Kd gas vs liquid

[CJKruger]

For flow and restriction orifices and nozzles, the Kd values are the same for liquids and gases.

Question: Why is there then such a big difference in Kd values for relief valves between gases (0.975) and liquids (0.62) ?

 

[JAlton]

In a word, "Compressibility". "Compressible" gases versus "incompressible" liquids. Expansion of gas during the lift of a pressure relief valve generates a reaction force to overcome spring tension and attain sufficient lift to permit full flow through the orifice relatively soon after opening, as compared to incompressible liquids which do not generate significant lift due to lack of reaction force. Typical Safety-Relief Valves in gas service will go to approx. 70% of full lift on initial "pop". Whereas, liquid service PRVs do not typically reach full lift until approx. 110% above set pressure.

JAC

 

[CJKruger]

JAlton, I thought the equations are all based on a full open relief valve at 110% of set. So, why would the partially open characteristics make any difference ?

 

[sheiko]

The values of discharge coefficients for gases are different from those of liquids because the gas coefficients are measured under choked flow for which nozzle is the flow controlling element in the valve, and is well represented by the isentropic nozzle flow model, but the liquid coefficients are determined under un-choked conditions reflecting the influence of the entire valve (nozzle and the body) on the flow which is not accounted by the isentropic nozzle model.

"We don't believe things because they are true, things are true because we believe them."

 

[JAlton]

The difference is primarily related to how the coefficients are determined, particularly the calculation of theoretical mass flow rate. The coefficients are the ratio of the measured actual mass flowrate / calculated theoretical mass flowrate. For sonic compressible (vapor) valves, the mass flowrate through the valve is solely dependent on the choked flow in the nozzle. The mass flow rate in this condition is dependent on inlet stagnation temperature and pressure and the nozzle throat bore area - downstream pressure has no effect on the flow rate. For liquid valves, the mass flow rate through the nozzle bore is a function of the square root of differential pressure across the nozzle (inlet minus discharge pressure). Since downstream pressure affects the flow rate, the effects of body bowl geometry fluid dynamics between the end of the nozzle and the exit of the body play a role in the actual measured capacity that cannot be easily captured in the theoretical mass flow calculation. Therefore, these effects reduce the measured capacity and when divided by the theoretical calculation that omits them, resulting in a lower coefficient of discharge.

Body bowl flow dynamics for sonic vapor valves have no effect on mass flow through the nozzle unless the downstream pressure exceeds the critical flow pressure and flow goes subsonic. At that point, body effects start to come into play and you'll notice that the coefficients for sub-sonic vapor valves start dropping to the liquid valve coefficient levels.



JAC

 

[CJKruger]

sheiko + JAlton, thanks for a very nice explanation.