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calculation of compressible flow through orifice plates at high dP (critical flow) appears
to be carried out incorrectly in most instances. This flow condition is often encountered Orifice
flow calculations typically use the following equations or some variant of them;
For
metering applications the ASME equation is often used to determine the Expansion Factor Y;
It is
then often assumed that the orifice flow goes critical (i.e. sonic velocity) at P2 =
0.528 x P1 (for air) and the choked flow equation is then applied;
For P2
less than Pcr this method assumes that the flow does not increase further. Experiments
carried out by RG Cunningham and published by ASME in July 1951 clearly demonstrated that
the assumption of a fixed limit to critical flow through thin square edged orifice plates
is not correct. The flow continued to increase as P2 was reduced below the
expected critical condition. Limiting flow was not evident even with P2 as low
as 0.1 x P1. Cunningham’s
work included tests with air and steam with the results and conclusions presented as
tables, charts and formulas. Limited information is provided for the tests with steam. The
results demonstrated that with suitable corrections to the Expansion Factor Y, the
formula for non-critical flow should be used in all cases for thin square edge orifice
plates. Critical flow can, however, be expected for thick orifice plates with t Cunningham’s paper also includes an equation for the Flow Coefficient,  , though
this appears to provide only a rough approximation and other methods may be preferable
(e.g. AGA 3).The ASME formula for Y was shown to be appropriate only down to P2 = 0.63 x P1; (not the normally expected 0.528 from thermodynamic analysis) at which point there is a distinct discontinuity in the flow to lower discharge pressures. Continued use of the ASME formula for Y produces errors of up to 12% if used for lower discharge pressures. Alternative methods reviewed involved errors of up to 40%. Analysis of the Cunningham data suggests the following formula may be used to
determine Y for flange taps at discharge pressures below 0.63 x P1;
The use
of a formula similar to the form of the ASME equation is based on an expectation that
there is a reasonable probability that the flow to lower pressures will be similarly
sensitive to the same geometric and process parameters. The use of ß (beta) to
the 4th power provides a reasonable fit to the experimental data. Since the
relationship between Y and the pressure ratio is linear the (0.63-P2/P1)
component is clearly appropriate. The inclusion of k as a direct divisor in the equation
is less obvious and difficult to confirm from the limited data available. The chart
first chart below is extracted directly from the Cunningham report and clearly shows the
discontinuity at a pressure ratio of 0.63 and the potential for error if the ASME formula
is used beyond this point. The chart second chart below is generated using the proposed
method.
The
information on the following page demonstrates the derivation of the proposed formula from
the published Cunningham experimental results. Plots on the last page show a comparison of
some alternative calculation methods. These indicated a good match of the proposed method
to that of Perry and another derived from the Grace-Lapple tests, but only for Beta ratios
less than 0.6 where significant discontinuities appear with these alternative methods. For additional charts and graph details, see this Adobe Acrobat Document. References: Technical Paper 410M, Crane, 1983 Issued:
By: Dennis
Kirk-Burnnand |
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