Relaxation Effects in Small Critical Nozzles

Aaron N. Johnson; Charles L. Merkle; Michael R. Moldover; John D. Wright

doi:10.1115/1.2137346

Journal of Fluids Engineering | Volume 128 | Issue 1 | TECHNICAL PAPERS

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TECHNICAL PAPERS

Relaxation Effects in Small Critical Nozzles

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

[+] 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 $293.15 K$ and $101.325 kPa$ .

The measured value of the throat diameter was adjusted by less than one micron by matching the experimental $C_{d}$ data to the computed results for $N_{2}$ .

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 $C_{d}$ 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

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We computed the flow of four gases (He, $N_{2}$ , $C O_{2}$ , and $S F_{6}$ ) through a critical flow venturi (CFV) 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 $(τ_{relax} = 0)$ underpredicts the flow through small CFVs (throat diameter $d = 0.593 mm$ ) by up to 2.3% for $C O_{2}$ and by up to 1.2% for $S F_{6}$ . When we used values of $τ_{relax}$ from the acoustics literature, the augmented CFD underpredicted the flow for $S F_{6}$ by only 0.3%, in the worst case. The augmented predictions for $C O_{2}$ were within the scatter of previously published experimental data $(\pm 0.1 %)$ . As expected, both conventional and augmented CFD agree with experiments for He and $N_{2}$ . Thus, augmented CFD enables one to calibrate a small CFV with one gas (e.g., $N_{2}$ ) and to use these results as a flow standard with other gases (e.g., $C O_{2}$ ) for which reliable values of $τ_{relax}$ and the relaxing heat capacity are available.

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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

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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

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

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Figure 2

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

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

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Figure 3

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

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Johnson AN, Merkle CL, Moldover MR, Wright JD. Relaxation Effects in Small Critical Nozzles. ASME. J. Fluids Eng. 2005;128(1):170-176. doi:10.1115/1.2137346.

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