Relaxation Effects in Small Critical Nozzles

Published

January 1, 2006

Author(s)

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

Abstract

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 τ_relax, 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 (τ_relax = 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 τ_relax 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 τ_relax and the relaxing heat capacity are available.

Citation

Journal of Fluids Engineering-Transactions of the ASME

Volume

128

Issue

1/1/06

Pub Type

Journals

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Keywords

flow standard

Citation

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], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=830846 (Accessed October 11, 2025)