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Relaxation Effects in Small Critical Nozzles



Aaron N. Johnson, C L. Merkle, Michael R. Moldover, John D. Wright


We computed the flow of four gases (He, N2, CO2, and SF6) through a critical nozzle by augmenting traditional computational fluid dynamics (CFD) with a rate equation that accounts for τrelax, a species-dependent relaxation time that characterizes the equilibration of the vibrational degrees of freedom with the translational and rotational degrees of freedom. Conventional CFD (τrelax = 0) under-predicts the flow through a small nozzle (throat diameter d = 0.593 mm) by up to 2.3 % for CO2 and by up to 1.2 % for SF6. When we used values of τrelax from the acoustics literature, the augmented CFD under-predicted the flow for SF6 by only 0.3 %, in the worst case. The augmented predictions for CO2 were within the scatter of previously published experimental data ({plus or minus}0.1 %). As expected, both conventional and augmented CFD agree with experiments for He and N2. Thus, augmented CFD enables one to calibrate a small nozzle with one gas (e.g., N2) and then to use it as a flow standard with any other gas (e.g., CO2) for which reliable values of τrelax and the relaxing heat capacity are available.
Journal of Fluids Engineering-Transactions of the ASME


flow standard


Johnson, A. , Merkle, C. , Moldover, M. and Wright, J. (2006), Relaxation Effects in Small Critical Nozzles, Journal of Fluids Engineering-Transactions of the ASME, [online], (Accessed April 23, 2024)
Created January 1, 2006, Updated June 2, 2021