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Research Papers: Fundamental Issues and Canonical Flows

# Comparison Between Theoretical CFV Flow Models and NIST’s Primary Flow Data in the Laminar, Turbulent, and Transition Flow Regimes

[+] Author and Article Information
Aaron Johnson

National Institute of Standards and Technology (NIST), 100 Bureau Drive, Mail Stop 8361, Gaithersburg, MD 20899aaron.johnson@nist.gov

John Wright

National Institute of Standards and Technology (NIST), 100 Bureau Drive, Mail Stop 8361, Gaithersburg, MD 20899

Unless otherwise noted, all volumetric flows in this paper are taken to be at standard conditions with a temperature at $293.15K$ and a pressure of $101.325kPa$.

In small CFVs, the mass flow could exhibit some dependence on $Pb$ attributed to pressure disturbances propagating upstream via the subsonic boundary layer.

Here, we assume that the discharge coefficient is calculated using the actual CFV throat diameter and that the mass flow is not affected by nontraditional mechanisms such as vibrational relaxation phenomena observed for $CO2$ and $SF6$ in geometrically small CFVs (26-27).

The first order terms of the models of Tang and Geropp are identical if the viscosity in Tang’s model is taken proportional to temperature, and the ideal gas isentropic relationships are used to relate the throat temperature to the stagnation temperature.

Since the theoretical models are corrections for the base line model, from which the ideal discharge coefficient is defined, these models describe $Cdi$ and not$Cdr$.

Errors associated with virial effects only apply when CFV calibrations performed using one gas are applied to a different gas.

The discharge coefficient for Curve A (i.e., accurately machined CFVs) is $CdA=0.9985–3.412Re−0.5$, while for Curve B (i.e., normally manufactured CFVs) is $CdB=0.9959–2.720Re−0.5$. Note that the Reynolds numbers in these expressions are based on the actual mass flow and not on the base line mass flow as previously defined in Eq. 5.

J. Fluids Eng 130(7), 071202 (Jul 22, 2008) (11 pages) doi:10.1115/1.2903806 History: Received August 16, 2006; Revised May 18, 2007; Published July 22, 2008

## Abstract

State-of-the art dimensional metrology was used to measure the throat diameter and throat curvature of nine critical flow venturis (CFVs) with nominal throat diameters ranging from $5mmto25mm$. The throat curvature was used in calculating the theoretical discharge coefficients, while the throat diameter was used in computing the experimental discharge coefficients. The nine CFVs were calibrated in dry air using two NIST primary flow standards with expanded uncertainties of 0.05% and 0.09%, respectively. The calibration data span a Reynolds number range from $7.2×104$ to $2.5×106$, including laminar, transition, and turbulent flow regimes. By correcting for both the throat diameter and curvature, the agreement between predicted and measured discharge coefficients was less than 0.17% in the turbulent regime and less than 0.07% in the laminar regime.

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## Figures

Figure 1

Percent difference between theoretical models and experimental data for nine normally manufactured CFVs

Figure 2

Moore M48 CMM (the left picture shows a full view of CMM while the right one shows a close-up of probe and CFV just prior to dimensional calibration)

Figure 3

Degree of roundness (in microns) for CFVs at five axial positions traversing the throat cross section (positive axial values correspond to positions upstream of the throat while negative values correspond to positions downstream of the throat)

Figure 4

Near throat CFV profiles (the shaded region indicates the ISO recommended values of the throat curvature ratio)

Figure 5

Axisymmetric cut of a toroidal shaped CFV with dimension specifications of the ISO 9300 standard (2)

Figure 6

Comparison of three models of the inviscid discharge coefficient

Figure 7

Measured discharge coefficient of CFVs 8 (left) and CFV 9 (right) versus predicted Cd values calculated using their measured Ω’s and an assumed value equal to ΩISO=0.25

Figure 8

Measured discharge coefficient of CFVs 1–7 compared to the piecewise theoretical model spanning the laminar, transition, and turbulent flow regimes (curves labeled A and B are the values of the discharge coefficient recommended by the IS0 9300 standard for accurately and normally machined CFVs (2))

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