Valve Open Area Calc From Thottled Valve Cv

[lnghrns]

I have a liquid flow application with abrasive solids that is causing excessive piping wear downstream of a ceramic control valve which has a characterized V-Port ball. Velocity estimates in piping throughout system are below our maximum allowed for liquid with solids in this application. I want to know what the valve open area is at a given "throttled Cv" so that I can calculate the liquid exit velocity from valve. In other words, is there a way to calculation "valve area vs. valve %open" from the manufacturers "valve Cv vs. valve %open" data? Application info is as follows: 1.5" valve, Cv=16 full open, operates in manual at 50% which is a Cv of 3.4 and flow through valve is 11 gpm.

 

[hacksaw]

Cv is proportional to the open area and a disch coeff.

the problem with ball valves is that they are classified as high recovery valves. have you checked for cavitation?

 

[davefitz]

I am not sure what the open area will give you- it is only slightly related to the max velocity of the fluid leaving the valve. If you actually need the area, you would have to calculate it based on the valve vendor's detailed ( proprietary) drawing of the chracterized trim. The reason it is not a direct relationship is that the fluid streamlines are not simple- they are contorted.

For a throttled ball valve, I would estimate the pressure drop thru the contorted flow passage as about 3 times the max "velocity head", based on max velocity, so I would estimate the max velocity by calculating backwards from the known flow and pressure drop.
DP= psi
W= flow (lb/hr) A= min flow area
velocity head = VH= sv/12 *(W/a/E5)**2
sv= inlet specific volume, ft3/lb

so DP=3*VH
we know DP, W, sv, so we can calculate the min effective flow area and the the max velocity is V=W*sv/3600/a

 

[Scotsinst]

I agree with Hacksaw that your problem is likely cavitation. Most slurry valves are flow-to-close so as not to erode the valve body with corresponding high pressure recovery.
If the body or piping right at the valve outlet (do you have reducers?) erodes then use a larger body size with reduced trim. If it is the downstream piping that erodes, and only downstream of the valve, then it is likely cavitation.
You could put in a sacrificial sleeve downstream of the valve which would wear out instead of the pipe.
Most slurry guidelines are 10ft/s or 3 m/s. I assume you are below that.

 

[lnghrns]

hacksaw: I had not thought to do a cavitation check yet. I am dealing with a Fujikin Cosmix ceramic valve. The .pdf file for this valve does not list valve recovery coefficients. I am contacting them for the info.

davefitz: Thanks for the explanation and equations for estimating the flow area and velocity.

Scotsinst: Only piping immediately downstream of valve is wearing significantly. The valve port is already small compared to valve body but high velocity flow is localized on side of port opening. We also use the 10 ft/sec rule of thumb here for slurry flows. All line flows are below this value except for valve exit flows which is why I wanted to get an open area estimate.

Thanks to all for input!

 

[4carats]

Check Appendix A, Crane Technical Paper 410.
There are formulas relating Cv and Equivalents of Resistance Coefficient (i.e. Loss Coefficient) K for geometry of flow through a circular hole.

I call the above equation, eq.(2), i.e. Cv/area = f(K)

You started with a known Cv. I call this equation, eq.(1).

Equation (1) divided by equation (2) gives you the effective flow area, provided you know how to calculate the Loss Coefficient,K, of your flow area. [a triangular shape]

For V-port, I would consider it as a sudden expansion and therefore K inlet = 0.5, K outlet = 1.0, and therefore K total = 1.5 (maximum).

Hence Cv / (Cv/area) = [Cv] known / [38/sq.root(K)] = area, were K = 1.5 in this case. [My best approximation].

The area calculated is the effective flow area because it takes the loss coefficient of the geometry (obstacle or channel) into account.

Ref.1: Granger, Fluid Mechanics. [K for needle valves & gate valves]
Ref. 2: White, Fluid Mehanics. [K for butterfly valves].

I hope these help.