Flow Field of an Impeller

FLOW FIELD OF AN IMPELLER

Module Code: NG3S239

Module Title: Computational Fluid Dynamics

Student Name: Kudzai Mutasa

Student Number: 11001259

Lecturer: Dr. Talal Maksoud

12/5/2013

Flow Field of an Impeller

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1.0 ABSTRACT

Turbomachinery has a great many number of uses in modern engineering and various components have different bearings on machinery performance. In this study a centrifugal pump impeller, commonly used to mix slurries of chemicals or to pump water, was modelled in solidworks and analyzed as it rotated around a centre in computational fluid dynamics (CFD) package Phoenics. The impeller hub was modified from 30mm length to 50mm length as well as the angular rotation speed at 600rpm, 1500rpm and 3000rpm. An inlet velocity on 25m/s was used due to the impellers low speed application and it was discovered that an increase in impeller hub length resulted in an overall decrease of the pressure domain as well as increase in velocity between hub and impeller blades. Hub geometry modification also reduced overall efficiency of the impeller.

CONTENTS

1.0 Abstract........................................................................................................................................................................1

2.0 Introduction ................................................................................................................................................................3

2.1 Turbomachinery ....................................................................................................................................................3

2.2 Centrifugal Pumps.................................................................................................................................................4

2.2.1 The Impeller.......................................................................................................................................................5

2.2.2 Slip Factor ..........................................................................................................................................................6

2.2.3 The effect of impeller blade shape on perfomance........................................................................................8

3.0 Case Study: improving centrifugal pump efficiency by impeller trimming......................................................9

3.1 Impeller trimming .................................................................................................................................................9

3.2 Experimental procedure ................................................................................................................................... 10

3.3 Results and Conclusion...................................................................................................................................... 10

3.0 Flow field investigation of impeller at changing hub design ........................................................................... 12

3.1 Impeller selection and modification ............................................................................................................... 12

3.2 Results and Discussion ...................................................................................................................................... 14

3.2.1 Dome shaped Impeller ................................................................................................................................. 14

3.2.2 Cone shaped Impeller ................................................................................................................................... 18

3.2.3 Graphical Pressure and velocity variation along domain length .......................................................... 22

3.2.4 Effect of rpm variations on impeller .......................................................................................................... 24


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3.2.5 Effect of shape on impeller performance ................................................................................................. 27

4.0 Conclusion and future improvements to the analysis...................................................................................... 27

5.0 References ................................................................................................................................................................ 28

6.0 Appendices ............................................................................................................................................................... 29


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2.0 INTRODUCTION

2.1 TURBOMACHINERY

A turbomachine can be defined as a device in which energy transfer occurs between a flowing fluid and a rotating element due to dynamic action, and results in a change in pressure and momentum of the fluid, as stated by Gorla and Khan (2003). Mechanical energy transfer can occur either inside or outside of the turbomachine and usually in a steady flow process. The turbomachine extracts energy from or imparts energy to a continuously moving stream of fluid except for in a positive displacement machine, where it is intermittent. There are various types of turbomachines and Gorla and Khan (2003) classify them as follows.

1. Turbomachines in which (i) work is done by the fluid and (ii) work is done on the fluid

2. Turbomachines in which fluid moves through the rotating member in axial direction with no radial movement of the streamlines.

Turbomachines can further be classified as follows

a) Turbines- machines that produce power by expansion of a continuously flowing fluid to a lower pressure

b) Pumps- machines that increase the pressure or head of flowing fluid c) Fans- these machines impart only a small pressure rise to a continuously flowing gas; usually with the

gas being considered incompressible d) Compressors- machines that impart kinetic energy to a gas by compressing it and then allowing it to

rapidly expand.


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Figure 1 turbomachinery

2.2 CENTRIFUGAL PUMPS


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Gorla and Khan (2003) mention that there are three important parts to centrifugal pumps which are

1) The impeller, 2) The volute casing and 3) The diffuser

2.2.1 THE IMPELLER

The centrifugal pump is used to raise l iquids from a lower to a higher level by creating the required pressure with the help of centrifugal action. Whirling motion will be imparted to the l iquid by means of backward curved blades mounted on a wheel known as an impeller. As the impeller rotates, fluid drawn into the blade passages at the impeller inlet or eye and is accelerated as it is forced radially outwards. This enables the static pressure at the outward radius to be much higher than at the eye inlet radius.

Figure 2

The high pressure fluid is then led to the pump casing at high velocity and in order to recover this kinetic energy into pressure energy, diffuser blades are mounted on a diffuser ring. The stationary blade passages have an increasing cross-sectional area and as the fluid moves through them, diffusion action takes place and hence kinetic energy converted into pressure energy. The fluid then moves from the diffuser blades into the volute casing, which collects water and conveys it to the pump outlet. Figure 2 shows a centrifugal pump impeller with its velocity triangles at the inlet and outlet.


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For best pump efficiency, Gorla and Khan (2003) mention that it should be assumed that water enters the pump radially at 𝛼1=90° and𝐶𝑤1 = 0. Using Eulers pump equation, the work done per second on the water per unit mass of fluid flowing is

𝐸 =𝑊𝑚

= 𝑈2𝐶𝑤2 − 𝑈1𝐶𝑤1

Where 𝐶𝑤 =component of absolute velocity in the tangential direction, E =Euler head, representing the theoretical head developed by the impeller only.

The flow rate is given as follows

𝑄 = 2𝜋𝑟1𝐶𝑟1𝑏1 = 2𝜋𝑟2𝐶𝑟2𝑏2

Where 𝐶𝑟= radial component of absolute velocity, perpendicular to the tangent at inlet and outlet. b= width of the blade

Work done on the water by the pump consists of the following parts

1. 𝐶22 −𝐶12

2 – the change in kinetic energy of the l iquid

2. 𝑈22−𝑈12

2 – the effect of the centrifugal head or energy produced by the impeller

3. 𝑉22−𝑉12

2 – the change in static pressure of the l iquid, if impeller losses are neglected

2.2.2 SLIP FACTOR

Gorla and Khan (2003) deduce from presented information how there is no assurance that the actual fluid will follow the blade shape, leaving the impeller in a radial direction. Figure 3 i l lustrates velocity triangles at impeller tip, with 𝐵2′ being the angle at which the fluid leaves the impeller and 𝐵2 the actual blade angle. 𝐶𝑤2 and 𝐶𝑤2′ are tangential components of absolute velocity corresponding to angles 𝐵2 and 𝐵2′ respectively. Therefore the difference ∆𝐶𝑤 is defined as the slip.

Figure 3: velocity triangle at impeller outlet with slip. Courtesy of Gorla and Khan (2003), section 2.4 fig 2.2


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Sl ip factor,𝜎 = 𝐶𝑤2′ 𝐶𝑤2

Gorla and Khan (2003) refer to Stodola’s theory which states that

‘’slip in centrifugal pumps and impellers is due to relative rotation of fluid in a direction opposite to that of impeller with the same angular velocity as that of an impeller.’’

Figure 4: Pressure distribution on an impeller vane, LP=low pressure, HP= high pressure

Figure 4 shows the leading side of the blade where a high pressure region is present while a low pressure region is present on the trail ing side. Due to the lower pressure region on the trail ing face, a higher velocity as well as a velocity gradient will be present across the passage. The flow may separate from the suction surface of the blade due to the fact that the pressure distribution is associated with the existence of circulation around the blade. This will mean that low velocity on high pressure side and high velocity on the low pressure side as well as velocity distribution will not be uniform along any radius, as Gorla and Khan (2003) state. This would mean that 𝐶𝑤2 < 𝐶𝑤2′ and the difference is defined as sl ip. The net result wil l be that fluid is discharged from the impeller at an angle relative to the impeller, which is less than the vane angle.

Slip factor,𝜎 = 𝐶𝑤2′ 𝐶𝑤2

For purely radial blades, used in centrifugal compressors, 𝛽2 = 90° and the Stodola sl ip factor becomes as follows

𝜎 = 1 −𝜋𝑛

Where n=number of vanes. Stanitz sl ip factor is given as follows

𝜎 = 1 −0.63𝜋𝑛

When a sl ip factor is applied, the Euler pump equation becomes

𝑤𝑚

= 𝜎𝑈2𝐶𝑤2 − 𝑈1𝐶𝑤1

Typically, the sl ip factor l ies in the region of 0.9 and slip occurs even when the fluid is ideal


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2.2.3 THE EFFECT OF IMPELLER BLADE SHAPE ON PERFOMANCE

Gorla and Khan (2003) classify blade shapes as follows

1. Backward curved blades (𝛽2 < 90° 2. Radial blades (𝛽2 = 90°) 3. Forward-curved blades (𝛽2 > 90°)

Figure 5

As the figure i l lustrates, for backward-curved vanes, the value of 𝐶𝑤2 is greatly reduced therefore such rotors will have a low energy transfer for a given impeller tip speed, with forward-curved vanes having a high value for energy transfer. This would imply that high values of 𝛽2 are favourable however these will also lead to a very high value for𝐶2. High kinetic energy isn’t usually required and its reduction to static pressure by diffusion in a fixed casing is difficult to perform in a reasonable sized casing. Radial vanes have particular advantages for very high speed compressors where the required pressure must be as high as possible.

Figure 6 characteristics for varying outlet blade angle; courtesy of Gorla and Khan (2003)


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Radial vanes are relatively easy to manufacture and introduce no complex bending stresses as i l lustrated by figure 6.

3.0 CASE STUDY: IMPROVING CENTRIFUGAL PUMP EFFICIENCY BY IMPELLER TRIMMING

Savar, Kozmar and Sutlovic (2008) investigate a method on improving efficiency in centrifugal pumps of impeller trimming which is said to be used by manufacturers worldwide. A centrifugal pump impeller of low specific speed was trimmed and test results were successful having performed a number of experiments.

3.1 IMPELLER TRIMMING

Impeller trimming involves machining of the impeller to improve its diameter and is based on affinity laws which state that pump impellers are considered to be similar if they satisfy geometric and kinematic similarity conditions, which were investigated by Tsang (1992).

However after the impeller had been trimmed, it was noted that geometric and kinematic similarity conditions were not completely preserved. This came in the form of not being able to obtain some characteristic dimensions such as ratio between impeller width and outlet diameter or impeller inlet to outlet diameter ratio. Kinematic similarity was not obtained because impeller blade angle varied with radius. On the other hand the following similarity conditions were satisfied in many elements to mention a few:

1. Impeller shape 2. Impeller disposition 3. Number of impeller blades 4. Kinematic conditions at the inlet 5. Ratio between impeller width and inlet diameter

Figure 7 impeller dimensions before initial trimming and after final trimming


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For the purpose of this experiment, the impeller was trimmed seven times by successively reducing the outlet diameter by a 10mm step on a low specific speed centrifugal pump of specific speed

{𝑛𝑠𝑝 }𝑟.𝑝.𝑚 . 𝑚0 .75𝑠−0.5 ={𝑛}𝑟.𝑝.𝑚. �{𝑄}𝑚3/𝑠

{𝐻}𝑚0.75

Where n=speed of rotation, Q=discharge and H=pump head

3.2 EXPERIMENTAL PROCEDURE

Figure 8 experimental apparatus

The impeller investigated had seven single radius curved blades and was trimmed in 10mm steps from the initial diameter D=190mm to the final D=130mm (figure 7) and the width was kept constant at 4mm. the pump characteristics were recorded for each of the impeller outlet diameters.

Pump characteristics were determined by measuring the following quantities at various discharge rates which was tuned using a control valve.

a) Pressure rise across the pump and flow meter b) Shaft moment c) Rotation speed d) Water temperature e) Ambient pressure

3.3 RESULTS AND CONCLUSION


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The results were plotted on a head versus discharge diagram (figure 9) and pump characteristics were depicted in the form of non-dimensional diagrams using the following characteristic coefficients:

-head coefficient 𝜓

𝜓 =2𝑔𝐻𝑢2

-flow coefficient 𝜑

𝜑 =𝑄𝑢𝐴

Where H=pump head, D=impeller outlet diameter, u=peripheral velocity at the impeller outlet diameter, g=9.80665 m/𝑠2 is the gravitational constant, b=impeller width, A=impeller outlet surface area A=Dπb.

Figure 9 Head vs. discharge diagram


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Figure 10

Savar, Kozmar and Sutlovic (2008) deduce the meaning of these coefficients being that each pair of dimensional values of discharge Q and head H has its own non-dimensional counterparts 𝜑 and ψ. Result were displayed in the non-dimensional form in a 𝜑 − ψ diagram as well as trend l ines for all diameters and affinity law line and ψ = ψ( 𝜑). This function was derived from the initial value of the diameter with its adherence to the trend l ine being observed. It was noticed that as the impeller diameter decreased, impeller efficiency decreased significantly.

In summary, the above method of pump impeller trimming found good experimental confirmation despite some theoretical constraints. Taking into account the relatively small measuring error it could be concluded that the disregarded geometry similarity by impeller only trimming showed strict adherence to affinity law, despite minor discrepancies.

3.0 FLOW FIELD INVESTIGATION OF IMPELLER AT CHANGING HUB DESIGN

3.1 IMPELLER SELECTION AND MODIFICATION


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Figure 11 centrifugal pump impeller

A centrifugal pump impeller was selected and the flow of various hub configurations was investigated with constant thickness. The impeller was then modified do increase the hub length to 30mm and a dome shape was selected and for such impellers, Stodola sl ip factor is low. The following parameters were then varied and assessed

a) Impeller hub length b) Angular velocity of rotation c) Impeller hub shape

Impeller characteristics were determined in the post-processing stage and were classified as follows

i) Pressure range across the domain ii) Flow velocity vectors along the hub iii) Velocity decrease on hub approach with varying shape iv) Effect of hub shape on impeller performance v) Effect of rpm variations on the impeller


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Perimeter

Size

Number of blades 6

Inlet velocity (m/s) 25

Hub length

30mm

50mm

Hub shape Dome shaped

Cone shaped

Table 1

All stagnation points were represented with an S on the diagrams.

3.2 RESULTS AND DISCUSSION

3.2.1 DOME SHAPED IMPELLER

A) HUB LENGTH: 30MM VERSUS 50MM AT 600RPM

i) Pressure range variation The results revealed a similar pressure field however the maximum pressure for the 30mm length hub in the domain was greater than for the 50mm hub length impeller. The 50mm length impeller showed greater negative values possibly due to more recirculation.


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Figure 12 30mm shaft length

Figure 13 50mm shaft length

ii) Velocity field

Figure 14 and 15 below show the variation of the inlet approach velocity with hub length. The highlighted areas indicate the presence of this phenomenon. Figure 14 displays only 2 different velocity fields whereas figure 15 shows 3 different flow fields, possibly due to the difference in hub length.

Pressure gradient is greater at 30mm possibly due to more sudden change in impeller geometry across domain


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Figure 14 30mm velocity field


30mm 50mm

Pressure range(Pa) 3160-(-10067.5) 2215-(-12582)

Average pressure value 434.1 301.1

Velocity range 1.0-135.1 0.8-123.0

Average velocity value 25.9 24.6

Table 2

B) 30MM VERSUS 50MM AT 1500RPM

Zone of recirculation of flow varies between hub lengths also reducing stagnation points.


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i) Pressure range variation The results display a distinct variation in the pressure field behind the impeller while the flow field in front is almost identical. At 1500rpm the difference becomes distinct that is caused by the variation in hub length.

Figure 16 30mm length pressure field

Figure 17 50mm length pressure field

ii) Velocity field The approach field representing velocity varies drastically at the two impeller lengths,

Possible impeller zone whose shape is responsible for flow variation. There is a clear distinction between the value for pressure behind the impeller.


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Figure 18 30mm hub velocity field

Figure 19 50mm hub velocity field

30mm 50mm

Pressure range(Pa) 2055.0-(-2234) 1507.6-(-4156.6)

Average pressure value 342.2

Velocity range 1.9-74.9 1.8-77.1

Average velocity value 24.0

Table 3

3.2.2 CONE SHAPED IMPELLER

5 different velocity fields present. Flow is then accelerated by blades.

Inlet flow is affected sooner by hub, due to increased length. Stagnation point present.


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A second shape was also put through the same design constraints and the fields were analysed so as to validate the variation in flow phenomenon with impeller hub length.

A) HUB LENGTH: 30MM VERSUS 50MM AT 1500RPM

i) Pressure field after impeller The increased speed of rotation evidently displays a decrease in the pressure of the domain. The flow reduces pressure immediately behind the impeller and is maximum at the tip of the cone.

Figure 20 30mm cone shaped impeller pressure field

Figure 21 50mm cone shaped impeller pressure field

Noticeable pressure drop, not as high as with the dome shaped impeller.

No stagnation points present [roving reduction of impeller efficiency.


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iii) Velocity field approaching impeller

The figure below displays the velocity flow field and stagnation points are visible. The speed of air is slowed down by the impeller from the yellow zone to the green zone upon reaching the tip of the cone.

Figure 22 30mm cone shaped impeller velocity field

Figure 23 50mm cone shaped impeller velocity fields

The table below indicates how the velocity range is almost identical showing the domain shows l ittle variation with impeller length.

30mm 50mm

Flow almost identical upon approach, however separation sti l l visible.

Variable flow separation. Flow becomes more excited at due to the impeller hub geometry change,


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Pressure range(Pa) 647.9-(-330.1) 723.3-(-373.5)

Velocity range 0.15-38.2 0.17-38.19

Table 4

B) 30MM VERSUS 50MM AT 1500RPM

I) Pressure field The results of the cone shaped impeller reveal varying results at each impeller hub length. At 30mm pressure is decreasing at the blades as shown and is approximately constant towards the outlet. Pressure is higher beyond the impeller for the 50mm length impeller.

Figure 24 30mm hub pressure field

Figure 25 50mm hub pressure field

Pressure decrease is more recognisable at 30mm. hub length increases


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i) Velocity field



30mm 50mm

Pressure range(Pa) 647.9-(-330.1) 723.3-(-373.5)

Velocity range 0.15-38.2 0.17-38.19

Table 5

3.2.3 GRAPHICAL PRESSURE AND VELOCITY VARIATION ALONG DOMAIN LENGTH

There is a notable increase of velocity at blades with similar observations as with 600rpm values.


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A) PRESSURE

The figures below il lustrate the variation of pressure with distance from the inlet. Despite the graphs being similar to 600rpm the values indicate that pressure decreases as displayed by the maximum and minimum values of the y-axis. The gradient also reduces from hub tip to blade tip with the increase in angular rotation.

Figure 28 Table 6 pressure vs distance for a) 30mm at 600rpm with pressure field insert(top left), b) 50mm at 600rpm(top right), c) 30mm at 1500rpm with pressure field insert (bottom left) and d) 50mm at 1500rpm (bottom right)

B) VELOCITY

The variation of velocity along the domain length is displayed with the stagnation zones displayed. Maximum velocity values are observed to decrease with variation in impeller geometry of the hub and this could be attributed to the shorter radius of curvature from hub tip to blade tip.


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Figure 29 velocity vs. distance for a) 30mm at 600rpm(top left), b) 50mm at 600rpm(top right), c) 30mm at 1500rpm(bottom left) and d) 50mm at 1500rpm (bottom right)

Similar results were obtained for the cone shaped impeller as well.

3.2.4 EFFECT OF RPM VARIATIONS ON IMPELLER

Stagnation zones


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The cone shaped impeller at 30mm hub length was analysed at three different angular rotation speeds in order to study the effects of rpm variations on the impeller performance. The figures below display the results of the impeller at 3000rpm and these were compared with 300rpm and 1500rpm results. The impeller selected had backward curved which as earlier discussed produce low energy transfer for a given impeller tip speed. Therefore the transfer of flow reduced in efficiency upon reaching 300rpm and 1500rpm revealed the best performance values of the impeller.

Figure 30 30mm hub at 3000rom

Figure 31 50mm hub at 3000rpm

Velocity gradient is high as compared to lower rotational speeds.

The pressure drop behind the impeller is not as noticeable in this case. The high speed of rotation results in a lower efficiency of the blades hence most of the air is unaffected. Figure 32 displays ideally the path air should follow upon approach of the hub and blades.


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Figure 32 ideal flow of air at 1500rpm

Figure 33 surface contours for 30mm impeller at 3000rpm

600rpm 1500rpm 3000rpm

Pressure range(Pa) 3160-(-10067.5) 647.9-(-330.1) 4023.8-(-8053.5)

Average pressure value 434.1 497.43

Velocity range 1.0-135.1 0.15-38.2 3.1-132.1

Average velocity value 25.9 34.0

Table 6


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3.2.5 EFFECT OF SHAPE ON IMPELLER PERFORMANCE

Figure 34 30mm cone shaped hub versus dome shaped hub at 600rpm pressure contours

Figure 33 above displays the difference in pressure distribution on the hub of the impeller. The dome shaped impeller experiences higher pressure up to the leading edge of the blades as the flow of air is more evenly distributed. The cone shaped impeller however displays a number of pressure fields developing from the impeller tip to the blades with a greater pressure gradient. Therefore a dome-shaped impeller produces more evenly distributed flow.

4.0 CONCLUSION AND FUTURE IMPROVEMENTS TO THE ANALYSIS

The following phenomena were achieved in Computational Fluid Analysis of the impeller with varying hub length and shape.

a) Hub length increase causes a decrease in overall pressure b) Hub length increase results in increase in velocity between hub and impeller blades c) Hub length increase results in a decrease in stagnation zones d) Impeller blades cause an increase in velocity and pressure being the impeller. e) Pressure behind the impeller was low as compared to In front of the impeller f) An increase in rotational speed of the impeller resulted in lower impeller efficiency.

It was however noted that this basic approach to CFD may not have been sufficient enough to fully analyse the performance of the impeller, despite its low efficiency. In future the following parameters may be implemented

i) Solution verification and validation equations may be implemented ii) Modification of the inlet velocity and domain may be performed in order to observe any changes. iii) A greater number of angular velocities may be analysed e.g. 400rpm, 500rpm. 600rpm, etc. iv) Parsol and finite grid volume modelling for each of the impeller shapes


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5.0 REFERENCES

R. S. R. Gorla, A. A. Khan, 2003, Turbomachinery design and theory, Marcel Dekker, New York, U.S.A. M. Savar, H. Kozmar, I. Sutlovic, 2009, ‘Improving centrifugal pump efficiency by impeller trimming’,

Desalination 249, p.654-659, [online], available at http://www.sciencedirect.com.ergo.glam.ac.uk/science/article/pii/S0011916409008388 (04-12-2013)

http://www.sciencedirect.com.ergo.glam.ac.uk/science/article/pii/S0011916409008388


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6.0 APPENDICES

Figure 35 dome shaped 30mm hub at 600rpm surface pressure contours



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Figure 37 dome shaped 30mm hub at 1500rpm surface velocity contours



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Figure 39 dome shaped 50mm hub at 1500rpm velocity streamlines

Figure 40 dome shaped 50mm hub at 1500rpm surface velocity contours


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Figure 42 cone shaped 30mm hub at 600rpm pressure streamlines


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Figure 43 cone shaped 30mm hub at 600rpm velocity streamlines

Figure 44 cone shaped 30mm hub at 1500rpm pressure streamlines


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Figure 45 cone shaped 30mm hub at 1500rpm velocity streamlines

Figure 46 impeller dome shape

Flow Field of an Impeller

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