The Internal Flow Investigation of a Centrifugal Pump
by
A. Akhras, M. El Hajem, R. Morel, J.Y. Champagne
Laboratoire de Mécanique des Fluides
Bât 302, 20 av. A. Einstein, 69621 Villeurbanne; France
ABSTRACT
This paper provides the results of a detailed flow investigation within a centrifugal pump equipped with a vaned
diffuser. The measurements made with a laser-Doppler velocimeter were carried out at the impeller design point. In a
previous paper concerning the same machine, El Hajem (1998) found a jet-wake structure developing at the impeller
exit. During the actual study, measurements were obtained in the impeller and the diffuser at different measuring planes
relative to the diffuser vanes. Results are presented as animations reconstituting a temporal evolution of the flow at the
diffuser inlet.
Unsteady velocity measurements obtained in phase with the impeller angular position gave access to the flow inside the
impeller channels where three sections were explored. For each section, results were obtained as a function of the
position of impeller blades relative to the diffuser vanes. Thus time resolved details of the flow could be examined for a
better understanding of the complex unsteady flow existing between the two interacting blade rows.
The analysis of the impeller flow field indicates the presence of a complex, unsteady and periodic flow. It is organised
in a jet-wake structure. The wake is characterised by low relative velocities and is localised in the suction side/shroud
corner. At this flow rate, it seems that presence of the vanes has only a limited effect on the impeller flow structure,
except when the blades suction side are facing the diffuser vanes.
At the impeller discharge, the time-resolved sequences show that the mixing process of the unsteady and periodic flow
leaving the impeller is affected by the presence of the diffuser. At the leading edge, at the suction side of diffuser vanes,
the flow is rapidly mixed. Whereas, when approaching the diffuser throat, the flow still shows its periodic character
observed at the impeller outlet. This indicates that the diffuser is subject to unsteady inlet conditions that can alter its
performances.
2
I INTRODUCTION
During the design of a turbomachine, the flow is considered steady and uniform at the entry of each element. For a
centrifugal pump with a vaned diffuser, satisfying this assumption requires a large interface between the rotor and the
stator so that the mixing process of the flow leaving the impeller can take place. Otherwise, the unsteady flow that
enters the diffuser represents a source of low efficiency. Furthermore, the internal flow of the impeller can be affected
by asymmetric downstream conditions, which results in extra flow unsteadiness and instabilities. A number of authors
have treated the problem of the interaction of the impeller and its surrounding. Miner [1] used a laser velocimeter to
measure velocities within the impeller and the volute of a centrifugal pump and found that the relative velocity
components distribution varies with the circumferential angle relative to the volute cutwater. Liu (1994) has also used
LDA for the internal flow investigation and found that the asymmetric volute alters the relative flow, the flow rate from
each impeller passage varied with the volute circumferential position by up to 25 percent at an off-design flow rate.
Inoue (1984), Sideris (1987) and Arndt (1989, 1990) have been concerned with the action of the diffuser. For internal
flow studies, a large number of the experimental investigations that revealed the presence of a jet-wake structure at the
discharge of centrifugal rotors was concerned with compressors as done by Eckardt (1975, 1976), Johnston (1976),
Johnson (1978), and more recently Rohne (1991) and Ubaldi (1993). However, Krain (1988) found a velocity profile
that differed widely from the jet-wake type flow. In a previous study, the authors (El Hajem et al., 1998) found a jetwake structure developing at the impeller exit During this study, LDA measurements, revealed the presence of a jetwake flow structure. The location and the extension of the wake seem to be affected by the proximity of the diffuser
vanes.
II EXPERIMENTAL SETUP
II.1 THE SHF IMPELLER
The test impeller, shown in Figure 1, is a low specific speed (ωs =0.577) shrouded impeller. It has seven backswept
blades with an exit angle of 22.5 degrees relative to the tangential direction. The main geometric data of the impeller
and its operating conditions are resumed in table 1. For optic access, the shroud was made out of clear Plexiglas and a
clear window was realized on the casing. The impeller was run with a vaned diffuser and a spiral casing of industrial
type. The diffuser is a straight wall constant width with six vanes (Figure 1). The main dimensions of the diffuser are
listed in table 2.
II.2 TEST RIG
Experiments were performed on a centrifugal pump test facility (1, figure 2) consisting of a closed rig equipped for the
overall performance characterization of the machine. Water enters the impeller through a straight suction pipe of 1.4 m
in length. The net flow rate traversing the pump is measured by an electromagnetic flow meter (11, figure 2) with a
precision of 0.2 percent at the actual experimental conditions. The impeller is driven by a variable speed DC motor of
45 kW power at 1500 rpm mounted in balance mode for torque measurement (10, figure 2).
Figure 1 : Test impeller and vaned diffuser
Figure 2 : Test rig Measuring equipment
3
Table 1 Impeller characteristics
impeller parameter
R1
R2
b
Z
β2
Qn
N
φ
ψ
ω
=
=
=
=
=
=
=
=
=
=
98.25
177.25
26.7
7
22.5
0.0774
1188
0.118
0.481
0.577
description
mm
mm
mm
inlet blade radius at the shroud
impeller exit radius
blade height
blade number
deg.
blade angle
m3/s
design flow rate
Rpm
rotational speed
Design flow coefficient
Design head coefficient
specific speed
Table 2 Diffuser characteristics
R3
R4
R5
b3
Z
α3
diffuser parameter
=
182
mm
= 199.3
mm
=
258
mm
=
28.1
mm
=
6
=
12
deg.
description
diffuser inlet radius
Leading edge radius
diffuser exit radius
Diffuser width
Vane number
Vane angle
Figure 3 : Research centrifugal pump with LDA optics
Table 3 Measuring Sections
Angular position
in the diffuser
pitch
α (deg)
I
0 (or 60)
II
10
III
17
IV
30
V
43
VI
50
VII
57
r* = r/R2
In the impeller
In the Diffuser
0.8182
0.9092
0.9784
1.0179
1.0451
1.0846
1.1298
1.198
Figure 4 : Optic access to the measuring vane
II.3 MEASURING EQUIPMENT
Measurements of velocity distribution at the impeller discharge and in the diffuser were obtained by using an LDA
system. The light source is a 5 W argon ion laser operating in multiline mode in order to operate with the blue (488 nm)
and green (514.5 nm) wavelengths. Modular optics with a 310 mm focusing lens are used to derive a three beam
configuration. The LDA system was used in a back-scatter mode. The optical components, including the laser and the
photomultipliers, were mounted on a three axis traversing system to place the probe volume at the location of interest
(figures 3, 4).
To relate the velocity measurement to the angular position of the impeller, an optical encoder is used to synchronize
measurement with machinery. The encoder fixed on the pump shaft gives the position of the measuring point in the
blade-to-blade plane with a resolution of 3600 angular readings for one shaft revolution.
For each test point M in the axial direction, an average of 10 000 data points were taken. The sampling rate was
arbitrary and depended on the nature of the LDA signals. The data processing system, consisting of two burst signal
analyzers with built-in synchronization inputs for cyclic phenomena, is connected to a PC. A software uses encoder
pulses to phase-sort the velocity samples versus the phase angle. The Data is also phase-averaged to compute the mean
velocity and the turbulence intensity.
In order to study the interaction of the impeller and the diffuser, the flow was investigated at 7 radial planes located at
different angular positions in the diffuser as given on table 3 and shown on figure 5. For each plane, the flow was
investigated at eight radial sections in the impeller and the diffuser (table 3), for each radii, sixteen points were
explored.
4
Figure 5 : Locations of the measurement planes within the impeller and the diffuser
20
20
Cu
Cr
r/R2 = 0.909
z/b = 0.5
5
15
Cr, Cu (m/s)
10
10
5
0
90
180
270
360
10
5
0
0
Cu
Cr
r/R2 = 0.978
z/b = 0.5
15
Cr, Cu (m/s)
15
Cr, Cu (m/s)
20
Cu
Cr
r/R2 = 0.818
z/b = 0.5
0
0
Angular position (deg)
90
180
270
Angular position (deg)
360
0
90
180
270
360
Angular position (deg)
Figure 6 : Fluctuating velocity at the impeller channels, plane I, z/b = 0.5
III DISCUSSION OF THE EXPERIMENTAL RESULTS
The laser Doppler velocimeter used for internal flow investigation is two dimensional, only the velocity components in
the radial and circumferential directions were measured; the velocity in the axial direction was not measured and was
supposed to be negligible.
III.1 VELOCITY FLUCTUATIONS OF THE IMPELLER INTERNAL FLOW
The absolute velocity is presented as a function of the angular position within the impeller channels and the axial
distance z/b. The shroud and the hub are located at z/b=0 and z/b=1 respectively (Figure 6). field evolution at the
nominal flow rate. The reported results correspond to the measurements obtained at passage midheight (z/b=0.5) for
three sections corresponding to r/R2= 0.818, 0909 and 0.978. In these figures, the same velocity distribution repeated
over seven periods corresponds to the flow in the seven impeller channels; it illustrates the periodic unsteadiness of the
flow at the impeller exit.
In figure 6 corresponding to measuring radial plane I facing the diffuser leading edge, a significant evolution of the flow
structure is present a long the impeller passages. At r/R2 = 0.818, the flow structure is the same as expected for a
potential flow having deep velocity gradients between the suction and pressure sides of the impeller passages. On the
pressure side, we notice a high tangential velocity component Cu, while the radial component Cr is low. In the next
section (r/R2 = 0.909), both components reach a minimum at the channel center. In fact, the flow pattern starts to
deviate from the theoretical model. This is particularly observed near the impeller exit (r/R2 = 0.978) where the velocity
gradient is inverted. The radial velocity is now increasing from the suction side to the pressure side. One should also
notice the important velocity fluctuations registered in the proximity of the suction side. The tangential component is
more uniform over a large area of the passage near the pressure side.
III.2 RELATIVE FLOW DISTRIBUTION AT THE IMPELLER EXIT
Figure 8 represents the temporal evolution of the phase averaged relative velocity, within a single impeller passage, as
sensed successively at the planes I, II, III, IV, V, VI located at different distances with respect to the diffuser leading
edge. These frames show an impeller passage with the blades rotating in the clockwise direction. The shroud and the
hub are respectively at the foreground and the background of the frames. The relative velocity is presented as constant
velocity contours in the blade-to-blade plane.
5
Ω
W (m /s)
20
W (m /s)
20
W (m /s)
20
17
17
17
13
13
13
10
10
10
7
7
7
3
3
3
0
0
0
Plane I
Plane II
Plane III
W (m /s)
20
W (m /s)
20
W (m /s)
20
17
17
17
13
13
13
10
10
10
7
7
7
3
3
3
0
0
0
Plane IV
Plane V
Plane VI
Figure 7 : Blade to blade flow distribution measured at planes I, II, III, IV, V, VI, r/R2 =0.978
A highly flow distortion is observed in the axial and blade-to-blade directions. A large area of the passage, extending
from the pressure side to the passage centre a n d f r o m the shroud to the hub, is traversed by a uniform flow. On the
contrary, the remaining passage is dominated by an important velocity gradient and an accumulation of low momentum
fluid in the suction side/shroud corner. The velocity reaches a minimum at the suction side, at about z/b=0.4.
The strong velocity gradient and the accumulation of low velocity fluid near the suction side show that the flow field
leaving the impeller is organized as a jet-wake structure as reported by previous investigations and as was expected
according to an analysis of the action of the centrifugal forces (El Hajem 1998) on the flow field. In this paper, the
authors found in a previous paper that the wake core corresponds to a flow separation.
The flow structure is almost the same at all the measuring planes, except the plane II where the wake core seems to
vanish when the suction side of the impeller blades has just passed behind the trailing edge of the diffuser vanes. We
also notice that the velocity gradient in the blade-to-blade direction is less pronounced as for the other planes.
III.4 TURBULENCE INTESITY DISTRIBUTION
In order to evaluate the importance of the flow fluctuations within the impeller passages, the turbulence intensity was
calculated by the same procedure given recently by Toussaint (1998). First, the periodic unsteady flow in the seven
impeller passages is ensemble (phase) averaged to constitute a mean average flow in a single passage. Each impeller
passage was divided into 51 measuring windows of an angular width ∆θ=1 degree. For each angular bin θ, the mean
velocity is computed by combining the n measurements of the equivalent locations in the different passages during the
measuring time :
C( M ) θ =
1
∆θ
∫
θ+
θ−
∆θ
2
C( M , t ) dt ≈
∆θ
2
i= n
ΣC
i =1
( M )θ
n
Therefor, for each angular position θ of the mean passage, the rms values associated with each fluctuating velocity is
defined as follow :
6
100
100
100
Tu (Cu)
Tu (Cr)
80
60
40
20
Tu (Cu)
Tu (Cr)
80
r/R2 = 0.978
z/ b = 0.5
Plane I
60
40
40
20
0
20
0
0
0
10
20
30
40
50
r/R2 = 0.978
z /b = 0.85
P lane I
60
Tu (%)
r/R2 = 0.978
z/ b = 0.17
Plane I
Tu (%)
Tu (%)
80
Tu (Cu)
Tu (Cr)
0
10
20
An gular position (deg)
30
40
50
0
10
An gular position (deg)
20
30
40
50
Angular position (deg)
Figure 8 : Turbulence intensity at impeller exit r/R2=0.978, plane I, design flow
100
100
100
Tu (Cu)
Tu (Cr)
80
60
40
20
Tu (Cu)
Tu (Cr)
80
r/R2 = 0.978
z/ b = 0.5
Plane II
60
Tu (%)
r/R2 = 0.978
z/ b = 0.17
Plane II
Tu (%)
Tu (%)
80
Tu (Cu)
Tu (Cr)
40
20
0
10
20
30
40
50
60
40
20
0
0
r/R2 = 0.978
z/ b = 0.85
Plane II
0
0
10
20
An gular position (deg)
30
40
50
0
An gular position (deg)
10
20
30
40
50
An gular position (deg)
Figure 9 : Turbulence intensity at impeller exit r/R2=0.978, plane II, design flow
i =n
rms =
Cθ'
2
Σ [C
θ
i =1
=
− Cθ
]
2
n
The turbulence level can be calculated for every angle using the following definition :
Tu =
rms
Cθ
×100 =
1
n
i=n
Σ [C
θ
i =1
1
n
− Cθ
i=n
Σ [C ]
i =1
]
2
× 100
2
θ
Sample plots of the turbulence intensity distribution in the interblade passage, just upstream of the impeller discharge,
are shown on figure 8 and 9. On figure 8 the evolution of turbulence is given for plane I at the shroud (z/b=0.17),
passage midheight (z/b=0.5) and at the hub (z/b=0.85). On these figure, the turbulence is given as a function of the
angular position for witch the suction side of the passage corresponding to zero, while the pressure side corresponds to
51 deg.
At the hub region, the turbulence intensity is low and its distribution is uniform in the impeller passages, it hardly
exceeds 15 percent. As reported by Cattanei et al. (1998), the high turbulence intensities up to 40 percent observed at
the suction side/shroud corner and the passage center are due to the presence of the wake as observed if figure 9. This
region of the passage is occupied by a low relative velocity flow having important velocity gradients. The hub region
where the jet is prevailing the turbulence intensity is much lower. This distribution of the turbulence intensity remains
almost identical in all the measuring planes except at plane II where a different turbulence distribution was observed
(figure 9). In this plane, the fluctuations are higher and the turbulence level reaches 80 percent at the suction side/shroud
corner. It is the same case at the passage midheight where it approaches 60 percent. The hub region (z/b = 0.85) is also
affected and is characterized by a distinct rise of flow unsteadiness at the passage midspan.
7
II
II
I II
T1
I II
T 11
S1
S1
IV
IV
V
V
VI
VI
R2
R2
VII
VII
C
C
17.8367
15.5102
12.4082
9.30612
6.97959
4.65306
2.32653
0
I
R1
S2
17.8367
15.5102
12.4082
9.30612
6.97959
4.65306
2.32653
0
I
R1
II
S2
II
I II
T 31
I II
T 41
S1
S1
IV
IV
V
V
VI
VI
VII
VII
C
R2
I
R1
S2
C
17.8367
15.5102
12.4082
9.30612
6.97959
4.65306
2.32653
0
I
R2
R1
S2
17.8367
15.5102
12.4082
9.30612
6.97959
4.65306
2.32653
0
Figure 10 : Time resolved flow field frames
III.5 ABSOLUTE FLOW DISTRIBUTION
On figure 10, the results are presented as constant absolute velocity contours. The frames represent, at different instants
T1, T11, T31 and T41, the impeller blades R1 and R2 rotating from left to right in front of the diffuser vanes S1 and S2.
The time period between the passage of two successive impeller blades, in front of a diffuser vane, corresponds to 51
instants.
The Frames show a very deep evolution of the flow structure as it approaches the impeller discharge. At the inner
sections of the impeller, a large part of the channel is occupied by the parallel constant velocity contours corresponding,
to the potential flow distribution with a negative gradient from the suction side to the pressure side. This inviscid
behavior of the flow is only altered in a small section of the channel confined to the suction side/shroud surface. In this
region where the flow has a high absolute velocity and an important velocity gradient is registered. As the fluid is
achieved to the impeller discharge, the core of the high velocity fluid moves from the suction side/shroud corner to the
suction side of the impeller. The flow is therefor organized in a jet-wake structure as reported by previous research
works on centrifugal machines. Even though there is a slight alteration of the velocity, the flow patterns in the impeller
remain almost unchanged when the distance between the measurement section and the leading edge of the diffuser is
modified. The frontier between the rotor and the stator seems to be not easily crossed. At the design point, The flow
within the impeller is hardly affected by the presence of the vaned diffuser as noticed by Toussaint (1998).
At the diffuser inlet, the mixing of the jet-wake structure depends on the proximity of the diffuser vanes. At the radial
planes III and IV, the wake core moves towards the channel mid height. In plane IV, the flow is almost uniform when it
reaches r/R2 =1.084, this indicates that the mixing process of the complex periodic flow coming out of the impeller has
finished. In the following planes, the jet-wake is still present. A more important radial component of the velocity, as
seen in figure 7, seems to delay the mixing process. When approaching the diffuser throat (planes VI and I), an
8
important velocity is registered on the pressure side of the vanes, the flow ruches to enter in the diffuser channels. In the
suction side, a flow slow down prevents the flow structure leaving the impeller to diffuse in the radial direction.
CONCLUSION
This detailed investigation of the internal flow within a centrifugal pump, at its design point, has permitted to study the
effect of a vaned diffuser on the flow inside the impeller. From the actual results, we can conclude that the impellerdiffuser interaction is limited to the impeller exit and it does not have any upstream influence on the flow. The frontier
between the rotor and the stator seems to be not easily crossed. The mixing process of the flow at the impeller discharge
is affected by the presence of the diffuser vanes. The first half of the diffuser pitch is characterized by an early mixing
of the flow. Whereas, in the second half, the flow entering the diffuser channel is still presenting its periodicity due to
the impeller. This results indicates, therefore, that the diffuser performances may be affected by the complex flow
coming out the impeller. Further investigations in the diffuser and at different operating conditions are projected to
better understand the rotor-stator interaction.
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9