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TECHNICAL PAPERS

# Relaxation Effects in Small Critical Nozzles

[+] Author and Article Information
Aaron N. Johnson

National Institute of Standards and Technology, 100 Bureau Drive, Stop 8361, Gaithersburg, Maryland, 20899-8361aaron.johnson@nist.gov

Charles L. Merkle, Michael R. Moldover, John D. Wright

National Institute of Standards and Technology, 100 Bureau Drive, Stop 8361, Gaithersburg, Maryland, 20899-8361

Standard reference conditions are at $293.15K$ and $101.325kPa$.

The measured value of the throat diameter was adjusted by less than one micron by matching the experimental $Cd$ data to the computed results for $N2$.

Even after correcting for real gas behavior the discharge coefficient has a weak dependence on $γ$ that diminishes with increasing Reynolds number.

The time marching approach differs from commonly used iterative approaches which omit the time derivative term when applied to steady state problems.

The contribution of the electronic energy is negligible over the temperature range of interest.

Greater than unity $Cd$ values are sometimes caused by inaccurate values of the CFV throat diameter. This is especially true for small-sized CFVs where the throat diameter is more difficult to measure.

J. Fluids Eng 128(1), 170-176 (Aug 10, 2005) (7 pages) doi:10.1115/1.2137346 History: Received July 10, 2003; Revised August 10, 2005

## Abstract

We computed the flow of four gases (He, $N2$, $CO2$, and $SF6$) through a critical flow venturi (CFV) 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 $(τrelax=0)$ underpredicts the flow through small CFVs (throat diameter $d=0.593mm$) 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 underpredicted 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 $(±0.1%)$. As expected, both conventional and augmented CFD agree with experiments for He and $N2$. Thus, augmented CFD enables one to calibrate a small CFV with one gas (e.g., $N2$) and to use these results as a flow standard with other gases (e.g., $CO2$) for which reliable values of $τrelax$ and the relaxing heat capacity are available.

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## Figures

Figure 1

Comparison of experimental calibration data of four gases with equilibrium (open symbols in (b)) and nonequilibrium CFD data (closed symbols) over a Reynolds number range from 2000 to 40,000

Figure 2

Critical nozzle used in this study. The diameter of the throat was d=0.593mm.

Figure 3

Effective critical flow function versus reference value of Γ* evaluated at the nozzle throat for CO2 (left) and SF6 (right)

## Errata

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