an 2314.. a _ .2 1.41.7 \n q 4’50 Q This is to certify that the thesis entitled DESIGN OF A CENTRIFUGAL PUMP FOR LIQUID FUEL PUMPING APPLICATION presented by David Thiepxuan Cao has been accepted towards fulfillment of the requirements for M.S. Mechanical Engineering degree in .. V ‘7 Majorérjifessor Date ‘- - 0 0-7639 MS U is an Affirmative Action/Equal Opportunity lnstitu (ion ltd-‘—~. *— ~ ‘5 x f '.- ““Q F _LIBRARY Michigan State L University PLACE IN RETURN Box to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 6/01 c:/CIRC/DateDue.p65~p. 15 DESIGN OF A CENTRIFUGAL PUMP FOR LIQUID FUEL PUMPING APPLICATION By David Thiepxuan Cao A THESIS Submitted to Michigan State University in partial fulfillment of requirements for the degree of MASTER OF SCIENCE Department of Mechanical Engineering 2002 ABSTRACT DESIGN OF A CENTRIFUGAL PUMP FOR LIQUID FUEL PUMPING APPLICATION By David Thiepxuan Cao This thesis studied the conventional and un-conventional design method of centrifugal pump of a liquid fuel to raise a low-pressure fuel supply to the pressure required for the combustion system. In addition, the operating processes of the current automotive fuel pump systems were analyzed. From this study, the feasibility in the replacement of automotive fuel pumps by the centrifugal pump was clarified. The fuel property requirements are: Density (p = 770 kg/m3), Viscosity (p. = 0.001 N-sec/mz). The duty points are: Head (H = 50.36m), Low flow rate (Q = 3.9”“10'5 m3/s), High rotational speed (N = 9000rpm). The “conventional pump design method” resulted in a centrifugal pump with a very poor theoretical efficiency, 11 = 7 %. Because of the poor performance, an “unconventional pump design method” has been carried out and the theoretical efficiency have been significantly improved, 1] = 54.15 %. Modifications of pump geometry in un-conventional design method were manipulated to optimize the pump performance. In the first case, the theoretical optimal pump efficiency is highest, 11 = 65.5942 %, when the number of blades is four and the exit blade angle is [32 = 90°. In the second case, the theoretical optimal pump efficiency is n = 65.0498 %, when the number of blades is four and the exit blade angle is [32 = 70°. In memory of my parents’ invaluable sacrifices and tireless support throughout my life 7 I ‘ddl pilt firth L35 “‘0 it: I'm In AKNOWLEDGEMENT S The author would like to express his deep gratitude and great appreciation to his advisor, Professor Abraham Engeda at Mechanical Engineering Department of Michigan State University. All the valuable advice, the considerate guidance, the constructive discussion, the willing attitude from his advisor throughout the course of the research work encouraged and supported him to accomplish the final goal in this Thesis. The “Design of A Centrifugal Pump for Liquid Fuel Pumping Application” was achieved with the best results and the expected success. Special thanks are given to Professor S. Paul Hess of Mathematical Department at Grand Rapids Community College for his helpful discussions. The author greatly appreciates Professor Craig W. Somerton, and Professor Norbert Miiller at Mechanical Engineering Department of Michigan State University for being members in examining committee for Thesis defense. Mr. Craig Gunn at Michigan State University is gratefully acknowledged for his useful help in preparing this thesis and the materials in publication of technical writing works. Moreover, the author also appreciates the assistance, the criticism and great friendships from all other students at the Turbomachinery Lab of Michigan State University: Yinghui Dai, Faisal Omar Mahroogi, Jae Wook Song, Mukarrum Raheel, Toshiyuki Sato, Zeyad Alsuhaibani, Donghui Zhang, and Guy Phuong The last thing but not the least important thing, the author would like to thank all the members in his family: his Dad, Man Xuan Cao, his Mother, Nguyet Xuan Tran, his younger brother, Hongan Xuan Cao. They continuously gave the author with great love during the time of the research work at Michigan State University. iv 1151 1151 X01 C111 1.1 1.3 1.4 1.5 1.8 1.9 TABLE OF CONTENTS LIST OF TABLES ........................................................................... x LIST OF FIGURES .......................................................................... xi NOMENCLATURE .......................................................................... xvi CHAPTER 1: INTRODUCTION TO CENTRIFUGAL PUMP .................... 1 1.1 Introduction .............................................................................. 1 1.2 Basics components of a centrifugal pump .......................................... 2 1.3 Inlet and flow mechanism in the inlet .............................................. 2 1.4 Inducer ................................................................................... 3 1.5 Impeller .................................................................................. 5 1.5.1 Types of impeller ........................................................... 5 1.5.2 Flow mechanism in the impeller .......................................... 7 1.5.3 Governing equations ....................................................... 11 1.5.4 Velocity triangles ........................................................... 13 1.5.5 Slip factor and various slip factor equations ............................ 14 1.5.6 Relative velocity in the impeller and rothalpy .......................... 18 1.6 Diffuser .................................................................................. 19 1.6.1 Flow mechanism in vaneless and vaned diffusers ...................... 19 1.6.2 Governing equations ........................................................ 20 1.7 Volute .................................................................................... 20 1.7.1 Flow mechanism in volutes ................................................ 20 1.7.2 Governing Equations ....................................................... 21 1.8 Design considerations and sixteen principal design variables .................... 21 1.9 Pump performance parameters and dimensionless design coefficients ......... 23 1.9.1 Overall performance parameters .......................................... 23 1.9.2 Dimensionless design coefficients ....................................... 26 1.10 Some loss factors influencing the pump performance ............................. 27 1.10.1 Disk friction losses on the impeller—External losses ................... 27 1.10.2 Leakage losses —External losses ........................................... 28 1.10.3 Incidence Losses—Internal losses ......................................... 29 1.10.4 Friction losses —Internal losses ............................................ 31 1. 10.5 Viscosity ..................................................................... 3 1 1.10.6 Reynolds number ............................................................ 32 1.10.7 Cavitations ................................................................... 32 Figures ........................................................................................... 34 CHAPTER 2: LITERATURE SURVEY OF FUEL PUMP ......................... 59 2.1 Fuel pump ............................................................................... 59 2.2 Requirements for fuel pump in fuel injection system .............................. 6O 3.1 3.5 3.6 2.3 Retumless fuel delivery of fuel pump in the fuel system ......................... 65 2.3.1 Electronic retumless of fuel pump in the fuel system .................. 66 2.3.2 Mechanical retumless of fuel pump in the fuel system ................ 67 2.4 Mechanical fuel pump ................................................................. 68 2.4.1 AC-Delco and SU mechanical diaphragm positive displacement fuel-lift pump ................................................ 68 2.4.2 Unitac mechanical diaphragm pump ..................................... 71 2.4.3 AC mechanical diaphragm pump ......................................... 72 2.4.4 AC Alpha mechanical pump .............................................. 72 2.4.5 Bosch plunger-type pump ................................................. 73 2.5 Electrical fuel pump .................................................................... 74 2.5.1 Electrical positive displacement fuel-lift pump ......................... 75 2.5.2 Roller-cell electrical positive displacement pump ..................... 77 2.5.3 Rotary electrical positive displacement pump .......................... 78 2.5.4 AC universal electronic solenoid fuel pump ............................ 81 2.5.5 SU electrical fuel-lift pump ................................................ 82 2.6 Advantages and disadvantages of mechanical & electrical fuel pump 83 2.6.1 Mechanical fuel pump ...................................................... 83 2.6.2 Electrical fuel pump ........................................................ 84 2.7 Conclusions of mechanical fuel pump and electrical fuel pump ................. 86 Figures ........................................................................................... 88 CHAPTER 3: CONVENTIONAL CENTRIFUGAL PUMP DESIGN METHOD 3.1 Specific speed, suction specific speed, and suction diameter ..................... 112 3.2 Impeller discharge velocity triangle ................................................. 113 3.3 Impeller discharge dimensions ....................................................... 116 3.4 Impeller inlet diameter ................................................................. 116 3.5 Impeller inlet vane angles .............................................................. 118 3.6 Impeller inlet velocity triangle ........................................................ 118 3.7 Flow areas between vanes ............................................................ 118 3.8 Volute casing ........................................................................... 120 3.9 Vaned diffuser .......................................................................... 121 3.10 Loss estimates, resultant efficiency, and shaft power .............................. 122 Figures ........................................................................................... 125 CHAPTER 4: UNCONVENTIONAL CENTRIFUGAL PUMP DESIGN METHOD 4.1 4.2 4.3 4.4 4.5 Analysis of Un-Conventional Centrifugal Pump Design ......................... 142 Circulation Head ........................................................................ 146 Impeller Friction Head Loss .......................................................... 148 Volute Head Loss ...................................................................... 151 Power due to Disk Friction Loss, Power due to Leakage Loss, Entrance-Bend Loss .................................................................... 159 4.5.1 Power due to Disk Friction Loss .......................................... 159 4.5.2 Power due to Leakage Loss ................................................ 162 vi 4.5.3 Entrance—Bend Loss ........................................................ 163 4.6 Optimizing Number of Blades and Blade Angle of A Logarithmic Vane Impeller ........................................................... 164 4.7 Derivation of Euler’s Head Equation ................................................ 168 4.8 Determination of Logarithmic Blade Length ....................................... 172 Figures ........................................................................................... 174 CHAPTER 5: DESIGN RECOMMENDATION ....................................... 188 Figures ........................................................................................... 194 CHAPTER 6: CONCLUSIONS ........................................................... 203 BIBLIOGRAPHY ............................................................................ 2 10 APPENDIX A ................................................................................. 218 CALCULATION OF CONVENTIONAL CENT RIFUGAL PUMP DESIGN APPENDIX B ................................................................................. 227 CALCULATION OF PUMP GEOMETRICAL PARAMETERS FOR UN- CONVENTIONAL CENTRIFU GAL PUMP DESIGN APPENDIX C ................................................................................. 232 CALCULATION OF PUMP EFFICIENCY FOR UN-CONVENTIONAL CENTRIFUGAL PUMP DESIGN APPENDIX D ................................................................................. 241 SUB/{MARY OF UN-CONVENTIONAL CENTRIFUGAL PUMP DESIGN APPENDIX E ................................................................................. 252 INTEGRATION OF VOLUTE ENERGY LOSS RATE EQUATION APPENDIX F ................................................................................. 271 COMPUTER PROGRAMS OF PUMP GEOMETRY DETERMINATION & PUMP EFFICIENCY DETERMINATION vii Table Table Table Table Table Table Table Table 5.1 Table 5.2 Table 5.3 Table 5.4 Table 5.5 Table A.1 Table A2 LIST OF TABLES Un-conventional Pump Efficiencies of twelve design cases at Design Point ............................................................................ Rotational speed, flow rate, head, specific speed in fifteen design cases of pump geometry determination ..................................... Necessary Impeller and Volute constants in determining the optimized pump geometrical parameters from fifteen design cases ............................................................................. Impeller Geometry of Conventional Centrifugal Pump Design ........ Impeller Geometry of Un-Conventional Centrifugal Pump Desi gn.. .. Volute dimensions ............................................................. Volute dimensions ............................................................. viii 189 191 191 199 200 224 225 Figure 1.1 Figure 1.2 Figure 1.3 Figure 1.4 Figure 1.5 Figure 1.6 Figure 1.7 Figure 1.8 Figure 1.9 Figure 1.10 Figure 1.11 Figure 1.12 Figure 1.13 Figure 1.14 Figure 1.15 Figure 1.16 Figure 1.17 Figure 1.18 Figure 1.19 Figure 1.20 Figure 1.21 Figure 1.22 Figure 1.23 Figure 1.24 Figure 1.25 Figure 1.26 Figure 1.27 Figure 1.28 Figure 1.29 Figure 1.30 Figure 1.31 Figure 1.32 LIST OF FIGURES Alternative suction systems for an end suction centrifugal pump ....... Simple suction pipe ............................................................ Ducted entry suction ........................................................... Pressure changes on a stream surface in the suction of a centrifugal machine ......................................................................... Unstable flow in the suction region of a centrifugal pump under “part flow” operating conditions ................................................... Inducer ........................................................................... Effect on the NPSHR curve for a pump of adding an inducer ............ Transient flow patterns in the suction region of a pump at low flow rates .............................................................................. Frontal and cross-sectional view of pump impeller ....................... Double-suction centrifugal impeller ......................................... Pump impeller .................................................................. Relative and absolute flow velocity vectors in a rotating impeller. Velocity triangle with C = Absolute velocity, W = Relative velocity, U = Blade velocity ............................................................. Impeller streamline locations for velocity and blade coordinate calculations ..................................................................... Velocity triangles at the impeller inlet (U1, C1, W1) and exit (U2, C2, W2) ...................................................................... Actual and Ideal diagrams at exit from an impeller caused by slip. Velocity diagram at the impeller exit with slip ............................. Fluid rotation relative to impeller and the resulting slip velocity ........ Velocity diagram at impeller exit ............................................ Conservation of energy equation and rothalpy in the rotating impeller .......................................................................... Nomenclature of impeller and diffuser geometry .......................... Vaned diffuser .................................................................. Vaned diffuser configurations ................................................ Arrangement of diffusers and impeller ...................................... Volute throat area .............................................................. Volute throat velocity ......................................................... Separated “Jet-Wake” flow in impeller ..................................... “Jet-Wake” flow pattern criterion ............................................ Fraction of streamline length ................................................. Pressure difference across the impeller blade: Blade Loading ........... Typical performance characteristics for a centrifugal pump of a given size operating at a constant impeller speed; Head Pump, Efficiency, Power-Flow Curve at constant speed ........................................ Head versus flow rate showing pump characteristics with unstable range .............................................................................. 35 36 36 36 37 37 37 38 39 39 40 40 4O 41 41 41 42 42 43 43 44 44 44 45 45 46 47 47 48 48 49 49 Figure 1.33 Figure 1.34 Figure 1.35 Figure 1.36 Figure 1.37 Figure 1.38 Figure 1.39 Figure 1.40 Figure 1.41 Figure 1.42 Figure 1.43 Figure 1.44 Figure 1.45 Figure 1.46 Figure 1.47 Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6 Figure 2.7 Figure 2.8 Figure 2.9 Figure 2.10 Figure 2.11 Figure 2.12 Figure 2.13 Figure 2.14 Figure 2.15 Head and flow coefficient diagram. The slip coefficient shown is for six blades ........................................................................ Effect of losses on the centrifugal pump head-flow rate curve .......... Flow velocity profiles in clearance between rotating impeller face and housing ..................................................................... Balancing of axial thrust on impeller: leakage flow ....................... Inlet blade incidence: (a) increased flow rate, Q >Qo; (b) reduced flow rate Q—-1 ‘ :17 (II? (to r _ .3 .7 (I (‘17 LA- ‘ 1 ”—1 Figure 2.16 Figure 2.17 Figure 2.18 Figure 2.19 Figure 2.20 Figure 2.21 Figure 2.22 Figure 2.23 Figure 2.24 Figure 2.25 Figure 2.26 Figure 2.27 Figure 2.28 Figure 2.29 Figure 2.30 Figure 2.31 Figure 2.32 Figure 2.33 Figure 2.34 Figure 2.35 Figure 2.36 Figure 2.37 Figure 2.38 Figure 2.39 Figure 2.40 Figure 2.41 Figure 2.42 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Mechanical retumless system using in-tank regulation .................. Mechanical fuel pump ........................................................ Mechanical fuel pump assembly ............................................ Section view of a mechanical diaphragm pump on the inlet and outlet strokes ................................................................... The AC-Delco fuel lift pump, with the inlet valve on the right and the delivery valve sectioned on the left. It has a glass dome retained by a stirrup. Under the dome is the inlet stack pipe, capped by a fine mesh filter for trapping water ....................................................... (a) SU AF700 fuel lift pump, and (b) SU AF800 fuel lift pump ........ Weber double diaphragm fuel lift pump. The inlet valve is on the left and the outlet on the right, above it, a domed accumulator to damp out pulsations ................................................................... The AC lift pumps for diesel engines ........................................ Representation of the Bosch plunger type pump .......................... An AC plunger type pump with, embodied on the right, a manual- priming pump ................................................................... Common problems with a mechanical pump .............................. Electric fuel pump components .............................................. Some models use an inertia switch to turn off the electric fuel pump in an accident ................................................................... Electric fuel pump with impellers ........................................... Electric fuel pump system located inside the fuel tank .................... Electric fuel pump located outside the fuel tank ........................... Bellows-type fuel pump ....................................................... The SU electric pump .......................................................... The SU electric fuel-lift pump ................................................ Weber plunger type electric fuel-lift pump ................................. The Weber roller-cell type pump with a section through the roller chamber .......................................................................... Roller-cell positive displacement pump - electric pump .................. The AC in-tank fuel pump .................................................... Bosch two-stage low-pressure rotary electric fuel pump ................. The AC Universal Electronic solenoid type pump ......................... In this AC medium pressure twin turbine fuel pump, the first stage impeller removes vapor by centrifuging the fuel outwards and thus leaving the vapor in the center, when it is returned to the tank. The delivery pressure is about 1 bar .............................................. Diagrammatic illustrations of five different fuel-pump Arrangements ................................................................... Efficiency as a function of specific speed and capacity ................... Efficiency of centrifugal pumps versus specific speed, size, and shape ............................................................................. Cm3/U2 versus specific speed ................................................. Impeller discharge angle versus specific speed ............................ Hydraulic efficiency versus capacity ........................................ xi 96 97 97 98 98 99 99 100 101 102 102 103 104 104 105 105 106 106 107 107 108 108 108 109 109 109 110 126 127 128 128 129 Figure 3.6 Figure 3.7 Figure 3.8 Figure 3.9 Figure 3.10 Figure 3.11 Figure 3.12 Figure 3.13 Figure 3.14 Figure 3.15 Figure 3.16 Figure 3.17 Figure 3.18 Figure 3.19 Figure 3.20 Figure 3.21 Figure 3.22 Figure 3.23 Figure 3.24 Figure 3.25 Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10 Figure 4.11 Figure 4.12 Figure 4.13 Figure 4.14 Figure 4.15 Figure 5.1 Figure 5.2 Figure 5.3 Vaned diffuser .................................................................. 129 Vaned diffuser with throat area .............................................. 129 Impeller profile ................................................................. 130 Impeller inlet velocity triangles .............................................. 130 Impeller velocity diagrams ................................................... 131 Impeller outlet velocity diagram ............................................. 131 Impeller discharge velocity triangles ........................................ 132 Can/U2 versus specific speed ................................................. 132 AMA“ versus specific speed ................................................. 133 Volute casing ................................................................... 134 The plan view of the impeller and the volute casing with leading dimensions ...................................................................... 135 Volute casing: a) Polar view; b) Meridional view including Section A-A of throat T ................................................................. 136 Volumetric efficiency as a function of specific speed and capacity. . 137 Ratio of mechanical power loss to water power as a function of specific speed and capacity ................................................... 137 Impeller with vanes extended into axial inlet .............................. 138 Impeller with cylindrical vanes ............................................... 138 Logarithmic spiral .............................................................. 139 Blade construction ............................................................. 140 Defining the geometry of a pump stage ..................................... 141 Hub and shroud profiles of centrifugal pump impeller ................... 141 Volute Constants ............................................................... 175 Impeller Constants ............................................................. 176 Pump Efficiency versus Specific Speed and Pump Size -Worthington .................................................................... 177 Secondary Flow in Bends ..................................................... 178 Bend Coefficients in Resistance of Bends Found by Various Investigators ..................................................................... 178 Character of the Flow in a 900 Bend and the Associated Loss Coefficient ...................................................................... 179 Resistance of 900 Bends ....................................................... 179 Variation of Resistance Coefficient K (= f UD) with Size .............. 180 Ideal Impeller Velocities (V1, W1; V2, W2 Without Slip Effect) and Actual Impeller Velocities (V1. , W1. ; V5,, W5 With Slip Effect) at Inlet and Exit .......................................................................... 181 Flow Through A Blade Passage .............................................. 182 Determination of 00 ............................................................ 183 Volute Element ................................................................. 184 Tangential Velocity of Fluid at any radius Vt“) ............................ 185 Forces and Velocities in an Impeller ........................................ 186 Logarithmic Profile ............................................................ 187 Pump Efficiency vs. Volume Flow Rate for P420 Blade Impeller ...... 195 Pump Efficiency vs. Volume Flow Rate for P430 Blade Impeller ...... 195 Pump Efficiency vs. Volume Flow Rate for P470 Blade Impeller ...... 195 xii figu figu figu figu figu fig; fieu figzu figu figu 1V F1511 Figure 5.4 Figure 5.5 Figure 5.6 Figure 5.7 Figure 5.8 Figure 5.9 Figure 5.10 Figure 5.11 Figure 5.12 Figure 5.13 Figure 5.14 Pump Efficiency vs. Pump Efficiency vs. Pump Efficiency vs. Pump Efficiency vs. Pump Efficiency vs. Pump Efficiency vs. Pump Efficiency vs. Pump Efficiency vs. Pump Efficiency vs. Volume Flow Rate for P490 Blade Impeller ...... 196 Volume Flow Rate for P620 Blade Impeller ...... 196 Volume Flow Rate for P630 Blade Impeller ...... 196 Volume Flow Rate for P670 Blade Impeller ...... 197 Volume Flow Rate for P690 Blade Impeller ...... 197 Volume Flow Rate for P820 Blade Impeller ...... 197 Volume Flow Rate for P830 Blade Impeller ...... 198 Volume Flow Rate for P870 Blade Impeller ...... 198 Volume Flow Rate for P890 Blade Impeller ...... 198 Un-conventional Centrifugal Pump Assembly Volute cover is removed, (Z = 4, B2 = 700, n = 65.0498%) .............. 201 Un-conventional Centrifugal Pump Assembly Cutting Section A-A (z = 4, [52 = 70°, 11 = 65.0498%) .................... 202 xiii NONU ALPH .5 ‘l . ,. .:.\4 v: ~Ni rd... l.‘ .| m . T . .I .5 Asia abnohmkuttnwtCCFWO.QFWFWCPWDMDDUDWDdd..nw~ElrLtrrF outeumHHHtH NOMENCLATURE ALPHABETICAL A Cross-sectional area A0 Clearance area between the tip of the tongue and the impeller periphery; Volute cross-sectional area at tongue clearance Ae Volute cross-sectional area at exit As Shear area a Coefficient b Impeller Blade width B Blade width in the axial direction bm Mean blade width bo Housing inside axial width in the volute region be Housing axial width at exit c Clearance width C Absolute velocity Ca Volute area variation constant Cd Volute hydraulic diameter variation constant Cf, Friction coefficient Cdi, Discharge coefficient CH Head coefficient Cq Volute flow variation constant CQ Capacity coefficient D Diameter Db Hydraulic diameter Do Volute hydraulic diameter at tongue clearance De Volute hydraulic diameter at exit Dv Volute hydraulic diameter Db Hydraulic diameter Dmi Impeller mean hydraulic diameter d Impeller diameter d, Pump Inlet diameter dm Mean Impeller diameter E Rate of internal energy change f Volute friction factor fc Friction coefficient F Weight at moment arm Ft Tare weight g Gravitational acceleration gc Gravitational constant hc Head drop across the wear ring HV Volute head loss H Pump output head Hc Euler head He Circulation head xiv It. “l. S M ii \\ . .1 .1: .t. . n .t .a 1.3 .D. .l . .. . IL .i 6 AL 6 m l .. RUMHmUWl LA ”NKaLLm humuNbrtnDDtpDuuDHLDIDIUDwiDWPQDQQTRRRRRSSTLIRTTLV Head due to finite number of blades Head loss due to entrance bend Friction head loss Output head for impeller with k number of blades and blade angle j Theoretical head Rothalpy 2 Hub-to—Shroud ratio, R = 1 — {Eh—J I.S Bend coefficient Stodola coefficient Blade length, the length of the channel Passage length Constant in disk friction loss Constant in disk friction loss Hydraulic radius of the channel section Impeller rotational speed Specific speed Net Positive Suction Head Pressure in volute element; Power Perimeter Power loss due to disk friction Power loss due to leakage Pump input power (theoretical) Pump output power (theoretical) Pressure on pressure side Pressure on suction side Total pressure Volume flow rate through A0 Volume flow rate/Pump capacity Leakage volume flow rate Radial direction; Impeller radius Impeller radius Wearing radius Reynolds number Impeller Reynolds number Volute Reynolds number Slip velocity Mean slip velocity Blade thickness Tongue clearance between the impeller and the tongue Volute radial clearance at exit Torque Peripheral velocity Velocity at the section with the hydraulic radius (mh) XV afiwiflnutnvnmato °..onUnqulAm .rtr Sl'PE H C §<5<< .— D 89"? “Nééé F: .8. ['11 7'1 3 (DOD-9'9 02mm peaosqeo “(/1 Absolute velocity Radial velocity Tangential velocity Tangential velocity Impeller mean velocity Relative velocity Pump output power Pump input power Number of impeller blades Axial direction Flow angle Flow angle at tongue clearance Blade angle Mean blade angle Axial clearance between impeller and housing Volute angle Flow coefficient Impeller circular angle Imaginary angle subtended by fluid Impeller friction factor Angular velocity Dynamic viscosity; Slip coefficient Kinematic viscosity Slip coefficient Pump efficiency Density Shear stress Head coefficient Incremental UPERSCRIPTS Ideal SUBSCRIPTS waaarvww— Impeller inlet Impeller exit Impeller discharge Blade Fluid; Flow Theoretical; Throat Meridional Ideal Radial xvi THSSUXWn—U chcmmme Tangential Hw fimw Suction Tangential; Circumferential Axial ww Tangential xvii Chapter 1 INTRODUCTION TO CENTRIFUGAL PUMP 1.1 Introduction A single-stage centrifugal pump consists of the inlet without an inducer or the inlet with an inducer at its center, the impeller, the diffuser, and the volute (Figure 1.40). When the impeller rotates, the liquid is sucked in through the eye of the casing near the axis of a hi gh-speed impeller and then the impeller will radially discharge liquid into the volute surrounding the impeller by the centrifugal force. The blades of the centrifugal pumps push the fluid in the direction of the blade motion. Therefore, the rotating impellers impart energy to the fluid, so work is done on the fluid by the rotating blades. This creates a large increase in kinetic energy of the fluid flow flowing through the impeller. This kinetic energy is transferred into an increase in pressure as the fluid flows from the impeller into the volute enclosing the impeller. As a result, both pressure and absolute velocity of the fluid are increased as the fluid flow from the eye to the periphery of the blades. The centrifugal pump can be classified as the single-stage and multi-stage pump. A single-stage centrifugal pump has only one impeller. Multi-stage centrifugal pump has two or more impellers in a single volute. The impeller can be a single suction or double suction. A single-suction impeller admits the liquid on only one side of the impeller. A double-suction impeller has two suction inlets, one on each side of the impeller. lire: The advantages of the centrifugal pump are as follows: 0 Compactness and low cost in large sizes 0 Smooth flow through the pump and uniform pressure in the discharge pipe 0 Power characteristics that make it an easy load for its driver. An increase in head reduces the power required, a characteristics that makes overloading of the motor by closing the discharger impossible. 1.2 Basic Components of A Centrifugal Pump The single-stage centrifugal pump consists of four main components: the inlet with the inducer or the inlet without the inducer, the impeller attached to a rotating shaft, the vaneless and vaned diffuser, and the volute enclosing the impeller (Figure 1.9 and Figure 1.40). Centrifugal pump can be single stage or multistage. For the single-stage centrifugal pumps, only one impeller is mounted on the rotor shaft. For the multi-stage centrifugal pumps, several impellers are mounted on the rotor shaft and a return channel (Figure 1.42) is used between the two single-stage centrifugal pumps. 1.3 Inlet and Flow Mechanism in the Inlet The simplest inlet system in centrifugal pumps is the straight pipe coaxial with the impeller centerline. However, space and suction system layout requires a ducted inlet. These can cause undesirable inlet velocity profiles and strong three-dimensional flow patterns in the eye of the impeller. This is particularly true in double suction impeller, where the shaft passes through the flow on both sides of the impeller. There are three alternatives of suction inlet system for an end suction pump. o A coaxial cylindrical straight suction line (Figure 1.1 a) 0 An inclined cone type suction (Figure 1.1 b) o A flared inlet that may be used for vertical designs (Figure 1.1 c) For the first alternative of the end suction design (Figure 1.1 a), the optimum inlet pipe is provided by a straight inlet pipe because this offers the best inlet flow patterns. The inlet line is often larger than the pump eye diameter, which is provided to reduce the suction line velocities and losses. For the second alternative (Figure 1.1 b), a conical reducer is provided for the inlet system because of installation reasons. This will give a more confused flow in the impeller eye. When there may be gas in the fluid, or solids are being carried, an offset reducer may be used. This assures that gas pockets do not form on shut down and also provides a route for solids to move away from the impeller when flow ceases. For the third alternative (Figure 1.1 c), a flared inlet is used for the vertical designs. This illustrates a bell mouth intake used when liquid is taken from a tank or vessel. The diameter Do is empirically determined from the design chart (Stepanoff 1976) or the approach to limit cavitation. Inlet zero whirl is assumed at design flow. If the inlet diameter Do is too large, re-circulation can occur. The flow patterns can arise at part flow observed by Grist (1988) (Figure 1.5 and Figure 1.8). If the diameter Do is too large, this re-circulation can occur at a flow rate quite close to the design value, and can result in an increase in the NPSH required. The re-circulation can cause the flow loss for the flow pattern. Hence, it is only the solution when the margin between NPSHR (Net Positive Suction Head required) and NPSHA (Net Positive Suction Head available) allows. 1.4 Inducer CC 811 Ht In some pump applications, the centrifugal pump provides a very low suction pressure to the impeller, and so this results in the cavitations in the pump. In order to avoid or mitigate the cavitation, a simple axial pump upstream from the impeller of a centrifugal pump, called an inducer (Figure 1.6), is used in the suction immediately before the impeller. This small pump is a high specific speed machine and provides a small pressure rise to increase the fluid energy in the main impeller suction. Therefore, the inducer can reduce the risk of cavitation problems and provides the NPSER (Net Positive Suction Energy required) of the centrifugal pump. In reality, the inducer tends to erode. However, it is cheaper to replace the inducer than the main impeller. Moreover, inducer allows bringing the fluid into the centrifugal pump more smoothly. Inducer consists of axial flow rotors with spiral-shaped blades (Figure 1.6). Designers use only three or four blades inclined 70 to 140 to the circumferential direction. The leading edge must be as sharp as possible. The axial or meridional velocity is kept low. The slight positive incidence is preferred because the inducer should make the flow leaving the inducer to meet the leading edges of the impeller blades at a reasonable incidence to minimize the incidence losses. The low axial velocity requires larger inlet cross sections than the normal impeller inlet. Consequently, pumps using inducers are intended for very low suction heads. They need an exceptionally large inlet cross section for the inducer. The flow passage cross section decreases at the centrifugal impeller inlet to increase the meridional velocity and results in reasonable inlet blade angles. The improvement in cavitation performance can be achieved (Figure 1.7). However, when comparing the performance between the impeller with inducer and the the im 15.1 1 318 3hr impeller without inducer, the improvement is not uniform across the flow range. The NPSH (NPSE) curve rises dramatically at low flow rate and high flow rate. 1.5 Impeller The impeller contains radial flow passages formed by rotating blades arranged in a circle. The flow enters axially near the center of rotation and turns in the radial direction inside the impeller (Figure 1.41). 1.5.1 Types of Impeller There are two types of impeller such as open impeller and shrouded impeller. For the shrouded impeller, the blades are covered on both hub and shroud ends. In the open impeller, the liquid enters the eye of the impeller where turning impellers add energy to the fluid and direct the liquid to the volute. A narrow clearance between the impellers and the casing is necessary to prevent most of the fluid from re- circulating back to the eye of the impeller. There are some characteristics of the open impeller as follows: 0 The efficiency can be maintained through impeller clearance adjustment. 0 The impeller can be easily adjusted for wear and so the pump can remain close to its best efficiency. The centrifugal pump doesn’t necessarily have to disassemble for the best efficiency. 0 The open impeller is less probable to clog with solids, and it is trouble-free to clean. 0 The pump is less expensive to manufacture with a simple open impeller design. 0 The open impeller has all the visible parts. 0 The open impeller can easily be cut or filed to increase the capacity. 0 Th rate lnl the impell betueenth fit ° It is ' Tm chi ' The ma ' Tm mu ' The uh . The im; . 11 is ' l‘nt Pm FgrlheSin meeller‘ F 0 The open impeller can provide a greater range of specific speed choices and flow rate. In the shrouded (closed) impeller, the liquid enters the eye of the impeller where the impellers add energy to the fluid and direct it to the volute. There is clearance between the impellers and the pump volute. There are some characteristics of the shrouded impeller as follows: 0 It is good for volatile liquids. - The shrouded impeller is very efficient at the beginning, but later it loses the efficiency as the shrouded impeller clearance increases because of wear. 0 The shrouded impeller adjustment is impossible. Therefore, the pump had to be disassembled to check the status of the wear. 0 The shrouded impeller can clog. It is difficult to clean out the solids between the shroud and the shrouded impellers. o The shrouded impeller is difficult to cast because the internal parts are hidden and difficult to inspect for flaws. o The closed impeller is a more complicated and expensive design because the impeller shape is required and the additional wear rings are needed. 0 It is difficult to modify the shrouded impeller to improve its performance. 0 The specific speed and flow rate ranges are limited because of the shape. Pump impellers can be categorized as the single suction and the double suction. For the single-suction impeller, the fluid enters through the eye on only one side of the impeller. For the double suction impeller, the fluid enters the impeller along its axis from determ ll Oper must b lmp’éllt assumc- to zero “Thule (111165 5111111613 ”COM. 1A «J cure timer ’1'! both sides. The double suction impeller can reduce the end thrust on the shaft, and so the net inlet flow area is larger, inlet velocities are reduced. 1.5.2 Flow Mechanism in the Impeller The shape of the impeller blades and the resulting flow pattern in the impeller determine how much the energy is transferred by a given impeller size and how efficient it operates. In order to evaluate the values of the exit angular momentum, the velocities must be examined at the inlet of the impeller (the leading edge of the blades), and at the impeller exit (the trailing edge of the blades). The flow entering the impeller is usually assumed to have no pre-whirl, and so the circumferential velocity component Cu is equal to zero. This assumption is valid for fluid flow on one particular streamline. The flow in a centrifugal impeller is highly complex. It is three-dimensional, turbulent, viscous, and unsteady. The flow at the impeller exit is highly non-uniform and differs from the one-dimensional calculation. The flow mechanism in the impeller was studied from three different areas: (1) “Jet-Wake” flow pattern, (2) Boundary layers and secondary-flows region, (3) Flow separation in the impeller. a. A “J et-Wake” flow pattern In the impeller, a shear layer, or separation streamline, between two flow regions of different fluid energy is stabilized if the acceleration and corresponding pressure rise perpendicular to the shear layer are directed from the low-energy region toward the high- energy region. When separation appears in the impeller, two flow regions of different energy can be distinguished: the separated region and the main stream flow region (Figure 1.27). The relative velocity (W) remains constant, but the values are different on either side of the streamline separating the two regions. The acceleration, and corresp lowent region. rrigrute 013 its rear th: sense 0 Expect: b- A 111' corresponding pressure increase, is directed from the suction side to the pressure side. A low-energy separated region on the suction side will be stable. A low-energy separated region, a boundary layer on the pressure side, would be unstable and would tend to migrate along the hub and shroud surfaces to the suction side. The flow pattern consisting of a stable separated region or “wake” on the suction side and a mainstream flow or “jet” near the pressure side of the blades is called “a jet-wake” flow pattern (Figure 1.27). The blades in most centrifugal pumps lean strongly backward, and so the flow angle (B) of the separation streamline from the radial in the direction opposite to the sense of rotation is relatively large. Consequently, “a jet-wake flow pattern” would not be expected in centrifugal pumps (Figure 1.28). b. A boundary-layers and secondary-flows region Moreover, the flow then enters the region of axial—to-radial bend. In this region, “boundary layers” and “secondary flows” will be developed in impellers after the liquid enters the blade impeller. In the radial part of the impeller, the balance between the local (blade-to—blade) pressure gradient sets up a secondary flow, which drives low-momentum fluid onto the blade suction side. This creates a separation zone towards the impeller tip. Separation in both the meridional plane and the blade-to-blade plane produces a “jet ” and a “wake” region at the impeller tip. The fluid in the “wake” region has very low fluid velocity relative to the flow elsewhere. High friction losses will happen as the “boundary layers” develop along the blade passages. “Secondary flows” contribute to the deterioration of the pump performance by different means. They contribute to the destabilization of the flow; hence eventually this promote the tumi c. How 1W1. ale measure defined and the suction bél‘ti €81 “blade dlifEtep 1011111 1'1 g SiPéitau bl 313p} 1011mm radial d promotes the separation of the flow near the shroud-suction side region. They also affect the turning of the flow and the associated pressure rise in the centrifugal pump. c. Flow separation in the impeller To illustrate the flow condition in the impeller, the plot of the relative velocity (W), along the pressure and the suction side of the blade, against the streamline length, measured from the leading edge, is constructed (Figure 1.29). The “blade loading” is defined by the relative velocity difference in the impeller. Because of the blade loading and the pressure difference across the blade, the pressure side velocity is lower than the suction side compared at the same fraction of the streamline length. The difference between the velocities on either side of the blade illustrates the pressure difference or “blade loading”, but only qualitatively. For a quantitative measure of the pressure difference, the squares of the velocities need to be plotted. From the plot, if the blade loading becomes too large, the velocity on the pressure side approaches zero. The flow separation must be avoided. An approximate estimation for the appearance of the separated flow is obtained by applying the principle of the angular momentum change to a very narrow annular volume (Figure 1.30). If the incremental increase in the angular momentum over a small radial distance of Ar is p(ACtrt), the pressure difference across the blade is _ _ AT _ Q _2_np(AC.ri) PP PS—Z(Ar)(Brl)—21t(Brl)Z (Ar) (1'1) PP --1>S =2—Z"cr flag—SQ (1.2) From the above equation, the energy added to the fluid is proportional to the pressure difference across the blade, which is the blade loading. In the flow passage TE \ pi. between two blades, the pressure decreases in the circumferential direction, approximately linear, from the “pressures side” of the blade facing in the direction of rotation to the “suction side”. As a result, there is a corresponding increase in the velocity from the “pressures side” to the “suction side” in the impeller. If the blade loading and the pressure difference across the impeller blade (Figure 1.29) become very high, the velocity at the pressure side of the blade can become very small or vanish. This results in flow separation or losses. Generally speaking, the “blade loading” provides a measure of the likelihood of the flow separation. In centrifugal pumps, the inlet relative velocity (W1) is usually larger than the exit relative velocity (W2). Therefore, certain diffusion, slowing of the velocity, must take place in the impeller and this diffusion should not be excessive. A tolerate velocity ratio for this required diffusion is W2/ W1 = 0.7. “Separation losses” and increasing flow losses would then present when the velocity ratios are beyond this value. The first flow separation in the impeller usually appears on the shroud and on the suction side of the blades. The highest inlet velocity occurs at this location, and the greatest diffusion deceleration takes place. A sharp curvature of the shroud in the radial plane contributes to the likelihood of separation and this should be avoided. The good centrifugal pump design demands that the “blade loading” and the corresponding velocity difference between the pressure sides and suction sides gradually grow at the inlet and taper off at the exit. 10 equ I012} The core The 51 Theht mi pu miPUu 1.5.3 Governing Equations The torque, the power and the theoretical head are determined by the Euler’s equation when the principle of conservation of angular momentum is applied. For a rotating shaft, the power transferred, Wshaft , is given by T = Tshaft = Q19 Ct2r2 ‘13 Curr ) = Q9 ( Ct2r2 ‘ Curr ) = m ( Ct2r2 — Curr) (1-3) wshaft =P=Tm=QP1Ct2r2 ‘Ctrrr)(°=PQchg (1.4) The power supplied to the shaft of the pump is transferred to the fluid by the following equation U1: I1(D,U2 = r2 (1) (1.5) Wshaft = shaft 03 =QP1Ct2f2 _Ctlrl)(0 = QP(Ct2U2 _CtlUl) (16) The shaft power per unit mass of flowing fluid is W wshaft — QShSfl =Ct2U2 _CtlUl (1-7) The theoretical head in the Euler’s equation is described by (Carz —Ct1ri)m = Ct2U2 —CtlUl g g H,h = (1.8) The pump ideal (theoretical) head rise is the work per unit weight added to the fluid by the pump. This ideal head rise can be presented by a different way. W wshaft = QShSfl =Ct2U2 —CtlUl (1-9) The following relation is established from the velocity triangle (Figure 1.12) C2 =c,2 +c;’; (1.10) Ci+(c,—U)2 =w2 (1.11) 11 The re the c; 11; - Crumb ‘16 rot Ctnm‘fL 111116161 dl‘L'HEIe 211mgSt . Cut ii. Ci+Cf—2C,U+U2=W2 (1.12) C2+C2+U2—W2 2 2_ 2 C,U= * ‘2 =C ”LUZ w (1.13) Wm, = W =c,,u,-ct,u, z(Ci-Cil+1U§—Ui)-1W2’-Wf) 1.14 2 ( ) The result of the theoretical head is U - U Hth J30 2 CH 1 =§1_[(c§-cf)+(U§-Uf)+(w,2-w§)1 (1.15) g g The first term, (Cg — C12), represents the increase in the kinetic energy of the fluid (the change in absolute kinetic energy occurring in the impeller). The second term, (U; - U12 ), represents the pressure head rise that develops across the impeller due to the centrifugal force. In other words, this represent the change of energy due to movement of the rotating air from one radius of rotation to another. This change of energy is the centrifugal energy, which raises the static pressure in the impeller. This term makes a difference between the centrifugal pump and the axial pump. The inlet (re) and exit diameter (re) of the axial pump has the same value, and so “U2 = retro” and “U1 = rim” are almost the same. However, The inlet diameter of the centrifugal pump is smaller than the exit diameter of the centrifugal pump, and so U2 and U; are different. The third term, (W12 —W22), represents the diffusion of the relative flow in the blade passage. In other words, this term expresses the change in kinetic energy due to the change of the relative velocity, and this results in a further change of static pressure within the rotor. Normally, the fluid has no tangential component of velocity Cu, or “no pre-swirl” (no Inlet Guide Vane, IGV), when the fluid enters the impeller. This means that the angle 12 between the absolute velocity and the tangential direction is 900 (or; = 900). As a result, the centrifugal pump is usually designed for no angular momentum at the inlet, Cur = 0. Hence, the theoretical head in Euler’s head equation is simplified by ch : 1" :: " : ['(U) (1.16) 1.5.4 Velocity Triangles of the Impeller The flow conditions, the velocities and the pressures in the impeller are described in terms of cylindrical coordinates: r, 0, 2. In the cylindrical coordinates, the three absolute velocity components are designated C,, C,, and C1. In the cylindrical coordinates, the three relative velocity components are designated W,, W1, and W2. The sign convention of velocity triangle has the absolute angle (or) and the relative angle (B) with respect to meridional direction (radial direction); or the absolute angle (or) and the relative angle (B) with respect to the tangential direction (Figure 1.43). The impeller inlet velocity triangles (Figure 1.44) and the impeller exit velocity triangles (Figure 1.45) are defined with both systems of sign convention of absolute angle (or) and relative angle (B). The components C12 and C,2 in the circumferential and radial directions construct the resultant absolute velocity C2. c; = C3, +c32 (1.17) Ct2 =U2 —Wt2 =U2 —W,2tanBF2 (1.18) The theoretical head, the energy added to a unit mass of fluid by the pump, can be written U2ct2 _ U: " Uzwrztanfirz g g (1.19) 13 The expression of the theoretical head is very important for calculating pump performance and for designing new centrifugal pumps. 1.5.5 Slip Factor and Various Slip Factor Equations The fluid entering the impeller can be considered to be irrotational. When the flow is viewed in the rotating frame of reference, a relative eddy rotating in a direction opposite to the impeller is required to maintain the flow irrotational in the absolute frame. More clearly, the flow will not be perfectly guided by the blades due to the presence of this relative eddy. Because of these phenomena, the fluid that flows through a radially bladed centrifugal impeller leaves the impeller tip with a fluid velocity component in the tangential direction that is less than the blade tangential velocity of the impeller tip. Therefore, the fluid must “slip” with respect to the impeller during its passage through the impeller. In other words, the relative flow leaving the impeller of a centrifugal pump will receive less perfect guidance from the vanes under the frictionless conditions. As a result, the flow is said to slip. Because of the slip, the actual flow does not follow the blade exactly. The flow angle B22 is not identical to the blade angle B2, because the relative exit velocity W2 is slightly more inclined opposite to the direction of rotation. This deviation takes place because the fluid, which retains its orientation in the absolute frame of reference, appears to rotate with respect to the rotating impeller in the opposite direction. This results in a tangential velocity component at the impeller exit opposed to the direction of rotation. A slip factor is defined by the ratio of the flow tangential absolute velocity C92 to the blade tangential absolute velocity C132 (Figure 1.16). In general, the slip factor is 14 described as a function of the impeller geometry and the number of blades on the impeller. o:,,=_ (1.20) The slip factor can be defined as fl£=CBZTCGS =1__Ci (121) C132 C02 C67 ‘- To compensate for this deviation of slip, a correction applied to the equation of the theoretical head is the slip coefficient 0. g g The slip factor is distinguished between the radial vaned impeller (no back sweep and no forward sweep)(B2b = 900), and backward vaned impeller (impeller with back sweep, backward-curved blade) (B21, < 900) or forward vaned impeller (impeller with forward sweep, forward-curved blade) (B21, > 90°). C o The slip factor for radial vane (B21, = 900) is o = Ufl; (1.23) 2 o The slip factor for backward vane (B21, < 90°) or forward vane (B21, > 90°) is (WEE: C02 = C92 (1.24) C62 COZ-Theory COZ-ldeal The flow coefficient is defined by C Cr in ¢2=—‘“2-=——2=-——— (1.25) U2 U2 Azszz 15 There are several different definitions for slip coefficients used for centrifugal pump design as follows: 1. Eck slip correlation: (B21, at 90°) C92_ C92 : C92 : 1 (1.26) CB2 CGZ-Theory COZ-ldeal l + 8111(sz ) 2211—3] d2 0 ___ C92 :1_(1r/Z)cos(B2b) =1— (1r/Z)cos(B2b) (1.27) 002-..... 1—¢. tanmz.) 1-(C.2/U2)tan(i32b) G: 2. Stodola slip correlation: (B21, ¢ 900) Or: 0 =l—gsinB2b (1.28) For straight radial bladed impellers: (B23: 90°) oz-Ci2=1—lsin13§] (1.29) U2 2 If a large number of impeller blades are assumed, the approximation sin(27t/ Z) E 21t/ Z is valid and the slip factor equation becomes o=1——l-E=1—£ (1.30) 2 z z 3. Stanitz slip correlation: (B21, ¢ 900) [0.6319] C62_ C62 C92 :1 Z (1.31) C132 COZ-Theory €92-1de 1 — ¢2 “1MB 2b) O: For straight radial bladed impellers: (sz = 900) C 21: . 1t . o = TIE =1— 0.315(—Z—]srn (2)2 =1— 063121811] ¢2 (1.32) 2 l6 c . Orzo: .92: C92 = CW =1—0.63%:—_1—-:— (1.33) C92 CGZ-Theory COZ-ldeal . Wiesner slip coefficient (Wiesner 1967): (B21, ¢ 900) C92 =1— \lcos(B2b)/ZO'7 o = (1.34) C92-ldeal 1 .- ¢2 tan(B 2b ) . Coppage slip correlation (Tom Sawyer): (B21, ¢ 900) — d d 0: C02 :1_ 1. , d, :M (1.35) COZ-ldeal 1+ M?— 2 2 Z[1- 91—] d2 . Balje slip correlation for radial bladed impellers: (B21, = 900) C Z 1'1 Z + 6.2[-—] r2 . Busemann slip correlation: (B22, at 90°) ,1sin O = C92 : l _ OEZD (1.37) C Z ' 62-1deal Busemann analyzed the flow in impellers with “logarithmic spiral vanes” to obtain a somewhat accurate model for slip factor. . Pfleiderer slip correlation for radial bladed impellers: (B2b = 900) _C92 _ 1 0' U2 - 3.6 1+ Z[1_(rl/r2)21 (1.38) A more general form of Pfleiderer slip correlation (B21, ¢ 900) 17 0: C92 = l (1.39) COZ-Tdeal 1+ _a_ [1 + 921;) _______2____ Z 60 l—(rl/r2)2 For a volute: a = 0.65 to 0.85; For a vaned diffuser: a = 0.6; For a vaneless diffuser: a = 0.85 to 1.0 9. Stechkin slip correlation for radial bladed impellers: (B2b = 900) G = z (1.40) 10. Amsler slip correlation for radial bladed impellers: (B2b = 900) ozfizi—izsc—mztth—Z (1.41) 2 U2 Zr, 11. Yadav and Misra slip correlation for radial bladed impellers: (B22, = 900) o=_c,_,:1_o.855n2 cm, __ 1.42 U, 2 U, ( ) The slip coefficient does not represent an energy loss. It only affects the magnitude of the head produced by a given size impeller. For operation at low flow rates, the slip factor is affected by suction side flow separation, which generally begins near the shroud. The velocity on the suction surface near the leading edge increases rapidly with increasing incidence (i = B1f —- B1b ). 1.5.6 Relative Velocity in the Impeller and Rothalpy The inlet relative velocity is defined by W = U? + C3 = coir,2 + C? (1.43) The total enthalpy is found by applying the Bemoulli’s equation to the inlet 18 Ber The: 1.611 CTlCTg' 1.6.1 1 2 2_ 2 2 2 2 2 hozh,+—Ci=h,+XV—‘———£D—i=hl+w‘ —‘° ’1 (1.44) 2g 2s 2g 2s The rothalpy equation, which represents the relationship equivalent to the Bemoulli’s equation, applies in the rotating impeller in terms of the relative velocity W 2 (021.2 I = h + — — losses (1.45) 2g 2g The rothalpy is also called the relative energy (Wislicenus 1965). 1.6 Diffuser The diffuser, following the impeller, can transform kinetic energy into pressure energy but cannot increase the total energy of the fluid. 1.6.1 Flow Mechanism in Vaneless and Vaned Diffusers The vaned diffuser follows the impeller exit. A short radial distance, a vaneless space or a vaneless diffuser, precedes the vaned diffuser. The diameter of the vaned diffuser inlet is usually about 5% to 10% greater than the impeller diameter. The pressure and the relative velocity vary from the pressure side of the blades to the suction side at the impeller exit. As a result, a fluctuating flow comes off the impeller. If the leading edge of the diffuser vane is too close to the impeller, the flow fluctuations impose on the diffuser vanes and can produce undesirable noise and pressure pulsation at the exit. In order to preclude this noise and vibration of pressure pulsation, the vanes of the vaned diffuser are located at certain distance from the impeller tip, which creates the “vaneless space” between the impeller tip and the vaned impeller. The “vaneless space” allows the flow to mix, becomes more uniform, and adjusts to the inlet of the vaned diffuser. The pressure pulsations can be reduced by slating the leading edge of the diffuser vanes in the circumferential direction with respect to the trailing edge of the 19 .917“ pm 1.7 1119 '9» 51“. ‘4‘” I 1‘ J1] diffuser vanes. Instead of overlapping exactly at a certain moment, the trailing edge of the impeller blades sweeps gradually across the leading edge of the diffuser vanes. The flow accelerating into the diffuser throat will result in less head loss than the flow slowing down. Theoretically, the diffuser should be correctly matched at design flow conditions. This happens because the flow can accelerate at flow rates above the design flow rate and can slow down at flow rates below the design flow rate. 1.6.2 Governing equations The diffuser throat velocity, assuming straight vanes and sidewalls, is given by the expression CQ3 =_Q_: Q =C3 =C,El (1.46) As 21tR3B3cosB3 R3 1.7 Volute The liquid leaves the impeller at a high velocity. Hence, the volute-shaped casing shape is designed to gradually reduce the velocity as the fluid leaves the impeller. This decrease in kinetic energy of the velocity head created by the impeller is converted into an increase in pressure head needed in the discharge pipe. The volute-shaped casing, with its increasing area in the direction flow, is used to produce an essentially uniform velocity distribution as the fluid moves around the casing into the discharge opening. 1.7.1 Flow Mechanism in Volutes The impeller often discharges the fluid directly into the volute. Its cross section increases gradually around the impeller periphery, starting from the volute tongue and ending at the volute throat. The volute tongue directs the total flow, which is collected from around the impeller, through the throat to the pump exit flange. The diffuser may or 20 1.2 the Mr may not exist between the volute throat and the exit flange. This depends on the available space and the flow velocities. When the flow rate is greater than the design flow rate, the flow generally accelerates in the volute, and the pressure tends to decrease in the circumferential direction. When the flow rate is less than the design flow rate, the volute velocity tends to decrease, and the pressure increase circumferentially around the impeller. Because of this pressure increase or decrease, a transverse pressure force appears on the impeller at off- design conditions, which must be resisted by the pump bearings. At flow rates less than the design flow rate, the volute tongue deflects some of the flow approaching the volute throat, which passes between the tongue and the impeller, and return into the volute. If the space between the tongue and the impeller is very large, too much flow return unnecessarily, and losses will increase. If the space is too small, strong pressure fluctuations at the blade frequency can occur. 1.7.2 Governing Equations The volute throat cross-sections are calculated from the flow rate and from an average tangential velocity at the volute cross-section center. The flow model assumes that the impeller exit tangential velocity decreases in proportion to the radius to maintain constant angular momentum. The volute throat cross-sections is defined by A = m (147) CQR ,/r 1.8 Design Considerations and Sixteen Principal Design Variables From the hydraulic standpoint, the ideal blade thickness will be zero. In reality, the hydraulic load must be taken, and the blades and shrouds must be thick enough to withstand them and also. give the stable structure to the impeller. As a result, the normal 21 casting thickness needed for good casting ability with cast iron or the other common materials give a good margin against failure. Minimum casting thicknesses are based on good foundry practice. There are some important assumptions of casting ability in centrifugal pump design. Blade thickness: The minimum blade thickness = Impeller Diameter/ 100 but not less than 4 mm. Outlet passage width: The minimum outlet passage width = 3-4 (Impeller outside diameter)/ 100 but not less than 12 mm or larger than 10 times blade thickness. Fillet radii — Vane to Shroud and to back plate: These should not usually be less than half of the sections being joined. Thickness of central dividing rib in a double suction impeller: The minimum thickness should be at least 4mm and the radius therefore at 2 mm or half the thickness of the dividing rib. Sixteen Principal Design Variables 1. 2. Impeller rotational speed. Impeller Vane outlet diameter. Impeller eye (shroud) and hub diameter. Impeller number of vanes. Impeller vane inlet tip positions. Impeller vane inlet tip angles. Impeller profile width. Impeller vane outlet angles. Impeller vane shape between inlet and outlet. 22 10. Impeller vane length. 11. Impeller symmetry and concentricity. 12. Collector throat shape and area. 13. Collector vane inlet tip radius. 14. Collector vane inlet tip angles. 15. Collector diffuser passage shapes. 16. Impeller and collector surface finish. 1.9 Pump Performance Parameters and Dimensionless Design Coefficients 1.9.1 Overall Performance Parameters The centrifugal pump uses shaft power to increase the energy, pressure, or head of the fluid. The flow rate (Q), head (H), and efficiency (n) define the overall performance parameters of a pump. The pump head (H) corresponds to the increase in total pressure, from inlet flange to exit flange, divided by the specific weight of the fluid. The pump overall efficiency is the ratio of power actually gained by the fluid to the shaft power supplied. _ Net hydraulic power gained by the fluid (1 48) Shaft power driving the pump ' H = P02 ‘ P01 (149) P g In the English system of units (lbf, ft, sec, and psi), (assuming water pg = 62.4 lbf/ft3) - ~ 2 2 H(ft)= P(psr)(1441n 3/ft ) (1.50) 62.4lbf/ft - 3 Q(ft3/sec)= Q(gpm) 1231‘“ ’gal) (1.51) (60 sec/min) (1728 in3/ft3) 23 The net hydraulic power P delivered by the pump can be calculated from P(hp) = P(kW) (1.333hp/kW) p g (lbf/ft3) H(ft) Q(ft3/sec) (1.52) p = (hp) 550 (ft -lbf/sec)/hp In the SI system of units (N, m, sec, and PA), (assuming water pg =9806 N/m3) 2 H(m) = __I:(N_/m_)_3_ (1.53) 9806 N/m P(hp) = P(kW) (1.333hp/kW) (1 54) P(hp) = p g (N/m3) H(m) Q(m3/sec) (0.001333 hp/W) . Shaft power = m (1.55) '1 The overall pump efficiency consists of three sources: the hydraulic efficiency (111,), the mechanical efficiency (nm), and the volumetric efficiency (m). n = (ni)(nm)(nv) (1.56) The overall pump efficiency is defined as a function of specific speed and capacity (Figure 1.46). From the given specific speed and capacity, there are some selection for profiles of pump blade impeller (Figure 1.47). The overall pump efficiency is affected by the “hydraulic losses” in the pump and by the “mechanical losses” in the bearing and seals. There may also be some power loss due to leakage of the fluid between the back surface of the impeller hub plate and the casing, or through other pump components. This leakage contribution to the overall efficiency is called the “volumetric losses”. The “hydraulic losses” are caused by: (1) “skin friction” and (2) “eddy and separation losses” due to changes in direction and magnitude of the velocity of flow. The “eddy losses” and “separation losses” include the 24 so-called “shock losses” and “diffusion losses”. Losses at the impeller entrance and exit are usually called “shock losses”. The nature of the hydraulic losses at the impeller entrance is caused by a sudden expansion or diffusion after separation when liquid approaches at a high angle of attack. “Shock losses” occur at the cutwater of a volute pump and at the entrance of diffusion vanes when a diffusion vane casing is used. These losses are of the same nature as “shock losses” at the entrance to the impeller. They are called “diffusion losses”. Performance characteristics for a centrifugal pump and operating speed are usually given in the plot of head, efficiency, and power (Figure 1.31). The pump efficiency is a function of the flow rate and reaches a maximum value at the normal flow rate or design flow rate or capacity for the centrifugal pump. The points on the various curves corresponding to the maximum efficiency are call “best efficiency points” (BEP). At the pump's best efficiency point, the power going into the pump is the closest power to the power coming out of the pump. The pump’s best efficiency point allows the pump shaft to experience the least amount of vibration. The pump head varies as the flow rate changes. The pump performance is shown by a plot of the head as a function of the flow rate for a certain shaft speed (Figure 1.31). The efficiency — the ratio of the output power and the input power, is also a function of the flow rate. To select a centrifugal pump for a particular application, it is necessary to utilize both the “system curve”, as determined by the system equation, and the “pump performance curve”. If both curves are plotted on the same graph (Figure 1.31), the intersection (point A) of the “pump performance curve” and the “system curve” represents the “operating point” for the system. This point gives the head and the flow 25 rate that satisfies both the system equation and the pump equation. Ideally, the “operating point” should be near the Best Efficiency Point (BEP) for the centrifugal pump. The stability of an operating point can be determined by slightly moving the operating point and observing where the centrifugal pump comes back to its steady operating point (Figure 1.32). The operating point at the lower flow rate is unstable, and the operating point at the higher flow rate is stable. 1.9.2 Dimensionless design coefficients There are some dimensionless design coefficients, which are also used to evaluate the pump performance. They are Head coefficient and Flow coefficient (Capacity coefficient). C C Head coefficient 1;; =94; = "2 = ’97- : gH (1.57) U, U, U, nUfi Flow coefficient ¢ = ESE 9i - ———Q—— (1.58) The plot (Figure 1.33) reproduces the velocity diagram at the impeller exit in a dimensionless form. The tangential direction is along the vertical axis, and the meridional direction along the horizontal. As the flow rate changes, the operating point of the pump moves along the straight line of constant angle B2. The velocities, Ca, proportional to the theoretical head, and Cm2 proportional to the flow rate, fully determine the pump performance. Head coefficient from the velocity triangle: in = o — tanB2 (1.59) Due to the general complexity of flow through the centrifugal pump, the actual performance of the centrifugal pump cannot be accurately predicted on a completely theoretical basis as indicated by the data (Figure 1.34). The losses, which make the actual 26 head small The exterr internal 1e Moreover. “Remolds 1.10 Some 1.1010151 The impeller. T absorb shat between the centrifugal 1 “1151 that is with the tire accelerate th tall lends tr imiller lac arcumlerent subsramia”y The c disk pelpend “lite On the head smaller than the theoretical head, include the external losses and the internal losses. The external losses are “disk friction losses” on the impeller, “leakage losses”. The internal losses are “incidence losses”, “friction losses”, and “separation losses”. Moreover, the actual performance of the centrifugal pump is also affected by “viscosity”, “Reynolds number”, and “cavitations”. 1.10 Some loss factors influencing the pump performance 1.10.1 Disk friction losses on the impeller— External losses The practical hydraulic centrifugal pump must consider all hydraulic forces on the impeller. The circumferential, fluid frictional force on the impeller, and disk friction absorb shaft power and affect the overall pump efficiency. Clearance spaces must exist between the stationary housing and the rotating hub and shroud faces of the impeller. In centrifugal pump, the external faces of the impeller on the hub and shroud side resemble a disk that is rotating in a stagnant fluid (Figure 1.35). The fluid at the disk surface rotates with the circumferential velocity of the disk. The fluid shear at the rotating disk tends to accelerate the fluid volume in the clearance and the fluid shear at the stationary housing wall tends to slow it down. Consequently, the fluid volume in the clearance between the impeller face and the housing will rotate with a velocity about half that of the circumferential velocity of the impeller. The outer periphery of the disk contributes substantially to the total frictional forces. The circumferential velocity of the fluid in the clearance changes rapidly near the disk, perpendicular to the surface, over a certain small distance. A similar boundary layer exists on the housing wall. If the clearance between the impeller and the housing is much 27 :r than the thickness of these boundary layers, the clearance width does not nce the magnitude of the friction force, the disk friction, on the impeller. The boundary layer thickness, and more generally the flow pattern in the me space, can be affected by the leakage flow rate through the clearance space; an ximate value of the boundary layer thickness can be obtained. In general, the disk in losses of the pump will be minimized if the clearance width, between the impeller and the housing walls is made much larger than the boundary layer thickness. fore, the overall pump efficiency can be increased. 1 Leakage losses - External losses The flow pattern in the front clearance space of the pump, between the shroud and )using, is complicated. On the outer periphery, it connects with the fluid at the ler exit, and at the inner periphery, with the pump inlet (Figure 1.36). A sleeve with clearance, a wear ring at the pump inlet, restricts the leakage flow from the pump ack to the inlet. In general, the leakage of fluid through the annular space due to the re difference between entrance and exit section. Furthermore, leakage is not :d by rotation, as long as turbulent flow in the clearance space persists. Leakage 3 affected by rotation whenever rotation changes the state of the flow from laminar tulent in the ring space. This leakage flow is a drain on the high-energy flow delivered by the pump, and are reduces the pump efficiency. The leakage flow rate must be deducted from the ate through the impeller to arrive at the actual net flow rate delivered by the pump. ge flow is usually kept to 1% to 2% of the total flow to minimize leakage losses. 28 Leak. gorer the le equau €111 VI funnir iflaee Slfiges 1.10.3 Leakage calculations assume that the pressure drop across the wear ring clearance alone governs the leakage flow rate q. A simple orifice flow equation will suffice to estimate the leakage flow rate: q=Cdi527tch 2ghW (1.60) 1;th (Re—Re.) hw =(h2_h1)— (1-61) 2g The static head rise (ht-h2) across the impeller is calculated by using Bernoulli’s equation from the theoretical head (Hg) and the velocity heads of the absolute inlet and exit velocities, C1 and C2. 2 2 h2 —h1 :ch __C_2+_(_:]_ 2g 2s (1.62) Leakage losses represent the head loss due to the flow passing through the running clearance between the rotating element and the stationary casing part. It takes place between the casing and the impeller at the impeller eye, between two consecutive stages in a multistage pump. 1.10.3 Incidence Losses— Internal losses The flow separates at the leading edge of the impeller blade if the direction of the relative velocity W1 does not align with the leading edge (Figure 1.37). Correct pump design usually assures correct alignment between the velocity vector and the blade at the inlet at the best efficiency flow rate. At flow rates greater than design flow rate, the flow angle (Bpt) measured from the meridional or radial direction is smaller than the blade angle at the inlet (Bu, = B1). 29 This Thei “suet ineid the b beeor doe] incid. This produces a “separated flow region” on the “pressure side” of the blade (Bib > Bin)- The incidence (i =13” —B1b) becomes “negative incidence”. At flow rates lower than design flow rate, “separated flow region” occurs on the “suction side” of the blade (Bf-‘1 > Bib). The incidence (i = B1f —B1b) becomes “positive incidence”. The term “incidence” designates the difference between the flow angle and the blade angle: BFI— B1. The “separated flow region” on the “pressure side” of the blade becomes unstable with “negative incidence”. Flow oscillation and rapid mixing will develop. “Separated flow region” on the “suction side” remains stable with “positive incidence” and persists far into the impeller. The blockage from leading-edge separation restricts the flow passage across the section and therefore increases the local velocity. The head loss incurred when the separated region mixing with the main stream can be considered a sudden expansion loss. This will adversely affect the overall pump performance. The real flow conditions at the impeller inlet at incidence are often much more complicated than those of the two-dimensional separation model. If the flow velocity meets the leading edge at a slant, a tip vortex can develop in the separated region along the leading edge, which trails away toward the hub (Figure 1.38). High-specific-speed centrifugal pumps are particularly sensitive to inlet conditions because the through-flow velocities are relatively high and the inlet diameter is also relatively large. The circumferential velocity on the shroud exceeds the circumferential velocity at the hub. meridional velocities are high on the shroud and low on the hub because of the curvature of the streamlines. Since flow losses vary with the square of the velocity, high velocities indicate high losses, which also reduce the overall pump performance. 30 1.10.4 Friction losses - Internal losses The viscous boundary layers are responsible for the friction losses. The expression developed for pipe flow is used to estimate the loss in total pressure due to friction. APtotal 2 4Cf, 2385 W2 9 2 h (1.63) L v h. = f. —— 4mh 2g (APO/p) 47. fr : ICZLL] : lpCZ 2 D 2 (1.64) Re = ”C D (1.65) 11 For pipe flow, the Moody chart (Figure 1.39) is used to find the friction coefficient as a function of the Reynolds number and the relative roughness. 1.10.5 Viscosity The viscosity results in the resistance to the ability of pumping liquid of the centrifugal pump. Therefore, an increase in the viscosity of the pumped liquid changes the performance characteristic’s curves for a centrifugal pump. The higher the viscosity of the pumped liquid is, the thicker the fluid enters the pump. A centrifugal pump used for higher viscous fluids will be impinged on by the following elements: 0 The brake horsepower requirement will increase. 0 A reduction in the head the pump will produce. 0 Some reduction in the flow rate will occur with moderate and high viscosities. o The pump’s efficiency will decrease. With more viscous fluids, the “hydraulic losses” is definitely applied to the so-called “through-flow” losses. These losses are directly the result of skin friction and eddy systems along the primary path of the fluid passing through the centrifugal pump. 1.10.6 Reynolds number The general trend of the Reynolds number characteristics indicates three different zones, within which the influence of the major losses is changing in weight. 1. For the range of water and air performance above Reynolds numbers Re >106, the efficiency losses are essential due to the hydraulic “through-flow” losses. These “through-flow” losses are produced by disk friction and leakage. 2. For the Reynolds numbers 106 > Re >104, the increase in power input is caused mainly by rapidly growing “disk and ring friction” losses, while “through-flow” losses increase at a comparative low rate. The “through-flow” losses are indicated by the relatively small decrease in head and capacity, which proves that turbulent flow persists essentially throughout the pump. “Leakage” losses have assumed a negligible part. 3. For the Reynolds numbers Re <104, the “through-flow” losses increase more rapidly as indicated by a downward trend in head and capacity. Laminar-flow conditions are gradually established for the main flow. “Disk and ring friction” losses become less dominant and due to the large dissipation of power into heat on account of the laminar-flow conditions, the pump efficiency losses cannot increase more by “disk and ring friction” losses. 1.10.7 Cavitations 32 The cavitations can occur when the high local velocity corresponding to low static pressure happens near the blade leading edge. Under cavitating conditions, the absolute local static pressure falls below the vapor pressure of the fluid, and steam or gas bubbles appear. The evolving gas corresponding to the volume increase can choke down the flow and prevent further increase of the flow rate. This will decrease the overall pump efficiency. Moreover, the cavitation bubbles and the re-entering fluid jet on the blade surface can generate very high local pressures and destroy the blade material. In order to specify a centrifugal pump to a certain application, the Net Positive Suction Head Available (NPSHA) from the system is calculated by estimating the total absolute pressure available from the system at the pump inlet, P01. P —P NPSHA = L—V" =hm—h ,p (1.66) pg The NPSHA must be greater than the NPSHR (Net Positive Suction Head Required) in order that the centrifugal pump performance can’t significantly reduce. The temperature of the fluid affects the vapor pressure and may also lead to premature cavitations. Hot or boiling fluids may require pressurization of the pump inlet. 33 FIGURES 34 1521 151 inclined (one t—Jzi (d (b ) \.. ,. 151 15%? ~~xi L ] - V 131 ( Figure 1.1 Alternative suction systems for an end suction centrifugal pump (a) A co-axial cylindrical straight suction line (b) An inclined cone type suction (c) A flared inlet that may be used for vertical design (after Turton, R. K., 1994) 35 - “" D :S- D Figure 1.2 Simple suction pipe (after Turton, R. K., 1984) r M, W“ Figure 1.3 Ducted entry suction (after Turton, R. K., 1984) l Suction Pressure energy pressure 1 Inlet edge . \ . Figure 1.4 Pressure changes on a stream surface in the suction of a centrifugal Machine (after Turton, R. K., 1984) 36 UNSTABLE PRE-ROTATION Figure 1.5 Unstable flow in the suction region of a centrifugal pump under “part flow” operating conditions (after Grist, 1988, Courtesy of the Institution of Mechanical Engineers) ” ’ gmmégfi’fi ’6, I, 9 I 2 4 Figure 1.6 Inducer (after John Tuzson, 2000) 9H t 11 NPSE Impeller Impeller with inducer Flow rate Figure 1.7 Effect on the NPSHR curve for a pump of adding an inducer (after Turton, R. K., 1984) 37 SPIRALLING FLOW TRANSIENT FLOR PATTERNS \ IIHE to STABLE Figure 1.8 Transient flow patterns in the suction region of a pump at low flow rates (after Grist, 1988, Courtesy of the Institution of Mechanical Engineers) 38 Exit blade Exit width, angina, I 82 1 / \/ Inlet blade angle. B1 \/ Figure 1.9 Frontal and cross-sectional view of pump impeller (after John Tuzson, 2000) L Shaft Figure 1.10 Double-suction centrifugal impeller (after Earl Logan, 1993) 39 q Backward curved vane Circulatory flow Figure 1.11 Pump impeller (after Earl Logan, 1993) Absolute velocity, C2 Tip speed. U2 = (DRZ A Relative velocrty. W2 32 6 ") R1 ' \ T ’ l Angular velocity, (0 Figure 1.12 Relative and absolute flow velocity vectors in a rotating impeller (after John Tuzson, 2000) C I X l¢ Ct —V Figure 1.13 Velocity triangle with C = Absolute velocity, W = Relative velocity, U = Blade velocity 40 r11 Inlet Shroud suction side Hub suction side Shroud pressure Exit +1 Hub pressure side Figure 1.14 Impeller streamline locations for velocity and blade coordinate calculations (after John Tuzson, 2000) Absolute Relative velocity, C1 velocity. W, Absolute Relative velocity, 02 C,2 velocity, W2 1 a U2 =3sz PM,“ \ / 0'2 / 6Q: \ <0 R2 Q7 \ / Figure 1.15 Velocity triangles at the impeller inlet (U 1, C1, W1) and exit (U2, C2, W2) (after John Tuzson, 2000) a . ,62 is the vane angle (Without slip) B2 is the relative flow angle (With slip) Figure 1.16 Actual and Ideal diagrams at exit from an impeller caused by slip 41 Flow angiefiF-z Blade anglefiz I 1 “(7217 C . W2 2 1 T -—- —-—->i 31:) W12 Cr2 U70 U2 = (flRz Absolute tangential velocrty, C,2 C22 = U2 — Wrz 13013;? = U20- Wr2 13“ 32 Radial velocity, W,2 = 0,2 = Q/IIDZBZ Figure 1.17 Velocity diagram at the impeller exit with slip (after John Tuzson, 2000) Blade angle, . Flow angle, " 13F2 132 N ,/R/otm 1 relative \to\impeller f’/\ + Figure 1.18 Fluid rotation relative to impeller and the resulting slip velocity (after John Tuzson, 2000) 42 Rim of Impeller Figure 1.19 Velocity diagram at impeller exit (after Earl Logan, 1993) Streamline r2 \ 112 1,»,er _\__ 2 + Ci _wr2C,; h+ 22g2g\2rt g \ \. ____.. \ 1. “ 2g 2g 9’2 Cz \ cur $1613}va ”S I W1 / )1, C1 1 ,1 l r,/ ', r1 /' /f\ ///\, /’:l—— w 1 \\\‘§?// Q0 5“ CE W2 (1)2!‘2 h,+—— I=Rtth1 :h ~-— --——— 2r/ 25’ n apy +21: 2g / Figure 1. 20 Conservation of energy equation and rothalpy in the rotating impeller (after John Tuzson, 2000) 43 Diffuser inlet angle. B2 \ Exit . Diffuser “mm“ 32 throat 1++1 _‘1I' QN (user inlet WT 53‘ diameter, D3 Inlet __ _ _ .5 _ diameter D, l: .1 1% —T a O. ; Shaft diameter, DO .1. ,v g é -\ /. Diffuser width, 33 Figure 1.21 Nomenclature of impeller and diffuser geometry (after John Tuzson, 2000) tel Vane l ess space Impeller Figure 1.22 Vaned diffuser (after Earl Logan, 1993) Figure 1.23 Vaned diffuser configurations (after Earl Logan, 1993) Diffuser Vane Impeller Eye Figure 1.24 Arrangement of diffusers and impeller (after Earl Logan, 1993) ,\ Volute throat .., 4 area. A . Cos * 3- ' 3,2; / t T u}. z / " ‘ ‘_ 0118118 ,/ Base ,‘ fl" / Circle ’ 1 " " / / / \5D3 1. / DZ / -/ 1 ~ / Impeller Figure 1.25 Volute throat area (after John Tuzson, 2000) 45 Impeller diameter Throat velocny, , D = g / Q3 A \ Volute throat area, A Volute tongue Figure 1.26 Volute throat velocity (after John Tuzson, 2000) 46 Blade suction // side Blade pressure side Figure 1.27 Separated “Jet-Wake” flow in impeller (after John Tuzson, 2000) 1 1.0 — Jet-wake 0'8 T flow pattern 68% :o N Z 0.6 7'" a4 + No jet wake :3: 0.4 L— o.2 - O l 1 1 1 1 1 _-L.--..--1.._.._ 1._._..,. o 30 60 90° Blade angle from radialfl Figure 1.28 “J et-Wake” flow pattern criterion (after John Tuzson, 2000) 47 Blade suction Side 5“. wt 3‘ '6 O ‘54)? Blade a: loading .2 ‘5 7.3 W2 0: Pressure side Inlet Exit Fraction of streamline length re 1.29 Fraction of streamline length (after John Tuzson, 2000) Radial Relative velocity, Cr velocity, Wp / T Relative velocity, W5 Absolute tangential velocity, C, Blade A (0 A W2—W2 2-1, .ch232__,.[_§_2_2) g re 1.30 Pressure difference across the impeller blade: Blade Loading 48 Shutoff head A H ead, H Operating point System curve \Y’ I Design Point I Ho Pump A’l’ performance Efficiency, 11 ,’ curve Efficiency. ’1’ Power, P U; 0 / — Pipe Head g x” friction ,v”/ loss Power, P ———— ______../ Normal or design flow rate 5 O E/ Q 0 Flow Rate, Q levation (static) head =Zz-Zi Figure 1.31 Typical performance characteristics for a centrifugal pump of a given size operating at a constant impeller speed; Head Pump, Efficiency, Power-Flow Curve at constant speed 4 Unstable range Head. H Tank surface level. h V Unstable Stable / operating point operating point Pump Head-flow curve (Pump performance curve) Flow Rate, Q Figure 1.32 Head versus flow rate showing pump characteristics with unstable range 49 Bz _ _ 0' 1.0 ‘1’ ‘° ““132 w, Slip, 0 I}: 0.8 CtZ 5' = _ ’6'; 0.6 . W U2 & .3 U, i: *g 0.4 —, C U I _ m2 3 I Exit blade angle 4’ r —U i) I from radial B2 2 0.2 T ’ i' I l I 0 0.2 0.4 0.6 Flow coefficient, a Figure 1.33 Head and flow coefficient diagram. The slip coefficient shown is for six blades Theoretical head, ht Friction losses Other losses Head Actual head, ha Flow rate Figure 1.34 Effect of losses on the centrifugal pump head-flow rate curve 50 1 Clearance 1” IVx Housmg \~~—--,§pace W811 \ \‘ Radial velocity i Rotating Figure 1.35 Flow velocity profiles in clearance between rotating impeller face and housing (after John Tuzson, 2000) Tangential velocity Rear seal Balance Leakage chamber ‘1 WW Wear ring Figure 1.36 Balancing of axial thrust on impeller: leakage flow (after John Tuzson, Blade angle. - I31 1 T..- 1 Flow 1 angle, 13m 1“ (a) (11) Figure 1.37 Inlet blade incidence: (a) increased flow rate, Q >Qo; (b) reduced flow rate Q 3:235: a: ohm—ME 623% “22534 _ l .................... Tl «Munoz— mL An: .. awdqwmx: uu 9 3. Au.— uz<>0 Ft Ap