università degli studi di pisa - core · a test facility called cprtf (cavitating pump...

Università degli Studi di Pisa

DOTTORATO DI RICERCA IN INGEGNERIA AEROSPAZIALE CURRICULUM: PROPULSIONE AEROSPAZIALE

XVIII CICLO

EXPERIMENTAL STUDY OF CAVITATION AND FLOW INSTABILITIES IN SPACE ROCKET TURBOPUMPS AND

HYDROFOILS

Candidata

Cristina Bramanti

Tutore Prof. Luca d’Agostino

Dipartimento di Ingegneria Aerospaziale

Via G. Caruso, 56122 – Pisa

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ABSTRACT

The present work is aimed at the description of the research activity performed by the author during the years 2003-2005 in the framework of the Ph.D. course in Aerospace Engineering at Pisa University.

The research activity was mainly focused on the experimental characterization of the dynamics of cavitation, and its impact on the development of fluid dynamic and rotordynamic instabilities of high performance turbopumps for space applications.

The experimental tests were carried out at Centrospazio Research Laboratory by means of a test facility called CPRTF (Cavitating Pump Rotordynamic Test Facility), which is based on a water loop specifically designed and engineered for the experimental analysis of turbopump cavitation and cavitation-induced instabilities in similar fluid dynamic and thermal cavitation conditions, in order to accurately reproduce the pump operation with common liquid propellants used in space propulsion rockets (LH2, LOX, NTO, MMH, etc.).

The realization, the assembly and validation of the facility and the design of the reconfiguration of the pump loop into a small water tunnel for thermal cavitation were one the subjects of the Master thesis of the author, while the experiments for investigating cavitation phenomena on test bodies by the use of the hydrodynamic tunnel were carried out during the first ten mounths of the Ph.D. research activity.

After a brief overview on space rocket turbopumps in the first Chapter and on the cavitation phenomenon in the second Chapter, useful for understanding the motivations and the aims of the research activity, the test facility and its alternative configurations are described in the third Chapter. The fourth and the sixth Chapters are dedicated to illustrate the main results of the experiments carried out for the characterization of the performance and the flow instabilities of four axial inducers: two commercial ones, the one manufactured by Avio S.p.A. and installed in the liquid oxygen turbopump of the Ariane Vulcain MK1 rocket engine and the one (also produced by Avio S.p.A.) which will be used in the liquid oxygen pump of the VINCI engine. The fifth Chapter describes an analytical model which has been developed to evaluate the inducer performance in non-cavitating conditions, while the seventh Chapter presents the preliminary experiments carried out in preparation for the rotordynamic experiments with a dynamometer. The main results of an experimental campaign carried out on a NACA 0015 hydrofoil is also be presented in the eighth Chapter.

Finally, the last Chapter is devoted to the description of the main additional research activities to which the author collaborated during the three years of the Ph. D. course.

The author would like to express her gratitude to Prof. Luca d’Agostino from Pisa University, who supervised her Master and Ph.D. research activity, for his constant support and precious advice. The final thoughts are dedicated to the colleagues/friends who collaborated with the author during these amazing years and made possible what seemed impossible at the time when the author first arrived at Centrospazio to carry out her Master thesis: in particular, the other Ph.D. student Angelo Cervone, with whom the author collaborated closely during these years, and all undergraduate students Renzo Testa, Nicola Saggini, Lucio Torre and Riccardo Parenti, who supported with their enthusiasm and work the research activities.

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Cosi’ in America quando il sole va giu’e io siedo sul vecchio diroccato molo sul fiume a guardare i lunghi, lunghissimi cieli sopra il New Jersey e avverto tutta quella terra nuda che si svolge in un’unica incredibile enorme massa fino alla costa occidentale, e tutta quella strada cha va, tutta la gente che sogna nell’immensità’ di essa e so che nello Iowa a quell’ora i bambini stanno certo piangendo nella terra in cui lasciano pianger i bambini, e che stanotte usciranno le stelle, e non sapete che Dio e’ l’Orsa Maggiore?, e la stella della sera deve star tramontando e spargendo il suo fioco scintillio sulla prateria, il che avviene proprio prima dell’arrivo della notte completa che benedice la terra, oscura tutti i fiumi, avvolge i picchi e rimbocca le ultime spiagge, e nessuno, nessuno sa quel che succederà di nessun altro se non il desolato stillicidio del diventar vecchi, allora penso a Dean Moriarty, penso persino al vecchio Dean Moriarty, il padre che mai trovammo, penso a Dean Moriarty.

Jack Kerouac ‘On the Road’

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A coloro che hanno creduto in me ed aiutato

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LIST OF CONTENTS

1 INTRODUCTION................................................................................................................................... 1

1.1 BRIEF HISTORY OF ROCKETS............................................................................................................. 1 1.2 GENERALITIES ON SPACE ROCKET TURBOPUMPS.............................................................................. 4 1.3 GEOMETRY OF A GENERALIZED TURBOPUMP ................................................................................. 10 1.4 TURBOPUMP PERFORMANCE........................................................................................................... 13 1.5 OBJECTIVES OF THE RESEARCH ACTIVITY ...................................................................................... 18

2 CAVITATION....................................................................................................................................... 21

2.1 CAVITATION.................................................................................................................................... 21 2.1.1 Cavitation undesired effects ...................................................................................................... 26

2.2 PARAMETERS FOR THE CHARACTERIZATION OF CAVITATION IN TURBOPUMPS.............................. 30 2.3 SCALING OF THE PUMP PERFORMANCE ........................................................................................... 32 2.4 FLOW INSTABILITIES GENERATED BY CAVITATION ........................................................................ 34

2.4.1 The rotating stall ....................................................................................................................... 35 2.4.2 The rotating cavitation .............................................................................................................. 36 2.4.3 The alternate blade cavitation................................................................................................... 37 2.4.4 The surge ................................................................................................................................... 38 2.4.5 The auto-oscillation................................................................................................................... 38 2.4.6 Rotordynamic instabilities......................................................................................................... 39

3 THE CPRTF.......................................................................................................................................... 41

3.1 INTRODUCTION ............................................................................................................................... 41 3.2 CPTF CONFIGURATION................................................................................................................... 45

3.2.1 The tank...................................................................................................................................... 48 3.2.2 The fill-drain and pressurization/depressurization circuits ..................................................... 49 3.2.3 The supporting structure ........................................................................................................... 51 3.2.4 The flow straighteners and the elastic coupling ....................................................................... 52 3.2.5 The flowmeters........................................................................................................................... 53 3.2.6 The “Silent Throttle Valve” ...................................................................................................... 53 3.2.7 The main engine and omokinetic coupling ............................................................................... 54 3.2.8 The test section .......................................................................................................................... 55

3.3 CPRTF CONFIGURATION ................................................................................................................ 56 3.3.1 The auxiliary motor ................................................................................................................... 58 3.3.2 The rotating dynamometer ........................................................................................................ 59

3.4 THE CI2TF AND CI2RTF CONFIGURATIONS ................................................................................... 60 3.5 THE DATA ACQUISITION SYSTEM .................................................................................................... 61

3.5.1 The piezoelectric transducers.................................................................................................... 62

4 TURBOPUMPS PERFORMANCE.................................................................................................... 65

4.1 INTRODUCTION ............................................................................................................................... 65 4.2 OVERVIEW OF THE EXPERIMENTAL VALIDATION OF THE FACILITY................................................ 68

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4.2.1 Experimental tests in noncavitating conditions.........................................................................71 4.2.2 Experimental tests in cavitating conditions...............................................................................74

4.3 EXPERIMENTAL CAMPAIGN ON FIP162 TURBOMACHINERY ...........................................................79 4.3.1 Noncavitating performance .......................................................................................................80 4.3.2 Cavitating performance .............................................................................................................82

4.4 EXPERIMENTAL CAMPAIGN ON MK1 INDUCER...............................................................................84 4.4.1 Noncavitating performance .......................................................................................................87 4.4.2 Cavitating performance .............................................................................................................89 4.4.3 Analysis of the cavity length ......................................................................................................95

4.5 EXPERIMENTAL CAMPAIGN ON FAST2 INDUCER ...........................................................................98 4.5.1 Noncavitating performance .....................................................................................................103 4.5.2 Cavitating performance ...........................................................................................................105

5 INDUCER ANALYTICAL MODELS..............................................................................................113

5.1 INTRODUCTION..............................................................................................................................113 5.2 THE “IDEAL” MODEL .....................................................................................................................114 5.3 THE QUASI-THREEDIMENSIONAL MODEL ......................................................................................115 5.4 THE “THROUGHFLOW” MODEL......................................................................................................118

5.4.1 Effect of the solidity on the pump performance.......................................................................125 5.4.2 Flow losses evaluation.............................................................................................................127

5.5 CONCLUSIONS ...............................................................................................................................129

6 TURBOPUMPS CAVITATION INSTABILITIES ........................................................................133

6.1 INTRODUCTION..............................................................................................................................133 6.2 CHARACTERIZATION OF THE FLOW INSTABILITIES IN FIP162 INDUCER .......................................135

6.2.1 Influence of thermal cavitation effects.....................................................................................140 6.3 CHARACTERIZATION OF THE FLOW INSTABILITIES IN THE MK1 INDUCER ...................................141 6.4 CHARACTERIZATION OF THE FLOW INSTABILITIES IN THE FAST2 INDUCER ................................145

6.4.1 Investigation of secondary flow instabilities ...........................................................................154 6.5 SUMMARY OF THE DETECTED INSTABILITIES ................................................................................157 6.6 HIGH SPEED CAMERA EXPERIMENTAL TESTS ................................................................................158

6.6.1 Integrated system for the optical analysis of the cavitating flow............................................158 6.6.2 Image Processing Algorithm ...................................................................................................161

6.6.2.1 Results................................................................................................................................................. 164 6.6.3 Conclusion................................................................................................................................168

7 FAST2 INDUCER ROTORDYNAMIC TESTS .............................................................................169

7.1 INTRODUCTION..............................................................................................................................169 7.2 EXPERIMENTAL TESTS IN NONCAVITATING CONDITIONS ..............................................................170 7.3 EXPERIMENTAL TESTS IN CAVITATING CONDITIONS .....................................................................173 7.4 WHIRLING ECCENTRICITY INSTABILITIES......................................................................................176

8 NACA0015 HYDROFOIL EXPERIMENTS...................................................................................179

8.1 INTRODUCTION..............................................................................................................................179 8.2 THE THERMAL CAVITATING TUNNEL (TCT CONFIGURATION) ....................................................184

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8.2.1 The effect of lateral constrains................................................................................................ 187 8.3 EXPERIMENTAL RESULTS.............................................................................................................. 189

8.3.1 Pressure coefficient ................................................................................................................. 189 8.3.2 Cavity oscillations ................................................................................................................... 192 8.3.3 Thermal effects on the pressure drop...................................................................................... 199

9 OTHER RESEARCH ACTIVITIES................................................................................................ 201

9.1 HYDROGEN PEROXIDE IN SPACE APPLICATIONS ........................................................................... 201 9.2 HYDROGEN PEROXIDE AS PROPELLANT FOR MONOPROPELLANT ROCKET................................... 206 9.3 HYDROGEN PEROXIDE-ETHANE PROPELLANTS FOR BI-PROPELLANT ROCKET ENGINES............... 211

9.3.1 Introduction ............................................................................................................................. 211 9.3.2 Fuel Vapor Pressurization (FVP) principle of operation ...................................................... 213

9.4 SOME TARGET MISSIONS FOR HP-BASED THRUSTERS .................................................................. 217 9.5 EXPERIMETAL CHARACTERIZATION OF ADVANCED MATERIALS FOR THE CATALYTIC

DECOMPOSITION OF HYDROGEN PEROXIDE ......................................................................................................... 218 9.5.1 Experimental apparatus for characterizing the catalyst: the test bench ............................... 220

9.5.1.1 Analytical Model of the Test Bench...................................................................................................221 9.5.2 Experimental results................................................................................................................ 223

10 CONCLUSIONS ................................................................................................................................. 227

11 REFERENCES.................................................................................................................................... 231

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LIST OF FIGURES

Figure 1.1 – Comparison between pressure fed systems and turbopump systems...................................5 Figure 1.2 – Schematic of a liquid propellant rocket ...............................................................................5 Figure 1.3 – Typical feeding cycles for turbopump systems....................................................................6 Figure 1.4 – Schematic of the high pressure turbopumps of the Space Shuttle Main Engine. ................8 Figure 1.5 – Cutaway views of several representative turbopumps. Clockwise from the top: the Mark

3, used in the Atlas, Thor, Jupiter and H-1 engines; the SSME HPF turbopump; the Marl 49F, used in the OTV; and the Mark 15F, used with the J-2....................................................................8

Figure 1.6– The liquid oxygen turbopump of the Vulcain 1 engine. .....................................................10 Figure 1.7– Sketch of the liquid oxygen turbopump (left) and the liquid hydrogen turbopump of the

Vulcain 1 engine (FIAT AVIO courtesy).......................................................................................10 Figure 1.8 – Sketch of a typical centrifugal turbopump.........................................................................11 Figure 1.9 – Cross-sectional view through the axis of a pump impeller (Brennen, 1994).....................11 Figure 1.10 – Developed meridional surface and velocity triangle (left side) blade detail (right)

(Brennen, 1994)..............................................................................................................................12 Figure 1.11 – Influence of the blade twisting on the velocity profile (Hill 1965)..................................12 Figure 1.12 – Schematic section of a typical centrifugal turbopump (Sutton, 1992).............................12 Figure 1.13 – Characteristic curve in noncavitating conditions of the inducer VII (Bhattacharyya,

1994) ..............................................................................................................................................15 Figure 1.14 – Comparison of calculated efficiency contours with test data on centrifugal pumps (Balje)

........................................................................................................................................................16 Figure 1.15 – Comparison of calculated efficiency of axial pumps (Balje)...........................................16 Figure 1.16 – Ranges of specific speed for typical turbomachines and typical pump geometries for

different design speeds (Sabersky, Acosta, Hauptmann) ...............................................................17 Figure 1.17 – Best efficiency turbopump diagram.................................................................................17 Figure 1.18 – A centrifugal pump impeller, “X”, tested at Caltech (Franz, 1989) ...............................17 Figure 1.19 – Two geometry of axial inducer (Brennen, 1994).............................................................18 Figure 1.20– The liquid oxygen turbopump of the LE-7 engine (left side); repechage of the Japanese

launcher H-II (right side)................................................................................................................19 Figure 1.21– View of the catastrophic effects of cavitation inside Hoover Dam (AZ). ........................19 Figure 2.1 – Generic phase diagram in the Temperature-Pressure plane...............................................22 Figure 2.2 – The supercavitating vehicle (left). The Russian supercavitating torpedo Shkval (right) ...23 Figure 2.3 – Types of cavitation in an unshrouded impeller (Brennen, 1994).......................................24 Figure 2.4 –Impeller caviation regions. .................................................................................................24 Figure 2.5 – Tip vortex cavitation on a marine propeller (Kuiper, 2001). .............................................25 Figure 2.6 –Cavitation on a marine propeller (Duttweiler). ...................................................................25 Figure 2.7 – Bubble cavitation on a hydrodynamic test body (Brennen, 1995).....................................25 Figure 2.8 – Partial cavitation (a) and supercavitation (b) on a profile (Brennen, 1995).......................26 Figure 2.9 – Bubble cavitation (left) and supercavitation (right) on a spherical test body (Brennen,

1995). .............................................................................................................................................26 Figure 2.10 – Centrifugal Pump Noise (Pearsall) ..................................................................................28 Figure 2.11 – Local damage due to cavitation erosion on the blades of a pump (Brennen, 1994). .......29

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Figure 2.12 – Extensive damage due to cavitation erosion on the blades of a pump (Brennen, 1994). 29 Figure 2.13 – Typical cavitating performance of a pump (Brennen, 1994). ......................................... 30 Figure 2.14 –Cavitating performance of “X” impeller for different flow coefficients (Brennen, 1994).

....................................................................................................................................................... 31 Figure 2.15 – Typical cavitating performance of a centrifugal pump at various temperatures (Brennen,

1994).............................................................................................................................................. 32 Figure 2.16 – The effect of tip clearance on the cavitating performance of an inducer (Brennen, 1994).

....................................................................................................................................................... 33 Figure 2.17 – Various modes of cavitating flow in a 12° helical inducer as a function of cavitation

number and flow coefficient.......................................................................................................... 35 Figure 2.18 – Schematic of a stall cell in a cascade of blades (Brennen, 1994).................................... 35 Figure 2.19 – Occurrence of rotating cavitation and auto-oscillation in the performance of a cavitating

inducer (Brennen, 1994). ............................................................................................................... 36 Figure 2.20 – Example of alternate blade cavitation (Tsujimoto, 2001) ............................................. 37 Figure 2.21 – Schematic of stable and unstable characteristic curves of a pumping system (Brennen,

1994).............................................................................................................................................. 38 Figure 2.22 – Cavitation performance of the SSME low pressure LOX pump model, showing the

onset and approximate desinence of the auto-oscillation at 6000rpm (from Braisted and Brennen 1980).............................................................................................................................................. 39

Figure 2.23 – Ratio of the auto-oscillation frequency to the pump rotating speed, as a function of the latter, for an helical inducer (Brennen, 1994)................................................................................ 39

Figure 3.1 – Picture of the test facility .................................................................................................. 42 Figure 3.2 – The facility operational envelope in the specific speed-specific diameter plane .............. 43 Figure 3.3 – Water temperature needed in the CPRTF for scaling pumps operating with different fluids

at a Reynolds number equal to 106, as a function of the Reynolds number in the real pump. ...... 44 Figure 3.4 – Water temperature needed in the CPRTF for scaling pumps operating with liquid oxygen,

as a function of the Reynolds number in the real pump and in the test model. ............................. 44 Figure 3.5- CPTF schematic.................................................................................................................. 46 Figure 3.6 - CPTF schematic................................................................................................................. 48 Figure 3.7- Schematic view of the tank................................................................................................. 49 Figure 3.8- Schematic of fill-drain circuit ............................................................................................. 50 Figure 3.9- Schematic of pressurization/depressurization circuit.......................................................... 50 Figure 3.10 – The system for the regulation of the position of the pipes (left) and the mechanism for

the assembling/disassembling of the suction line (right)............................................................... 52 Figure 3.11- Schematic of the flow straighteners.................................................................................. 52 Figure 3.12- Schematic view of the elastic coupling............................................................................. 52 Figure 3.13- Picture of the flowmeter 8732C from Fisher Rosemount (modello da 6”)....................... 53 Figure 3.14- Silent ThrottleValve.......................................................................................................... 54 Figure 3.15- The main engine and the omokinetic coupling between the main engine and the pump

shaft ............................................................................................................................................... 54 Figure 3.16- Schematic of the test section............................................................................................. 55 Figure 3.17- Schematic view of the test section .................................................................................... 55 Figure 3.18 – Schematic of the test section, the motors and the transmission in the CPRTF. .............. 56 Figure 3.19- Schematic of the auxiliary engine disposition in the facility ............................................ 57

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Figure 3.20- Schematic of the cynematic mechanism and eccentricity vectorial composition..............57 Figure 3.21 – Cut-off drawing of the CPRTF test section. ....................................................................58 Figure 3.22- Schematic view from the rear part of the CPRTF .............................................................58 Figure 3.23 – The auxiliary motor with the CPRTF omokinetic coupling (left) and detail of the

transmission belt (right). ................................................................................................................59 Figure 3.24 – The rotating dynamometer (left) and detail of one of the measuring posts (right). .........59 Figure 3.25 – The test bench used for the calibration of the rotating dynamometer..............................60 Figure 3.26 – Schematic of the Plexiglas conduct with the pressure sensors ........................................60 Figure 3.27 – The piezoelectric transducers installed on the Plexiglas inlet section. ............................61 Figure 3.28 – Schematic of the piezoelectric effect in a quartz crystal..................................................62 Figure 3.29 – Schematic drawing of the M112A22 piezoelectric transducers (left) and detail of their

installation on the Plexiglas inlet section (right). ...........................................................................62 Figure 3.30 – Schematic of the possible radial mounting of the dynamic pressure transducers. ...........63 Figure 3.31 – Schematic of the dynamic pressure transducers set up (left) and picture of the Plexiglas

conduct with the dynamic pressure transducers (right)..................................................................63 Figure 3.32 – Picture of the test section and detail of the pressure transducers positions. ....................63 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.....................................................................................................................................67

Figure 4.2 – Detailed drawing of the FIP 120 inducer. ..........................................................................68 Figure 4.3 – Picture of the FIP 120 impeller and casing. .......................................................................69 Figure 4.4 – Picture of the FIP 120 inducer (top) and impeller (lower side) .........................................69 Figure 4.5 – FIP centrifugal impeller head (m) as function of the volumetric mass flow (m3/h) at

rotational speed of 1450 rpm..........................................................................................................70 Figure 4.6 – Pressure coefficient and efficiency as function of flow coefficient in the FIP 120 impeller.

........................................................................................................................................................70 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)..............................................................................................................................................70

Figure 4.8 –Performance of the FIP120 impeller in noncavitating conditions and comparison with the data provided by F.I.P. company....................................................................................................71

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).......72

Figure 4.10 – Comparison between performance of the pump system impeller+inducer and the only impeller ..........................................................................................................................................72

Figure 4.11 – Performance of the FIP120 inducer in noncavitating conditions.....................................73 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).........................74 Figure 4.13 – Impeller cavitating performance curve for several flow coefficients at ambient

temperature and rotational speed 2000rpm ....................................................................................75 Figure 4.14 – Impeller+inducer cavitating performance curve for several flow coefficients at ambient

temperature and rotational speed 2000 rpm ...................................................................................75 Figure 4.15 – Inducer cavitating performance curve for several flow coefficients at ambient

temperature and rotational speed 2000 rpm ...................................................................................76

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Figure 4.16 – Comparison between the breakdown coefficient of the impeller and impeller+inducer (left) and the inducer (right) at several flow coefficient................................................................ 76

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..... 77

Figure 4.18 – Impeller+inducer cavitating performance curve for several temperatures and rotational speed 2000rpm............................................................................................................................... 77

Figure 4.19 – Water vapor pressure as function of the temperature...................................................... 78 Figure 4.20 – Cavitation development in the FIP120 inducer for several cavitation numbers and a fixed

flow coefficient (φ=0.07)............................................................................................................... 78 Figure 4.21 – Effects of cavitation detected after the test campaign on the FIP120 inducer ................ 79 Figure 4.22 – The FIP162 inducer......................................................................................................... 79 Figure 4.23 – Detailed drawing of the FIP162 inducer. ........................................................................ 80 Figure 4.24 – FIP162 noncavitating performance curve for several rotational speed values................ 81 Figure 4.25 – Specific speed (left) and incidence angle at medium radius (right) as function of the flow

coefficient at several rotational speeds .......................................................................................... 81 Figure 4.26 – Comparison between the Balje envelope (ΩS,rS) and the noncavitating performance of

the FIP162 inducer. ....................................................................................................................... 82 Figure 4.27 – FIP162 performance curve in cavitating conditions at several flow coefficients and

ambient temperature ...................................................................................................................... 82 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)................................................... 83 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)................................................... 83 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). .................................................................................................................................... 83

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). .................................................................................................................................... 84

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). .................................................................................................................................... 84

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). .................................................................................................................................... 84

Figure 4.34 – The ARIANE 5 first stage liquid propulsion system (left), Vulcain1 (center) and Vulcain2 (right), (Courtesy of Snecma Moteurs). ......................................................................... 85

Figure 4.35 – Picture of the MK1 inducer............................................................................................. 86 Figure 4.36 – Geometry and dimensions of the MK1 inducer. ............................................................. 86 Figure 4.37 – MK1 performance in noncavitating conditions at ambient temperature and several

rotational speed values .................................................................................................................. 87 Figure 4.38 – Specific speed (left) and incidence angle at medium radius (right) as function of the flow

coefficient at several rotational speed ........................................................................................... 88

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Figure 4.39 – Comparison between the Balje envelope (ΩS,rS) and the noncavitating performance of the MK1 inducer. ...........................................................................................................................89

Figure 4.40 – Hydraulic efficiency of the MK1 inducer as a function of the flow coefficient. .............89 Figure 4.41 – MK1 inducer performance curve in cavitating conditions at ambient temperature and

2800 rpm rotational speed for several flow coefficients ................................................................90 Figure 4.42 – Development and inception of cavitation in the MK1 inducer at Φ=0.0549 and ambient

temperature.....................................................................................................................................90 Figure 4.43 – Development and inception of cavitation in the MK1 inducer at Φ=0.0037 and ambient

temperature.....................................................................................................................................91 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 ................................................92 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) ...................................................92 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) ....................................................93 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). ...............................................................................................................................93

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). ...............................................................................................................................93

Figure 4.49 – Visualization of “attached sheet cavitation” on MK1inducer at room temperature, 2800 rpm rotating speed φ = 0.023 for several cavitation numbers. .......................................................94

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 ........................94

Figure 4.51 – Visualization of backflow on the MK1 inducer at room temperature, 2800 rpm rotating speed φ = 0.0549 and σ = 0.0489 ...................................................................................................95

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 ........................................................................................................................96

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.....................................................................................................................................96

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. ....................................................................................................................97

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. ........................................................98

Figure 4.56 – The ARIANE5 VINCI engine (Courtesy of Snecma Moteurs). ......................................99 Figure 4.57 – Different views of the FAST2 inducer...........................................................................100 Figure 4.58 – Cavitation inception number as function of the ratio between the radial clearance and the

blade height ..................................................................................................................................101

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Figure 4.59 – Detail of the dynamic transducers mounted on the Plexiglas conduct.......................... 101 Figure 4.60 – Picture of the planetary gearbox between the test section and the main engine ........... 102 Figure 4.61 – Detailed pictures of the “loss packages” to increase the flow losses ............................ 102 Figure 4.62 – Dependence of the cavitation number σ from the air content in water (Brennen, 1994).

..................................................................................................................................................... 102 Figure 4.63 – FAST2 inducer performance in noncavitating conditions at ambient temperature and

several rotational speed values .................................................................................................... 103 Figure 4.64 – Comparison between the FAST2 inducer performance according to the experimental

results and the theoretical results of AVIO. ................................................................................ 104 Figure 4.65 – Specific speed as function of the flow coefficient at several rotational speeds ............ 104 Figure 4.66 – Comparison between the Balje envelope (ΩS,rS) and the noncavitating performance of

the FAST2 inducer. ..................................................................................................................... 105 Figure 4.67 – FAST2 inducer performance curve in cavitating conditions at ambient temperature and

4000 rpm rotational speed for several flow coefficients ............................................................. 106 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. ..................................... 107 Figure 4.69 – Cavitation number σ, evaluated according to the performance drop between 5% to 30%,

as function of the flow coefficient. .............................................................................................. 107 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. .................................. 108 Figure 4.71 – FAST2 inducer performance curve in cavitating conditions at ambient temperature and

Φ=0.010....................................................................................................................................... 109 Figure 4.72 – FAST2 inducer performance curve in cavitating conditions at ambient temperature and



Φ=0.090....................................................................................................................................... 110 Figure 4.75 – Pictures of the FAST2 inducer at ambient temperature and Φ=0.070. ......................... 111 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)................................................. 111 Figure 5.1 – Comparison between the FAST2 performance in noncavitating conditions obtained by the

“ideal” model and the experimental results ................................................................................. 115 Figure 5.2 – Schematic of a meridional streamtube[Brennen] ............................................................ 116 Figure 5.3 – Comparison between the FAST2 performance in noncavitating conditions obtained by the

“quasi-threedimensional” model and the experimental results ................................................... 118 Figure 5.4 – Geometry of a streamtube ............................................................................................... 119 Figure 5.5 – Schematic of velocity components inside an axial turbomachine with the approximation

of the “throughflow” model......................................................................................................... 121 Figure 5.6 – Velocity triangle in the inlet (1) and outlet (2) section. .................................................. 121 Figure 5.7 – Inducer geometry ............................................................................................................ 122 Figure 5.8 – Axial flow velocity at the exit section of the inducer evaluated according to the

“throughflow” model................................................................................................................... 124

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Figure 5.9 – Circumferential flow velocity at the exit section of the inducer evaluated according to the “throughflow” model....................................................................................................................124

Figure 5.10 – The effect of solidity on the cavitation performance of a cavitating inducer (Acosta, 1958, from Brennen). ...................................................................................................................126

Figure 5.11 – The effect of tip clearance on the cavitation performance of a cavitating inducer (Henderson and Tucker, 1962, from Brennen).............................................................................126

Figure 5.12 – The effect of stagger and gap-chord ratio on the lift of a flat plate in cascade. .............127 Figure 5.13 – Variation of the loss coefficient in radial direction........................................................128 Figure 5.14 – Comparison between the performance of the FAST2 inducer (left) and the MK1 inducer

(right) in noncavitating conditions obtained by the “throughflow” model with the solidity correction and with and without the Lakshminarayana losses and the experimental results .......129

Figure 5.15 – Comparison between the performance of the FAST2 inducer (left) and the MK1 inducer (right) in noncavitating conditions obtained by the “throughflow” model and the experimental results. Evaluation of the “expected” total losses.........................................................................130

Figure 5.16 – Comparison between the performance of the FAST2 inducer (left) and the MK1 inducer (right) in noncavitating conditions obtained by the “throughflow” model with and without the solidity correction and with and without the Lakshminarayana losses and by the experimental results. ..........................................................................................................................................130

Figure 5.17 – Comparison between the performance of the FAST2 inducer (left) and the MK1 inducer (right) in noncavitating conditions obtained by the “ideal” model, the “quasi-threedimensional” model and the “throughflow” model with the solidity correction and the experimental results. .131

Figure 6.1 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the FIP162 inducer at room temperature, 2500 rpm rotating speed and φ = 0.06 (left) and φ = 0.057 (right).......................................................................................................................................................136




Figure 6.5 –Power spectrum (blue), phase of the cross-correlation (red) and scaled coherence function (cyan) of the pressure signals from two transducers with 90° angular spacing in the inlet section of the FIP162 inducer at room temperature, 2500 rpm rotating speed, φ = 0.053 and various cavitation numbers. ......................................................................................................................138

Figure 6.6 –Power spectrum (blue), phase of the cross-correlation (red) and scaled coherence function (cyan) of the pressure signals from two transducers with 90° angular spacing in the inlet section of the FIP162 inducer at room temperature, 2500 rpm rotating speed, φ = 0.034 and various cavitation numbers. ......................................................................................................................139

Figure 6.7 –Power spectrum (blue), phase of the cross-correlation (red) and scaled coherence function (cyan) of the pressure signals from two transducers with 90° angular spacing in the inlet section

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of the FIP162 inducer at room temperature, 2500 rpm rotating speed, φ = 0.017 and various cavitation numbers....................................................................................................................... 139

Figure 6.8 –Power spectrum (blue), phase of the cross-correlation (red) and scaled coherence function (cyan) of the pressure signals from two transducers with 90° angular spacing in the inlet section of the FIP162 inducer at room temperature, 2500 rpm rotating speed, φ = 0.008 and various cavitation numbers....................................................................................................................... 140

Figure 6.9 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the FIP162 inducer at 70 °C temperature, 2500 rpm rotating speed and φ = 0.008. ...................................... 141

Figure 6.10 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the FIP162 inducer at 70 °C temperature, 2500 rpm rotating speed and φ = 0.057. ...................................... 141

Figure 6.11 – The Plexiglas inlet section of the facility during the tests for the characterization of the flow instabilities in the MK1 inducer. ......................................................................................... 142

Figure 6.12 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the MK1 inducer at room temperature, 2800 rpm rotating speed and φ = 0.064 (left) and φ = 0.059 (right)...................................................................................................................................................... 142

Figure 6.13 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the MK1 inducer at room temperature, 2800 rpm rotating speed and φ = 0.0549 (right) and φ = 0.048 (left)...................................................................................................................................................... 143



Figure 6.16 –Power spectrum (blue), phase of the cross-correlation (red) and scaled coherence function (cyan) of the pressure signals from two transducers with 45° angular spacing in the inlet section of the MK1 inducer at room temperature, 2800 rpm rotating speed, φ = 0.007 and various cavitation numbers....................................................................................................................... 144

Figure 6.17 –Power spectrum (blue), phase of the cross-correlation (red) and scaled coherence function (cyan) of the pressure signals from two transducers with 45° angular spacing in the inlet section of the MK1 inducer at room temperature, 2800 rpm rotating speed, φ = 0.007 and various cavitation numbers....................................................................................................................... 145

Figure 6.18 – The Plexiglas inlet section of the facility instrumented with piezoelectric pressure transducers for the characterization of the flow instabilities in the FAST2 inducer. .................. 146

Figure 6.19 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the FAST2 inducer at room temperature, 4000 rpm rotating speed and φ = 0.09 (left) and 0.083 (right). .... 146

Figure 6.20 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the FAST2 inducer at room temperature, 4000 rpm rotating speed and φ = 0.076 (left) and φ = 0.07 (right)...................................................................................................................................................... 147

Figure 6.21 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the FAST2 inducer at room temperature, 4000 rpm rotating speed and φ = 0.065 (left) and φ = 0.06 (right)...................................................................................................................................................... 147

Figure 6.22 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the FAST2 inducer at room temperature, 4000 rpm rotating speed and φ = 0.05 (left) and φ = 0.04 (right). 147

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Figure 6.23 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the FAST2 inducer at room temperature, 4000 rpm rotating speed and φ = 0.03 (left) and φ = 0.02 (right). 148

Figure 6.24 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the FAST2 inducer at room temperature, 4000 rpm rotating speed and φ = 0.01...........................................148

Figure 6.25 – Waterfall plot of the real amplitude of inlet pressure fluctuations in the FAST2 inducer at room temperature, 4000 rpm rotating speed and φ = 0.09 (left) and φ = 0.01 (right). A digital notch filter has been applied to eliminate the rotating frequency and its multiples. ....................149

Figure 6.26 –Power spectrum (blue), phase of the cross-correlation (red) and coherence function (green) of the pressure signals from two transducers with 45° angular spacing in the inlet section of the FAST2 inducer at room temperature, 4000 rpm rotating speed, φ = 0.09 and σ = 0.161(left) and σ = 0.09 (right). .....................................................................................................................150

Figure 6.27 –Power spectrum (blue), phase of the cross-correlation (red) and coherence function (green) of the pressure signals from two transducers with 135° angular spacing in the inlet section of the FAST2 inducer at room temperature, 4000 rpm rotating speed, φ = 0.09 and σ = 0.161. .150

Figure 6.28 –Power spectrum (blue), phase of the cross-correlation (red) and coherence function (green) of the pressure signals from two transducers with 45° angular spacing in the inlet section of the FAST2 inducer at room temperature, 4000 rpm rotating speed, φ = 0.09 and σ = 0.296 (left) and σ = 0.19(right). .............................................................................................................151









Figure 6.37 – Waterfall plot of the filtered power spectrum of inlet pressure fluctuations in the FAST2 inducer at room temperature, 4000 rpm rotating speed and φ = 0.09...........................................154

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Figure 6.38 – Waterfall plot of the filtered power spectrum of inlet pressure fluctuations in the FAST2 inducer at room temperature, 4000 rpm rotating speed and φ = 0.01. ......................................... 155

Figure 6.39 –Power spectrum (blue), phase of the cross-correlation (red) and coherence function (green) of the pressure signals from two transducers with 45° angular spacing in the inlet section of the FAST2 inducer at room temperature, 4000 rpm rotating speed, φ = 0.09 and σ = 0.341. 156




Figure 6.43 – High Speed camera data sheet....................................................................................... 159 Figure 6.44 – Picture of the high-speed video camera and the halogen lamps installed in the facility.

..................................................................................................................................................... 160 Figure 6.45 – Successive frames of the FAST2 inducer taken at a frame rate of 1000 fps (φ = 0.07, σ =

0.14)............................................................................................................................................. 160 Figure 6.46 – Successive frames of the FAST2 inducer taken at a frame rate of 1000 fps (φ = 0.07, σ =

0.09)............................................................................................................................................. 160 Figure 6.47 – Successive frames of the FAST2 inducer taken at a frame rate of 1000 fps (φ = 0.008, σ

= 0.3). .......................................................................................................................................... 161 Figure 6.48 – Flow chart of the image processing algorithm. ............................................................. 161 Figure 6.49 – Comparison between the original frame (a) and the processed binary image (b) in a

sample case. ................................................................................................................................. 162 Figure 6.50 – Selection of the cavitating area on a grayscale image (left), luminosity histogram

(center) and binarized image (right). Inducer: FAST2, Flow conditions: Ф = 0.04.................... 162 Figure 6.51 – Example of the image division and the masked portions............................................. 163 Figure 6.52 – Flow chart of the semi-automatic algorithm. ................................................................ 163 Figure 6.53 – Flow chart of the semi-automatic algorithm. ................................................................ 164 Figure 6.54 – Example of a frame which can not be analyzed using the image processing algorithm.

..................................................................................................................................................... 165 Figure 6.55 –Development of cavitation on the FIP162 inducer........................................................ 165 Figure 6.56 – Evaluation of the azimuthal extension of the cavitation on a blade.............................. 166 Figure 6.57 – Evaluation of the azimuthal extension of the cavitation on a blade.............................. 166 Figure 6.58 – Power spectrum of the tip cavity length on third blade (blue). Phase of the cross-

correlation between 3rd and 2nd blade (second plot), 2nd and 1st blade (third plot), 1st and 3rd blade (fourth plot). ................................................................................................................................ 167

Figure 6.59 – Sinusoidal signal at frequency f1 superimposed to the measured non-dimensional ..... 168 Figure 6.60 – Oscillation of the cavity length on the blades of the FIP inducer (a). Example of

asymmetric blade cavitation (b). ................................................................................................. 168 Figure 7.1 – Schematic of the eccentricity mechanism ....................................................................... 170

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Figure 7.2 – Comparison between the noncavitating performance of the FAST2 inducer at Ω =2000 rpm, two different tip clearances and ω/Ω =0..............................................................................171

Figure 7.3 – Comparison between the noncavitating performance of the FAST2 inducer at a variable eccentricity and constant speed ratio ω/Ω ....................................................................................172

Figure 7.4 – Comparison between the noncavitating performance of the FAST2 inducer at a constant eccentricity and variable speed ratio ω/Ω ....................................................................................173

Figure 7.5 – Comparison between the cavitating performance of the FAST2 inducer at several tip clearances and flow coefficients for ω/Ω=0 and e=0..................................................................174

Figure 7.6 – Comparison between the cavitating performance of the FAST2 inducer inducer at a constant eccentricity and variable speed ratio ω/Ω ......................................................................175

Figure 7.7 – Comparison between the cavitating performance of the FAST2 inducer at a variable eccentricity and constant speed ratio ω/Ω ....................................................................................176

Figure 7.8 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the FAST2 inducer under forced vibration conditions at / 0.7refφ φ = , Ω = 3000 rpm, ω / Ω = 0.02 and room water temperature. The eccentricity of the whirl motion is 0.244 mm. .......................................177

Figure 7.9 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the FAST2 inducer under forced vibration conditions at / 0.7refφ φ = , Ω = 3000 rpm, ω / Ω = 0.2 and room water temperature. The eccentricity of the whirl motion is 0.244 mm ........................................178

Figure 8.1 – Cavitation number on the suction side of a NACA 16-012 hydrofoil as function of incidence angles α in different flow conditions (Franc). ............................................................180

Figure 8.2 – Strouhal number as function of the cavitation number on a NACA0015 hydrofoil (Kato, 1998). ...........................................................................................................................................180

Figure 8.3 – Development of the cavity on the suction side of the hydrofoil and of the re-entrant jet (left). Vorticity component at different instants at s=1.2 and a=6.2° (right) (Franc). ..................181

Figure 8.4 – Development of the cavity on the suction side of a NACA0012 hydrofoil as function of the time at two angles of attack and cavitation numbers (de Lange, 1996). ................................181

Figure 8.5 – NACA 0015 pressure profile (a) and vorticity (b) for a noncavitating flow (σ=2.5) and α=8° (left); the lift coefficient as function of the time (right)......................................................182

Figure 8.6 – NACA 0015 pressure profile (a, b, c) and vorticity (d, e, f) for a cavitating flow (σ=2) and α=8° (left); the lift coefficient as function of the time (right)......................................................182

Figure 8.7 – NACA 0015 pressure profile (a, b, c) and vorticity (d, e, f) for a cavitating flow (σ=1.5) and α=8° (left); the lift coefficient as function of the time (right). ..............................................183

Figure 8.8 – NACA 0015 pressure profile (a, b, c) and vorticity (d, e, f) for a cavitating flow (σ=1) and α=8° (left); the lift coefficient as function of the time (right)......................................................183

Figure 8.9 – NACA 0015 pressure profile (a, b, c) and vorticity (d, e, f) for the supercavitating condition (σ=0.05) and α=8° (left); the lift coefficient as function of the time (right)................183

Figure 8.10 – Schematic of the position of the Thermal Cavitating Tunnel in the CPRT (left). Three-dimensional sketch of the Thermal Cavitating Tunnel (right). ....................................................185

Figure 8.11 – Geometrical characteristics of the NACA0015 hydrofoil in term of percent of chord (right)............................................................................................................................................186

Figure 8.12 – Schematic of the test section with the NACA 0015 hydrofoil and the locations of the pressure taps on the hydrofoil surface (x), at the section inlet (o) and outlet (o). ........................186

Figure 8.13 – Two-dimensional schematic of the test section and detail of the pressure taps.............187 Figure 8.14 – Schematic of the NACA0015 hydrofoil and detail of the pressure taps. .......................187

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Figure 8.15 – Several views of the NACA0015 hydrofoil test section ............................................... 188 Figure 8.16 –Several pictures of the thermal Cavitating Tunnel and the NACA0015 hydrofoil ........ 188 Figure 8.17 – Pressure coefficient on the suction side of the NACA 0015 hydrofoil in noncavitating

conditions for various incidence angles α at room water temperature. CFD simulation at 8° incidence angle and room water temperature (solid line)............................................................ 190

Figure 8.18 – Comparison of the pressure coefficient distribution obtained by the experimental results and four numerical solver methods. Initial conditions: ambient temperature and angle of attack 4° [Beux et Al, 2005; Bramanti, 2002]. .......................................................................................... 190

Figure 8.19 – Comparison between the experimental noncavitating pressure coefficient on the suction side of the NACA 0015 hydrofoil and the theoretical one in unconstrained flow, for three incidence angles........................................................................................................................... 190

Figure 8.20 – Pressure coefficient on the suction side of the NACA 0015 hydrofoil in noncavitating and cavitating conditions for 5° (top), 6° (left) and 8° (right) incidence angles and room water temperature. CFD simulation at 8° incidence angle and room water temperature (solid line).... 191

Figure 8.21 – Influence of thermal cavitation effects on surface pressure distribution on the NACA 0015 hydrofoil at constant angle of attack α and cavitation number σ for several water temperatures T ............................................................................................................................ 192

Figure 8.22 – Pictures of the cavity length development within 1 sec (30 pictures).......................... 193 Figure 8.23 – Optical identification of cavitating region (left) and evaluation of mean cavity length

along the span (right)................................................................................................................... 193 Figure 8.24 – Optical identification of cavitating region and evaluation of minimum (left) and

maximum (right) cavity length along the span. ........................................................................... 194 Figure 8.25 – Normalized maximum and minimum lengths of the cavity as function of the cavitation

number σ for various incidence angles α at room water temperature. ..................................... 194 Figure 8.26 – Characteristics of cavity length at 8° incidence angle and room water temperature.

Experimental uncertainty in the evaluation of the cavity length is about 4% of the chord length...................................................................................................................................................... 194

Figure 8.27 – Frequency spectrum of the upstream pressure at 8° incidence angle and room water temperature. ................................................................................................................................. 195

Figure 8.28 – Typical cavitation appearance in “Supercavitation” case α=8°, σ=1.1, T=25°C. ........ 195 Figure 8.29 – Typical cavitation appearance in “Bubble+Cloud” case α=8°, σ=1.3, T=25°C, St=0.2.

..................................................................................................................................................... 196 Figure 8.30 – Typical cavitation appearance in “Bubble” case α=8°, σ=2.1, T=25°C....................... 196 Figure 8.31 – L.E., maximum and minimum lengths of the cavity for three different water

temperatures T at 8° incidence angle. ........................................................................................ 197 Figure 8.32 – Frequency spectrum of the upstream pressure at 8° incidence angle and 50 °C water

temperature. ................................................................................................................................. 197 Figure 8.33 – Frequency spectrum of the upstream pressure at 8° incidence angle and 70 °C water

temperature. ................................................................................................................................. 198 Figure 8.34 – Cavity thickness for three different water temperatures T at the same incidence angle α

and cavitation number σ ( 8 , 2.5)α σ= ° = . ................................................................................. 198 Figure 8.35 – Cavitation appearance at higher freestream temperature ( 8 , 2, 70 )T Cα σ= ° = = ° . ..... 199 Figure 8.36 – Normalized pressure drop caused by the hydrofoil for various incidence angles α at

room water temperature............................................................................................................... 199

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Figure 8.37 – Normalized pressure drop caused by the hydrofoil for three different water temperatures T at 8° incidence angle................................................................................................................200

Figure 9.1 – Flame temperature (left) and specific impulse (right) versus oxidizer/fuel mass ratio for equilibrium adiabatic reaction at 3.45 MPa and frozen flow expansion to 13.8 kPa of nitrogen tetroxide, N2O4, and several hydrazine fuels (hydrazine, N2H4, monomethyl hydrazine, MMH, and unsymmetrical dimethyl hydrazine, UDMH). .......................................................................202

Figure 9.2 – Historical evaluation of fueling costs versus payload hardware costs for space missions......................................................................................................................................................202

Figure 9.3 – Vacuum specific impulse of hydrogen peroxide at various concentrations (Ventura and Muellens, 1999)............................................................................................................................205

Figure 9.4 – Vacuum specific impulse of hydrazine and hydrogen peroxide at various concentrations, as a function of the nozzle expansion ratio (Ventura and Muellens, 1999) .................................205

Figure 9.5 – Vacuum specific impulse of hydrogen peroxide at different concentrations, compared to other oxidizers, with various fuels in bipropellant rockets (Ventura and Muellens, 1999) .........206

Figure 9.6 – Vacuum specific impulse of hydrogen peroxide at different concentrations, compared to other oxidizers, in hybrid rockets (Ventura and Muellens, 1999) ................................................206

Figure 9.7 –Three-dimensional drawings of the 5 N (left) and the 25 N thruster (right).....................209 Figure 9.8 – Cut-off drawing of the 25 N thruster. ..............................................................................209 Figure 9.9 – Saturation pressure (left) and density (right) of ethane as function of the temperature...211 Figure 9.10 – Combustion temperature (left) and specific impulse (right) versus oxidizer/fuel mass

ratio for equilibrium adiabatic reaction at 3.45 MPa and frozen flow expansion to 13.8 kPa of hydrogen peroxide and ethane for different H2O2 mass concentration (0.70; 0.85; 0.98). ..........212

Figure 9.11 - Ideal volume specific impulse of several bipropellants, as a function of the oxidizer/fuel mixture ratio .................................................................................................................................212

Figure 9.12 – Schematic of H2O2-C2H6 rocket engine with fuel pressurization...................................213 Figure 9.13 – Temperature drifts of the propellant tank under adiabatic conditions as function of the

propellant extraction for 98% H2O2 mass concentration and several values of the mass mixture ratio (O/F= 7, 8, 9) .......................................................................................................................216

Figure 9.14 – Schematic of the test bench............................................................................................220 Figure 9.15 – Time histories of the liquid mixture temperature (left) and the exhaust mass flow of

gaseous oxygen (right) during a test on Mn2O3 powder (20 mg total mass) . ..............................224 Figure 9.16 – Typical appearance of the reactant mixture during a test (Mn2O3 powder, mass = 20 mg).

......................................................................................................................................................224 Figure 9.17 – Appearance of the silver coil during the “cold” test. .....................................................226

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LIST OF TABLES

Table 1.1 - High pressure SSME Tubopump characteristics ...................................................................9 Table 1.2 - Mark 3 Tubopump characteristics .........................................................................................9 Table 1.3 - Vulcain 1 Tubopumps characteristics ..................................................................................10 Table 2.1 – Typical frequency ranges of pump instabilities ..................................................................34 Table 3.1 – Operational parameter of the facility ..................................................................................42 Table 3.2 – Temperature needed in the CPRTF for scaling full-scale tests of some space rocket

turbopumps at Rem = 106.................................................................................................................45 Table 4.1 – Main dimensional characteristics of the pumps used for the validation of the facility. ......68 Table 4.2 – Flow coefficient and pressure coefficient evaluated at the maximum efficiency for the

experimental tests and the F.I.P. data.............................................................................................73 Table 4.3 – Main dimensional characteristics of the FIP162 inducer. ...................................................80 Table 4.4 – Experimental test parameters in noncavitating conditions..................................................81 Table 4.5 – Main characteristics of the ARIANE 5 main engine...........................................................85 Table 4.6 – Geometric characteristics of the Vulcain inducer ...............................................................86 Table 4.7 – Monel K-500 characteristics. ..............................................................................................87 Table 4.8 – Experimental test parameters in noncavitating conditions..................................................87 Table 4.9 – Main characteristics of the ARIANE 5 VINCI engine........................................................99 Table 4.10 – Experimental test parameters in noncavitating conditions..............................................100 Table 4.11 – Operational parameters of the FAST2 inducer at the design point. ................................100 Table 4.12 – Experimental test parameters in noncavitating conditions..............................................103 Table 4.13 – Experimental test parameters in for the tests of Figure 4.67...........................................105 Table 4.14 – Experimental test parameters in for the tests of Figure 4.68...........................................106 Table 6.1 – Summary of the flow instabilities detected in the FIP162 inducer. ..................................140 Table 6.2 – Summary of the flow instabilities detected in the MK1 inducer.......................................145 Table 6.3 – Summary of the flow instabilities detected in the FAST2 inducer. ..................................154 Table 6.4 – Characteristics of the secondary flow instabilities detected in the FAST2 inducer. .........157 Table 6.5 – Summary of the flow instabilities detected in the inducers...............................................157 Table 7.1 – Experimental tests matrix of the FAST2 inducer according to different speed ratio and

eccentricity values in noncavitating conditions............................................................................171 Table 7.2 – Experimental tests matrix of the FAST2 inducer in respect to different speed ratio and

eccentricity values in cavitating conditions..................................................................................174 Table 8.1 –Main characteristics of Thermal Cavitating Tunnel (TCT)................................................185 Table 9.1 – Physical properties of hydrogen peroxide at various concentrations ...............................204 Table 9.2 – Comparison of hydrazine, hydrogen peroxide and ethane main characteristics ..............204 Table 9.3 – Features and benefits of hydrogen peroxide as propellant ................................................204 Table 9.4 – Main preliminary requirements and specifications for the prototype thrusters................207 Table 9.5 – Main performance characteristics of the prototype thrusters, evaluated by means of

simplified isentropic relations. .....................................................................................................208 Table 9.6 – Comparison of hydrazine, hydrogen peroxide and ethane main characteristics ..............211

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NOMENCLATURE

Latin symbols

A Reference surface

At Needle valve throat section

B2 Outlet blade height

c Real frequency of pressure oscillations, hydrofoil chord

cPL Specific heat of the working fluid

C Moore function, needle valve throat function

Cp Pressure coefficient

d Ratio of blade thickness to the normal spacing between the blades

d1 Distance between two axial stations for piezoelectric pressure transducers

df Frequency resolution of the Fourier transform

dS Specific diameter

DN Pipes diameter

e Whirl eccentricity, eccentricity of the elliptical orbit

e1,e2 Eccentricities of the pump shaft casing (CPRTF configuration)

f Frequency

f1 .. f9 Frequencies of the detected flow instabilities

fc Nyquist frequency

fN Blade passing frequency

FD Atmospheric drag

g Gravity acceleration

Isp Vacuum specific impulse

k Parameter of linear-sine steering trajectory model

L Latent heat of the working fluid

Lcav Cavity length

m1 Mass of the gas in the air-bag

1 2,m m Depressurization circuit mass flows

mb Mass of the gas in the vacuum reservoir

n, nC Number of rotating cells

nd Number of data blocks for Fourier transform

xxviii

N Number of points of each data block for Fourier transform

p Static pressure

p Mean pressure

p∞ Freestream static pressure

p1 Inlet static pressure, air-bag static pressure

p1max Maximum pressure in the suction line

pb Vacuum reservoir static pressure

bp Mean (constant) value of the vacuum reservoir static pressure

pT1 Inlet total pressure

pV Vapour pressure of the working fluid

Pmax Maximum power of the main motor

P2max Maximum power of the auxiliary motor

Q Flow rate

Qmax Maximum flow rate

R Universal gas constant, planetary radius

Re Reynolds number

Rem Reynolds number of the test model

Rer Reynolds number of the real pump

RT Tip blade radius

RT1 Inlet tip blade radius

RT2 Outlet tip blade radius

St Strouhal number

Sxx,Syy Power density of auto-correlation

Sxy,Syx Power density of cross-correlation

t Time

T Temperature, time length of data sets for Fourier transform

T Mean temperature

T2max Maximum torque of the auxiliary motor

TL Temperature of the working fluid

Tm Water temperature for thermal cavitation scaling

Tmax Maximum water temperature, maximum torque of the main motor

v1 Flow velocity (relative to the blades)

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vθ1 Flow azimuthal velocity

V Freestream velocity

V∞ Freestream velocity

V1 Air-bag volume

Vb Vacuum reservoir volume

VV Volumetric flow rate of the vacuum pump

w1 Flow velocity (relative to the blades)

wθ1 Flow azimuthal velocity

x Single data point for Fourier transform, space coordinate

X Fourier transform

Y Fourier transform

Greek symbols

α Incidence angle

αL Thermal diffusivity of the working fluid

βb Inlet tip blade angle

∆p Static pressure rise

∆pT Total pressure rise

∆t Time length of each data block for Fourier transform

∆tC Time interval between two acquisitions from the same transducer

∆θ Angular separation between two transducers

∆σ Cavitation number variation for Moore scaling

ε Whirl eccentricity

εmax Maximum whirl eccentricity

φ1 Inlet flow coefficient

φnom Nominal flow coefficient

ϕ Phase of the cross-correlation

γ Specific heat ratio

γxy,γyx Coherence function

ν,νL Kinematic viscosity of the working fluid

ψ,ψ1 Head coefficient

ψnom Nominal head coefficient

xxx

ψref Noncavitating value of the head coefficient at the nominal flow coefficient

ψS Static head coefficient

ρ Density of the working fluid

ρ1 Density of the gas in the air-bag

ρb Density of the gas in the vacuum reservoir

ρL Density of the working fluid at liquid phase

ρV Density of the working fluid at vapour phase

σ Cavitation number, structural coefficient

σa Critical cavitation number

σb Breakdown cavitation number

σc Choked cavitation number

σi , σi1 Cavitation inception number

σreal Cavitation number of the real pump

σtest Cavitation number of the test pump

σTH Thoma cavitation number

θ Angle of the mechanism for eccentricity adjustment

ω Whirl speed, frequency of oscillations

ωmax Maximum whirl speed

Ω Rotating speed, detected frequency of the pressure oscillations

ΩA Auto-oscillation frequency

Ωmax Maximum rotating speed

ΩS Specific speed

ΩSS Suction specific speed

Acronyms

ADN Ammonium DiNitramide

ASI Agenzia Spaziale Italiana

CI2RTF Cavitation Induced Instabilities and Rotordynamic Test Facility

CI2TF Cavitation Induced Instabilities Test Facility

CPRTF Cavitating Pump Rotordynamic Test Facility

CPTF Cavitating Pump Test Facility

DSMC Direct Simulation Monte Carlo

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EADS European Aeronautic, Defence and Space Company

ESTEC European Space Research and Technology Centre

FFT Fast Fourier Transform

FIP Fabbrica Italiana Pompe

HAN Hydroxyl Ammonium Nitrate

HTP High Test Peroxide

HP Hydrogen Peroxide

LH2 Liquid Hydrogen

LOX,LO2 Liquid Oxygen

MMH MonoMethyl Hydrazine

MK1 Mark 1

MK2 Mark 2

NASA National Aeronautics and Space Administration

NTO Nitrogen TetrOxide

SSME Space Shuttle Main Engine

TCT Thermal Cavitation Tunnel

UDMH Unsymmetrical DiMethyl Hydrazine

Chapter 1 - Introduction

1

1 INTRODUCTION

The presented research activity has been related to the design, realization and validation of a test facility for the experimental characterization of centrifugal and axial pumps in fluid dynamic and inertial/thermal cavitation similarity conditions. Experiments have been carried out on various kinds of hydrofoils, centrifugal pumps and axial inducers, in cavitating and noncavitating conditions, in water at ambient and elevated temperature.The aim of this Chapter is to provide a general background about the space rocket turbopumps, their geometries and conventional performance. In the final section, a description of the main objectives of the research activity will also be addressed.

1.1 Brief history of rockets Today’s rockets are remarkable collections of human inventiveness that have their roots in the

science and technology of the past. One of the first devices to successfully employ the principles essential to rocket flight was a wooden bird. The writings of Aulus Gellius tells a story of Archytas who around the year 400 B.C., mystified and amused the citizens of Taranto by flying a pigeon made of wood. Escaping steam propelled the bird suspended on wires. The pigeon used the action-reaction principle, which was not to be stated as a scientific law until the 17th century.

Just when the first true rockets appeared is unclear. Stories of early rocket-like devices appear sporadically through the historical records of various cultures. In the first century A.D., the Chinese reportedly had a simple form of gunpowder made from saltpetre, sulphur, and charcoal dust. They used the gunpowder mostly for fireworks in religious and other festive celebrations. To create explosions during religious festivals, they filled bamboo tubes with the mixture and tossed them into fires. The Chinese began experimenting with the gunpowder-filled tubes. Soon they discovered that these gunpowder tubes could launch themselves just by the power produced from the escaping gas. The true rocket was born. The date reporting the first use of true rockets was in 1232. Many records describe rocket experiments through out the 13th to the 15th centuries. In England, Roger Bacon worked on improved forms of gunpowder that greatly increased the range of rockets. In France, Jean

Experimental Study on Cavitation and Fluid Instabilities in Space Rocket Turbopumps and Hydrofoils

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Froissart achieved more accurate flights by launching rockets through tubes. Froissart’s idea was the forerunner of the modern bazooka. Joanes de Fontana of Italy designed a surface-running rocket-powered torpedo for setting enemy ships on fire.

By the 16th century rockets fell into a time of disuse as weapons of war, though they were still used for fireworks displays, and a German fireworks maker, Johann Schmidlap, invented the “step rocket,” a multi-staged vehicle for lifting fireworks to higher altitudes. A large sky rocket (first stage) carried a smaller sky rocket (second stage). When the large rocket burned out, the smaller one continued to a higher altitude before showering the sky with glowing cinders. Schmidlap’s idea is basic to all rockets today that go into outer space.

During the latter part of the 17th century, Isaac Newton (1642-1727) laid the scientific foundations for modern rocketry. About 1720, a Dutch professor, Willem Gravesande, built model cars propelled by jets of steam. Rocket experimenters in Germany and Russia began working with rockets with a mass of more than 45 kilograms. During the end of the 18th century and early into the 19th, rockets experienced a brief revival as a weapon of war. In 1898, a Russian school teacher, Konstantin Tsiolkovsky (1857-1935), proposed the idea of space exploration by rocket. In a report he published in 1903, Tsiolkovsky suggested the use of liquid propellants for rockets in order to achieve greater range. Tsiolkovsky stated that only the exhaust velocity of escaping gases limited the speed and range of a rocket. Early in the 20th century, an American, Robert H. Goddard (1882-1945), conducted practical experiments in rocketry, in particular, he was interested in a way of achieving higher altitudes than were possible for lighter-than-air balloons. From his tests, he stated that a rocket operates with greater the efficiency in a vacuum than in air and that multistage or step rockets were the answer to achieving high altitudes and that the velocity needed to escape Earth’s gravity could be achieved in this way. Goddard’s earliest experiments were with solid-propellant rockets, measuring the exhaust velocities of the burning gases. While working on solid-propellant rockets, Goddard became convinced that a rocket could be propelled better by liquid fuel. Goddard achieved the first successful flight with a liquid propellant rocket on March 16, 1926, fuelled by liquid oxygen and gasoline. Goddard’s gasoline rocket became the forerunner of a whole new era in rocket flight.

A third great space pioneer, Hermann Oberth (1894-1989) of Germany, published a book in 1923 about rocket travel into outer space. Due to his many publications, many small rocket societies sprang up around the world. In Germany, the formation of one such society, the Verein fur Raumschiffahrt (Society for Space Travel), led to the development of the V-2 rocket, which the Germans used against London during World War II. In 1937, German engineers and scientists, including Oberth, assembled in Peenemunde on the shores of the Baltic Sea. There, under the directorship of Wernher von Braun, engineers and scientists built and flew the most advanced rocket of its time. It achieved its great thrust by burning a mixture of liquid oxygen and alcohol at a rate of about one ton every seven seconds. With the fall of Germany, the Allies captured many unused V-2 rockets and components. Many German rocket scientists came to the United States. Others went to the Soviet Union. The German scientists, including Wernher von Braun, were amazed at the progress Goddard had made. Both the United States and the Soviet Union recognized the potential of rocketry as a military weapon and began a variety of experimental programs. At first, the United States began a program with high-altitude atmospheric sounding rockets, one of Goddard’s early ideas. Later, they developed a variety of medium and long-range intercontinental ballistic missiles. These became the starting point of the U.S. space program. Missiles such as the Redstone, Atlas, and Titan would eventually launch astronauts into space.


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On October 4, 1957, the Soviet Union stunned the world by launching an Earth-orbiting artificial satellite, the Sputnik I. Less than a month later, the Soviet Union followed with the launch of a satellite carrying the dog Laika on board. In October of that 1958, the United States formally organized its space program by creating the National Aeronautics and Space Administration (NASA), which became a civilian agency with the goal of peaceful exploration of space for the benefit of all humankind. Both Russia and the United States began programs to investigate the Moon. The United States launched the first unmanned lunar probe, but the launch vehicle, an Atlas with an Able upper stage, failed 45 seconds after lift off when the payload fairing tore away from the vehicle. The Russians were more successful with Luna 1, which flew past the Moon in January of 1959. Later that year the Luna program impacted a probe on the Moon, taking the first pictures of its far side. Between 1958 and 1960 the United States sent a series of missions, the Pioneer Lunar Probes, to photograph and obtain scientific data about the Moon. Only one of eight probes accomplished its intended mission to the Moon, though several, which were stranded in orbits between Earth and the Moon, did provide important scientific information on the number and extent of the radiation belts around Earth.

In April of 1961, Yuri Gagarin became the first man to orbit Earth. Less than a month later the United States launched the first American, Alan Shepard, into space. The flight was a sub-orbital lofting into space, which immediately returned to Earth. Twenty days later, though still technically behind the Soviet Union, President John Kennedy announced the objective to put a man on the Moon by the end of the decade. In February of 1962, John Glenn became the first American to orbit Earth in a small capsule and he remained in orbit for four hours and fifty-five minutes before splashing down in the Atlantic Ocean. The Mercury program had a total of six launches: two suborbital and four orbital. These launches demonstrated the United States’ ability to send men into orbit, allowed the crew to function in space, operate the spacecraft, and make scientific observations.

The first was the Ranger series, which was the United States first attempt to take close-up photographs of the Moon. The spacecraft took thousands of black and white photographs of the Moon as it descended and crashed into the lunar surface. Though the Ranger series supplied very detailed data, mission planners for the coming Apollo mission wanted more extensive data. Lunar Orbiter provided an extensive map of the lunar surface. Surveyor provided detailed colour photographs of the lunar surface as well as data on the elements of the lunar sediment and an assessment of the ability of the sediment to support the weight of the manned landing vehicles. By examining both sets of data, planners were able to identify sites for the manned landings. However, a significant problem existed; the Surveyor spacecraft was too large to be launched by existing Atlas/Agena rockets, so a new high energy upper stage called the Centaur was developed to replace the Agena specifically for this mission. The Centaur upper stage used efficient hydrogen and oxygen propellants to dramatically improve its performance, but the super cold temperatures and highly explosive nature presented significant technical challenges. In addition, they built the tanks of the Centaur with thin stainless steel to save precious weight. Moderate pressure had to be maintained in the tank to prevent it from collapsing upon itself. The Gemini was the second manned capsule developed by the United States. It was designed to carry two crew members and was launched on the largest launch vehicle available— the Titan II. It paved the way for the Apollo program by demonstrating rendezvous and docking required for the lunar lander to return to the lunar orbiting spacecraft, the extravehicular activity (EVA) required for the lunar surface exploration and any emergency repairs, and finally the ability of humans to function during the eight day manned lunar mission duration. The Gemini program


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launched ten manned missions in 1965 and 1966, eight flights rendezvous and docked with unmanned stages in Earth orbit and seven performed EVA. Launching men to the moon required launch vehicles much larger than those available. To achieve this goal the United States developed the Saturn launch vehicle. The Apollo capsule, or command module, held a crew of three. The capsule took the astronauts into orbit about the Moon, where two astronauts transferred into a lunar module and descended to the lunar surface. After completing the lunar mission, the upper section of the lunar module returned to orbit to rendezvous with the Apollo capsule. The Moonwalkers transferred back to the command module and a service module, with an engine, propelled them back to Earth. After four manned test flights, Apollo 11 astronaut Neil Armstrong became the first man on the moon. The United States returned to the lunar surface five more times before the manned lunar program was completed. After the lunar program the Apollo program and the Saturn booster launched Skylab, the United State's first space station. In addition, scientists began to explore other planets. Mariner 2 successfully flew by Venus in 1962, becoming the first probe to fly past another planet. The United States’ interplanetary space program then took off with an amazing string of successful launches. After the Apollo program the United States began concentrating on the development of a reusable launch system, the Space Shuttle. Solid rocket boosters and three main engines on the orbiter launch the Space Shuttle. The reusable boosters discard little more than 2 minutes into the flight, their fuel expended. Parachutes deploy to decelerate the solid rocket boosters for a safe splashdown in the Atlantic Ocean, where two ships recover them. The orbital manoeuvring system thrusters fire to slow the spacecraft for reentry into Earth’s atmosphere, heating up the orbiter’s thermal protection shield up to 816° Celsius.

Since the earliest days of discovery and experimentation, rockets have evolved from simple gunpowder devices into giant vehicles capable of travelling into outer space, taking astronauts to the Moon, launching satellites to explore our universe, and enabling us to conduct scientific experiments. For this to happen, rockets must become more cost effective, reusable and more reliable as a means of getting to space.

1.2 Generalities on space rocket turbopumps The selection of a particular feed system and its components is governed primarily by the

application of the rocket, its size, propellant, thrust, flight program, duration, number or type of thrust chambers, past experience, mission velocity, and by general requirements of simplicity of design, ease of manufacture, reliability of operation, and minimum weight. One of the most common means of pressurizing the propellants before the entry into the combustion chamber is represented by pressure fed systems and turbopump systems. In the first of these, a gas such as helium or nitrogen is stored in a high pressure tank as high as 35 MPa. The main advantage of this system is represented by the simplicity of its piping and control, but, on the other hand a dedicated design of high pressure tank is necessary. For large fuel consumption, missions with high specific impulse, the mass of the required tanks would be prohibitive, due to the required high pressure, and turbopump systems are preferred (Figure 1.1). The turbopump rocket feed system pressurizes the propellants by means of pumps, which in turn are driven by turbines. The turbines derive their power from the expansion of the hot gases.

Figure 1.2 presents a schematic of a liquid propellant rocket engine: the turbopumps, the turbine, the gas generator and the thrust chamber, which consists of injector, combustion chamber, throat, and exhaust nozzle. Gas generator burns a mixture of fuel and oxidizer to generate hot gas which propels the turbine.


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Figure 1.1 – Comparison between pressure fed systems and turbopump systems.

Figure 1.2 – Schematic of a liquid propellant rocket

The turbopump rocket engine systems can be classified into two classes: open cycles and closed cycles (Figure 1.3). In the first ones, the working fluid exhausting from the turbine is discharged overboard, after having been expanded in a nozzle of its own, or into the engine nozzle. To this class belong:

- the gas generator cycle, in which the fuel and oxidant, after being pressurized by the pumps, are driven into a gas generator chamber separate from the main chamber. The products of combustion in this small chamber are then used to drive the turbines before being exhausted to ambient pressure.


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- the combustion tap-off cycle, in which the hot gases needed by the turbine are bled from the engine combustion chamber at a point near the injector face which supplies gases at the desired temperature.

- the coolant tap-off or bleed cycle in which vaporized hydrogen is bled from the thrust chamber jacket and supplied to the turbine. Like the previous cycle, the main advantage is the absence of the gas generator.

In closed cycle all the working fluid from the turbine is injected into the engine combustion chamber to allow a most efficient use of its remaining energy. In closed cycles the turbine exhaust gas is expanded through the full pressure ratio of the main thrust chamber nozzle, thus giving a little more performance than the open cycle, where these exhaust gases expand only through a relatively small pressure ratio. To this class belong:

- the expander cycle, in which most of the engine coolant is fed to low-pressure-ratio turbines after having passed through the cooling jacket where it picked up energy. Part of the coolant, between 5% and 15%, bypasses the turbine and rejoins the turbine exhaust flow before the entire coolant flow is injected into the engine combustion chamber where it mixes and burns with the oxidizer. It doesn’t require a separate gas generator combustion chamber, and uses all the propellants in the main combustion chamber.

- the staged combustion cycle, in which the coolant flow path through the cooling jacket is the same as that of the expander cycle. Here a high-pressure gas generator burns all the fuel with part of the oxidizer to provide high energy gas to the turbines. The total turbine exhaust gas flow is injected into the main combustion chamber where it burns with the remaining oxidizer. This cycle is capable of providing the highest specific impulse. The Space Shuttle Main Engine uses this cycle, except that separate gas generators are used for hydrogen and oxygen turbopumps.

vaporized fuel

COOLANT BLEED CYCLE

EXPANDER CYCLE

( CLOSED CYCLES )

STAGED-COMBUSTION CYCLE

precombustor

GAS GENERATOR CYCLE

gas generator

( OPEN CYCLES )

COMBUSTION TAP-OFF CYCLE

hot chamber gas bleed

oxidizer pump

fuel turbine

oxidizer turbine

fuel pump

Figure 1.3 – Typical feeding cycles for turbopump systems.


7

With the engine requirements established, the turbopump configuration is selected based on optimizing the pumps for each propellant, the turbine for the drive gas available energy, and the mechanical design arrangement for life, weight and feasibility considerations.

Pumps for engines with similar density fuel and oxidizer propellants such as RP-1/LOX and similar discharge pressure requirements will typically be optimum at approximately the same speed (Table 1.2).This permits the fuel and oxidizer pumps to be placed on a common shaft and driven by a common turbine (Redstone, Atlas, RS-27, F-1, and XLR-132). Maximum pump speed is generally limited by the suction performance requirements to avoid cavitation. The minimum weight turbine has the highest speed and smallest diameter within the structural and mechanical arrangement limitations.

When the Atlas booster and turbopumps were designed, the speed of the pumps and the turbine were optimized independently and linked together with a speed reduction gear box. This required the development of a highly loaded gear train to minimize the turbopump weight, but was considered the best design selection based on suction performance, turbine performance and material technology at that time.

When the F-1 turbopump was designed, canted inducer technology had been developed to increase the pump suction performance capability. This permitted designing the pumps and turbine to operate at the same speed on a common shaft and eliminated the need for a 60,000-hp reduction gearbox, which was probably not feasible anyhow.

The J-2 was the first gas generator cycle engine to use liquid hydrogen (LH2) as the fuel and liquid oxygen (O2) as the oxidizer. The low-density liquid hydrogen introduced the need to operate the fuel pump at a much higher speed than the LO2 pump in order to develop the high head required. High solidity inducer technology had been developed which permitted optimizing the LH2 pump at a higher speed and driving the pumps with separate turbines. The turbines were arranged in series to best utilize the large pressure ratio available energy and maximize the turbine efficiencies at their respective speeds.

Selecting a 3,000-psi chamber pressure and staged combustion cycle for the SSME (Figure 1.4 and Table 1.1 ) to maximize the specific impulse significantly increased the turbopump requirements compared to the F-1 or J-2 engines. Adding preburner and turbine pressure drops in series with the high combustion chamber pressure resulted in discharge pressure requirements of 8,500 psia and 7,000 psia for the LO2 and LH2 pumps, respectively.

Propellant tank pressures were also minimized to optimize the Space Shuttle vehicle weight. The combination of low inlet pressures (low NPSP) and high required discharge pressures introduced the need for separate boost pumps to optimize the turbomachinery weight. The low pressure fuel turbopump and low pressure oxidizer turbopump receive the propellants at low NPSP and raise their pressures sufficiently to optimize the high pressure fuel and oxidizer turbopumps at high speed. The added complexity of four turbopumps is justified to optimize the turbomachinery weight and maintain suction performance margin for safe engine operation. The combination of high pump discharge pressure and flow requirements, combined with high horsepower turbines driven by high-pressure hydrogen-rich steam, have made the SSME turbopumps a significant advancement in the state of the art for rocket engine turbomachinery. Figure 1.5 presents several cutaway views of selected turbopumps used for different rocket systems.


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Figure 1.4 – Schematic of the high pressure turbopumps of the Space Shuttle Main Engine.

Figure 1.5 – Cutaway views of several representative turbopumps. Clockwise from the top: the Mark 3, used in the Atlas, Thor, Jupiter and H-1 engines; the SSME HPF turbopump; the Marl 49F, used in the

OTV; and the Mark 15F, used with the J-2.


9

High Pressure SSME Turbopumps Pump Fuel Oxidizer Propellants H2 O2

Flow rate [kg/s] 67.7 407 Exit pressure [Mpa] 42.1 49.7 Rotational speed [rpm] 34386 27263 Turbine Fuel Oxidizer Stage number 2 2 Flow rate [kg/s] 74.1 27.3 Pressure ratio 1.48 1.53 Inlet pressure [MPa] 33.6 34.7 Inlet temperature [K] 997 804

Table 1.1 - High pressure SSME Tubopump characteristics

Mark 3 Turbopump Fuel Oxidizer Turbine

Propellants RP1 O2 Flow Rate [ 3m / s ] 0.138 0.198 Exit Pressure [Mpa] 15.9 15.9

Rotational speed [rpm] 2188 3148 33178 Table 1.2 - Mark 3 Tubopump characteristics

The Vulcain 1 engine for the European launcher Ariane 5 is shown in Figure 1.6, Figure 1.7 and Table 1.3. Its design is based on the gas generator cycle: two turbopumps are driven by a single gas generator which is fed by propellants tapped (3% of total) from the main flow of fuel and oxidizer to the combustion chamber.

The engine thrust is 1,140 kN (about 256,300 Ib), obtained by ejection of gases produced by burning the propellants in the combustion chamber under high pressure (110 bar) and at high temperature (3,500 K).

A frontal injection system sprays the liquid oxygen (oxidizer) and liquid hydrogen (fuel) into the combustion chamber. Because of the extremely high combustion temperature, the chamber is regeneratively cooled by routing liquid hydrogen through 360 longitudinal channels machined in the chamber wall. Gases are accelerated by the nozzle to a supersonic speed of 4,000 m/s, the limit under ambient pressure. The nozzle is also cooled by a small fraction of the hydrogen flow. The engine's high-pressure propellant supply is ensured by two separate turbopumps:

- the hydrogen turbopump operates at 33,200 rpm and a power level of 11.8 MW, operates beyond its critical speeds. It comprises a two-stage centrifugal pump connected to an axial inducer and a two-stage supersonic turbine.

- the oxygen turbopump, rotating at 13,400 rpm and developing 3.7 MW of power, operates below its first critical speed.


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Figure 1.6– The liquid oxygen turbopump of the Vulcain 1 engine.

Figure 1.7– Sketch of the liquid oxygen turbopump (left) and the liquid hydrogen turbopump of the

Vulcain 1 engine (FIAT AVIO courtesy).

Vulcain 1 Turbopumps Fuel Oxidizer Propellants H2 O2

Flow rate [kg/s] 43 228 Exit pressure[Mpa] 11 11 Rotational speed [rpm] 33200 13400

Table 1.3 - Vulcain 1 Tubopumps characteristics

1.3 Geometry of a generalized turbopump The turbomachine geometry consists of a set of rotor blades attached to a hub and rotating within

a static casing Figure 1.8.


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Figure 1.8 – Sketch of a typical centrifugal turbopump

The distances of the inlet blade tip (RT1), inlet blade hub (RH1), the outlet blade tip (RT2) and outlet blade hub (RH2) are represented in Figure 1.9. In the case of a centrifugal pump the discharge blade passage is inclined to the axis of rotation at an angle, θ, around 90°, while in the case of an axial flow machine it is much smaller near zero. ``Mixed flow'' type machines present a typical mean discharge angle, 0< θ <90°.

Figure 1.9 – Cross-sectional view through the axis of a pump impeller (Brennen, 1994).

The next figure shows the flow through a general rotor normally visualized by developing a meridional surface, on which the fluid velocity in a non-rotating coordinate system is denoted by v(r) and the corresponding velocity relative to the rotating blades is denoted by w(r). The velocities, v and w, have components vθ and wθ in the circumferential direction, while vm and wm in the meridional direction. Axial and radial components are denoted by the subscripts a and r.

The velocity of the blades is Ω r. The flow angle β(r) is defined as the angle between the relative velocity vector in the meridional plane and a plane perpendicular to the axis of rotation, while the blade angle βb(r) is defined as the inclination of the tangent to the blade in the meridional plane and the plane perpendicular to the axis of rotation. If the flow is precisely parallel to the blades, β=βb. Specific values of the blade angle at the leading and trailing edges (1 and 2) and at the hub and tip are denoted by the corresponding suffices, so that, for example, βbT2 is the blade angle at the discharge tip.


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Figure 1.10 – Developed meridional surface and velocity triangle (left side) blade detail (right) (Brennen,

1994).

The influence of blade twisting on the exit velocity profile is shown in Figure 1.11. The turbomachines are usually designed in order to satisfy the condition β2 >0 to avoid potential instabilities, which trigger if β2 <0 (it can be noted that, in this latter case, the turbomachine performance are higher due to an higher pressure drop).

Figure 1.11 – Influence of the blade twisting on the velocity profile (Hill 1965)

Figure 1.12 presents a schematic section of a centrifugal pump. Fluid entering the impeller is accelerated within the impeller channels and leaves the impeller periphery with a high velocity to enter the volute and thereafter the diffuser where conversion from kinetic energy to potential energy (pressure) takes place.

Figure 1.12 – Schematic section of a typical centrifugal turbopump (Sutton, 1992)


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1.4 Turbopump performance The power input, P, to a centrifugal turbomachine, if there is no whirl in the incoming flow is

determined by the following:

.

2 2P T m U cθ= ⋅Ω = ⋅ ⋅ (1.1)

where T , Ω , 2U , 2ϑc ,

•

m represent the torque, rotating speed, impeller tip speed, tangential component of the absolute fluid velocity leaving impeller tip and fluid mass flow rate respectively. For incompressible flow, 2ϑc , is strongly coupled to the exit fluid angle and the impeller geometry (Figure 1.10). In particular:

2 2 2 2 2 2tan( )rc U w U wθ θ β= + = − ⋅ (1.2)

or

(1.3)

where ω is the relative velocity and Lρ the density of the working fluid. If we consider the fluid adiabatic, we obtain the power per mass flux unit:

(1.4) From the mass balance equation we can obtain the mass fluid flow rate:

2 2 2 1 1 12 2L T r L T r Lm Q R b w R b wρ π ρ π ρ= ⋅ = ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ (1.5)

where Q , 1TR , 2TR are the volumetric mass flow, the inlet and outlet tip radius respectively. To identify the performance of a turbomachine two other parameters have to be considered the total pressure Tp :

(1.6)

and the total head, TH :

(1.7)

)tan(2 222 β

ρπϑ ⋅⋅⋅⋅

−=

•

bmUc

))tan(2

1( 222

22 β

ρπ⋅

⋅⋅⋅⋅⋅−⋅=

•

• UbrmU

m

P

L

2

21 Vpp LT ⋅⋅+= ρ

L

Tt g

pH

ρ⋅=


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If the hypothesis of isentropic fluid is considered, the hydraulic power, iP , can be written as:

(1.8)

while the hydraulic efficiency, iη is:

(1.9)

where trueP is the effective power absorbed by the flux. The hydraulic efficiency iη has usually a higher value from the global efficiency due to friction losses. In general, the main operational parameters for a pump are therefore: the flow rate Q, the rotating speed Ω, the total pressure rise ∆pT and the inlet pressure p1, which combined together allow to obtain dimensionless quantities, useful to characterize the pump performance in scaled conditions. The “flow coefficient” φ is defined as:

(1.10)

where A is a reference surface and RT is the tip radius of the pump. The “head coefficient” ψ is:

(1.11)

The ideal performance of an impeller can be written as: (1.12) The torque coefficient is defined by: (1.13) The Reynolds number, for a pump, is generally defined as:

(1.14)

where νL is the kinematic viscosity of the working fluid.

The noncavitating performance of a pump is generally summarized in a “characteristic curve” like the one in Figure 1.13, referred to a 3-bladed inducer, showing the head coefficient as a function of the flow coefficient. When the flow inside of the pump is completely turbulent (typically for Re>106), the dimensionless characteristic curve is not dependant on the Reynolds number.

TLTL

Ti HgQpQpmP ∆=∆=

∆= ρ

ρ

true

ii P

P=η

T

QAR

φΩ

=

222

T

L T

pR

∆ψρ Ω

=

222Re T

L

RΩν

=

)tan(1 2βφψ ⋅−=

LTRAT

ρτ

⋅⋅Ω⋅= 3

22


15

Figure 1.13 – Characteristic curve in noncavitating conditions of the inducer VII (Bhattacharyya, 1994)

In order to design a turbomachine, the starting requirements which have to be satisfied are usually the volumetric mass flow, Q , the total pressure rate Tp∆ . Two other adimensional parameters are established in order to make Q and Tp∆ uncoupled, the specific speed:

(1.15)

and the specific radius: (1.16)

The specific speed and radius can be connected to φ and ψ , in particular: (1.17)

(1.18)

Combining together the above parameters the power, P, can be written as: (1.19)

the power is directly proportional to the cubic of the rotational speed and to the fifth power of the tip radius.

5

2

3

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛ΩΩ

⋅=S

T

SP

L

rRP

ηρ

221

SS rΩ=ψ

3

1

SS rΩ=

πφ

21

41

2

Q

pRr L

TT

S

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆

=ρ

43

21

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆

Ω=Ω

L

T

S

p

Q

ρ


16

Figure 1.14 – Comparison of calculated efficiency contours with test data on centrifugal pumps (Balje)

In the Figure 1.13 each point represents a different design and the efficiency contours indicate the characteristic efficiency to be associated with each point. The main conclusions are the following:

- Best efficiency operation occupies a narrow zone on the ns ( SΩ )- ds plane. In order to obtain efficiency around 90% the specific speed has to be chosen between 0.4 and 1.2.

- At lower specific speed, the passages inside the impeller are longer and thinner, the maximum efficiency is decreased due to the increase of the friction losses.

- Best efficiency is associated with highest specific speed impellers for given Q , ρ , Tp∆ , the specific speed has to be increased by increasing the number of stages.

A similar diagram for axial turbomachines is represented in the next Figure.

Figure 1.15 – Comparison of calculated efficiency of axial pumps (Balje)

The correlation between the turbomachine performance and the geometry is shown in Figure 1.16. At low values of SΩ (0.2-1), it is convenient working with centrifugal turbomachines, while the axial ones are more efficient at higher values of the specific speed ( SΩ >3 ). At intermediate values mixed flow turbomachines are preferable. The “Cordier line” in Figure 1.17 shows the best effiency diagram according to different pump geometries.


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Figure 1.16 – Ranges of specific speed for typical turbomachines and typical pump geometries for different design speeds (Sabersky, Acosta, Hauptmann)

Figure 1.17 – Best efficiency turbopump diagram

Figure 1.18 Figure 1.19 presents the impeller “X” tested at Caltech (USA) and two different geometries of axial inducer respectively.

Figure 1.18 – A centrifugal pump impeller, “X”, tested at Caltech (Franz, 1989)


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Figure 1.19 – Two geometry of axial inducer (Brennen, 1994)

1.5 Objectives of the research activity In the space rocket scenario, the main goal of turbomachines designers is devoted to the

achievement of high power densities. As previously pointed out, the hydraulic power of a pump is proportional to the mass flow rate and to the pressure rise given to the propellant and, it can also be shown, to the fifth power of a characteristic dimension (the tip blade diameter, for instance) and to the third power of the rotating speed. This requirement leads to reduce the pump dimensions to obtain a lighter machine and increase the rotating speed, designing supercritical machines which can be affected by phenomena like the rotordynamic instabilities and cavitation. The main relevant examples of the influence of cavitation and instabilities on space rocket turbomachines are represented by:

- Both the High Pressure Fuel Turbopumps (HPFTP) and the High Pressure Oxidizer Turbopump (HPOTP) of the Space Shuttle Main Engine suffered from severe, unexpected problems. The HPFTP was designed to run between its second and third critical speeds (37000 rpm). During early engine tests, nonsynchronous rotor whirl became acute at speed above 19000 rpm; with accelerometer cutoff at around 22000 rpm. In one case, the characteristics of the vibration were remarkably consistent and were marked by a forward precession at less than the shaft speed with bearing loads rapidly increasing in a nonlinear manner at a frequency typically 0.5 to 0.6 of the shaft speed until a destructive limit cycle was reached. In another case, the inception (of the whirl) occurred at a shaft speed of approximately twice the first critical speed, and the whirl frequency thereafter followed the critical speed of the system at approximately one-half the shaft speed

- High pressure compressors have also experienced whirl problems in which fluid dynamic effects may play a part. For example, for over seven months, full-load plant startup was delayed in the chevron-owned Kaybob natural gas plant. The problem was due to rotor instabilities in a set of nine-stage high pressure centrifugal compressors designed to operate just below the third critical speed.

- The pumps of the cooling water in the Three Miles Island nuclear power plant, having a nominal power of several MW, were affected by a strong performance decay due to rotordynamic forces caused by cavitation.

- The liquid oxygen turbopump of the LE-7 engine of the Japanese launcher H-II showed a failure, caused by cavitation instabilities during the take-off of the vehicle on November 15th 1999. The mission was aborted and the engine was found in the Ocean, at a depth of 3000 meters (Figure 1.20).


19

- the high mass flow rate, the high cavitation level and the not optimised shape of the Hoover Dam caused the development of a big hole inside it (Figure 1.21). The hole is 35 m long, 9 m wide and 13.7 m deep

The list could continue much longer. The one important fact that emerged from the investigations

of these incidents was that the state of knowledge was not adequate enough. It could not satisfactory explain all the facets of the problems encountered. Nor could it provide proper design guidelines that would assure trouble free operation. (da Jery)

Figure 1.20– The liquid oxygen turbopump of the LE-7 engine (left side); repechage of the Japanese launcher H-II (right side)

Figure 1.21– View of the catastrophic effects of cavitation inside Hoover Dam (AZ).

In space rockets, turbopumps used for propellant feeding are crucial components of all primary propulsion concepts powered by liquid propellant engines. Severe limitations are associated with the design of high power density, dynamically stable machines capable of meeting the extremely demanding suction, pumping and reliability requirements of space transportation systems (Stripling & Acosta1, 1962). In typical pumps used in space rocket engines an axial inducer is placed upstream of the centrifugal stages in order to improve the suction performance and reduce the propellant tank


20

pressure and weight. They are typically designed in order to operate in slightly cavitating conditions (The inlet pressure can not be kept sufficiently high to avoid cavitation, because this would lead to higher storage pressures of the propellants and, as a consequence, to heavier tanks). For this reason, it is preferred to “control” the cavitation on the pump, taking its operational conditions as far as possible from the onset of the performance breakdown. The inducer is one of the most critical components of the turbopump assembly due to the significant cavitation levels occurring in it and, as a consequence, to the development of flow instabilities that can seriously degrade the performance of the machine, or even cause its rapid failure. The research activity on rotordynamics, cavitation and the related flow instabilities has begun in the sixties, but the most interesting publications have appeared only by 1980 (see for instance Brennen, 1994 and 1995) and many studies were performed to further characterise the instabilities connected to cavitation phenomenon. However, a number of aspects of unsteady flow phenomena in cavitating turbopumps and hydrofoils are still partially understood and imperfectly predicted by theoretical means alone: technology progress in this field must therefore heavily rely on detailed experimentation on scaled models.

During my Ph.D. thesis work, performed between 2003-2005 during my Ph.D. program, I carried out part of experimental test in collaboration with the Ph.D. student Angelo Cervone, who performed his Ph.D. work between 2002-2004. In particular Angelo and I covered the following main topics:

• experimental characterization of four different types of inducer in noncavitating and inertial/thermal cavitating conditions under geometrical, fluidynamic and thermal similarity: two commercial inducers (FIP 120 and FIP 162), the Ariane 5 MK1 inducer and the VINCI LOX inducer.

• extensive comparative analysis through power spectrum characterization of cavitation-induced instabilities such as surge and auto-oscillations detected by piezoelectric transducers mounted at several axial and azimuthal stations on the above described inducers

I covered the following main topics:

• characterization of cavitation instabilities through the analysis and comparison of different frames taken by the use of a high speed camera

• development of analytical models to evaluate the inducer performance in noncavitating conditions.

• experimental characterization of the cavitation-induced instabilities on a NACA 0015 hydrofoil: evaluation and analysis of the cavity length oscillations at different incidence angles, cavitation numbers and freestream temperatures.

• experimental characterisation for evaluating the pump performance in noncavitating and cavitating conditions, varying the shaft eccentricity through the dedicated eccentricity mechanism and the engines speed ratio

• assessment of the possible application of hydrogen peroxide as a rocket propellant in space. Design and testing of a hydrogen peroxide monopropellant rocket, experimental characterisation of different advanced materials for the catalysis of hydrogen peroxide and assessment study on an innovative concept for a bipropellant rocket using hydrogen peroxide and ethane as propellants.

Chapter 2 - Cavitation

21

2 CAVITATION

The aim of this Chapter is to provide a general overview of the cavitation phenomenon with a particular attention to cavitation induced instabilities. Cavitation refers to an abnormal condition inside the pump that arises during pump operation due to formation and subsequent collapse of vapor filled cavities or bubbles inside the liquid being pumped. The condition of cavitation can obstruct the pump, impair performance and flow capacity, and damage the impeller and other sensitive components.

2.1 Cavitation The term ‘cavitation’ comes from the Latin word cavus, which means a hollow space or a cavity.

The word ‘cavitation’ is defined as the rapid formation and collapse of cavities in a flowing liquid in regions of very low pressure. It was introduced for the first time by R. E. Froude in 1895 and by the French naval engineer A. Normand (1839-1906). The first dangerous effects of cavitation were detected on naval propeller and on torpedoes.

In the context of centrifugal pumps, the term cavitation implies a dynamic process of formation of

bubbles inside the liquid, their growth and subsequent collapse as the liquid flows through the pump. Generally, the bubbles that form inside the liquid are of two types: Vapor bubbles or Gas

bubbles: - Vapor bubbles are formed due to the vaporisation of a process liquid that is being

pumped. The cavitation condition induced by formation and collapse of vapor bubbles is commonly referred to as Vaporous Cavitation. It is the most common form of cavitation found in process plants. Generally it occurs due to insufficiency of the available NPSH or internal recirculation phenomenon. It generally manifests itself in the form of reduced pump performance, excessive noise and vibrations and wear of pump parts.

- Gas bubbles are formed due to the presence of dissolved gases in the liquid that is being pumped (generally air but may be any gas in the system). The cavitation condition


22

induced by the formation and collapse of gas bubbles is commonly referred to as Gaseous Cavitation. It occurs when any gas (most commonly air) enters a centrifugal pump along with liquid. If the amount of air is increased to 6%, the pump starts cavitating. The main effect of gaseous cavitation is loss of capacity.

Both types of bubbles are formed at a point inside the pump where the local static pressure is less

than the vapor pressure of the liquid (vaporous cavitation) or saturation pressure of the gas (gaseous cavitation) at a given temperature. In this way cavitation is different from boiling, which appears when temperature is increased at constant pressure (Figure 2.1). As a result of that, cavitation and boiling are two really different phenomena. The temperature of a fluid generally increases due to conductive heat transfer through solid walls, and so boiling initially affects only the regions of the fluid near to the hot walls, while cavitation is a global phenomenon which can involve the whole volume of the liquid, as it’s easier to obtain an uniform pressure decrease in a fluid.

Figure 2.1 – Generic phase diagram in the Temperature-Pressure plane

One application of cavitation phenomenon is the supercavitating vehicle, the so called “supercavitator” (Figure 2.2). A supercavitating body has extremely low drag, because its skin friction almost disappears. Instead of being encased in water, it is surrounded by the water vapour in the supercavity, which has much lower viscosity and density. So in a supercavitating vehicle, only the nose of the craft causes significant drag, because this is the only part of the body actually in contact with the water. The overall drag reduces enormously once you reach the supercavitating regime and then increases only linearly with speed. With much of the drag eliminated, very high speeds become possible. An example is represented by the so-called “supercavitating torpedoes” like the Russian Shkval. The Shkval has an operating range of about 7 km and a maximum velocity of 360 km/h, 3÷4 times that of ordinary torpedoes.


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Figure 2.2 – The supercavitating vehicle (left). The Russian supercavitating torpedo Shkval (right)

The caviation phenomenon is a stepwise process, which is characterized by:

1 - Formation of bubbles inside the liquid being pumped. Vapour bubbles form due to vaporization of the liquid being pumped when the local static pressure at any point inside the pump becomes equal to or less than the vapour pressure of the liquid at the pumping temperature. The reduction of static pressure in the external suction system occurs mainly due to friction in suction piping. The reduction of static pressure in the internal suction system occurs mainly due to the rise in the velocity at the impeller eye. 2 - Growth of bubbles Unless there is no change in the operating conditions, new bubbles continue to form and old bubbles grow in size. The bubbles then get carried in the liquid as it flows from the impeller eye to the impeller exit tip along the vane trailing edge. Due to impeller rotating action, the bubbles attain very high velocity and eventually reach the regions of high pressure within the impeller where they start collapsing. The life cycle of a bubble has been estimated to be in the order of 0.003 seconds. 3 - Collapse of bubbles As the vapor bubbles move along the impeller vanes, the pressure around the bubbles begins to increase until a point is reached where the pressure on the outside of the bubble is greater than the pressure inside the bubble. The bubble collapses. The process is not an explosion but rather an implosion (inward bursting). Hundreds of bubbles collapse at approximately the same point on each impeller vane. Bubbles collapse non-symmetrically such that the surrounding liquid rushes to fill the void forming a liquid microjet. The micro jet subsequently ruptures the bubble with such force that a hammering action occurs. Bubble collapse pressures greater than 1 GPa (145x106 psi) have been reported. The highly localized hammering effect can pit the pump impeller.

In particular, the cavitation phenomenon on an impeller can be classified in respect with its appearance and form. Brennen (1994) introduced a precise classification of cavitation types. Figure 2.3 and Figure 2.4 present a two and three dimensional schematic representation of the blades of an unshrouded impeller. In particular, the first Figure shows the so called “backflow cavitation”, which refers to the formation of cavitating bubbles and vortices in the annular region upstream of the inlet


24

plane of the pump. This condition is typically observed when the pump operate at low flow rates (below the design point value).

Figure 2.3 – Types of cavitation in an unshrouded impeller (Brennen, 1994).

Figure 2.4 –Impeller caviation regions.

Decreasing the inlet pressure, cavitation inception occurs in the form of a vortex (“tip vortex cavitation”) generated at the corner between the leading edge and the tip of the blades (Figure 2.5 and Figure 2.6).

When the inlet pressure is further lowered, the cavitation nuclei start to grow, spread (“bubble cavitation”) on the blade suction surface and later to collapse when they move into regions of high pressure, as shown in Figure 2.7 on the suction side of a NACA 4412 hydrofoil at 0° incidence angle.


25

Figure 2.5 – Tip vortex cavitation on a marine propeller (Kuiper, 2001).

Figure 2.6 –Cavitation on a marine propeller (Duttweiler).

Figure 2.7 – Bubble cavitation on a hydrodynamic test body (Brennen, 1995).


26

At lower pressures, the bubbles combine to form attached cavities on the suction surface of the blades (generally called “attached cavitation” or also “blade cavitation” when it appears on pumps) and tend to extend on the whole suction surface and to collapse on that surface as a result of the increased pressure in the blade passage (at this point, cavitation damage is often observed).

When the blade cavitation extends on the suction blade surface is called “partial cavitation”. When the pressure reaches very low values, the cavity can extend downstream of the trailing edge, the so-called “supercavitation”. Figure 2.8 illustrates the difference between partial cavitation and supercavitation, while Figure 2.9 shows the two forms of cavitation on a spherical test body. In some cases, pumps have been intentionally designed in order to operate under supercavitating conditions, because of the bubble collapse occurs downstream of the blades, minimizing cavitation damage.

Figure 2.8 – Partial cavitation (a) and supercavitation (b) on a profile (Brennen, 1995).

Figure 2.9 – Bubble cavitation (left) and supercavitation (right) on a spherical test body (Brennen, 1995).

2.1.1 Cavitation undesired effects Perceptible indications of the cavitation during pump operation are more or less loud noises,

vibrations and an unsteadily working pump. Fluctuations in flow and discharge pressure take place with a sudden and drastic reduction in head rise and pump capacity. Depending upon the size and quantum of the bubbles formed and the severity of their collapse, the pump faces problems ranging


27

from a partial loss in capacity and head to total failure in pumping along with irreparable damages to the internal parts.

In particular, cavitation is generally considered a dangerous phenomenon, which leads to different kinds of undesired effects:

- Reduction in the capacity of the pump: The formation of bubbles causes a volume increase decreasing the space available for the liquid and thus diminish pumping capacity. For example, when water changes state from liquid to gas its volume increases by approximately 1,700 times. If the bubbles get big enough at the eye of the impeller, the pump “chokes” i.e. loses all suction resulting in a total reduction in flow. The unequal and uneven formation and collapse of bubbles causes fluctuations in the flow and the pumping of liquid occurs in spurts. This symptom is common to all types of cavitation. - Decrease in the head developed: Bubbles unlike liquid are compressible. The head developed diminishes drastically because energy has to be expended to increase the velocity of the liquid used to fill up the cavities, as the bubbles collapse. The Hydraulic Standards Institute defines cavitation as condition of 3% drop in head developed across the pump. Like reduction in capacity, this symptom is also common to all types of cavitation. Thus, the hydraulic effect of a cavitating pump is that the pump performance drops off of its expected performance curve, referred to as break away, producing a lower than expected head and flow. The Figure 2.15 depicts the typical performance curves and the performance breakdown due to cavitation. - Abnormal sound and vibrations: The movement of bubbles with very high velocities from low-pressure area to a high-pressure area and subsequent collapse creates shockwaves producing abnormal sounds and vibrations. It has been estimated that during collapse of bubbles the pressures of the order of 104 atm develops. The sound of pumps operating while cavitating can range from a low-pitched steady knocking sound (like on a door) to a high-pitched and random crackling (similar to a metallic impact). The disappearance of noise will be an indication of cavitation. Similarly, vibration is due to the uneven loading of the impeller as the mixture of vapour and liquid passes through it, and to the local shock wave that occurs as each bubble collapses. Very few vibration reference manuals agree on the primary vibration characteristic associated with pump cavitation. Formation and collapsing of bubbles will alternate periodically with the frequency resulting out of the product of speed and number of blades. Some suggest that the vibrations associated with cavitation produce a broadband peak at high frequencies above 2,000 Hertz. Some suggest that cavitation follows the vane pass frequency (number of vanes times the running speed frequency) and yet another indicate that it affects peak vibration amplitude at one times running speed. All of these indications are correct in that pump cavitation can produce various vibration frequencies depending on the cavitation type, pump design, installation and use. The excessive vibration caused by cavitation often subsequently causes a failure of the pump’s seal and/or bearings. This is the most likely failure mode of a cavitating pump.


28

Figure 2.10 – Centrifugal Pump Noise (Pearsall)

- Onset of flow instabilities. The dynamic response of a pump is strongly affected by cavitation, as a result of the significant amount of turbulence and unsymmetrical phenomena associated with the two phase flow. The consequent flow instabilities can be divided in three main categories: global oscillations, local oscillations and instabilities caused by radial or rotordynamic forces. The most interesting and well-recognized global instability is represented by the auto-oscillations or the POGO oscillations, pressure and flow vibrations which affect the whole suction line of the machine and are influenced by all the components of the propulsion system. The next section will describe in detail the main instabilities caused by cavitation. - Damage to pump parts. o Cavitation erosion or pitting

During cavitation, the collapse of the bubbles occurs at sonic speed ejecting destructive micro jets of extremely high velocity (up to 1000 m/s) liquid strong enough to cause extreme erosion of the pump parts, particularly impellers. The bubble is trying to collapse from all sides, but if the bubble is lying against a piece of metal such as the impeller or volute it cannot collapse from that side. So the fluid comes in from the opposite side at this high velocity and bangs against the metal. The resulting long-term material damage begins to become visible (Figure 2.11 depict the cavitation pitting effect on impeller and diffuser surface). Cavitation erosion from bubble collapse occurs primarily by fatigue fracture due to repeated bubble implosions on the cavitating surface, if the implosions have sufficient impact force. High head pumps are more likely to suffer from cavitation erosion, making cavitation a “high-energy” pump phenomenon. The most sensitive areas where cavitation erosion has been observed are the low-pressure sides of the impeller vanes near the inlet edge. The pitting has also been


29

observed on impeller vanes, diffuser vanes, and impeller tips etc. In some instances, cavitation has been severe enough to wear holes in the impeller and damage the vanes to such a degree that the impeller becomes completely ineffective. A damaged impeller is shown in Figure 2.12. The damaged impeller shows that the shock waves occurred near the outside edge of the impeller, where damage is evident. When cavitation is less severe, the damage can occur further down towards the eye of the impeller. The extent of cavitation erosion or pitting depends on a number of factors like presence of foreign materials in the liquid, liquid temperature, age of equipment and velocity of the collapsing bubble.

Figure 2.11 – Local damage due to cavitation erosion on the blades of a pump (Brennen, 1994).

Figure 2.12 – Extensive damage due to cavitation erosion on the blades of a pump (Brennen, 1994).

o Mechanical deformations Apart from erosion of pump parts, in bigger pumps, longer duration of cavitation condition can result in unbalancing (due to un-equal distribution in bubble formation and collapse) of radial and axial thrusts on the impeller. This unbalancing often leads to following mechanical problems: bending and deflection of shafts, bearing damage and rubs from radial vibration, thrust bearing damage from axial movement, breaking of impeller check-nuts, seal faces damage etc. These mechanical deformations can completely wreck the pump and require replacement of parts. The cost of such replacements can be huge.


30

o Cavitation corrosion Frequently cavitation is combined with corrosion. The implosion of bubbles destroys existing protective layers making the metal surface permanently activated for the chemical attack. Thus, in this way even in case of slight cavitation it may lead to considerable damage to the materials. The rate of erosion may be accentuated if the liquid itself has corrosive tendencies such as water with large amounts of dissolved oxygen to acids.

2.2 Parameters for the characterization of cavitation in turbopumps For the characterization of the cavitating performance of a turbopump, the relevant operational

parameter is the inlet pressure. The corresponding dimensionless coefficient is the “cavitation number” σ, defined as:

where pV is the vapour pressure of the working fluid. In the same way of the specific speed, a

“suction specific speed” ΩSS can be introduced:

The cavitating performance of a pump is summarized in characteristic curves like the one of

Figure 2.13, in which the head coefficient is shown, for a given flow coefficient, as a function of the cavitation number. The Figure highlights three particular values of the cavitation number:

- The “cavitation inception number” σi, where the cavitating region begins to appear; - The “critical cavitation number” σa, for which a certain head loss (3%, for example) has been

reached; - The “breakdown cavitation number” σb, for which the head rise of the pump is drastically

reduced.

Figure 2.13 – Typical cavitating performance of a pump (Brennen, 1994).

( )1

21

12

V

L T

p p

Rσ

ρ Ω

−=

34

1

SS

T V

L

Q

p p

ΩΩ

ρ

=⎛ ⎞−⎜ ⎟⎝ ⎠


31

Figure 2.14 –Cavitating performance of “X” impeller for different flow coefficients (Brennen, 1994).

When the temperature of the working fluid is increased, a clear decrease of the breakdown cavitation number is typically observed. This is well shown in Figure 2.15, which shows cavitation performance data for a centrifugal pump operating with water, as working fluid, at different inlet temperatures.

The explanation of this thermal effect can be given referring to the case of travelling bubble cavitation. When a single bubble, which begins to grow, enters a region of low pressure, the liquid on the surface of the bubble vaporize to provide the increase in volume of vapour filling the bubble. At lower temperatures the density of the saturated vapour is low and, therefore, the mass rate of evaporation of liquid as well as the rate at which latent heat, which are needed, are low. Since the heat is transferred from the bulk of the liquid and the rate of heat transfer is small, the temperature of the interface decreases slightly and the vapour pressure in the cavity only falls slightly below the corresponding value at bulk liquid temperature. Therefore, the driving force for the bubble growth (difference between the vapour pressure and the pressure far from the bubble) is not much influenced by thermal effects.

At higher temperatures, the vapour density can be many orders of magnitude higher than the one at lower temperatures, in this way, the evaporation process involves a higher liquid mass. The heat needed at the interface for the liquid-vapour change is higher the temperature in the bubble is substantially below that of the bulk liquid and the vapour pressure in the bubble is lower. Consequently, the driving force for the bubble growth is reduced and the bubble growth is inhibited.

Since the cavitation head loss is primarily due to the disruption of the flow by volumes of vapour growing and collapsing near the blades of the pump, the reduction in the rate of the bubble growth lessens the disruption, resulting in an improved performance and explaining the behaviour shown by Figure 2.15.


32

Figure 2.15 – Typical cavitating performance of a centrifugal pump at various temperatures (Brennen, 1994).

2.3 Scaling of the pump performance In the experimentation of pumps used in space rocket engines one of the main goals is represented

by the possibility of testing them in scaled conditions in order to obtain the performance of the pump carrying out tests at lower power level and, as a consequence, safer and cheaper operating conditions.

The geometric scaling is obtained if the test pump has the same dimensions of the real one, or if every dimension of the test pump is scaled with the same factor from the real one.The fluid dynamic scaling is obtained if the value of the two dimensionless parameters φ and ψ is the same in the test and real conditions. The Reynolds number has to be kept greater than 106 in both cases, in order to have noncavitating performance independent from Re, as the flow inside the pump is completely turbulent.

In noncavitating conditions, the pump performance can be scaled by satisfying the geometric and fluid dynamic scaling criteria. When the pump works in cavitating conditions, the scaling of the performance is complicated due to the need of an accurate reproduction of the shape and the characteristics of the cavitating region. The test and real pump have not only to work at the same cavitation number σ, but they have to satisfy also the following aspects:

- The test pump has not only to be geometrically scaled by the real one, but the shape of the blades has also to be exactly reproduced. The geometry of the leading edge and the trailing edge of the blade, in fact, strongly affects the formation of tip vortex cavitation.

- The tip clearance between the blades and the casing also plays an important role, as showed in Figure 2.16: but, when the clearance is less than 2% of the blade height, it has practically no influence on the performance.


33

Figure 2.16 – The effect of tip clearance on the cavitating performance of an inducer (Brennen, 1994).

For scaling the thermal cavitation effects, it is possible to make use of empirical or semi-empirical models like the one proposed by R. D. Moore (1970), based on experimental observations of cavitating Venturis. A detailed description of the Moore scaling criteria can be found, for example, in Bramanti (2002). The main result can be explained by the following equation between the test and the real pump, which, if satisfied, guarantees the thermal scaling:

where:

ρV, ρL,,TL,,αL , cPL , L are the vapour and liquid phase densities, the temperature, the thermal diffusivity, the specific heat and the latent heat of the working fluid, respectively, and Ω is the rotating speed of the pump and RT1 is the inlet tip radius of the pump, In order to obtain the cavitating scaling of the pump performance, the two cavitation numbers σtest and σreal have necessarily to be equal, and so the scaling conditions simply become:

( ) ( )1 1, , , ,Ltest test T test Lreal real T realC T R C T RΩ Ω=

1test test

real real

σ σσ σ

+ ∆=

+ ∆

( )( )

1

1

, ,, ,

Ltest test T testtest

real Lreal real T real

C T RC T R

Ω∆σ∆σ Ω

=

( )1.2 22

1 21

1, , VL T

T PL L L L

LC T RR c T

ρΩΩ ρ α

⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠

1test

real

∆σ∆σ

=


34

Given the operating parameters of the real pump (working fluid, dimensions, working temperature and rotating speed) and the working fluid, dimensions and rotating speed of the test pump, the above equations give the possibility to calculate the working temperature necessary for the test pump in order to assure the thermal cavitation scaling.

2.4 Flow instabilities generated by cavitation The significant cavitation levels typically occurring in space rocket inducers often lead to the

development of flow instabilities that can seriously degrade the performance of the machine, or even cause its rapid failure. According to Brennen (1994), these flow instabilities can be divided in three main categories: global flow oscillations, local flow oscillations and instabilities caused by radial or rotordynamic forces. The most dangerous and well recognized instabilities in cavitating pumps are due to global flow oscillations, i.e. vibrations (rotating stall, rotating cavitation, surge, auto-oscillation, supercavitation, unsteady blade cavitation) which affect not only the pump but also the entire propulsion system on a large scale. Some examples of local flow oscillations are represented by the blade flutter and the blade excitation due to rotor-stator interaction or to vortex shedding or cavitation oscillations. Radial and rotordynamic forces, finally, are global forces perpendicular to the axis of rotation: the first one are caused by circumferential nonuniformities in the inlet flow, casing or volute; the second ones occur as a result of an eccentric movement on the axis of rotation. The next table presents in detail the typical frequencies ranges of the above mentioned flow instabilities.

Instability type Frequency range

Surge System dependant,

3-10 Hz in compressors

Auto-oscillation System dependant,

0.1-0.4 Ω

Rotating stall 0.5-0.7 Ω

Vaneless diffuser stall 0.05-0.25 Ω

Rotating cavitation 1.1-1.2 Ω

Partial cavitation oscillation < Ω

Excessive radial force Some fraction of Ω

Rotordynamic vibration Some fraction of Ω when critical speed is

approached

Blade flutter Natural frequency of blade in liquid

Cavitation noise 1-20 kHz

Table 2.1 – Typical frequency ranges of pump instabilities

The next Figure presents the appearance of some forms of instabilities according to the cavitation number and flow coefficients.


35

Figure 2.17 – Various modes of cavitating flow in a 12° helical inducer as a function of cavitation number

and flow coefficient

2.4.1 The rotating stall Rotating stall is a phenomenon which may occur in a cascade of blades operating at a high angle

of incidence, close to that at which the blades stall. In a pump this usually implies that the flow rate is particularly low, close to the point of maximum in the noncavitating characteristic curve. Figure 2.18 shows the schematic of a set of blades operating at a high angle of incidence: if the blade B is stalled, this generates a separated wake and an increased blockage to the flow in the passage between blades A and B. This tends to deflect the flow as indicated in the figure, resulting in an increase in the angle of incidence on blade A and a decrease in the angle of incidence on blade C: blade A will tend to stall, while the stall on blade C will tend to diminish. As a consequence the stall moves upwards in the figure, or rotates around the axis in the real pump, with a typical rotating speed equal to 50-70% of the pump rotational speed.

Figure 2.18 – Schematic of a stall cell in a cascade of blades (Brennen, 1994).


36

The rotating stall causes a redistribution of the flow, but not necessarily any oscillation in the total mass flow rate through the turbomachine, as surge. On the other hand, it is always possible that the perturbation caused by rotating stall could resonate with one of the acoustic modes in the inlet or discharge line, in which case significant oscillation of the mass flow rate could occur.

The rotating stall is most frequently observed in compressors having a large number of blades. A useful approximate criterion for the identification of rotating stall in a rotor is that it occurs when the point of maximum in the total head rise curve is approached as the flow coefficient decreases. This is, however, no more than an approximation and there are a number of observed cases in which rotating stall occurs when the slope of the performance curve is still negative.

2.4.2 The rotating cavitation The first visual observation of rotating cavitation was made by Kamijo et al. (1980) on a three

bladed inducer with the inlet blade angle 10° and the solidity 2.5 at the tip. Inducers or pump impellers which do not show rotating stall under noncavitating conditions can

exhibit a similar phenomenon, known as “rotating cavitation” at lower cavitation numbers. The first report of rotating cavitation was made by Rosemann (1965) on a three bladed inducer. Even if they appear to be somewhat similar, a significant difference exists between the two phenomena. The rotating stall occurs at locations of the head-flow characteristic for which the slope of the curve is positive and therefore unstable. The rotating cavitation, on the other hand, is normally observed in the stable zone (negative slope), for cavitation numbers between 2 and 3 times the breakdown value, and has a frequency between 1.1 and 1.2 times the rotating speed of the pump. This is confirmed by Figure 2.19, referred to a cavitating inducer tested in a Japanese laboratory, which shows that rotating cavitation occurs when the head coefficient begins to be affected by the cavitation.

Figure 2.19 – Occurrence of rotating cavitation and auto-oscillation in the performance of a cavitating

inducer (Brennen, 1994).

It is possible then to outline that: - the rotating cavitation is observed at the design flow rate. This is quite different from the

rotating stall which occurs at partial flow rate. - the cavitating region rotates faster than the impeller. This is also different from rotating stall

in which the stalled region rotates slower than the impeller.


37

- in a certain range of cavitation number the radial force rotates fixed to the rotor and sometimes wanders at random. This is called attached asymmetric cavitation. The radial force decreases when the head starts to decrease steeply (“head breakdown”). This means that rotating cavitation occurs in a range of cavitation number just above the head breakdown cavitation number. The small head decrease under the occurrence of rotating cavitation and the attached asymmetric cavitation is a result of those cavitation instabilities.

2.4.3 The alternate blade cavitation The alternate blade cavitation is another form of instability, in which the cavity length differs

alternately and may occur for inducers with an even number of blades. The flow field around alternate blade cavitation is shown in the next Figure, with those around

shorter equal length cavities. It is possible to note that there exists a region near the trailing edge of cavities in which the flow is inclined towards the suction surface of the blades and the incidence angle to the neighboring blade is smaller. This region starts to interact with the leading edge of the neighboring blade when the cavity length exceeds 65% of the blade spacing. If the cavity on one blade becomes longer than 65% of the blade spacing for some reason, the incidence angle to the neighboring blade will decrease and hence the cavity length on the neighboring blade will also decrease. Then the incidence angle to the original blade will increase and the length of the cavity on it will increase further. This is the mechanism of the development of alternate blade cavitation (Tsujimoto , 2001).

According to Tsujimoto et al., this mode appears for equal cavitation longer than 65% of the blade spacing, h, which shows that the longer equal cavitation is statically unstable to a disturbance corresponding to the transition to alternate blade cavitation. The alternate blade cavitation does not have this mode and hence it is statically stable. The above discussion applies only for the cases with even number of blades. With odd number of blades, we do not have a solution corresponding to alternate blade cavitation. The equal length cavity is statically stable for all values of σ α /2 .

Figure 2.20 – Example of alternate blade cavitation (Tsujimoto, 2001)


38

2.4.4 The surge Surge and auto-oscillation are system instabilities that involve not just the characteristics of the

pump but those of the rest of the pumping system, resulting in pressure and flow rate oscillations that can not only generate excessive vibration and reduce performance, but also threaten the structural integrity of the components of the system. Figure 2.21 shows the onset mechanism of this flow instability.

Figure 2.21 – Schematic of stable and unstable characteristic curves of a pumping system (Brennen, 1994).

In the left part of the figure, the steady-state characteristic of the pump (in terms of head rise as a function of the mass flow) is plotted together with the steady-state characteristic of the rest of the system (in terms of head drop as a function of the mass flow). In steady-state operation, the head rise of the pump must equal the head drop of the rest of the system for the same flow rate (equilibrium point O). If the flow rate decreases just below the equilibrium point, the pump A, which has a characteristic curve with negative slope, tends to produce more head than the head drop in the rest of the system, causing the flow rate to increase and re-approach the equilibrium point. As a result, for pump A the point O represents a stable operating point. On the other hand, the system with a pump B, which has characteristic curve with positive slope, the point O is unstable.

The best known example of this instability occurs in multistage compressors, in which the characteristic curve is similar to the one showed in the right part of Figure 2.21: in this case the point A is stable, the point B is neutrally stable and the point C is unstable, leading to an instability known as “compressor surge”. The typical frequency of surge oscillations is particularly low, not higher than 3-10 Hz in compressors.

2.4.5 The auto-oscillation In many installations involving a pump that cavitates, violent oscillations in the pressure and flow

rate in the entire system occur when the cavitation number is decreased to values at which the head rise across the pump begins to be affected (Braisted and Brennen 1980, Kamijo et al. 1977, Sack and Nottage 1965, Natanzon et al. 1974, Miller and Gross 1967, Hobson and Marshall 1979). These oscillations can also cause substantial radial forces on the shaft of the order of 20% of the axial thrust (Rosenmann 1965). This surge phenomenon is known as auto-oscillation and can lead to very large flow rate and pressure fluctuations in the system. It occurs when the slope of the pump head rise/flow rate curve is still strongly negative. Another characteristic of auto-oscillation is that it appears to occur


39

more readily when the inducer is more heavily loaded; in other words at lower flow coefficients (Figure 2.22). Unlike the case of surge, the frequency of auto-oscillation usually scales with the rotating speed of the pump, in the way showed in Figure 2.23

Figure 2.22 – Cavitation performance of the SSME low pressure LOX pump model, showing the onset

and approximate desinence of the auto-oscillation at 6000rpm (from Braisted and Brennen 1980).

Figure 2.23 – Ratio of the auto-oscillation frequency to the pump rotating speed, as a function of the latter, for an helical inducer (Brennen, 1994).

2.4.6 Rotordynamic instabilities Rotordynamic instabilities have been receiving ever increasing attention among designers,

manufactures and operators of high performance turbomachines. Difficulties such as rough running (noise and vibration), excessive loads and wear on both stationary and rotating components, loss of performance (drop in head), and in some cases catastrophic failures, can often be caused by some kind


40

of rotor vibration. These vibrations are referred to as rotor “whirl”. By definition, whirl describes motion of a rotor combining both: pure rotation of the rotor around its deflected centreline and random or organized excursions (in time and space) of this centreline around its undeflected position. According to Brennen (1995) the two main categories are:

- Radial forces are forces perpendicular to the axis of rotation caused by circumferential nonuniformities in the inlet flow, casing, or volute. While these may be stationary in the frame of the pump housing, the loads that act on the impeller and, therefore, the bearings can be sufficient to create wear, vibration, and even failure of the bearings.

- Fluid-induced rotordynamic forces occur as the result of movement of the axis of rotation of the impeller-shaft system of the turbomachine. Contributions to these rotordynamic forces can arise from the seals, the flow through the impeller, leakage flows, or the flows in the bearings themselves. Sometimes these forces can cause a reduction in the critical speeds of the shaft system, and therefore an unforeseen limitation to its operating range. One of the common characteristics of a fluid-induced rotordynamic problem is that it often occurs at subsynchronous frequency.

Chapter 3 - The CPRTF

41

3 THE CPRTF

In the following section a detailed description of the facility where the experimental tests were carried out, will be presented. The main components of the basic configuration CPTF (Cavitating Pump Test Facility) will be described and the upgraded versions will be analyzed in detail: in particular, the CI2TF (Cavitation Induced Instabilities Test Facility) designed to investigate the fluid-dynamic instabilities and the CI2RTF (Cavitation Induced Instabilities and Rotordynamic Test Facility) designed to measure the rotordynamic forces and the induced instabilities. In the last part of the section the acquisition system and the procedure to post-process the data will be reported in detail.

3.1 Introduction The CPTF (Cavitating Pump Test Facility), Figure 3.1, has been designed, procured and

assembled at Centrospazio, Space Research Laboratory, under ESA and ASI funding and represents a low-cost, versatile and instrumentable cavitation test facility, which can be presently arranged in three alternative configurations, which will be described in detail in the next sections, are the following:

• The CPTF, designed for general experimentation on cavitating/non-cavitating turbopumps under fluid dynamic and thermal cavitation similarity;

• The CPRTF (Cavitating Pump Rotordynamic Test Facility), an upgraded version of the CPTF also capable of investigating rotordynamic fluid forces in forced vibration experiments on turbopumps with rotors of adjustable eccentricity and sub-synchronous or super-synchronous whirl speed;

• The CI2TF (Cavitation Induced Instabilities Test Facility) and CI2RTF (Cavitation Induced Instabilities and Rotordynamic Test Facility), upgraded versions of the CPTF and the CPRTF specifically designed for the characterization of the flow instabilities generated by the test pump under cavitating or non-cavitating conditions;

• The TCT (Thermal Cavitation Tunnel), an alternative configuration of the CPTF specifically designed for the investigation of 2D or 3D cavitating flows over test bodies in thermal similarity conditions. The TCT description will be reported in the section 8.


42

Figure 3.1 – Picture of the test facility

Table 3.1 shows the main operational parameters of the facility, while Figure 3.2 presents the facility operational envelope in the specific speed-specific diameter plane. The yellow area demonstrates that the CPTF facility allows the tests on many different pump geometries with operational characteristics.

Table 3.1 – Operational parameter of the facility

CPRTF operational characteristics Pump rotational speed Ω = 0 ÷ 3000 rpm Main motor power P ≤ 30 kW Main motor torque M ≤ 100 Nm Suction pressure pt1 = 0.01÷ 6 bar Discharge pressure pt2 ≤ 11 bar Volumetric flow rate 30.1 m sQ ≤ Flow temperature T = 10 ÷ 90 °C Suction line diameter DN = 6” Discharge line diameter DN = 4” Impeller eye radius rT1 ≤ 90 mm Impeller outlet radius rT2 ≤ 112 mm Adjustable eccentricity e = 0 ÷ 2 mm Whirl rotational speed ω = −3000 ÷ 3000 rpm Nominal suspended mass mS = 4 kg Dynamometer loads: lateral Fx = Fy ≤ 2400 N axial Fz ≤ 15000 N bending Mx = My ≤ 1400 Nm torque Mz ≤ 400 Nm


43

Figure 3.2 – The facility operational envelope in the specific speed-specific diameter plane

As previously pointed out, the method of Moore allows to predict the pump performance in cavitating conditions but also to evaluate the temperature of working fluid (for example water in our case) necessary to simulate the thermal effects of several fluids commonly used in liquid rocket propulsion, as liquid oxygen, liquid hydrogen, nitrogen tetroxide and monomethil-hydrazine. The importance of Moore scaling laws is founded on the possibility to obtain the same results in terms of pump performance by using a safe fluid such as water instead “more complex” fluids. Cryogenic fluids, in fact, have be stored in liquid phase at very low temperature (90 K for the oxygen, while 20 K for the hydrogen), are inflammable, complicated to handle and many precautions have to be assured. Nitrogen tetroxide and monomethil-hydrazine are extremely toxic, need health and safety protection procedures during the propellant production, storage and handling.

Figure 3.3 shows the curves of the water temperature, as a function of the Reynolds number in the real pump, (Rer), needed in the CPRTF for scaling real pumps, operating with different fluids, at a Reynolds number, (Rem), equal to 106 in the facility. The water temperature needed in the CPRTF for scaling pumps operating with liquid oxygen, as a function of the Reynolds number in the real pump and in the test model is presented in Figure 3.4.

Finally Table 3.2 reports a list of the main turbopumps used in liquid rockets, their working fluid, their working Reynolds numbers and the minimum temperature that have to be achieved in order to scale the thermal effects and to test them in water with a minimum Reynolds number of the pump model of 106 .


44

Figure 3.3 – Water temperature needed in the CPRTF for scaling pumps operating with different fluids at

a Reynolds number equal to 106, as a function of the Reynolds number in the real pump.

Figure 3.4 – Water temperature needed in the CPRTF for scaling pumps operating with liquid oxygen, as a function of the Reynolds number in the real pump and in the test model.


45

Table 3.2 – Temperature needed in the CPRTF for scaling full-scale tests of some space rocket turbopumps at Rem = 106.

3.2 CPTF configuration The first configuration of the facility, the CPTF (Cavitating Pump Test Facility), has been

designed for conducting experiments on pumps in noncavitating/cavitating conditions under geometrical, fluid dynamic and thermal cavitation similarity, with no impeller whirl motion. It is also possible to characterize the most important cavitation instabilities of the test pump (cavitation surge and auto-oscillations, rotating cavitation, POGO instabilities). The design of the facility involved a number of technical problems and trade-offs in order to best satisfy the operational, economic and performance requirements. Priority has been given to safety and cost considerations: the facility was designed to operate at rotational speeds considerably lower than those of turbopump systems for liquid-propellant rockets using a non-dangerous fluid (water), but satisfying all of the similarity conditions essential for accurately scaling the real pump performance. This makes it possible to use the CPTF also as a “didactic” tool by graduate and undergraduate students willing to improve their experimental knowledge of turbopumps.

Another important characteristic of the CPTF is its versatility: it is capable of testing a wide variety of pumps (axial, centrifugal and mixed-flow) and can be easily reconfigured to carry out investigations on a large number of fluid dynamic phenomena relevant to turbopump operation (rotating cavitation, POGO instabilities, cavitation noise, tip leakage, vortex shedding, blade flutter, transient phenomena, liquid quality effects, flow visualization, etc.).

The next Figure presents the architecture of the CPTF, which consists of a closed water loop comprising the necessary equipment for controlling the operational parameters of the pump, and an instrumented test section where the pump itself is located. The Figure also shows a picture of the facility. The working fluid is water which allows to carry on the experiments in safe conditions and maintaining low cost and to simulate the cavitating condition behaviour of more dangerous cryogenic fluid by warming up the water temperature.

Turbopump Working fluid Working Rer Minimum water

temperature Tm

Vulcain LH2 Liquid hydrogen 3.8*108 90°C

Vulcain LOX Liquid oxigen 9.7*107 70°C

RD - 253 NTO 108 51°C

ATE pump NTO 5.7*107 58°C


46

Figure 3.5- CPTF schematic

The starting point of the water loop facility can be considered the tank (B), in which an air-bag (CA) is inserted to uncouple the inlet/outlet volume fluctuations generated by cavitation in the pump during the different working conditions and to allow the control of the water pressure in the tank and in the entire facility as it is connected to the pressuring depressurizing loop. After the exit from the tank, the fluid flux passes respectively a 90° pipe, the flow straighteners (RF), honeycomb-filled pipe sections that drastically reduce the flow turbulence and rotation for better operation of the flowmeters providing more regular flow conditions at the pump inlet and the electromagnetic flowmeters (FM), used to measure flow rate and velocity.

Following the suction line, the fluid flux arrives to the test section (CP) which is composed by the “housing” where the test pump is mounted together with its volute. The dimensions and interfaces of the test section have been chosen in order to house a large number of different pumps, in particular the new evolution (called “Mark 2”) of the liquid oxygen turbopump of the Ariane 5 “Vulcain” engine, used as the reference pump for the design of the facility. The inlet of the test section (AO) consists of a transparent tube with plane external surfaces, allowing for optical visualization of the flow into the axial stage of the test pump. Another optical access is the window (SV), which can be mounted in the


47

suction line and allow the visualization of the pump in a front view (in this case the removal of the honeycomb will be necessary).

In order to avoid the excessive vibration propagation, two elastic couplings (CE) are inserted. The pump shaft is connected to the main engine (MP) through an omokinetic coupling rotates

The test pump is driven by a main motor (MP), which can be electronically controlled in order to maintain a practically constant value of the rotational speed. The main motor and the pump shaft are connected by means of an omokinetic coupling (G), able to transfer torsional loads also when small misalignments between the two shafts are present.

At the exit of the test section, after the elastic coupling and another 90° elbow, there are a second flow straightener and another flow meter, having the scope of monitoring the flow conditions in the discharge line and, if necessary, to provide a comparison with the measurement of the same quantities in the suction line. Finally, the valve (V) gives the possibility to provide a pressure drop in the working fluid and, as a result, to guarantee the continuous flow in the water loop. It is a non-conventional item, called “Silent Throttle Valve”, able to provide the required pressure drop smoothly, without generating cavitation in the working fluid.

The loop is made of flanged stainless steel (AISI 316) pipes, with an internal pipe diameter of 6” on the suction line and 4” on the discharge line; the active portion of the facility (motors, mechanical transmissions, test section and inlet line) is mounted on a very stiff carbon-steel beam structure.

Referring to Figure 3.6, the main components of the CPTF are: • The 0.5 m3 stainless steel tank (T) used to regulate water properties (temperature and

pressure) and to uncouple the inlet/outlet volume fluctuations generated by cavitation in the pump. To this purpose the tank makes use of a 5 kW electrical resistance and a 40 liters air-bag (AB) connected to an air compressor or a water ring vacuum pump.

• The valve (V), which generates the adjustable pressure drop necessary to load the pump and separates the suction and discharge lines. The particular valve used, called “Silent Throttle Valve”, creates a distributed loss capable of yielding large pressure drops without inducing unsteady cavitation, which would generate unwanted dynamic noise and additional cavitation nuclei (microbubbles) in the working fluid.

• The electromagnetic flowmeters (FM), one on the suction line and one on the discharge line, used to measure flow rate and velocity.

• The main motor (MM), a 6-pole, 30 kW, brushless motor driven by power electronics capable of controlling one or more motors in angular position or speed. The motor is connected to the pump by a omokinetic, torsionally stiff coupling, in order to accommodate the misalignments due to mounting or manufacturing errors.

The next Figure shows the 2D-schematic of the facility whose main components will be presented

in the next paragraphs.


48

Mot

ore

prin

cipa

le

Giu

nto

omo c

inet

ico

Cam

era

di p

rov a

Trav

i di s

oste

gno

Sta

ffe d

i sm

onta

ggio

Bolli

tore

Valv

o la

F lus

sim

etro

4"

Rad

driz

zato

re 4

"

Com

pens

a tor

e 4"

Flus

sim

e tro

6"

Rad

driz

z ato

re 6

"

Com

pens

ator

e 6"

Spe

col a

vis

iva

Figure 3.6 - CPTF schematic

3.2.1 The tank The tank (Figure 3.7) has to accomplish the following main functions:

• to reserve the water in the facility

• to regulate the working fluid temperature by heating the water up to 80°C through a 5 W stainless-steel resistor installed inside the tank and by cooling it down through a heat exchanger, having a 3 m2 exchange surface in order to avoid the excessive increase of


49

water temperature during the tests and to allow a faster return to water temperature after the heating process

• to sustain the volume fluctuations of the working fluid caused by the flow oscillations in cavitating conditions and the water density variations due to the temperature variation. This result can be accomplished by an air-bag inserted inside the tank, an EPMD membrane which can be inflated to reach a volume up to 40 litres

• to control the pressure inside the tank and the inlet pressure to the pump, by regulating the pressure inside the airbag through a pressurizing/depressurizing circuit

• to allow the evacuations of the larg part of air bubbles from the working fluid; the larger bubbles (100 µm diameter or more), after entering the tank from the discharge line, do not follow the water flow and are drained upwards by the Archimede force, until they remain trapped at the top of the tank from where they can be evacuated by means of a vacuum pump.

Figure 3.7- Schematic view of the tank

The main tank is made of AISI 316 stainless steel and has a volume of 500 litres (1690 mm height, 650 mm diameter). It contains a magnesium anode for preventing metal corrosion, a safety valve for maintaining the pressure lower than 6 atm, a barometer and a thermometer. The discharge line terminates with a 90° elbow inside the tank, in order to obtain a partial “centrifugation” of the fluid and to facilitate the evacuation of the air bubbles upwards.

3.2.2 The fill-drain and pressurization/depressurization circuits The tank is connected with a pressurization/depressurization system (Figure 3.8). The fill-drain

circuit connects the tank with an axiliary plastic tank (1000 liters volume), where the water is collected before and after filling the facility. Two electro-pumps assure the fill and drain of the facility; their mass flow rate is 50 liters per minute and head is 2 atm. The air-bag pressurization is accomplished by


50

a air compressed line, while the depressurization and the air drain is guaranteed by a liquid ring vacuum pump; this pump is allow to reach vacuum level of about 0.05 atm, providing low aspiration rate between 5 and 10 m3/h, necessary due to drain air from the little air-bag volume.

Figure 3.8- Schematic of fill-drain circuit

The experimental tests, performed in order to characterize the inducer performance in cavitating conditions, were carried out in certain cases in the so called “continuous conditions” by varying constantly the static pressure. A schematic of the system used is shown in detail in the Figure 3.9. The pressure p1 inside the air-bag was regulated by a mass flow balance consideration. The air-bag is connected to a neddle valve S, which has a double derivation one to the bottle and the other one to the vacuum pump, P. To maintain the “continuous conditions”, the procedure is the following:

o to fix the pressure inside the bottle, read by the vacuum-meter V, o to keep the pressure pb constant (at a value bp ) during each experiment by opportunely

opening or closing the needle valve and, consequently, regulating the two mass flows 1m and 2m .

p1

1

bp

.m2

V

S

vV.

Figure 3.9- Schematic of pressurization/depressurization circuit


51

Since the needle valve can be considered critical for practically the whole experiment and the vacuum pump works at a constant volumetric flow rate VV , the following equations can be written:

11

1 2b

dm mdt

dm m mdt

⎧ = −⎪⎪⎨⎪ = −⎪⎩

with cosvV t= , 1 1 /p RTρ = and /b bp RTρ = (3.1)

while the flow rate inside the valve is:

( )1 1;tm C A pγ= with ( )112;

1t tC A ART

γγγγ

γ

⎛ ⎞+⎜ ⎟−⎝ ⎠⎛ ⎞

= ⎜ ⎟+⎝ ⎠ At is the throat area

The system becomes, considering that the pressure bp inside the bottle is maintained constant:

( )

( )

1 11

1

;

;

t

b b vt b

V dp C A pRT dtV dp V

C A p pRT dt RT

γ

γ

⎧ = −⎪⎪⎨⎪ = −⎪⎩

→

( )

1

1

1 ;

v b

b tv

V pdpdt V

RTp p C AV

γ

⎧= −⎪

⎪⎨⎪ =⎪⎩

(3.2)

The first of the above equations confirms that the drain velocity dp1/dt in the air-bag results constant and is controlled by the initial pressure inside the bottle, which is constant, bp . From the second equation, bp can be kept constant if C is varied during the experiment in order to follow the variation of the pressure p1. This result can be obtained by opening or closing the needle valve and, as a consequence, varying the dimensions of the throat section At. The decreasing rate of the pressure in the air-bag, being proportional to bp , can be regulated by varying the vacuum reservoir pressure.

3.2.3 The supporting structure The suction line of the facility is firmly fixed to the floor, in order to provide good stiffness and to

avoid dangerous vibrations of the structure during tests in heavy operating conditions (i.e. for the characterization of global flow instabilities like the surge and the auto-oscillations). The suction line pipes, the test chamber and the main motor are sustained by an I-shaped beam, fixed to the floor by means of M16 bolts. The alignment of the pipes axes is obtained using a particular system, illustrated in the left part of Figure 3.10: the pipe is supported by two cilindrical guides, whose distance can be regulated by means of a transversal screwed bar. When the desired position is reached, the position of the pipe is fixed by bolts.

The assembling and the disassembling of the suction line, on the other hand, are facilitated by the use of the mechanism represented in the right part of Figure 3.10, which gives the possibility to easily connect or disconnect the last tube of the suction line to/from the inlet of the test chamber.


52

Figure 3.10 – The system for the regulation of the position of the pipes (left) and the mechanism for the

assembling/disassembling of the suction line (right).

3.2.4 The flow straighteners and the elastic coupling The turbulence of flow which occur after the passage in the 90° tubing and the inducer is reduced

by the use of flow straighteners (Figure 3.11) mounted at the exit of tank and the test chamber. The flow inside the flow straighteners becomes laminar due to the presence of an aluminum honeycomb with an hexagonal section (50 mm length), fixed inside a tubing.

Figure 3.11- Schematic of the flow straighteners

The elastic coupling allow to compensate possible axial, radial or angular misalignments between the tubing due to errors during the realization or mounting and to assure a better insulation from the vibrations in order to decouple dynamically the suction line with the rest of the circuit and from sudden pump arrest. The elastic coupling Figure 3.12 allow an easier facility disassembly.

Figure 3.12- Schematic view of the elastic coupling


53

3.2.5 The flowmeters Two electromagnetic flowmeters (Figure 3.13) are mounted in the suction line and in the drain

line respectively, in order to measure and control the mass flow rate in the facility. The flowmeters are able to measure mass flow rate between 0.3 and 10 m/sec with a resolution of

0.5% and to sustain temperature up to 40 atm. The internal coating of Tefzel® (ETFE) allows a temperature range between -29°C and 149°C.

Figure 3.13- Picture of the flowmeter 8732C from Fisher Rosemount (modello da 6”)

3.2.6 The “Silent Throttle Valve” This component has the function of generating a pressure drop in the working fluid, in order to

“load” the test pump. Regulating the pressure drop across the valve, in fact, it is possible to force the pump to work at different operating conditions, giving the possibility to cover a large part of its performance curve. The Silent Throttle Valve (Figure 3.14) is a non conventional item, whose peculiarity is to create the pressure drop in the working fluid without generating cavitation nucleii, so reducing vibrations and erosion problems and, at the same time, reducing the amount of vapour bubbles in the water loop and at the inlet of the test pump.

The cylindrical outer casing of the valve (3), made of stainless steel, contains a deformable rubber element (2), connected to two perforated metal plates, (9) and (8). Two hundred holes are made on the rubber element and on the two rigid plates. The plate (8) is connected to the component (7) and to the piston (4), moved by pressurized oil (up to 300 atm) coming from a manual lever pump. The movement of the piston gives the possibility to lengthen or shorten the deformable rubber element, so varying the holes diameter and, as a consequence, the amounts of the pressure drop across the valve. This pressure drop is principally caused by viscous forces and is particularly gradual, so preventing the inception of cavitation nucleii (as it should be in a conventional valve, characterized by a very “localized” pressure drop) and assuring a really smooth and silent functioning.


54

Figure 3.14- Silent ThrottleValve

3.2.7 The main engine and omokinetic coupling The main engine (Figure 3.15), a MOOG model FASF3V8029, is a “brushless” with six poles,

with 30 kW maximum power and 100 Nm maximum torque. The rotational speed, Ω, is up to 3000 rpm. The engine is controlled in position and speed by a dedicated electronics with a error range of ± 1° and ± 3 rpm, respectively. A pc program allows to set the engine working parameters and to acquire simultaneously the angular position, the speed and the torque.

The main characteristics are: - the capability to maintain constant the rotational speed, before starting the test - the possibility to add a secondary engine in order to provide a whirl motion to the pump and

to set the rotational velocity ratio between a secondary engine and the main engine ω/Ω at values positive and negative minor or major than the unity

- the possibility to constantly know the angular speed, angular position, torque - the possibility to attain angular velocity very low (few rpm), assuring the required torque

Figure 3.15- The main engine and the omokinetic coupling between the main engine and the pump shaft

The omokinetic coupling (Figure 3.15) between the engine shaft and the pump shaft assures:

• - a high torsional stiffness in order to maintain the same angular position between the main engine and the pump shafts

• - the possibility to compensate possible axial, radial or angular misalignments between the shafts

• - to transmit the torque moment between the two shafts


55

3.2.8 The test section The test section (Figure 3.16 and Figure 3.17) is the fulcrum of the facility. The turbopump is, in

fact, mounted inside it. The test section design was performed in order to be easily reconfigurable and to allow the possibility to mount several types of test pumps with few modifications.

Figure 3.16- Schematic of the test section

Figure 3.17- Schematic view of the test section

The main three parts of the test section are the following:

• The inlet section

• It is made by two concentric Plexiglas conducts in order to allow an optical access to visualize the flux at the inlet of the pump. Between the two conducts, there is 1 mm slit, which is filled by a NaI solution to avoid distortion phenomena because it has a similar refraction coefficient to Plexiglas. The more external conduct can be not present, while the internal one can be substituted according to the dimensions of the pump, which has to be tested.


56

- The test body and closing part

• An aluminum hallow cylinder is the test section casing, while two caps assure the front and back test section closures. The test section has been conceived to allow the test many model of pumps in combination with different volute geometries and dimensions in order to better investigate the turbopump performance. The casing has a diameter of 500 mm, axial length 281 mm and allow a maximum working pressure of 11 bar.

- The shaft, bearings and seals

• These elements are the most critical ones in the entire test chamber. One bearing with cylindrical rolls is mounted on the shaft front while two oblique bearings with spheres in the shaft rear. The radial seals were chosen to be suitable for rotating and alternate motion.

3.3 CPRTF configuration As previously pointed out, the facility has been designed to be easily reconfigurable through the

design and substitution of few parts, such as interfaces and components inside the test section, according to prototypes, which have to be tested. An upgraded version of the CPTF (Cavitating Pump Test Facility) is the CPRTF (Cavitating Pump Rotordynamic Test Facility), which has been conceived to allow the study of rotordynamic forces acting on turbopumps in noncavitating and cavitataing conditions under geometric, fluiddynamic and thermal similarity. A forced whirl motion of adjustable eccentricity and rotational speed can be given to the pump. The main differences between the CPTF and the CPRTF are related to the test section, the motors and the transmission, and are schematically summarized in Figure 3.18 and Figure 3.19.

An auxiliary motor (MS) is used to generate the whirl motion. The electronic controllers drive the two motors in order to maintain a constant ratio between the whirl speed ω and the rotational speed Ω. This ratio ω/ Ω can be varied between values minor or major than 1 or also equal to 1, obtaining in this way a subsychronous, supersynchronous and synchronous whirl motion. The transmission of the whirl motion from the auxiliary motor to the pump is obtained by a belt. The omokinetic coupling (G) is different from the one used in the CPTF configuration, because it must sustain significant radial misalignments due to the forced eccentricity. This leads to a longer coupling with respect to the one depicted in the basic configuration.

Figure 3.18 – Schematic of the test section, the motors and the transmission in the CPRTF.


57

Figure 3.19- Schematic of the auxiliary engine disposition in the facility

The system for adjusting the shaft eccentricity is based on the principle schematized in Figure 3.20. The pump shaft casing is divided in two parts, having eccentricities e1=e2=1 mm. When the inner part of the casing is rotated into the outer part, the two eccentricity vectors can be composed in order to obtain a total eccentricity variable from a minimum of 0 mm (no eccentricity, when the two vectors have opposite directions or the θ angle of Figure 3.20 is equal to 0°) to a maximum of 2 mm (when the two vectors have the same direction or θ is equal to 180°). A vast number of intermediate positions (or θ values) are possible, so giving the possibility of a fine eccentricity adjustment in the range 0÷2 mm.

Rotazionedel sistemaeccentrico(ω)

Rotazione dell’albero della pompa (Ω)

θ

e1

e2

e

Figure 3.20- Schematic of the cynematic mechanism and eccentricity vectorial composition

Figure 3.21 shows a cut-off drawing of the test section in the CPRTF configuration. It is possible to see the mechanism for the eccentricity adjustment, the two labyrinth face seals (whose leakage can be adjusted in the range 0.1-0.7 mm in order to investigate the effect of this parameter on the pump performance and the fluid forces) and the rotating dynamometer (orange item), the custom-designed component used for the measurement of the rotordynamic forces on the test pump. The internal dynamometer chamber is kept dry by means of specifically designed O-ring seals, and the wires for transmitting the force signals from the measuring strain gauges pass through the internal cavity of the pump shaft and are taken to the data acquisition system through a slip ring assembly.

Motore secondario Slip ring Motore PrincipaleRFTF


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Figure 3.21 – Cut-off drawing of the CPRTF test section.

Figure 3.22- Schematic view from the rear part of the CPRTF

3.3.1 The auxiliary motor As for the main motor, the auxiliary is brushless-type and produced by Moog, mod.

FASF2V4030. The maximum power is 5.6 kW and the maximum torque is 18 N, with a rotating speed ranging from 0 to 3000 rpm. The auxiliary motor is controlled by its power electronics in angular position and velocity with reference to the main motor, in order to retain a specified velocity ratio ω Ω and initial/final angular positions during test runs. The motor controller also generates digital readouts of the angular position and rotational speed of the eccentricity for the data acquisition system. Figure 3.23 shows the auxiliary motor with the CPRTF omokinetic coupling and the belt for the transmission of the whirl motion to the pump.


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Figure 3.23 – The auxiliary motor with the CPRTF omokinetic coupling (left) and detail of the transmission belt (right).

3.3.2 The rotating dynamometer The rotating dynamometer is the main component of the CPRTF, which makes this configuration

of the facility particularly powerful and consents the measurements of rotordynamic forces and moments acting on the test pump. The dynamometer is a custom-designed item realized in just one piece of phase hardening steel AISI PH 17-4 and comprises two flanges connected by four square cross-section posts acting as flexing elements. Their deformation is sensed by 40 semiconductor strain gauges (Micron, mod. SS-060-033-1000P-S4, 500 Ω, 155 gauge factor) arranged in 10 full Wheatstone bridges, which provide redundant measurements of the forces and moments acting on the impeller. Each bridge is temperature self-compensated and, for increased precision, has separate bipolar excitation and read-out. The temperature dependence of the gauge factors is accounted for in the data reduction process. The sizing of the sensing posts trades off sensitivity against structural resistance, operational stability and position control (stiffness). The four posts have a length of 27.5 mm and a 5 mm square section, and their distance from the dynamometer axis is equal to 70 mm. The suspended mass is 4.3 kg. The design conditions are ω = 1500 rpm and Ω =1500 rpm, which lead to a fatigue life greater than one million cycles. Ten strain gauges are installed on each post: 4 at ¼ length and 4 at ¾ length for the measurement of torque and radial forces, while the other 2 strain gauges are in the central section of the post, on two opposite sides, for the measurement of the axial force. Figure 3.24 shows a picture of the rotating dynamometer.

Figure 3.24 – The rotating dynamometer (left) and detail of one of the measuring posts (right).


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The calibration of the dynamometer was carried out by means of a dedicated, self-designed test bench showed in Figure 3.25 (Saggini, 2004). Six linearly independent loading conditions were applied by means of calibrated masses connected to a pulley system. As a result, the dynamometer calibration matrix was obtained, i.e. the correlation between the voltage outputs of the Wheatstone bridges and the forces and moments applied on the dynamometer. It has to be noted that, as a consequence of the redundant measurement of the forces and moments, the dynamometer calibration matrix is not a square one but has 10x6 elements (10 Wheatstone bridges, 6 measured components of forces and moments).

Figure 3.25 – The test bench used for the calibration of the rotating dynamometer.

3.4 The CI2TF and CI2RTF configurations The CI2TF (Cavitation Induced Instabilities Test Facility) represents a further upgraded version of

the CPTF and allows to study and analyze the fluiddynamic instabilities due to pressure oscillations of the fliud on the turbopumps under noncavitating and cavitating conditions. The next Figure shows a schematic of the inlet section of the CI2TF with a test inducer installed in it. It represents a further upgraded version of the CPRTF and allows to combine the study of the fluiddynamic instabilities and the analysis of the rotordynamic forces acting on the turbopumps under noncavitating and cavitating conditions.

plexiglas

Figure 3.26 – Schematic of the Plexiglas conduct with the pressure sensors


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This configuration is meant to provide the possibility to perform very innovative experiments due to the capability to supply a forced whirl motion to the shaft, to increase the water temperature. It will be possible to correlate complex phenomena such as the influence of thermal effects on the flow instabilities and the rotordynamic forces in presence of whirl motion. The flow instabilities are characterized by means of piezoelectric transducers for the measuring of the pressure oscillations near the test pump, which is typically an axial inducer because the most significant (and dangerous) instabilities have been historically observed on this kinds of pumps. In this configuration the inducer is installed in a more advanced position to be completely contained by the transparent Plexiglas inlet section. In this way, a full optical access to the inducer blades allows to observe and characterize cavitation inception and its development as well as to install the piezoelectric transducers for the acquisition of the pressure oscillations on the walls of the Plexiglas tube. The piezoelectric transducers are flush-mounted on the inlet section through custom-designed connectors, in order to avoid concerns related to system frequency response, typical in recess mountings. Between the two possible flush mountings, tangent or secant to the cylindrical inner wall of the tube, the first has been chosen because considered less dangerous in terms of triggering cavitation nucleii in the fluid flow.

The Figure shows that the piezoelectric transducers can be installed at three different axial stations: immediately upstream of the test inducer, at the middle of the blade chord and immediately downstream. For each axial station many azimuthal positions are available, in order to consent cross-correlation of the pressure signals from transducers at different axial and angular positions and to characterize the rotating and/or longitudinal nature of the detected instabilities. More details on the test procedure for the characterization of flow instabilities will be given in following section. Figure 3.27 shows a picture of the transparent inlet section, in which the piezoelectric transducers at different axial and angular positions are visible.

Figure 3.27 – The piezoelectric transducers installed on the Plexiglas inlet section.

3.5 The data acquisition system The data coming from the sensors and transducers installed in the facility are acquired and

transferred to a Personal Computer by means of a National Instruments acquisition board mod. 6024E, able to acquire 8 analogical and 8 digital channels at a maximum scan rate of 250 kS/sec. The acquisition board is connected to a SCXI 1520 module for the conditioning and the filtering of the acquired signal. The pressure at the inlet of the test pump is measured by means of an absolute


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pressure transducer, Druck mod. PMP 1400, having a measuring range of 0-1 atm, a maximum error of 0.15% of the maximum measurable value and compensated for temperatures between -20 °C and 80 °C. The pressure rise generated by the test pump is redundantly measured by means of two differential pressure transducers: a Druck mod. PMP 4170 and a Kulite mod. BMD 1P 1500 100, having a measuring range of 0-100 psi, a maximum error of 0.1% of the maximum measurable value and compensated for temperatures between -29 °C and 82 °C. The water temperature is measured by a digital thermometer based on a PT 100 probe installed inside the main tank.

3.5.1 The piezoelectric transducers These sensors are based on the well known “piezoelectric effect”: in some materials, when

suffering a deformation as an effect of an external force, an internal movement of electric charges is generated (Figure 3.28). As a result, a voltage can be read between the two sides, and this reading gives the possibility of knowing the value of the driving force.

Figure 3.28 – Schematic of the piezoelectric effect in a quartz crystal.

The piezoelectric effect can be used only for measurement of dynamic (unsteady) signals. This is because a steady driving force generates a slowly decaying signal and, as a consequence, a piezoelectric transducer acts as a filter which cuts off low frequency signals. The piezoelectric transducers used in the CI2TF and in the CI2RTF are mod. M112A22 produced by PCB Piezotronics, able to read unsteady pressures generated by turbulence, acoustic phenomena and cavitation. An excellent robustness makes them particularly useful in a cavitating environment, where the supersonic collapse of vapour bubbles can result in serious sensors damages. The dynamic range of these piezoelectric transducers is from 0.07 to 345 kPa, their maximum operating pressure is 3450 kPa and the operational temperature range is from -73 °C to 135 °C. The minimum observable frequency is 0.5 Hz, the maximum one is 250 kHz. A schematic of the sensors and a detail of their installation on the transparent inlet section are shown in Figure 3.29. Signals from the piezoelectric transducers are acquired and conditioned by means of a 8-channels National Instruments module, mod. SCXI 1531.

Figure 3.29 – Schematic drawing of the M112A22 piezoelectric transducers (left) and detail of their

installation on the Plexiglas inlet section (right).


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The transducers are flush mounted in order to allow the complete contact of the sensible surface of the transducer with the flow and to guarantee the right measurement and the resolution in term of minimum pressure fluctuations. The next Figure shows two possible radial mountings in respect to the internal cylindrical surface of Plexiglas: the secant and tangent configurations are presented in detail. The height of the circular segment, resulted by the circular section of the cylinder and the transducer, is 94 µm; the two solutions appears equivalent.

tangente secante Figure 3.30 – Schematic of the possible radial mounting of the dynamic pressure transducers.

The next Figure presents the pressure taps configuration on the Plexiglas used for the experiments on the FAST2 inducer, which will be illustrated in the next sections. In this particular case, 24 pressure taps in the Plexiglas conduct were designed but in only 8 pressure taps were mounted the dynamic pressure transducers, as it appears in the left side of the next Figure.

Figure 3.32 shows the position of pressure transducers mounted in the test section.

Figure 3.31 – Schematic of the dynamic pressure transducers set up (left) and picture of the Plexiglas

conduct with the dynamic pressure transducers (right).

Figure 3.32 – Picture of the test section and detail of the pressure transducers positions.

absolute pressure transducer

differential pressure transducers taps

dynamic pressure transducers PCB


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università degli studi di pisa - core · a test facility called cprtf (cavitating pump...

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