# Converting a Non-Linear Valve Installed Flow Characteristic to a Linear Flow vs. Controller Output

Submitted by Jon Monsen
In Jon Monsen's book, Control Valve Application Technology (published and distributed by Valin Corporation), Jon explains how to properly size and select a control valve. Jon recently received inquiries from customers interested in a further explanation of one of the graphs featured in his book. This article will cover that explanation.

Figure 2-12 in the book (reproduced below with some explanatory additions in red and green), shows how a non-linear valve installed flow characteristic (dashed line) can be converted to a linear flow vs. controller output by programming a modification (upper graph) into either a digital positioner’s input block or a DCS output block. There really isn’t a simple way of adding or subtracting points on the installed flow characteristic to explain how the modification works. Hopefully the following will clarify how the modification graph is constructed: I will do this by randomly choosing two controller output values on the horizontal axis, a controller output (and therefore a uncorrected valve position) of 45% and of 60%.

When the controller output (and the valve position) is 45% the flow at Point 1 will be 10% of the fully open flow. If it is desired for the system to have a linear relationship between controller output and flow (the heavy line on the graph “Desired Flow vs. Controller Output” when the controller output is 45% the valve must be positioned, not at 45% but at a point where the flow will be 45% of the fully open flow. Following the dashed installed flow curve to Point 2 on the installed flow curve where the flow will be the desired 45% the valve will need to be 81% open. So at this point the modification must convert the controller’s 45% output to 81%, Point 3 on the modification graph.

Looking at a second point, where the controller output is 60%, Point 4 on the installed flow graph would put the flow at 20%, not the desired 60%. Following 60% flow to Point 5 on the installed flow graph tells us that to get 60% flow, the valve needs to be at 88% open. So at this point the modification must convert the controller’s 60% output to 88%, Point 6 on the modification graph.

If we were to repeat this process, say, for a total of ten evenly spaced controller outputs  we would get the modification (lower graph) in the figure.

If you have a graph of a valve’s installed flow characteristic such as the left hand graph in Figure A (which can be obtained from Metso’s Nelprof® valve sizing software) you can easily create the required modification needed to linearize flow vs. controller output. Alternately, if you have a system with little pipe or other pressure consuming elements, but need to use a valve with an equal percentage inherent flow characteristic that you would like to modify to have a linear installed characteristic, simply graph the valve’s Cv  curve with its Cv points on a relative scale of 0 (zero) to 1, where each point on the Cv axis is that points Cv divided by the Cv at 100% travel.

Note that in Figure 2-12 in my book, the installed flow characteristic is an approximately equal percentage characteristic, and in the left hand graph of Figure A the installed flow characteristic is quick opening.

All you have to do is re-label the axes of the installed characteristic graph (shown here at the left side of Figure A). (1) Change the “Flow” or “Q” axis to be the “Input” (that is the input to the modification algorithm. (2) Change the “Valve Travel” or “h” axis to be the “Output” (that is the output of the modification algorithm).

The graphs at the center and right of the figure are not necessary, but are shown here just to put the graph in conventional format, with the input, or independent variable, on the horizontal axis and the output, or dependent variable, on the vertical axis and the origin an the lower left. ##### A lesson for me is that I need to involve you earlier in the program.

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