CENTRIFUGAL PUMPS: IMPELLER REVERSE DESIGN

by M. L. Tartavel, P.Eng & S. Benzimra, P.Eng

OVERVIEW

Contents:

Introduction

Input Data

Preliminary Evaluation

Shroud modeling

Point to Point calculations

Other Controls

Introduction

There is a growing interest in the fabrication of large size impellersat minimum cost. In the past few years, users came to realize thatpump manufacturers offer replacement spare parts at exorbitantprices. We responded to this increased demand by developing our ownsoftware to provide users with efficient impellers at a fraction of thecost.

Although most applications revolve around large water pumpingfacilities, our services extend practically to all centrifugal pumps,regardless of size.

The following is a brief description of the detailed engineering workto be carried out on a case by case basis.

Input Data

The user provides the pump's performance curve showing flow, head, efficiency and NPSH (Net PositiveSuction Head), as received from the pump manufacturer. In some instances the pump's test curve will berequired to confirm the actual position of the BEP (Best Efficiency Point) and the design Ns (SpecificSpeed, dimensionless) as precisely as possible.

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In order to appreciate some of the most critical impeller characteristics, a series of non-destructivemeasurements shall be performed on the impeller, at the Client's expense. We could provide anyassistance, as required.

For a detailed list of data required, click here.

Preliminary Evaluation

Based on Bernouilli's and Euler's equation, acomprehensive computer program was developedto simulate the design parameters used in theconstruction of the original impeller, at thepump's rated conditions. This reverseengineering procedure closely follows thetheoretical and practical findings of a number ofleading authors in the field, most particularlyAlexey J. Stepanoff, whose seminal workconstitutes the basis of pump design to this day.

Since all pumps are actually designed for onesingle operating point (BEP), it is of paramountimportance to identify this point with the greatestaccuracy. It is generally difficult to pinpoint thesespecific conditions, by looking graphically at theperformance curve, especially when the curve issignificantly steep.

A small error in the selection of this critical pointwould lead to a substantial deviation in theangular profile of the blade. A regressionanalysis, based on about a dozen points from thecurve leads to a polynomial expression of highorder on which several mathematical operationscan be performed with the desired accuracy.

The accurate positioning of the tangent to theBEP enables the drawing of the discharge vanetriangle (Euler's triangle), thus setting the outletangle of the blade in relation to the impeller rim.

Similarly, the inlet vane angle is first approximated on the basis of the appropriate range of impelling

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ratios, compatible with the type of pump considered. This value is later adjusted separately for both thefront and back shroud vanes.

Shroud modeling

Whereas the inlet and discharge angles are physical characteristics of the impeller in its three dimensionalreality, the pattern maker, at fabrication time, can only use the corresponding projected values on ahorizontal plane, normal to the pump shaft.

For strictly radial pumps with very low Ns, where both shrouds are essentially normal to the shaft, theactual angular values are obviously equal to the projected values. However, in practically all casesinvolving large pumps, the shape of the impeller shrouds depart significantly from straight vertical lines,especially around the inlet area.

Therefore, a considerable difference exists between theactual angular values and their projected counterparts.These differences vary point to point along the length ofthe vanes, as a function of the geometric curvature ofthe shrouds.

It is then necessary to mathematically simulate thecurvature of both shrouds, from the eye of the impeller tothe point of discharge. We found that an exponentialtype equation provides the best fit for the shrouds'geometry.

In fact, two different equations are used for each shroud(lower and upper sides), because at some point towardsthe discharge, there is generally a sharp departure fromthe original curve into an almost linear pattern. This isparticularly so for radial pumps with a Ns lower than3000. But even in the case of essentially linear shrouds,an exponential fit is in order, to properly appreciate theinlet area.

The coefficients of these equations are determined by calculus, to ensure a common tangent at thetransition point.

Point to Point Calculations

The impeller is then divided into 360° and, foreach shroud, the actual and projected position ofthe vane are determined trigonometrically, on

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polar angle increments of one degree. Alogarithmic equation correlates the radius to thepolar angle, at each point, as a function of thehydraulic blade angle, thus ensuring a smoothvariation of the blade angle throughout.

Past experience suggests that hydraulic angleincrements are generally proportional to radiusincrements. However, we may test differentconfigurations, if need arises.

These results are then plotted in polar coordinates, for the use of the pattern maker, as shown above.

It is interesting to note that, on very curved front shrouds, where the inlet portion is almost tangent to thepump's axis for a significant length, the projected vane angle becomes almost zero (tangent to the hub),regardless of the actual physical angle of the blade. This effect is not observed on the back shroud becausethe inlet angle of the blade is significantly higher, and the slope of the inlet portion of the back shroud isconsiderably steeper.

Other Controls

The results obtained are cross-checked against a number of evaluations to ensure the replication of theoriginal pump characteristics, as developed by the pump designer.

In that regard, we calculate and plot at least one so called mid-streamline, an imaginary vane locatedbetween the front and back shroud vanes, which represents the hydraulic locus separating the channel intoequal flows.

The determination of this line, carried out as accurately as the front and back vanes, permits to adjust theinlet vane angle, to ensure the smoothest flow pattern possible.

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