Solenoid Valve Selection: Don't Be Fooled by Flow Rate

Flow rate values might not mean what you think they do. Applying ISA's two-coefficient formula can help optimize selection.

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V

where:
Q is the flow rate in scfm
CV is the incompressible flow coefficient
PUP s the upstream pressure in psia
TUP is the upstream temperature in °F
SG is the specific gravity of the gas relative to air at standard conditions
Y is the expansion factor defined by:

with choked flow situations exclusive to compressible fluid flows, thereby eliminating some of the inaccuracies of the other, derived methods. Typical values of XT for solenoid valves can range from 0.25 to 0.5, the lower value applying to valves with more tortuous flow paths. While the type of flow path can provide an approximate value for XT, compressible flow testing is the best method to determine actual values.

 

where:
X is the non,"dimensional pressure drop
XT is the second flow coefficient
FK is the gas constant ration defined by FK = k / kAIR

This equation was developed from the widely used standards for major orifice flowmeters. It was later adopted by ISA for process control valve flow calculations. It can reliably predict the points at which a valve will choke. Its primary advantage is that it is designed specifically around the special circumstances of compressible fluid flows. It can, therefore, more accurately show how a solenoid valve will react at higher pressure drops.

Here is an example of a single valve in which compressible flow rate is calculated using, first, the average pressure method, then using the ISA two-coefficient equation.

Example Calculation (Given CV Determine Q)

CV=0.75 (Pavg method)
Pressure Drop=40 psig
Upstream Pressure=75 psia
Downstream Pressure=35 psia
Upstream Temperature=75F
Flow rate (Q)=34 scfm

CV=0.75 (ISA method)
Nondimensional Pressure Drop (X)=0.54
Flow rate (Q)=19 scfm
for XT=0.5 (-44% from 34 scfm)
Flow rate (Q)=9 scfm for XT=0.25 (-73% from 34 scfm)

Example Calculation (Given Q, Determine CV)

Flow Rate (Q)=34.4 scfm
Pressure Drop=40 psig
Upstream Pressure=75 psia
Downstream Pressure=35 psia
Upstream Temperature=75°F
Nondimensional Pressure Drop (X)=0.54
Flow Coefficient (CV)=0.64 for Upstream Pressure method
Flow Coefficient (CV)=0.75 for Average Pressure method
Flow Coefficient (CV)=0.94 for Downstream Pressure method
Flow Coefficient (CV)=2.29 for ISA Upstream Pressure method
with XT=0.25

Software and third-party testing: no panacea

Today, software alone is not simple or inexpensive enough to serve as the industry's answer. At the same time, while independent testing agencies such as UL or CSA may provide unimpeachable results, tests can cost thousands of dollars per product.

Computational fluid dynamics (CFD) software programs, used to determine flow rates, are becoming more precise with every new version. They give good results for incompressible flow and the programs do well at making predictions for flow behaviors; however, the difficulty in using them comes in establishing the correct models to use for comparing predictions with test data accurately.

In an ideal world, customers and manufacturers would know that the same flow rate measures are being used everywhere. Until that becomes a reality, ISA's two-coefficient equation can replace guesswork with certainty, providing a multi-dimensional view of a solenoid valve's compressible flow rate at a wide range of pressure drops.

Charles Bald has been a senior design engineer with Parker's Fluid Control Division for the past five years. His 15 years of industry experience include thermal and flow analysis of gas turbine jet engine components, centrifugal compressor designs and refrigeration systems for vacuum distillation. Richard Condon has held various posts for the past eight years, and currently specializes in valve actuation, mobile, fuel cell and industrial equipment for Parker's Fluid Control Division.

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