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Chapter 5
5.
CAVITATING PUMP ROTORDYNAMIC
TEST FACILITY (CPRTF)
The experimental campaign of the present thesis has been carried out in the Cavitating Pump Rotordynamic Test Facility (CPRTF) at ALTA S.p.A.. Originally set-up under ASI (Italian Space Agency) and ESA (European Space Agency) funding, is one of the few experimental test benches in the world and the first openly documented facility in Europe capable of carrying out the direct measurement of the unsteady rotordynamic fluid forces. This facility is specifically designed for the evaluation of the rotordynamic forces and the performance of cavitating/noncavitating turbopumps for axial, radial or mixed flow configuration. Indeed the aim of the research has been the characterization of the rotordynamic forces exploited during different operational conditions of various type of pumps. The facility is capable to operate with water at temperatures up to 90 °C and the experimental investigations can be conducted on any kind of fluid dynamic phenomena that are developed during the operation of high performance turbopumps.
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The housing and the test section can be readily adapted to different pump geometries. An inlet section made in transparent Plexiglas allows the optical visualization of cavitation developed by the operating pump and it can be easily replaced to allow different tip diameters or clearances. Many different transducers are also provided for the measure of various parameters:
• The inlet pressure at two different points; • The static pressure rise;
• The volumetric flow rate at suction and discharge line; • The fluid temperature in the main tank;
• The absolute angular position of the driving shaft and of the eccentric shaft through two contrast sensors;
• The forces and moments acting on the impeller through a rotating dynamometer positioned on the main shaft.
Figure 5.2 Main elements of the CPRTF. Modified C.Bramanti et. Al [3] The test section for turbopump tests can be seen in Figure 5.3.
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The eccentricity for the whirl motion is generated by a two-shafts mechanism and it can be set in a range between 0 and 2 mm with a speed regulated by means of a brushless motor which drives the external shaft whereas the rotation of the impeller is developed by the main motor acting on the internal shaft.
5.1.
MAIN TANK
The main water tank is made of stainless steel (T element in Figure 5.2) and it can contain up to 500 liters. An inner tube (bladder, BA) with an elastic membrane is present and its aim is to uncouple the inlet/outlet volume fluctuations generated by cavitation in the pump and to pressurize the water in the tank/circuit by means of a pressurization system. The bladder capacity is 40 liters and it can reach pressures between 0.01 and 6 atmospheres. Moreover a heat exchanger with a 5 kW electrical heater is present and it is capable to set the water temperature from room conditions to values near boiling point (90°C). For temperature and pressure feedback a temperature transducer and a pressure gauge are used. Finally a safety valve is set at a pressure of 6 atmospheres.
The aim of the main tank is not only to contain and to set water properties, such as temperature and pressure, but another important task is to increase the residence time for cavitating bubbles so they can be re-absorbed, allowing also the bigger bubbles to ascend up to the free surface at the top of the tank. This allows also to vent the air present in the water at the beginning of the test, cleaning the circuit from cavitating nuclei.
Figure 5.4 External (center) and cut-off (left) views of main tank with a picture as in working position (right), placed above a vibrating platform. A. Bonaguidi [4]
5.2.
VIBRATING TABLE
The vibrating platform, manufactured by Movind, produces a vertical vibration of the main tank by means of a couple of counter vibrators and they are fixed to each other with bolts. Different vibration motions can be obtained with the regulation of the eccentric masses inside the vibrators. The maximum amplitude that can be obtained is equal to 1 mm with a frequency between 10 and 30 Hz whereas with a mass balance of 50% it can be obtained an amplitude of 0.5 mm in a frequency range
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between 30 and 50 Hz. The Table 5.1contains the technical and operating characteristics of the vibrating platform.
Maximum payload 500 Kg
Operating range 10-30 Hz with amplitude of 1 mm 30-50 Hz with amplitude of 0,5 mm Elastic suspensions 4 supports ROSTA AB-D 27 Motor system 2 vibrators (model ITALVIBRAS MVSI3/2100)
Maximum power 2200 W (x2)
Power supply three-phase 400 V at 50 Hz Table 5.1 Main characteristics of the vibrating table.
Figure 5.5 CAD sketch (left) and picture (right) of the vibrating platform. A. Bonaguidi [4]
5.3.
SUPPORTS AND CONCRETE COLUMNS
Two concrete columns are placed at the sides of the main tank to incorporate the two pipes at the exit and at the inlet. Their aim is to eliminate the high vibrations of the circuit during the experimental POGO campaign that uses the vibrating platform. Indeed the vibration of the pipes connected to the circuit lead to wrong measurements of the pressure.
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5.4.
TEMPERATURE EXCHANGER
The water cooling system is made of a circuit of pipes which exchange heat with the water inside the tank. The temperature of the water flowing in these pipes can be at room temperature as well as at a lower temperature, reached by the use of a chiller.
On the other hand the heating system is developed by two electric heaters covered by stainless steel, each one with 5 kW and connected to a thermostat that allows to set the temperature.
5.5.
SACRIFICIAL ANODE
When metal components come into contact with electrolytes they reacts with an electrochemical reaction: galvanic corrosion. This reaction cause the metal to disintegrate, becoming weak.
Sacrificial anode are highly active metals that prevent surface corrosion for the elements that require protection. They are created from metal alloy with higher negative electrochemical potential with respect to the metal that will be protected. The material used for the realization of these components is the magnesium.
5.6.
PRESSURIZATION SYSTEM
The main tank is connected to the racking circuit as well as to the pressurization circuit like shown in Figure 5.7. The former connects the main tank with the auxiliary tank which has a capacity of 1000 liters and is made of plastic. Its capacity is capable to contain all the water used by the circuit and present in the main tank. Two pumps with a volumetric flux of 50 liters per minute and a head rise of two atmospheres.
On the other hand, the pressurization system allows the elimination of the gas that is formed at the top of the main tank and allows also the pressurization of the liquid by means of the air regulation inside the bladder. The pressurization of the circuit is obtained by means of a feeding line of pressurized air whereas the depressurization is obtained by a vacuum pump capable to generate conditions near vacuum at 0.05 atm. The volumetric flow rate for this pump is between 5 and 10 m3/h.
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5.7.
PIPES
The circuit is assembled by means of pipes with different diameter. The suction line is composed by two sections that from main tank to pump inlet have respectively a radius of 164.3 mm and 144.4 mm. A third divergent duct has been placed to adapt the size of the inlet area to the duct size. The latter element has an inlet radius of 144.4 mm and a discharge radius of 164.3, with a length of 2090 mm. On the other hand the discharge line is made of pipes with a constant internal radius of 110.3 mm with an overall length of 2850 mm. All the pipes are in AISI316 steel and have a thickness of 2 mm. The steel used for these elements is not much affected by temperature variations in the range of the experimental campaign (0-90 °C) and the resistance against corrosion is high.
5.8.
FLOW STRAIGHTENER
Two flow straighteners (FS) are placed right before the flowmeters for better measurements and to provide a uniform flow condition at the inlet of the pump. Indeed they can drastically reduce the flow turbulence and rotation (minimizing the lateral velocity components) and they are made of honeycomb-filled pipe sections with length of 50 mm and regular hexagonal cells shape (Figure 5.8). The large scale turbulence is a result of the 90 degree turns in the circuit as shown in Figure 5.9 and the reason is that a nonuniform pressure field is set as a result of the different velocities during the flow turn, leading to the origin of vorticity.
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Figure 5.9 Generation of turbulence in pipe’s curves. Modified from [5]
5.9.
EXPANSION JOINTS
Rubber expansion joints (EJ) are used to absorb pipe’s dimensional variations due to ambient or fluid’s temperature changes and generated forces, limiting vibrations and making acceptable pipe’s misalignments for lateral as well as angular movements.
The expansion joints attenuates also the water hammers due to fluid’s flow or sudden valve closing and they allow an easier mounting of the pipes due to their axial elastic properties.
In the facility, two different expansion joints have been used: a 4″ version and a 6″ version. In total, there are four pieces of the former and two of the latter.
Figure 5.10 Rubber expansion joint DILATOFLEX K. A. Bonaguidi [4]
Duct section Discharge Suction
Nominal diameter 4″ 6″
Total length at rest (Lf) 130 mm 130 mm
Maximum operational pressure 16 bar 16 bar
Maximum axial compression allowed (Lc) 105 mm 110 mm
Maximum axial length allowed (Le) 140 mm 145 mm
Maximum radial deformation allowed 15 mm 15 mm
Maximum angular deformation allowed 14° 10°
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5.10. FLOWMETERS
Two electromagnetic flowmeters (FM) are used in suction and discharge lines to measure the volumetric flow rate of the flow in liters per seconds (Figure 5.11).
Figure 5.11 Electromagnetic flowmeter 8732E with integral transmitter 8732 C, produced by Fisher rosemount. A. Bonaguidi [4] The induced electromagnetic field generated by the flowmeter in the cross sectional area of the pipe tend to polarize the water of the flow, creating a potential difference between the electrodes and therefore an electric field is set, where E = BdV (with B the magnitude of the magnetic field, d the distance between electrodes and V the potential difference between electrodes).
Figure 5.12 Electromagnetic field generated by the flowmeter with resulting molecules polarization. [6]
The potential difference is linearly proportional to the mean velocity of the flux that is in turn proportional to the volumetric flow rate.
The flowmeters are capable to measure fluxes with pressure up to 40 atm and mean velocities between 0.3 and 10 m/s with an accuracy of 0.5%. Internal coating in Tefzel (ETFE) ensures a
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temperature resistance at values between -29 °C and 149 °C. The electrodes are in AISI 316L steel whereas flanges and holding block is made in carbon steel. Moreover an integral transmitter 8732 C provides information properties.
Another property of these elements is the possibility to invert the magnet poles at frequencies of 5 or 37 Hz. This property is fundamental because it allows the elimination of the stored electric charge.
5.11. AUXILIARY PUMP
An auxiliary pump (AP) Grundfos TPE 100-390/2 is present and it is used for two main reasons: • The first aim is to reach higher flow coefficients than those usually obtained with only
inducers or centrifugal pumps, to obtain complete cavitating or noncavitating performance curves. The auxiliary pump can reach a maximum volumetric flow rate of 59 lt/s.
• The second reason is that it allows a correct adjust and regulation of the flow in the circuit during the tests. Hence it is possible to consider the flow rate as constant even in the presence of strong cavitation. The pump is designed to exert an active control of the flow rate, reducing the possible introduction of cavitation nuclei inside the flow. For this purpose it receives a feedback from one of the flowmeters.
Figure 5.13 Auxiliary pump Grundfos TPE 100-390/2. A. Bonaguidi [4]
5.12. SILENT THROTTLE VALVE
The silent throttle valve (V) produces the pressure drop needed to load the pump (according to the first thermodynamic principle through the transformation of pressure into internal energy), recovering the pressure imposed by the bladder in the main tank, and separates the suction and discharge lines. The particular valve used, generates a distributed loss capable of yielding large pressure drops without the production of unsteady cavitation, which would lead to dynamic noise and additional cavitation nuclei in the flow.
64 1. Troncoconical elements, 2. Elastomeric block, 3. Cylindrical housing, 4. Hydraulic piston, 5. Plug, 6. Piston rod, 7. Perforated plate, 8. Perforated plate,
The valve consists of a cylindrical intermediate housing (3), at which extremities are attached two troncoconical elements (1) that constitute the interface with the rest of the circuit. These three elements are made of stainless steel. Inside the housing is inserted a deformable elastomeric block (2), bonded to two rigid perforated plates, (7/8). In the elastomeric block, which has a length of 8" and a diameter of 6", 200 longitudinal holes are made, and the same number of holes is present on the two rigid plates. The piston rod (7), connected to the hydraulic piston (4), acts on the plate (8), and is governed by a pressurized fluid introduced into the two chambers delimited by the piston itself, through the two holes visible in Figure 5.14. The construction is completed by the plug (5), which guarantees the closing of the piston chamber, and a diverging element, which allows to direct the flow in the passages formed at the sides of this chamber.
Figure 5.14 Cut-off of the silent throttle valve. A. Bonaguidi [4]
The piston movement allows the compression and elongation of the elastomeric block (2), varying the diameter of the holes present in it and providing a further resistance to the flow passage; thus the pressure drop, which is mainly due to viscous effects, is uniform with respect to the whole extent of the hole: for this reason the operation of the valve does not produce noise, and this justifies the name assigned to it.
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5.13. MAIN MOTOR
The main motor is a brushless MOOG FASF3V8029 with 6 poles, a maximum power of 30 kW and a maximum torque of 100 Nm. Moreover its speed of rotation can reach values of 3000 rpm under controlled conditions and 6000 rpm under uncontrolled conditions (overspeed). The motor is also controlled by its power electronics in velocity and angular position with maximum errors of ±3 rpm and ±1° respectively. Aside from velocity and angular position control, a torque control of the motor is possible and it allows the motor to keep constant the torque imparted to the shaft with a maximum error of 10%.
The motor is connected to the pump by a homokinetic, torsionally stiff coupling, in order to allow misalignments due to manufacturing or mounting errors, or intentionally applied misalignments.
Figure 5.15 Main motor MOOG FASF3V8029.
5.14. SECONDARY MOTOR
The whirl motor is a brushless 6-poles MOOG FASF2V4030 with a maximum power of 5.6 kW and a maximum torque of 18 Nm. The range for the speed of rotation that this motor can reach is between 0 and 3000 rpm in controlled condition. Moreover, it is possible to control it through its power electronics in angular position and velocity with respect to the main motor, in order to set a certain value of the whirl frequency ratio ω/Ω.
The secondary motor is therefore used whenever a rotordynamic test is performed, to generate e whirl motion of the axis of rotation of the impeller, through a master-slave system. The controller of this motor is capable to set a whirl frequency ratio between 0.05 and 10, in both concordant and discordant configurations.
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Figure 5.16 Relative position of the whirl motor with respect to the main motor. A. Bonaguidi [4]
5.15. CV JOINT
A homokinetic joint Roba-D911.400 is used to connect the shaft of the main motor to the shaft of the pump and its task is to compensate axial misalignments between the two shafts. Its main properties are:
• High torsional stiffness to ensure the correspondence between the reading of the angular position of the motor shaft and the pump shaft.
• Accept axial, radial and angular misalignments.
• Transmission of a torque equal to the maximum that the main motor can deliver.
Figure 5.17 CV joint.
5.16. TEST CHAMBER
The test chamber (or test section) is the place in which the impeller is placed and therefore is the most important point of the facility. The design of the chamber (Figure 5.18) allows different geometries for many type of pump configurations.
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Figure 5.18 Test section (external view). A. Bonaguidi [4]
The test chamber is composed by two main parts: the pump housing, and the transparent inlet duct (Figure 5.19).
The former consists in a hollow aluminum cylinder fixed through a support structure and closed by two lids. A front lid is connected to the transparent inlet duct and allows the access during the disassembly whenever a change in configuration is needed. On the opposite side, the rear lid is externally connected to the mechanical mechanism that drives the shaft whereas on the internal side supports the pump and a possible presence of a volute. The internal pressure can reach 11 bar whereas its internal diameter is 500 mm with axial length of 281 mm. Thus a wide range of full-scale turbopumps are allowed.
The transparent inlet duct is realized in Plexiglas although a steel version is available. The Plexiglas version allows an optical access to take pictures and observe the cavitation phenomenon in details. Its dimensions make it possible to accommodate pumps and inducers with 200 mm of diameter.
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5.17. ROTATING DYNAMOMETER
Inside the test chamber a rotating dynamometer (orange element in Figure 5.19) is present for the measurement of forces and moments acting on the impeller. This instrument is made of AISI 630 H1025 phase hardening steel (Young’s modulus E = 197 GPa) and it consists in two circular plates connected by four posts with square cross-section (Figure 5.20). Forty semiconductor strain gauges, with 500 Ω produced by BLH, are placed on the posts to measure the deformations. These elements are arranged in 10 full Wheatstone bridges (Figure 5.24) each of which is temperature self-compensated up to 120 °C, with separate bipolar excitation. The semiconductors exploit the piezoresistive effect that transform the deformations in a change of electrical resistance (see Figure 5.21). In the present thesis, the fundamental basis about the dynamometer is extracted from the work of G.Pace [8].
Figure 5.20 Rotating dynamometer: design (left, [7]) and picture (right)
Figure 5.21 Behavior of the semiconductors (A,B,C) and positioning on the posts (top-right, A. Bonaguidi [4])
Moreover their positions with respect to the rotating reference system is shown in Figure 5.22. In this figure every single semiconductor is indicated by a combination of three numbers like Rijk where
• i indicates the post where the semiconductor is placed • j indicates the faces
69 • k indicates the position with respect to the faces
The numeration of the posts is made in clockwise direction starting from positive x direction whereas the numeration of the faces is made in counterclockwise direction starting from positive x direction. The numeration for k is like in figure.
The dynamometer can be modeled as two rigid plates to which are bound the four deformable posts that can be therefore schematically represented as beams of length l with a constraint of fixed support on one side and with a constraint of smooth pin on the other (see Figure 5.23).
Figure 5.22 Semiconductor positions with respect to rotating reference of system. G. Pace [8]
Figure 5.23 Mechanical representation of a post. G. Pace [8]
With a normal force directed as z, the deformation of the beam is equal to ε𝑧 = 𝐹𝑧/𝐸𝐴. Hence if the semiconductor has the main direction as the axis z it will measure a deformation equal to εz whereas if it is placed orthogonally to z it will measure a deformation equal to -νεz where ν is the Poisson’s ratio.
70 1 2
x y y
M = −F z+ F l (5.1)
and from the combination of Navier equation with stress-deformation relation the deformation of the beam is x z x M y EJ ε (5.2)
where Jx is the moment of inertia with respect to x.
A similar expression can be found if the force is directed as x:
1 ; 2 y y x x z y M M F z F l x EJ ε = − = − (5.3)
It is clear that as the semiconductors are in fact resistances, a variation of their modulus will affect the potential difference between C and D. The hypothesis for the evaluation of VCD are
• R1 = R2 = R3 = R4 = R • VCD = 0 • 1 2 x R R ∆
and from the electric relations that describe the Wheatstone bridges:
1 2 1 4 2 3 ; AB AB V V I I R R R R = = + + (5.4) 3 4 2 3 1 4 CD R R AB V V R R R R = − + + (5.5) and finally 1 2 3 4 1 4 CD AB V R R R R V R ∆ ∆ − ∆ + ∆ − ∆ = (5.6)
Moreover, considering the relation between deformation and resistance variation 1
F
R G R
ε= ∆ (5.7)
where GF is the gain factor and combining it with equation 5.6, the following expression can be obtained: 1 2 3 4 ( ) 4 CD CD F AB V V G V E ε ε ε ε ∆ ∆ = = − + − (5.8)
Hence, from the equation 5.8 it is possible to obtain the unbalance of the bridge, finding the force acting on the dynamometer. Any bridge is then temperature self-compensated.
The relation between the potential difference, that arises due to the deformations, and the forces and moments exerted on the dynamometer can be found for any bridge and the overall result is that a matrix [D] can be defined from the equations system in order that
71 [ ] F
V= D ⋅ (5.9)
Figure 5.24 Wheatstone bridge. G.Pace [8]
5.18. SHAFT, BEARINGS AND SEALS
The aim of these elements is to transfer the rotational motion from the main motor to the pump. It is important to note that in POGO experiments, in which additional axial forces are set, the axial movement has to be avoided and therefore a high axial stiffness is needed.
Indeed in POGO tests, for a typical flow velocity of 3 m/s with a fluctuation of the mass equal to 2% at 40 Hz, the obtained error is of about 5% if the axial displacement is 0.0127 mm and therefore in the bearings’ design a maximum axial displacement of 0.0127 mm is allowed.
The kinematic unit consists in three bearings: one cylindrical roller bearing at front and two angular contact ball bearings at the rear positioned one opposed to the other. The seals used are of the radial type, consisting of a flanged body in plastic material and an activating element composed by a stainless steel spring.
5.19. CIRCUIT CONFIGURATIONS
The facility can accomplish different type of tasks and various types of testing can be easily performed through small modifications of the circuit. The possible configurations obtained from the facility are:
• CPTF (Cavitating Pump Test Facility): it is the basic configuration and it is used for the characterization of the performance of different type of pumps. The secondary motor is not used in this configuration.
• CPRTF (Cavitating Pump Rotordynamic Test Facility): it is similar to the CPTF and it has been designed to evaluate the rotordynamic forces both in centrifugal and axial pumps in cavitating or noncavitating conditions.
• CI2TF (Cavitating Induced Instabilities Test Facility): it is a further modification of the
CPTF in which hydrodynamic instabilities, originated from pressure oscillations due to cavitating inducers, are evaluated for centrifugal or axial pumps in cavitating or noncavitating conditions.
• CI2RTF (Cavitating Induced Instabilities and Rotordynamic Test Facility): it allows to
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5.19.1.
CPRTF
The CPRTF configuration of the facility uses the secondary motor which set a circular motion of the axis of rotation (precession) at a certain angular speed ω. This whirl motion, as seen in chapter 4.2, simulates eccentric motions due to axis misalignments. The two motors are connected through a transmission system that regulates and keep constant the whirl frequency ratio which can be:
• Subsynchronous: |ω| < |Ω| • Synchronus: |ω| = |Ω| • Supersynchronous: |ω| > |Ω| both positive as well as negative.
The eccentricity (the radius of the whirl) is set by means of a kinematic mechanism composed by three cylinders as shown in Figure 5.25, where the schematic representation (left) and the mechanism’s design (right) are shown. The external one is attached to the frame whereas the others can be fixed to each other through splines. The internal cylinders are then connected to the whirl motor which rotates them, moving also the main shaft due do the eccentricity. In Figure 5.26 there are two pictures of the developed mechanism.
Figure 5.25 Schematic representation (left, modified from [7]) and mechanism design (right, Raposelli [9]) of the kinematic system.
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The primary shaft, is positioned in correspondence to the hole of a cylindrical element, with eccentricity equal to e/2, with respect to the axis of the outer casing, which instead has its outer surface fixed with the frame. Hence the shaft can rotate with respect to the cylinder, which, however, during the motion, is connected with the secondary motor thanks to a proper locking system. When the system is at rest, it is possible to adjust the eccentricity acting on the kinematic system by rotating the cylinder with respect to the secondary motor shaft and the main motor shaft with respect to the cylinder, until the desired eccentricity is reached. The eccentricity can assume values between 0 and 2 mm. In Figure 5.27 it is possible to observe the resulting eccentricity vector as vector composition of the two displacements e1 and e2.
Figure 5.27 Vector composition of the eccentricity. G. Pace[8]
The wires of the dynamometer passes inside the hole of the main motor shaft and are connected with an acquisition system provided by means of slip rings.
Figure 5.28 Hollow of the main motor’s shaft for the dynamometer’s wires (left) and electric connection with slip rings (right). G.Pace [8]
The main characteristics for the CPRTF configuration are indicated in Table 5.3.
The CPRTF is the facility used in the present thesis for experimental campaign. One of the configurations analyzed involves the DAPROT3 axial inducer (see next chapters) and the cut-off of this configuration is shown in Figure 5.29.
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Maximum speed of rotation of the motors 3000 rpm (6000 rpm for main motor during tests on axial inducers) Maximum power of main motor 30 kW
Maximum torque of main motor 100 Nm Maximum power of secondary motor 5 kW Maximum torque of secondary motor 20 Nm
Maximum eccentricity 2 mm
Maximum loads for dynamometer
lateral 2400 N
axial 15000 N
bending 1400 Nm
torque 400 Nm
Table 5.3 Main characteristics of the facility. A. Bonaguidi [4]
Figure 5.29 Rotordynamic configuration for DAPROT3 in CPRTF facility.
1 Tie-beam 2 DAPROT3 Nose 3 DAPROT3 4 Conical attachment 2 5 Volute 6 Conical attachment 7 Locking nut 8 Inlet duct 9 Plexiglas 10 Dynamometer
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5.19.2.
CI
2TF
The Cavitating Induced Instabilities Test Facility is a modified configuration of the CPTF used to enhance the study of the hydrodynamic instabilities through the measurement of the oscillating pressure in cavitating inducers.
The CI2TF has different shaft with a conical attachment to be compatible with the interface of
CPRTF configuration.
In these kind of tests the inducers are placed with a certain axial displacement to allow the inducer to be entirely inside the Plexiglas section, where different differential pressure transducers (PCB) are placed with an axial distance between them as shown in Figure 5.30.
The Plexiglas design depends on the inducer geometry, thus the Plexiglas element is changed whenever a different inducer is used, allowing a correct positioning of the pressure transducers for any configuration.
A Plexiglas version without holes is used if the aim of the test is to take pictures and videos in cavitating (or also noncavitating) conditions.
Figure 5.30 CI2TF configuration for tests on hydrodynamic instabilities. G. Pace [8]
5.19.3.
CI
2RTF
The Cavitation Induced Instabilities and Rotordynamic Test Facility allows the study of either hydrodynamic instabilities or rotordynamic forces acting on the impeller at the same time, by using PCB transducers and rotating dynamometer. The main characteristics of this configuration are shown in Table 5.5.
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Duct's diameter DN = 4″ (discharge) DN = 6″ (suction) Maximum dimensions of the turbopump
used (based on Vulcain motor)
RT1 = 82 mm
RT2 = 112 mm
B2 = 30 mm
Maximum pressure rise at the pump pTmax = 10 atm
Maximum inlet pressure p1max = 6 atm
Minimum inlet pressure (pT1-pV)min = 1000 Pa
Maximum volumetric flow rate Qmax = 0.1 m3/s
Maximum temperature Tmax = 100 °C
Maimum rotational speed of the motors Ωmaxtests on axial inducers) = 3000 rpm (6000 rpm for Ωmax = 3000 rpm
Torque and power of the main motor TPmax = 30 kW
max = 100 Nm
Torque and power of the secondary motor P2max = 5 kW
T2max = 20 Nm
Eccentricity εmax = 2 mm
Table 5.5 Main characteristics of CI2RTF configuration. G. Pace [8]
5.20. DATA ACQUISITION SYSTEM
The instruments and the transducers used for the data acquisition consists in:
• Two Fisher Rosemount 8732E electromagnetic flowmeters mounted on suction and discharge ducts.
• One Druck PMP 1400 absolute pressure transducer with a range scale between 0 and 1 bar, maximum error of 0.15% temperature and self-compensated between -15 °C and +80°C. This transducer has been used for the evaluation of the inlet pressure after the tapered duct. • One Druck PMP 4170 differential pressure transducer with range scale between 0 and 1
bar, temperature self-compensated between -20 °C and +80°C with a 0.08% precision class. This transducer has been used for the measure of the pressure rise across the pump. • One GE UNIK 5000-A5073 differential pressure transducer with a range scale between 0
and 5 bar, temperature self-compensated between -20 °C and +80 °C with a precision of ± 5 𝑚𝑏𝑎𝑟.
• One GE UNIK 5000-A5073 absolute pressure transducer with a range scale between 0 and 6 bar, temperature self-compensated between -20 °C and +80 °C with a precision of ± 6 𝑚𝑏𝑎𝑟.
• One Kulite BMD 1P 1500 100 differential pressure transducer, with a range scale between 0 and 7 bar, maximum error of 0.1% and temperature self-compensated between -29 °C and +82 °C.
• Eight PCB M112A22 piezoelectric transducers are used when the behavior of the dynamic pressure variations is studied (as in CI2RTF and CI2TF configuration of the facility). The
piezoelectric effect of these instruments are represented in Figure 5.31, where if an external force is applied to the transducer, a potential difference is observed due to the charge displacements.
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Figure 5.31 Piezoelectric effect. G. Pace [8]
The material used in these transducer is the quartz, due to its piezoelectric properties and for its stiffness (100 GPa) that allows the generation of high tension output with small deformation. The main peculiarity is that they measure only dynamic variations whereas in presence of a constant signal the output will decay in time from its initial value.
Moreover they are placed at particular positions on Plexiglas as previously described for CI2TF facility. The choice of their positions is critical for the knowledge of the instability
inception and therefore a careful analysis is needed to find the best evaluation of the phenomenon with the specific inducer studied.
• A thermocouple that consists in a resistance temperature detector and a thermostat placed inside the main tank to measure and control the temperature of the water.
• Two Datasensor TL46-WL contrast sensors for the measure of the angular position of the two motors (see Figure 5.32).
Figure 5.32 Contrast sensors for main (left) and secondary (right) motor.
• A National Instruments acquisition system at medium velocity with a 16-channel signal based on a PCI 6024E card with acquisition speed of 250 kS/s that collects all the analogic signals from the transducers (suction/discharge pressures and flow rates, rotational and whirl speeds and water temperature) and convert them in digital signal for the PC connected to the card.
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On the other hand a high speed data acquisition system based on two modules of SCXI 1520 where each module is capable to deal with 10 signals and is therefore used for the dynamometer that produces 10 Wheatstone bridge signals. The system is capable to provide a 10 V tension for the transducer that need a power supply. Differential and absolute pressure transducer are also connected to these modules.
Another SCXI 1531 module with 125 kS/s acquisition speed and 8-channel system collects the signals coming from the piezoelectric transducers also providing them with the power supply.
• A PC with Labview installed used for control and management of the channels, the digital acquisition of the data and the management of the software’s motors.
5.21. LOSSES ACROSS A TEST CHAMBER
Evaluation of the pressure at the discharge of a test chamber, where a transducer for differential static pressure is placed, is affected by losses that comes into play from the impeller exit to the discharge line. In order to obtain the total pressure difference between inlet and discharge, some further considerations are needed.
In case of centrifugal pump, the swirl velocity is recovered by the volute and since that the latter is considered as a component of the specific centrifugal pump along with the impeller, the total pressure difference is simply given by the following expression
2 2 (w w ) 2 TOT out in p p ρ ∆ = ∆ + − (5.10)
where wout and win are given by the volumetric flow rate ; out in out in Q Q w w A A = = (5.11)
For axial pumps or inducers the issue is rather complicated than the centrifugal configuration as the swirl component is totally lost in the test chamber. One assumption that can be made is to consider negligible the losses due to the entrance in the discharge line and the dynamic pressure at the exit of the inducer completely lost in the diffusion inside the test chamber. For this reason, the bulk static pressure measured at the discharge line is considered equal to the one at the exit of the pump. For what concern the dynamic pressure, it can be considered that it is completely lost due to the rapid diffusion in the test chamber. The total pressure rise is therefore given by the following expression:
2 2 2 2 2 (v w w ) 2 TOT in p p δ ρ ° ∆ = ∆ + + − (5.12)
where the three components of the dynamic pressure are derived from the following
in in Q w A = (5.13) 2 2 2 2 (r r )T H2 Q Q w A π = = − (5.14)
79 2 2 2 2 2 2 1 T 2 H r r v rv dr A δ° =
∫
π δ° (5.15)where Ain is the inlet area of the duct, rT is the radii of the duct right after the pump (rT2 plus clearance), rH2 is the hub radii at discharge and v2δ° is the azimuthal velocity at a specific radial position.
From equation 5.13 it is clear that the inlet velocity at the pump is considered equal to the axial velocity at the pressure transducer, some diameters upstream, and therefore where prerotation is not present. Indeed prerotation is not considered and the flow is completely axial.
On the other hand the velocity at the discharge of the pump is composed by an axial and an azimuthal component, w2 and v2δ° respectively. The value of v2δ° can be obtained from the deviation angle δ by means of Carter’s rule:
2 2 2tan( )2 2tan( 2 ) 2 w v r w r w r P δ π β γ δ °= Ω − = Ω − + = Ω − (5.16)
where β2 is the
relative discharge flow angle and γ
2is the blade angle with respect to the axial
direction
2
2 2
tan( ) tan( Tte T Tte) r r P= γπ δ = γπ δ + + (5.17)
(
)
0.23 0.1 50TteTte Tle Tte
γ δ γ γ σ ° ° ° ° + ° ≅ − (5.18)
where σ is the solidity of the blades, subscript le stands for leading edge and subscript te stands for trailing edge. In equation 5.18 the angles are expressed in degree whereas in the others, radians are used.
Substituting Eq. 5.17 and 5.18 in Eq. 5.16, the following result is obtained:
(
)
(
)
2 4 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 T H r T H r T H r r w v rv dr A r r P δ δ π π ° ° − = = Ω − − ∫
(5.19)5.22. REFERENCES
[1] L. Torre, A. Pasini, A. Cervone, L. Pecorari, A. Milani e L. d’Agostino, Rotordynamic Forces on a Three Bladed Inducer, ALTA S.p.A., 2010.
[2] Torre L., Pasini A., Cervone A., d’Agostino L., 2011,Experimental Characterization of the Rotordynamic Forces on Space Rocket Axial Inducers, ASME J. of Fluids Engineering, Vol. 133, Is. 10, October 2011, ISSN: 0098-2202.
[3] C. Bramanti, A. Cervone, E. Raposelli, L. d’Agostino, Experimental activities on liquid propellant turbopumps at Centrospazio, VII Congresso Nazionale AIDAA, 15-19 September 2003, Roma.
[4] A. Bonaguidi, Caratterizzazione delle prestazioni e delle forze rotodinamiche di turbopompe per uso spaziale, Tesi di Laurea in Ingegneria Aerospaziale, Università degli studi di Pisa, 2013.
80 [5] http://www.vortab.com
[6] http://www.processautomatic.com/
[7] E. Raposelli, A. Cervone, L. d’Agostino, A new cavitating pump rotordynamic test facility, AIAA PAPER, ISSN: 0146-3705, 2002
[8] G. Pace, Caratterizzazione sperimentale di induttori cavitanti e del sistema di misura delle forze rotodinamiche, Tesi di Laurea in Ingegneria Aerospaziale, Università degli studi di Pisa, 2009.
[9] E. Raposelli, A. Cervone, C. Bramanti, L. d’Agostino, A New Cavitation Test Facility at Centrospazio, 4th International Conference on Launcher Technology "Space Launcher Liquid Propulsion", 3-6 December 2002, Liege (Belgium).
[10] Torre L., Pasini A., Cervone A., d’Agostino L., 2011,Experimental Characterization of the Rotordynamic Forces on Space Rocket Axial Inducers, ASME J. of Fluids Engineering, Vol. 133, Is. 10, October 2011, ISSN: 0098-2202.
