Centrifugal Pumps

Johann Friedrich Gülich

Fourth Edition

Centrifugal Pumps

Johann Friedrich Gülich

Centrifugal PumpsFourth Edition

123

Johann Friedrich GülichVilleneuve, Switzerland

ISBN 978-3-030-14787-7 ISBN 978-3-030-14788-4 (eBook)https://doi.org/10.1007/978-3-030-14788-4

1st–3rd editions: © Springer-Verlag Berlin Heidelberg 2008, 2010, 20144th edition: © Springer Nature Switzerland AG 2020This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, expressed or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral with regardto jurisdictional claims in published maps and institutional affiliations.

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Preface

Life is linked to liquid transport, and so are vital segments of economy. Pumpingdevices - be it the human heart, a boiler feeder or the cooling water pump of amotorcar - are always part of a more or less complex system where pump failurecan lead to severe consequences. To select, operate or design a pump, someunderstanding of the system is helpful, if not essential. Depending on the appli-cation, a centrifugal pump can be a simple device which could be built in a garagewith a minimum of know-how - or a high-tech machine requiring advanced skills,sophisticated engineering and extensive testing. When attempting to describe thestate of the art in hydraulic engineering of centrifugal pumps, the focus is neces-sarily on the high-tech side rather than on less-demanding services even thoughthese make up the majority of pump applications.

Centrifugal pump technology involves a broad spectrum of flow phenomenawhich have a profound impact on design and operation through the achievedefficiency, the stability of the head-capacity characteristic, vibration, noise, com-ponent failure due to fatigue, as well as material damage caused by cavitation,hydro-abrasive wear or erosion corrosion. Operation and life cycle costs ofpumping equipment depend to a large extent on how well these phenomena and theinteraction of the pump with the system are understood.

This book endeavors to describe pump hydraulic phenomena in their broadestsense in a format highly relevant for the pump engineer involved in pump designand selection, operation and troubleshooting. Emphasis is on physical mechanisms,practical application and engineering correlations for real flow phenomena, ratherthan on mathematical treatment and theories of inviscid flow.

Vibrations and noise remain among the most persistent pump problemsencountered by manufacturers and operators alike. Major additions in the present4th English edition focus on this theme. Specifically, additional topics discussed inthe 4th edition are as follows:

1. Chapter 10.14 “Vertical-pump vibrations” has been added; it focuses on largecooling water pumps with power of up to 4000 kW. Time and again, theapproach flow through the large intake structures induces vibrations in spite of

v

sump model testing done to eliminate vortices. The case histories reportedsuggest that Froude model testing is not sufficient to guarantee trouble-freeoperation since the inertia effects associated with large Reynolds numbers arenot sufficiently modeled. Non-uniform approach flows create forces on thepump body, and correlations are offered to estimate this type of excitationforces.

2. With the object of helping with vibration diagnostics, Chap. 10 has been againsignificantly enhanced by a more detailed discussion of various unsteady flowphenomena and their impact on hydraulic excitation forces. Case histories areprovided which afford additional insight into excitation mechanisms.Experimental data on lateral excitation forces and pressure pulsations at bladepassing frequency are presented in a generic format which facilitates applicationto other projects.

3. New correlations to estimate the rotordynamic coefficients of annular seals andthe hydraulic impeller interaction are provided in Chap. 10.6.

4. With ever-increasing computing power, steady or unsteady numerical flowcalculations of entire pumps have meantime become state of the art. Chapter 8has been revised accordingly. A statistical evaluation of the discrepanciesbetween test and CFD has been done with the object of assessing the accuracywhich can be expected from numerical flow calculations.

5. In Chap. 7, a new correlation for estimating the required NPSH of inducers fromgeometric parameters has been developed and methods for designing twinvolutes for multistage pumps and vaned inlet chambers are provided.

6. A new correlation for estimating the radial pump performance in two-phase flowhas been developed, Chap. 13. The viscosity anomality linked to emulsions isillustrated by some test data.

7. Impeller stresses and failure modes have been discussed in more detail and thecorrelations developed for estimating the risk of failure.

8. Some additions were made in most of the chapters, and some printing errorswere corrected. The below table gives a detailed list of new items.

Villeneuve, Switzerland Johann Friedrich GülichJanuary 2019

vi Preface

Supplements to the 4th Edition

For readers familiar with the 3rd (2014-) edition, the following table might be helpfulto get a quick overview of the topics which have been added in the present edition.

Chapter Topic Figs., Tables, Eqs.

1.6 Pressure recovery in curved diffusers Fig. 1.24, Eq. (1.54)

3.2.6 Calculation of friction factors, and optimization, ofannular seals with deep serrations

Figs. 3.14-1 to 3.14-3,Table 3.7(4)

4.5.1 Design of inlet rings and low-flow impellers: remediesfor over-sized impeller inlets causing noise andvibrationsExponents for trimming impellers

Eqs. (4.15a), (4.17a)

5.2.6 Additional test data on impeller inlet recirculation Eq. (5.7c), Table D5.1,Fig. 5.16

5.6.6 Casing grooves for suppression of instabilities in theQ-H-curve of semi-open impellers (semi-axial)

Fig. 5.43-1

5.9 Some comments on the limits of understanding3D-flow phenomena

6.2.4 Some test data on the limit of the suction specificspeed

Eq. (6.8a)

6.3.1 Effect of seal clearances on NPSH3

6.8.2.3 Unsteady volute cavitation Fig. 6.47

6.8.3 Inlet rings for reducing cavitation problems duringpartload operation

Figs. 6.48 and 6.49

7.2.4 Suction impeller design with flat pressure distributions Table D7.1-1,Fig. 7.10-1

7.3.4 “Double-acting” impellers with specific speeds ofnq < 10: two additional concepts reported in theliterature

7.5 Selection of speed and head for large semi-axialcooling water pumps

Eqs. (7.11a) and (7.11b)

(continued)

vii

(continued)

7.7.3 Inducer performance prediction from geometry Eq. (7.23a),Fig. 7.37-1

7.7.4 Inducer design systematic

7.8.2 Multistage pumps with double volutes Figs. 7.42-1 to 7.42-3

7.13 Design of vaned inlet casings for multistage pumps Figs. 7.51-1 to 7.51-4

7.14 Update of impeller design according an analyticalprocedure

Table 7.10, Fig. 7.53

8.6.3 Unsteady CFD calculations update

8.8.4 Accuracy of numerical performance calculations Table 8.3, Figs. 8.22 to8.24

8.8.5 CFD set-up parameters Table 8.4

9.2.1 Static pressure at the impeller outlet for axial forcecalculations

Figs. 9.14-1 to 9.14-3

9.3.4 Radial forces in double volute Fig. 9.30-1

9.3.7 Influence of the approach flow on radial forces: newtest data

Fig. 9.32

10.6.2 Additional method for calculating the rotordynamicreaction force coefficients for annular seals

Table 10.4(1)

10.6.3 A set of correlations for calculating the rotordynamiccoefficients for the hydraulic impeller interaction hasbeen developed based on test data

Table 10.4(2)

10.6.6 Two case histories of super-synchronous rotorinstabilities are discussed

10.7.1 This chapter has been thoroughly revised:(1) Guidelines for staggering double-entry impellers;(2) Rotor/stator interaction: effect of incidence atdiffuser or volute; (3) Test data for pressure pulsationsat blade passing frequency; (4) Alternate stall in vaneddiffuser; (5) Test data for lateral excitation forces atblade passing frequency

Figs. 10.25-1, 10.25-2,10.26-1 and 10.28-1

10.7.3 Vibrations caused by cavitation in a pump withdouble-entry impellerVibrations caused by inlet recirculation

Figs. 10.32-1 to 10.32-4

10.12.4 Trailing edge design for reduced vortex shedding

10.14 Extensive discussion of vertical-pump vibrations andproblems related to unsteady and non-uniformapproach flow through the intake structure

Figs. 10.65 to 10.78Tables 10.14, 10.15

13.1.5 Performance impairment when pumping emulsions ofimmiscible liquids

Fig. 13.12-1

13.2.4 A new model is presented for estimating the headreduction when pumping gas-liquid mixtures

Eqs. (13.19b to d)Figs. 13.23 and 13.24

14.1.2 Impeller fractures - analysis and prediction Figs. 14.7-1 to 14.7-4Eqs. (14.2a) to (14.2e)

viii Supplements to the 4th Edition

Acknowledgements

The 1st English edition owed its existence to the initiative and sponsoring of themanagement of Sulzer Pumps. For this, I am most grateful to Dr. A. Schachenmannwho initiated the project, R. Paley and Dr. R. Gerdes.

The book benefited from the help which I got from many colleagues at SulzerPumps in the USA and the UK to whom my sincere thanks are extended. Mostimportant were the reviews of the English text. M. Cropper was instrumental in thisactivity. S. Bradshaw, R. Davey, Dr. J. Daly, D. Eddy, M. Hall, Dr. A. Kumar,P. Sandford, D. Townson and C. Whilde reviewed individual chapters.

J. H. Timcke meticulously checked most of the 1st English edition for consis-tency with the 2nd German edition and made many suggestions for making the textand figures easier to understand. Mrs. H. Kirchmeier helped with the figures andcomputer problems. Last but not least, my wife Rosemarie Gülich was a tremen-dous help in checking and improving the final text.

I am grateful to various individuals who provided me with the literature andgranted permission for using figures: Prof. Dr.-Ing. F. Avellan, Dr. M. Farhat,Dr. O. Braun and Dr. S. Berten from the Ecole Polytechnique Lausanne;Prof. Dr.-Ing. D. H. Hellmann, Prof. Dr.-Ing. M. Böhle and Dr.-Ing. H. Roclawskifrom the Technical University of Kaiserslautern; Prof. Dr.-Ing. G. Kosyna,Prof. Dr.-Ing. habil. U. Stark, Mrs. Dr.-Ing. I. Goltz, Mrs. P. Perez, Dr.-Ing.H. Saathoff from the Technical University of Braunschweig; C. H. van den Berg,MTI Holland; Prof. Dr.-Ing. H. Wurm, A. Töws, Wilo, Dortmund; Dr. P. Dupont,Sulzer; U. Diekmann, Wilo-Emu; A. Nicklas, Sterling Fluid Systems, T. Folsche,CP Pumpen AG; and H. Bugdayci, IHC Merwede. I am especially gratefulR. Palgrave for sharing with me a number of instructive photographs of pumpcomponents which have been subject to abrasive wear.

The 1st and 2nd editions benefited from the reviews of individual chaptersprovided by: Dr.-Ing. G. Scheuerer, ANSYS München; Dr. P. Heimgartner,W. Bolliger, W. Schöffler, Dr.-Ing. W. Wesche, Dr. P. Dupont, Dr. S. Berten,G. Caviola, E. Leibundgut, T. Felix, A. Frei, E. Kläui, W. Handloser (all fromSulzer); and J. H. Timcke.

ix

The following organizations or individuals kindly granted permission for usingfigures:

– Sulzer Pumps Ltd, Winterthur– T. McCloskey, Electric Power Research Institute, Palo Alto, CA, USA– VDMA, Frankfurt– VDI Verlag, Düsseldorf– Mr. J. Falcimaigne, Institut Français du Pétrole, Paris– ASME New York

The appropriate references are given in the figure captions.

x Acknowledgements

Symbols, Abbreviations, Definitions

Hints for the reader: The text is written according to US-English spelling rules.As is customary in English publications, the decimal point is used.

Nomenclature: Unfortunately, there is no commonly accepted nomenclature anduse of technical terms. As far as possible, I have consulted various standards as tothe most accepted terms. The reader is referred to the extensive list of symbolsgiven below. For easy reference, this list defines the chapters, tables or equationswhere the respective symbols are introduced. A number of subscripts from theGerman original were left unchanged since replacing them by meaningful Englishabbreviations involved too much of a risk of overlooking some items which areused throughout the text and the equations.

Conventions: Equations, tables and figures are numbered by chapter. The geo-metrical dimensions of impellers, diffusers and volutes are defined in Table 0.2.

To improve the readability, simplified expressions have sometimes been used(e.g., “volute” instead of “volute casing”). In order to avoid monotonous repetitionof technical terms, synonyms are (sparingly) employed.

Formulae frequently used in practice were gathered in tables which present thesequence of calculation steps required to solve a specific problem. These tables helpto find information quickly without looking through a lot of text; they also facilitateprogramming. The equations presented in the tables are labeled by “T”. Forexample, Eq. (T3.5.8) refers to equation 8 in Table 3.5. Most of the tables arelabeled as “Table 6.1,” for example. Some “data tables” are referred to as“Table D6.1” for instance; this subterfuge was made necessary by the layout of theGerman editions which contained “tables” and “plates.”

Mathematical expressions: Empirical data in the literature are frequently pre-sented in graphical form. In most cases, such data are given in this book in the formof approximate equations in order to ease programming and to save space.

For reasons of simplicity, the upper limit of a sum is not specified whenthere can be no doubt about the variable. For example,

Pst PRR stands for

xi

Pi¼zsti¼1 PRR;i and represents the sum of the disk friction losses in all stages of a

multistage pump.An equation of the form y = a � exp(b) stands for y = a � eb, where “e” is

the base of the natural logarithm.The symbol * is used for “proportional to”; for example, PRR * d2

5 stands for“the disk friction loss is proportional to the fifth power of the impeller diameter.”

Frequent reference is made to the specific speed nq which is always calculatedwith n in rpm, Q in m3/s and H in m. For conversion to other units, refer toTable D2.1 or Table 3.4. For simplicity, the specific speed nq is treated as adimensionless variable even though this is not true.

Many diagrams were calculated with MS Excel which has limited capabilitiesfor graphic layout. For example, 1E + 03 stands for 103; curve legends cannot showsymbols or subscripts. The sketches should not be understood as technical draw-ings. Equations in the text are written for clarity with multiplier sign, i.e., a � b(instead of a b). This is not done in the numbered equations.

Literature: There is a general bibliography quoted as [B.1], [B.2], etc., whilestandards are quoted as [N.1], [N.2], etc. The bulk of the literature is linked to theindividual chapters. This eases the search for the literature on a specific topic. Theroughly 800 quotations provided represent only 1 % (order of magnitude) if not lessof the relevant literature. This statement applies to all topics treated in this book.The literature quoted was selected with the objectives: (1) to provide the sources ofspecific data or information; (2) to back up a statement; (3) to refer the reader tomore details on the particular investigation or topic; (4) to provide reference to theliterature in neighboring fields. In spite of these criteria, the selection of the liter-ature quoted is to some extent coincidental.

In order to improve the readability, facts which represent the state of the art arenot backed up systematically by quoting the literature where they may have beenreported. In many cases, it would be difficult to ascertain where such facts werepublished for the first time.

Patents: Possible patents on any devices or design features are not necessarilymentioned. Omission of such mention should not be construed so as to imply thatsuch devices or features are free for use to everybody.

Disclaimer of warranty and exclusion of liabilities: In spite of careful checkingtext, equations and figures, neither the Springer book company nor the author:

– makes any warranty or representation whatsoever, express or implied, (A) withrespect of the use of any information, apparatus, method, process or similar itemdisclosed in this book including merchantability and fitness for practical pur-pose, or (B) that such use does not infringe or interfere with privately ownedrights, including intellectual property, or (C) that this book is suitable to anyparticular user’s circumstances; or

xii Symbols, Abbreviations, Definitions

– assumes responsibility for any damage or other liability whatsoever (includingconsequential damage) resulting from the use of any information, apparatus,method, process or similar item disclosed in this book.

In this context, it should well be noted that much of the published information onpump hydraulic design is empirical in nature. The information has been gatheredfrom tests on specific pumps. Applying such information to new designs harborsuncertainties which are difficult to asses and to quantify.

Finally, it should be noted that the technological focus in the various sectorsof the pump industry is quite different. Low-head pumps produced in vast quantitiesare designed and manufactured to other criteria than engineered high-energypumps. This implies that the recommendations and design rules given in this bookcannot be applied indistinctly to all types of pumps. Notably, issues of standard-ization and manufacturing are not addressed in this text to any extent.

The recommendations and application limits are considered to be mostly on thesafe side. There are certainly pumps on the market and in service with provenoperation records, which exceed some of the limits given in this book.

Symbols, Abbreviations and Definitions

Unless otherwise noted all equations are written in consistent units (SI-System).Most symbols are defined in the following. As appropriate, the equation or chapteris quoted where the symbol has been defined or introduced. Vectors in the text andin equations are printed as bold characters. Symbols with local significance only aredefined in the text.

The following tables may help in understanding the physical meaning of variousparameters of prime importance:

– Table 0.1 and 0.2: Geometric dimensions of the flow channels, flow angles andvelocities

– Table 2.2: Head and net positive suction head (NPSH)– Tables 3.1 and 3.2: Velocity triangles– Table 3.4: Model laws and dimensionless parameters

A area, cross section Chapter or equationA [%] elongation at rupture (ductility of material) Chap. 14A amplitude Chap. 10A1q impeller inlet throat area (trapezoidal:

A1q = a1 � b1)A2q area between vanes at impeller outlet

(A2q = a2 � b2)A3q diffuser/volute inlet throat area (A3q = a3 � b3)a distance between vanes (subscript 1 to 6) Table 0.2a sound velocity in a pipe Eq. (10.17)

(continued)

Symbols, Abbreviations, Definitions xiii

(continued)

ao sound velocity in the fluid Eq. (10.17)aL sound velocity in the casing material Eq. (T6.1.7)BEP best efficiency pointb accelerationb width of channel in the meridional sectionb2 impeller outlet width; if double-entry, per impeller

sideb2tot (b2ges) impeller outlet width including shrouds Eq. (9.6)bks solid-borne noise acceleration Eq. (10.6)CNL cavitation sound pressure Table 6.1CV solid-borne noise as RMS of accelerationCV* dimensionless solid-borne noise acceleration CV* = CV � d1/u1

2

c absolute velocity Chap. 1.1c rotor damping coefficient Eq. (10.7)cA axial thrust reduction coefficient Eq. (9.4), Table 9.1cA approach-flow velocity in pump sump Chap. 10.14cd flow velocity in discharge nozzlecFe concentration of iron ions Eq. (14.7), Table 14.7c3q average velocity in diffuser throat c3q = QLe/(zLe � A3q)cc cross-coupled damping Eq. (10.7)ceq roughness equivalence factor Eq. (1.36b)cf friction coefficient of a flat plate Eq. (1.33)cp pressure recovery coefficient Eqs. (1.11), (1.40),

(T9.1.5)cp specific heat at constant pressure Chap. 13.2cph phase velocity Chap. 10.7.1cs flow velocity in suction nozzlecs concentration of solids Table 14.16cs,eq equivalent concentration of solids Table 14.16cT velocity at inlet to suction bell Eq. (11.15)cv solid volume concentration Table 13.5CWP cooling water pumpD damping coefficient Chap. 10.6.5D, d diameterDfz diffusion factor Table 7.5DR liquid/gas density ratio DR � q* = q′/q″ Chap. 13.2DT inlet diameter of suction bell Fig. (11.20)d3q equivalent diameter of volute throat Eq. (T7.7.7)db arithmetic average of diameters at impeller or

diffuser e.g., d1b = 0.5 (d1 + d1i); defined suchthat: A1 = p � d1b � b1

Table 0.2

dd inner diameter of discharge nozzledk ball passage (sewage or dredge pumps) Chap. 7.4dm geometric average of diameters at impeller or

diffuser, e.g., d1m =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0.5(d21a + d

21i)

q Table 0.2

dn hub diameterdD diameter at shaft seal Table 9.1ds inner diameter of suction nozzleds diameter of solid particles Table 14.16

(continued)

xiv Symbols, Abbreviations, Definitions

(continued)

E Young’s modulus of elasticityER maximum erosion rate (at location of highest

metal loss)Table 6.1

ER,a metal loss rate in mm/a Tables 14.7 and 14.16e vane thickness Table 0.2F forceFax axial force (“axial thrust”)FDsp radial thrust correction factor for double volutes,

Fig. 9.18 Table 9.4FR radial force (“radial thrust”) Eq. (9.6), Table 9.4Fr Froude number Chaps. 10.14, 11.7.3Fr, Ft radial and tangential forces on rotor Eq. (10.8)Fcor corrosion factor Table 6.1FMat material factor for cavitation Table 6.1, for abrasion:

Table 14.16f frequencyfEB natural frequency at operational speed Chap. 10.6.5fe1 natural frequency Chap. 10.6.2fkr critical speed (as frequency) Chap. 10.6.5fL influence of leakage flow on disk friction Eq. (T3.6.7), Table 3.6fn frequency of rotation fn = n/60fq impeller eyes per impeller: single-entry fq = 1;

double-entry fq = 2fH correction factor for head (roughness, viscosity) Eq. (3.32)fQ correction factor for flow rate (viscosity) Eq. (3.32)fR roughness influence on disk friction Eq. (T3.6.6)fRS frequency of rotating stallfη correction factor for efficiency (roughness,

viscosity)Eq. (3.31)

g acceleration due to gravity (g = 9.81 m/s2,rounded)

Appendix 17.4

H head per stage Tables 2.2 and 3.3HMat hardness of material Table 14.16Hs hardness of solid particle Table 14.16Htot total head of a multistage pump Table 2.2Hp static pressure rise in impeller Eq. (T3.3.8)htot total enthalpy Eq. (1.4)h casing wall thickness (at location of

accelerometer)Table 6.1

hD casing cover wall thickness Table 6.1Iac acoustic intensity Table 6.1IRef reference value for intensity Table 6.1i incidence (i = blade angle minus flow angle) Table 3.1Jsp integral over diffuser or volute throat area Eqs. (3.15), (4.13)k rotation of fluid in impeller sidewall gap k = b/x Eq. (9.1), Table 9.1kE, kz rotation of fluid at inlet to impeller sidewall gap Fig. 9.1k stiffness Eq. (10.7)kc cross-coupled stiffness Eq. (10.7)kn blockage caused by hub: kn = 1 − dn

2/d12

kR radial thrust coefficient (steady component) Eq. (9.6)kR,D radial thrust coefficient referred to d2 (steady) Table 9.7

(continued)

Symbols, Abbreviations, Definitions xv

(continued)

kR,dyn dynamic (unsteady) radial thrust coefficient Table 9.7kR,tot total radial thrust coefficient (steady and unsteady) Table 9.7kR,o radial thrust coefficient (steady) for operation at Q

= 0Table 9.7

kRu radial thrust coefficient (steady) Eq. (9.7)kRR disk friction coefficient Table 3.6L lengthLPA A-type sound pressure level Table 10.4LDam damage lengthLcav cavity lengthM torquem difference of impeller and diffuser periodicity Chap. 10.7.1m mass coefficient Eq. (10.7)_m mass flow ratemc cross-coupled mass Eq. (10.7)NPSH net positive suction headNPSHA net positive suction head available Tables 2.2 and 6.2NPSHi net positive suction head required for cavitation

inceptionNPSHR net positive suction head required according to a

specific cavitation criterionChaps. 6.2.2, 6.2.5, 6.3

NPSHx net positive suction head required for operationwith x-percent head drop

Chap. 6.2.2

NL fluid-borne sound pressure as RMS value;NL* = 2NL/(q � u1)

NLo background sound pressure Chap. 6.5n rotational speed (revolutions per minute)n(s) rotational speed (revolutions per second)nN nominal speednq specific speed [rpm, m3/s, m] Tables D2.1 and 3.4,

Chap. 3.4nss suction specific speed [rpm, m3/s, m] Chap. 6.2.4, Table 3.4P power; without subscript: power at couplingPi inner power Table 3.5Pm mechanical power losses Table 3.5Pu useful power transferred to fluid

Pu = q � g � Htot � QTable 3.5

PRR disk friction power Tables 3.5 and 3.6PER specific erosion power PER = UR � ER Table 6.1Per disk friction power loss caused by balance device Table 3.6Ps3 power loss dissipated in interstage seal Tables 3.5 and 3.7 (1)PI pitting index Eq. (14.8)p static pressurep periodicity Chap. 10.7.1pamb ambient pressure at location of pump installation

(usually atmospheric pressure)pe pressure above liquid level in suction reservoir Table 2.2pg gas pressure (partial pressure) Appendix 17.3pi implosion pressure Table 6.1pv vapor pressure

(continued)

xvi Symbols, Abbreviations, Definitions

(continued)

Q flow rate, volumetric flowQLa flow rate through impeller:

QLa = Q + Qsp + QE + Qh = Q/ηvQLe flow rate through diffuser: QLe = Q + Qs3 + QE

QE flow rate through axial thrust balancing deviceQCB flow rate through center bush, Figs. 2.9 and 2.10 back-to-back pumpsQh flow rate through auxiliaries (mostly zero)QR rated flow or nominal flow rate Chap. 15Qsp leakage flow rate through seal at impeller inlet Tables 3.5 and 3.7 (1)Qs3 leakage flow rate through interstage seal Tables 3.5 and 3.7 (1)q* flow rate referred to flow rate at best efficiency

pointq* � Q/Qopt

R, r radius or gas constant Table 13.3RG degree of reaction Chap. 3.2Re Reynolds number, channel: Re = c � Dh/n; plate

or blade: Re = w � L/nRo Rossby number Chap. 5.2Rm tensile strengthRMS root mean squarer3q equivalent radius of volute throat area Table 7.7S submergence Chap. 11.7.3S sound absorbing surface of inlet casing Table 6.1SG specific gravity; SG � q/qRef with qRef = 1000

kg/m3

SStr Strouhal number Table 10.13s radial clearance Eq. (3.12), Figs. 3.12,

3.15 Table 3.7 (1) and (2)sax axial distance between impeller shrouds and

casingFig. 9.1

T temperaturet timet pitch t = p � d/zLa (or zLe)tax axial casing part in impeller sidewall gap Fig. 9.1U wetted perimeter (of a pipe or channel)UR ultimate resilience: UR = Rm

2/(2 � E) Table 6.1u circumferential velocity u = p � d � n/60V volumew relative velocityw1q average velocity in impeller throat area w1q = QLa/(zLa � A1q)x dimensionless radius x = r/r2 Table 9.1x gas (or vapor) mass content; mass concentration of

solidsChap. 13

xD mass concentration of dissolved gas Appendix 17.3xov overlap at impeller/diffuser side disks Fig. 9.1Y specific work Y = g � HYsch � Yth specific work done by the impeller blades:

Yth = g � Hth

Table 3.3

Yth∞ specific work done by the impeller blades withvane congruent flow

y+ dimensionless distance from the wall Table 8.1Z real gas factor Table 13.3

(continued)

Symbols, Abbreviations, Definitions xvii

(continued)

Zh hydraulic losses (impeller: ZLa diffuser: ZLe)z height coordinatezLa number of impeller bladeszLe number of diffuser vanes (volute: number of

cutwaters)zR number of return vaneszpp number of pumps operating in parallelzst number of stages (in Fig. 2.9, 2.10: zst

= zst1 + zst2)zst1 number of stages in first group of stages back-to-back pumpszst2 number of stages in second group of stages back-to-back pumpszVLe number of vanes of prerotation control devicea � GVF gas content, gas volume fraction, void fraction Table 13.2a angle between direction of circumferential and

absolute velocityak notch factor Eq. (T14.1.7)aT total absorption coefficient Table 6.1b angle between relative velocity vector and the

negative direction of circumferential velocityb angular velocity of fluid between impeller and

casingChap. 9.1

b mass transfer coefficient Chap. 14.3, Table 14.8c impeller discharge coefficient (“slip factor”) Table 3.2d* displacement thickness Eq. (1.18)Dp*d pressure pulsations(dimensionless) Eq. (10.1)Dpa amplitude of pressure pulsations Chap. 10.2.6Dpp-p pressure pulsations measured peak-to-peak Chap. 10.2.6e angle in polar coordinate systeme equivalent sand roughness Chap. 1.5.2esp wrap angle of the inner volute (for double volutes) Table 0.2f loss coefficient (with subscript La, Le, Sp etc.) Table 3.8fa lift coefficient Tables 7.1 and 7.4fw drag coefficient Table 7.4ηvol, ηv volumetric efficiency Eq. (T3.5.9)η overall efficiency (at coupling) Eq. (T3.5.3)ηi inner efficiency Eq. (T3.5.5)ηh hydraulic efficiency Eq. (T3.5.8) and Table 3.

8ηD diffuser efficiency Eq. (1.43)ηst stage efficiency Eq. (T3.5.7)hu similarity parameter for cavitation erosion Table 6.10 diffuser opening angle Eq. (1.42)j exponent of isentropic expansion/compression Table 13.3 (2)k angle between vanes and side disks (impeller or

diffuser)Table 0.1

k power coefficient Table 3.4k wave length Table 10.12kc, kw coefficient for NPSH calculation Eq. (6.10)kR friction coefficient for pipes and channels Eq. (1.36)l dynamic viscosity: l = q � mm kinematic viscosity: m = l/q

(continued)

xviii Symbols, Abbreviations, Definitions

(continued)

m hub ratio n = dn/d1am1, m2 vibration orders, natural numbers (1, 2, 3, ….)n hydraulic vane loading according to [7.2] Table 7.1q densityq″ density of gas or saturated vaporqmat density of materialqp density of casing materialqs density of solids suspended in the fluids Chaps. 13.4, 14.5r cavitation coefficient (same subscripts as NPSH) Table 3.4r mechanical stress Chap. 14.1s blade blockage factor Table 0.1s shear stressφ flow coefficient Table 3.4φsp flow coefficient of impeller sidewall gap Table 9.1ψ head coefficient Table 3.4ψp pressure coefficient of static pressure rise in

impellerTable 3.3

X orbit- (vibration-)circular frequency Chap. 10.6.2Xlimit orbit frequency of stability limit Eq. (10.9)x angular rotor velocityxE circular natural frequency Chap. 10xs universal specific speed Tables D2.1 and 3.4

Subscripts, Superscripts and Abbreviations

Sequence of calculations: in the pumping mode the fluid flows from station 1 to 6,in the turbine mode from 6 to 1:

1 impeller blade leading edge (low pressure)2 impeller blade trailing edge (high pressure)3 diffuser vane leading edge or volute cutwater4 diffuser vane trailing edge5 return vane leading edge6 return vane trailing edgeA planta plant, executed pump, prototypeal allowableax axiala, m, i outer, mean, inner streamlineB blade angle (impeller, diffuser, volute cutwater)BEP best efficiency point Chap. 2.2.4BPF impeller blade passing frequency zLa � fn Chap. 10cor corrosionCP column pipe of a vertical pumpDE drive end (coupling end of a pump shaft)Ds (FS) front shroud

(continued)

Symbols, Abbreviations, Definitions xix

(continued)

d discharge nozzleER erosioneff effectiveFS front shroudGap A radial gap between impeller shrouds

and diffuser side plateTable 0.2 (2)

Gap B radial gap between impeller bladesand diffuser vanes or volute cutwater

Table 0.2 (2)

Gap E, Gap F axial gap between impeller(rear and front) shrouds and casing

Table 0.2 (2)

GVF gas volume fraction, void fraction Table 13.2ISR impeller side room (impeller sidewall

gaps E, F) Table 0.2Chap. 9.1

h hydraulicL runaway in turbine mode (M = 0) Chap. 12La impellerLe diffuserLE leading edgeM modelm meridional componentmax maximummin minimummix two-phase mixtureNDE non-drive end (of a pump shaft)o shut-off operation (Q = 0)opt operation at maximum (best)

efficiency (BEP)P pumping mode Chap. 12PS (DS) pressure surface (pressure side)pol polytropic Chap. 13.2q average velocity calculated from continuity

(to be distinguished from velocity vector)RB onset of recirculationRec (Rez) recirculationRef reference valueRR disk friction Chap. 3.6.1,

Table 3.6RS rear shroud or hubRSI rotor–stator interaction Chap. 10.7.1r Radials inlet or suction nozzles solid particle Chap. 13.4sch blade or vaneSF shockless flow (zero incidence) Eq. (T3.1.10)SM separation margin Chap. 10.14Sp volutesp annular seal, leakage flowSPL single-phase liquidSS suction surface (suction side)st stagestat static

(continued)

xx Symbols, Abbreviations, Definitions

(continued)

T turbine mode Chap. 12TE trailing edgeTP two-phaseTs (RS) rear shroud or hubth theoretical flow conditions

(flow without losses)tot total (total pressure = static pressure

+ stagnation pressure)u circumferential componentv lossv viscous fluid Chap. 13VPF diffuser vane passing frequency zLe � fn Chap. 10w water Chap. 13.1w resistance curve in turbine mode locked rotor (n = 0) Chap. 12zul (al) allowable

The following are superscripts

′ with blade blockage Tables 0.1 and 3.1* dimensionless quantity: all dimensions are referred to d2 e.g.,

b2* = b2/d2, velocities are referred to u2, e.g., w1* = w1/u2′ liquid phase Chaps. 6 and 13″ gaseous phase Chaps. 6 and 13

Symbols, Abbreviations, Definitions xxi

xxii Symbols, Abbreviations, Definitions

ε

α

α

αα

β

β

α

Symbols, Abbreviations, Definitions xxiii

Impeller sidewall gaps and diffuser in-let geome-try for multistage pumps

Q S P

xo v

G ap A

d 2

sax

d w

Q S 3

d s3

d sp

d 3

Gap B

G ap F

G ap E

Im peller sidewall gap

Im peller sidew all g ap

Diffuser in-let geome-try with chamfer, for multi-stage pumps, Chap. 10 [61]

Q SP

xov

Gap A

d2

sax

dw

Q S3

ds3

dsp

d3

Gap B

Gap F

Gap E

Impeller sidewall gap

Impeller sidewall gap

Chamfer

H2 d2

H3

H4

Triangular sectionDiffusing channel

Throat

Table 0.2 (2) Geometric dimensions

xxiv Symbols, Abbreviations, Definitions

Pump Styles

OHH—Overhung Single StageISO 13709 (API 610) Type OH2

BBS—Between Bearings Single StageISO 13709 (API 610) Type BB2

OHC—Overhung Single Stagewith Canned MotorAPI 685

GSG—Inline or Opposed ImpellerDiffuser Barrel TypeISO 13709 (API 610) Type BB5

OHM—Overhung Single Stagewith Magnetic Coupling, API 685 OHV—Vertical Inline

ISO 13709 (API 610) Type OH3

Symbols, Abbreviations, Definitions xxv

BBT-D—Between BearingsTwo-Stage Double SuctionISO 13709 (API 610) Type BB2

BBT—Between Bearings Two-StageISO 13709 (API 610) Type BB2

CP—Dual Volute OpposedImpeller Barrel TypeISO 13709 (API 610) TypeBB5

MSD—Dual Volute OpposedImpeller Horizontally SplitISO 13709 (API 610) Type BB3

xxvi Symbols, Abbreviations, Definitions

Contents

1 Fluid Dynamic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Flow in the Absolute and Relative Reference Frame . . . . . . . 11.2 Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Conservation of Mass . . . . . . . . . . . . . . . . . . . . . 21.2.2 Conservation of Energy . . . . . . . . . . . . . . . . . . . . 31.2.3 Conservation of Momentum . . . . . . . . . . . . . . . . . 5

1.3 Boundary Layers, Boundary Layer Control . . . . . . . . . . . . . . 71.4 Flow on Curved Streamlines . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4.1 Equilibrium of Forces . . . . . . . . . . . . . . . . . . . . . 111.4.2 Forced and Free Vortices . . . . . . . . . . . . . . . . . . . 151.4.3 Flow in Curved Channels . . . . . . . . . . . . . . . . . . . 17

1.5 Pressure Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.5.1 Friction Losses (Skin Friction) . . . . . . . . . . . . . . . 191.5.2 Influence of Roughness on Friction Losses . . . . . . 211.5.3 Losses Due to Vortex Dissipation (Form Drag) . . . 25

1.6 Diffusers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271.7 Submerged Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341.8 Equalization of Non-uniform Velocity Profiles . . . . . . . . . . . 361.9 Flow Distribution in Parallel Channels, Piping Networks . . . . 38References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2 Pump Types and Performance Data . . . . . . . . . . . . . . . . . . . . . . . 452.1 Basic Principles and Components . . . . . . . . . . . . . . . . . . . . . 452.2 Performance Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.2.1 Specific Work, Head . . . . . . . . . . . . . . . . . . . . . . 502.2.2 Net Positive Suction Head, NPSH . . . . . . . . . . . . 512.2.3 Power and Efficiency . . . . . . . . . . . . . . . . . . . . . . 512.2.4 Pump Characteristics . . . . . . . . . . . . . . . . . . . . . . 53

2.3 Pump Types and Their Applications . . . . . . . . . . . . . . . . . . . 542.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

xxvii

2.3.2 Classification of Pumps and Applications . . . . . . . 572.3.3 Pump Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.3.4 Special Pump Types . . . . . . . . . . . . . . . . . . . . . . 75

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3 Pump Hydraulics and Physical Concepts . . . . . . . . . . . . . . . . . . . 813.1 One-Dimensional Calculation with Velocity Triangles . . . . . . 813.2 Energy Transfer in the Impeller, Specific Work and Head . . . 853.3 Flow Deflection Caused by the Blades. Slip Factor . . . . . . . . 873.4 Dimensionless Coefficients, Similarity Laws and Specific

Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923.5 Power Balance and Efficiencies . . . . . . . . . . . . . . . . . . . . . . 953.6 Calculation of Secondary Losses . . . . . . . . . . . . . . . . . . . . . 98

3.6.1 Disk Friction Losses . . . . . . . . . . . . . . . . . . . . . . 983.6.2 Leakage Losses Through Annular Seals . . . . . . . . 1023.6.3 Power Loss Caused by the Inter-stage Seal . . . . . . 1133.6.4 Leakage Loss of Radial or Diagonal Seals . . . . . . 1143.6.5 Leakage Losses in Open Impellers . . . . . . . . . . . . 1153.6.6 Mechanical Losses . . . . . . . . . . . . . . . . . . . . . . . . 116

3.7 Basic Hydraulic Calculations of Collectors . . . . . . . . . . . . . . 1173.8 Hydraulic Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1233.9 Statistical Data of Pressure Coefficients, Efficiencies

and Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1303.10 Influence of Roughness and Reynolds Number . . . . . . . . . . . 140

3.10.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1403.10.2 Efficiency Scaling . . . . . . . . . . . . . . . . . . . . . . . . 1413.10.3 Calculation of the Efficiency from Loss

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1433.11 Minimization of Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1493.12 Compendium of Equations for Hydraulic Calculations . . . . . . 150References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

4 Performance Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1694.1 Head-Capacity Characteristic and Power Consumption . . . . . 170

4.1.1 Theoretical Head Curve (Without Losses) . . . . . . . 1704.1.2 Real Characteristics with Losses . . . . . . . . . . . . . . 1724.1.3 Component Characteristics . . . . . . . . . . . . . . . . . . 1754.1.4 Head and Power at Operation Against Closed

Discharge Valve . . . . . . . . . . . . . . . . . . . . . . . . . 1834.1.5 Influence of Pump Size and Speed . . . . . . . . . . . . 1864.1.6 Influence of Specific Speed on the Shape

of the Characteristics . . . . . . . . . . . . . . . . . . . . . . 1874.2 Best Efficiency Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1884.3 Prediction of Pump Characteristics . . . . . . . . . . . . . . . . . . . . 193

xxviii Contents

4.4 Range Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1944.5 Modification of the Pump Characteristics . . . . . . . . . . . . . . . 196

4.5.1 Impeller Trimming . . . . . . . . . . . . . . . . . . . . . . . . 1974.5.2 Under-Filing and Over-Filing of the Blades

at the Trailing Edge . . . . . . . . . . . . . . . . . . . . . . . 2074.5.3 Collector Modifications . . . . . . . . . . . . . . . . . . . . 208

4.6 Analysis of Performance Deviations . . . . . . . . . . . . . . . . . . . 2094.7 Calculation of Modifications of the Pump Characteristics . . . 212References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

5 Partload Operation, Impact of 3-D Flow PhenomenaPerformance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2195.1 Basic Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2195.2 The Flow Through the Impeller . . . . . . . . . . . . . . . . . . . . . . 223

5.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2235.2.2 Physical Mechanisms . . . . . . . . . . . . . . . . . . . . . . 2255.2.3 The Combined Effect of Different Mechanisms . . . 2315.2.4 Recirculation at the Impeller Inlet . . . . . . . . . . . . . 2335.2.5 Flow at the Impeller Outlet . . . . . . . . . . . . . . . . . 2395.2.6 Experimental Detection of the Onset

of Recirculation . . . . . . . . . . . . . . . . . . . . . . . . . . 2415.3 The Flow in the Collector . . . . . . . . . . . . . . . . . . . . . . . . . . 244

5.3.1 Flow Separation in the Diffuser . . . . . . . . . . . . . . 2445.3.2 Pressure Recovery in the Diffuser . . . . . . . . . . . . . 2465.3.3 Influence of Approach Flow on Pressure Recovery

and Stall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2485.3.4 Flow in the Volute Casing . . . . . . . . . . . . . . . . . . 2505.3.5 Flow in Annular Casings and Vaneless

Diffusers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2515.4 The Effects of Flow Recirculation . . . . . . . . . . . . . . . . . . . . 252

5.4.1 Effects of Flow Recirculation at the ImpellerInlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

5.4.2 Effect of Flow Recirculation at the ImpellerOutlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

5.4.3 Effect of Outlet Recirculation on the Flowin the Impeller Sidewall Gaps and onAxial Thrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

5.4.4 Damaging Effects of Partload Recirculation . . . . . . 2675.5 Influence of Flow Separation and Recirculation

on the Q-H-Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2685.5.1 Types of Q-H-Curve Instability . . . . . . . . . . . . . . 2685.5.2 Saddle-Type Instabilities . . . . . . . . . . . . . . . . . . . 2695.5.3 Type F Instabilities . . . . . . . . . . . . . . . . . . . . . . . 277

Contents xxix

5.6 Means to Influence the Shape of the Q-H-Curve . . . . . . . . . . 2785.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2785.6.2 Influencing the Onset of Recirculation

at the Impeller Inlet . . . . . . . . . . . . . . . . . . . . . . . 2795.6.3 Influencing the Onset of Recirculation

at the Impeller Outlet . . . . . . . . . . . . . . . . . . . . . . 2795.6.4 Eliminating a Type F Instability . . . . . . . . . . . . . . 2825.6.5 Influencing the Saddle-Type Instability

of Radial Impellers with nq < 50 . . . . . . . . . . . . . 2835.6.6 Influencing the Saddle-Type Instability

of Radial Impellers with nq > 50 . . . . . . . . . . . . . 2865.6.7 Influencing the Instability of Semi-axial and Axial

Impellers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2865.6.8 Reduction of Head and Power at Shut-off . . . . . . . 289

5.7 Flow Phenomena in Open Axial Impellers . . . . . . . . . . . . . . 2905.8 Flow Instabilities in Double-Entry Impellers and Double

Volutes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2985.9 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

6 Suction Capability and Cavitation . . . . . . . . . . . . . . . . . . . . . . . . 3076.1 Cavitation Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

6.1.1 Growth and Implosion of Vapor Bubblesin a Flowing Liquid . . . . . . . . . . . . . . . . . . . . . . . 307

6.1.2 Bubble Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 3106.2 Cavitation in Impeller or Diffuser . . . . . . . . . . . . . . . . . . . . . 313

6.2.1 Pressure Distribution and Cavity Length . . . . . . . . 3136.2.2 Required NPSH, Extent of Cavitation, Cavitation

Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3156.2.3 Scaling Laws for Cavitating Flows . . . . . . . . . . . . 3166.2.4 The Suction Specific Speed . . . . . . . . . . . . . . . . . 3206.2.5 Experimental Determination of the Required

NPSHR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3236.2.6 Cavitation in Annular Seals . . . . . . . . . . . . . . . . . 333

6.3 Determination of the Required NPSH . . . . . . . . . . . . . . . . . . 3336.3.1 Parameters Influencing NPSHR . . . . . . . . . . . . . . . 3336.3.2 Calculation of the NPSHR . . . . . . . . . . . . . . . . . . 3376.3.3 Estimation of the NPSH3 as Function of the Flow

Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3416.4 Influence of the Fluid Properties . . . . . . . . . . . . . . . . . . . . . 345

6.4.1 Thermodynamic Effects . . . . . . . . . . . . . . . . . . . . 3456.4.2 Non-condensable Gases . . . . . . . . . . . . . . . . . . . . 3486.4.3 Nuclei Content and Tensile Stresses

in the Liquid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

xxx Contents