Modeling Component Curves with Abrupt Changes

When pump or component data is entered, PIPE-FLO generates a "best fit" equation to model the device. If the curve has abrupt changes in its slope, this method may result in an inaccurate model. To more accurately model these types of curves, the data can be adjusted to give a better fit over the operating range. Or, the data can be broken up into separate pumps or components in order to model the performance over more than one operating range.

In modeling pumps and components in PIPE-FLO, users occasionally run into a problem where the model does not accurately reproduce the curve data that it is based on. This usually occurs because the curve has abrupt changes in its slope. For example, a component curve may start out relatively flat and then become very steep.

Shown below is a set of data that a PIPE-FLO user had for his component:

Flow (lb/hr)  dP (psi)
00
300001
7500050
125000100
175000150

The following curve is obtained when this data is plotted by hand:


When this data is entered in PIPE-FLO 2009, the program uses a spline to come up with a "best fit" for the curve, which is shown below:

There are some readily apparent issues with the area around the abrupt change in slope. PIPE-FLO 12 no longer uses this approach for curve fit and consequently avoids problems like this one.

As can be seen in the above comparison, there is quite a bit of difference between the actual input data and the values produced by the equation.

A good way to model components such as these is to eliminate the abrupt changes in the curve by adding more data points around the area of the abrupt change. Making these adjustments can sometimes be a trial and error process. However, in PIPE-FLO's Pump and Component dialog boxes the data can be graphed as soon as it is entered, giving users instant feedback on their adjustments.

For this particular example, there are essentially two linear regions to the curve: Region 1 is from 0 to 30000 lb/hr and Region 2 is from 30000 to 175000 lb/hr. By specifying two additional points on each side of the 30000 lb/hr data point, the transition is focused in that area and the resulting curve gives a much more accurate model of the component. The additional data points can be found by linear interpolation between the known points.

Flow  Input dP
00
150000.5
280000.9333
290000.9667
300001
310002.028
320003.055
7500050
125000100
175000150


With this revised component model, the resultant curve is an acceptable fit for the original performance data.



The above example demonstrated how to adjust a component's data to get more accurate representation of the device in PIPE-FLO. This same methodology can be used when modeling a pump that has abrupt slope changes in its performance curve.