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临界流喷嘴喉部氢气等熵指数解析计算与进化回归方法
Analytical calculation and evolutionary regression metho d for isentropic exp onent of hydrogen gas at the throat of critical nozzle
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摘要: 氢气作为最有希望的清洁可再生能源之一，已被广泛应用于航天、工业和燃料电池等领域.临界流喷嘴由于其测量过程不受下游扰动的影响，越来越多地被应用于氢气特别是高压氢气的流量测量.而作为真实气体的氢气在临界流喷嘴中的流动规律更加复杂，准确获得喷嘴喉部氢气的热力学参数对于氢气的精确测量至关重要.结合真实气体显式亥姆霍兹能量方程，利用熵焓关系分析并通过迭代获得了喷嘴喉部容积等熵指数这一基本流动参数.提出了最优化获取显式快速计算模型的回归算法，引入了进化算法思想，利用选择、交换和变异等方式寻找显著性和精度最优的种群个体.回归标准偏差为0.0089%，平均残差为0.0285%，最大残差为0.1781%.结果表明，所提出的算法能快速搜索满足显著性和精度要求的最优解，在提高回归方程质量的同时使方程项数达到最少，具有较好的抑制过拟合的能力.所提出的算法也可用于其他各类流体设备的不同介质流场特性参数模型的建立.Abstract: As one of the most promising renewable energy resources, the hydrogen has been used in the fields such as aerospace, industry, and fuel cells. Critical nozzles are widely used for mass flow-rate measurement of high hydrogen gas, since the flow measurement process is not affected by its downstream flow disturbance. The flow rule of real hydrogen gas through a critical nozzle is complicated and the thermophysical property of hydrogen at the nozzle throat is vital to the accurate measurement of hydrogen flow. In this paper, based on explicit Helmholtz energy and entropy-enthalpy equations, the basic flow parameter and isentropic volume change exponent are analytically calculated. In addition, an accurate explicit equation is determined by the nonlinear regression analysis where the ways of selection, exchange and mutation derived from evolutionary algorithm are introduced to search for optimal population individual. The regression standard deviation is 0.0089%, mean residual deviation is 0.0285%, and maximum residual deviation is 0.1781%. The result shows that it not only can rapidly find the optimal solution which has the lowest number of equation items and the great overfitting suppression capability, but also has a high computation accuracy. This algorithm can also be applied to modeling flow characteristic parameters for every other flow device.
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