Valve capacity calculation based on compressible flow

[andrewgrace2]

All,
I have a simple question regarding gas flow rate through a valve. How do you calculate it??

To be more precise I am aware of the governing ISA equations for compressible flow through valves etc but I need to dervive this expression from first principles. I have reviewed the liquid eqn and note that bernoullis equation is the basis for the ISA eqn. But for gas flow where do I start??? Based on a pressure drop across the valve, I know that the flow rate will increase until choked flow is reached and I know at what point that will occur- I can figure out where specific gravity affects the flow- but where can I add in compressbility etc..

I need to generate this eqn for first principles in order to write on independant calculator for multi-phase flow through a valve and then I want to compare my calculator to an ISA calculator.

Any and all help would be very greatly appreciated. Thank you.

 

[davefitz]

Most valves will begine to "choke" before the theoretical liit , becasue their internals are not sufficiently streamlined so as to generoate only one chock wave. The multiple shock waves that arae formed can occur at a bulk mach number below 1.0 , and they are titled" oblique shockwaves". I suppose a test on compressible flow will provide a relationship between flow, pressure drop, area, and geometry that will be siialr to the ISA compressible flow relatiionship.

 

[andrewgrace2]

Right...I am familiar with that, and from my understanding the ISA eqns for gas flow are based on bernoullis eqn but with some correction factors- i.e. the standard assumes the flow is incompressible to a certain limit and then applies correction factors to this eqn to gernerate the comprressible flow eqn from the limit onwards (which is probably about .3 Mach)- my question is where do these corection factors come from.

At this point I am really looking for a "first principles" approach- as in testing was completed, reference document blah blah blah....thanks for all your help

 

[JimCasey]

I can send you a (pdf) copy of the Durco Instrument Engineer's handbook with all the sizing equations. Various coefficients like Cv depend on valve size and geometry, otherl like Fl are more strongly linked to geometry. The equations are known; the coefficients are determined by testing.

 

[vzeos]

andrewgrace2,

I would suggest getting a copy of Fisher Controls Technical Monograph 15 – Development of a Universal Gas Sizing Equation for Control Valves. Although it is not specifically about the ISA equation, it will give some insight into equation development. It is not listed on the Fisher Regulators website; you may need to contact your area representative.

 

[andrewgrace2]

Again,
thank you all and indeed I have all the fisher monographes (they are particularly intesting). But what I am really looking for is the basics of how the math was generated- this is not as you would have guessed an industrial problem but rather one of academics at the moment. Most of the formulas I can find are either refined for industry or only have a brief outline of where they come from.

I am of the understandong that Leslie R Driskill wrote an interesting paper in 1983 about the topic but i haven't been able to track this down. Either way it discusses the fundamental formulas that he used to generate the formulas and has he altered these with experimental data and it was this paper that formed the basis of the ISA governing equations.

I have dervived the liquid eqns from first principles (a simple problem using bernoullis eqn) however now I need to generate the compressible eqn and I'm not sure where the dervation starts???? Does anyone know?