• Transactions of the Korean Society of Mechanical Engineers B
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• v.37 no.12
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• pp.1167-1173
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• 2013

This study aimed to calculate the CFFs (critical flow functions) of a sonic nozzle bank with a 12-nozzle package within 1 s. Toward this end, the Helmholtz free energy of natural gas was formulated by using the AGA8-dc equation of state in a form without integral terms, and thereafter, thermodynamic properties such as the enthalpy, entropy, speed of sound, and heat capacity, which are used in CFF calculation, were derived in analytical form. As a result, the calculation time of CFFs was improved from 6.7 s in a previous study to 0.6 s per 12-nozzle package and kept almost constant regardless of the number of components in natural gas. Furthermore, it was confirmed that the calculated CFF values were in agreement with the results of a CFF international comparison test carried out under ISO management in 1998-1999.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.7
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• pp.911-917
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• 1999

The sonic nozzle is widely used as reference device for calibrating flowmeters In gas flow measurement and its use requires the Critical Flow Factor(CFF) based on the thermodynamic properties of the gas at the nozzle throat. ISO-9300 provides the calculating method of the factor. But since the CFF from this method show an error over ${\pm}0.5%$ In specific conditions and of ${\pm}0.1{\sim}{\pm}0.2%$ in common Natural Gas(NG) custody transfer condition. this method cannot be applied for gas flow measurement with sonic nozzle. Each research bodies or organizations of the world have joined in order to calculate the CFF more accurately. They have performed these works using their own method and compared the results with each other under the management of ISO. KOGAS have joined those works, because the high-pressure natural gas flow calibration facility of KOGAS will be constructed in late 1999, and then had necessities to calculate a CFF accurately. The calculation method of KOGAS was using the equation of state from AGA-8('94), high accuracy model of ideal gas properties and the solutions of thermodynamic equations. The evaluation results have had a very good consistency within ${\pm}0.05%$ in most NO custody transfer conditions compared to the speed of sound for methane and also shown that the CFF was within ${\pm}0.1%$ compared to the results of other works of the world.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.38 no.7
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• pp.625-638
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• 2014

In this study, the uncertainties in the critical flow functions (CFFs) calculated by the AGA8-dc equation of state were estimated. To this end, the formulas for enthalpy, entropy, and speed of sound, which are used in calculating the CFF, were expressed in the form of dimensionless Helmholtz free energy and its derivatives, and the uncertainty in Helmholtz free energy was inferred. To consider the variations in the compressibility-dependent variables induced by the variation (i.e., uncertainty) in compressibility, the form of the AGA8-dc equation was modified to have a deviation equal to the uncertainty under each flow condition. For each independent uncertainty component of the CFF, a model for uncertainty contribution was developed. All these changes were applied to GASSOLVER, which is KOGAS's thermodynamic database. As a result, the uncertainties in the CFF were estimated to be 0.025, 0.055, and 0.112 % at 10, 50, and 100 bar, respectively, and are seen to increase with the increase in pressure. Furthermore, these results could explain the deviations in the CFFs across the different labs in which the CFF international comparison test was conducted under the ISO management in 1999.