Numerical simulations of centrifugal pump efficiency · Numerical simulations of centrifugal pump...
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Numerical simulations of centrifugal pump efficiency Haoyu Wang This thesis is presented for the Degree of Master of Engineering by Research at the School of Mechanical Engineering, University of Western Australia. March, 2012
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Numerical simulations of centrifugal pump efficiency
Haoyu Wang
This thesis is presented for the Degree of Master of Engineering by Research at the School of Mechanical Engineering,
University of Western Australia.
March, 2012
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Abstract
It has been recognised that some of the vital characteristics such as flow patterns and pressure
fluctuations of the centrifugal pump will affect the overall pump efficiency. However, most
of past research based on theoretical analysis or experiments, which are time consuming and
expensive. With the development of computer science, it is possible now to investigate the
three dimensional unsteady flow patterns in the centrifugal pump. Then the study can be
applied to establish the correlation between the pump characteristics and efficiency
numerically.
This thesis describes some experiments which establish the performance curve of a particular
commercial centrifugal pump, which then be used as the basic data for the numerical results
to be compared with. The modal test of this centrifugal pump was conducted for both its
components and assembly to verify the structural rigid assumption in the numerical
simulation.
Both static numerical method (Frozen Rotor) and transient numerical method (Sliding Mesh)
were used in this thesis. The key findings are summarized as follows:
• From the results obtained by Frozen Rotor method, it can be seen that the general
trend of global properties including water head and pump efficiency were captured
well while there existed some differences when compared them with experimental
data. This was possibly due to the limitations of Frozen Rotor method to predict
unsteady flow phenomenon.
• When the Sliding Mesh method applied, the results indicate that: First of all, it was
possible that the position of the large vorticity zone could be a factor which would
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result in the change of the pump efficiency. Secondly, if the helical region
distributed uniformly, the pump is more likely to operate at BEP. On the other hand,
the pump efficiency would drop if non-uniform helical regions observed. Finally, it
can be found that the pump efficiency decreases as the magnitude of dynamic
pressure increases. In other words, more energy has been used to generate vibration
when the pump operates at off-design conditions.
• A similar trend can be observed for the pump efficiency, the magnitude of dynamic
pressure, the amplitude of velocity and the vibration energy. The minimum of these
properties can be seen when the pump operated under design condition while an
increase of these properties can be observed for off-design pump operating condition.
This corresponds to the statement that if more energy had been used to generate
vibration, less pump efficiency can be expected. An empirical correlation between
the pump vibration and efficiency then has been established in this project.
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Statement of Originality
The work in this thesis contains no material which has been submitted for any other degree or
institution. To the best of the author’s knowledge, this thesis contains no material previously
published or written by another person, except where references are made in the text.
Haoyu Wang
February, 2012
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Acknowledgements
I would like to give my most heartfelt thanks to my principle supervisor, Winthrop Prof. Jie
Pan. It is no doubt that this thesis could not be completed without his continually valuable
advice, guidance and encouragement. Also thanks to my co-supervisor, Dr. Angus Tavner.
He helped me to overcome many difficulties and proposed many fantastic idea in the process
of doing this project.
Special thanks to Dr. Andrew Guzzomi for his selfless help in my experiments and thesis
English editing. I also give my acknowledgement to all the technical staff at the School of
Mechanical Engineering.
Finally, I am forever grateful for the love and support from my parents, Jianxing Wang and
Suijiang Xian.
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Table of Contents Abstract………………………………………………………………………………………………………………………………………………i
Statement of Originality………………………………………………………………………………………………………………..….iii
Acknowledgements…………………………………………………………………………………………………..……………..………iv
Chapter 1 Introduction ........................................................................................................................... 5
1.1 General background and motivation ...................................................................................... 5
1.2 Literature review ..................................................................................................................... 6
1.2.1 Introduction .................................................................................................................... 6
1.2.2 Pump efficiency prediction ............................................................................................. 7
1.2.3 Unsteady flow within the pump ............................................................................................ 7
1.2.4 Pressure fluctuation ...................................................................................................... 11
1.2.5 Pressure fluctuation related energy conversion ........................................................... 12
1.2.6 Vibration Condition Monitoring .................................................................................... 14
1.2.7 The correlation between vibration and pump efficiency ............................................. 14
1.2.8 Summary ....................................................................................................................... 15
1.3 Thesis structure ..................................................................................................................... 16
Chapter 2 Basics of Centrifugal Pumps ................................................................................................. 18
2.1 Introduction ................................................................................................................................ 18
2.2 Centrifugal pumps ....................................................................................................................... 18
2.3 Definition of pump performance properties .............................................................................. 20
2.3.1 Pump capacity ...................................................................................................................... 20
2.3.2 Total water head He ............................................................................................................. 20
2.3.3 Power ................................................................................................................................... 21
2.3.4 Pump performance curve .................................................................................................... 22
2.4 Pump vibration ............................................................................................................................ 24
Chapter 3 Experiment Setup ................................................................................................................. 26
3.1 Introduction ................................................................................................................................ 26
3.2 Description of the pump test rig ................................................................................................. 27
3.2.1 Centrifugal pump ................................................................................................................. 29
3.2.2 Motor ................................................................................................................................... 32
3.2.3 Flow meter ........................................................................................................................... 33
3.2.4 Accelerometer ...................................................................................................................... 34
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3.2.5 Pressure transducers ........................................................................................................... 34
3.2.6 Data acquisition card ........................................................................................................... 34
Chapter 4 Modal testing of the centrifugal pump ................................................................................ 36
4.1 Introduction ................................................................................................................................ 36
4.2 Results ......................................................................................................................................... 38
4.2.1 Finite Element Analysis of Pump Impeller ........................................................................... 38
4.2.2 Impact Hammer Test of the Pump Impeller ........................................................................ 40
4.2.3 Finite Element Analysis of Pump Volute Casing ................................................................... 45
4.2.4 Impact Hammer Test of the Pump Volute Casing ................................................................ 50
4.2.4 Assembled on to the Pump Testing System......................................................................... 54
4.2.4.2 Mode Shapes and Frequencies in the Radial Direction .................................................... 59
4.3 Conclusion ................................................................................................................................... 64
Chapter 5 Numerical Simulations for a Hypothetical Pump Model...................................................... 65
5.1 Introduction ................................................................................................................................ 65
5.2 Hypothetical numerical model .................................................................................................... 65
5.3 Numerical methods ..................................................................................................................... 66
5.3.1 Model and computational method: Frozen Rotor ............................................................... 66
5.3.2 Model and computational method: Sliding Mesh ............................................................... 68
5.4 Simulation results ....................................................................................................................... 69
5.4.1 Pump efficiency curve .......................................................................................................... 69
5.4.2 Water head .......................................................................................................................... 70
5.4.3 Static pressure distribution .................................................................................................. 70
5.4.4 Flow velocity profile ............................................................................................................. 73
5.4.5 Pressure fluctuation ............................................................................................................. 75
5.4.6 Blade loading ........................................................................................................................ 81
5.4 Summary ..................................................................................................................................... 82
Chapter 6 Numerical Analysis of Centrifugal Pump: Steady Flow Model ............................................. 83
6.1 Introduction ................................................................................................................................ 83
6.2 Model and computational method: Frozen rotor ....................................................................... 83
6.2.1 Solid model of commercial centrifugal pump ...................................................................... 83
6.2.2 Frozen rotor method ............................................................................................................ 84
6.2.3 Geometry, grid and flow Solver ........................................................................................... 85
6.2.4 Boundary conditions ............................................................................................................ 87
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6.2.5 Numerical solution control .................................................................................................. 87
6.3 Results and discussion ................................................................................................................ 87
6.3.1 Water head .......................................................................................................................... 87
6.3.2 Efficiency .............................................................................................................................. 88
6.3.3 Flow structure inside the centrifugal pump ......................................................................... 90
6.4 Summary ..................................................................................................................................... 96
Chapter 7 Numerical analysis of centrifugal pump: transient flow ...................................................... 97
7.1 Introduction ................................................................................................................................ 97
7.2 Model and computational method: Sliding Mesh ...................................................................... 97
7.2.1 Solid model of the commercial centrifugal pump ............................................................... 97
7.2.2 Sliding mesh method ........................................................................................................... 97
7.2.3 Geometry, grid and flow solver ........................................................................................... 98
7.2.4 Boundary conditions ............................................................................................................ 98
7.2.5 Numerical solution control .................................................................................................. 98
7.2.6 Initial condition .................................................................................................................... 99
7.3 Numerical results ........................................................................................................................ 99
7.3.1 Water head .......................................................................................................................... 99
7.3.2 Efficiency ............................................................................................................................ 100
7.3.3 Flow field ............................................................................................................................ 102
7.3.4 Static pressure.................................................................................................................... 104
7.3.5 Flow vorticity ...................................................................................................................... 106
7.3.6 Flow helicity ....................................................................................................................... 108
7.3.7 Pressure fluctuation ........................................................................................................... 110
7.4 Summary ................................................................................................................................... 114
Chapter 8 The correlation between vibration and efficiency ............................................................. 115
8.1 Introduction .............................................................................................................................. 115
8.2 The correlation between efficiency and flow rate .................................................................... 115
8.3 The correlation between pressure fluctuation and efficiency .................................................. 116
8.4 Velocity variation in the frequency domain .............................................................................. 116
8.5 Vibration energy on the inner surface of pump volute casing ................................................. 119
8.6 Summary ................................................................................................................................... 121
Chapter 9 Conclusions and future work ............................................................................................. 122
9.1 Conclusions ............................................................................................................................... 122
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9. 2 Future work .............................................................................................................................. 123
References .......................................................................................................................................... 124
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Chapter 1 Introduction
1.1 General background and motivation
How to use energy efficiently has drawn increasingly more public awareness. Increasing
energy efficiency is not only an effective means to reduce financial cost, but also contributes
to the solution of environmental problems such as pollution and climate change.
The pump industry is advancing at a staggering rate and represents a mature technology.
Some advanced design techniques have been applied in this area to improve the pump
performance by increasing efficiency.
Most of the early developments in pump research were based on theoretical analysis or
experiments. The main contributions of these developments were to investigate the
possibilities to increase the pump efficiency by classical mathematical means and
experiments; the latter being time-consuming and expensive. The flow pattern in the pump is
three dimensional and unsteady. To take a more advanced step to increase pump efficiency,
far more in-depth research should be carried out by taking the unsteady flow phenomenon
into account.
With the advances in computer technology and more in-depth understanding of unsteady flow
phenomenon, it is now feasible to carry out numerical calculations to investigate the flow
phenomenon within pumps in an economic way and a reasonable time.
One of the most popular concerns associated with unsteady numerical methods for modelling
centrifugal pumps is the pressure fluctuation experienced in the pump during daily operation.
It has been found that the pressure fluctuations caused by the flow structure exiting the pump
impeller and the unsteady flow-dynamic interaction near the volute casing tongue are higher
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at the blade passing frequency than that at other frequencies [1]. Centrifugal pumps with such
complicated geometrical features under different working conditions may experience
different flow profiles and then provide different performance [1]. Therefore, it is worth to
carry out an in-depth numerical research on this topic for a centrifugal pump under a series of
working conditions.
This project was carried out on a commercial centrifugal pump manufactured by Goulds
Pumps. The 3D commercial pump model was generated and a whole set of numerical
simulations were carried out to investigate some unsteady flow patterns and dynamical
features under different working conditions.
The main objective of this project was to investigate some vital characteristics of centrifugal
pumps stated above numerically. Those characteristics are including pump efficiency, flow
patterns, flow field analysis and pressure fluctuation analysis. Once these analyses were
fulfilled, the correlations between those vital characteristics and the pump efficiency can be
established. The correlations can be helpful for further centrifugal pump applications such as
structural vibration analysis and condition monitoring.
1.2 Literature review
1.2.1 Introduction
In this section three main aspects are covered. First of all, previous experimental and
numerical results on pump prediction are discussed. Secondly, unsteady flow patterns
including velocity vectors and static pressure distribution within the centrifugal pump are
briefly shown. Then the available experimental and numerical predicted pressure fluctuation
is fully presented. Some qualitative work with regard to the energy transferring from input
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energy to vibration is discussed. Finally, a brief introduction of vibration Condition
Monitoring is at the end of this section. The correlation between vibration and pump
efficiency can be used to establish a vibration based Condition Monitoring system in the
future.
1.2.2 Pump efficiency prediction
Dick et al. [2] applied both the steady and unsteady methods to predict the pump performance
of a volute centrifugal pump. They stated that the unsteady numerical method, often referred
to as the sliding mesh method, can provide a better pump performance prediction. The reason
why steady numerical method cannot be used confidently because it is involves the
recognition which is unable to accurately represent the effect of fluid leaving the impeller.
Blanco et al. [3] have investigated the accuracy of pump efficiency prediction numerically by
taking the centrifugal force and unsteady terms into account. They found that the water head
and efficiencies for different flow rates can provide good agreement with experimental data.
However, the correlation with efficiency was not reasonable at lower flow rates. They
proposed that this was due to the velocity inlet condition being a mismatch for low flow rates.
Jose et al. [4] conducted a more in-depth pump efficiency comparison using both the
numerical and experimental results. Although the disk friction losses and mechanical losses
at the bearings were not considered, the numerical method was still able to provide a good
agreement with the experimental data.
1.2.3 Unsteady flow within the pump
Due to the complex pump geometry associated with both the impeller and volute casing,
coupled with the unsteady flow, an extremely distorted flow pattern is often presented [5]. As
shown in middle graph of Figure 1.1, these graphs were obtained at the mid-cross plane of a
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centrifugal pump. If the pump operates at the design condition (i.e. operating at the nominal
flow rate of the pump), the absolute velocity vector graph shows the stagnation point is at the
volute tongue symmetry position. While at the off-design conditions, the stagnation moves
around the volute tongue accordingly [6] as the stagnation point moves to the discharge side
of the pump at low flow rates, and to the impeller side at high flow rates.
As far as the pressure distributions are concerned, the position of stagnation point was first
considered by Jose et al. [7] as shown in Figure 1.2. Qn stands for nominal flow rate of the
pump. The stagnation point shifted from the discharge side to the volute side as the flow rate
increased which corresponds to velocity vector distribution. However, a more uniform
pressure distribution and hence flow pattern can be found at the design condition. The
pressure increases at different impeller channels is uniform. When the pump is operating at
off-design conditions, an asymmetrical pressure distribution pattern can be observed
indicating the impeller blade loadings are different [6]. These asymmetrical pressure
distributions can be seen as an indication for the level of pump vibration. Due to these effects,
CFD analysis can be used to determine whether the pump is operating efficiently or not.
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Figure 1.1: Velocity vector field in an intermediate pseudostream surface plotted in a 0–14.5 m/s scale (top
graph), nominal (middle graph) and high flow rate (bottom graph), according to Jose et al. [6].
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0.24Qn
0.95Qn
1.57Qn
Figure 1.2: Contours of static pressure in the tongue region at a time instant for different flow rates, according to
Jose et al. [7].
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1.2.4 Pressure fluctuation
Several experiments on pressure fluctuations of centrifugal pumps are available. These are
both historic [8,9] and current [10-14]. By using piezoresistive pressure transducers and a
telemetry system, Kaupert and Staubli [12] measured the unsteady pressure field inside the
volute of a centrifugal pump. It has been observed that pressure fluctuation amplitudes were
higher at the trailing edge of the impeller blade. This is caused by the nonuniform pressure
distributions between different impeller blades.
Guo et al. [15] presented experimental results showing that both the volute static pressure and
the pressure fluctuations on the impeller are nonuniform at the off-design conditions. The
asymmetric shape of the volute casing of the pump results in a circumferential distortion of
the flow pattern, especially at off-design conditions [16]. When the impeller is rotating, the
flow at the impeller outlet interacts strongly with the volute flow generating pressure
fluctuations.
The pressure fluctuation at the blade passing frequency is caused by two factors: the
nonuniform flow distribution through both sides of the impeller blade (jet-wake pattern) and
the fluid-dynamic interaction of the impeller blades with the volute tongue.
Experimental studies have been conducted to investigate the influence of pressure
fluctuations at the blade passing frequency. Much experimental work has been done in this
area. Some examples include Arndt et al. [17] and Hagelstein et al. [18]. In 2002, Jorge et al.
[1] conducted a series of tests to measure pressure fluctuation distribution at the blade passing
frequency along two different centrifugal pump volutes. They found that pressure fluctuation
amplitude at nominal flow rate is lower than those at off-design conditions. They related
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pressure fluctuation shift to the shift of stagnation point at the tongue and different
characteristics of recirculation flow through the gap between impeller and volute tongue.
Different numerical simulations have also demonstrated the capability to investigate flow
pattern details in centrifugal pumps [19-21]. Some of them applied mixing plane or Frozen
Rotor method [19, 20]. However, this method ignores the relative impeller movement to the
volute casing which is the driving mechanism of the dynamic effects within a centrifugal
pump. It has subsequently been found that a fully unsteady flow model is necessary to take
the flow-dynamic interaction into account [19].
Blanco et al. [3] predicted time domain pressure fluctuations in the volute wall by sliding
mesh method and compared it with experimental data. The comparison showed reasonable
agreement for the pressure fluctuation at nominal flow rate.
Jose 2002 et al. [4] provided a more in-depth experimental and numerical research into
pressure fluctuation at different flow rates by obtaining pressure fluctuation distributions
from 36 points on a circumference with a radius slightly bigger than that of the impeller.
From their result, it can be concluded that the numerical method was able to predict pressure
fluctuation well for nominal and higher flow rates, but not for low flow rates. The difference
was also profound in the near tongue region. The predicted pressure fluctuation amplitudes
were always lower than the measured ones. They stated that this was possibly due to pump-
piping circuit interaction which was ignored in the numerical simulations.
1.2.5 Pressure fluctuation related energy conversion
The nonuniform pressure distributions produce a static radial thrust when the pump is
operating at off-design conditions [22]. The pressure fluctuations interact with the volute
casing give rise to dynamic effects (mainly unsteady forces). These unsteady forces are
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mostly caused by pressure fluctuations due to frequency of rotation and blade passing
frequency [23]. Also these unsteady forces are one of the most important sources of pump
vibration and hydraulic noise [24].
Jose 2002 [23] induced a simple acoustic model in which two point sources radiated plane
sound waves along the volute to quantify the blade-tongue interaction. After fitting the
experimental data by means of a least-square error procedure, the results showed these two
ideal sources were coupled forming a dipole. Therefore, they concluded that the blade-tongue
interaction possibly played a dominant role in the generation of noise for pump off-design
conditions. It appeared the pump efficiency was reduced in such conditions since more
energy was dissipated in the form of noise.
Fred et al. [25] have noted that some of the energy produced by pressure fluctuations due to
wake flow from the impeller trailing edge and its interaction with the volute casing is
dissipated as structural vibration. They also stated that the interaction between the wake flow
and the volute tongue is another noise source. The energy produced by impeller discharge
velocity fluctuations is dissipated as heat due to liquid drag and vortex decay. Based on
conservation of energy principles, it seems highly probable that the conversion of input
energy into other forms (heat, noise, vibration) results in a reduction of pump efficiency.
Hence this also provides an incentive for new research.
Although the pump efficiency monitoring methods based on heat have been developed, it
appears that vibration based technology has not. Therefore, there is a potential need to
investigate the correlation between vibration and pump efficiency to establish the foundation
of vibration Condition Monitoring.
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1.2.6 Vibration Condition Monitoring
The modern vibration Condition Monitoring of pump stems from Crawford [26] who
established the instrumentation and frequency analysis to identify defects from frequency
patterns. The analogue instruments and computers coupled with microprocessors and circuits
allowed the vibration signals to be collected [27]. Then Taylor [28] improved the method for
producing frequency spectra from the time domain signal using FFT. The development of
both equipment and methods was permits ever more in-depth research to investigate the
correlation of vibration signature and other parameters. In this context, it is now feasible to
apply such technology to pump efficiency monitoring.
The traditional research provides a method to identify the faults of operating pumps by using
various signal filtration and enhancing methods [29]. The vibration analysis involves the
vibration data collection in time domain and the corresponding frequency spectrum. The
frequency spectrum of the signal can provide information in terms of magnitude of blade
passing frequency and other important frequency components. These can then be used with
the pump operating condition to work out the correlation between them.
1.2.7 The correlation between vibration and pump efficiency
In 2004, Pan and Hodkiewicz conducted a series of experiments to investigate the effect of
partial-flow operation on the axial vibration of double-suction centrifugal pumps. Partial flow
was defined as a flow rate below the point which can result in the best efficiency. They found
that some unsteady flow phenomenon was affecting flow separation, secondary flows and
recirculation when the pump was operating at partial flow condition [30,31].
The main findings of their work were obtained based on the short-time fourier techniques
(STFT) [31]. First of all, the axial vibration was a minimum when the pump operateing at the
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design condition. There were transient with high magnitude of axial vibrations operating
below the BPF which established at partial-flow conditions. These transient events had no
correlation with the pump fundamental frequency and the magnitudes sometimes exceeded
the magnitude at BPF. They concluded that this phenomenon may be due to the unsteady
axial thrust coming from two sources: the pressure on the impeller shroud surfaces and the
change in axial momentum through the pump [31].
Although the above study was conducted on a double-suction pump, it can still be used as a
foundation of this thesis. Similar correlation between pump efficiency and vibration can also
be expected for a single-suction pump. However, there are limitations in the above study. The
study only investigated the axial vibrations below the best efficiency point.
1.2.8 Summary
In this chapter, both experimental and numerical results on the centrifugal pump efficiency
prediction and pressure fluctuation were reviewed. This thesis focuses on the numerical
simulations to determine the vital characteristics of a selected centrifugal pump and then to
obtain correlations between these characteristics and pump efficiency. The main questions
addressed in this thesis are:
(1) What is the specific performance curve of the commercial centrifugal pump? In other
word, how will the pump efficiency change against the flow rate?
(2) By comparing with available experimental data, such as efficiency, water head and
pressure fluctuations, is the numerical method sufficient to provide reliable
predictions?
(3) Which numerical method gives better predictions; is it Frozen Rotor method or
Sliding Mesh method?
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(4) What are the unsteady flows and how does the unsteady flow pattern including
velocity, pressure, vorticity etc. affect qualitatively, the pump efficiency?
1.3 Thesis structure
The work in this thesis is presented in the following chapters. Their contents are briefly
described below.
Chapter 2 presents the basics of a centrifugal pump and provide a brief introduction on the
topic of pump vibration.
Chapter 3 describes the components of the pump, test rig configuration, the equipment and
experimental method applied in this work.
The modal tests of the pump in order to validate assumptions within the numerical simulation
are described in Chapter 4. More specifically, in order to verify the feasibility of considering
volute casing and impeller as rigid in the CFD model, modal tests were conducted. The setup
and results are discussed in this chapter.
A hypothetical numerical model is described in Chapter 5. The main purpose of this chapter
is to check the validity of numerical methods by comparing the numerical predictions with
published results.
The numerical simulation methods and results are shown in Chapters 6 and 7. Chapter 6 is
focuses on the numerical simulations obtained from Frozen Rotor method while Chapter 7
explains the results obtained using Sliding Mesh method.
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Specifically: in Chapter 6, some global varieties including pump efficiency and water head
are compared with experimental data. Then the static pressure, the velocity vector
distributions, the vorticity and helicity within the pump were discussed.
Chapter 7 is focuses on the unsteady phenomenon of the pump. Different pump parameters
including water head and efficiency and unsteady flow patterns were analysed. Then
empirical numerical correlations between the pump efficiency and these pump characteristics
were established.
The correlation between vibration and efficiency of the centrifugal pumps is described in
Chapter 8. Different aspects related to the pump vibration are also discussed in this chapter.
Then the vibration energy density is calculated based on the velocity variation for a series of
selected points at the inner surface of the volute casing to establish the correlation.
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Chapter 2 Basics of Centrifugal Pumps
2.1 Introduction
The main purpose of this chapter is to give a general perspective of centrifugal pumps. First
of all, the function and the main components of a centrifugal pump are described. Secondly,
the terminology used to define a centrifugal pump is presented. Finally, the pump vibration is
briefly discussed in the last section of this chapter.
2.2 Centrifugal pumps
The centrifugal pump (Figure 2.1) is a member of rotating machines family [32]. A
centrifugal pump consists of two basic components: the rotary part, known as the impeller,
and the stationary part, called the volute casing.
Figure 2.1: Main components of a centrifugal pump [33]
The principal function of a centrifugal pump is to impart energy to the fluid to make it flow
and rise to higher level. They achieve this through the fluid leaves the impeller with a higher
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speed than it enters the pump. This increases the kinetic energy which is proportional to the
square of the velocity at the edge or vane (i.e. blade) tip of the impeller. As the impeller
rotates, a pressure drop can be observed at the impeller eye region which allows more fluid to
enter. The fluid speed is converted to pressure in the discharge outlet of the volute casing.
The volute casing is the stationary component of a centrifugal pump. Due to its asymmetrical
geometry, it converts the kinetic energy into pressure by decreasing the speed of liquid
coming out of the impeller. Also it can balance the hydraulic pressure on the shaft of the
pump only at the best manufacturer’s recommended capacity. Due to the lateral stress on the
shaft of the pump, wear may occur on the seals and bearings if the centrifugal pump is
running at a lower capacity. The suction and discharge are part of the volute casing. The
suction is located concentric to the shaft while the discharge is typically mounted on the top
of the casing perpendicular to the pump shaft (Figure 2.1).
The impeller is the most important rotating part of the pump which accelerates the fluid. The
acceleration of the fluid is achieved by the centripetal force. The name centrifugal pump
derives from this phenomenon. There are two types of impellers in the pump industry. The
most common type is called open impeller. An open impeller refers to an impeller without
any shroud surface on the top of it. This kind of impeller is less likely to become blocked.
However, manual adjustment to the volute or back-plate is needed to prevent pump internal
re-circulation. The closed impeller means pump shrouds or sidewall enclosing the blades.
This kind of impeller requires wear rings and these rings often results in more maintenance
problems.
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2.3 Definition of pump performance properties
The most important properties used to define centrifugal pumps are capacity, head, BHP
(Brake Horse Power) and BEP (Best efficiency point). These properties can be compared and
analysed in a graph called pump performance curve.
2.3.1 Pump capacity
Capacity often refers to the flow rate in which the operating fluid is pumped to a certain
operating point. For example, to obtain the best efficiency, different types of pump may
require different flow rates (capacities) to achieve it. The capacity is typically measured in
cubic meters per hour (m3/hr).
There are a number of factors which can affect the capacity including liquid characteristics,
impeller rotational speed and impeller size. For a given pump, with a certain impeller rotating
at a fixed rotational speed, the only means to change the capacity of the pump are the
pressures at the pump suction and discharge.
The capacity of the pump can be expressed by [33]:
3.13Q VA= (1)
where V is the velocity of flow in the suction pipe in m/s and A is the cross-sectional area of
the discharge pipe in m2.
2.3.2 Total water head He
The total water head, also known as the effective head of a pump, can be expressed as the
energy increase between the suction and discharge side of the pump. This energy increase
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includes the discharge head increase and the increase in suction head. Therefore the total
water head is:
e D SH H H= + (2)
where HD the discharge head and Hs is the suction head
2.3.3 Power
2.3.3.1 Brake Horse Power (BHP) Pb
The BHP is the actual horsepower input at the pump shaft coupling. In the case of a pump
connected directly to an electric motor, the brake horse power can be considered as the same
as the power output of the motor.
bP VIPF= (3)
where PF is a power factor and stands for the motor efficiency and I is the phase current.
2.3.3.2 Effective power Pe
The effective power of a pump is a product of the effective water head, the discharge flow
rate Qr and the specific weight 1γ = gρ which can be expressed as:
1e r eP Q Hγ= (4)
2.3.3.3 Pump efficiency
The total efficiency of a pump is the ratio of the effective power to the shaft power which can
be expressed by the formula:
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e
sh
PP
η = (5)
The efficiency of the pump is less than 1, which means there are some mechanical and
hydraulic losses within the pump.
2.3.3.4 Best efficiency point (BEP)
Best efficiency point is the capacity at a certain impeller diameter at which the efficiency is
the highest. BEP is of great importance to identify the optimum energy conversion. Since the
pump efficiency is related to the change in kinetic energy into pressure, BEP means the
energy change from kinetic energy to pressure energy at a given capacity is the maximum.
The pump is operating in the most efficient condition at BEP.
If a pump is operating at other than BEP, it may suffer from many mechanically unstable
conditions such as increased vibration, overheat and unexpected thrust. These abnormal
conditions can cause bearing and mechanical seal failures. Moreover, the temperature rise
would be the main cause for the pump cavitation.
2.3.4 Pump performance curve
A complete and thorough test is conducted by the pump manufacturer to analyse the
characteristics of the pump including efficiency, required input brake horsepower (BHP curve)
and head (Figure 2.2).
The capacity and pressure needs of any system can be defined by the system curve. Moreover,
the relation between the capacity and pressure variation for a particular pump can be shown
as the pump curve. The intersection of these two curves defines the operating point of both
pump and process.
23
All these properties are plotted against the pump capacity to cover pump performance curve.
Other information like pump size and type, impeller size and rotational speed. are normally
also stated in this kind of graph (not shown in this example). This curve is often drawn at a
certain rotational speed and for a specific impeller diameter. For a given pump, the
performance curve shows all of its operating characteristics.
From the pump performance curve (Figure 2.2), the normal operating range can be
determined. It can be observed that the curve starts at zero flow rates with a shut-off head.
The curve then gradually decreases to a point called run-out point which shows the maximum
flow rate and the minimum head. The pump cannot work beyond this point since cavitation
would occur.
Figure 2.2: Typical pump performance curve [33]
24
2.4 Pump vibration
Many pump vibration problems result from dynamic effects (mainly pressure fluctuations)
caused by jet-wake flow pattern and non-uniform pressure distributions in each of the
impeller passages.
In general, the pressure fluctuations are generated by unsteady flow in a compressible
medium. Although water is of low compressibility, it is enough to allow pressure fluctuation
to occur [34].
There are two main causes responsible for the generation of pressure fluctuation. The wake
flow at the impeller outlet is the main source of pressure fluctuations in a centrifugal pump
[7]. The frequency of pressure fluctuation refers to blade passing frequency and its harmonics.
Also the pressure fluctuation with the rotational frequency and its harmonics are generated
due to the asymmetries in the impeller channels. The pressure fluctuations are enhanced if the
pump is operating at off-design conditions. These frequencies can be observed as sharp peaks
(also known as discrete frequencies) in the vibration FFT analysis.
The pump impeller produces vibration at multiple frequencies. The most common frequency
associated with the impeller is the Vane Pass Frequency or Blade Pass Frequency (BPF). This
is a measure of how many times the tip of the impeller vanes passes through a fixed point
which is, in this case, the tongue region of pump casing. The BPF, can be calculated from the
rotational frequency and number of blades:
bpff nRPS= (6)
where: f bpf is the Blade Passing Frequency (Hz) and RPS is the impeller revolutions per
second (Hz).
25
Secondly, vortices formed due to the flow separation and recirculation also contribute to the
generation of pressure fluctuations. Unlike the discrete frequencies generated by weak flow,
the turbulence effect shows a more continuous spectrum (i.e. broadband pressure fluctuation
or white noise) over the frequency range. Moreover, this pressure fluctuation source is rather
weak if the pump is running under attached flow conditions. The attached flow condition
means the flow never separate from the impeller blades. However, if the pump is operating at
off-design condition, strong vortices are generated due to the flow separation and
recirculation. According to the experiment conducted by Fred et al [34], this could increase
the broadband pressure fluctuations below blade passing frequency.
26
Chapter 3 Experiment Setup
3.1 Introduction
A series of experiments was conducted for this project. The main focus was the measurement
of efficiency under different operating conditions. Another important experiment was the
modal testing of both the impeller and volute casing. The purpose of this latter series of
experiments was to investigate the feasibility of rigid structure assumption in the CFD model.
The pump efficiency under different conditions was calculated using the standard method
[35]. This requires that electrical power input of the motor and the hydraulic power output be
measured.
The impact hammer vibration technique was applied for modal testing of the pump
components. The test was first conducted for the pump impeller and volute casing
individually to obtain the mode shapes and the corresponding natural frequencies. The pump
components were then resembled to the test rig and tested to determine the mode shapes and
natural frequencies of the pump assembly, these tests were performed both with and without
fluid. Finally, the frequencies obtained were compared to the blade passing frequency to
confirm the validity of rigid assumption in CFD model. More details were described in the
next chapter.
27
3.2 Description of the pump test rig
The pump test rig used in this project to investigate the correlation between the vibration
signature and efficiency is located in the Boiler Room in the UWA Civil and Mechanical
Engineering Laboratory (Figure 3.1).
Figure 3.1: Picture of experimental setting [35]
Legend 1. Power supply 8. Bearing Housing 2. VFD control box 9. Coupling guard 3. Main water tank 10. Electric Motor 4. Discharge side 11. Data Acquisition PC 5. Suction Side 12. Pressure transducer 6. Impeller casing 13. Filter 7. Baseplate 14. Flexible hose
28
It can be observed from the schematic diagram of the pump test rig, Figure 3.2, that, besides
the centrifugal pump, four important components are included. These are the water supply
tank, pressure transducers, flow meter and pipe-valve system. The water in the supply tank is
connected to the suction side of the pump which comprises of a series of valves, pressure
transducer and flexible hoses to enable precise control of water flow into the pump. The
discharge side of the pump consists of a flexible hose, pressure transducer, flow meter and
valves installed within the piping system which is connected to the main supply tank.
Accelerometers were attached to the pump in order to obtain the vibration signals on the
shroud surface of the casing and bearings. The signals from accelerometers and pressure
transducers were converted to voltage signals, recorded and analysed via a data acquisition
card (DAC).
Figure 3.2: Schematic diagram of the experimental pump rig [35]
29
3.2.1 Centrifugal pump
The commercial pump used in this project was a Goulds 3196 i-Frame MTX pump (Figure
3.2). It comprises a pump casing, impeller, baseplate and the electrical motor, which will be
described in detail in Section 3.3. It is designed to replicate pumping systems commonly
found in industry whilst maintaining high accessibility to allow gathering of flow related data.
The pump parameters can be managed via a series of valves and flow channels. This permits
for various tests to be performed and results to be gathered in a controlled manner.
Figure 3.3: Goulds 3196 i-Frame MTX pump [27]
Since its commissioning in 2001, the pump rig has been used extensively for laboratory
demonstrations purposes as well as a research tool for honours and postgraduate students
working on pump related projects. Rig operation and modification at UWA does not require a
formal recording of changes to the system in the form of a log book. Hence, the system was
also cleaned and flushed while disassembled during the modal testing conducted in this
project. This also permitted accurate measurements of the impeller and casing to be made so
30
that solid CAD models could be drawn for subsequent meshing for the CFD and finite
element analyses (FEA).
3.2.1.1 Baseplate
To prevent severe vibration and motor misalignment, a rigid baseplate designed by Goulds
Pumps made from cast iron, is incorporated to helps withstand forces and moments of the
pump piping system. All the components, including bearing housing, pump casing and
electrical motor are mounted on the baseplate. The heavy weight of the baseplate also serves
to impede the inherent vibration of the pump. All the components mounted on the baseplate
are secured with stainless steel bolts and with no vibration isolation [36].
It is not expected that the baseplate have a significant contribution to vibrations when the
pump is running. Since there is no vibration insulation material between the baseplate and the
concrete ground, any vibration from other sources near the pump could be transferred to the
pump body and recorded by the accelerometers. The baseplate, therefore, could be considered
as a medium in terms of external vibrations and signal contamination.
3.2.1.2 Pump volute casing
The pump volute casing is one of the most important components of the pump. It directs the
fluid from the suction side to the discharge side through the inner volute as the impeller
rotates. The casing is sand cast from austenitic stainless steel and has a 2 inch suction port
and 1 inch discharge port. A maximum 10 inch (254mm) diameter impeller can be
accommodated. The impeller must match closely with the casing’s allowable impeller size or
the gap between the casing walls and the edge of impeller vanes will cause recirculation flow
that will, in turn, generate excessive vibrations [37].
31
Since the pump casing covers the impeller and the fluid, all the hydraulic excitation forces
generated will be in this region and directly transferred to the casing. Water serves as an
ineffective damping medium; therefore the impeller casing will be able to provide a great
deal of information about hydrodynamic forces. One of the main focuses of this project is to
obtain the hydraulic force information on the shroud surface of the volute casing, This is
essential in terms of providing pump vibration signatures and in order to compare with the
numerical simulations.
3.2.1.3 Impeller
The impeller fitted on this Goulds 3196MTX centrifugal pump is a five backward curved
blade open impeller with a diameter of 192mm. It is shown in Figure 3.4. The top of the
impeller is facing the suction inlet (shown in the left of Figure 3.4). An open impeller
essentially comprises of only blades perpendicular to the central hub and with no shrouds to
enclose the blades. This arrangement is superior for solids and stringy material handling,
while in reality, a partial shroud may be used to strengthen the blades [36]. This design also
provides about two times more surface area for hydraulic forces to act on when compared to a
closed impeller. As a result, this leads to less wear across all the critical areas and a longer
fatigue life.
This impeller is built with back pump out vanes (POV). These serve to reduce pressure on the
shaft seals and axial thrust on the shaft. POV works by further reducing the gap between the
impeller and the casing wall [36]. By accelerating the fluid contained in this region, the net
axial force acting to the shaft is reduced.
32
Figure 3.4: Front (suction side) and back (motorside) view of the impeller
3.2.2 Motor
Limited electronically to 1.5kW by the Variable Frequency Drive (VFD), the pump motor
can produce a maximum flow rate of 12 cubic meters per hour for a direct suction and
discharge configuration where the water does not pass through any kind of filter or pressure
regulating valves to constrict the flow.
Coupled to the pump, a Weg 4-pole 1.5kW electric motor is controlled by a MSC-3 Variable
Frequency Drive (VFD) controller made by Zener Electric. It can precisely regulate the
power delivered to the motor and hence the speed of the impeller.
The VFD works by manipulating the frequency of the applied voltage to the motor. A 4-pole
motor used in this pump consists of 2 pole pairs. If supplied with a 50 Hz line frequency
voltage, the motor will rotate at 50 Hz/2 = 25 revolutions per second, resulting in a rotational
speed of 1500 RPM. The MSC-3 VFD has been programmed to limit the pump speed to a
theoretical maximum of 1500 RPM. However, when running at the maximum allowable
speed on the VFD, calculations from the tachometer signal results in around 1453 RPM. This
is not a significant concern as the tachometer signal was synchronized and recorded together
33
with the vibration signal and the calculated speed will be used for all other calculations
requiring the pump speed.
To determine the background vibration produced, a test was conducted on the pump casing
and a spike at 100 Hz could be clearly seen even when the motor is not running. This is likely
caused by the electrical noise generated from the circuitry of the VFD and will be inherent in
all test measurements regardless of shaft rotating frequency or pump conditions.
3.2.3 Flow meter
A flow meter (Figure 3.5) is mounted on the pipe near the pump discharge outlet. As shown,
dials indicate the flow rate of the pump test rig. A slotted disk is coupled with the rotor in the
flow meter which rotates in the same rotational speed as the rotor. An opto-transistor is
applied to get the infrared pulses and the signal is then sent to a custom built digital circuit to
show the instantaneous flow rate.
Figure 3.5: Top view of the flow meter
34
3.2.4 Accelerometer
The accelerometers used in this experimental setup were of type B&K 4396 and 608A11 ICP
accelerometers made by IMI. The 608A11 ICP accelerometers have a sensitivity of
10.2mV/(m/s2) and a maximum frequency range of 10 kHz. The B&K 4396 similarly, has a
sensitivity of 10.2mV/(m/s2) and a frequency range of up to 14 kHz. As the sampling
frequency is set to 20 kHz, there was no need for an accelerometer with a higher frequency
range than the Nyquist frequency of 10 kHz.
Accelerometers were used to measure the acceleration of the shroud surface alone one axis of
the volute casing. There are 36 positions selected for the acceleration measurement just as the
same the setup applied in the past numerical simulations [4]. These 36 positions were located,
one at every 10 degree, on the shroud surface of the volute casing along a circumference with
a diameter of 194mm.
3.2.5 Pressure transducers
There are two static pressure transducers installed on both the suction and discharge side of
the pump. They are Novus NP-430D pressure transducers with a detection range of 0-2Bar.
The transducers produce a linear change in current proportional to the static pressure
measured. The current signals were then converted to a linear change in voltage which was
recorded by the DAC.
3.2.6 Data acquisition card
Two data acquisition cards were used in the experiments since the PCI card only has 8
analogue inputs. A PCI-4472 Data Acquisition Card, made by National Instruments (NI), was
used to record all the analogue signals from the accelerometers. A second NI DAC was used
to record operating parameters from the pressure transducers, tachometer and flow meter.
35
This second DAC is a NI USB-6259 BNC 16-bit capable of sampling rates up to 1.25MS/s.
The DACs were controlled by a Labview programme. All the signals were sampled at 20 kHz
for 10 seconds in each run.
36
Chapter 4 Modal testing of the centrifugal pump
4.1 Introduction
A journal paper is currently in progress based on the work has been done in this chapter. The
purpose of conducting modal testing of the pump volute casing and the impeller (Figure 4.1)
is to verify the feasibility of considering the volute casing and impeller as rigid in the CFD
model. In order to achieve this goal, the natural frequencies and mode shapes of the volute
casing and impeller are required. These will be compared to the BPF of the pump at the
maximum testing speed. If the natural frequencies of the volute casing and the impeller are
well above the BPF, then it is sufficient to consider these components as rigid in the CFD
simulation.
Due to the complex geometry of the pump impeller, both experimental and Finite Element
Methods (FEM) are applied.
The experiments were conducted for pump components first separately. The axial and radial
mode shapes of the impeller which is mounted on the pump were obtained by impact hammer
test. Then the volute casing was mounted on a concrete footing to test its axial and radial
mode shapes isolated from the pump body. Finally, to investigate the system vibration
signature in terms of vibration modes and the effect of water, the impact hammer test was
carried on for the volute casing which was assembled to the piping system and pump (i.e.in
the assembled for operation position) .
Experimental Modal Testing
37
Modal testing is a form of vibration testing of an object. It permits the determination of the
natural (modal) frequencies, modal masses, modal damping ratios and mode shapes of the
object [38].
There are several techniques used for modal test an artifact. Impact hammer testing and
shaker (vibration tester) testing are the most readily used. In both cases energy is supplied to
the system with known frequency content. Where structural resonances occur there will be an
amplification of the response in the response spectra. Using the response spectra and force
spectra, a frequency response function (FRF) can be obtained or estimated by curve fitting.
Impact Hammer Modal Testing
An ideal impact to a structure produces perfect impulse of infinite amplitude and close zero
time duration. This subjects a constant amplitude in the frequency domain and results in
many modes of vibration being excited with equal energy. The impact hammer test is
designed to replicate this. However, the duration of a hammer strike is controlled by the
contact time. The duration of the contact time directly influences the frequency content of the
force; with a larger contact time causing a smaller range of frequency bandwidth. A load cell
is attached to the end of the hammer to record the force. As impact hammer testing is ideal
for small structures, this method was adopted for the modal testing of the pump and its
components [38].
It is noted that the mono-axial accelerometers can only measure the acceleration parallel to
their axis and hence perpendicular to the surface to which they are mounted. As such, it
should be apparent that coupling may occur between measurement directions and hence
modal responses. These aspects should be kept in mind when considering the results.
38
(a) (b)
Figure 4.1: Volute (a) and Impeller (b)
4.2 Results
In this section the results of Finite Element Analysis (FEA) and impact hammer techniques
will be presented and compared.
4.2.1 Finite Element Analysis of Pump Impeller
The first step in the analysis process was to transfer the 3-D impeller geometry generated in
SolidWorks into Ansys Workbench. A very accurate representation of stiffness and mass of
the impeller is required. Hence the use of a sound mesh topology and a high density parabolic
tetrahedral mesh was crucial for accurate frequency prediction (Figure 4.2). The FEA
simulation then calculates the natural frequencies and mode shapes based on boundary
conditions and material properties. Specifically, the hub to which the shaft is connected was
the location where the boundary conditions were imposed. The bottom surface and radial
39
surface of the shaft were both fixed. This means there was no disturbance coming from the
shaft. The material property was set as normal steel.
Figure 4.2: Finite element model
Figure 4.3 displays the first three mode shapes and natural frequencies for the impeller.
Figure 4.3a corresponds to the first mode shape of the pump impeller and its natural
frequency is 1697Hz. The second mode shape occurs at 1866Hz, Figure 4.3b. The third mode
shape can be observed at the natural frequency of 3515Hz, Figure 4.3c. The unit of legend
here is mm.
40
a) b) c)
Figure 4.3: Mode shapes of the pump impeller, a) First transversal mode shape, f=1697Hz; b) Second
transversal mode shape, f=1866Hz; c) Third transversal mode shape, f=3515Hz.
4.2.2 Impact Hammer Test of the Pump Impeller
The equipment used in this test included a PULSE (B&K, Type 2825) which is a noise and
vibration acquisition platform, a computer, three IMI accelerometers and an impact hammer
(B&K, Type 8206) (Figure 4.4a). The accelerometers were mounted directly on the impeller
at certain locations. The locations were selected so as to give an indicative topology of the
vibration profile (Figure 4.4b). The amplified signals from the accelerometers were
connected to the Pulse. The multi-analysis capability of the PULSE permits FFT, 1/n-octave
(CPB), order, and overall analyses simultaneously on the same or different channels/signals
while displaying real-time results on the screen. The impact hammer signal was also
connected to the PULSE. The PULSE software allows the FRF and the coherence function
graphs to be obtained.
41
To obtain the axial vibration mode shape of the impeller, sixteen points were selected on the
impeller. These points were located radially on the circumference of the impeller, on the half-
radius of the impeller and at the center of the impeller. The excitation point was chosen to be
the tip of the impeller blade. It was assumed that the impeller would be subjected to pressure
fluctuation at this location during normal operation (i.e. blade passing etc.).
Figure 4.5 illustrates the average energy per unit force of the impeller. It can be seen that the
first peak occurred at a frequency of around 250Hz. In spite of this, it cannot be concluded
that the occurrence of the first mode shape is at 250 Hz, even though it is a peak value. To
verify the real first natural frequency, FEA results were used for the comparison with the
experimental data. It can be noted that the first natural frequency should be at 1700Hz which
is the second peak measured in Figure 4.5. The difference between the FEA and experimental
data is only 10Hz which shows an excellent agreement. Considering geometric and material
inaccuracies, the existence of the first and second peak in the experiment could be explained
by the structural coupling in the real system and it is likely to be due to structural modes.
Also the way to hold the impeller in FEA method is “fixed” while the impeller is simply sit
on the ground, this could be a possible explanation for the first and second peaks observed.
From Figure 4.6, it is also apparent that this lower peak value is much more damped than the
higher modes. This also supports this mode being structural as the impeller generated a clear
high pitch ringing tone when struck. As for the second and third mode shapes of the impeller,
both are confirmed from the FEA results. The natural frequency difference between the FEA
result and experimental data of the second mode shape of the impeller is of 2% discrepancy
while it is of 12% discrepancy for the third mode shape of the impeller.
42
Figure 4.4: Impeller impact hammer test: a) equipment (i.e. Computer, Pulse and Impact Hammer); b) Test
points distribution on installed impeller
Figure 4.5: Average energy per unit force of the impeller in the axial direction
0 500 1000 1500 2000 2500 3000
10 -8
10 -6
10 -4
10 -2
Frequency (Hz)
Aver
age
Ener
gy A
mpl
itude
(m)
43
a) b) c)
Figure 4.6: Axial mode shapes of the impeller: a) 1708Hz; b) 1908Hz; c) 3104Hz.
To obtain the radial vibration mode shape of the impeller, ten points were selected on the
impeller (Figure 4.4b). These were located radially on the circumference of the impeller and
on the half-radius of the impeller. The excitation point was chosen on the edge of the impeller
blade tip.
In terms of the radial vibration energy, Figure 4.7 illustrates the average energy per unit force
of the impeller. The first two peaks appeared to be result from coupling with the structure
behind the impeller. The third peak can be seen at the frequency of 1704Hz while the fourth
one can be observed at 3108Hz. However, one peak is not present between these two peaks
compared to that of axial vibration, which could be due to the insufficient excitation energy
applied on the impeller. The corresponding mode shapes are illustrated in Figure 4.8.
It can be observed that the first natural frequency at 1697 Hz in the transverse direction and
1704 Hz in the radial direction of the pump impeller is well above the pump rotating
frequency at 24 Hz. As per HIS (Hydraulic Institute Standards -9.6.4-2000) clause 9.6.4.4,
the first natural frequency should be 10% above or below the pump rotating frequency.
Therefore, there should be no risk for the occurrence of resonance.
44
Figure 4.7: Average energy per unit force of the impeller in the radial direction
a) b)
Figure 4.8: Radial mode shapes of the impeller: a) 1704Hz; b) 3108 Hz.
0.5 1 1.5 2 2.5
30
210
60
240
90
270
120
300
150
330
180 0 0.5 1 1.5 2 2.5
30
210
60
240
90
270
120
300
150
330
180 0
0 500 1000 1500 2000
2500 3000
10 -11
10 -10
10 -9
Frequency (Hz)
Ave
rage
Ene
rgy
Am
plitu
de (m
)
45
4.2.3 Finite Element Analysis of Pump Volute Casing
The geometric model of the pump volute casing is shown in Figure 4.9. The Finite element
model of it is shown in Figure 4.10. The mesh applied in this model is 8mm parabolic
tetrahedral. Since natural frequencies and mode shapes of the pump volute casing were
obtained experimentally with the casing feet fixed, so the same boundary condition should
apply to the volute casing finite element model. The material property was set as normal steel.
Figure 4.9: Pump volute casing geometric model
Figure 4.10: Pump volute casing Finite element model
46
It can be seen that there were seven natural frequencies of the pump volute in the transverse
direction which are shown in Table 4.1 and in the radial direction in Table 4.2. The first mode
shape of the pump volute casing occurred at a natural frequency of 58 Hz. This is
corresponding well to the experimental results. Figures 4.11-16 illustrate different mode
shapes of the pump volute casing at different natural frequencies. As for the rest of mode
shapes of the volute casing, nearly all of them are confirmed by the experimental results.
As explained in early part of this chapter, it was not possible to mount the accelerometers to
measure solely the transverse vibration. Hence there may be coupling between modal
responses. This may explain the 866Hz frequency measured experimentally in the radial
vibration.
Table 4.1: Natural frequencies of the pump volute casing in the transverse direction
Mode No. Natural frequency obtained numerically (Hz)
Natural frequency obtained experimentally (Hz)
1 57.6 56 2 296 340 3 566 600 4 595 640 5 1328 856 6 1425 1364 7 1699 1404
Table 4.2: Natural frequencies of the pump volute casing in the radial direction
Mode No. Natural frequency obtained numerically [Hz]
Natural frequency obtained experimentally [Hz]
1 57.6 300 2 295.95 340 3 565.4 516 4 594.9 640 5 1328.3 696 6 1424.5 880 7 1699.4 1084 8 1356
47
(a) vertical mode shape (b) radial mode shape
Figure 4.11: 1st mode shape at natural frequency of 57.6 Hz
(a) vertical mode shape (b) radial mode shape
Figure 4.12: 2nd mode shape at natural frequency of 295.95 Hz
(a) vertical mode shape (b) radial mode shape
Figure 4.13: 3rd mode shape at natural frequency of 565.4 Hz
48
(a) vertical mode shape (b) radial mode shape
Figure 4.14: 4th mode shape at natural frequency of 594.9 Hz
(a) vertical mode shape (b) radial mode shape
Figure 4.15: 5th mode shape at natural frequency of 1328.3 Hz
(a) vertical mode shape (b) radial mode shape
Figure 4.16: 6th mode shape at natural frequency of 1425.5 Hz
49
It can be observed that the first natural frequency at 1697 Hz in the transverse direction and
1704 Hz in the radial direction of the pump impeller is well above the pump rotating
frequency at 24 Hz. As per HIS (Hydraulic Institute Standards -9.6.4-2000) clause 9.6.4.4,
the first natural frequency should be 10% above or below the pump rotating frequency.
Therefore, there should be no risk for the occurrence of resonance.
50
4.2.4 Impact Hammer Test of the Pump Volute Casing
The equipment used for the impact hammer test of the pump volute casing was the same as
that used for the pump impeller.
To obtain the axial vibration mode shapes of the volute casing, twenty four points were
selected on the volute casing shroud surface. These were located radially on the
circumference and the half-radius of the shroud surface of the volute casing. Two excitation
points were chosen on the shroud surface of the volute casing. The volute casing was secured
rigidly to a concrete footing to approximate its installation condition (Figure 4.1).
According to Figure 4.17, there were a series of peaks at frequencies of 56Hz, 340Hz, 600Hz,
640Hz, 680Hz, 856Hz, 1364Hz and 1404Hz. Their corresponding mode shapes are shown in
Figure 4.18.
Figure 4.17: Average energy per unit force of the volute casing in the axial direction
0 500 1000 1500 2000 2500 3000
10 -20
10 -19
10 -18
10 -17
Frequency (Hz)
Ave
rage
Ene
rgy
Am
plitu
de (m
)
51
a) b) c)
d) e) f)
g) h)
Figure 4.18: Axial mode shapes of the volute casing at natural frequencies of: a) 56Hz; b) 340Hz; c) 600Hz; d)
640Hz; e) 680Hz; f) 856Hz; g) 1364Hz and h) 1404Hz.
52
In terms of the radial vibration signature of the volute casing, Figure 4.19 describes the
relation between the average energy and frequency while the corresponding mode shapes are
illustrated in Figure 4.20.
Figure 4.19: Average energy per unit force of the volute casing in the radial direction
0 500 1000 1500 2000 2500 3000 10
-21
10 -20
10 -19
10 -18
10 -17
Frequency (Hz)
Ave
rage
Ene
rgy
Am
plitu
de (m
)
53
a) b) c)
d) e) f)
g) h)
Figure 4.20: Radial mode shapes of the volute casing at natural frequencies of a) 300Hz; b) 340Hz; c) 516Hz; d)
640Hz; e) 696Hz; f) 880Hz; g) 1084Hz; h) 1356Hz.
2e-005 4e-005 6e-005 8e-005 0.0001
30
210
60
240
90
270
120
300
150
330
180 0
1e-005 2e-005 3e-005 4e-005
30
210
60
240
90
270
120
300
150
330
180 0
1e-005
2e-005
3e-005
30
210
60
240
90
270
120
300
150
330
180 0
1e-005
2e-005
3e-005
30
210
60
240
90
270
120
300
150
330
180 0
1e-005
2e-005
3e-005
30
210
60
240
90
270
120
300
150
330
180 0
1e-005 2e-005 3e-005 4e-005
30
210
60
240
90
270
120
300
150
330
180 0
5e-006
1e-005
1.5e-005
30
210
60
240
90
270
120
300
150
330
180 0
2e-006 4e-006 6e-006 8e-006
30
210
60
240
90
270
120
300
150
330
180 0
54
4.2.4 Assembled on to the Pump Testing System
In order to obtain mode shapes and mode frequencies of the pump volute casing assembled to
the pump testing system, the same procedure was applied. There were two sets of
experiments conducted: these were 1) without water and 2) with water.
4.2.4.1 Mode Shapes and Frequencies in the Axial Direction
To obtain the axial vibration mode shape of the volute casing, twenty four points were
selected on the volute casing shroud surface. These were located radially on the
circumference and the half-radius of the shroud surface of the volute casing. An excitation
point near the pump tongue position was chosen on the shroud surface of the volute casing.
For the case of pump system without water, it can be shown Figure 4.21a that there are series
of peaks at frequencies of 716Hz, 956Hz, 1088Hz, 1132Hz, 1228Hz, 1292Hz, 1372Hz,
1424Hz and 1828Hz, of which the mode shapes are shown in Figure 4.22.
55
a)
b)
Figure 4.21: Average energy per unit force of the volute casing for excitation in the axial direction: a) without
water; b) with water.
500 1000 1500 2000 2500 3000
10 -12
10 -11
10 -10
10 -9
Frequency (Hz)
500 1000 1500 2000 2500 3000 10 -12
10 -11
10 -10
10 -9
Frequency (Hz)
Ave
rage
Ene
rgy
Am
plitu
de (m
) A
vera
ge E
nerg
y A
mpl
itude
(m)
56
Table 4.3: Natural frequencies of the pump in the axial direction under different condition
Mode No. Natural frequencies (Hz) of the pump without water
Natural frequencies (Hz) of the pump with water
1 716 712 2 956 944 3 1088 1080 4 1132 1116 5 1228 1220
Figure 4.21b shows the peaks according to the increase of the mode frequencies. When the
pump testing system is full of water, the situation is different. Most likely as a result of mass
loading of water, it can be seen that the modal frequencies are consistently lower from 656Hz
to 1816Hz, the mode shapes of which are illustrated in Figure 4.23.
It can be observed in Table 4.3 that the first natural frequencies at 716 Hz of the pump
assembly without water and 712 Hz of the pump with water in the transverse direction are
well above the rotating frequency at 24 Hz. As per HIS (Hydraulic Institute Standards -9.6.4-
2000) clause 9.6.4.4, the first natural frequency should be 10% above or below the pump
rotating frequency. Therefore, there should be no risk for the occurrence of resonance.
57
a) b) c)
d) e) f)
g) h) i)
Figure 4.22: Axial mode shapes of the volute casing without water at natural frequencies of a) 716Hz, b) 956Hz,
c) 1088Hz, d) 1132Hz, e) 1228Hz, f) 1292Hz, g) 1372Hz, h) 1424Hz and i) 1828Hz.
58
a) b) c)
d) e) f)
g) h) i)
Figure 4.23: Axial mode shapes of the volute casing with water at natural frequencies of: a) 712Hz; b) 944Hz; c)
1080Hz; d) 1116Hz; e) 1220Hz; f) 1292Hz; g) 1328Hz; h) 1432Hz and i) 1816Hz.
59
4.2.4.2 Mode Shapes and Frequencies in the Radial Direction
As for the radial vibration signature of the volute casing without water, Figure 4.24a
describes the relation between peaks and frequencies without water and corresponding mode
shapes are illustrated in Figure 4.25.
Table 4.4: Natural frequencies of the pump in the radial direction under different condition
Mode No. Natural frequencies (Hz) of the pump without water
Natural frequencies (Hz) of the pump with water
1 184 184 2 336 224 3 448 340 4 932 660 5 1040 708 6 1152 748 7 1284 1124 8 1512 1276 9 1824 1520 10 1824 11 1860 12 1968
60
a)
b)
Figure 4.24: Average energy per unit force of the volute casing in the radial direction : a) without water; b) with
water.
500 1000 1500 2000 2500 3000 10 -13
10 -12
10 -11
10 -10
10 -9
Frequency (Hz)
500 1000 1500 2000 2500 3000
10 -12
10 -11
10 -10
Frequency (Hz)
10-9
Ave
rage
Ene
rgy
Am
plitu
de (m
) A
vera
ge E
nerg
y A
mpl
itude
(m)
61
a) b) c)
d) e) f)
g) h) i)
Figure 4.25: Radial mode shapes of the volute casing without water at natural frequencies of a) 184Hz; b)
336Hz; c) 448Hz; d) 932Hz; e) 1040Hz; f) 1152Hz; g) 1284Hz; h) 1512Hz and i) 1824Hz.
0.02 0.04 0.06 0.08
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180 0
62
From Table 4.4, it can be observed the natural frequencies in the radial direction in the case
of pump without water are completely different from the case of pump with water except the
first mode. Others are relatively smaller than the case without water. Also the number of
natural modes that produced in the case of pump with water is more than the natural modes
produced in the case of pump without water. Figure 4.24b showed the average energy trend
against the change of the mode frequencies. The corresponding mode shapes are illustrated in
Figure 4.26.
It can be observed that the first natural frequencies at 184 Hz of the pump assembly without
and with water in the transverse direction are well above the rotating frequency at 24 Hz. As
per HIS (Hydraulic Institute Standards -9.6.4-2000) clause 9.6.4.4, the first natural frequency
should be 10% above or below the pump rotating frequency. Therefore, there should be no
risk for the occurrence of resonance.
63
a) b) c)
d) e) f)
g) h) i)
j) k) l)
0.01 0.02 0.03 0.04 0.05
30
210
60
240
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270
120
300
150
330
180 0
0.01
0.02
0.03
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180 0
0.02 0.04 0.06 0.08 0.1
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180 0
0.02 0.04 0.06 0.08 0.1
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180 0
0.02 0.04 0.06 0.08
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180 0 0.02 0.04 0.06 0.08 0.1
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0.05 0.1 0.15 0.2
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180 0
0.05
0.1
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180 0
0.1
0.2
0.3
30
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180 0
0.1 0.2 0.3 0.4
30
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330
180 0
0.1
0.2
0.3
30
210
60
240
90
270
120
300
150
330
180 0
64
Figure 4.26: Radial mode shapes of the volute casing with water at natural frequencies of : a) 184Hz; b) 224Hz;
c) 340Hz; d) 660Hz; e) 708Hz; f) 748Hz; g) 1124Hz; h) 1276Hz; i) 1520Hz; j) 1824Hz; k) 1860Hz and l)
1968Hz.
4.3 Conclusion
In terms of the frequency magnitude, it can be concluded that the lowest natural frequency of
125 Hz is above the BPF, regardless of the impeller and the volute casing. This is not only
true for pump components, but also can be proved for the pump assembly with and without
water. Therefore, both of the impeller and the volute casing can be considered as rigid body
in numerical simulation. On the other hand, blade passing has harmonics; therefore the
identified resonance may amplify the response at the harmonics.
65
Chapter 5 Numerical Simulations for a Hypothetical Pump Model
5.1 Introduction
The purpose of this chapter is to identify the feasibility of numerical methods in predicting
both the steady and unsteady flow phenomenon in a hypothetical pump model. Also, some
basic unsteady flow patterns can be investigated and compared with those published in the
literature to clarify understanding of some vital characteristics of centrifugal pumps such as
flow patter and pressure fluctuation.
The hypothetical pump model was generated based on the basic dimensions of a commercial
pump. The diameter of the impeller and the rotational speed were set the same as the
commercial pump while other parameters such as blade height and blade shape were
generated based on reasonable mechanical assumptions.
Both the frozen rotor and the sliding mesh method were applied in the numerical simulations.
The results obtained were compared with the past available experimental data. A perfect
agreement from this comparison was not expected because the geometry of the hypothetical
pump model was not exactly the same as those applied in the past [4]. The most important
focus was to investigate whether similar trends of important properties (e.g. pump efficiency,
pressure distribution, blade passing frequency etc.) could be found from this simulation. If so,
the same method may be applied for the commercial pump and the numerical method could
be considered as sufficiently effective.
5.2 Hypothetical numerical model
66
The hypothetical numerical pump model generated (Figure 5.1) was a single suction duct and
a vaneless volute casing. It comprised a five backward curved blade centrifugal pump. The
main characteristics of the pump are included in Table 5.1:
Table 5.1: Main characteristics of hypothetical model
D2=192mm Impeller outlet diameter b2=10mm Blade height ω=1450rpm Rotational speed Qn=2kg/s Nominal flow rate fBP=120Hz Blade passing frequency
Figure 5.1: Hypothetical numerical model
5.3 Numerical methods
5.3.1 Model and computational method: Frozen Rotor
67
The steady flow method is used in this model. More specifically, the rotor of the pump is kept
at a fixed position. The flow governing equations are solved in a rotating reference frame
which includes the centripetal force, while the governing equations for the stator are solved in
an absolute reference frame. The continuity of velocity and pressure equilibrium are taken
into account with the coupling between the rotor and stator. However, the main source of the
unsteadiness, which is the rotational movement of the rotor, is neglected. Therefore, the flow
field is highly dependent on the relative position of the rotor and the stator.
Mesh
Due to the geometrical complexity of the centrifugal pump model, structured cells are not
applicable in such a case. Therefore, unstructured tetrahedral cells were applied to mesh the
impeller and volute: 506014 cells for the impeller and 256319 cells for the volute. Some
prism cells were used to refine the region near the tongue of the volute since there was a
special focus on the flow velocity and pressure stagnation point position there.
Turbulence model and discretization scheme
After generating the mesh, CFX, a commercial CFD code, was applied to run the simulations.
Turbulence was simulated with the standard K-e model and high resolution used for the
advection scheme.
Boundary conditions
The boundary conditions were selected based on the condition which was most physically
meaningful. More specifically, the total pressure was set at the inlet and flow rate at the outlet.
Flow rate changes simulated the closure of a valve at the discharge outlet. By using these
boundary conditions, the uniform velocity profile, which is not robust, can be avoided. At the
impeller blades and sidewalls, a no-slip wall condition has been imposed. 17cm long inlet and
68
outlet duct were applied to keep the simulation results away from the imposed boundary
conditions.
5.3.2 Model and computational method: Sliding Mesh
The Sliding Mesh method is a completely unsteady method. Not only are the rotating and
absolute reference frames used, but also the movement of the impeller is taken into account.
At each time step, the fluxes are interpolated on the mesh between the rotor and stator.
Although some diffusion can be seen due to the interpolation, there is no major
approximation of the unsteadiness.
Geometry and grid
The geometry and grid used for the sliding mesh technique was the same as that used by
frozen rotor method.
Turbulence model
The K-e turbulence model was applied. High resolution was used for the advection scheme.
Second order backward Euler method was applied as the transient scheme.
Boundary conditions
The total pressure condition was chosen at the inlet and flow rate condition was selected at
the outlet.
Numerical solution control
The time step used for the unsteady simulation was set to 0.00166s (i.e. 602Hz) which is
obtained from 0.3/ω provided by Ansys best practice guide for turbomachinery [39]. Thus, a
complete revolution is performed each 25 steps. This setup is used to keep the frequency
69
resolution well above the BPF and its basic harmonics. Moreover, in order to get a reasonable
frequency resolution of 1Hz, the time duration of 1s was chosen for the simulation. The RMS
of given variables has been set to 10-4 to obtain a reasonably accurate results at an acceptable
time expense [39].
5.4 Simulation results
5.4.1 Pump efficiency curve
It has been found that the BEP can be observed at the nominal flow rate (eg. 2.0kg/s) of the
pump model. After this point, the efficiency drops gradually with respect to the change of the
flow rate (Figure 5.2). This graph showed good agreement with a normal pump performance
curve in Figure 2.2. The pump efficiency keeps increasing until reaching the BEP at nominal
flow rate, a decrease of efficiency can be observed if the pump is operating beyond the
nominal flow rate.
48.05%51.35%
44.43%
32.55%
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
0 1 2 3 4 5
Effic
ienc
y
Flow rate (kg/s)
Figure 5.2: Efficiency obtained from Sliding Mesh method
70
5.4.2 Water head
The water head provided by the pump (Figure 5.3) decreased with the increase of the flow
rate which showed a good agreement with the normal pump performance curve in Figure 2.2.
7.97
6.49
4.7
3
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5
Wat
er h
ead
(m)
Flow rate (kg/s)
Figure 5.3: Head-flow rate obtained from Sliding Mesh method
5.4.3 Static pressure distribution
Previous research [7] has illustrated the pressure distributions near the pump tongue (Figure
1.2). In that work, the stagnation point shifted from the discharge side to the volute side as the
flow rate increased, was also consistent with the incidence of the velocity vectors shown in
Figure 1.1.
The same trend can be observed from the numerical results of this hypothetical pump model.
It seems that the incidence of the velocity angle determines the position of the stagnation
point at the tongue-tip. This can be clearly seen in the Figure 5.4 below which represents the
static pressure distribution at the tongue zone obtained from the Frozen Rotor and Sliding
71
Mesh methods for the 192 mm impeller and for four different flow-rates. The stagnation
point shifts around the tongue tip from the diffuser side to the volute side when increasing the
flow rate from minimum to maximum values.
Moreover, for both the frozen rotor and sliding mesh methods, the static pressure
distributions are similar. Both of these methods can predict the pressure pattern well.
However, the pressure obtained from frozen rotor method is much higher than that obtained
from sliding mesh method. This could probably due to less energy is lost in unsteady
phenomenon, thus more kinetic energy is converted to pressure head.
72
a)
b)
c)
Figure 5.4: Static pressure distribution for different flow rate obtained by frozen rotor method (left column) and
sliding mesh method (right column) for: a) 1 kg/s; b) 2 kg/s; and, c) 3 kg/s.
73
5.4.4 Flow velocity profile
It can be seen in the upper graph in the left column of Figure 5.5 that the velocity profile is
captured well when compared with past numerical results shown in Figure 1.1 by using
frozen rotor method for four flow rates. However, the predicted velocity is a bit lower than
that obtained by sliding mesh method.
The right column of Figure 5.5 presents the velocity vectors in the tongue region for the 192
mm impeller and four flow-rates, at equivalent time instants by applying sliding mesh method
showing the effect of the flow-rate on the position of the stagnation point on the tongue-tip.
At flow-rates close to nominal, the matching between the flow coming out the impeller and
the volute is good, whereas at off-design conditions the absolute velocity at the impeller
outlet forms a large incidence angle with respect to the mean flow in the volute. This is
clearly noticeable at high flow-rates, for which most of the flow is directed towards the outlet
duct, and at low flow-rates, for which the recirculation of the flux through the impeller-
tongue gap is evident.
From the Figure 5.6, the large recirculation zones can be seen in the impeller channels which
are exposed to the large volute pressure. This means the work exchanged by the impeller and
the flow is lower than the energy increase in the fluid. As a result, the calculated hydraulic
efficiency is larger than one which is un-physical. Therefore, it can be concluded that the
sliding mesh method can give a more physical meaningful prediction for the velocity profile.
74
a)
b)
c)
Figure 5.5 Flow velocity profile for flow rate at different flow rates obtained by frozen rotor (left column) and
sliding mesh method (right column) for: a) 1 kg/s; b) 2 kg/s; and, c) 3 kg/s
75
Frozen Rotor Sliding Mesh
Figure 5.6 Flow velocity profile for flow rate at 1.0kg/s obtained by frozen rotor and sliding mesh method for
recirculation zone prediction
5.4.5 Pressure fluctuation
Pressure at different flow rates is obtained numerically from 10 monitoring points on the
shroud wall of the volute. This corresponds to one point every 36 degrees and similar
locations to which experimental data was recorded. Once the pressure fluctuation information
was obtained, FFT calculation was performed and relevant dynamic pressure magnitude was
obtained for the different frequencies and particularly for the BPF.
The experimental data of pressure pulsations magnitude at the angular position of 20 degrees
is shown in Figure 5.7 [23]. The fR is the fundamental frequency of the rotating pump
impeller. It can be observed that the minimum magnitude of dynamic pressure fluctuation at
the blade passing frequency occurred at nominal flow rate of the pump. The magnitude
increased significantly when the pump operated at off-design conditions. The reason for these
76
trends may involve the recognition that the fluid-dynamic interaction between the impeller
and volute casing is more intense when the pump is operating at off-design conditions.
The magnitude of pressure fluctuations distribution along the volute casing at blade passing
frequency obtained from experiment is shown in Figure 5.8 [23]. The magnitude fluctuated
strongly near the tongue region (i.e. 0—90 degrees anticlockwise). The fluctuation of the
dynamic pressure magnitude is stronger when the pump is operating at off-design conditions.
Figure 5.9 shows the evolution with respect to the flow rate of the numerical magnitude of
the dynamic pressure pulsations at 36 degree angular position for the hypothetical pump
model. After the comparison between the experimental and numerical results, as expected,
the predominant peaks correspond to the frequency of rotation of the impeller and in
particular to the BPF, together with their respective harmonics. Also it is clear that these
peaks are varying with the operating point. More specifically, the minimum peak value can
be seen at the nominal flow rate while an increase can be expected when the pump is
operating at off-design conditions. The hypothetical numerical model applied in this project
can capture this trend well.
When the pump is operating close to the nominal flow-rate, the magnitude of pressure
fluctuations distribution along the volute casing at BPF is small and quite uniform, but for
both small and high flow rates the magnitude of the pressure fluctuation distribution increases.
These results indicate a progressive reinforcement of the blade tongue interaction when
deviating from nominal operating conditions.
77
When Figure 5.10 was compared with Figure 5.7, a similar trend can be observed for the
magnitude of dynamic pressure at blade passing frequency at different flow rate. The
minimum magnitude of dynamic pressure occurred when the pump operated at nominal flow
rate while the value was much higher when the pump was under off-design conditions.
Figure 5.11 illustrates the magnitude of pressure fluctuation distribution along the volute
casing at the BPF of the hypothetical pump model. The change of magnitude of the dynamic
pressure fluctuation is quite intense near the pump tongue region (i.e. 0—90 degrees anti-
clockwise) as obtained in Figure 5.8. For the rest of the shroud surface of the volute casing,
the magnitude distribution was quite uniform.
Figure 5.7 Pressure pulsations magnitude. Spectrum
as a function of flow-rate for angular position at 20 degrees by experimental method [23]
Frequency (Hz)
Q/Qn
Non
-dim
ensi
onal
Pre
ssur
e
78
Figure 5.8 Magnitude of the pressure fluctuations distribution along the shroud surface of the volute casing at
fBP, from experimental results [7]
Q=0.99Qn
Q=1.23Qn
Angular Position (degree)
Angular Position (degree)
Non
-dim
ensi
onal
Pre
ssur
e
N
on-d
imen
sion
al P
ress
ure
79
Flow Rate at 1.0kg/s
1.07501
00.20.40.60.8
11.21.41.61.8
20 41 62 83 104 125 146 167 189 210 231 252 273 294Frequency (Hz)
Magnitude of dynamic pressure (kPa)
Flow Rate at 2.0kg/s
0.459132
00.20.40.60.8
11.21.41.61.8
20 41 62 83 104 125 146 167 189 210 231 252 273 294
Frequency (Hz)
Magnitude of dynamic pressure (kPa)
Flow Rate at 3.0kg/s
Figure 5.9: Pressure pulsations magnitude .zero-to-peak. Spectrum
as a function of flow-rate for angular position at 36 degrees by numerical method
80
Figure 5.10: The correlation between magnitude of dynamic pressure and the flow rate ratio (Q/Qn) at blade
passing frequency
Figure 5.11: Magnitude of the pressure fluctuations distribution along the shroud surface volute casing at fBP at
a flow rate of 3kg/s, from numerical results
Mag
nitu
de o
f dyn
amic
pre
ssur
e (k
Pa)
Q/Qn
81
5.4.6 Blade loading
The fluctuating pressure field gives dynamic forces which can cause fatigue failure of the
pump shaft, especially at off-design operating conditions. Once the pressure predictions have
been proven to be accurate, the numerical model developed has shown its validity and can be
used to calculate these forces. The total radial force can be obtained by an integration
procedure which takes the value and angular phase of the pressure fluctuation into account
[37]. From this total force, the fluctuating terms can be obtained by subtracting the average
value for a blade passing period. In Figure 5.12, a polar representation is chosen for these
terms, where the modulus and phase of the fluctuating force with respect to the horizontal
direction can be obtained.
Figure 5.12: Polar representation of the fluctuating force at the blade passing period from numerical results. At
nominal flow rate of 2.0kg/s
82
5.4 Summary
In this chapter, a series of numerical simulations has been conducted for a hypothetical pump
model to investigate the feasibility of the numerical methods. As for the global parameters of
the pump concerned, both the trend of efficiency and water head seems reasonable when
compared with normal pump performance curve. The main trend caused by unsteady flow
phenomenon can also be captured in terms of dynamic pressure fluctuations and blade
loading.
Based on these simulation results obtained, it seems that the Sliding Mesh method was
capable of providing reasonable predictions for the unsteady flow pattern in the centrifugal
pump. However, in order to find out the correlation between the pump efficiency and
vibration, it suggested that more aspects can be investigated for the commercial pump
including torque, velocity gradient and vorticity in the pump volute casing.
83
Chapter 6 Numerical Analysis of Centrifugal Pump: Steady Flow Model
6.1 Introduction
The purpose of this chapter is to investigate global variations such as efficiency, water head
of a commercial centrifugal pump by applying steady flow numerical method, namely the
Frozen Rotor Method. The numerical results will be compared with available experimental
data to check the accuracy and validity of the numerical method. Both the velocity vector and
static pressure distributions will be examined. Finally, the flow properties including vorticity
and helicity will be investigated to provide a general perspective of unsteady flow pattern in
the centrifugal pump.
6.2 Model and computational method: Frozen rotor
6.2.1 Solid model of commercial centrifugal pump
The solid model of commercial pump is generated based on the real dimensions measured in
the laboratory. The pump was dismantled and the impeller geometry measured. The main
characteristics of the commercial pump are shown in Table 6.1. The geometrical data was
used to generate a 3D model (Figure 6.1).
Table 6.1: Main characteristics of the centrifugal pump
D2 = 192mm Impeller outlet diameter b2 = 21mm Impeller outlet width Ω = 1450rpm Rotational speed QN = 3.33kg/s Nominal flow rate
84
Figure 6.1: 3D model of the Goulds (model 3196 MTX) pump
6.2.2 Frozen rotor method
The Frozen Rotor method is essentially a steady flow method. The rotor of the pump is kept
at a fixed position. The flow governing equations are solved in a rotating reference frame.
This includes the centripetal force while the governing equations for the stator are solved in
an absolute reference frame. The continuity of velocity and pressure is taken into account to
describe the coupling between the rotor and stator. However, the main source of the
unsteadiness due to the rotation of the rotor is neglected. Therefore, the flow field is highly
dependent on the relative position of the rotor and the stator.
85
6.2.3 Geometry, grid and flow Solver
Unstructured tetrahedral cells are applied to mesh the impeller and volute, 650696 cells for
the impeller, 331169 cells for the volute and 82893 cells for the inlet. 6135 prism cells are
used to refine the region near the tongue of the volute since there is a special focus on the
flow velocity and pressure stagnation point position there. The grid generated for both the
volute and the impeller is shown in Figure 6.2.
After the grid was generated, a commercial CFD code, CFX was used to simulate.
Turbulence was simulated with the standard K-e model and high resolution for the advection
scheme.
a)
86
b)
c)
Figure 6.2: Generated grid of commercial pump model: a) impeller; b) volute casing; c) finer mesh in the volute
tongue region
87
6.2.4 Boundary conditions
Boundary conditions for the total pressure at the inlet and flow rate at the outlet were
implemented. The flow rate can be adjusted to simulate the closure of the outlet valve. By
using these boundary conditions, the uniform velocity profile which is not robust can be
avoided. As for the impeller blades and sidewalls, a no-slip wall condition has been imposed.
A length of 17 cm inlet and outlet were applied to keep the simulation results away from the
imposed boundary conditions. According to Jose et al. [7] the pipe length of the inlet and
outlet can have an unavoidable effect on the final solution. Therefore, in this project,
reasonable pipe lengths have been applied to the pump model.
6.2.5 Numerical solution control
The pump can operate at different rotational speeds. However, in this case, 1450rpm was
chosen for this project. Accordingly, the physical time step used for the unsteady simulation
has been set to 0.00166. To reduce the residuals to an acceptable value, the numbers of
iterations were set accordingly. The RMS (the ratio between the sum of the residuals and the
sum of the fluxes for a given variable in all the cells) has been set to 10-4 to obtain reasonable
accurate results at an acceptable time expense.
6.3 Results and discussion
6.3.1 Water head
The water heads obtained at five different flow rates by applying Frozen Rotor method are
shown as red dots in Figure 6.3. The experimental water head data of five different flow rates
are shown as blue dots in Figure 6.3. It can be observed that the water head prediction is quite
88
good at the nominal flow rate (i.e. 12m3/hr). However, the quality of prediction deteriorates if
lower flow rates are considered. The predicted values of water head are always
underestimated for low flow rate cases.
Figure 6.3 Comparison of water head obtained by both the Frozen Rotor method and Experimental data
6.3.2 Efficiency
The pump efficiency obtained by applying numerical method can be expressed as:
2
HQgTRPS
ηπ
=
(7)
where H is the water head in meter, Q is the mass flow rate in kg/s, T is the torque applied on
the impeller in Nm and RPS is the rotational speed in revolution per second.
The comparison of pump efficiency obtained experimentally and numerically is shown in
Figure 6.4. The experimentally data was measured experimentally and shown by the blue
Flow rate (kg/s)
Wat
er H
ead
(m)
89
dots and numerical results were shown in red dots in Figure 6.4. Figure 6.5 is a characteristics
graph of Goulds Pumps which was provided by the pump manufacturer.
Figure 6.4: Comparison of pump efficiency obtained by both the Frozen Rotor method and Experimental data
Figure 6.5: The characteristics of 3196MTi centrifugal pump [27]
Flow rate (kg/s)
Effic
ienc
y
90
The numerical pump efficiency was calculated based on the torque values corresponding to
the rotor inner surfaces without taking the disk friction losses and mechanical losses at the
bearings. However, the experimental pump efficiency was obtained by applying the shaft
torque. Therefore, a direct comparison of numerical and experimental pump efficiency was
not possible.
However, it can be seen from Figure 6.4 that the numerical calculated efficiency were quite
close to those obtained experimentally. There was only slightly difference can be observed
for low flow rate cases.
6.3.3 Flow structure inside the centrifugal pump
It is widely accepted that applying numerical methods to study the flow pattern inside a pump
has more possibilities than experiments and is less expensive. Numerical methods can
provide in-depth understanding of the flow structure in terms of flow field and pressure
distribution inside the pump. Both of these results can be utilised to find out the mechanism
behind the pump efficiency change under different flow conditions.
The left column of Figure 6.6 illustrates the absolute velocity vector near the tongue region
for five different flow rates. The velocity vectors are shown on a mid-plane inside the pump
and the velocity scale is set from 0—15m/s for all graphs. It can be noticed that the stagnation
point moves around the tongue with respect to the flow rate. More specifically, the stagnation
point is on the tongue symmetry position only at the nominal flow rate. For low flow rate
cases, it can be noted there is low flow velocity region on the discharge pipe side, resulting in
the stagnation point moving to the discharge pipe side. For high flow rates, the flow
velocities on the discharge pipe side are much higher. This makes the stagnation point move
91
towards the impeller side. Also some recirculation zone can be seen near the impeller in these
cases.
Moreover, it can be observed that the velocity at the impeller side was higher than that at the
discharge side for the low flow rates cases. The opposite trend can be seen for the high flow
rates cases. For the case at the nominal flow rate, the value of velocity at the impeller and
discharge side was somehow closes, which produce a uniform velocity field.
The right column of Figure 6.6 shows the corresponding static pressure distributions near the
pump tongue. Again, the static pressure data is displayed on the same plane as that of the
velocity vectors. The static pressure scale is set from 0—200kPa for all graphs.
Referring to the pump efficiency for different flow rates, when the fluid conditions in the
pump are near the nominal flow rate, the static pressure distribution is reasonably uniform.
This implies that the energy losses due to the impeller-tongue interaction are relatively small.
Therefore, the best efficiency point can be expected near these flow conditions.
92
a.
b.
c.
d.
93
e.
Figure 6.6: Absolute velocity vectors (left column) and static pressure distributions (right column) for the
different flow rates of: a) 0.5Qn; b) 0.8Qn; c) Qn; d) 1.5Qn; e) 1.8Qn
The velocity curl is a flow property which is equal to the vorticity. The vorticity is expressed
as twice of the angular velocity of the fluid element. It implies the strength of turbulence
inside the pump. The velocity helicity is another flow property defined by the dot product of
the vorticity and the velocity vectors. It provides information on the vorticity aligned with the
fluid stream [40].
As far as pressure distribution in the centrifugal pump is concerned (left column of Figure
6.7), the local pressure in the discharge outlet gradually decreases from low flow rate to high
flow rates. Also the pressure distribution in the whole plane for different flow rates depicts a
similar pressure distribution pattern as the pressures in the vicinity of the impeller exit was
lower than any other places. As the pump operates more close to the nominal flow rate, the
pressure distribution looks more uniform. A small region between the impeller and the tongue
experiences the lowest local pressure and a pressure decrease from low flow rates to high
flow rates as well.
The high value of velocity curl was often associated with high rotational flow (i.e.
turbulence). It is usually possible to see vortices in these regions. If the contours of pressure
94
distribution and the velocity curl are compared, the high value velocity curl region often
corresponded to the low pressure region (e.g. the impeller exit). Moreover, it can be observed
that these regions occupied the whole plane for lower flow rates cases. On the other hand, the
high vorticity region occurred in the impeller exit before the volute casing tongue and seemed
much smaller for high flow rates cases.
The right column of Figure 6.7 shows the velocity helicity in the centrifugal pump. It can be
seen the value of velicity in the volute casing keep increases as the flow rate changes from
the minimum to maximum. This means the strength of vortex aligned with the fluid flow
grows by increasing the flow rates. Moreover, the highest helicity appeared to occur before
the volute casing tongue at the low flow rate (right column of Figure 6.7a) and moving closer
to the tongue in the vicinity of nominal flow rates (right column of Figure 6.7c,d). Finally
moves further when flow rate keeps increasing (right column of Figure 6.7e).
It is interesting to note that the vorticity and helicity of the fluid did not correspond well with
each other. Although the movement of high value region in the impeller exit showed a similar
trend, the flow pattern in the volute casing was different. The vorticity value experienced a
decrease while an increase of helicity can be observed in the helicity contours. This was
probably due to the limitation of Frozen Rotor method to predict unsteady flow pattern when
the centrifugal pump was operating at off-design conditions.
95
a.
b.
c.
d.
e.
Figure 6.7: Contours of Pressure distribution (left column), Velocity Curl (middle column) and Helicity (right
column) for the different flow rates of: a) 0.5Qn; b) 0.8Qn; c) Qn; d) 1.5Qn; e) 1.8Qn
96
6.4 Summary
In this chapter, the Frozen Rotor method was firstly described together with numerical
settings.
The global parameters including water head and efficiency of the commercial centrifugal
pump were discussed. It can be seen that the general trend of global varieties were captured
well while there existed some differences when compared them with experimental data. This
was possibly due to the limitations of Frozen Rotor method to predict unsteady flow
phenomenon.
As stated in Chapter 1, some research has been done based on the Frozen Rotor method. For
example: the flow properties including velocity vectors and static pressure distributions near
the volute casing tongue, which provided a good agreement with the past available numerical
results. In this thesis, some new features of the flow structure were presented including flow
vorticity and helicity. There seemed to be some difference and contradictions when the
vorticity and helicity were taken into account. This was possibly also caused by the Frozen
Rotor method. Because this method is basically a steady flow method, this means the effect if
displacement due to rotation was ignored. A more in-depth research is presented in the next
chapter by applying Sliding Mesh method which may account for this rotation movement.
97
Chapter 7 Numerical analysis of centrifugal pump: transient flow
7.1 Introduction
More in-depth research conducted by applying the Sliding Mesh method is presented in this
chapter. First of all, the numerical setups are described. Then the numerical results of water
head and efficiency are again compared with experimental data.
The flow pattern in terms of velocity and static pressure inside the pump is discussed fully.
The unsteady flow properties including vorticity and helicity all be investigated and the
pressure fluctuation on the shroud surface of the volute casing will be analysed to work out
the empirical correlation with the flow rates.
7.2 Model and computational method: Sliding Mesh
7.2.1 Solid model of the commercial centrifugal pump
The solid model of the commercial centrifugal pump used in this chapter is the same one
described in Section 6.2.1. The main characteristics of the centrifugal pump were shown in
Table 5.1.
7.2.2 Sliding mesh method
The Sliding Mesh method is a completely unsteady method. The method permits the
rotational and absolute reference frames to be used and the movement of the impeller is taken
into account. At each time step, the fluxes are interpolated on the mesh between the rotor and
stator. Although some diffusion can be seen due to the interpolation, the unsteadiness is
98
accounted for. It is thus generally accepted that there was no major approximation for the
representation of the unsteadiness is made. Therefore, it was expected that Sliding Mesh
method could provide a reasonable prediction for the calculation of the hydraulic
performance of the centrifugal pump.
7.2.3 Geometry, grid and flow solver
The same geometry and grid as described in Section 6.2.3 were applied. The grid generated
for both the volute and the impeller is shown in Figure 6.2. Again, the commercial CFD code,
CFX was used for numerical simulations. Turbulence was simulated with the standard K-e
model and high resolution for the advection scheme. The second order backward Euler was
defined as simulation transient scheme.
7.2.4 Boundary conditions
Similar boundary conditions as described in Section 6.2.4 were used.
The impeller of the centrifugal pump was set as rotational part with an angular velocity of
1450rpm and the volute casing and pump inlet were set as stationary parts. Therefore, a fluid-
fluid interface was generated between these parts. The frame change model was defined as
transient rotor stator.
7.2.5 Numerical solution control
The pump can operate at different rotational speed. However, in this case, 1450rpm was
chosen for this project. Accordingly, the time step used for the unsteady simulation has been
set to 0.00166 sec. Thus, a complete revolution is performed at each 25 steps. This setup is
used to keep the frequency resolution well above the BPF and its low wider harmonics. In
order to get a reasonable frequency resolution of 1Hz, the time duration of 1s has been
99
chosen for the simulation. To reduce the residuals to an acceptable value, the numbers of
iterations were set as 8 accordingly. The RMS (the ratio between the sum of the residuals and
the sum of the fluxes for a given variable in all the cells) has been set to 10-4 to obtain a
reasonable accurate result at an acceptable time expense.
7.2.6 Initial condition
The initial conditions provide the flow field when the numerical calculation starts. For the
transient calculation, an acceptable initial condition could be obtained from a steady state
calculation with the same boundary conditions. Thus, the steady flow field data obtained by
applying Frozen Rotor method were used as the initial condition for the transient calculation
applying Sliding Mesh method.
7.3 Numerical results
7.3.1 Water head
The water heads obtained with five different flow rates by applying Sliding Mesh method are
shown as red dots in Figure 7.1. Since the value of water head keep fluctuating against time,
the mean value of water head over a time period for 1 second was used to stand for the total
water head. The experimental water head data of five different flow rates are shown as blue
dots in Figure 7.1. Although the quality of prediction also deteriorates if lower flow rates are
considered. The predicted values of water head are always underestimated for low flow rate
cases. It can be observed that the water head prediction were slightly better than those
predicted by Frozen Rotor method shown in Figure 5.3.
100
Figure 7.1: Comparison of water head obtained by using the Sliding Mesh method and Experimental data
7.3.2 Efficiency
The pump efficiency can be calculated using the same equation described in section 5.3.2.
The mean value of torque in a complete revolution (i.e. 25 time steps) was used for the torque.
The comparison of pump efficiency obtained experimentally and numerically is shown in
Figure 7.2. The experimentally data are measured shown in blue dots and numerical results
are shown in red dots in Figure 7.2.
101
44.14%43.57%
41.58%
38.23%
30.87%
41.43%43.75%
44.01%
42.29%
38.38%
30.00%
32.00%
34.00%
36.00%
38.00%
40.00%
42.00%
44.00%
46.00%
0 5 10 15 20
Experimental data
Numerical results
Flow rate (kg/s)
Effic
ienc
y
Figure 7.2: Comparison of pump efficiency obtained by using the Sliding Mesh method and Experimental data
Compared to Figure 5.4, it can be observed that the Sliding Mesh method can provide a better
prediction of pump efficiency. Although the disk friction and mechanical losses were ignored
in the pump efficiency calculation which is consistent with [4], the numerical calculated
pump efficiency displayed a reasonable agreement with experimental data.
102
7.3.3 Flow field
Figure 7.3 illustrates the absolute velocity vectors on a reference plane for three flow rates
(i.e. 0.8Qn, Qn and 1.2Qn). The reference plane is chosen at a distance of 0.015m above the
pump bottom surface. The magnitude scale of velocity vectors is set from 0—17m/s for all
graphs. Since one revolution of the five-blade impeller was represented by twenty five time
steps, five time steps are needed for a single blade passage period. Therefore, the velocity
vectors of five continuous time steps were selected for the flow field analysis.
Some similar phenomenon can be seen from these velocity vectors graphs. Firstly, the flow
velocity on the blade surface which is opposite to the rotation direction was much higher than
that on the other blade surface. Secondly, the main recirculation zones existed in the blade
passage. This means it was highly rotational and unsteady in these regions. Finally, the
largest recirculation zone can be observed in the blade passage close to the volute casing
tongue. This recirculation zone has become smaller as the impeller spins.
As the factor of increasing flow rates is taking into account, it can be observed that the largest
recirculation zone and the high velocity region occurred at the back surface of the blade
become smaller. Moreover, the velocity on the impeller side is high at low flow rates while
the velocity on the discharge side becomes higher at high flow rate. A relatively uniform
velocity distribution can be seen at the nominal flow rate.
It seems there is no direct correlation between the pump efficiency and the recirculation zone
in the blade passage. However, the velocity distribution near the volute casing tongue had
more effect on the pump efficiency.
103
a) b) c)
Figure 7.3: Absolute velocity vectors at five time steps for the different flow rates of: a) 0.8Qn; b) Qn; c) 1.2Qn
104
7.3.4 Static pressure
Figure 7.4 illustrates the static pressure distributions on the same reference plane used for
flow field analysis for three flow rates (i.e. 0.8Qn, Qn and 1.2Qn). The magnitude scale of
static pressure is set for all graphs from 93.5—187kPa which was the local static pressure
value at the nominal flow rate. Similar to the flow field analysis, the static pressure
distribution at five continuous time steps were chosen for the static pressure analysis.
Furthermore, according to the flow field analysis, the pressure on both side of the blade was
different. Moreover, the static pressure zone corresponded to those regions with high velocity.
The low velocity and recirculation zone stand for the regions with high pressure. The local
lowest static pressure regions were in the blade passage.
It can also be observed that the stagnation point on the volute casing zone moves from the
discharge side to the impeller side from low to high flow rate. It was on the symmetry centre
point of the volute casing tongue when the pump was operating at nominal flow rate.
Meanwhile, the static pressure distribution was also much more uniform compared to other
flow rates. This is consistent with the description in Chapter 1.
It seems probably true that the position of the pressure stagnation point has an effect on the
pump efficiency. When the stagnation point occurred on the symmetry centre of the volute
casing tongue, the pump seemed operating at BEP.
105
a) b) c) Figure 7.4: Static pressure distribution at five time steps for the different flow rates of: a) 0.8Qn; b) Qn; c)
1.2Qn
106
7.3.5 Flow vorticity
As described in the previous chapter, vorticity is a flow property which can be used to stand
for the rotational motion of fluid elements.
Figure 7.5 illustrats the vorticity change for different flow rates at different time constants.
The magnitude scale of vorticity is set for all graphs from 9.57—3676.05Hz which was the
local vorticity value at the nominal flow rate.
The large value of the vorticity can be observed in the blade passages. As the flow rate
increases, the local value of the vorticity decreased. There exists a large vortex region in the
volute casing for low flow rate cases. This region became smaller when the flow rate
increased.
The zone of largest value of vorticity can be observed in the blade passage which was close
to the volute casing tongue. However, for the high flow rate cases, the largest value of
vorticity moved to the left bottom blade passage.
It was possible that the position of the large vorticity zone could be a factor which would
result in the change of the pump efficiency.
107
a) b) c)
Figure 7.5: Contour of vorticity at five time steps for the different flow rates of: a) 0.8Qn; b) Qn; c) 1.2Qn
108
7.3.6 Flow helicity
Flow helicity is a property which can be a representation of the vorticity aligned with the
fluid stream. If a parcel of fluid is moving and also undergo a rotating motion about an axis
parallel to the moving direction, it will have helicity. The positive value means the rotation is
clockwise about the fluid elements moving axis while the negative value means anti-
clockwise rotation.
Figure 7.6 illustrats the helicity change for different flow rates and time constants. The
magnitude scale of helicity is set for all graphs from -13249—19140s-2 which was the local
helicity value at the nominal flow rate.
As shown in Figure 7.6, the overall local strength of the helicity became larger for high flow
rates. It can also be found that there were some separate negative helicity regions in the
volute casing. Meanwhile, a large positive helicity region can be observed in the volute
casing for high flow rate. The helicity region was uniform when the pump was operating at
the nominal flow rate.
Moreover, the rotation direction of vortex in the blade passage changed from clockwise to
anti-clockwise in the single passage period for all three flow rate cases. These regions were
corresponding to those with high velocity if compared Figure 7.5 with Figure 7.3.
Therefore, it seems the distribution of helical region imposes some effects on the pump
efficiency. If the helical region distributed uniformly, the pump is more likely to operate at
BEP. On the other hand, the pump efficiency would drop if nonuniform helical regions are
observed.
109
a) b) c)
Figure 7.6: Contour of helicity at five time steps for the different flow rates of: a) 0.8Qn; b) Qn; c) 1.2Qn
110
7.3.7 Pressure fluctuation
There were 36 monitor points located at every 10 degrees around the shroud surface of the
volute casing at a radial distance of 2mm out from the impeller outlet were chosen to
investigate the dynamic pressure fluctuation inside the pump volute casing.
Figure 7.7 shows a typical power spectrum of the dynamic pressure when the pump was
operating at nominal flow rate at one position in the volute casing tongue region, 20 degrees
from the tongue edge. It can be seen that the predominant peak correspond to the frequency
of rotation of the impeller which was 24Hz and also to the blade passing frequency at 121Hz,
together with their harmonics.
299.828
1278.25
0
200
400
600
800
1000
1200
1400
20 41 62 83 104 125 146 167 189 210 231 252 273 294
Mag
nitu
de o
f dyn
amic
pre
ssur
e (P
a)
Frequency (Hz)
Figure 7.7: Dynamic pressure spectrum at a position of 20 degree from the volute casing tongue in the rotating
direction
111
The estimated distribution of dynamic pressure along the shroud surface of the volute casing
for nominal flow rate is shown in Figure 7.8. The dynamic pressure fluctuation near the
volute casing tongue was more intense as expected.
0
200
400
600
800
1000
1200
1400
1600
1800
0 60 120 180 240 300 360
Mag
nitu
de o
f dyn
amic
pre
ssur
e (P
a)
Position (Degree)
Figure 7.8: The distribution of dynamic pressure fluctuation along the shroud surface of volute casing tongue in
the rotating direction
The change of dynamic pressure magnitude at rotational frequency and blade passing
frequency for different flow rates rates (i.e. 0.5Qn, 0.8Qn, Qn, 1.2Qn and 1.5Qn) were
illustrated in Figure 7.9 and 7.10. The position was selected at 20 degrees from the volute
casing tongue in the rotating direction.
112
12584 49
508
817
0
100
200
300
400
500
600
700
800
900
0.5 0.8 1 1.2 1.5
Mag
nitu
de o
f dyn
amic
pre
ssur
e (P
a)
Q/Qn
Figure 7.9: Change of dynamic pressure magnitude at rotational frequency at a position of 20 degree from the volute casing tongue in the rotating direction
15151273
1010
1870
2957
0
500
1000
1500
2000
2500
3000
3500
0.5 0.8 1 1.2 1.5Mag
nitu
de o
f dyn
amic
pre
ssur
e (P
a)
Q/Qn
Figure 7.10: Change of dynamic pressure magnitude at blade passing frequency at a position of 20 degree from the volute casing tongue in the rotating direction
113
For the magnitude of dynamic pressure at rotational frequency and blade passing frequency,
it can be observed that the dynamic pressure magnitude has the minimum value at the
nominal flow rate. It increases when the pump is operating at off-design conditions.
Moreover, the dynamic pressure magnitude at blade passing frequency was much higher than
those at rotational frequency.
From Figure 7.9, there probably existed a linear correlation between the dynamic pressure
magnitude and the flow rate at the rotational frequency. For the flow rate lower than the
nominal flow rate, the dynamic pressure magnitude is,
152(1 )DP NFn
QM MQ
= + − (8)
MDP stands for the dynamic pressure magnitude at any flow rate an MNF represent the
dynamic pressure magnitude at nominal flow rate.
For the high flow rate cases, the correlation can be approximately expressed as:
1536( 1)DP NFn
QM MQ
= + − (9)
From Figure 7.10, the correlation between flow rate and dynamic pressure magnitude can
also be expressed in similar manner. For the low flow rate, the correlation can be expressed
as:
1010(1 )DP NFn
QM MQ
= + − (10)
For the high flow rate:
3894( 1)DP NFn
QM MQ
= + − (11)
114
7.4 Summary
In this chapter, the Sliding Mesh method was applied on different aspects of flow patterns to
investigate their correlations with pump efficiency. It has been found that velocity
distribution near the volute casing tongue, the position of stagnation point and the pressure
fluctuation on the volute. These were also described by some early researchers (see section
1.2.2-1.2.4 in Chapter 1).
The creativity and originality of this work including:
• The vorticity trend and distribution of a series of time steps at different flow rate
• The helicity trend and distribution of a series of time steps at different flow rate
• Established an empirical correlation between the flow rates and magnitude of
dynamic pressure
115
Chapter 8 The correlation between vibration and efficiency
8.1 Introduction
As the main objective of this project is to establish the correlation between centrifugal pump
vibration and efficiency, this chapter provides some preliminary numerical evidence to
illustrate this correlation.
It should be noted that the total energy transferred from the motor to the pump were
consumed in a number of ways such as pumping the water, vibrating the pump and bearing,
dissipating as thermal energy and so on. Therefore, the vibration energy on the pump is only
part of the transferred energy. However, it is expected that there existed a correlation between
the vibration energy and the efficiency. If more input energy is transformed into vibration
energy, low pump efficiency can be expected.
In this chapter, a general correlation between the efficiency and flow rate will be described
first. Then different aspects related to the pump vibration including pressure fluctuation, and
velocity amplitude will be analysed numerically. Then the vibration energy density on the
inner surface of pump volute casing was calculated numerically. Then the results were used
to establish the empirical correlation with the pump efficiency will be shown.
8.2 The correlation between efficiency and flow rate
The efficiency reduction can be observed in Figure 7.2. For high flow rate from Qn to 1.5Qn,
the pump efficiency decreased by 0.6% and from Qn to 1.2Qn, an efficiency reduction of 5.9%
can be observed. For low flow rates from Qn to 0.5Qn, there can be seen a reduction of 3.9%
116
and from Qn to 0.8Qn, an efficiency reduction of 12.8% can be seen. The decrease of pump
efficiency is more pronounced for low flow rates when the change ratio of flow rate is kept
the same.
8.3 The correlation between pressure fluctuation and efficiency
As can be seen in Figure 7.10, if we compare the magnitude of dynamic pressure when the
pump operates at BPF, it can be found that the magnitude of dynamic pressure increased by
85.1%from Qn to 1.2Qn and 192.8% from Qn to 1.5Qn. For low flow rates, there can be seen
an increase of 26% from Qn to 0.8Qn and 50% from Qn to 0.5Qn at the BPF. The increase of
magnitude of dynamic pressure is more evident for high flow rates and the rate of the
increase is much more significant than that of pump efficiency.
Therefore, it can be found that the pump efficiency decreases as the magnitude of dynamic
pressure on the pump volute casing surface increases. In other words, more energy has been
used to generate vibration when the pump operates at off-design conditions.
8.4 Velocity variation in the frequency domain
It can be seen from Figure 8.1, the yellow cross symbols are 36 selected points on the pump
volute casing for calculating the fluid particle velocity. These points were chosen the same as
the pressure fluctuation analysis. Velocity FFT analysis was then performed at each of these
points to obtain a whole image of the velocity variation of the centrifugal pump.
117
Figure 8.1: Selected points for vibration energy calculation
Figure 8.2 showed the velocity variation in the frequency domain at a certain point near the
pump tongue (shown as Observation Point in Figure 8.1) at different flow rates. As can be
seen in Figure 8.2, the amplitude of velocities varied in a similar manner as pressure
fluctuation. More specifically, the minimum value of velocity amplitude can be observed at
the nominal flow rate. In other words, the pump is operating at its BEP in this case. When the
pump operated under off-design condition, an increase of the velocity magnitude can be
expected. From Figure 8.2, the magnitude of velocity increased by 127% at the pump rotating
frequency and 139.5% at the blade passing frequency from Qn to 1.2Qn. For low flow rates
from Qn to 0.8Qn, there can be seen an increase of 68.4% at the pump rotating frequency and
20% at the blade passing frequency. The increase of magnitude of velocity is more evident
for high flow rates and the rate of the increase is much more significant than that of pump
efficiency.
118
0.8Qn
Qn
1.2Qn
Figure 8.2: FFT of variation of velocity amplitude in the frequency domain at different flow rates
Frequency (Hz)
Frequency (Hz)
Frequency (Hz)
Velo
city
Am
plitu
de (m
/s)
Velo
city
Am
plitu
de (m
/s)
Velo
city
Am
plitu
de (m
/s)
119
8.5 Vibration energy on the inner surface of pump volute casing
It can be seen from Figure 8.1, the yellow cross symbols are 36 selected points on the pump
volute casing, the velocity at these points were used to calculate the vibration energy in the
fluid near the surface of pump volute casing. The vibration energy can be expressed as:
(12)
E stands for the vibration energy density, 𝜌 is the water density which is equal to 1000kg/m3,
vn is the velocity of the selected point and n is the number of the selected points. n is equal to
36 in this case.
It should be noted that the velocity in the equation is not the same as the structural surface
velocity. Since the boundary condition of the surface in CFD was set as non-slip wall which
means the surface is with no velocity. The velocities in the equation were obtained on a
certain fluid point. However, the velocities of these fluid points are similar to the structural
surface velocity; therefore, the calculated energy density can be considered as similar as the
structural vibration energy density.
Figure 8.3 described the trend of vibration energy density from low flow rate to high flow
rate. When the pump operated at BEP at nominal flow rate, the value of the vibration energy
density is the smallest. More input energy from the motor may transferred to increase the
effective power of the pump. On the other hand, large value of vibration energy density can
be observed when the pump operated under off-design condition.
From Qn to 1.2Qn, the vibration energy density increased by 365% at the pump rotating
frequency and 328% at the BPF. For low flow rates from Qn to 0.8Qn, there can be seen an
120
increase of 132% at the pump rotating frequency and 13.1% at the BPF. The increase of
vibration energy density is more evident for high flow rates and the rate of the increase is
much more significant than that of pump efficiency.
Figure 8.3: Vibration energy for different flow ratio at rotating frequency (top) and BPF (bottom)
Vibr
atio
n En
ergy
Den
sity
(J/m
3 )
Flow Ratio
Flow Ratio
Vibr
atio
n En
ergy
Den
sity
(J/m
3 )
121
8.6 Summary
As described above, the similar trend can be observed for the pump efficiency, the magnitude
of dynamic pressure, the amplitude of velocity and the vibration energy density. This
corresponds to the statement that if more energy had been used to generate vibration, less
pump efficiency can be expected. However, there was an opposite trend of the rate of the
increase. More specifically, more energy had been transferred to the form of vibration for
high flow rates while the decrease of pump efficiency was not that significant. The reason for
this phenomenon may lies on even if some input energy had been used to generate vibration,
more energy had been used for the increase the velocity and pressure head within the pump
which were contribute to the increase of effective power.
122
Chapter 9 Conclusions and future work
9.1 Conclusions
The main contributions of this project can be concluded as follows:
First of all, the modal tests of pump components and assembly have been conducted. The
original purpose of this experiment was to verify the feasibility of considering the volute
casing and impeller as rigid in the CFD model. After the data analysis, it is found that the
modal test results can be used as a valuable tool to identify different contribution of
components (volute casing and impeller) to the assembly. This is rather important for the
pump condition monitoring since any resonance should be avoided during the pump
operation.
Secondly, some numerical research has been done based on the Frozen Rotor method such as
the flow properties including velocity vectors and static pressure distributions near the volute
casing tongue. The results obtained in this work gave a similar trend of these properties. In
addition, some new features of the flow structure were presented in this thesis including flow
vorticity and helicity. There seemed to be some difference and contradictions. This was
possibly also caused by the Frozen Rotor method. Because this method is basically a steady
flow method, which means the effect of displacement due to rotation was ignored.
Then the Sliding Mesh method was applied on different aspects of flow patterns to
investigate the correlation with pump efficiency. The velocity distribution near the volute
casing tongue, the position of stagnation point and the pressure fluctuation on the volute have
been investigated and analysed.
The creativity and originality of this work including:
123
• The vorticity trending and distribution of a series of time steps at different flow rate
• The helicity trending and distribution of a series of time steps at different flow rate
Finally, by calculating the velocity variation at a series of selected points on the pump volute
casing surface, the structural vibration energy density was obtained. Then an empirical
correlation between pump vibration and efficiency is established numerically.
9. 2 Future work
Firstly, although the FEA has been applied for both the impeller and volute casing, it has not
been used for the pump assembly. It could be a logical next step to finalise the comparison
between the FEA and experimental results.
Secondly, the CFD simulations were completed under different working conditions, so it is
possible to investigate the structural vibration of the pump by integrating the CFD data with
an accurate pump FEA model.
Finally, more experiments are needed to establish the correlation between the pump vibration
and efficiency. More specifically, some tiny holes can be drilled near the tongue region of the
pump and then one can put some pressure probes in these holes to collect the time-dependent
dynamic pressure data. The data should be collected under different working conditions.
Then a more accurate correlation between pump vibration and efficiency can be established.
The numerical means can be used to verify the correlation and provide the in-depth
explanation behind the phenomenon.
124
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