With all of these potential issues, calculating compressible fluid flow rates for solenoid valves can be tricky. Compounding the confusion is the fact that there are multiple methods by which calculations can be made.
Downstream pressure: This method is used by the National Fire Protection Association for pneumatic directional control valves. This equation approximates flow through an ideal nozzle. In the valve industry, it often is used to calculate CV for pneumatic directional control valves. However, it can overestimate the choked flow,"the point where decreases in valve outlet pressure cannot cause flow to increase, as commonly seen in ball, butterfly and solenoid valves.
Today, a few methods can be used to calculate compressible fluid flow rate values for solenoid valves:
Average pressure: The mean density equation is derived directly from equations for fluid flow through valves, and, because of its simplicity, is widely used in industry. However, because of the differences between gas and fluid (compressible and incompressible) flows, this equation can significantly overestimate flow for most valve styles, especially at high pressure drops.
Upstream pressure: This equation, like the others, is derived from an equation used for liquid flow. It, therefore, cannot be relied upon to work with choked flow situations. Again, it will overestimate flow for most valve types, especially at high pressure drops, and fail to predict choking.
So, what's the problem?
So, why isn't there a single standard? Solenoid valves are used across a large variety of industries, whose end users are concerned about vastly different things.
These equations are all used extensively by respected organizations and industrial governing bodies. There is nothing inherently wrong about any of them. However, dealing with the specific circumstances of compressible fluid flows and solenoid valves, these equations can provide only a non-dimensional view of flow rate.
However, it is clear that derivations of standard equations for incompressible fluid flow cannot reliably be applied to compressible fluid flows. The unpredictable nature of gases and their density changes means these equations can give inaccurate CV values at high pressure drops. Using these equations where they are best suited, at low pressure drops, gives a more precise, if one-dimensional, view of the valve's capabilities, not ideal for a prospective buyer.
There are other considerations as well. For customers in the chemical processing industries, the CV measurement is typically a benchmark for solenoid valve purchasing. Often, customers familiar with their applications know an approximate CV value needed for a new valve. However, they might be relying on an inaccurate number calculated using any one of the previously discussed methods. A manufacturer should, in this case, work backward with the customer and ask how this estimated CV was determined. If this is the case, the application usually needs to be analyzed again to determine the proper CV so that the manufacturer can apply the correct model valve.
Testing to verify flow rate is always a good idea, especially in chemical processing applications. When a solenoid valve is being used for actuation, the wrong CV can result in vibration or other anomalies in the system. In other cases, a valve may actuate a larger valve irregularly, causing the larger process or control valve to drop too quickly, slowly or forcefully.
Finally, consider the issues that arise for a potential end user trying to choose a new solenoid valve. These equations' non-dimensional views of valves' capabilities can result in incorrect information. Manufacturers can test a valve at a given pressure drop to determine the flow rate at a variety of data points, then plug these into any one of the above-mentioned empirical equations of their choosing to determine a coefficient. This coefficient may not describe the valve in a multi-dimensional way. Take the same valve and calculate different coefficients using the different methods and you could get different, less flattering CV values. A lot of calculations are averaged. It even is possible to rerun tests and calculations until the most favorable numbers are gleaned. Figure 2 demonstrates how even valves with the same nominal CV values might actually prove to have very different flow rates. The valves were made by different manufacturers, noted in the graphs by MFR X and MFR Y.
Figure 2. Big Differences For 0.75Cv Solenoids
Plotted above are flow rate and compressible flow coefficients vs. pressure drop for various valves at 0.75Cv. The valves were made by different manufacturers (designated here as MFR X and Y).
The argument for ISA's two-coefficient equation
The equation is as follows:
ISA developed an equation for determining flow rate that includes a second flow coefficient, XT. This second coefficient is developed specifically to correlate C
Q is the flow rate in scfm
CV is the incompressible flow coefficient
PUP s the upstream pressure in psia