H YDROFOILS I NSTABILITIES IN S PACE R OCKET T URBOPUMPS AND E XPERIMENTAL S TUDY OF C AVITATION AND F LOW

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Università degli Studi di Pisa

DOTTORATO DI RICERCA IN INGEGNERIA AEROSPAZIALE CURRICULUM:PROPULSIONE AEROSPAZIALE

XVIIICICLO

E

XPERIMENTAL

S

TUDY OF

C

AVITATION AND

F

LOW

I

NSTABILITIES IN

S

PACE

R

OCKET

T

URBOPUMPS AND

H

YDROFOILS

Candidata

Cristina Bramanti

Tutore

Prof. Luca d’Agostino

Dipartimento di Ingegneria Aerospaziale Via G. Caruso, 56122 – Pisa

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A

BSTRACT

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.

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L

IST OF

C

ONTENTS

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 CI2_TF_AND_CI2_RTF_{CONFIGURATIONS}_{... 60}

3.5 THE DATA ACQUISITION SYSTEM... 61

3.5.1 The piezoelectric transducers... 62

4 TURBOPUMPS PERFORMANCE... 65

4.1 INTRODUCTION... 65

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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

4.4.3 Analysis of the cavity length ...95

4.5 EXPERIMENTAL CAMPAIGN ON FAST2 INDUCER...98

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

6.2 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

7.2 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

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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

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L

IST OF

F

IGURES

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

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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

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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

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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=0.050... 109

Φ=0.070... 110

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

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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 6.2 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the FIP162

inducer at room temperature, 2500 rpm rotating speed and φ = 0.017 (left) and φ = 0.008 (right). ...137 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

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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 6.14 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the MK1

inducer at room temperature, 2800 rpm rotating speed and φ = 0.036 (left) and φ = 0.023 (right). ... 143 Figure 6.15 – Waterfall plot of the power spectrum of the inlet pressure fluctuations in the MK1

inducer at room temperature, 2800 rpm rotating speed and φ = 0.007 (left) and φ = 0.0037 (right). ... 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

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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 6.29 –Power spectrum (blue), phase of the cross-correlation (red) and coherence function

(green) of the pressure signals from two transducers with 90° angular spacing in the inlet section of the FAST2 inducer at room temperature, 4000 rpm rotating speed, φ = 0.01 and σ = 0.354. .153 Figure 6.37 – Waterfall plot of the filtered power spectrum of inlet pressure fluctuations in the FAST2

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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 6.40 –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 = 0.01 and σ = 0.601. 157 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 2}nd_{blade (second plot), 2}nd_{and 1}st_{blade (third plot), 1}st_{and 3}rd_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 φ φ =/ ref 0.7, 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 φ φ =/ ref 0.7, 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 (α= °8 ,σ =2.5). ... 198 Figure 8.35 – Cavitation appearance at higher freestream temperature (α= °8 ,σ=2,T =70°C). ... 199 Figure 8.36 – Normalized pressure drop caused by the hydrofoil for various incidence angles α at

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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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L

IST OF

T

ABLES

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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N

OMENCLATURE

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

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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 b

p 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

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vθ1 Flow azimuthal velocity

V Freestream velocity

V∞ Freestream velocity

V1 Air-bag volume

Vb Vacuum reservoir volume

V

V 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

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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

CI2_{RTF Cavitation}_Induced_{Instabilities}_{and Rotordynamic Test Facility}

CI2_TF _{Cavitation Induced Instabilities Test Facility}

CPRTF Cavitating Pump Rotordynamic Test Facility

CPTF Cavitating Pump Test Facility

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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

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Chapter 1 - Introduction

1 I

NTRODUCTION

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 15}th_{centuries. In England, Roger Bacon}

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

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 19}th_{, 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.