Control Valve

2%, 3%,...,100%. Good grief, what else?

Any % change in the opening from its current existing value changes the flow by same percentage of its current value at current opening.'

Means if current opening is say 10% & u change it to 15% than the change in opening from its current value (of 10%) is 50%, so the flow will also increase by 50% of its existing value at 10% opening. This means if flow was say 20% of the total range (Or capacity of the valve) at 10% opening it will become 30% (50% higher compared to 20%) of the total range.

The only way to really know the flow vs. stem position function for any valve is to first know how its Cv (flow coefficient) changes with stem position, then plot the intersection of the valve's flow/pressure curves for different stem positions against the pressure function of the entire piping system which includes piping friction losses and pump curve.

Check with the manufacturer for the Cv vs. stem position function. Fisher happens to publish Cv/opening tables for their valves, for all trim characteristics. Here is a set of opening curves plotted based on some data obtained from Fisher manuals (assuming Cv=50 for full-open):

As you can see, the "linear" valve is not exactly linear as textbooks might have you believe. I have yet to encounter an equation that fits well with the plots of any real control valve data; whether the characteristic be linear, quick-opening, or equal-percentage.

The next graph shows how a perfectly linear valve (with a max. Cv=18) would behave when installed in a piping system where the available pressure drop to the valve is shown as the "load line":

The term "load line" is no accident: plotting the intersection of nonlinear functions to determine real-world behavior is precisely the same principle behind load-line plots for transistor amplifier circuits: determining voltage drop and current for transistors in various "throttling" states given reductions in available voltage as current increases. In either case, the throttling component (e.g. transistor, valve) "runs out of steam" as flow rate (e.g. current, fluid flow) increases.

The idea of an equal-percentage valve is that it opens slowly at first, then more aggressively at higher stem positions, to help cancel out this natural effect. Equal percentage valves generally give the most linear response given a piping system where the pressure drop available to the valve diminishes as flow increases. However, your mileage can and WILL vary according to the valve manufacturer's peculiar characteristics and the peculiar characteristics of your piping system.

*** In other words, there is no easy answer to your question ***

If you absolutely must have linear valve response, install a flowmeter in the line and use a cascade control strategy, where flow control is the slave loop receiving a remote setpoint signal from your other loop controller.