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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Wiley-ASME Press Series
- Sprache: Englisch
- Veröffentlichungsjahr: 2024
Mixed-flow Pumps Modeling, Simulation, and Measurements Learn to improve and optimize the design and operation of mixed-flow pumps Mixed-flow pumps have a huge range of applications in agriculture, hydroelectric power, and other industries that incorporate fluid transport. They are centrifugal pumps incorporating the characteristics of both axial and radial pumps to increase the flow rate and discharge pressure. Though essential in a variety of industries, they pose serious challenges to numerical simulation methods, challenges which are starting to be met by the application of computational fluid dynamics using high-performance computing. Mixed-flow Pumps introduces engineers and researchers to this subject and its important applications. Incorporating all major varieties of mixed-flow pumps used in industrial applications, it employs methods from advanced computational fluid dynamics and high-precision flow field experimentation to characterize and analyze these crucial technologies. Moving from the fundamentals of the technology to its most advanced applications, it's an essential resource for engineers and industry practitioners looking to develop their understanding of fluid transport. Mixed-flow Pumps readers will also find: * Detailed information on how to design and optimize mixed-flow pumps to meet the increasingly stringent industry demands * Detailed information on energy performance tests and experiments, methods for data analysis, entropy production theory, CFD solutions using Reynolds-Averaged Navier-Stokes (RANS) equations, and more * An authoritative team with immense global experience in flow pumps and broader industrial experience Mixed-flow Pumps is a useful reference for mixed-flow pump design by academic researchers, including graduate students, industry practitioners, and test engineers.
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Preface
Acknowledgments
List of Acronyms
List of Symbols
Nomenclature
1 Introduction
1.1 What Is a Mixed-flow Pump?
1.2 Types of Mixed-flow Pumps
1.3 Agricultural and Industrial Applications of Pumps
1.4 Summary
References
2 Basic Concepts and Theory of Mixed-flow Pumps
2.1 Basic Flow and Performance Parameters
2.2 Typical Type of Flows in the Mixed-flow Pumps
2.3 Summary
Nomenclature
References
3 Brief Review of Computational Fluid Dynamics
3.1 CFD as a Flow Simulation Tool
3.2 Geometry Modeling
3.3 Mesh Generation
3.4 Governing Equations of Fluid Dynamics
3.5 Simulation of Turbulent Flows
3.6 Turbulence Modeling
3.7 Numerical Solution Algorithms
3.8 Near-wall Flow Treatment
3.9 Boundary Conditions
3.10 Uncertainty Analysis
3.11 Summary
Nomenclature
References
4 Pump Performance Analysis Methods
4.1 Entropy Production Analysis
4.2 Vortex Identification and Vorticity Transport
4.3 Transient Flow Analysis Using the Wavelet Method
4.4 Summary
References
5 Experimental Methods, Data, and Analysis
5.1 External Characteristics Experiment
5.2 Experiment for Measuring Pressure Fluctuations
5.3 PIV Measurement
5.4 Orbit of Shaft Centerline
5.5 Summary
References
6 CFD Simulations of a Mixed-flow Pump Using Various Turbulence Models
6.1 Comparison and Validation of Numerical Results from Three Two-equation Turbulence Models (SST
k–ω
,
k–ω,
and Standard
k–ε
)
6.2 Application of Wray–Agarwal (WA) One-Equation Turbulence Model
6.3 Summary
References
7 Tip Leakage Flow In a Mixed-flow Pump
7.1 Energy Characteristics
7.2 Flow Structures
7.3 Unsteady Flow Characteristics
7.4 Transient Flow Field Due to Rotor–Stator Interaction (RSI)
7.5 Summary
References
8 Rotational Stall in a Mixed-flow Pump
8.1 Energy Characteristics
8.2 Flow Structure in the Critical and Deep Stall Conditions
8.3 Effect of the Tip Clearance on the Rotating Stall
8.4 Propagation Characteristics of Rotating Stall
8.5 Inducements for the Circumferential Propagation of the Rotating Stall
8.6 A Stall Prediction Model of the Mixed-flow Pump
8.7 Summary
References
9 Passive Suppression of Rotating Stall in Mixed-flow Pump
9.1 Introduction
9.2 Impeller Blade Rim Structures for Stall Suppression
9.3 Influence of the Circumferential Spokes
9.4 Summary
References
10 Cavitation in a Mixed-flow Pump
10.1 Numerical Model
10.2 Flow Characteristics of the Mixed-flow Pump Under Cavitation
10.3 Analysis of Cavitation Energy Characteristics
10.4 Summary
References
11 Analysis of the Vortex Dynamics Characteristics in the Tip Region of the Mixed-flow Pump Under Cavitation
11.1 The Tip Leakage Flow Characteristics Under Cavitation
11.2 Analysis of the Vorticity Transport Characteristics in the Tip Region
11.3 Summary
References
12 Multiphase Flow Simulations of Sediment Particles in Mixed-flow Pumps
12.1 Introduction
12.2 Governing Equations of the Mixture Model of Multiphase Flow
12.3 Pump Model and Mesh Generation
12.4 Two-phase Flow Characteristics of the Solid–Liquid Flow in Mixed-flow Pumps
12.5 Two-phase Flow Characteristics in the Guide Vane of Mixed-flow Pumps
12.6 Summary
References
Index
End User License Agreement
List of Tables
Chapter 3
Table 3.1 Parameters of the mixed-flow pump model.
Table 3.2 Model constants of WA 2017 model.
Table 3.3 Computational setup.
Table 3.4 Head of the mixed-flow pump with different numbers of mesh element...
Table 3.5 Uncertainty parameters related to mesh convergence.
Table 3.6 Validation of grid independence of the solution.
Table 3.7 Number of mesh elements for each component of the pump.
Chapter 4
Table 4.1 Two types of generating functions and their properties.
Chapter 5
Table 5.1 Computational process of the experimental uncertainties.
Chapter 7
Table 7.1 Comparison of rim leakage flow for various tip clearances.
Chapter 8
Table 8.1 The flow distortion factor
B
b
and the average velocity at the moni...
Chapter 9
Table 9.1 The flow rates under critical and deep stall for different blade t...
Table 9.2 Key dimensions of the “O-Spoke”.
Chapter 11
Table 11.1 Comparison of tip leakage flow for various
NPSH
a
values.
Chapter 12
Table 12.1 Pump head and efficiency of the mixed-flow pump at various volume...
List of Illustrations
Chapter 1
Figure 1.1 Mixed-flow pump impeller and mixed-flow pump model.
Figure 1.2 Classification of mixed-flow pumps. (a) Structural diagram of vol...
Figure 1.3 Pumping station of Zaohe River in Suqian, Jiangsu province, China...
Figure 1.4 Qushou pumping station of Qinglongshan irrigation area in Heilong...
Chapter 2
Figure 2.1 Diagram showing circumferential development of rotating stall....
Figure 2.2 Comparison of the snapshot images of cavitation in the tip region...
Figure 2.3 Internal flow characteristics of the pump with limiting streamlin...
Chapter 3
Figure 3.1 CFD as a multidisciplinary field.
Figure 3.2 Computational solution process.
Figure 3.3 Mixed-flow pump model: (a) 3D diagram of mixed-flow pump and (b) ...
Figure 3.4 Whole computational domain and domain discretization.
Figure 3.5 Numerical solution models for turbulent flow simulations.
Figure 3.6 Velocity profiles in the near-wall region of the turbulent bounda...
Figure 3.7 Typical convergence characteristics of the residuals of flow vari...
Chapter 4
Figure 4.1 Fourier analysis results of the two signals. (a) Stationary signa...
Chapter 5
Figure 5.1 Experimental test system.
Figure 5.2 (a) Mixed-flow pump impeller, (b) Mixed-flow pump guide vane, and...
Figure 5.3 Turbine flowmeter.
Figure 5.4 Flowmeter.
Figure 5.5 Pressure transmitter.
Figure 5.6 Torque measuring instrument.
Figure 5.7 Pump measuring instrument.
Figure 5.8 Frequency converter.
Figure 5.9 Experimental energy performance of the mixed-flow pump with diffe...
Figure 5.10 MPM480 piezoresistive pressure sensor.
Figure 5.11 Sensor installation positions.
Figure 5.12 Arrangement of external characteristic and pressure pulsation me...
Figure 5.13 Time-domain characteristic of the impeller inlet, middle, and ou...
Figure 5.14 Wavelet modulus spectrum of the pressure pulsation at the impell...
Figure 5.15 Wavelet modulus spectrum of the pressure pulsation at the impell...
Figure 5.16 Wavelet modulus spectrum of the pressure pulsation at the impell...
Figure 5.17 Wavelet coherence spectrum of the pressure pulsation of adjacent...
Figure 5.18 Wavelet coherence spectrum of the pressure pulsation of axis sym...
Figure 5.19 PIV measurement setup and principle.
Figure 5.20 Displacement of tracer particles.
Figure 5.21 PIV system and equipment: (a) sheet light source, (b) double cav...
Figure 5.22 Effect diagram of PIV tracer particles: (a) inlet vertical axis ...
Figure 5.23 Calibration tank.
Figure 5.24 Calibration process: (a) adjustment of the side surfaces in the ...
Figure 5.25 Fixing of lens set and camera.
Figure 5.26 Lens bracket diagram.
Figure 5.27 Camera bracket.
Figure 5.28 Shooting sections of experiment.
Figure 5.29 Relative position of the guide vane and the impeller in differen...
Figure 5.30 Position of the laser and camera.
Figure 5.31 Inlet layout for PIV tests.
Figure 5.32 PIV measurement results of inlet axial section: (a) 0.8
Q
des
, (b)...
Figure 5.33 PIV measurement results of the section between impeller and guid...
Figure 5.34 PIV measurement results of the section in guide vane: (a) 0.8
Q
de
...
Figure 5.35 Velocity distribution of flow field at different phases under pa...
Figure 5.36 Vorticity distribution of flow field at different phases under p...
Figure 5.37 Monitor lines.
Figure 5.38 Relative velocity distributions at monitoring lines which are at...
Figure 5.39 Relative velocity distributions at different phases of the pump ...
Figure 5.40 Position of the eddy current displacement sensors.
Figure 5.41 Bentley 408 data acquisition system.
Figure 5.42 Measurement of rotor axis locus: (a) position of eddy current di...
Figure 5.43 Rotor axis locus chart and time-domain chart of the original rot...
Figure 5.44 Rotor axis locus chart and time-domain chart of the 1X frequency...
Figure 5.45 Rotor axis locus chart and time-domain chart of the 2X frequency...
Figure 5.46 Frequency spectrogram in
X
and
Y
direction.
Figure 5.47 Frequency domain diagram of pressure fluctuation and axis orbit....
Chapter 6
Figure 6.1 Comparison of experimental results with simulations using the thr...
Figure 6.2 Positions of the target area and monitoring lines in the PIV expe...
Figure 6.3 Velocity contours and streamlines in the target area at 0.4
Q
des
f...
Figure 6.4 Comparison of velocities from simulations using the three turbule...
Figure 6.5 Velocity distributions at the section of the impeller outlet usin...
Figure 6.6 Pressure distributions in the blade passages in the plane at 50% ...
Figure 6.7 Velocity distributions in the blade passages in the plane at 50% ...
Figure 6.8 Initial stall vortex structure in the impeller flow passage.
Figure 6.9 Axial velocity in the impeller inlet under the initial stall cond...
Figure 6.10 Velocity circulation distribution in the impeller inlet in the i...
Figure 6.11 Comparison of simulations using the SST
k–ω
and WA tu...
Figure 6.12 Selected section in the mixed-flow pump model.
Figure 6.13 Velocity comparisons between simulations using the SST
k–ω
...
Figure 6.14
R
distribution in the middle cross-section of the mixed-flow pum...
Figure 6.15
R
distribution on the turbo surface of the impeller at 90% span ...
Figure 6.16
R
distribution and tip leakage vortex in the impeller at the des...
Chapter 7
Figure 7.1 Comparison of head and efficiency for various tip clearances at d...
Figure 7.2 The head-drop loss coefficient for various flow rates. (a) 0.2
Q
de
...
Figure 7.3 Total entropy production in the mixed-flow pump for different tip...
Figure 7.4 Variation in the total entropy production with the flow rate in d...
Figure 7.5 Comparison of the head-drop loss and the entropy production at de...
Figure 7.6 Average entropy production in the different volumes of the impell...
Figure 7.7 Proportion of the total entropy production in each volume for var...
Figure 7.8 Distribution of local entropy production on blade-to-blade surfac...
Figure 7.9 Local average entropy production in different parts of the guide ...
Figure 7.10 Local entropy production on blade-to-blade surfaces for various ...
Figure 7.11 Morphology of tip leakage vortex (TLV) and the distribution of t...
Figure 7.12 Vortex intensity distribution of the tip leakage flow for variou...
Figure 7.13 Diagram of the core of the leakage vortex for various tip cleara...
Figure 7.14 Time-domain plots of the pressure fluctuation at various monitor...
Figure 7.15 Time-domain plots of pressure fluctuation at various monitoring ...
Figure 7.16 Flow fields and streamlines in the impeller before the RSI zone....
Figure 7.17 Relative velocity distributions and streamlines in the RSI zones...
Figure 7.18 Streamlines on the blade-to-blade sections at the middle span fo...
Figure 7.19 Iso-surfaces at
Q
=37421.5 s
−2
in the impeller and the guid...
Figure 7.20 The spatial distribution of monitoring points.
Figure 7.21 Pressure fluctuation in the time domain along the main flow for ...
Figure 7.22 Pressure fluctuation in the time domain in the RSI zone at diffe...
Figure 7.23 Pressure fluctuation in the frequency domain along the main flow...
Figure 7.24 Pressure fluctuation in the frequency domain in the RSI zone at ...
Chapter 8
Figure 8.1 Variation in the energy head difference
Δ
H
along the directi...
Figure 8.2 Streamlines distribution on the blade surface in stall condition:...
Figure 8.3 Flow rates distribution in each passage at the impeller outlet at...
Figure 8.4 Turbulent kinetic energy distribution at 50% span location at var...
Figure 8.5 Change in the average turbulent kinetic energy in the four passag...
Figure 8.6 Pressure and velocity distribution at 50% blade height at various...
Figure 8.7 Distribution of vortex core in the impeller. (a) Enlarged view of...
Figure 8.8 3D streamlines at the impeller inlet and 2D streamlines at the ax...
Figure 8.9 Inflow angle of blade number # 3 for various operating conditions...
Figure 8.10 Turbulent kinetic energy dissipation in the impeller at differen...
Figure 8.11 Distribution of velocity field on the pressure iso-surface of th...
Figure 8.12 Inducement of stall vortex generation and turbulent kinetic ener...
Figure 8.13 Distribution of stall vortex core in the impeller passage at sta...
Figure 8.14 Flow cross-section diagram at the impeller outlet.
Figure 8.15 Axial velocity distribution at the impeller outlet for various o...
Figure 8.16 Velocity vector distribution in the meridian plane B of the impe...
Figure 8.17 TLF fields for various blade tip clearances at design flow rate....
Figure 8.18 TLF fields for various blade tip clearances at the largest head ...
Figure 8.19 TLF fields for various blade tip clearances at the lowest head i...
Figure 8.20 Distance of TLV core for various tip clearances (a) to suction s...
Figure 8.21 Average axial velocity for various span parameters in the inlet ...
Figure 8.22 Velocity on the blade-to-blade section for various span paramete...
Figure 8.23 Schematic diagram of the disordered factor.
Figure 8.24 Positions of the impeller monitoring points. (a) Front view and ...
Figure 8.25 Time domain characteristics of the pressure coefficient in the i...
Figure 8.26 Frequency domain distribution of pressure coefficients in the im...
Figure 8.27 Relationship between the transient head and the pressure.
Figure 8.28 Charts of flow field in the impeller at different time.
Figure 8.29 Stall propagation process under CSP.
Figure 8.30 Distribution of monitoring points on the suction surface.
Figure 8.31 Pressure fluctuation characteristics of the monitoring points at...
Figure 8.32 Process of stall evolution in a single flow path (the iso-surfac...
Figure 8.33 Inducements of pre-stall stage. (a) Transient flow in a fixed se...
Figure 8.34 Inducements of tip initial stall (the iso-surface is based on th...
Figure 8.35 Energy characteristic of mixed-flow pump with different number o...
Figure 8.36 The process of impeller entering stall with different blade numb...
Figure 8.37 Flow distribution of blade tip region surface and blade suction ...
Figure 8.38 Monitoring line for dividing different streamwise and spanwise p...
Figure 8.39 Distribution of pressure load on blade suction surface. (a) 4-bl...
Figure 8.40 Velocity distribution of blade suction surface. (a) 4-blade impe...
Figure 8.41 Velocity distribution of blade suction surface monitoring line u...
Figure 8.42 Area of impeller inlet and outlet span≥0.85.
Figure 8.43
C
v_Taylor
curve under different flowrate.
Figure 8.44
k
T
curve under different flowrate.
Chapter 9
Figure 9.1 Various types of blade rim structures of the impeller blade. (a) ...
Figure 9.2 Comparison of the head curves for various blade rim structures.
Figure 9.3 Comparison of the efficiency curves for various blade rim structu...
Figure 9.4 Definition of the position parameters at the blade rim.
Figure 9.5 Definitions of the dimensionless position parameters in the rim c...
Figure 9.6 Distributions of the velocity and the turbulent kinetic energy in...
Figure 9.7 Distributions of the velocity and the turbulent kinetic energy in...
Figure 9.8 Distributions of the velocity and the turbulent kinetic energy in...
Figure 9.9 Distributions of the velocity and the turbulent kinetic energy in...
Figure 9.10 Distributions of the velocity and the turbulent kinetic energy i...
Figure 9.11 Inlet angle distributions of the blades for various blade rim st...
Figure 9.12 The velocity triangles of the fluid at the blade inlet rim at va...
Figure 9.13 Inlet angle distributions of the blades for various rim structur...
Figure 9.14 Vortex structures in each impeller and the turbulent kinetic ene...
Figure 9.15 Vortex structures in each impeller and the turbulent kinetic ene...
Figure 9.16 Vortex structures in each impeller and the turbulent kinetic ene...
Figure 9.17 Distributions of stall vortex structures in the impeller in deep...
Figure 9.18 Distributions of stall vortex core for various blade rim structu...
Figure 9.19 Schematic diagram of the “O-Spoke”.
Figure 9.20 External characteristic curves. (a) Head curve and (b) Efficienc...
Figure 9.21 Aligned Turbo Surface flow cross-section.
Figure 9.22 Velocity distribution maps in the impeller cross-section. (a) Th...
Figure 9.23 Pressure distribution maps in the impeller cross-section. (a) Th...
Figure 9.24 Impeller shroud region flow field plots. (A) 0.54
Q
des
(a) The or...
Figure 9.25 Impeller single passage vortex plots. (A) 0.54
Q
des
(a) The origi...
Figure 9.26 Local entropy generation distributions at various operating cond...
Figure 9.27 The flow streamlines in various sections at 0.62
Q
des
. (a) Span =...
Chapter 10
Figure 10.1 High-speed photography experiment.
Figure 10.2 Numerical and experimental comparison of cavitation performance ...
Figure 10.3 Cavitation structure in impeller passage for various cavitation ...
Figure 10.4 Pressure load distribution on the suction side (SS) of the blade...
Figure 10.5 Impeller outlet streamlines diagram and vortex core distribution...
Figure 10.6 Tip clearance vortex core distribution for various
NPSH
a
values....
Figure 10.7 Time evolution of leakage vortices for
NPSH
a
= 5 m. (a) Transien...
Figure 10.8 Variation of head coefficient Ψ along the axial direction for di...
Figure 10.9 Turbulent kinetic energy distribution in the impeller for variou...
Figure 10.10 Domain and section divisions.
Figure 10.11 Output power of the impeller for various
NPSH
a
values.
Figure 10.12 Output power of each area of the impeller for various
NPSH
a
val...
Figure 10.13 Turbulent dissipation loss in each region of the impeller for v...
Figure 10.14 Friction loss of each section of the impeller for various
NPSH
a
Figure 10.15 Energy loss in the impeller area for various
NPSH
a
values.
Chapter 11
Figure 11.1 Schematic diagram of the partition of the tip leakage flow regio...
Figure 11.2 Distribution of the tip leakage flow intensity in various cavita...
Figure 11.3 Three-dimensional flow streamlines of the tip leakage flow at va...
Figure 11.4 Vorticity distribution in various cavitation conditions. (a)
NPS
...
Figure 11.5 Vortex strength distribution in various cavitation conditions.
Figure 11.6 Vortex strength distribution per unit area in various cavitation...
Figure 11.7 Distribution of the turbulent kinetic energy in various cavitati...
Figure 11.8 Turbulent kinetic energy (TKE) distribution in various cavitatio...
Figure 11.9 Turbulent kinetic energy (TKE) distribution per unit area in var...
Figure 11.10 Vorticity and turbulent kinetic energy distributions at
λ
...
Figure 11.11 Axial velocity
V
a
and the radial velocity
V
r
distributions at
λ
...
Figure 11.12 Radial vorticity
ω
r
distribution in various cavitation con...
Figure 11.13 Axial distribution of each transport term in the vorticity tran...
Figure 11.14 Circumferential vorticity
ω
c
distribution in various cavit...
Figure 11.15 Circumferential distribution of each transport term in the vort...
Figure 11.16 Axial vorticity
ω
a
distribution in various cavitation cond...
Figure 11.17 Axial distribution of each transport term in the vorticity tran...
Figure 11.18 Vorticity transport intensity distribution curves in various ca...
Figure 11.19 Radial, circumferential, and axial distribution of different me...
Figure 11.20 Quantitative distribution of different measures of vorticity in...
Chapter 12
Figure 12.1 Comparison of the energy characteristics between the clean water...
Figure 12.2 Distribution of the solid phase at a cross-section in the impell...
Figure 12.3 Particle dynamic scale at the mid-streamline in the impeller.
Figure 12.4 Percentage of the entropy production in various fluid components...
Figure 12.5 The location of each monitoring line in the impeller and the cro...
Figure 12.6 Distribution of the local entropy production in various flow fie...
Figure 12.7 Distribution of the local entropy production in different spanwi...
Figure 12.8 Distribution of the average entropy production along the flow di...
Figure 12.9 Distribution of the turbulent kinetic energy for various volume ...
Figure 12.10 Distribution of the vorticity and volume fractions of solid par...
Figure 12.11 Distribution of the solid particles in a plane section of the g...
Figure 12.12 Dynamic scale of particle motion along the midstream line in th...
Figure 12.13 Distribution of the high-entropy production regions in a cross-...
Figure 12.14 Distribution of the entropy production in various cross-section...
Guide
Cover
Title Page
Copyright
Preface
Acknowledgments
List of Acronyms
List of Symbols
Table of Contents
Begin Reading
Index
End User License Agreement
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Mixed-flow Pumps
Modeling, Simulation, and Measurements
Wei Li
Jiangsu University, China
Leilei Ji
Jiangsu University, China
Ramesh Agarwal
Washington University in St. Louis, USA
Weidong Shi
Nantong University, China
Ling Zhou
Jiangsu University, China
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Library of Congress Cataloging-in-Publication Data:
Names: Li, Wei (Professor of engineering), author. | Ji, Leilei, author. | Agarwal, R. K. (Ramesh K.), author. | Shi, Weidong (College presidents), author. | Zhou, Ling (Professor), author.
Title: Mixed-flow pumps : modeling, simulation, and measurements / Wei Li, Leilei Ji, Ramesh Agarwal, Weidong Shi, Ling Zhou.
Description: Hoboken, NJ : Wiley, [2024] | Series: Wiley-ASME press series | Includes index.
Identifiers: LCCN 2024009766 (print) | LCCN 2024009767 (ebook) | ISBN 9781119910787 (hardback) | ISBN 9781119910794 (adobe pdf) | ISBN 9781119910374 (epub)
Subjects: LCSH: Centrifugal pumps. | Computational fluid dynamics.
Classification: LCC TJ919 .L38 2024 (print) | LCC TJ919 (ebook) | DDC 621.6/7–dc23/eng/20240319
LC record available at https://lccn.loc.gov/2024009766LC ebook record available at https://lccn.loc.gov/2024009767
Cover Design: WileyCover Image: Courtesy of Wei Li, Leilei Ji, Ramesh Agarwal, Weidong Shi, Ling Zhou
Preface
Pumps are among the most power-consuming general-purpose equipment in energy conversion devices and significantly impact the modern industrial economy. A mixed-flow pump can be considered a type of pump design between centrifugal pump and axial flow pump since it employs the combined effect of centrifugal force and thrust generated by the rotation of the impeller to convey fluid, and the fluid flows axially in and diagonally out through the impeller. It can also be called oblique flow pump with high flow rate, high efficiency, strong anti-cavitation performance, etc. It is widely used for agricultural irrigation, municipal water supply and drainage, water circulation in power industry, naval water jet propulsion, underwater weapon launches, and regional water transfer projects.
Compared to other pump types, the internal flow of mixed-flow pumps is more complex, and the secondary flow and deliquescence are more prominent. There are not only inherent unsteady flow problems caused by the static and dynamic interference but also unsteady problems induced by the wheel edge leakage vortex and its trailing off, rotational stall, and other complex flow phenomena which seriously affect the operational stability and efficiency of the mixed-flow pumps. Therefore, there is a need to explore the spatial and temporal evolution of flow structures and flow dynamics of the internal flow field of a mixed-flow pump as well as to achieve the desired targeted optimized solutions. In addition, the internal vortex energy loss characteristics of mixed-flow pumps, cavitation damage, and other phenomena also need to be studied systematically. Understanding and mastering the physical mechanisms of the internal flow in a mixed-flow pump is a prerequisite for improving the operational stability, reliability, and efficiency of the pump.
In previous studies, the flow field and performance characteristics of a mixed-flow pump were generally determined and analyzed by experimental means; however, the experimental approach is not only expensive, but it is often difficult to observe and obtain all the details of the flow field experimentally due to its complex structure. In recent years, the emergence of computational fluid dynamics has provided an effective tool to study the finer details of the flow structure inside the hydraulic machinery, which is uniquely beneficial in analyzing the internal flow field in a mixed-flow pump at multiple scales for a full range of operating conditions. Currently, there are no reference books providing the computational approach for the study of the flow fields and performance of mixed-flow pumps. Therefore, this book selects a typical model of a guide vane-type mixed-flow pump as the object of study and systematically investigates the complex internal flow structure through numerical simulations and experiments aiming to provide a reference work for industrial practitioners, academics, and students interested in the field of hydraulic machinery.
The book is divided into 12 chapters; the content of each chapter is as follows.
The first chapter provides a brief introduction to the definitions, types, and applications of mixed-flow pumps. The second chapter provides a detailed description of the basic concepts of mixed-flow pumps and the related theories. Chapter 3 focuses on computational fluid dynamics (CFD) simulation technology including geometric modeling, meshing, governing equations of fluid flow, CFD methods classification, turbulence models, solution algorithms, near-wall surface treatment, and boundary conditions. Chapter 4 describes different analysis methods including entropy production analysis, vortex analysis, and wavelet methods. Chapter 5 details the experimental methods, data, and analysis such as pressure pulsation measurements, PIV measurements, and axial trajectory measurements. Chapter 6 covers the application of turbulence models and compares the applicability of several turbulence models in the performance prediction of mixed-flow pumps. Chapter 7 investigates and analyzes the energy characteristics, flow structure, instability characteristics, and dynamic and static interference of the tip leakage flow of the mixed-flow pump. Chapter 8 investigates and analyzes the energy characteristics, flow structure, and the effect of tip clearance on the rotational stall and its propagation characteristics as well as the causes of incipient and deep rotational stall in the mixed-flow pump. Chapter 9 provides several passive suppression techniques to control the rotating stall in the mixed-flow pump. Chapter 10 analyzes the cavitation flow field and cavitation energy characteristics of the mixed-flow pump. Chapter 11 describes a special application of the Wray–Agarwal (WA) one-equation turbulence model to analyze the vortex dynamics characteristics in the tip region of the mixed-flow pump to demonstrate the accuracy and efficiency of the WA model for computing such complex flows compared to the other widely used turbulence models. Chapter 12 investigates the influence of the sediment particles on internal energy dissipation of the mixed-flow pump with different solid-phase volume fractions.
This book has been limited in terms of the depth and breadth of data collection. Furthermore, there could inevitably be some shortcomings and errors in the book. We hope that readers will provide comments and input so that future editions can be improved.
Acknowledgments
This work was sponsored by the Key International Cooperative Research Program of the National Natural Science Foundation of China (No. 52120105010), the National Key R&D Project (No. 2020YFC1512405) of China, the National Natural Science Foundation of China (No. 52179085 and No. 52309112), the Sixth “333 High Level Talented Person Cultivating Project” of Jiangsu Province, projects of the “Blue Project” in Jiangsu Colleges and Universities, and China Postdoctoral Science Foundation (No. 2022TQ0127 and No. 2023M741414); Open Research Subject of Key Laboratory of Fluid and Power Machinery (Xihua University), Ministry of Education (LTDL-2022010).
The publication of this book was made possible by the help of several colleagues and students at the National Engineering Research Center for Pumps and Systems of Jiangsu University and the CFD Laboratory of Washington University in St. Louis, USA, to whom the authors would like to express their sincere gratitude.
In particular, special thanks go to Mingjiang Liu, Shuo Li, Yi Yang, Shenglei He, and others from Jiangsu University for completing the translation of part of this book from Chinese.
The authors would like to dedicate this book to their respective families for their unwavering support, perseverance, and encouragement during the preparation of this book.
List of Acronyms
BPF
blade-passing frequency
BV
bounded vortex
CFD
computational fluid dynamics
CFL
Courant–Fredrick–Levy
DES
detached Eddy simulation
DNS
direct numerical simulation
FFT
fast Fourier transform
GCI
grid convergence index
HRN
high Reynolds number
LE
leading edge
LES
large eddy simulation
LNG
liquefied natural gas
LRN
low Reynolds number
LVC
local vortical cavitation
PDE
partial differential equation
PIV
particle image velocimetry
PS
pressure side
PTLV
primary tip leakage vortex
PV
passage vortex
RANS
Reynolds-averaged Navier-Stokes
RHD
right-hand side
RSI
rotor-stator interaction
RSM
Reynolds stress model
SA
Spalart–Allmaras
SGS
subgrid-scale
SIMPLE
semi-implicit method for pressure-linked equations
SS
suction side
SST
shear stress transport
STLV
secondary tip leakage vortex
SV
secondary vortex
TCC
tip clearance cavitation
TE
trailing edge
TLF
tip leakage flow
TLV
tip leakage vortex
TLVC
tip leakage vortex core
TMR
turbulence modeling resource
WA
Wray–Agarwal
WTC
wavelet transforms coherence
List of Symbols
Nomenclature
b
2
the width of the impeller, mm
C
p
pressure pulsation coefficient
D
1
the inlet diameter of the impeller, mm
D
2
the outlet diameter of the impeller, mm
D
3
the inlet diameter of the guide vane, mm
D
4
the outlet diameter of the guide vane, mm
D
ω
the cross-diffusion term in turbulence models
G
b
generation of turbulence due to buoyancy in turbulence models
G
k
generation of turbulent kinetic energy due to the mean velocity gradients in turbulence models
G
ω
production term of the turbulent dissipation rate in turbulence models
h
Δ
p
head drop loss coefficient
H
head, m
H
t
theoretical head, m
i
,
j
stands for the
x
,
y
,
z
direction
k
turbulent kinetic energy, m
2
/s
2
M
t
turbulent Mach number in turbulence models
m
ji
time-averaged viscous stress tensor
ṁ
mass discharge from each domain of the pump, kg/s
NPSH
net positive suction head, m
NPSH
a
net inlet pressure available, m
NPSH
r
net inlet pressure required, m
n
rated speed of the impeller, r/min
n
s
specific speed
p
1
,
p
2
total pressure at the inlet and outlet of each domain, Pa
P
e
effective power, W
P
tol
total input power, W
q
heat flux, J/s
Q
flow rate, m
3
/h
Q
des
designed flow rate, m
3
/h
energy transfer rate
R
the cross-diffusion term in WA model (=
k
/
ω
)
R
(
a,b
)
the coherence coefficient
S
strain rate, smoothing operator, standard deviation
s
specific entropy, J/(kg K)
local entropy production rate, kW/m
3
/K
3
entropy production rate induced by time-averaged movement, kW/m
3
/K
3
entropy production rate induced by velocity fluctuation, kW/m
3
/K
3
t
time, s
T
temperature, K
u
velocity, m/s
u
j
stands for the velocity in different coordinate directions
x
coordinate, m
x
j
stands for the coordinate directions
Y
M
the effect of the expansion of compressible turbulence on the total dissipation rate in turbulence models
Y
k
,
Y
ω
the dissipation terms of
k
and
ω
in turbulence models
y
the distance from the wall
Z
number of impeller blades
Z
d
number of guide vane blades
α
3
average inlet blade angle of guide vane, °
α
4
average outlet blade angle of guide vane, °
β
the coefficient of thermal expansion
β
1
average inlet blade angle of the impeller, °
β
2
average outlet blade angle of the impeller, °
Γ
k
,
Γ
ω
the coefficients of diffusion term for
k
and
ω
in turbulence models
δ
ij
Kronecker delta symbol
ε
turbulent dissipation rate, m
2
/s
3
in turbulence models
η
efficiency of mixed-flow pump, %
μ
dynamic viscosity, Pa s
μ
t
turbulent viscosity, m
2
/s
ρ
density, kg/m
3
σ
k
, σ
ε
turbulent Prandtl numbers for
k
and
ε
in turbulence models
φ
scalar variable
ω
turbulent eddy frequency, s
−1
in turbulent models
1Introduction
1.1 What Is a Mixed-flow Pump?
A mixed-flow pump is a centrifugal pump with a mixed-flow impeller [1]. The specific speed (ns) lies between 35 and 80 rpm for low-speed mixed-flow pumps and between 80 and 160 rpm for higher-speed mixed-flow pumps (in special cases, even higher). It has characteristics of both radial flow and axial flow pumps. As liquid flows through the impeller of a mixed-flow pump, the impeller blades push the liquid out away from the pump shaft and to the pump suction at an angle greater than 90°. The impeller of a typical mixed-flow pump and the flow through a mixed-flow pump are shown in Fig. 1.1.
1.2 Types of Mixed-flow Pumps
Based on the type of suction chamber, mixed-flow pumps can be divided into two types: volute mixed-flow pumps and guide vane mixed-flow pumps, as shown in Fig. 1.2. The former is close to the design of a centrifugal pump, and the latter is close to the design of an axial flow pump.
At present, majority of mixed-flow pumps are volute mixed-flow pumps which are similar to a single-suction centrifugal pump but are different in the type of impeller: the impeller of a mixed-flow pump of high specific speed is similar to that of an axial flow pump which is open type with adjustable blades; the impeller of a mixed-flow pump of low specific speed, on the other hand, is closed type which is similar to that of a single-suction centrifugal pump, but its flow channel is wider and the blade outlet is inclined.
Compared to the axial flow pump, the guide vane mixed-flow pump has slightly higher efficiency and a relatively flat efficiency characteristic curve. In other words, it can ensure higher efficiency when the water level changes; hence, it is very suitable for farmland drainage and irrigation and saves power, but compared to the volute mixed-flow pump, its diameter is smaller. For the vertical guide vane mixed-flow pump, the impeller is submerged in water during operation, so there is no need for water diversion equipment, and therefore the needed floor area is small. Therefore, in places where the axial flow pump is used (except for the axial flow pump with large adjustable blades), it is advantageous to replace it with an appropriate model of guide vane mixed-flow pump.
Other classifications of mixed-flow pumps are:
According to the inspection and disassembly form, they can be divided into the extractable mixed-flow pump and the non-extractable mixed-flow pump.
According to the blade regulation type, they can be divided into the fixed mixed-flow pump, the semi-regulated submersible axial flow pump, and the fully regulated mixed-flow pump.
Figure 1.1 Mixed-flow pump impeller and mixed-flow pump model.
Figure 1.2 Classification of mixed-flow pumps. (a) Structural diagram of volute mixed-flow pump 1. Pump cover, 2. Impeller, 3. Packing, 4. Pump body, 5. Bearing body, 6. Pump shaft, 7. Pulley, 8. Bolt. (b) Structural diagram of guide vane mixed-flow pump. 1. Suction horn, 2. Impeller, 3. Guide vane, 4. Outlet elbow, 5. Pump shaft, 6. Rubber bearing, 7. Stuffing box.
1.3 Agricultural and Industrial Applications of Pumps
Due to the characteristics of moderate head and large flow rate, the mixed-flow pump is widely used in farmland irrigation, flood prevention and drainage, sewage treatment, power station cooling systems, and other applications.
In agricultural production, the main function of the mixed-flow pump is irrigation and drainage. There are vast rural areas in the world, thus a large number of pumps are needed every year. Generally, agricultural pumps account for more than half of the total output of the pumps.
In the mining and metallurgical industries, mixed-flow pumps are also widely used. The mixed-flow pump is used for drainage and water supply in the process of beneficiation, smelting, and rolling in mines.
In the power sector, power stations need a large number of boiler feed pumps, condensate pumps, circulating pumps, and ash pumps, among which mixed-flow pumps account for the majority.
In the shipbuilding industry, many advanced water jet propulsion pumps are of mixed-flow pump types.
The following are examples of large-scale mixed-flow pump station projects in which Chinese companies have been engaged inside China as well as in neighboring countries for development of shipping, flood discharge, and other functions. The three representative projects are briefly described below:
Pumping station of Zaohe River in Suqian, Jiangsu province, China
[2]
.
The first-stage renovation project of the Zaohe River pumping station in the eastern route of the south-to-north water diversion project is located in Zaohe town, Suyu district, Suqian City, Jiangsu Province, China. Its primary task is to pump the diverted water from the Liulaodian pumping station into Luoma Lake, achieving a target water delivery of 175 m3/s to Luoma Lake and addressing the drainage needs in the regions of Pihong River and Huangdun Lake.
The Zaohe pumping station, shown in Fig. 1.3 is currently equipped with two sets of 5700HLQ100-4.78 vertical fully adjustable guide vane mixed-flow pumps. The pumps are designed with a net head of 4.78 meters, a design flow rate of 100 m3/s, an impeller diameter of 5.70 meters, a rated speed of 75 r/min, and an adjustable blade angle in the range +2° to −18°. They are paired with TL7000-80/7400 vertical synchronous electric motors with a rated capacity of 7000 kW and a total installed capacity of 14 000 kW. The first unit was successfully started on April 8, 2011, at 15:40 in the afternoon.
Qushou pumping station of Qinglongshan irrigation area in Heilongjiang Sanjiang Plain, China
[3]
.
Figure 1.3 Pumping station of Zaohe River in Suqian, Jiangsu province, China.
Source: [2]. Jiangsu Aerospace Hydraulic Equipment Co., Ltd. https://www.pumpcj.com/case/95.html. Last accessed 17 January, 2024.
Figure 1.4 Qushou pumping station of Qinglongshan irrigation area in Heilongjiang Sanjiang Plain, China.
Source: [3]. Jiangsu Aerospace Hydraulic Equipment Co., Ltd. https://www.pumpcj.com/case/97.html. Last accessed 17 January, 2024.
The installed flow rate capacity of the Qushou pumping station of Qinglongshan irrigation area is 381 m3/s, and the total installed power capacity is 56 000 kW. It has six sets of 3300HLQ38.1-9.74 fully adjustable mixed-flow pumps to irrigate the largest irrigation area in Heilongjiang province. Furthermore, it is the second largest mixed-flow pump station in China, as shown in Fig. 1.4. This infrastructure plays a crucial role in realizing increased grain production and efficiency, optimizing the regional water resource allocation, and implementing the coordinated scheduling of surface water, groundwater, and rainwater resources for irrigation in the Sanjiang region – the largest granary in the country. It contributes significantly to promoting the coordinated and sustainable development of the economy, society, and ecology in the region.
The Belt and Road project of Chongqing Electromechanical Group – the Hyderabad flood control irrigation project in Telangana, India – has been successfully tested recently
[4]
. The 24 large, closed-volute mixed-flow pumps and 12 large synchronous motors used in the project have all been developed by Chongqing Hydro Turbine Co. Ltd. with independent intellectual property rights. Twenty-four large mixed-flow pumps are installed in this flood control and irrigation project. Each water pump has a flow of 41 m
3
/s, a lift of 11 m, and a rotational speed of 136.6 r/min. It is the largest closed mixed-flow pump with single unit power of 6500 kW synchronous motor. The energy index and stability index of water pumps and synchronous motors have reached an international advanced level.
1.4 Summary
This chapter provides an overview of the main structural forms of the mixed-flow pump, its classifications, and industrial applications. In terms of the rotational speed, the specific speed (ns) ranges between 35 and 80 rpm for low-speed mixed-flow pumps and between 80 and 160 rpm for higher-speed mixed-flow pumps. Considering the structure of the suction chamber, mixed-flow pumps can be categorized as volute mixed-flow pumps and guide vane mixed-flow pumps. Additionally, the broad applications of mixed-flow pumps in agricultural irrigation and other major industrial projects attest to their excellent operational range, performance, and stability.
References
1
https://www.ksb.com/centrifugal-pump-lexicon/mixed-flow-pump/192030
.
2
https://www.pumpcj.com/case/95.html
.
3
https://www.pumpcj.com/case/97.html
.
4
https://rmh.pdnews.cn/Pc/ArtInfoApi/article?id=7493665
.
2Basic Concepts and Theory of Mixed-flow Pumps
2.1 Basic Flow and Performance Parameters
The parameters characterizing the performance of the pump are as follows.
2.1.1 Volume Flow Q
Flow is the volume (or mass) of liquid delivered in unit time. Volume flow is expressed in Q, the unit is m3/s, m3/h, or L/s, etc. The mass flow is expressed as Qm and the unit is ton/h, kg/s, etc. The relationship between the mass flow and volume flow is
where ρ is the density of the liquid in kg/m3; ρ of clean water is generally taken as 1000 kg/m3 at room temperature.
2.1.2 Head H
Head is the increment of energy per unit weight of liquid pumped by the pump from the pump inlet to the pump outlet. It is the effective energy obtained by 1 kg of liquid through the pump. The unit therefore is (N • m/N) = m, which is the equivalent liquid column height pumped by the pump shaft; the liquid column height is called the pump head H and is conventionally given in meters (m). The pump head can be written as
where Ed is energy per unit weight of liquid at the pump outlet in meters and Es is energy per unit weight of liquid at the pump inlet in meters.
The energy per unit weight of the liquid is called head in hydraulics, which is usually composed of the pressure head (m), the velocity head (m), and the position head z (m), i.e.
and
Therefore
where pd and ps are the static pressure of the liquid at the pump outlet and inlet respectively, vd and vs are the liquid velocity at the pump outlet and inlet, respectively, and zd and zs are the distance from the pump outlet and inlet to a specified measuring datum plane respectively.
The head H of the pump is a key performance parameter of the pump, which is only related to the energy of the liquid at the inlet and outlet flanges of the pump and is not directly related to the type of the pump. However, using the energy equation, the pump head can be expressed by the energy of the liquid in the pump device.
2.1.3 Speed n
The speed n is the number of revolutions per unit time of the pump shaft, and its unit is revolutions r/min.
2.1.4 NPSH
The NPSH, an abbreviated form for the net positive suction head, is the main parameter indicating the cavitation performance of the pump. The NPSH has also been represented by Δh in the literature by some scientists.
2.1.5 Power and Efficiency
Pump power usually refers to the input power; it is the power transmitted by the prime mover to the pump shaft and is also known as the shaft power expressed by P.
The effective power of the pump, also known as the output power is expressed by Pe. It is the effective energy obtained by the liquid output from the pump per unit time.
Since the pump head is the effective energy obtained from the pump by the unit mass of liquid output from the pump, the product of head, mass flow, and gravity acceleration is the effective energy obtained from the liquid output from the pump in unit time, which is the effective power of the pump.
or
where ρ is the density of liquid delivered by the pump in kg/m3, γ = ρ g is the specific gravity of the liquid delivered by the pump in N/m3, Q is the pump flow in m3/s, H is the pump head in m, and g is the gravitational acceleration in m/s2.
If the unit of specific gravity of the liquid is kg f/m3, then
The difference in the shaft power Р and the effective power Pe is the power loss in the pump, which is used to determine and define the efficiency of the pump. The efficiency of the pump is the ratio of the effective power to the shaft power expressed as
2.2 Typical Type of Flows in the Mixed-flow Pumps
2.2.1 Tip Leakage Flow
Since the tip leakage flow (TLF) in turbomachinery has significant impact on the performance and even safety of the machine, it is very important in the study of hydraulic machinery. Since the 1950s, the understanding of the TLF has been one of the major research topics in fluid mechanics of pumps, compressors, and turbines. The TLF model developed by Rains [1] is considered as the first original and seminal contribution which has served as a stepping stone toward the comprehensive understanding of this important flow phenomenon in turbomachines. Using this model, the velocity of TLF at the top of the outlet of the suction surface can be approximately estimated. At the same time, the change in the runner efficiency caused by TLF can be analyzed, but this model cannot calculate the micro-flow structure of the flow field. Later, Chen et al. [2] simplified the TLF model and deduced the trajectory coordinates of the two-dimensional tip leakage vortex (TLV) theoretically. Early experimental research and numerical simulations in the field of gas turbines provided a lot of information and data for exploring and analyzing the cause of formation as well as flow field structure of the flange leakage vortex [3, 4]. All these research efforts have enormously contributed to the present understanding of TLF and TLV.
Compared to the gas turbine, due to the large viscosity of water and more complex flow field in the end wall region, the research progress on TLF of the mixed-flow pump has been relatively slow. Yi et al. [5] employed the Reynolds-Averaged Navier-Stokes (RANS) equations with the SST k-ω turbulence model, revealing the formation mechanism of TLV and its influence on the performance of mixed-flow pump. Liu et al. [6] studied the shape and trajectory of the TLV in the mixed-flow pump, qualitatively and quantitatively analyzed the TLV, and determined that the TLV formed by the mixing of TLF and mainstream is the main reason for the deterioration of flow pattern and performance of the mixed-flow pump. Wu [7, 8], and Miorini et al. [9] used PIV technology to test and measure the flow field structure of TLV in the axial-flow water-jet propeller. It was found that the instantaneous TLV structure was formed by the unsteady vortex propagating to the top area of the blade channel, entraining with the mainstream and then breaking when reaching the pressure surface of adjacent blades. Using the PIV measurements, Masahiro et al. [10] tried to determine the generation mechanism of TLV of the mixed-flow pump at low flow rates and its impact in creating instability in the flow. It was found that the load on the impeller blade inlet rim increased with an increase in the leakage flow, and the TLV developed further with a decrease in the flow rate, forming a shroud of leakage flow.
Since TLF has a direct relationship with the clearance size, many researchers have studied the TLF under different tip clearances. Hah [11] and Li et al. [12] employed the LES to reveal the unsteady flow properties of TLF and TLV and analyzed the structure of TLF for five different tip clearances. Li et al. [13] studied the leakage flow for different tip clearances by performing numerical calculations and analyzed the formation and development process as well as the losses due to TLF and TLV for different tip clearances, and found that the strength of TLV increases with increase in tip clearance resulting in increase in losses. Zhang et al. [14] conducted the numerical simulation of a mixed-flow pump with low specific speed and analyzed its internal flow field for different tip clearances and found that the larger the tip clearance, the greater the effect of entrainment between the TLF and the mainstream flow. Goto [15] numerically analyzed the interaction mechanism of secondary flow and the formation mechanism of jet wake structure in the end wall region of the mixed-flow pump for four different tip clearances using the three-dimensional RANS equations and found that the reverse flow caused by the TLF at larger clearances is the main reason for thickening of the boundary layer in the end wall region resulting in the deterioration of the entire flow field. Zhong et al. [16] studied the mixed-flow water-jet pump and analyzed the influence of different blade tip clearances on the performance and internal flow field of the water-jet pump and improved the blade profile in order to reduce the losses. Shi and Zhang [17, 18] studied the external flow characteristics as well as the internal flow field of the mixed-flow pump for different tip clearances through the combination of numerical simulation and experiment to analyze the evolution process of TLV and determine the influence of different tip clearances on formation and evolution of TLV and its effect on hydraulic performance and cavitation characteristics of the pump. Bing et al. [19] experimentally studied the efficiency drop of a mixed-flow pump (Δη/Δδ) due to an increase in tip clearance Δδ
