ABSTRACT A critical nozzle (sonic nozzle) is used to measure the mass flow rate of gas. It is well known that the coefficient of discharge of the flow in the nozzle is a single function of Reynolds number. The purpose of the present study is to investigate the effect of unsteady downstream condition on hydrogen gas flow through a sonic nozzle, numerically. Navier-Stokes equations were solved numerically using 3rd-order MUSCL type TVD finite-difference scheme with a second-order fractional-step for time integration. A standard k-ε model was used as a turbulence model. The computational results showed that the discharge coefficients in case without pressure fluctuations were in good agreement with experimental results. Further, it was found that the pressure fluctuations tended to propagate upstream of nozzle throat with the decrease of Reynolds number and an increase of amplitude of pressure fluctuations.
Cite this paper
J. Nagao, S. Matsuo, T. Setoguchi and H. Kim, "Numerical Study on the Effect of Unsteady Downstream Conditions on Hydrogen Gas Flow through a Critical Nozzle," Open Journal of Fluid Dynamics, Vol. 2 No. 4, 2012, pp. 137-144. doi: 10.4236/ojfd.2012.24014.
 S. P. Tang and J. B. Fenn, “Experimental Determination of the Discharge Coefficients for Critical Flow through an Axisymmetric Nozzle,” The American Institute of Aeronautics and Astronautics Journal, Vol. 16, No. 1, 1978, pp. 41-46. doi:10.2514/3.60854
 S. Nakao, Y. Yokoi and M. Takamoto, “Development of a Calibration Facility for Small Mass Flow Rates of Gas and Uncertainty of a Sonic Venturi Transfer Standard,” Flow Measurement and Instrumentation, Vol. 7, No. 2, 1996, pp. 77-83. doi:10.1016/S0955-5986(97)00006-X
 S. Nakao, T. Irayama and M. Takamoto, “Relations between the Discharge Coefficients of the Sonic Venturi Nozzle and Kind of Gases,” Journal of the Japan Society of Mechanical Engineers, Series B, Vol. 66, No. 642, 2000, pp. 438-444.
 R. C. Johnson, “Real Gas Effects in Critical-Flowthrough Nozzles and Tabulated Thermodynamic Properties,” NASA TN D-2565, 1965.
 R. D. McCarty and L. A. Weber, “Thermophysical Properties of Parahydrogen from the Freezing Liquid Line to 5000R for Pressures to 10,000 Psia,” NBS TN 617, 1972.
 R. D. McCarty, J. Hord and H. M. Roder, “Selected Properties of Hydrogen (Engineering Design Data),” NBS MN 168, 1981.
 R. D. McCarty, “Hydrogen Technological Surveythermophysical Properties,” NASA SP 3089, 1975.
 H. D. Kim, J. H. Kim, K. A. Park, T. Setoguchi and S. Matsuo, “Computational Study of the Gas Flow through a Critical Nozzle,” Proceedings of the Institution of Mechanical Engineers. Part C, Journal of Mechanical Engineering Science, Vol. 217, No. 10, 2003, pp. 1179-1189.
 H. D. Kim, K. Matsuo, S. Kawagoe and T. Kinoshita, “Flow Unsteadiness by Weak Normal Shock Wave/Turbulent Boundary Layer Interaction in Internal Flow,” JSME International Journal. Series 2, Fluids Engineering, Heat Transfer, Power, Combustion, Thermophysical Properties, Vol. 34, No. 4, 1991, pp. 457-465.
 K. Matsuo, Y. Miyazato and H. D. Kim, “Shock Train and Pseuedo-Shock Phenomena in Internal Gas Flows,” Progress in Aerospace Sciences, Vol. 35, No. 1, 1999, pp. 33-100. doi:10.1016/S0376-0421(98)00011-6
 E. Von Lavante, A. Zachcizl, B. Nath and H. Dietrich, “Unsteady Effects in Critical Nozzles Used for Flow Metering,” Measurement, Vol. 29, No. 1, 2001, pp. 1-10.
 H. D. Kim, J. H. Kim, K. A. Park, T. Setoguchi and S. Matsuo, “Study of the Effects of Unsteady Downstream Conditions on the Gas Flow through a Critical Nozzle,” Proceedings Institution of Mechanical Engineers. Part C: Journal of Mechanical Engineering Science, Vol. 218, No. 10, 2004, pp.1163-1173.
 J. Nagao, S. Matsuo, T. Setoguchi and H. D. Kim, “Effect of Unsteady Downstream Conditions on the Gas Flow through a Supersonic Nozzle,” International Journal of Turbo and Jet Engines, Vol. 27, No. 2, 2009, pp.95-108.
 J. Nagao, M. Mamun, S. Matsuo, T. Hashimoto, S. Toshiaki and H. D. Kim, “Numerical Study of Air Gas Flow through a Critical Nozzle,” International Journal of Turbo and Jet Engines, Vol. 26, No. 4, 2009, pp.223-234.
 B. E. Launder and D. B. Spalding, “The Numerical Computation of Turbulent Flows,” Computer Methods in Applied Mechanics and Engineering, Vol. 3, No. 2, 1974, pp. 269-289. doi:10.1016/0045-7825(74)90029-2
 S. Sarkar and L. Balakrishnan, “Application of a Reynolds Stress Turbulence Model to the Compressible Shear Layer,” NASA CR 182002, 1990.
 D. C. Wilcox, “Turbulence Modeling for CFD,” 3rd Edition, DCW Industries, Inc., La Canada, 2006.
 H. C. Yee, “A Class of High-Resolution Explicit and Implicit Shock Capturing Methods,” NASA TM-89464, 1989.
 ISO 9300, “Measurement of Gas Flow by Means of Critical Flow Venturi Nozzles,” 1990.
 S. Nakao, “A Study on the Conversion Factor of Sonic Venturi Nozzles,” AIST Bulletin of Metrology, Vol. 1, No. 2, 2002, pp. 387-405.