Andrej Predin1, Ignacijo Biluš2
and Roman
Klasinc3
1Ass. Prof. Dr., Head of Laboratory for turbine machines at Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, SI-2000 MARIBOR, Slovenia, phone:+386 2 220 77 41 fax:+386 2 220 77 49, E-mail: andrej.predin@uni-mb.si
2Researcher at Laboratory for turbine machines at Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, SI-2000 MARIBOR, Slovenia,
phone:+386 2 220 77 45 fax:+386 2 220 77 49, E-mail: ignacijo.bilus@uni-mb.si
3Asoc. Prof. Dr., Department of Hydraulic Structures and Water Resources Management, Technical University Graz, Stremayrgasse 10, A-8010 Graz, Austria,
phone +43 316 873 83 65, fax: +43 316 873 83 57, E-mail: klasinc@kwb.tu-graz.ac.at
Abstract:
Prerotation flow in the entrance pipe of turbomachines is created as a
result of the larger category of secondary flows and it is important for pump
hydraulic performance determination. This flow is an interaction, with the pump
cavitation, especially regarding cavitation swirl, that is the time and place
depending on the flow properties (of pump operating capacity and pump head).
Experimental analysis of the cavitation swirl pressure pulsation, measured at
the entrance (suction) pipe is given. A tested radial pump is installed in a
special testing system. The results are discussed and given regarding time and
frequency domain depending on the pump operating properties, especially those of
the entrance flow pressure. Basic outlines for mathematical model for swirl
frequency and magnitude modeling are given.
Keywords: cavitation swirl, centrifugal pump, operating characteristics
Cavitation swirl is directly associated with the prerotation flow, Predin [1]. in the intake pipe of the radial pump. The intensity and direction of the prerotation swirl depends on the operating capacity, in regard to the design capacity or capacity at BEP of the pump. According to the analyses, Predin, Biluš [2], of the prerotation flow in the entrance pipe it can be concluded that the prerotation flow appears as a result of circulating flow activity, Douglas et. al. [3], in the impeller channels and/or around the impeller blades, which have (through the fluid friction) an influence on the whirl flow in the entrance pipe.
When pump operating
at under-optimal (usually design point) capacities the absolute flow velocity
component in the circumferential direction at the entrance diameter D1
appears in the impeller rotation direction (same direction as circumferential
direction at entrance diameter u1).
The reason for the creation of this flow velocity component (c1u) can
probably be found in the appearance of secondary flow near the entrance edge of
the impeller blades and across the gap between the tip impeller shroud and the
pump casing. Because of the higher pressure at the pump impeller exit this part
of the flow penetrates through the gap between the impeller tip shroud and the
pump casing then back to the pump impeller eye near the tip impeller shroud
where the flow rotates by velocity u1.
This is as some "tongue" of flow that over the flow viscosity creates
prerotation flow in the intake pipe even far from the impeller eye, namely up to
three intake pipe diameter lengths. According to this operating regime it can be
considered that the circulation around the blades increases because of the
larger blade load (achieved by larger pump energy difference), which causes an
increase of the pressure at the impeller exit. The strengthening of the
circulation around the impeller blades could be explained by the entrance flow
angle decrease at the entrance of the impeller channels or by the flow intake on
the blade, where the flow cutting and flow separation from the blade suction
surface near the blade entrance edge appears. While the flow vortices and flow
separation cause the pressure decrease, that part of the flow from the area of
higher pressure (near the exit edge of the impeller blade) penetrates to the
lower flow pressure area and, in this way, strengthens the circulation around
the blades. With capacity increase over optimal capacity, the absolute flow
velocity c1u in the circumferential direction at the entrance diameter
and therefore, a prerotation flow with a direction opposite to the direction of
the impeller rotation is created. To achieve increased operating capacities the
prerotation flow must be diverted in front of the impeller eye to the direction
of smallest resistance, which is the direction opposite to the direction of
impeller rotation. Using this flow redirection an increase in the flow entrance
angle and thus a shorter path are achieved. This increased circulation flow
causes the secondary flows near the entrance blade edge in the intake pipe,
similar to the case of reated flow tongue" drive, the prerotation flow
being far from the impeller eye in the intake pipe over the flow viscosity in
the opposite direction of the impeller rotation. This direction change applies
gradually which is evident from the measurement results, Predin, Biluš [2],
whilst after an operating capacity change, the prerotation flow appears after a
short time of period, when new operation conditions are stabilized. The
cavitation swirl associated with the prerotation flows and at the impeller eye
creates back flow, Breugelmans and Sen [4], where part of the entrance flow is
redirected back into the pump entrance pipe. Driving power for the water
evaporation, during pump operating by near zero capacities, is strong
recirculation back flow that is created at the entrance part of the impeller
channels. Neuman [5], discovered that the area of the active flow through the
impeller is narrowed at the impeller entrance eye as well as at the discharge
area (Fig. 1), where recirculation flow appears as a result of decreased
capacity through the pump impeller. Both recirculation flows are divided in the
impeller channel by area line between the higher and lower pressure using
minimal capacity pump operating. An area of increased pressure is created at the
impeller entrance blade edge near to the impeller hub shroud, and at the
impeller discharge blade edge near to the impeller tip shroud. In this way the
entrance (b1), as well as
the discharge blade edge (b2),
are narrowed.
By further pump capacity decrease, at almost zero capacity, the active flow area through the impeller is blocked and the fluid in the pump impeller circulates inside the pump or in the impeller channels. In created vortex motion, the streamlines form a set of concentric circles and the changes of total energy per unit weight are governed by following equation:
If we assume, that there is no change
of total energy per unit weight with radius, so that
, we get:
(2)
Integrating,
(3)
or:
(4)
Which is well
known equation of potential vortex and
is a constant known as the strength
of vortex at any radius
. Since at any point:
(5)
Substituting for
from equation (3)
(6)
For horizontal plane
is constant and the pressure
variation is given by:
(7)
Thus, in the potential vortex, pressure decreases and
circumferential velocity increases as we move towards the center. Theoretically,
the velocity becomes infinite at
. Since the friction losses vary as the square of the velocity, they will cease
to be negligible. However, we can say, that velocity increase is sufficiently
large to cause pressure decrease below vapour pressure at given temperature.
Conditions for water evaporation near to the impeller axis in the impeller eye
are created and a cavitation swirl is developed (Fig. 2). The cavitation swirl
is propagated from the impeller eye into the entrance pipe. The cavitation swirl
is driven by the circulating back flow GBF
"tongue" over the flow viscosity. The cavitation swirl can propagate
far from the impeller eye, depending on the pressure in the intake pipe. As the
pressure is low at the entrance eye of the impeller a larger swirl develops in
the intake pipe, sometimes up to 15 intake pipe diameters from the impeller eye
upstream from the intake flow. Presence of added heat at zero flow-rate
magnifies flow surging and this result in it taking on a potentially more
dangerous form. Grist [6], derived a equation of pressure pulsations in
following form:
(8)
where
is bulk modulus of the liquid in
volume
of unheated area,
is the volume of the heated system
area,
is vapour volume,
is enthalpy,
is heat content,
is latent heat of vaporization and
subscript
and
denotes values appropriate to
unconstrained and constrained system respectively.
Fig. 2 The cavitation swirl formation and propagation
The special
measuring system (Fig. 3) is developed for pump cavitation measurement. The pump
testing system is constructed as a closed pipe system where the pressure at the
suction side can be decreased. In this way the pump suction head (NPSH) can be
changed. PTS is constructed based on the recommendations for pump cavitation
tests performance – ISO 24548, [7]. The measuring system consists of six
pressure transducers; four HBM P19, one HBM PE 30, and one differential pressure
transducer ROSEMOUNT 3051, personal computer + A/D 12 bit computer board DASport
PCI-20450P-25 with maximal sampling frequency 100.000 Hz. The measuring points
are taken at the transparent suction pump entrance pipe.
The pressure of the cavitation swirl is measured at the four positions (P0, P1, P2 and P3) in the intake pipe.
The measuring results of flow pressure at the measuring point P0 when the cavitation swirl occurs in the entrance pipe are presented in diagram form (Fig. 4) in the time and frequency domains. From time pressure pulsation records (Fig. 4.a, d, e) no developed pulsation form is evident. This fact shows that the origin cavitation swirl does do not pulsate in a radial direction, and means, that the swirl is relatively well cantered with the impeller shaft axis. In frequency domain records (Fig. 4.b, e, h) the small frequency peaks in the area around 800 up to 900 Hz are evident. This shows on the developed cavitation at the impeller eye, but individual cavities are not formed as a swirl. This is cavitation turbulence in the impeller eye and at the individual impeller channels. In the zoomed frequency domain recordings (Fig. 4.c, f, i) some frequency peaks are well expressed.
In the recording (Fig. 4.c) three frequency peaks 5, 10 and 25 Hz are evident. The third one (25 Hz) belongs to impeller speed frequency (1500 rpm ~ 25 Hz), the first one (5 Hz) probably belongs to the flow oscillation in the pump testing system, and the second one (10 Hz) is probably the first higher harmonic of the first one. From the recordings (Fig. 4) is also evident, that with pressure decrease no pulsation amplitude increase occurs.
Fig. 4 Flow pressure at the measuring point P0 when the cavitation swirl occurs in the entrance pipe
In the measuring position P1 more formed pulsation form of the cavitation swirl are evident. From time domain recordings (Fig. 5.a, d, g) it is evident that with pressure decrease the swirl pulsation magnitudes decrease. This phenomenon could be explained by the fact that the swirl dilapidated at smaller pressures while whole the area at the impeller eye and the entrance suction pipe is filed up with water vapour and with air eliminated from the water. This fact is also confirmed by zoomed recordings in the frequency domain (Fig. 5.c, f, i) where in the last recording (Fig. 5.i) the frequency peak 25 Hz disappears, which means that no swirls with impeller rotation speed occur. In the recordings in frequency domain (Fig. 5.b, e, h) more frequency peaks are evident. This shows on the swirl with more small swirls around the main one (25 Hz), and on bigger cavity turbulence.
In the measuring position P2 well-developed cavitation swirl is evident (Fig. 6.a). A swirl pulsation form is also evident at decreased pressure (Fig. 6.d, g) but with smaller amplitudes. From the zoomed recording in the frequency domain (Fig. 6.c) it is clearly evident that the second and third frequency peaks dominate. This shows at the cavitation swirl pulsate with a common frequency between 10 and 25 Hz, near by the impeller speed frequency. This fact confirms that the cavitation swirl is driven by back flow "fluid tongues" as is proposed in the chapter of circulating flow mechanism.
In the measuring
position P3 the pulsation form of the cavitation swirl is still evident (Fig.
7.a, d, g). The pulsation shape (Fig. 7.a) is slightly different than the one at
the measuring position P2 (Fig. 7.a). This shows that at the end of the swirl
the swirl starts to dilapidate or tear to pieces. By pressure decrease the
pulsation amplitude decreases whilst the swirl dies away. In the recordings
(Fig. 7.b, e, h) it is clearly evident in that frequency domain the pulsation
frequency in the range of up to 1500 Hz decreases with pressure decrease. With
the zoomed recordings in the frequency domain (Fig. 7.c, f, i) is evident that
the impeller rotation frequency (Fig. 7.a and 7.f) dominate in these recordings.
In the recording (Fig. 7.i) the impeller rotation frequency is present but it is
not well expressed (the swirl is dilapidated).
Fig. 5 Flow pressure at the measuring point P1 when the cavitation swirl occurs in the entrance pipe
Fig. 6 Flow pressure at the measuring point P2 when the cavitation swirl occurs in the entrance pipe
Fig. 7 Flow pressure at the measuring point P3 when the cavitation swirl occurs in the entrance pipe
5 CONCLUSIONS
The cavitation swirl occurs as a consequence of the impeller channels blockage by the circulation flow in the impeller channels; Water evaporation starts is a cause of the fluid friction of “fluid tongues” at the axis or at the small diameter near by the impeller shaft axis. In this way the flow temperature increases and the local pressure decreases; The frequency of the developed cavitation swirl in the entrance pipe of radial pumps is equal to the frequency of impeller rotation and this confirms that the swirl is driven by "fluid tongues" of back flow from the individual impeller channels and transferred over the liquid viscosity to the cavitation swirl; The maximum amplitudes of the cavitation swirl pulsation occur under particular conditions or flow pressure if the pressure is increased or decreased the cavitation swirl dilapidated. If the flow pressure is increased the cavitation process are stops, if the flow pressure decreases the swirl dilapidated whilst the water evaporates is so big that the whole area of the impeller eye and part of the entrance pipe is filled up by steam and air eliminated from the water; The higher frequency peaks in the FFT recordings show that more small swirls around the main cavitation swirl occur. They also show at larger cavitation cavity turbulence in the intake flow; The pulsation shape of the cavitation swirl is changed by pressure and in respect of the distance from the impeller eye; The best developed cavitation swirl occurs at the distance of three intake pipe diameters from the impeller eye upstream, somewhere at 2/3 of swirl length; The cavitation swirl is probably composed from small swirls of the main one, which can be determined, by laser anemometer measuring of the flow velocities in the swirl.
References
[1] Predin A., Torsional vibrations at guide-vane shaft of pump-turbine model, Shock & Vibration, 1997, Vol. 4, Issue 3, pp. 153-164.
[2] Predin A., Biluš I., Prerotation flow at the Entrance to a Radial Impeller, Journal of Mechanical Engineering, 2000, Vol. 46, Issue 5, pp.275-290.
[3] Douglas F. J., Gasiorek M. J., Swaffield A.J., 1995, Fluid Mechanics, 3rd Edition, Longman Singapore Publishers (Pte) Ltd., Printed in Singapore, pp. 655-659.
[4] Breugelmans F.A.E, Sen M., 1982, rerotation and Fluid Recirculation in the Suction Pipe of Centrifugal Pumps, Turbomachinery, 11th Ann. Symposium, Shamrock, December 1982, pp. 165-180.
[5] Neumann B., 1991, The interaction between Geometry and Performance of a Centrifugal Pump, Mechanical Engineering Publications Limits, London.
[6] Grist E., Cavitation and the centrifugal Pump, A guide for pump users, Taylor & Francis Philadelphia 1999.
[7] International Organization for Standardization: ISO 2548, Centrifugal, mixed flow and axial pumps – Code for acceptance tests – Class C, First edition – 1973-06-01, Ref. No. ISO 2548-1973 (E).