Sizing Needle Valves for Air Flow | 0.025 m^3/s

[Kimusubi]

I am trying to size a needle valve to make sure that it can allow the required flow rate at the fully open position (0.025 m^3/s). For a given Cv you should be able to calculate the maximum flow rate through the needle valve provided that you know the temperature of the gas and the pressure drop across the valve, but my problem is that I do not know what the outlet pressure of the needle valve is going to be ahead of time. Wouldn't P2 (outlet pressure) be dependent upon the needle valve itself? I seem to be confused on this point which is preventing me to get the correct size for the valve.

The flow conditions are:

Medium: Air
Upstream Pressure: 2 atm
Maximum flow rate required: 0.025 m^3/s
T = 300 K


Any help would be highly appreciated.

 

[SteamKing]

0.025 m^3/s is 25 liters per second. Even assuming air as the fluid, that's some needle valve.

http://en.wikipedia.org/wiki/Needle_valve

Needle valves are used for relatively low flow rates.

When flowing air through a needle valve, you will also need to be aware that choked flow may develop, which will limit the maximum flow rate thru the valve. You are going to need to know the pressure drop characteristics of the valve in order to determine what the outlet pressure is.

 

[Kimusubi]

Yeah, it seems to be that way. I chose a needle valve for its ability to finely adjust the flow rate. Do you know why the manufacturers only give the Cv and not the DP across the valve? If you need to know about the pressure drop across the valve in order to calculate the volumetric flow rate, then what good is it to only have the Cv (flow coefficient) value? Or is there something else that I am missing?

 

[Travis_King]

Cv is the DP across the valve. Cv = Q * Sqrt(SG / DP). However, because the pressure loss depends on the flow, it's impossible to say "this valve has a loss of X psi" as that value changes with the flow conditions. The valve has a specific geometry, and they have tested that valve in a multitude of conditions in order to come up with its Cv value for various open/closed positions. Instead of saying "You'll see a pressure drop of X psi in water with a flow rate of Y when the needle is in Z position" they can just say, "The Cv is 50 in that position" and that tells you, the piping engineer/designer/guy everything you need to know to work your calculations for your specific pipe geometry.

Calculating things like this isn't always straight forward, sometimes you have to use iterative processes. Control valves typically require iteration (or that you select a valve based on a desired Cv). If you know the discharge conditions (atmosphere, pressure vessel, etc) and the inlet conditions, and you know the geometry of the piping, then you can work your way through the calculations to try to hone in on the effect of the valve on flow.

 

[Travis_King]

edit, sorry I thought this was water.

 

[Kimusubi]

Well, I figured there would be charts/plots that would give the dP for various incoming flow velocities and pressures. I did find some relations in regards to the pressure loss based on the Cv (from the Handbook of Valve Selection). I am not sure on how accurate it is, but it states that

dP = z*0.5*rho*V^2 (where z is resistance coefficient)
z = (899*d^4)/Cv^2 (where d is the orifice diameter in inches)

When running this for a Cv = 1.31, D = 3.12", and V = 15.51 m/s, I get a total head loss of only 0.1044 psi. Given the following equation (for gases):

Q = (Cv*1360*(dp*P2)^0.5)/sqrt(SG*T) (where P2 = P1 - dP, SG = specific gravity, and T is temperature in Rankine)

I only get a 127 SCFH which comes down to almost nothing when corrected for pressure and temperature (~ 1 ft^3/min). This corresponds to 0.0005003 m^3/s, which when taking into account the 0.312" diameter, means that the valve allows only 10.14 m/s velocity through. Is there really a 5 m/s flow loss across the valve? That seems extremely unreasonable.