临界流喷嘴喉部氢气等熵指数解析计算与进化回归方法

丁红兵; 王超; 赵雅坤

doi:10.7498/aps.63.164701

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.

关键词:

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.

Keywords:

作者及机构信息

1.
天津大学电气与自动化工程学院, 天津市过程检测与控制重点实验室, 天津 300072

基金项目: 国家自然科学基金（批准号：61072101）和教育部新世纪优秀人才支持计划（批准号：NCET-10-0621）资助的课题.

Authors and contacts

1.
Key Laboratory of Process Measurement and Control of Tianjin, School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61072101) and the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-10-0621).

参考文献

[1]	Fan J, Bao K, Duan D F, Wang L C, Liu B B, Cui T 2012 Chin. Phys. B 21 086104
[2]	Sun B G, Zhang D S, Liu F S 2012 Int. J. Hydrogen Energ. 37 932
[3]	Ni M, Leung M K H, Sumathy K, Leung D Y C 2006 Int. J. Hydrogen Energ. 31 1401
[4]	Zhou J J, Chen Y G, Wu C L, Zheng X, Fang Y C, Gao T 2009 Acta Phys. Sin. 58 4853 (in Chinese) [周晶晶, 陈云贵, 吴朝玲, 郑欣, 房玉超, 高涛 2009 58 4853]
[5]	Zheng J Y, Kai F M, Liu Z Q, Chen R, Chen C P 2006 Acta Energ. Solar. Sin. 27 1168 (in Chinese) [郑津洋, 开方明, 刘仲强, 陈瑞, 陈长聘 2006 太阳能学报 27 1168]
[6]	Ding H B, Wang C, Zhao Y K 2014 Int. J. Hydrogen Energ. 39 3947
[7]	Nagao J, Matsuo S, Suetsugu S, Toshiaki S, Kim H D 2013 Int. J. Hydrogen Energ. 38 9043
[8]	Li C H, Mickan B 2013 Flow Meas. Instrum. 33 212
[9]	Wang C, Ding H B, Wang H X 2013 IEEE Trans. Instrum. Meas. 62 1154
[10]	Lim J M, Yoon B H, Oh Y K, Park K A 2011 Flow Meas. Instrum. 22 402
[11]	Morioka T, Nakao S, Ishibashi M 2011 Trans. Jpn. Soc. Mech. Eng. Ser. B 77 1088
[12]	Johnson R C 1964 J. Basic Eng. 86 519
[13]	Kim J H, Kim H D, Setoguchi T 2008 J. Propul. Power 24 715
[14]	Kim J H, Kim H D, Setoguchi T 2009 Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci. 223 617
[15]	Nagao J, Matsuo S, Mohammad M, Setoguchi T, Kim H D 2012 Int. J. Turbo Jet Eng. 29 21
[16]	Redlich O, Kwong J N S 1949 Chem. Rev. 44 233
[17]	Lee B L, Kesler M F 1975 AIChE J. 21 510
[18]	Peng D Y, Robinson D B 1976 Ind. Eng. Chem. Fund. 15 59
[19]	Du C, Xu M Y, Mi J C 2010 Acta Phys. Sin. 59 6331 (in Chinese) [杜诚, 徐敏义, 米建春 2010 59 6331]
[20]	Lemmon E W, Tillner R 1999 Fluid Phase Equilibr. 165 1
[21]	Leachman J W, Jacobsen R T, Penoncello S G 2009 J. Phys. Chem. Ref. Data. 38 721
[22]	Travis J R, Koch D P, Xiao J, Xu Z 2013 Int. J. Hydrogen Energ. 38 8132
[23]	Setzmann U, Wagner W 1989 Int. J. Thermophys. 10 1103
[24]	Wang N, Chen K A 2010 Acta Phys. Sin. 59 2873 (in Chinese) [王娜, 陈克安 2010 59 2873]
[25]	Xu Z X, Ma R Z 1990 Acta Phys. Sin. 39 875 (in Chinese) [徐祖雄, 马如璋 1990 39 875]
[26]	Papadrakakis M, Lagaros N D, Thierauf G, Cai J B 1998 Eng. Comput. 15 12
[27]	Ratkowsky D A 1993 J. Ind. Microbiol. 12 195
[28]	Long W, Jiao J J 2012 Acta Phys. Sin. 61 110507 (in Chinese) [龙文, 焦建军 2012 61 110507]
[29]	ISO 9300 2005 Measurement of Gas Flow by Means of Critical Flow Venturi Nozzles (London: British Standards Institution) pp4-10
[30]	Stewart D G, Watson J T R, Vaidya A M 1999 Flow Meas. Instrum. 10 27

施引文献

[1]	Fan J, Bao K, Duan D F, Wang L C, Liu B B, Cui T 2012 Chin. Phys. B 21 086104
[2]	Sun B G, Zhang D S, Liu F S 2012 Int. J. Hydrogen Energ. 37 932
[3]	Ni M, Leung M K H, Sumathy K, Leung D Y C 2006 Int. J. Hydrogen Energ. 31 1401
[4]	Zhou J J, Chen Y G, Wu C L, Zheng X, Fang Y C, Gao T 2009 Acta Phys. Sin. 58 4853 (in Chinese) [周晶晶, 陈云贵, 吴朝玲, 郑欣, 房玉超, 高涛 2009 58 4853]
[5]	Zheng J Y, Kai F M, Liu Z Q, Chen R, Chen C P 2006 Acta Energ. Solar. Sin. 27 1168 (in Chinese) [郑津洋, 开方明, 刘仲强, 陈瑞, 陈长聘 2006 太阳能学报 27 1168]
[6]	Ding H B, Wang C, Zhao Y K 2014 Int. J. Hydrogen Energ. 39 3947
[7]	Nagao J, Matsuo S, Suetsugu S, Toshiaki S, Kim H D 2013 Int. J. Hydrogen Energ. 38 9043
[8]	Li C H, Mickan B 2013 Flow Meas. Instrum. 33 212
[9]	Wang C, Ding H B, Wang H X 2013 IEEE Trans. Instrum. Meas. 62 1154
[10]	Lim J M, Yoon B H, Oh Y K, Park K A 2011 Flow Meas. Instrum. 22 402
[11]	Morioka T, Nakao S, Ishibashi M 2011 Trans. Jpn. Soc. Mech. Eng. Ser. B 77 1088
[12]	Johnson R C 1964 J. Basic Eng. 86 519
[13]	Kim J H, Kim H D, Setoguchi T 2008 J. Propul. Power 24 715
[14]	Kim J H, Kim H D, Setoguchi T 2009 Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci. 223 617
[15]	Nagao J, Matsuo S, Mohammad M, Setoguchi T, Kim H D 2012 Int. J. Turbo Jet Eng. 29 21
[16]	Redlich O, Kwong J N S 1949 Chem. Rev. 44 233
[17]	Lee B L, Kesler M F 1975 AIChE J. 21 510
[18]	Peng D Y, Robinson D B 1976 Ind. Eng. Chem. Fund. 15 59
[19]	Du C, Xu M Y, Mi J C 2010 Acta Phys. Sin. 59 6331 (in Chinese) [杜诚, 徐敏义, 米建春 2010 59 6331]
[20]	Lemmon E W, Tillner R 1999 Fluid Phase Equilibr. 165 1
[21]	Leachman J W, Jacobsen R T, Penoncello S G 2009 J. Phys. Chem. Ref. Data. 38 721
[22]	Travis J R, Koch D P, Xiao J, Xu Z 2013 Int. J. Hydrogen Energ. 38 8132
[23]	Setzmann U, Wagner W 1989 Int. J. Thermophys. 10 1103
[24]	Wang N, Chen K A 2010 Acta Phys. Sin. 59 2873 (in Chinese) [王娜, 陈克安 2010 59 2873]
[25]	Xu Z X, Ma R Z 1990 Acta Phys. Sin. 39 875 (in Chinese) [徐祖雄, 马如璋 1990 39 875]
[26]	Papadrakakis M, Lagaros N D, Thierauf G, Cai J B 1998 Eng. Comput. 15 12
[27]	Ratkowsky D A 1993 J. Ind. Microbiol. 12 195
[28]	Long W, Jiao J J 2012 Acta Phys. Sin. 61 110507 (in Chinese) [龙文, 焦建军 2012 61 110507]
[29]	ISO 9300 2005 Measurement of Gas Flow by Means of Critical Flow Venturi Nozzles (London: British Standards Institution) pp4-10
[30]	Stewart D G, Watson J T R, Vaidya A M 1999 Flow Meas. Instrum. 10 27

[1]	程亮元, 徐进良. 流动方向对超临界二氧化碳流动传热特性的影响. , 2024, 73(2): 024401. doi: 10.7498/aps.73.20231142
[2]	李逢超, 付宇, 李超, 杨建刚, 胡春波. 铝液滴撞击曲面的流动特性分析. , 2022, 71(18): 184701. doi: 10.7498/aps.71.20220442
[3]	单明广, 刘翔宇, 庞成, 钟志, 于蕾, 刘彬, 刘磊. 结合线性回归的离轴数字全息去载波相位恢复算法. , 2022, 71(4): 044202. doi: 10.7498/aps.71.20211509
[4]	郑所生, 黄瑶, 邹鲲, 彭倚天. 刮膜蒸发器内非牛顿流体流场特性数值模拟. , 2022, 71(5): 054701. doi: 10.7498/aps.71.20211921
[5]	单明广, 刘翔宇, 庞成, 钟志, 于蕾, 刘彬, 刘磊. 结合线性回归的离轴数字全息去载波相位恢复算法. , 2021, (): . doi: 10.7498/aps.70.20211509
[6]	卞晓鸽, 周胜, 张磊, 何天博, 李劲松. 基于标准样品回归算法和腔增强光谱的NO₂检测方法. , 2021, 70(5): 050702. doi: 10.7498/aps.70.20201322
[7]	郑所生, 黄瑶, 邹鲲, 彭倚天. 刮膜蒸发器内非牛顿流体流场特性数值模拟. , 2021, (): . doi: 10.7498/aps.70.20211921
[8]	张宝军, 王芳, 沈稼强, 单欣, 邸希超, 胡凯, 张楷亮. 钴掺杂MoSe₂共生长中氢气的作用分析及磁电特性研究. , 2020, 69(4): 048101. doi: 10.7498/aps.69.20191302
[9]	田淙升, 陈新亮, 刘杰铭, 张德坤, 魏长春, 赵颖, 张晓丹. 氢气引入对宽光谱Mg和Ga共掺杂ZnO透明导电薄膜的特性影响. , 2014, 63(3): 036801. doi: 10.7498/aps.63.036801
[10]	闫寒, 张文明, 胡开明, 刘岩, 孟光. 随机粗糙微通道内流动特性研究. , 2013, 62(17): 174701. doi: 10.7498/aps.62.174701
[11]	张文专, 龙文, 焦建军. 基于差分进化算法的混沌时间序列预测模型参数组合优化. , 2012, 61(22): 220506. doi: 10.7498/aps.61.220506
[12]	龙文, 焦建军. 基于混合交叉进化算法的混沌系统参数估计. , 2012, 61(11): 110507. doi: 10.7498/aps.61.110507
[13]	潘克家, 陈华, 谭永基. 基于差分进化算法的核磁共振T2谱多指数反演. , 2008, 57(9): 5956-5961. doi: 10.7498/aps.57.5956
[14]	王钧炎, 黄德先. 基于混合差分进化算法的混沌系统参数估计. , 2008, 57(5): 2755-2760. doi: 10.7498/aps.57.2755
[15]	董芳, 金宁德, 宗艳波, 王振亚. 两相流流型动力学特征多尺度递归定量分析. , 2008, 57(10): 6145-6154. doi: 10.7498/aps.57.6145
[16]	郝鹏飞, 姚朝晖, 何枫. 粗糙微管道内液体流动特性的实验研究. , 2007, 56(8): 4728-4732. doi: 10.7498/aps.56.4728
[17]	赵松峰, 周效信, 金成. 强激光场中模型氢原子和真实氢原子的高次谐波与电离特性研究. , 2006, 55(8): 4078-4085. doi: 10.7498/aps.55.4078
[18]	朱红毅, 李军, 沈建其, 何赛灵. 利用脑磁图-多重信号分类算法求解真实头模型中磁源定位问题. , 2003, 52(7): 1812-1817. doi: 10.7498/aps.52.1812
[19]	宁鼎, 胡恺生, 傅怀杰. 氢气氛对光纤损耗特性的影响. , 1990, 39(1): 82-88. doi: 10.7498/aps.39.82
[20]	徐祖雄, 马如璋. 重迭穆斯堡尔谱的逐步回归分析方法. , 1990, 39(6): 33-39. doi: 10.7498/aps.39.33

计量

文章访问数: 6295
PDF下载量: 544
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板