叶轮机械叶片全三维反问题优化设计方法研究
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摘要
本文以工程应用为背景,基于数值求解N-S(Navier-Stokes)方程,对叶轮机械叶片全三维反问题优化设计方法进行研究,开发了相应的流场正问题计算和叶片反问题设计程序,并针对轴流风扇/压气机中的跨音速转子开展了优化研究。
在叶片内部流场计算方面,采用圆柱坐标系下的N-S方程和Spalart-Allmaras湍流模型、MUSCL差分格式、LU-SGS隐式方法进行求解；计算域网格选用H型,便于反问题优化设计过程中改变叶片的几何形状后,网格进行自动更新。
在程序调试和验证部分,将跨音速叶片Rotor67和Rotor37的流场数值模拟结果与各自的试验数据进行对比,考察了5种常用差分格式限制器以及入口边界条件中湍流粘性的选取对计算效果的影响,结果表明：程序能够较准确地捕捉流场中的激波、附面层分离等主要特征,满足工程应用的精度要求。
反问题设计方法通过给定叶片表面的静压分布以反求叶型。假设叶表的网格点存在虚拟移动速度,迭代过程中由原叶片、过渡叶片表面的实际静压与目标静压之差来驱动叶型修改。详细介绍定解条件给定方法、叶片表面型线的修改和光滑方法、计算域网格更新等内容,并采用对静叶减薄和动叶加厚的返回试验来验证该方法的可行性,收敛结果能很好地满足给定的目标静压分布。
在对典型跨音速转子内部流动机理认识的基础上,根据流道内不同叶高截面的流场结构、损失和稳定性特点,提出分区优化的原则和具体实施步骤,即调整流向负荷分配和叶表局部静压梯度,以减弱亚音速流动区域中吸力面附近的附面层分离和超音速区激波的强度、位置及其与附面层的干涉。
以Rotor67转子为研究对象,将分区优化原则应用到叶片的部分及整体叶展优化中,分析亚音速和超音速流动各自的静压、负荷分布控制规律及其对总性能、流场细节和出口参数的影响；反问题优化设计耗费约2倍的正问题计算时间即达到收敛,效果良好,可减少流场的分离和激波损失,使新叶片在近设计点级间匹配参数基本不变的情况下,绝热效率提升约0.6%,设计转速下的堵塞流量增加约0.5%,体现该方法的有效性。
This paper investigated turbomachinery problems regarding the engineering applications. Full-3D inverse optimization design method for turbomachinary blade was studied based on numerical solver of N-S (Navier-Stokes) equations. Computer programs of direct problem for flowfield and inverse problem for blade design were developed, and investigation on optimization of transonic rotor in axial fan/compressor was carried out.
In terms of flowfield calculation within blade passage, it adopted N-S equations and Sparlart-Allmaras turbulence model in cylindrical coordinate, MUSCL scheme and LU-SGS implicit solver. The H-type grid was used for the computational domain, which was convenient for re-generating new grid of modified blade in inverse optimization design process.
During debugging and validation of the direct program, the flowfield simulation results were compared with the experimental data of Rotor67and Rotor37respectively. Five kinds of discretization form limiters and inlet turbulence viscosity of boundary condition were discussed to evaluate their effects on numerical calculation. The results indicated:the program of direct problem could capture major characteristics such as shock wave and boundary layer separation well. The computer program could satisfy accuracy requirements of engineering applications.
In the inverse problem, static pressure on blade surface was specified for obtaining the corresponding blade profile. It was assumed there was a virtual velocity of grid node on blade surface. Then, the blade geometry was modified by the difference between surface pressure and target pressure of the Original balde and temporary blades during iterative procedure. Methodologies of the inverse problem were introduced in detail, which included the set of inverse problem, blade profile modifying and smoothing method, grid re-generating method etc. The inverse design program was validated by the returning tests, in which the stator blade was made thinner and the rotor blade was thickened initially. The convergence solutions of new blade profiles were in good agreement with the target pressure well.
Based on the research of typical internal flow mechanism of transonic rotor, the principle of partitional optimization and specific implement steps were proposed according to the flow constructure, losses, and stability of flowfield at different blade span sections. It was to adjust the loading distribution at flow direction and part static pressure gradient on blade surface to weaken separation in boundary layer near suction surface of subsonic area, and intensity and position of shock and interference with boundary layer of supersonic aera.
The principle of partitional optimization was applied to optimize part and all span of Rotor67. The thesis analyzed the influences of controlling discipline of static pressure, loading distribution and their effects to performance, flowfield details, and outlet parameters in respect of subsonic and supersonic area. The calculation time of inverse optimization design was2times of that of direct problem. The optimized blade reduced flow separation and shock wave losses. The adiabatic efficiency was increased by0.6%at near design point in the case of the same row interface parameters of. The block massflow was increased by0.5%at design speed. The above results revealed the effectiveness of the inverse optimization design method.
在叶片内部流场计算方面,采用圆柱坐标系下的N-S方程和Spalart-Allmaras湍流模型、MUSCL差分格式、LU-SGS隐式方法进行求解；计算域网格选用H型,便于反问题优化设计过程中改变叶片的几何形状后,网格进行自动更新。
在程序调试和验证部分,将跨音速叶片Rotor67和Rotor37的流场数值模拟结果与各自的试验数据进行对比,考察了5种常用差分格式限制器以及入口边界条件中湍流粘性的选取对计算效果的影响,结果表明：程序能够较准确地捕捉流场中的激波、附面层分离等主要特征,满足工程应用的精度要求。
反问题设计方法通过给定叶片表面的静压分布以反求叶型。假设叶表的网格点存在虚拟移动速度,迭代过程中由原叶片、过渡叶片表面的实际静压与目标静压之差来驱动叶型修改。详细介绍定解条件给定方法、叶片表面型线的修改和光滑方法、计算域网格更新等内容,并采用对静叶减薄和动叶加厚的返回试验来验证该方法的可行性,收敛结果能很好地满足给定的目标静压分布。
在对典型跨音速转子内部流动机理认识的基础上,根据流道内不同叶高截面的流场结构、损失和稳定性特点,提出分区优化的原则和具体实施步骤,即调整流向负荷分配和叶表局部静压梯度,以减弱亚音速流动区域中吸力面附近的附面层分离和超音速区激波的强度、位置及其与附面层的干涉。
以Rotor67转子为研究对象,将分区优化原则应用到叶片的部分及整体叶展优化中,分析亚音速和超音速流动各自的静压、负荷分布控制规律及其对总性能、流场细节和出口参数的影响；反问题优化设计耗费约2倍的正问题计算时间即达到收敛,效果良好,可减少流场的分离和激波损失,使新叶片在近设计点级间匹配参数基本不变的情况下,绝热效率提升约0.6%,设计转速下的堵塞流量增加约0.5%,体现该方法的有效性。
This paper investigated turbomachinery problems regarding the engineering applications. Full-3D inverse optimization design method for turbomachinary blade was studied based on numerical solver of N-S (Navier-Stokes) equations. Computer programs of direct problem for flowfield and inverse problem for blade design were developed, and investigation on optimization of transonic rotor in axial fan/compressor was carried out.
In terms of flowfield calculation within blade passage, it adopted N-S equations and Sparlart-Allmaras turbulence model in cylindrical coordinate, MUSCL scheme and LU-SGS implicit solver. The H-type grid was used for the computational domain, which was convenient for re-generating new grid of modified blade in inverse optimization design process.
During debugging and validation of the direct program, the flowfield simulation results were compared with the experimental data of Rotor67and Rotor37respectively. Five kinds of discretization form limiters and inlet turbulence viscosity of boundary condition were discussed to evaluate their effects on numerical calculation. The results indicated:the program of direct problem could capture major characteristics such as shock wave and boundary layer separation well. The computer program could satisfy accuracy requirements of engineering applications.
In the inverse problem, static pressure on blade surface was specified for obtaining the corresponding blade profile. It was assumed there was a virtual velocity of grid node on blade surface. Then, the blade geometry was modified by the difference between surface pressure and target pressure of the Original balde and temporary blades during iterative procedure. Methodologies of the inverse problem were introduced in detail, which included the set of inverse problem, blade profile modifying and smoothing method, grid re-generating method etc. The inverse design program was validated by the returning tests, in which the stator blade was made thinner and the rotor blade was thickened initially. The convergence solutions of new blade profiles were in good agreement with the target pressure well.
Based on the research of typical internal flow mechanism of transonic rotor, the principle of partitional optimization and specific implement steps were proposed according to the flow constructure, losses, and stability of flowfield at different blade span sections. It was to adjust the loading distribution at flow direction and part static pressure gradient on blade surface to weaken separation in boundary layer near suction surface of subsonic area, and intensity and position of shock and interference with boundary layer of supersonic aera.
The principle of partitional optimization was applied to optimize part and all span of Rotor67. The thesis analyzed the influences of controlling discipline of static pressure, loading distribution and their effects to performance, flowfield details, and outlet parameters in respect of subsonic and supersonic area. The calculation time of inverse optimization design was2times of that of direct problem. The optimized blade reduced flow separation and shock wave losses. The adiabatic efficiency was increased by0.6%at near design point in the case of the same row interface parameters of. The block massflow was increased by0.5%at design speed. The above results revealed the effectiveness of the inverse optimization design method.
引文
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