Digitization methods are critical when using pump selection software.
First of Two Parts
More than 150 pump manufacturers present their pump performance data electronically. These digital pump catalogs can be found online, within stand-alone pump selection software and through select hydraulic analysis software packages. Thousands of engineers worldwide use these catalogs to evaluate and select the pumps that best meet their needs.Based on experience in digitizing more than 135,000 pump curves for manufacturers throughout the industry, Part One outlines how digital pump curves are created, as well as some of the accuracy issues that may arise from the methods of curve digitization. It covers pump performance curves and the accuracy ramifications from different digitization methods. As the industry moves toward electronic pump catalogs, end users should know how accurate they are and how they are generated.
Pump Selection Programs
The main function of a pump selection program is the ability to digitally reproduce the manufacturer's pump performance data accurately and to create a selection list of pumps that meet the customer's criteria. All pump manufacturers have “paper curves” representing the performance of their pumps, and most also have these curves available in pdf format. These curves reproduce the manufacturers' bench test data and are the most accurate depictions of the pumps' performance.
However, for a software program to understand and use this pump performance data, the data must first be converted into a form that can be read by the program. This is referred to as the digitization of the pump curves. There are various methods of digitizing pump performance data, but occasionally, depending on the method used, some vital information can get lost in the translation. The accuracy of this translation can be critical to the pump selection and evaluation process.
To better understand the performance of the digitized curves, consider an example of a typical published pump curve from a manufacturer. Figure 1 shows a detailed curve that includes the flow versus head performance curves as well as isometric curves for efficiency, power and net positive suction head required (NPSH). These curves accurately represent the test performance of the indicated pump in accordance with the ANSI/HI 1.6-2000 Centrifugal Pump Tests standard.
Figure 1. A manufacturer's published curve
If a pump were required for a system with design conditions of 800 U.S. gallons per minute and 35 feet of head and this particular pump were being evaluated, the system designer could feel confident that this pump, with a 10-inch impeller, would successfully fit the bill. The pump selection and evaluation software must accurately reproduce the manufacturer's published pump curve to aid the customer's evaluation of the pump for the application. The key to generating accurate digital curves is the method with which the pump performance data is saved and displayed.
All forms of pump curve digitization involve obtaining data points from the pump manufacturers. These points can either be extracted from the published paper curves or gathered directly from the manufacturers.
One simple method is to take several points along the performance curve and perform a polynomial regression analysis. This results in a polynomial expression describing the performance curve, which can be saved and used in a pump selection program.
The original data points are then discarded, and the pump performance data is now represented solely by a curve drawn from that equation. Depending on the shape of the original published curve, this polynomial expression may or may not be an accurate representation.
A second, more accurate method is to collect as many data points as necessary to accurately fit the shape of the published performance curve and use these saved data points to represent the original published curve in the pump selection program. Storing the original data points is an integral step in maintaining the pump curve's accuracy, and interpolation between those data points is the most accurate method of properly sizing a pump.
When it comes to displaying the pump curve in the software, a simple polynomial regression curve can have a tendency to miss the original pump curve at critical points. On the other hand, if a more robust numerical analysis is performed, such as a cubic spline regression, then a curve can be drawn that precisely represents the original published curve.
Polynomial Regression
A closer look at some actual pump curve data illustrates the problems associated with the simple polynomial regression method of curve digitization. Figure 2 depicts flow versus head performance curves, which are the primary search parameters for sizing a pump. The black curves are the actual tested performance curves provided by a pump manufacturer. Overlaid in pink are the performance curves generated by a pump selection tool using a simple polynomial regression. The inset is a close-up view of the anomalies in this case study.
Notice that pump performance curves with anomalies, such as inflection points, are not well represented by the polynomial regression. The polynomial regression has a tendency to smooth out the anomalies such as those shown in Figure 2. The consequences of this curve characterization can be minor, or they can be significant. In this case, if an end user were sizing for a design point of 300 U.S. gallons per minute, at a total head of 126 feet, then this pump might not even be considered for evaluation.
Figure 2. Performance curves with polynomial regression curves
A more detrimental scenario could occur if the polynomial regression curve rose significantly above the actual curve. In this case, the program may suggest a viable pump that might not meet the design point criteria. In addition, if the pump performs in areas where the polynomial regression curve deviates from the manufacturer's published performance curve, an end user will get erroneous energy usage figures and operating costs.
Cubic Spline Regression
Figure 3 depicts the same manufacturer's performance curves in black. The green, overlaid curves are generated by a pump selection tool that uses a cubic spline regression analysis. This method forces the curves to pass through every collected data point. It then smooths the curves from point to point to provide clean, accurate pump performance curve displays. Flow and head are never significantly overstated or understated at any point in the curve range. End users can use these displays with confidence when performing pump evaluations.
Figure 3a. Performance curves with cubic spline regression curves
Even the best numerical analysis techniques cannot predict anomalies between data points. If the performance curve to be digitized has these types of dips or abnormalities, it is imperative that enough data points are collected in and around that range. At a minimum, data points should be collected at the edges and at the peak (or valley) of the anomaly. Ideally, a couple more points should be collected between them. This allows the selection tool to display the most accurate representation of the original performance data and for the evaluation and selection process to proceed without any false selections.
In the January 2012 issue, Part Two will cover the methods of collecting pump efficiency and power data and displaying isometric curves for each.
Pumps & Systems, December 2011