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Is This Valve Choked?

Under sub-sonic gas flow conditions, loss models can use the familiar K, Cv or resistance curve methods. At choked flow, however, the dynamics of compressible flow require a different method to characterize the loss, which AFT Arrow users will see as the optional 'CdA' input value on the valve and other junctions specifications window. The product of coefficient of discharge and effective flow area under choked conditions, AFT Arrow can directly calculate the CdA for some cases, such as at the discharge from a pipe. For other components, such as valves, determining these values is most commonly done through flow testing. Indeed, it is the product of Cd and area that is directly available from test results rather than the individual value of each, hence the term CdA. When a CdA value is included in the valve specifications window, AFT Arrow can determine if choked flow exists at the valve and, if so, calculate the choked flow through the valve.

So where do you obtain the CdA for a valve in your gas piping system? Most likely from the manufacturer. Unfortunately this data is not always available. AFT Arrow's output for junctions includes the 'Sonic Area', the CdA value at the junction that would result in choked flow, and in conjunction with the pipe flow area, can be used to make a reasonable judgement as to whether a valve may choked. ('Sonic Area' and 'Flow Area' may be selected to include in the output from the Junction and Pipe tabs of Output Control.)

Let's take an example of a globe valve with a sonic area of 0.5 in2 mounted in a 1-1/2", sch 80 pipe with a flow area of 1.767 in2. From specific data or experience, we know this valve's physical flow area is approximately 80% of the connected pipe. For CdA to equal the sonic are of 0.5 in2, Cd would have to be ~0.35 (0.5 / (1.767 in2 x 0.8). This is a very low value and we could safely conclude the valve will not be choked and we can model its loss using a K, Cv or resistance curve. On the other hand, if sonic area were, say, 1 in2, this would equate to a Cd of about 0.7. Given that an orifice has a high Reynolds number Cd in the range of 0.6, we would not reasonably expect the more convoluted flow path through our globe valve to have such a high Cd and would conclude flow is going to be choked through this valve. While we haven't determined the choked flow conditions through the valve, but we can conclude that we need to use a larger valve or a different type of valve to avoid choked flow at this location, and this is usually our goal in selecting isolation or stop valves for gas piping systems.

This example has focused on valves but is equally applicable to a wide range of piping system components.

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