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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.
[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
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[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
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