P ERFORMANCE 4 T URBOPUMPS

4

T

URBOPUMPS

P

ERFORMANCE

In the following section a detailed description of the turbopumps tested in the CPTF (Cavitating Pump Test Facility) will be presented. The main results of the experimental tests carried out to characterize the turbomachineries in noncavitaing and cavitating conditions will be discussed in detail. The experimental campaigns have been performed on four different turbopumps: two commercial turbopumps used to validate the facility, the Vulcain LOX inducer of Ariane 5 and a prototype of the VINCI LOX inducer.

In the last part of the section is dedicated to a comparative analysis of the different performance of the turbopumps and to and assessment of the main pump design parameters which can lead to improve the performance.

4.1 Introduction

The experimental campaign for the characterization of the noncavitating and cavitating performance of the different turbomachineries was carried out in the CPFT (Cavitating Pump Test Facility) by measuring the following parameters:

− The pump inlet pressure, by means of the Druck absolute transducer installed upstream of the Plexiglas inlet duct;

− The pressure rise given by the pump, by means of the Kulite differential transducer or the Druck pressure transducer, installed between the Plexiglas inlet duct and the discharge pipe immediately downstream of the test section for the tests carried out with the FIP120 turbopump, while between the Plexiglas inlet duct and the immediately downstream the inducer inside the test section for the other turbopumps tested;

− The mass flow rate, by means of the two electromagnetic flow meters; − The torque given by the main motor, obtained by the electronic drive itself; − The water temperature, by means of the probe installed in the main tank.

During the experimental campaign for characterizing the inducer noncavitating performance, the following procedure has been defined and performed:

− Pressurization of the water in the circuit slightly higher than 1 atm;

− Acquisition of the pressure transducers signals before the experiments in order to acquire the pressure transducer offset;

− Electronic ignition of the engine and selection of the engine rotational speed Ω;

− Regulation of the silent throttle valve aperture in order to adjust the flow mass rate _.

i

Q and then the pump head;

− Continuous acquisition of the pressure transducer signals (absolute and differential), through the dedicated Labview program, at an adequate scan rate in order to properly mediate the signal during the post processing process (scan rate/sec=200, total acquisitions=1000);

− Shouting down the engine till the successive experimental tests.

The tests for the characterization of the cavitating performance of the FIP162, FAST2 and VULCAIN inducers were carried out under “continuous” conditions, i.e. continuously decreasing the pump inlet pressure. For the characterization of the performance of the FIP120 inducer in cavitating conditions, the inlet pressure has been increased from the lower attainable value to higher values in discrete way. More in detail, the test procedure was the following:

− Degassing the working fluid, in order to reduce the number and the mean dimensions of the cavitation nucleii;

− In the case of thermal cavitation experiments, heating the working fluid up to the required temperature;

− Acquisition of the pressure transducers signals before the experiments in order to acquire the pressure transducer offset;

− Setting the air-bag pressure to the initial value required for the experiment (typically near to atmospheric pressure);

− Electronic ignition of the engine and selection of the engine rotational speed Ω;

− Regulation of the silent throttle valve aperture in order to adjust the flow mass rate Q._iand then the pump head;

− Regulation of the pressure in the vacuum reservoir of the depressurization circuit, in order to set the value of the decreasing rate for the air-bag pressure (see 3.2.2);

− Continuous acquisition of the pump inlet pressure by means of the absolute transducer and of the pump pressure rise by means of the two differential pressure transducers. The flow rate has to be maintained uniform during the whole experiment;

− Shouting down the engine till the successive experimental tests.

Figure 4.1 shows the typical behaviour of the inlet pressure and the differential pressure during a 6 minutes continuous test. It can be observed that the inlet pressure decreasing rate is maintained practically constant throughout the test, until the minimum attainable value is reached. The breakdown of the pressure rise is also evident for lower values of the inlet pressure.

Figure 4.1 – Typical behaviour of the inducer inlet pressure and pressure rise during a continuous test on the FIP162 inducer, for 22.5 L/sec flow rate, 2000 rpm rotating speed and ambient temperature. One possible problem related to this kind of experimental procedure could be the deterioration of water quality during the experiment, due to progressive formation of cavitation nucleii caused by the pressure decrease. By the way, it has been demonstrated (Figure 4.62, Brennen, 1994) that the number and dimensions of cavitation nucleii has an influence on the cavitation inception but not on the breakdown and so, as a consequence, the cavitating performance curves are not expected to be influenced by this aspect.

The procedure used to extract the performance information from data similar to those showed in Figure 4.1 has to be analyzed with particular attention. A typical cavitating performance curve of a pump is formed by a set of “steady” points, which have to be obtained in this case by an “unsteady” test (i.e. by a set of data related to a not uniform inlet pressure). In order to obtain this result, the test data have to be divided in “quasi-steady” time fractions, having a length short enough to not show a significant variation of the mean inlet pressure during each interval. At the same time, the intervals have to be sufficiently long, in order to obtain a mean head coefficient not influenced by the significant pressure oscillations typically showed observed in the acquired data.

In order to reduce data dispersion, the mean values of inlet and differential pressure for each point of the performance curve are obtained by mediating the values of the corresponding time interval with those of four adjacent intervals (two after and two before it).

After a long trade-off for the optimization of the procedure parameters (Testa, 2004), a 1-second duration for each time interval has been found to be the best choice. It can be noted that, if the mediating operation through adjacent intervals is taken into account, each point on the performance curve is representative of a 5-seconds time interval, i.e. the same acquisition length of each “steady” experimental point of the noncavitating tests.

The other important parameter to be taken into account is, obviously, the inlet pressure decreasing rate during the test. It has been shown (Testa, 2004) that this parameter does not influence the aspect of the cavitating performance curve obtained by the test. In particular, the points obtained by “steady” cavitating tests are perfectly coincident with those from “continuous” tests. The typical decreasing rate used for the experiments discussed in the following was in the range 3÷5 mbar/sec.

4.2 Overview of the experimental validation of the facility

The first set of experimental tests have been carried out in order to validate the test facility in its basic configuration, CPTF (Cavitating Pump Test Facility). The turbopump (so called “FIP120”) used for these preliminary experiments is a commercial turbopump procured from F.I.P. (Fabbrica Italiana Pompe), whose main dimensional characteristics are reported in Table 4.1, while a detailed drawing of the FIP120 inducer is shown in Figure 4.2.

The turbomachinery is composed by the centrifugal impeller, axial inducer (Figure 4.4) and the volute (Figure 4.3), which allows the positioning in the dedicated pump housing. During the design phase the possibility to test separately or together the inducer and impeller have been taken into account.

Inlet tip blade radius of the centrifugal impeller 60 mm Outlet tip blade radius of the centrifugal impeller 107 mm Outlet blade width of the centrifugal impeller 22 mm

Inducer hub radius 19 mm

Inducer tip radius 60 mm

Inducer tip blade angle 16°

Inducer axial pitch 110 mm

Table 4.1 – Main dimensional characteristics of the pumps used for the validation of the facility.

Figure 4.3 – Picture of the FIP 120 impeller and casing.

Figure 4.4 – Picture of the FIP 120 inducer (top) and impeller (lower side)

The pumping performance as function of the volumetric mass flow of the only centrifugal impeller was provided by the F.I.P. company and is presented in Figure 4.5. The curve was obtained by F.I.P. company through a mathematical interpolation of experimental data related to results nearby the condition of maximum efficiency (φ1 = 0.2). For this reason the data could not be considered

particularly accurate far from that zone.

Figure 4.6 shows the head coefficient ψ and the efficiency η of the centrifugal impeller as a function of the inlet flow coefficient φ1, while Figure 4.7 shows the cavitation number at cavitation

inception σi as a function of the pressure coefficient and the cavitation number at cavitation inception

16 8 H Q( ) 110 0 Q 0 10 20 30 40 50 60 70 80 90 100 110 8 9 10 11 12 13 14 15 16

Figure 4.5 – FIP centrifugal impeller head (m) as function of the volumetric mass flow (m3_{/h) at rotational}

speed of 1450 rpm 0.678 0 ψ 2 φ 2 η 2 φ 2 0.13 0 0.087 φ 2 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0 0.068 0.14 0.2 0.27 0.34 0.41 0.47 0.54 0.61 0.68

Figure 4.6 – Pressure coefficient and efficiency as function of flow coefficient in the FIP 120 impeller. 0.844 0.424 σ i ψ( ) 0.54 0.27 ψ 0.27 0.3 0.32 0.35 0.38 0.41 0.43 0.46 0.49 0.51 0.42 0.47 0.51 0.55 0.59 0.63 0.68 0.72 0.76 0.8 0.84 _0.843584 0.42453 σ i1 φ 1 0.3 0.12 φ 1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.42 0.47 0.51 0.55 0.59 0.63 0.68 0.72 0.76 0.8 0.84

Figure 4.7 – Inception cavitation number as function of pressure coefficient in the FIP 120 impeller (left). Inception cavitation number as function of inlet flow coefficient in the FIP 120 impeller (right).

4.2.1 Experimental tests in noncavitating conditions

In this section the experimental tests in noncavitating conditions on the FIP120 turbomachinery (impeller, inducer, impeller+inducer) carried out to evaluate the performance and efficiency will be presented. Figure 4.8 presents the performance of the impeller in noncavitating conditions and the relative comparison with the data provided by F.I.P. company. As expected, the pump performance at a flow coefficient around the working point is similar to the one predicted, while diverge far from it.

Figure 4.8 –Performance of the FIP120 impeller in noncavitating conditions and comparison with the data provided by F.I.P. company

The Figure 4.9 presents the preliminary experimental tests, which were carried out in order to validate the facility and demonstrate that, in noncavitating conditions, the pump performance is independent from the fluid temperature (if we operate in cavitating conditions, the temperature plays a very important role on the pump performance breakdown), from the inlet pressure and from the rotational speed if the geometric, fluiddynamic silimilarity are met. In particular, the Reynolds number was maintained between

7.1 10

⋅

5 e

2.3 10

⋅

6, in order to maintain the fluid in turbulent conditions.

The second phase of the facility validation consisted on perfoming experimental tests on the whole pump system, impeller mounted with its inducer. Figure 4.10 presents a comparison between the performance of the impeller and the impeller mounted together with the inducer. The performance of the system impeller+inducer are slightly lower than the ones for the only impeller, unlike in space rocket turbopumps in which the addition of the inducer to the impeller improves the performance of around 20%. These results can be explained taking into account that the inducer used for experiments is not optimised and there is not a good “matching” between the inducer exit and the impeller as the impeller was design not to work with the inducer. Its surface finishing is quite normal, the channel between the blades is too long due to the high tip blade angle ( normally the tip blade angle is around 9° for space inducers) and the blade extends for almost one pitch. These characteristics enhance the losses and then reduce the pump head.

Temperature 25°C Mass flow variable Inlet pressure 1 atm Rotational speed 1450 rpm

Figure 4.9 –Performance of the FIP120 impeller in noncavitating conditions at various inlet pressure (Top-left), at several rotational speeds (Top-right) and two different temperature (low side)

Figure 4.10 – Comparison between performance of the pump system impeller+inducer and the only impeller

Figure 4.11 presents the characteristic curve of performance of the FIP120 inducer in noncavitating conditions. At lower flow coefficient the slope of the curve is positive and represents the unstable performance zone where surge can be detected, as previously pointed out. The working point of the FIP120 inducer belongs to the zone where the slope is negative, stable.

Figure 4.12 shows the efficiency and the pressure coefficient of the impeller as function of the flow coefficient. The maximum efficiency value for the impeller is 0.64 , slightly different from 0.68, indicated by F.I.P., while for the system impeller+inducer is 0.593 (around 8% less than for the configuration with the only impeller, as expected for the not optimized shape of the inducer), as shown in the next Table. The maximum efficiency for a space rocket turbopump is around 0.90.

Figure 4.11 – Performance of the FIP120 inducer in noncavitating conditions

Experimental Tests F.I.P.

ηmax Ψηmax Φηmax ηnom Ψηnom Φηnom

Impeller 0.64 0.445 0.3 0.6 0.52 0.2

Impeller+Inducer 0.593 0.27 0.45 0.55 0.51 0.2 Table 4.2 – Flow coefficient and pressure coefficient evaluated at the maximum efficiency for the

Figure 4.12 – Impeller efficiency and pressure coefficient as function of the flow coefficient (top) and comparison between the impeller and the impeller+inducer efficiency (bottom).

4.2.2 Experimental tests in cavitating conditions

In this section the experimental tests on the FIP120 turbomachinery (impeller, inducer, impeller+inducer) carried out to evaluate the performance and the efficiency in cavitating conditions will be presented. Figure 4.13 presents the impeller performance in cavitating condition for several flow coefficients (φnom corresponds to the value of φ at maximum efficiency provided by F.I.P. company). As expected, when there is not extensive cavitation development, the impeller performance remains constant. It is possible to note that the performance breakdown is shifted towards higher cavitation number increasing the flow coefficient.

Figure 4.14 presents the impeller+inducer performance in cavitating condition for several flow coefficients (φnom corresponds to the value of φ at maximum efficiency provided by F.I.P. company). As in the previous case, the cavitation number increases if the flow coefficient increases and, at the same time, the pressure coefficient decreases as well as the performance breakdown is shifted towards higher cavitation number increasing the flow coefficient. The insertion of the inducer to the impeller plays a beneficial effect to the performance in cavitating condition: at the same Φ/Φnom (for example

0.98) the cavitation inception and breakdown, in fact, is shifted towards lower cavitation number (around 25%).

Figure 4.13 – Impeller cavitating performance curve for several flow coefficients at ambient temperature and rotational speed 2000rpm

Figure 4.14 – Impeller+inducer cavitating performance curve for several flow coefficients at ambient temperature and rotational speed 2000 rpm

Figure 4.15 presents the inducer performance in cavitating conditions. The cavitation inception and breakdown are shifted towards lower values of cavitation numbers at higher flow coefficient and lower pressure coefficients, (different result from the impeller and impeller+inducer performance).

Figure 4.15 – Inducer cavitating performance curve for several flow coefficients at ambient temperature and rotational speed 2000 rpm

Figure 4.16 shows the breakdown coefficient as function of the flow coefficient for the configurations impeller, impeller+inducer and inducer. It demonstrates what previously pointed out: the inducer has a beneficial effect on the performance in cavitating conditions, the cavitation breakdown moves towards lower values of the cavitation number.

Figure 4.16 – Comparison between the breakdown coefficient of the impeller and impeller+inducer (left) and the inducer (right) at several flow coefficient.

Figure 4.17 demonstrates the simultaneous breakdown of the pressure coefficient and the efficiency at the breakdown cavitation number. Figure 4.18 presents the thermal cavitation effects illustrated in the previous section: at higher temperatures, due to the higher vapour density, the bubble growth involves a higher liquid mass so that the heat needed for the phase change is higher, the local temperature and the local vapour pressure pV decrease. In these conditions the bubble growth is

inhibited and the breakdown cavitation number is lower than without thermal effects, as shown in the Figure. The thermal effects are detachable only at temperatures sufficiently high (see Figure 4.18, this phenomenon is present at 68°C). due to the behaviour of the water vapour pressure Figure 4.19 .

Figure 4.17 – Impeller+inducer pressure coefficient and efficiency as function of the cavitation number at ambient temperature, rotational speed of 2000rpm and flow coefficient of 0.238

Figure 4.18 – Impeller+inducer cavitating performance curve for several temperatures and rotational speed 2000rpm

0.229271

3.906857 10. 4 p v °K( )

400

260 °K

Figure 4.19 – Water vapor pressure as function of the temperature

The development of cavitation on the FIP120 inducer at a fixed flow coefficient and various cavitation numbers is presented in Figure 4.20, while the detrimental effects of cavitation phenomenon detected after the experimental campaign are shown in Figure 4.21. In particular, pitting and erosion were the main effects identified on the blades and on the hub of the inducer.

Figure 4.20 – Cavitation development in the FIP120 inducer for several cavitation numbers and a fixed flow coefficient (φ=0.07)

Figure 4.21 – Effects of cavitation detected after the test campaign on the FIP120 inducer

4.3 Experimental campaign on FIP162 turbomachinery

The second set of experimental tests have been carried out in the configuration CPTF (Cavitating Pump Test Facility) on a commercial turbopump (Figure 4.22, so called “FIP162”) procured from F.I.P., whose main dimensional characteristics are reported in Table 4.3, while a detailed drawing of the FIP162 inducer is shown in Figure 4.23.

Figure 4.23 – Detailed drawing of the FIP162 inducer.

Number of blades 3

Tip diameter [mm] 162

Hub/tip diameter ratio (uniform) 0.278

Tip blade angle (uniform) 9°

Tip solidity 3.05

Design flow coefficient 0.06

Axial pitch [mm] 81

Mass [kg] 0.55

Table 4.3 – Main dimensional characteristics of the FIP162 inducer.

The FIP162 inducer was manufactured by welding the blades to the hub, so the blade channels and tip blade angle are not completely uniform, in particular near the hub. Aluminium was chosen to obtain a lower value of the mass suspended and pump surface was anodised for making the blades more resistant to corrosion and cavitation erosion. The FIP162 is a three-bladed aluminium made inducer of extremely simple geometry, with a tip radius of 81 mm, an uniform hub radius of 22.5 mm, a constant tip blade angle equal to 9°, a tip solidity of 3.05 and 2 mm thick back-swept blades with blunt leading and trailing edge. The blades channels extend for about one half the axial pitch of the helix. This turbomachinery has a lower tip blade angle than the FIP120 and comparable with the common space turbopumps (high tip angle, in fact, lead to decrease of the pump performance due to significant friction losses in flow passage).

4.3.1 Noncavitating performance

As in the previous test campaign, the experiments in noncavitating conditions were the first to be carried out to evaluate the inducer performance. Table 4.4 presents the test conditions during the noncavitating experiments on the FIP162 inducer. Figure 4.24 presents the FIP162 inducer performance in noncavitating conditions, while Figure 4.25 shows the specific speed and the incidence

angle at medium radius as function of the flow coefficient for several rotational speeds. The large scatter of the pressure coefficient at low flow coeffients in Figure 4.24 are probably due to asymmetric stall on the roughly finished inducer blades.

Table 4.4 – Experimental test parameters in noncavitating conditions.

Figure 4.24 – FIP162 noncavitating performance curve for several rotational speed values

Figure 4.25 – Specific speed (left) and incidence angle at medium radius (right) as function of the flow coefficient at several rotational speeds

The next Figure shows the Balje diagram in the plane

(

Ω_S,r_S

)

and a comparison with the results obtained during the experimental tests on the FIP162 inducer in the same plane.

Engine rotational speed [rpm] 1000 1500 2000

Inlet Pressure [atm] 1.2 1.2 1.2

Figure 4.26 – Comparison between the Balje envelope (ΩS,rS) and the noncavitating performance of the

FIP162 inducer.

4.3.2 Cavitating performance

This section is dedicated to present the results of the experimental tests carried out on the FIP162 inducer in order to analyze the FIP162 performance in cavitating conditions. The following Figures highlight some characteristics of the inception and development of cavitation under different flow conditions and temperatures (ambient temperature, Figure 4.27) and (higher temperatures, Figure 4.28 and Figure 4.29). As previously pointed out (see section 2, and the experimental tests on the FIP120 inducer), the temperature has a significant role on the pump performance. The thermal effects, in fact, are detachable only at temperatures sufficiently high and during our experiments on the FIP162 inducer also at higher flow coefficient (see Figure 4.29 right).

Figure 4.27 – FIP162 performance curve in cavitating conditions at several flow coefficients and ambient temperature

Figure 4.28 – Comparison between the performance in cavitating conditions at two different temperatures, 2000 rpm and Φ=0.0400 (left), Φ=0.0458 (right)

Figure 4.29 – Comparison between the performance in cavitating conditions at two different temperatures, 2000 rpm and Φ=0.0500 (left), Φ=0.0529 (right).

The following Figures show several pictures of the FIP162 during the development of cavitation phenomenon. In particular, they present the appearance of cavitation on the inducer blades at a fixed flow coefficient (φ=0.046, Figure 4.30 and Figure 4.31; φ=0.057, Figure 4.32 and Figure 4.33), at various cavitation numbers and different temperatures. In fact, specific interest has to be given to the pictures related to thermal cavitation.

Figure 4.30 – Pictures of the cavitating FIP162 inducer at room temperature, 2000 rpm rotating speed and flow coefficient φ = 0.046, for cavitation numbers σ = 0.65 (left), σ = 0.51 (center) and σ = 0.27 (right).

Figure 4.31 – Pictures of the cavitating FIP162 inducer at room temperature, 2000 rpm rotating speed and flow coefficient φ = 0.046, for cavitation numbers σ = 0.20 (left), σ = 0.18 (center) and σ = 0.15 (right).

Figure 4.32 – Pictures of the cavitating FIP162 inducer at 70 °C temperature, 2000 rpm rotating speed and flow coefficient φ = 0.057, for cavitation numbers σ = 0.43 (left), σ = 0.35 (center) and σ = 0.27 (right).

Figure 4.33 – Pictures of the cavitating FIP162 inducer at 70 °C temperature, 2000 rpm rotating speed and flow coefficient φ = 0.057, for cavitation numbers σ = 0.20 (left), σ = 0.17 (center) and σ = 0.15 (right).

In particular, they present the appearance of cavitation on the inducer blades at a fixed flow coefficient (φ=0.046, Figure 4.30 and Figure 4.31; φ=0.057, Figure 4.32 and Figure 4.33), at various cavitation numbers and different temperatures. In fact, specific interest has to be given to the pictures related to thermal cavitation.

4.4 Experimental campaign on MK1 inducer

The third set of experimental tests have been carried out in the configuration CPTF (Cavitating Pump Test Facility) on the so called “MK1” inducer. This prototype was procured from FIAT AVIO during the spring 2003. The same type of inducer is mounted on the LOX turbopump system of the

ARIANE 5 first stage engine, called Vulcain 1. The opportunity to test a space inducer represented a motivating challenge for the team to work on an optimized machine with high performance. Figure 4.34 present the a schematic of the propulsion system of ARIANE 5 first stage and a picture of the VULCAIN 1 and the uploaded version VULCAIN 2. Table 4.5 shows the main characteristics of the VULCAIN 1 propulsion system.

Figure 4.34 – The ARIANE 5 first stage liquid propulsion system (left), Vulcain1 (center) and Vulcain2 (right), (Courtesy of Snecma Moteurs).

Table 4.5 – Main characteristics of the ARIANE 5 main engine.

A picture and a detailed drawing of the MK1 inducer are shown in Figure 4.35 and Figure 4.36 respectively, while the main dimensional characteristics are reported in Table 4.6. The inducer has

been machined from an unique piece (unlike FIP120 and FIP162 inducers which have been prepared by welding the blade on a hub of constant diameter). The geometry of the MK1 inducer is very sophisticated as it presents a tapered hub and a tapered blade thickness and has a variable pitch, tip blade angle and radius.

Figure 4.35 – Picture of the MK1 inducer.

Figure 4.36 – Geometry and dimensions of the MK1 inducer.

Number of blades 4

Tip diameter [mm] 1682

Hub/tip diameter ratio (uniform) 0.428

Inlet Tip blade angle (uniform) 7.7°

Exit angle at the medium radius 17.7°

Tip solidity 2.1

Design flow coefficient 0.0856

Mass [kg] 3.5

Table 4.6 – Geometric characteristics of the Vulcain inducer

Table 4.7 reports some of the main characteristics of the Monel K-500 alloy (copper and nickel alloy). This alloy has been chosen for its high corrosion resistance level and high mechanical properties.

Table 4.7 – Monel K-500 characteristics.

4.4.1 Noncavitating performance

As in the previous test campaign, the experiments in noncavitating conditions were the first to be carried out to evaluate the inducer performance. Table 4.8 presents the test conditions during the noncavitating experiments on the MK1 inducer, while Figure 4.37 shows the inducer performance.

Table 4.8 – Experimental test parameters in noncavitating conditions

Figure 4.37 – MK1 performance in noncavitating conditions at ambient temperature and several rotational speed values

As expected, the maximum value of the pressure coefficient of the MK1 inducer is higher than the FIP inducer, as well as the absolute value of the slope at high flow coefficients (in fact,

Component % weight Ni 63 Cu 27-33 Al 2.3-3.15 Fe 2 (max) Mn 1.5 (max) Ti 0.35-0.85 C 0.25 (max) Si 0.5 (max) S 0.01 (max) Characteristics Density 8.44 Kg/m3

Ultimate strenght (at ambient temperature) 1100 MPa Yield point (at ambient temperature) 790 Mpa Thermal dilatation coefficient (at 20°C) 13.7 mm/m°C

Engine rotational speed [rpm] 1000 1500 2000

Inlet Pressure [atm] 1.2 1.2 1.2

(

)

max/ max 1.15

Ψ Ψ Φ ≅ for the FIP inducer, while Ψ_max/Ψ Φ

(

_max

)

≅1.64 for the MK1 inducer). At lower flow coefficients the pressure coefficients are less dispersed in the MK1 inducer than in the FIP inducer. This is due to the different geometry of the leading edge which can trigger the onset of cavitation instabilities if the fluid is not fully guided by the blade (as in the case of the FIP inducer, which presents a higher blade thickness and less accurate blade finishing).

Figure 4.38 illustrates the specific speed and the incidence angle at medium radius as function of the flow coefficient for several rotational speeds. From the Figure (right side) the stall angle can be estimated around 9° at the maximum pressure coefficient (for the FIP inducer it was around 6.5°).

Figure 4.38 – Specific speed (left) and incidence angle at medium radius (right) as function of the flow coefficient at several rotational speed

Figure 4.39 shows the Balje diagram (referred to single stage pumps) in the plane

(

Ω_S,r_S

)

and a comparison with the results obtained during the experimental tests on the MK1 inducer in the same plane, in particular it is possible the estimation of the efficiency between the MK1 and FIP162 inducers (see Figure 4.26). In Figure 4.26 and Figure 4.39 the Reynolds number and ratio between the radial clearance and blade height are shown for both the inducers (Re 2= ΩrT2

ν

=108and

0.02 h

δ

= , for the FIP inducer and _{Re 2} 2 ₁₀6

T

r

ν

= Ω = and

δ

h=0.0208, for the MK1 inducer). The efficiency is around 85-90 %. Figure 4.40 presents experimental results to characterize the hydraulic efficiency of the MK1 inducer. If the internal efficiency of the engine is supposed almost constant with the torque, the hydraulic efficiency, according to the (1.8), is defined by:

( )

( ) t idr wat _dry V p T T

η

= ∆ Ω − Ω  (4.1)

( )

TΩ wetand

( )

TΩ dryrepresent the results of the power of the engine, measured during two

experiments carried out when there was or not the water in the facility, respectively. ∆p_t is the total pressure rise across the inducer, calculated considering only the axial component of the velocity, and not the circumferential one (it will be demonstrated in the next section that this component should be taken into account). The next Figure shows the degradation of the efficiency at higher rotational speeds, due to a decreased engine efficiency at higher torque.

Figure 4.39 – Comparison between the Balje envelope (ΩS,rS) and the noncavitating performance of the

MK1 inducer.

Figure 4.40 – Hydraulic efficiency of the MK1 inducer as a function of the flow coefficient.

4.4.2 Cavitating performance

This section is dedicated to present the results of the experimental tests carried out on the MK1 inducer in order to analyze the performance in cavitating conditions. The Figure 4.41 highlights some characteristics of the inception and development of cavitation under different flow conditions and at ambient temperature. The MK1 inducer presents the phenomenon of the “head recovery” just before the cavitation breakdown number at low flow coefficients and high flow coefficient even if with less evidence. This phenomenon was also observed in the FIP162 inducer. According to Oshima, Kawaguchi [5] and Brennen this particular phenomenon can be addressed to a increased improvement of the flow geometry due to the development of cavitation.

Figure 4.41 – MK1 inducer performance curve in cavitating conditions at ambient temperature and 2800 rpm rotational speed for several flow coefficients

Figure 4.42 and Figure 4.43 present the appearance of cavitation at two different flow coefficients. Each picture corresponds to a point in the σ−ψ plane, in order to understand the influence of the extension of cavitation on the head coefficient. The performance breakdown occurs when the cavitation is sufficiently developed to completely obstruct the blade channel and blocking the low passage. Till this point the cavitation development do not affect the pump performance. As previously pointed out, the temperature has a significant role on the pump performance.

Figure 4.42 – Development and inception of cavitation in the MK1 inducer at Φ=0.0549 and ambient temperature

Figure 4.43 – Development and inception of cavitation in the MK1 inducer at Φ=0.0037 and ambient temperature

As previously pointed out, the temperature has a significant role on the pump performance. Figure 4.44 shows the pump performance at two different temperatures, 50°C and 80°C, and several flow coefficients. It must to be pointed out that in the experiments carried out at 80°C it was not possible to reach the cavitation breakdown number, not allowing the detect of the thermal effects.

Figure 4.45 and Figure 4.46 show four graphs of the pump performance. Each one presents a comparison of the pump performance at a fixed flow coefficient and three different temperatures (ambient temperature, around 50°C and 80°C), in order to verify effectiveness of the thermal cavitation scaling criteria.

The accurate analysis of the graphs leads to the following conclusions:

• The nominal head coefficient seems to be reduced at higher temperature (it should be expected to remain the same)

• The cavitation number seems to be shifted towards higher cavitation number at higher temperatures (completely opposite behaviour with respect to what expected in the other pumps tested in the facility)

These results seem to be totally different to what presented in the open literature and to what expected. In order to confirm them, it would be necessary to perform other experimental tests in different facilities. A possible explanation of the reduction of head coefficient could be addressed to the malfunctioning of the sensors or to the temperature dependence of head loss factors such as viscous losses or tip leakage.

Figure 4.44 –MK1 inducer performance curve in cavitating conditions at 2800 rpm rotational speed and 50°C (upper) and 80°C (lower) for several flow coefficients

Figure 4.45 – Comparison between the performance in cavitating conditions at three different temperatures, 2800 rpm and Φ=0.0485 (left), Φ=0.0549 (right)

Φ=0.0037

Φ=0.0073

Φ=0.0037

Figure 4.47 and Figure 4.48 show in more detail the characteristics of the cavitating region which develops in the inducer at this particular value of the flow coefficient.

Figure 4.46 – Comparison between the performance in cavitating conditions at three different temperatures, 2800 rpm and Φ=0.0595 (left), Φ=0.0641(right)

Figure 4.47 – Pictures of the cavitating MK1 inducer at room temperature, 2800 rpm rotating speed and flow coefficient φ = 0.0549, for cavitation numbers σ = 0.214 (left), σ = 0.144 (center) and σ = 0.115 (right).

Figure 4.48 – Pictures of the cavitating MK1 inducer at room temperature, 2800 rpm rotating speed and flow coefficient φ = 0.0549, for cavitation numbers σ = 0.082 (left), σ = 0.069 (center) and σ = 0.049 (right).

Examples of “attached sheet cavitation” are detachable at Φ=0.0229, near the stall conditions and shown in Figure 4.49. The cavity remains attached to the blade in a thin zone, where there is the recirculation of the flow at low pressure. This zone tends to extend in radial direction at lower

cavitation numbers and to become instable even if still attached as results evident in Figure 4.49. A turbulent vortex occurs the cavitating region is highly unstable and oscillating, promoting the separation of the cavity.

Figure 4.49 – Visualization of “attached sheet cavitation” on MK1inducer at room temperature, 2800 rpm rotating speed φ = 0.023 for several cavitation numbers.

Figure 4.50 presents two pictures, made at two different time frames, which depict a detail of the cavity behaviour on the blade surface. It is possible to visualize the “attached sheet cavitation”. Figure 4.51 shows the backflow phenomenon on the MK1 inducer.

Figure 4.50 – Visualization of two phases of the vortex tip blade cavitation on the blade of MK1 inducer at room temperature, 2800 rpm rotating speed φ = 0.023 and σ = 0.1939

Figure 4.51 – Visualization of backflow on the MK1 inducer at room temperature, 2800 rpm rotating speed φ = 0.0549 and σ = 0.0489

4.4.3 Analysis of the cavity length

An other set of experimental tests have been performed on the MK1 inducer in order to further investigate, by the means of optical visualization and analysis, the influence of thermal effects on the steady and unsteady characteristics of cavitation in various flow conditions, with particular attention to cavity length and oscillations. Figure 4.52 illustrates the observed behaviour of the cavity length and oscillations on an inducer blade. Similar plots have been obtained for each blade in several flow conditions. Each plot refers to fixed values of the flow coefficient and water temperature, and presents the normalized cavity length Lcav in the direction of the blade channel as a function of the cavitation number. With the same procedure used for the hydrofoil, a mean value of Lcav along the blade span has been used. Finally, the cavity length has been normalized using the inducer tip diameter. For each value of the cavitation number, the plot shows all the values obtained for Lcav from the 30 frames of the 1 s movie taken during each test run (crossed points). The mean cavity length (solid line) and its maximum and minimum values (dotted lines) are also reported. Analysis of Figure 4.52 shows that the behaviour of the cavity length is very similar to that observed on the NACA 0015 hydrofoil (which will be presented one of the following section). In both cases the amplitude of the cavity oscillations first increases at smaller cavitation numbers until a critical value of σ is reached and then decreases when breakdown or supercavitating conditions are approached. It is also worth noticing that the amplitude of the cavity oscillations peaks when the mean cavity length is about 65% of the azimuthal blade spacing, this condition corresponds to highly unstable cavitation in blade cascades (Tsujimoto et al.). The variations of the cavity length on a typical blade of the inducer are presented in the right side

of the Figure 4.52., where a sequence of six frames taken at σ = 0.204 and the same flow coefficient and water temperature of the left side of the Figure is shown.

Figure 4.52 – Normalized mean, maximum and minimum values of the cavity length on the blade no. 2 of the test inducer as a function of the cavitation number σ at φ = 0.029 and room water temperature (left).

Sequence of six frames showing cavitation on blade no. 2 of the test inducer in the same conditions Figure 4.53 shows a comparison between the cavity lengths observed on the four blades of the inducer at the same flow conditions of the above Figure. It is evident that the blade 2 (corresponding to red curves and points) behaves slightly differently from the other blades, with wider oscillations, higher values of the mean cavity length, and breakdown or supercavitating conditions occurring at a higher value of the cavitation number. This is probably due to some imperfections of the blade surface, in particular of its leading edge, which result in worse cavitation performance.

Figure 4.53 – Normalized mean, maximum and minimum values of the cavity length on the four blades of the test inducer as functions of the cavitation number σ at φ = 0.029 and room water temperature.

Thermal cavitation tests have been carried out, with the same procedure, at the same flow coefficient (φ = 0.029) and higher water temperatures (50 °C and 70 °C), in order to investigate the influence of thermal effects on the unsteady behaviour of inducer cavitation. Some typical results are shown in Figure 4.54 (here presented for blade 1), and indicate that the mean length of the cavity tends to decrease at higher flow temperatures, as expected.

On the other hand, the influence of thermal effects on the oscillations of inducer cavitation is significantly different from trends observed on the NACA 0015 hydrofoil. In particular, the maximum amplitude of the cavity length oscillations seems to remain practically constant regardless of the flow temperature and the intensity of thermal cavitation effects.

Further experiments to better establish this finding, are showing that the frequencies of cavitation oscillations are equally independent of the occurrence of thermal effects (which will be presented in the next section).

Figure 4.54 – Normalized mean, maximum and minimum values of the cavity length on blade no. 1 of the test inducer as functions of the cavitation number σ at φ = 0.029 and three different values of the water

temperature.

As a final consideration, Figure 4.55 presents the mean cavity length on the inducer blade no. 3 as a function of the cavitation number for several values of the flow coefficient and room water temperature. It is possible to note that, as expected, smaller values of the flow coefficient lead to longer cavities, due to a higher value of the incidence angle of the fluid flow. In the plot, the crossed points correspond to 5% head degradation and approximately indicate the inception of the inducer breakdown. It should be noted that, regardless of the value of the flow coefficient, head breakdown initiates at a nearly constant value of the cavity length.

Finally, an other observation can be added: at breakdown the ratio of the cavity length to the azimuthal blade spacing (h) is approximately equal to the critical value for the occurrence of large cavitation instabilities, which effectively promote the blockage of the flow in the blade channels (Brennen).

Figure 4.55 – Normalized mean cavity length on blade no. 3 of the test inducer as a function of the cavitation number σ for room water temperature and several values of the flow coefficient φ . Crossed

points indicate the inception of inducer breakdown.

4.5 Experimental campaign on FAST2 inducer

The fourth set of experimental tests has been carried out in the configuration CPTF (Cavitating Pump Test Facility) on the so called “FAST2” inducer. This prototype was designed by AVIO S.p.A. using the criteria followed for VINCI180 inducer and taking into account the results derived from past experience (VULCAIN MK1 and MK2, ATE, VINCI150).

It was procured during the winter 2004. Its geometry is characterized by a shallow spiral angle, high-solidity and low aspect ratio blading. The FAST2 inducer is of the same type of the one, mounted in the LOX turbopump system in the VINCI engine, the ARIANE 5 ESC-B second stage engine. The main difference is represented by the number of blades: two for the FAST2 inducer and three for the inducer mounted in the VINCI engine. Figure 4.56 presents the a schematic of the propulsion system of ARIANE 5 second stage, while Table 4.9 shows the main characteristics of the VINCI propulsion system.

A picture and a detailed drawing of the FAST2 inducer are shown in Figure 4.57, while the main dimensional characteristics are reported in Table 4.10. The inducer has been machined from an unique piece (unlike FIP120 and FIP162 inducers which have been prepared by welding the blade on a hub of constant diameter).

The FAST2 is a two-bladed stainless steel axial inducer with a tip radius rT=41.1 mm and a profiled, variable-radius hub (15 mm inlet radius, 28 mm outlet radius).The geometry of the FAST2 inducer is very sophisticated as it presents a tapered hub (from15 mm to 28.3 mm) and a tapered blade thickness and has a variable pitch, tip blade angle and radius. The blades are backswept, with variable thickness and nonuniform blade angle. The inlet tip blade angle is 7.38°, the outlet tip blade angle is 21.24° and the tip solidity is 1.59.

Figure 4.56 – The ARIANE5 VINCI engine (Courtesy of Snecma Moteurs).

Figure 4.57 – Different views of the FAST2 inducer FAST2 Geometric Characteristics

Inlet tip radius[mm] 41.1

Inlet hub radius[mm] 15

Outlet hub radius[mm] 28.3

Inlet tip blade angle[deg] 7.38

Inlet medium blade angle[deg] 9.37

Outlet tip blade angle[deg] 17.51

Outlet medium blade angle[deg] 21.24

Tip solidity 1.59

Medium blade chord[mm] 195

N° blade 2

Tip radial clearance[mm] 0.5

Table 4.10 – Experimental test parameters in noncavitating conditions

The next Table presents the operational parameters of the FAST2 inducer at the design point.

FAST2 inducer Operational Parameters

Mass Flow Rate [kg/s] 20.78

Rotational Speed [rpm] 13000

Flow Coefficient (Φ) 0.07

AVIO Flow Coefficient Φ+ [m^3] _1.52

₁₀

−5

Table 4.11 – Operational parameters of the FAST2 inducer at the design point.

In order to allow the experimental campaign on the FAST2 inducer the CPRT was reconfigurated as follows:

1- the optical access and the flanges for the pressure transducers were redesigned in order to take into account the dimensions of the tubes, which were modified due to the reduced dimensions of the FAST2 inducer (the tip diameter is around one half of the VUCAIN inducer one). The tip radial clearance was fixed about 0.4 mm, corresponding to the final configuration of the VINCI engine (Figure 4.59). Figure 4.58 shows the dependence of the inception cavitation number as function of tip clearance in the “unshrouded” inducer. The tip clearance, in fact, effects the inception of the “backflow” cavitation, affecting the drop of the pressure

coefficient and the inducer performance. In this view the choice of the tip clearance results of peculiar importance. According to the Figure the optimum inception cavitation number σi

(minimum value) corresponds to a value of the ratio between the radial tip clearance and the blade height (δ/ h ) of about 0.01. In the case of the FAST2 inducer the parameter δ/ h corresponds to: 0.4 0.015

26.1 h

δ

_{= =}

Figure 4.58 – Cavitation inception number as function of the ratio between the radial clearance and the blade height

Figure 4.59 – Detail of the dynamic transducers mounted on the Plexiglas conduct

2- the volute inside the test section was removed due to the FAST2 inducer rotational direction opposite to the one of the facility. A shaped conduct was introduced in order to direct the flow at the inducer outlet

3- due to the small dimensions of the FAST2 inducer it was necessary to guarantee the breakdown conditions. In this way it is possible to increase the rotational speed (Ω) and reduce the minimum pressure at the pump inlet (p1). As previously mentioned the engine is able to

provide a maximum speed of about 6000 rpm, but in order not to arrive to this limit a planetary gearbox was bought (model PD1010/MN1/3.38 from Brevini company). It is able to multiply the engine rounds of a maximum factor about 3.38. At 6000 rpm, in fact, the engine is able to maintain 1775 rpm. Figure 4.60 shows the planetary gearbox mounted in the facility.

One omokinetic couplings was added in order to avoid misalignments between the pump shaft and the planetary gearbox.

Figure 4.60 – Picture of the planetary gearbox between the test section and the main engine 4- another contribute for assuring the breakdown conditions was obtained by adding several “loss

packages” (Figure 4.61) before the honeycomb, in order to increase the flow losses and decreasing the inlet pump pressure. The pressure losses for each “loss package” resulted 0.04 bar at 3000 rpm

Figure 4.61 – Detailed pictures of the “loss packages” to increase the flow losses

Some concerns were addressed due to the insertion of these “loss packages”. The quality of the water can degrade due to the passage into these loss packages and the cavitation nuclei can increase. During the experimental tests we have not observed these detrimental effects on the water quality. Furthermore it has to be noted that, according to Figure 4.62, the air content in water has a large effect on the onset of cavitation, while it is extremely reduced on the cavitation breakdown.

4.5.1 Noncavitating performance

As in the previous test campaign, the experiments in noncavitating conditions were the first to be carried out to evaluate the inducer performance. The next Table presents the test conditions during the noncavitating experiments on the FAST2 inducer, while Figure 4.63 shows the inducer performance.

Table 4.12 – Experimental test parameters in noncavitating conditions

Figure 4.63 – FAST2 inducer performance in noncavitating conditions at ambient temperature and several rotational speed values

The above Figure demonstrates that the performance curve is fully independent from the rotational speed and then from the Reynolds number, if it the flow is fully turbulent (Re>106_{). If we} compare the FAST2 inducer performance with the VULCAIN inducer performance in noncavitating conditions, it is evident that they are extremely equivalent. The effect of the outlet tip blade angle plays, in fact, a primary role on the inducer performance more than the dimensions and the number of blades. The next Figure presents the comparison between the experimental results and the results obtained by AVIO in a numerical simulation. The theoretical results agrees around the design point, while they don’t match far from it. The parameters used by AVIO are defined by:

Q

Φ

Ω

+ _{= [m}3_{] AVIO flow coefficient (4.2)}

2 p

∆

Ψ

ρ Ω

+ _{= [m}2_{] AVIO pressure coefficient (4.3)}

Engine rotational speed [rpm] 2000 2500 3000

Inlet Pressure [atm] 1.16 1.15 1.13

Temperature [°C] 23 22.3 19.2

Maximum Flow Rate (silent throttle valve fully open)[L/sec] 7.56 6.23 4.89 Minimum Flow Rate (silent throttle valve “close”) [L/sec] 0.28 0.28 0.28

3 5 2 5

10 0.0625( 10 ) 0.0058( 10 ) 0.477

Ψ

+_{⋅ = −}

Φ

+_{⋅ −}

Φ

+_{⋅ + (4.4)}

The (4.4) represents the theoretical curve of the pressure coefficient provided by AVIO.

0 0.5 1 1.5 2 2.5 x 10-5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10 -4 φ+_[m3_] ψ +[m 2] ω=2000 rpm ω=2500 rpm ω=3000 rpm curva AVIO

Figure 4.64 – Comparison between the FAST2 inducer performance according to the experimental results and the theoretical results of AVIO.

Figure 4.65 illustrates the specific speed as function of the flow coefficient for several rotational speeds. 0 0.02 0.04 0.06 0.08 0.1 0.12 0 1 2 3 4 5 6 φ ve lo ci tà s p e c if ic a ω=2000 rpm ω=2500 rpm ω=3000 rpm

Figure 4.65 – Specific speed as function of the flow coefficient at several rotational speeds The next Figure shows the Balje diagram (referred to single stage pumps) in the plane

(

ΩS,rS

)

and a comparison with the results obtained during the experimental tests on the FAST2 inducer in the same plane, it is possible an estimation of the efficiency. The efficiency is around 85-90%.

Figure 4.66 – Comparison between the Balje envelope (ΩS,rS) and the noncavitating performance of the

FAST2 inducer.

4.5.2 Cavitating performance

This section is dedicated to present the results of the experimental tests carried out on the FAST2 inducer in order to analyze the performance in cavitating conditions. The Figure 4.67 presents the performance of the FAST2 inducer in cavitating conditions at ambient temperature and varying the flow coefficient, while Table 4.13 shows the experimental conditions for these experimental tests at a rotational speed of 4000 rpm.

Inducer rotational speed = 4000 rpm

Flow rate (L/sec) Flux Coeff. (Φ) Initial temperature (°C) Final temperature (°C)

8.22 0.090 22.8 23.3 7.58 0.083 23.3 23.8 6.94 0.076 21.0 21.1 6.39 0.070 20.0 20.3 6.03 0.066 19.2 19.6 5.48 0.060 24.8 25.2 4.57 0.050 21.7 22.2 3.65 0.040 25.2 25.6 2.74 0.030 25.6 26.1 1.83 0.020 26.1 26.4 0.91 0.010 26.4 27.2

Figure 4.67 – FAST2 inducer performance curve in cavitating conditions at ambient temperature and 4000 rpm rotational speed for several flow coefficients

In order to confirm the independence of the performance from the rotational speed and then from Reynolds number, the experiments were repeated at a rotational speed of 3500 rpm under the same flow coefficients. The next Table shows the experimental conditions for these experimental tests at a rotational speed of 3500 rpm, while Figure 4.68 presents the comparison between the two experimental tests. Figure 4.69 presents the cavitation number, for which the pressure drops between the 5% to 30% from the regime conditions, as function of the flow coefficient. Figure 4.70 shows the performance of the FAST2 inducer in cavitating conditions at ambient temperature and at flow coefficients around the design point.

Table 4.14 – Experimental test parameters in for the tests of Figure 4.68.

Inducer rotational speed = 3500 rpm

Flow rate (L/sec) Flux Coeff. (Φ) Initial exp. temperature (°C) Final exp. temperature (°C)

7.19 0.090 21.9 22.4 6.64 0.083 22.6 23.0 6.08 0.076 22.6 22.6 5.60 0.070 23.2 23.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.05 0.1 0.15 0.2 0.25 σ ψ φ=0.090 φ=0.083 φ=0.076 φ=0.070 φ=0.066 φ=0.060 φ=0.050 φ=0.040 φ=0.030 φ=0.020 φ=0.010

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 σ ψ φ=0.090 4000 rpm φ=0.083 4000 rpm φ=0.076 4000 rpm φ=0.070 4000 rpm φ=0.090 3500 rpm φ=0.083 3500 rpm φ=0.076 3500 rpm φ=0.070 3500 rpm

Figure 4.68 – FAST2 inducer performance curve in cavitating conditions at ambient temperature and 4000 rpm and 3500 rpm rotational speed for several flow coefficients.

0.07 0.075 0.08 0.085 0.09 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 φ σ 5% 10% 15% 20% 25% 30%

Figure 4.69 – Cavitation number σ, evaluated according to the performance drop between 5% to 30%, as function of the flow coefficient.

Figure 4.70 – FAST2 inducer performance curve in cavitating conditions at ambient temperature and 4000 rpm rotational speed for flow coefficients around the design point.

The Figures between Figure 4.71 and Figure 4.74 present the appearance of cavitation at two different flow coefficients. Each picture corresponds to a point in the σ−ψ plane, in order to understand the influence of the extension of cavitation on the head coefficient. The performance breakdown occurs when the cavitation is sufficiently developed to completely obstruct the blade channel and blocking the low passage. Till this point the cavitation development do not affect the pump performance.

The Figures highlight the different aspect of cavitation corresponding to various flow coefficients. In particular, at low flow rates and low cavitation number the “backflow” cavitation can be envisaged: the vapour bubbles tend to occupy the channel upstream the inducer and to go back the suction line. It was observed that in these conditions, the inlet static pressure tend to rise due to this “backflow” pumping effect. At higher flow coefficients the “backflow” almost disappears: the vortex which leaves the blades is absorbed by the incoming turbulent flow.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 σ ψ φ=0.064 φ=0.066 φ=0.068 φ=0.070 φ=0.072 φ=0.074 φ=0.076 φ=0.078 φ=0.080

Figure 4.71 – FAST2 inducer performance curve in cavitating conditions at ambient temperature and

Φ=0.010.

Figure 4.72 – FAST2 inducer performance curve in cavitating conditions at ambient temperature and

Figure 4.73 – FAST2 inducer performance curve in cavitating conditions at ambient temperature and

Φ=0.070.

Figure 4.74 – FAST2 inducer performance curve in cavitating conditions at ambient temperature and

Φ=0.090.

Figure 4.75 presents the development of cavitation in the FAST2 inducer at the design point (φ=0.07) through several pictures taken at various cavitation numbers. During the experimental tests a very particular phenomenon was observed. As the flow coefficient increases, cavitation inception has been observed to move from the leading edge of the blades towards their trailing edge. Cavitation develops in the backward direction and, in a less extensive way, on the pressure side of the leading edge. This phenomenon, not typically observed on the inducers used for space rockets applications, is

thought to be due to the blade camber of the FAST2 inducer and to the corresponding shape of the pressure profile for lower incidence angles and higher flow coefficients. Conversely, when the flow coefficient decreases cavitation on the trailing edge becomes less extensive and another cavitating region develops at the leading edge. The cavitating region developing from the trailing edge, still present at flow coefficients higher than about 1.2 times the nominal one, completely disappears at lower values of the flow coefficient. Figure 4.76 shows some pictures of trailing edge cavitation on the inducer at high flow coefficients and the appearance of regular leading edge cavitation at lower values of φ.

Figure 4.75 – Pictures of the FAST2 inducer at ambient temperature and Φ=0.070.

Figure 4.76 – Pictures of the FAST2 inducer at ambient temperature and different flow rates (rotational speed =3500 rpm and inlet static pressure=0.11 bar).

5 I

NDUCER

A

NALYTICAL

M

ODELS

The following section is dedicated to a description of three different analytical models introduced in order to evaluate the inducer performance in noncavitating conditions. The analytical models are: an “ideal” model, a quasi-threedimensional model and the “ throughflow” model. In the last part of the section a comparative analysis between the results of the experimental tests and analytical models will be described.

5.1 Introduction

As previously pointed out in the previous sections, the inducer contains fewer blades (usually 3 to 4) than conventional pumps. Long and narrow blade passages provide the time and space for the collapse of the cavitation bubbles and for gradual addition of energy. The blades in most practical inducers used in rocket pumps wrap around almost 360 deg. The purpose of the inducer is to pressurize the flow sufficiently to enable the main pump to operate satisfactory. The major characteristic features of the inducer are low flow coefficient (0.05 to 0.2), large stagger angle (70 to 85 deg) and high solidity blade (ratio between the blade chord and the blade spacing), for the presence of few blades of very long chord. The resulting configuration, even though beneficial from the point of view cavitation, results in highly viscous, turbulent and non adiabatic (due to the blade cooling) flow inside the passages. Many analyses have been carried out for the prediction of the inducer flow field in noncavitating and cavitating conditions.

Two classical analytical models, the “ideal” and “quasi-threedimensional” models, were developed by Brennen and his Team for the prediction of the inducer performance in noncavitating conditions, and will be presented in this section. These models allow to determine the pressure

coefficient as function of the flow coefficient considering the total pressure pump rise, using very strong simplifications.

The “throughflow” model, which have been developed since my thesis work for the Laurea degree and further developed during my Ph.D. research, will be described in detail. Unlike the classical models, it allows, under still very strong assumptions, to evaluate the pressure coefficient as function of the flow coefficient in terms of the static pressure pump rise, leading to an easier comparison with the experimental results. The pressure transducers measure the static pressure and the performance curves, presented in the last section, are based on the static pressure. The “throughflow” model allows also the prediction of the radial and circumferential flow velocity at the exit section of the inducer.

5.2 The “ideal” model

The “ideal” model introduced by Acosta-Brennen is the first one to be presented. The following assumptions were taken into account:

- incompressible fluid - axialsymmetric flow - steady flow - infinite thin blades - negligible viscous loss

As previously pointed out, the pump power can be written as:

( )

t

(

t2 t1

)

P m= 

∆

h =m h −h (5.1)

where :

m= ρQ : mass flow rate

( )

ht

∆

:the total enthalpy difference between the exit and the inlet

from the Euler equation it is possible to obtain (v_θ is the circumferential velocity along the circumferential coordinate θ)

2 2 1 1

( )

P m= 

Ω

r v_θ −r v_θ

with the hypothesis of the only axial inlet velocity (v_θ1= 0): 2 2

P m= 

Ω

r v_θ (5.2)

If the fluid is incompressible and the process isentropic, the total enthalpy is

∆

h_t =

∆

p_t/

ρ

, it’s possible to obtain from (5.1) and (5.2):

2 2 t/

r v_θ p

If we assume that the exit flux is parallel to the blade (deviation angle=0) it is possible to obtain 2

v_θ from the exit velocity triangle and then the performance curve in noncavitating conditions:

( )

2 1 cot _b

Ψ

= −

Φ

β

(5.4)

In this model the inlet and exit conditions have been considered uniform, unlike what happens in the real case, the equations (5.1) e (5.4) are then referred to each meridional streamtube and should be integrated to obtain the correct pump characteristic curve. Usually the only equation (5.4) is considered in order to attain a rough evaluation of the pump performance. Figure 5.1 shows the comparison between the FAST2 performance in noncavitating conditions obtained by the “ideal” model and the experimental results ( the exit blade angle was considered the medium one).

Figure 5.1 – Comparison between the FAST2 performance in noncavitating conditions obtained by the “ideal” model and the experimental results

5.3 The quasi-threedimensional model

This model was developed by Brennen & Al to analyze the difficulties to analytically evaluate the performance of the turbomachines due to their complex geometry. This model is called quasi-three-dimensional model.

It assumes that the flow in a real turbomachine could be synthesized using a series of these two-dimensional solutions for each meridional annulus. In doing so it is implicitly assumed that each annulus corresponds to a streamtube such as depicted in Figure 5.2. The streamsurfaces are considered axisymmetric, and, therefore, the more complicated three-dimensional aspects of the secondary flows axis neglected. Nevertheless, this method allows the calculation of useful turbomachine performance characteristics, particularly under circumstances in which the complex secondary flows are of less importance, such as close to the design condition. When the turbomachine is operating far from the

design condition, the flow within a blade passage may have streamsurfaces that are far from axisymmetric. The method also assumes that the geometric relations between the inlet location, r1, and

thickness, dr1, and the discharge thickness, dn, and location, r2, are known a priori.

Figure 5.2 – Schematic of a meridional streamtube[Brennen] According to Figure 5.2 the mass balance equation can be written:

( )(

)

1 1 1 2 2 cos

m m H

v r dr =v n R +n

θ

dn (5.5)

If we use the hypothesis of radial equilibrium, which assumes that all of the terms in the equation of motion normal to the axisymmetric streamsurface are negligible, except for the pressure gradient and the centrifugal acceleration terms, so that

2 1 dp v dr r ϑ

ρ

= (5.6)

the pressure distribution at the exit plane can be written:

(

)

2 2 2 2 cos 1 cos H v p n R n ϑ

ϑ

ρ

θ

∂ ₌ ∂ + (5.7)

The hypothesis of radial equilibrium relates the pressures in the different streamtubes upstream of the rotor (or stator), and a similar condition to connect the pressures in the streamtubes downstream of the rotor (or stator). Considering the variation of the discharge blade angle, βb2(n), with position, for

example helical blades with zero deviation angle, the formulation of the problem is completed and it is possible to eliminate the term p2(n) through the Bernoulli equation written in a rotating system ( w is

the relative velocity in the rotating system).

2 2 2 2 2 2 1 2 1 1 2 2 2p 2p w r

Ω

w r

Ω

ρ

+ − =

ρ

+ − (5.8)

Using the velocity triangle and the continuity equation it is possible to arrive to a single equation with variable vm2(n).

Assuming an uniform flow at the inlet and integrating at the outlet surface, then:

(

2 1

)

2 2 1 tip ₂ hub n t t t m n p p p r v dn Q

∆

=

_∫

−

π

(5.9) In dimensionless form: 1 2 2 3 2

Ψ Σ Σ Φ

= + +

Σ Φ

(5.10) or 3 1 2 1 2 1 2 1 1 A A A A

Σ

Ψ Σ

Σ Φ

Φ

= + + (5.11) with:

(

)

2 2 2 2 2 2 * * * 2 4 3 2 3 2 _{* *} 2 1 3 2 2 2

cot sin cos

1 ln ln cos tan 1 ln cot tan bT bT bT bT bT bT bT

Γ

β

Γ

β

β

Σ

Γ

Γ

Γ

Γ

β

Σ

β

Γ

Γ

Σ

Σ

β

Σ

β

⎧ ⎡ ⎤ = + ⎪ ⎢ ⎥ ⎣ ⎦ ⎪ ⎪ _{⎡ ⎤} ⎪ _{= ⎢ − ⎥} ⎨ _{⎢ ⎥} ⎪ _{⎣ ⎦} ⎪ = − − ⎪ ⎪ ⎩ and 2 2 2 1 H T R R

Γ

_{= − ⎜}⎛ ⎞_⎟ ⎝ ⎠ ; * 2 2 1 cos _bT

Γ

= −

Γ

β

; ₁ 1 T1 Q A R

Φ

Ω

= ; ₂ 2 T2 Q A R

Φ

Ω

=

A1 and A2 are the inlet and outlet area respectively.

As in the previous case the result depend on the geometry of the pump. This model is more precise than the previous one, but the pressure coefficient still remain two times the experimental one, also due to the fact that the pressure coefficient in the model is calculated taking into account the total pressure rise. Figure 5.3 shows the comparison between the FAST2 performance in noncavitating conditions obtained by the “quasi-threedimensional” model and the experimental results (the exit blade angle was considered the medium one).