动力积分的结果来看,优化叶栅的气动阻力比初始叶栅减小3.2%,升阻比增加了8.3%。针对某带分流叶片的离心压缩机叶轮,以极大化其等熵效率作为目标函数,以流量和总压比不小于初始叶轮为性能约束条件和叶轮参数设定的变化范围为几何约束条件,运用本文发展的基于近似模型的单目标多约束优化方法通过改变轮毂、轮缘型线和叶片形状对初始叶轮进行了优化设计。优化后叶轮的等熵效率较初始叶轮提高了1.06%,同时总压比也提高了0.52%。
以极小化上述透平叶栅三个工况点的总压损失系数为目标函数,同样以叶栅的几何进出口角不变,叶栅截面的面积不小于初始叶型的20%为约束条件,运用本文发展的基于近似模型的多目标Pareto类优化设计方法对叶栅进行优化设计。优化后叶栅的目标函数在i=-10o,0o,10o的三个工况点分别比初始叶栅下降了8.31%、8.43%、8.52%。
根据某一工业用超低比转速离心鼓风机叶片的特点和性能要求,提出了楔形叶片的设计概念,发展了一套基于近似模型的鼓风机叶型叶片的多工况多约束优化方法。该优化方法的目标函数是极大化在三个指定工况点上的总压升,性能约束条件是效率和流量分别不小于初始叶型值,几何约束条件是设计变量的变化范围。为验证优化前后叶型的性能,将优化前后叶型加工成模型样机,并搭建了试验台,进行性能试验和叶轮内部流动的PIV测试。数值优化和试验结果都表明,优化楔形叶片在满足约束条件的前提下,三个指定工况点上的压升都有大幅度的提高,同时也验证了本文发展的优化设计方法是有效的。
通过将本文发展的多工况多约束条件叶片优化设计方法成功地应用于不同的优化对象,以及对某工业用超低比转速离心鼓风机的实验研究和数值模拟,更加全面和深入地认识了叶片形状对其性能和流场的影响,进一步丰富了叶片优化设计技术,为提高叶轮机械的研制水平提供了技术依据。
The competitive pressure to improve performance, reduce research cost and design duration has always pushed turbomachinery designers to develop better and faster design methods. In recent years, CFD technology has been widely applied to numerical simulation of the three-dimensional viscous flow field inside turbomachinery, which has been verified by many researchers. Meanwhile, several effective optimization algorithms have been proposed. Fortunately, the rapid development of software and hardware of computers makes it possible for turbomachinery optimum design with the combination of CFD technology and those algorithms. To establish an optimum design system for turbomachinery impellers and blades, the author made an in-depth investigation of the related optimization methods, and developed several multi-point and multi-constraint optimization approaches for turbomachinery blades or impellers according to their individual characteristics. The developed approaches have been successfully applied to corresponding optimization cases.
The balance of computation time frame and computation precision must be achieved so that CFD technology can be effectively applied to the aerodynamic optimization design of turbomachinery. The author has studied the discretization scheme and numerical solution of steady Reynolds-Averaged Navier-Stokes equations, illustrated the formulation of Baldwin-Lomax model, Spalart-Allmaras model and k-εmodel, and introduced the convergence criteria of the present study. The NASA Low speed compressor’s impeller was selected as the reference case for numerical simulation and experimental validation. The influences of the turbulence models and grid distributions on the simulation results were discussed, which provided the ongoing optimum design with guidance.
A CFD-based multi-point and multi-constraint blade optimization approach was developed, which can be convenient to develop different proper approach for specific optimum object with regard to different computation cost and the number of operating points. The approach was successfully applied into the single- and multi-point optimum design for cascade blade, the single-point and multi-constraint optimum design for a centrifugal compressor impeller with splitter, and the multi-point and multi-constraint optimum design for a very low-specific-speed industrial centrifugal blower blade.
To realize these four optimization approaches, the corresponding optimization algorithms were developed. The parametrization methods for cascades and blades were developed to greatly reduce the number of the design variables. The proposed PANN has the improved mapping quality and training efficiency, which are superior to those of the traditional artificial neural networks. Inspired by the competitions occurring in populations and between populations in nature and society, HFCGA-DN was developed to overcome premature convergence. It is very efficient in global search. To improve the diversity of Pareto GA, the distribution function was introduced into NSGA-II algorithm, and INSGA-II was then developed. The data interface programs were also developed to combine the above algorithms with design of experiment (DOE) method and CFD technology.
As for the optimization case for a two-dimensional cascade, the maximum lift-to-drag ratio was selected as the objective. That the leading edge metal angle and trailing edge metal angle are kept constant, the section area of the optimized is greater than or equal to that 20% of the original one, and the drag coefficient of the optimized is less than or equal to that of the original one, were selected as the constraints. From the results of the nondimensional aerodynamic forces, the drag coefficient of the optimized blade is 3.2% reduction over that of the original one, while the lift-drag ratio of the optimized blade is 8.3% higher than that of the original one.
As for the same cascade, the minimum total pressure loss coefficients over three operating points, i=-10o,0o,10o, were selected as objective. And the constraints are the same as those of the above case. The multi-objective Pareto optimization approach based on approximate model was applied to the optimization process. The loss coefficients of the three points of the optimized cascade are decreased by 8.31%, 8.43% and 8.52%, respectively.
As for a centrifugal compressor impeller with splitters, a single-objective optimization approach based on approximate model was developed. The maximum isentropic efficiency was selected as the objective. That the mass flow and total pressure ratio are greater than or equal to those of the original one was selected as the performance constraints, and the variation ranges of the design variables were selected as the geometric constraints. The optimized impeller was obtained by varying the profiles of the impeller hub, shroud and blade. The isentropic efficiency is improved by 1.06%, while the total pressure ratio is also increased by 0.52%.
An optimization approach based on approximate model was proposed against many time-consuming CFD calculations during the numerical optimization process of turbomachinery. The core of this approach is a sample database, which is to build the approximate mode between the geometric information and its performance of samples. This proposed approach was applied to the optimum design of a set of three-dimensional compressor blades presented in this paper. The control points’ordinates of characteristic polygon of Bezier curve representing the profile of meridian plane and blade were selected as design variables, while maximum isentropic efficiency was selected as objective function. The maximum pressure rises at the three points were selected as the objective. That the mass flow and efficiency at each point are greater than or equal to those of the original one was selected as the performance constraints, and the variation ranges of the design variables were selected as the geometric constraints. The objective function of the optimized impeller is 1.06% higher than that of the original one on the condition that the pressure ratio does not fall, and flow quality on the meridian plane and in the flow channels is improved.
A multipoint optimization approach to a very low-specific-speed industrial centrifugal blower blade was developed with the consideration of its structural characteristics and performance requirements. The total pressure rise at three specified operating points were selected as the objective function. That the flow rate and impeller total pressure efficiency are not less than those of the original one was selected as the performance constraints. The numerical optimization was carried out in two phases, the optimization phases of constant thickness blade and varying thickness blade. To validate their aerodynamic performances, the original and optimized blower blades were made into experimental prototypes. Their performances were tested on the same experimental facilities, and their internal flow patterns inside the impeller were measured by PIV system. The results of both the numerical optimization and performance experiment show that significant improvement has been obtained in the optimization objective, which validates the effectiveness of the developed optimization approach. In addition, the performance variation rule of this very low-specific-speed blower is different from that of the traditional ones.
With the development of the multi-point and multi-constraint optimization approaches, successful application to different optimization cases, and numerical simulation and experimental investigation of a very low-specific-speed centrifugal blower, the author had a better knowledge of the influence of the blade profile on its performance and flow field, and made contribution to the optimization technology of turbomachinery.
为了在计算时间与计算精度之间寻求良好的平衡,使CFD技术可以有效地应用于叶轮机械的气动优化设计,作者研究了叶轮机械定常流动数值模拟中RANS方程的空间离散形式与求解方法,阐述了代数Balding-Lomax模型、一方程Sparlart-Allmaras模型和标准k-ε模型的构造形式,并介绍了本文计算中遵循的收敛准则。以NASA Low Speed Centrifugal Compressor (LSCC)实验叶轮为研究对象,结合其试验结果,讨论了湍流模型和网格等因素对计算结果的影响,为后续优化设计中湍流模型与网格的选取提供指导。
本文发展了一套基于CFD流场分析的多工况多约束条件的叶片优化设计方法。针对优化对象计算成本和优化工况或目标多少的不同,该方法可以灵活地发展成适合其具体特征的优化设计方法,本文将该优化方法分别应用于平面叶栅的单、多工况多约束条件优化设计、带分流叶片的离心叶轮优化设计单目标多约束条件和某一工业用超低比转速离心鼓风机叶片的多工况多约束条件优化设计中。
为实现上述优化方法,根据优化对象的不同特点和要求,发展了相应的实现算法。发展了适于叶栅和离心压缩机/鼓风机叶型参数化方法,大大减少了优化的设计变量;提出了并行神经网络算法,其映射质量和训练效率较传统神经网络算法有较大的提高;为避免基本遗传算法存在的早熟或陷入停滞现象等问题,受自然界和人类社会进化现象的启发,发展了一种新的遗传算法—改进的等级公平竞争遗传算法HFCGA-DN;发展了改进的INSGA-II算法,将分布函数引入NSGA-II算法中,提高了多目标Pareto遗传算法的多样性;并将上述算法与试验设计方法和CFD技术通过发展的数据接口有机地连接起来。
针对某二维透平叶栅优化问题,以极大化其升阻比作为优化目标函数,以叶栅的几何进出口角不变,叶栅截面的面积不小于初始叶型的20%和优化叶型阻力系数不大于初始叶型为约束条件,运用本文针对平面叶栅发展的单目标优化设计方法对叶栅进行优化设计。从气动力积分的结果来看,优化叶栅的气动阻力比初始叶栅减小3.2%,升阻比增加了8.3%。针对某带分流叶片的离心压缩机叶轮,以极大化其等熵效率作为目标函数,以流量和总压比不小于初始叶轮为性能约束条件和叶轮参数设定的变化范围为几何约束条件,运用本文发展的基于近似模型的单目标多约束优化方法通过改变轮毂、轮缘型线和叶片形状对初始叶轮进行了优化设计。优化后叶轮的等熵效率较初始叶轮提高了1.06%,同时总压比也提高了0.52%。
以极小化上述透平叶栅三个工况点的总压损失系数为目标函数,同样以叶栅的几何进出口角不变,叶栅截面的面积不小于初始叶型的20%为约束条件,运用本文发展的基于近似模型的多目标Pareto类优化设计方法对叶栅进行优化设计。优化后叶栅的目标函数在i=-10o,0o,10o的三个工况点分别比初始叶栅下降了8.31%、8.43%、8.52%。
根据某一工业用超低比转速离心鼓风机叶片的特点和性能要求,提出了楔形叶片的设计概念,发展了一套基于近似模型的鼓风机叶型叶片的多工况多约束优化方法。该优化方法的目标函数是极大化在三个指定工况点上的总压升,性能约束条件是效率和流量分别不小于初始叶型值,几何约束条件是设计变量的变化范围。为验证优化前后叶型的性能,将优化前后叶型加工成模型样机,并搭建了试验台,进行性能试验和叶轮内部流动的PIV测试。数值优化和试验结果都表明,优化楔形叶片在满足约束条件的前提下,三个指定工况点上的压升都有大幅度的提高,同时也验证了本文发展的优化设计方法是有效的。
通过将本文发展的多工况多约束条件叶片优化设计方法成功地应用于不同的优化对象,以及对某工业用超低比转速离心鼓风机的实验研究和数值模拟,更加全面和深入地认识了叶片形状对其性能和流场的影响,进一步丰富了叶片优化设计技术,为提高叶轮机械的研制水平提供了技术依据。
The competitive pressure to improve performance, reduce research cost and design duration has always pushed turbomachinery designers to develop better and faster design methods. In recent years, CFD technology has been widely applied to numerical simulation of the three-dimensional viscous flow field inside turbomachinery, which has been verified by many researchers. Meanwhile, several effective optimization algorithms have been proposed. Fortunately, the rapid development of software and hardware of computers makes it possible for turbomachinery optimum design with the combination of CFD technology and those algorithms. To establish an optimum design system for turbomachinery impellers and blades, the author made an in-depth investigation of the related optimization methods, and developed several multi-point and multi-constraint optimization approaches for turbomachinery blades or impellers according to their individual characteristics. The developed approaches have been successfully applied to corresponding optimization cases.
The balance of computation time frame and computation precision must be achieved so that CFD technology can be effectively applied to the aerodynamic optimization design of turbomachinery. The author has studied the discretization scheme and numerical solution of steady Reynolds-Averaged Navier-Stokes equations, illustrated the formulation of Baldwin-Lomax model, Spalart-Allmaras model and k-εmodel, and introduced the convergence criteria of the present study. The NASA Low speed compressor’s impeller was selected as the reference case for numerical simulation and experimental validation. The influences of the turbulence models and grid distributions on the simulation results were discussed, which provided the ongoing optimum design with guidance.
A CFD-based multi-point and multi-constraint blade optimization approach was developed, which can be convenient to develop different proper approach for specific optimum object with regard to different computation cost and the number of operating points. The approach was successfully applied into the single- and multi-point optimum design for cascade blade, the single-point and multi-constraint optimum design for a centrifugal compressor impeller with splitter, and the multi-point and multi-constraint optimum design for a very low-specific-speed industrial centrifugal blower blade.
To realize these four optimization approaches, the corresponding optimization algorithms were developed. The parametrization methods for cascades and blades were developed to greatly reduce the number of the design variables. The proposed PANN has the improved mapping quality and training efficiency, which are superior to those of the traditional artificial neural networks. Inspired by the competitions occurring in populations and between populations in nature and society, HFCGA-DN was developed to overcome premature convergence. It is very efficient in global search. To improve the diversity of Pareto GA, the distribution function was introduced into NSGA-II algorithm, and INSGA-II was then developed. The data interface programs were also developed to combine the above algorithms with design of experiment (DOE) method and CFD technology.
As for the optimization case for a two-dimensional cascade, the maximum lift-to-drag ratio was selected as the objective. That the leading edge metal angle and trailing edge metal angle are kept constant, the section area of the optimized is greater than or equal to that 20% of the original one, and the drag coefficient of the optimized is less than or equal to that of the original one, were selected as the constraints. From the results of the nondimensional aerodynamic forces, the drag coefficient of the optimized blade is 3.2% reduction over that of the original one, while the lift-drag ratio of the optimized blade is 8.3% higher than that of the original one.
As for the same cascade, the minimum total pressure loss coefficients over three operating points, i=-10o,0o,10o, were selected as objective. And the constraints are the same as those of the above case. The multi-objective Pareto optimization approach based on approximate model was applied to the optimization process. The loss coefficients of the three points of the optimized cascade are decreased by 8.31%, 8.43% and 8.52%, respectively.
As for a centrifugal compressor impeller with splitters, a single-objective optimization approach based on approximate model was developed. The maximum isentropic efficiency was selected as the objective. That the mass flow and total pressure ratio are greater than or equal to those of the original one was selected as the performance constraints, and the variation ranges of the design variables were selected as the geometric constraints. The optimized impeller was obtained by varying the profiles of the impeller hub, shroud and blade. The isentropic efficiency is improved by 1.06%, while the total pressure ratio is also increased by 0.52%.
An optimization approach based on approximate model was proposed against many time-consuming CFD calculations during the numerical optimization process of turbomachinery. The core of this approach is a sample database, which is to build the approximate mode between the geometric information and its performance of samples. This proposed approach was applied to the optimum design of a set of three-dimensional compressor blades presented in this paper. The control points’ordinates of characteristic polygon of Bezier curve representing the profile of meridian plane and blade were selected as design variables, while maximum isentropic efficiency was selected as objective function. The maximum pressure rises at the three points were selected as the objective. That the mass flow and efficiency at each point are greater than or equal to those of the original one was selected as the performance constraints, and the variation ranges of the design variables were selected as the geometric constraints. The objective function of the optimized impeller is 1.06% higher than that of the original one on the condition that the pressure ratio does not fall, and flow quality on the meridian plane and in the flow channels is improved.
A multipoint optimization approach to a very low-specific-speed industrial centrifugal blower blade was developed with the consideration of its structural characteristics and performance requirements. The total pressure rise at three specified operating points were selected as the objective function. That the flow rate and impeller total pressure efficiency are not less than those of the original one was selected as the performance constraints. The numerical optimization was carried out in two phases, the optimization phases of constant thickness blade and varying thickness blade. To validate their aerodynamic performances, the original and optimized blower blades were made into experimental prototypes. Their performances were tested on the same experimental facilities, and their internal flow patterns inside the impeller were measured by PIV system. The results of both the numerical optimization and performance experiment show that significant improvement has been obtained in the optimization objective, which validates the effectiveness of the developed optimization approach. In addition, the performance variation rule of this very low-specific-speed blower is different from that of the traditional ones.
With the development of the multi-point and multi-constraint optimization approaches, successful application to different optimization cases, and numerical simulation and experimental investigation of a very low-specific-speed centrifugal blower, the author had a better knowledge of the influence of the blade profile on its performance and flow field, and made contribution to the optimization technology of turbomachinery.
引文
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