POLITECNICO DI MILANO

School of Industrial and Information Engineering

Master of Science in Aeronautical Engineering

Design and simulation of a 1N hydrogen peroxide monopropellant thruster

Supervisor: Prof. Luciano GALFETTI

Master Thesis by:

Andrea URAS 898198

Academic Year 2018 - 2019

Sommario

L’utilizzo del perossido di idrogeno come monopropellente per applicazioni che richiedono bassi livelli di spinta `etornato ad essere di grande interesse negli ultimi anni. L’obiettivo principale `equello di trovare un sostituto dell’idrazina, altamente tossica e cancerogena, e il perossido di idrogeno ne rappresenta una valida alternativa per via del suo basso impatto ambientale. Questo lavoro di tesi si `eoccupato del design, del dimensionamento e della simulazione di Fluidodinamica Computazionale (CFD) di un monopropellente, alimentato ad acqua ossigenata, capace di produrre 1 Newton di spinta nel vuoto. Il design e il dimensionamento sono stati effettuati con l’ausilio di Chemical Equilib- rium with Applications (CEA), un software sviluppato della NASA utilizzato per appli- cazioni termochimiche. La simulazione CFD, effettuata con il software ANSYS® Fluent, ha riguardato l’analisi dell’ugello e della scia di scarico a diverse altitudini. Ci`oha permesso di valutare l’efficienza dell’ugello confrontando i parametri ideali con quelli ottenuti attraverso le simulazioni, mostrando come il propulsore risulti pi`uefficiente quando opera in regime adattato op- pure sottoespanso. Inoltre, `estato possibile apprezzare come la pressione esterna influenzi la struttura delle scia di scarico dell’ugello, composta da una serie di onde d’urto e di es- pansioni di Prandtl-Meyer.

I Abstract

The use of hydrogen peroxide as a monopropellant for low-thrust applications had a renewed interest in the last years. The main goal is to find a substitute for hydrazine, highly toxic and cancerogenic, and hydrogen peroxide represents a valid alternative for its low environmental impact. This thesis work concerned about design, sizing and Computational Fluid Dynamics (CFD) simulation of a hydrogen peroxide monopropellant thruster capable to produce 1 Newton of thrust in vacuum. The design and the sizing have been carried with the aid of Chemical Equilibrium with Applications (CEA), a software developed by NASA used for thermochemical applications. The CFD simulation, carried by means of ANSYS® Fluent software, concerned the analysis of the nozzle and the exhaust plume at different altitudes. It has been then pos- sible to evaluate the nozzle efficiency, comparing ideal parameters with the one obtained with the simulations, showing how the engine results to be more efficient in adapted or underexpanded regime. Moreover, it has been possible to observe how the external pres- sure influences the structure of the exhaust plume, composed of a series of oblique shocks and Prandtl-Meyer expansions.

II Ringraziamenti

Prima di tutto vorrei ringraziare la mia famiglia, la quale mi ha supportato, economica- mente e moralmente, per tutta la durata del mio percorso universitario e mi ha sempre sostenuto nelle scelte fatte. Senza di voi non sarebbe stato possibile tutto questo. Un grazie a quella che `estata per quasi due anni la mia seconda famiglia: Mattia, Fede e Luca. Con voi mi sono sentito a casa e non avrei potuto chiedere compagni di viaggio migliori. Insieme a loro vorrei ringraziare anche Andrea, Marco e Matteo che, nonostante non abbiano partecipato alla spedizione meneghina, fanno comunque parte della grande famiglia made in UniGe di CXVIII. Vorrei poi ringraziare anche gli amici della parentesi francese: Fede, che dopo Genova e Milano ha deciso che non poteva lasciarmi partire da solo per Poitiers, Fede Boni, Irene e, last but not least, Paola, una delle persone migliori che abbia mai conosciuto. Un grazie agli amici di sempre, Viola e Gli Amici del Mietitore, con cui sono cresciuto e che continuano ad essere una felice costante all’interno della mia vita. Grazie anche a Dario e Yuri, con cui ho condiviso gli ultimi mesi a Milano, e a Mario, che mi ha risolto parecchi problemi lasciandomi la sua stanza.

Ringrazio il mio relatore, Professor Luciano Galfetti, il quale, nonostante tutti i prob- lemi e gli impegni, ha sempre trovato il modo di dedicarmi del tempo. Ringrazio anche il gi`acitato Mattia, il quale mi ha dato un aiuto non indifferente per quanto riguarda la parte di simulazione fluidodinamica. Ringrazio anche lo staff e gli altri ragazzi di SPLab che, proprio nel momento in cui stavamo iniziando a conoscerci, non ho avuto la possibilit`adi salutare per via della terribile emergenza che ha colpito il nostro paese negli ultimi mesi.

III Nomenclature

Acronyms ACS Attitude Control System ATO Assisted-Take-Off CEA Chemical Equilibrium with Applications CFD Computational Fluid Dynamics DLR Deutsches Zentrum f¨ur Luft- und Raumfahrt (German Aerospace Center) DNS Direct Numerical Simulation DSGS Dynamic Subgrid-scale ESA European Space Agency FVM Finite Volume Method GEO Geostationary Earth Orbit HTP High Test Peroxide HYPROGEO Hybrid Propulsion System for LEO, MEO and GEO transfer LEO Low Earth Orbit LES Large Eddy Simulation LPT Low pressure tank MEO Medium Earth Orbit MMH Monomethylhydrazine MON Mixed Oxides of Nitrogen NASA National Aeronautics and Space Administration NTO Nitrogen Tetroxide PDE Partial Differential Equation PTFE Polytetrafluoroethylene RACS Roll and Attitude Control System RANS Reynolds Average Navier-Stokes RATO Rocket-Assisted-Take-Off RCS Reaction Control System SME Small and Medium Enterprises UDMH Unsymmetrical Dimethyl Hydrazine

Chemical formulas (g) Gaseous (l) Liquid Cr Chrome Cu Copper Fe Iron H2O2 Hydrogen peroxide H2O Water in vapour form H2 Hydrogen

IV HO2 Hydroperoxyl radical H Atomic hydrogen Mn Manganese M Third body N2H4 Hydrazine N2O4 Nitrogen tetroxide O2 Oxygen OH Hydroxyl radical O Atomic oxygen Operators (∗)0 Fluctuating component in Reynolds average (∗)00 Fluctuating component in Favre average (∗)i,(∗)j,(∗)α,(∗)β Components along i, j, α, β direction (∗) Reynolds average (c∗) Filtered variable (f∗) Favre average Symbols (qΦ)P source term evaluated at cell centre αconv Convergent angle αdiv Divergent angle ∆Pi Pressure drop of injector ∆Pv Pressure drop of solenoid valve ∆Pcp Pressure drop in the catalyst pack ∆t Time step ∆V Velocity change ∆ Filter width in LES δij Kronecker Delta m˙ p Propellant mass flow rate  Area ratio Γ Diffusion term γ Ratio of the specific heats κ Reaction rate coefficient λ Thermal conductivity µ Viscosity µT Turbulent viscosity ν Kinematic viscosity νT Kinematic turbulent viscosity νt Subgrid viscosity ω Characteristic frequency of turbulence ωr Reaction rate Ωv Volume of integration Φ Reaction scalar φ Bed loading ΦE Reaction scalar evaluated at center of ”East” cell Φe Reaction scalar evaluated at ”East” frontier of cell ΦP Reaction scalar evaluated at cell center ρ Density

V ρe Exit nozzle density ρHTP Density of HTP

ρIsp Density specific impulse σiα Stress tensor τ Turbulence time scale τij Subgrid stress term n Normal vector ε Dissipation rate of turbulent kinetic energy A Pre-exponential factor Ac Chamber area Ae Nozzle exit area At Throat area At Throat area C Courant number c Chamber speed of sound c∗ Characteristic velocity ce Exit nozzle speed of sound CF Thrust coefficient Cp Specific heat at constant pressure Cs Smagorinsky coefficient Cµ, σk, σ, C1, C2, σω, Cω1, Cω2, σΦ Empirical constants

CDi Discharge coefficient of the injector

CFCFD Thrust coefficient evaluated from CFD

CFideal Ideal thrust coefficient d Mass diffusivity Dc Chamber diameter De Exit nozzle diameter Di Injector diameter Dt Throat diameter Ea Activation energy F Thrust G Generic filter g Acceleration of gravity h Enthalpy hS Enthalpy at constant entropy

ISPvac Specific impulse in vacuum Isp Specific impulse k Turbulent kinetic energy Kv Flow coefficient of solenoid valve l∗ Length scale l0 Integral scale lk Kolmogorov lenght scale lm Mixing lenght Lconv Convergent length Lcp Catalyst pack length Ldiv Divergent length Me Exit nozzle Mach number mp Propellant mass

VI mtot Total mass N Number of mesh points P Nozzle pressure p Pressure Pa Ambient pressure Pc Chamber pressure Pe Nozzle exit pressure Pk Production of turbulent kinetic energy

PeCFD Exit nozzle pressure evaluated from CFD

Peid Ideal exit nozzle pressure Ppt Propellant tank pressure qc Heat released by reaction QP Volumetric flow rate of the propellant qΦ Source term for scalar Φ R Gas constant Re Reynolds number Re0 Turbulent Reynolds number sm Mesh spacing Sij Strain rate tensor SG Specific gravity T Temperature t Time Tc Chamber temperature Te Exit nozzle temperature Tt Throat temperature Tad Adiabatic temperature tboost Boost time Tij Shear stress term to be solved in LES tres Residence time u Velocity 0 u0 RMS of velocity u∗ Velocity scale uτ Friction velocity V Nozzle velocity Ve Exit nozzle velocity

VeCFD Exit nozzle velocity evaluated from CFD

Veid Ideal exit nozzle velocity vprod Specific volume of products Vpt Propellant tank volume x, y Spatial coordinates Y Mass fraction y+ Dimensionless wall distance ∆h Enthalpy variation

VII Contents

1 Introduction 1 1.1 Motivation ...... 1 1.2 Goal of the thesis ...... 1 1.3 Structure of the work ...... 2

2 State of the art 3 2.1 Hydrogen Peroxide for propulsion applications ...... 3 2.1.1 Historical background ...... 3 2.1.2 Current developments ...... 7 2.2 Theory of rocket propulsion ...... 8 2.2.1 Fundamental equations ...... 11 2.2.2 Expansion in convergent-divergent nozzle ...... 12 2.2.3 Plume structure ...... 13 2.3 Hydrogen Peroxide safety, handling and storage ...... 15 2.4 Decomposition of Hydrogen Peroxide ...... 21 2.4.1 Catalytic decomposition ...... 22 2.4.2 Thermal decomposition ...... 23

3 Preliminary design 25 3.1 Computation of operating parameters with NASA CEA code ...... 25 3.2 Sizing of the thruster ...... 26 3.3 Feed line design ...... 28 3.4 Example of research stand for experimental investigation ...... 30

4 CFD Simulation and modelization 31 4.1 Description and resolution of Navier-Stokes equations ...... 32 4.1.1 Direct Numerical Simulation (DNS) ...... 33 4.1.2 RANS Equations ...... 34 4.1.3 Large Eddy Simulation (LES) ...... 38 4.2 Finite Volume Method ...... 39

5 Simulation Set-Up 41 5.1 Geometry ...... 41 5.2 Mesh ...... 42 5.3 Fluent Set-Up ...... 44

6 Results 46 6.1 Case 1: Optimal ...... 46 6.2 Case 2: Underexpanded ...... 48

VIII 6.3 Case 3: Overexpanded ...... 50 6.4 Case 4: Highly overexpanded ...... 52 6.5 Comparison among the cases ...... 54 6.5.1 Nozzle ...... 54 6.5.2 Exhaust plume ...... 57 6.6 Verification of the model ...... 60 6.6.1 Convergence of the solution ...... 60 6.6.2 y+ verification ...... 61

7 Conclusions and future work 62 7.1 Conclusions ...... 62 7.2 Recommendation for future work ...... 62

IX List of Figures

2.1 The V-2 rocket ...... 4 2.2 The Black Knight rocket...... 5 2.3 The X-15 ...... 6 2.4 Liquid bipropellant rocket ...... 9 2.5 Liquid monopropellant rocket ...... 9 2.6 Solid propellant rocket ...... 10 2.7 Hybrid propellant rocket ...... 10 2.8 Gasdynamic expansion in a supersonic nozzle ...... 12 2.9 Schematic of the plume structure in the near field ...... 13 2.10 Overexpanded nozzle ...... 14 2.11 Underexpanded nozzle ...... 14 2.12 Shock-wave diamonds ...... 15 2.13 Example of pure solid silver wire catalyst screen of 20 x 20 mesh ...... 16 2.14 HTP stored in PTFE containers ...... 17 2.15 Explosive range of hydrogen peroxide ...... 19 2.16 The reaction pathway ...... 22

3.1 Examples of feed lines for propulsive systems ...... 29 3.2 Research stand at IoA: 1-Nitrogen valve, 2-Pressure reductor, 3-Low pres- sure nitrogen tank, 4-HTP filling valve, 5-Safety valve, 6-HTP filter, 7- Injection valve, 8-Heater, 9-Decomposition chamber, 10-Power supply, 11- Thrust measurement system...... 30

4.1 Process of CFD ...... 31 4.2 2D Structured Grid Domain ...... 40

5.1 Global geometry ...... 41 5.2 Detail of nozzle geometry ...... 42 5.3 Global mesh ...... 42 5.4 Detail of nozzle mesh ...... 43 5.5 Orthogonal Quality ...... 43 5.6 Skewness ...... 43 5.7 Named Selections ...... 44

6.1 Contour of static pressure ...... 47 6.2 Contour of velocity magnitude ...... 47 6.3 Contour of Mach number ...... 47 6.4 Contour of mass fraction of air ...... 47 6.5 Contour of static temperature ...... 48 6.6 Contour of turbulent intensity ...... 48

X 6.7 Contour of static pressure ...... 49 6.8 Contour of velocity magnitude ...... 49 6.9 Contour of Mach number ...... 49 6.10 Contour of mass fraction of air ...... 49 6.11 Contour of static temperature ...... 50 6.12 Contour of turbulent intensity ...... 50 6.13 Contour of static pressure ...... 50 6.14 Contour of velocity magnitude ...... 51 6.15 Contour of Mach number ...... 51 6.16 Contour of mass fraction of air ...... 51 6.17 Contour of static temperature ...... 51 6.18 Contour of turbulent intensity ...... 52 6.19 Contour of static pressure ...... 52 6.20 Contour of velocity magnitude ...... 53 6.21 Contour of Mach number ...... 53 6.22 Contour of mass fraction of air ...... 53 6.23 Contour of static temperature ...... 53 6.24 Contour of turbulent intensity ...... 54 6.25 Static pressure and Mach number along nozzle axis ...... 55 6.26 dV/dy at nozzle exit ...... 55 6.27 Pressure along axis of exhaust plume ...... 58 6.28 Mach number along axis of exhaust plume ...... 58 6.29 Mass fraction of air along axis of exhaust plume ...... 59 6.30 Convergence of pressure at nozzle exit ...... 60 6.31 Convergence of temperature at nozzle exit ...... 60 6.32 Contour of y+ ...... 61

XI List of Tables

2.1 Calculated adiabatic temperature of decomposition products and their vol- ume for solutions of H2O2 ...... 20 2.2 Reaction mechanism for H2O2 decomposition. Rate constants are expressed in Arrhenius’ form with SI unit (kilomol, meter, second). ∆h is in Joule/kilomol. The “ ” symbol represents that the backward reactions are also con- sidered. ”M” represents third-body and reactions involving ”M” are third- body mediated pressure dependent...... 24

3.1 Input parameters in the CEA code ...... 25 3.2 Data output in the CEA code ...... 26 3.3 Design parameters of the thruster ...... 27 3.4 Design parameters of the feed line ...... 29

4.1 Comparison between simulation and experimental approach ...... 32

5.1 Mixture properties ...... 44 5.2 Boundary Conditions at inlet ...... 45 5.3 Boundary Conditions at walls ...... 45 5.4 Outlet Boundary Conditions ...... 45

6.1 Exit nozzle parameters ...... 56

6.2 Comparison between CFideal and CFCFD ...... 56

XII Chapter 1

Introduction

1.1 Motivation

Most of the satellites require some kind of Attitude Control System (ACS) to fulfil their missions. There are many techniques to control and stabilize an attitude of a spacecraft e.g. momentum wheels, magnetic torquers, passive stabilization methods. The choice depends on mission objectives, required accuracy and also funding issues. One commonly used solution for ACS application is a system based on low thrust electrical or chemical rocket thrusters. When the mission requires a thrust on level of single newtons the first choice is a monopropellant thruster. It uses a single substance in liquid state which is delivered into decomposition chamber and decomposes into hot, gaseous products which are then delivered into the nozzle producing thrust. Due to the simple construction and well known technology they are also characterised by high reliability. Very widely used propellant for today’s monopropellant systems is hydrazine, which is able to deliver a specific impulse on the level of 2300 m/s. Despite good performance of hydrazine there are many research all over the world focused on finding its replacement. It is strictly connected with the problematic testing, ground handling and environmental protection issues due to its toxicity, flammability and carcinogenic effects. Many so called green propellants are under investigation and one very important is hydrogen peroxide. Hydrogen peroxide (H2O2) decomposes into hot mixture of oxygen and steam making it completely safe for environment. It is also stable, accessible and easy to use. All those features together with reasonable specific impulse on the level of 1600-1700 m/s and relatively high density makes it a strong competitor for hydrazine [1]. Therefore, with the rise of demand of small satellites for telecommunication and the necessity for green propellants, hydrogen peroxide is one of the most attractive solutions for the next years.

1.2 Goal of the thesis

The first step of this Master Thesis is to design a hydrogen peroxide monopropellant thruster able to produce a single Newton of thrust in vacuum condition. For the design of the thruster the NASA program Chemical Equilibrium with Applications (CEA) has been used. Once the thruster has been designed and correctly sized, different CFD sim- ulations of the nozzle have been performed at different altitudes in order to evaluate the efficiency of the thruster by varying external condition. In order to have a more complete understanding of the phenomena occurring downstream the nozzle, the characterization of the exhaust plume has been object of study inside this work and it has been included

1 in the CFD simulation. ANSYS® Fluent 2020, of which Politecnico di Milano provided the license, has been used for CFD calculation. It is a very modern and complete soft- ware which allows also to design and mesh the geometry and to post-process all the data without using other programs.

1.3 Structure of the work

The work is organized in the following chapters:

ˆ Chapter 2: past and present uses of hydrogen peroxide applications as a propellant are illustrated. A basic review of theory of rocket propulsion is presented, including a brief overview of the phenomena occurring in the exhaust plume. Problems related to safety and storage of hydrogen peroxide are discussed and the different types of decomposition mechanism are presented.

ˆ Chapter 3: preliminary design of the thruster and the feed line with the aid of NASA CEA code.

ˆ Chapter 4: presentation of the fundamental methods for CFD modelization and solution of turbulent flows.

ˆ Chapter 5: set-up of the simulation, including design and mesh of the geometry and set-up of Fluent.

ˆ Chapter 6: presentation of the results obtained by CFD simulation.

ˆ Chapter 7: Conclusions and future work recommendation.

2 Chapter 2

State of the art

2.1 Hydrogen Peroxide for propulsion applications

2.1.1 Historical background The industrial manufacture of hydrogen peroxide can be traced back to the work done by L. J. Thenard in 1818, when he started producing aqueous H2O2 in low concentrations by reacting barium peroxide with nitric acid. A succession of improvements in the man- ufacturing technique eventually led to large scale production of 100% concentration with respect to weight (wt%) hydrogen peroxide. High concentration hydrogen peroxide above approximately 80% is more commonly known as High Test Peroxide (HTP). However, its potential as a propellant was recognized more than one century later [2]. The pioneer of hydrogen peroxide for propulsive application is the german engineer Hell- muth Walter. Germany developed quite safe concentrations of 80 to 82% H2O2 between 1933 and 1936. Based upon the availability of the new propellant, Walter began in 1935 the Walter-Werke, his own company of hydrogen peroxide combustion devices, and by 1936 he designed an Assisted-Take-Off (ATO) engine and a submarine turbine powered by H2O2. His ATO for the Heinkel He 176, an experimental aircraft powered by rocket engine, first flown in 1938. This device was fueled by 80% hydrogen peroxide, catalyzed with liquid injection of permanganate salts. With the objective to increase the performance of the ATO and other rocket engines of the time, Walter developed a hypergolic liquid fuel made from hydrazine hydrate and methyl alcohol. This was used in the Walter HWK 109-509 engine, which powered the Messerschmidt Me 163B Komet rocket plane. The ME163 has been used during the war, however the technological limits allowed the Komet to be deployed only near sites to be defended. For sure, the most significative german application of hydrogen peroxide in that period was the V-2 (Fig.2.1) turbo-pump gas generator, which brought H2O2 into the common use in rocket propulsion systems after WWII. The V-2 used 80% H2O2 catalyzed with liquid injection of potassium permanganate. Another Walter business product was the V-1 catapult, largely used during the war. This simple device was fueled by 80-85% H2O2 and sodium permanganate as catalyst. As previously mentioned, one of the first proposed propulsion and power application of H2O2 as a propellant was for submarines. A significant application was the Type 18X submarines, which burned H2O2 with kerosene. A natural parallel application to the submarine was the torpedo. Germany also began the development of torpedo propulsion

3 Figure 2.1: The V-2 rocket and deployed several devices. The work of England on hydrogen peroxide received a significant influence from the Walter ATO’s and the Walter 109-509 rocket engine. Initially the English imported 80% H2O2 from Germany, but later developed a more pure and high concentration peroxide (85%) manufactured by LaPorte, which today is Solvay Interox. The German engines were used as the initial design points to make the U.K. Sprite, a monopropellant Rocket-Assisted- Take-Off (or RATO) by de Havilland Engine Company, and later the Super Sprite, a bipropellant RATO using kerosene as fuel and hydrogen peroxide as oxidant. The United Kingdom started in 1952 the development of the Spectre HTP/kerosene rocket engine for the Saunder Roe SR53 aircraft. A back-up system to the Spectre was also started based upon some rocket engine component development projects currently in work and another rocket engine was developed designated the Gamma 2. The Gamma 2 evolved into the Gamma 201, and in 1957, was used by Saunders Roe in the Black Knight launch vehicle. In addition, England would pursue hydrogen peroxide for applications in aircraft rocket assist systems, submarine propulsion, and torpedo’s. The Black Knight and Black Arrow programs were with no doubt the pinnacle of English use of H2O2 for rocket application. Black Knight (Fig.2.2) was one of most successful hydrogen peroxide launch platforms and the engine technology is probably the highest in

4 the field of HTP engine ever produced. The vehicle development started in July 1955 by the Armstrong Siddeley Motors. Black Knight was a single-stage vehicle with a Gross- Lift-Off-Mass (GLOW) of approximately 6200 kg. The Black Knight was powered by four Gamma 201 engines. Each combustion device provided approximately 17.8 kN of thrust, with about 71.2 kN of total vehicle thrust. The propulsive system was a pump fed regeneratively cooled gas generator cycle engine. The hydrogen peroxide was pre- decomposed in a silver screen catalyst bed and the hot gases were then after-burned with kerosene at a mixture ratio of 8:1. An upgrade to the Gamma 201 was the Gamma 301. This engine was later used on B.K. and increased the thrust level from 71.2 kN to 96.1 kN, thanks to the automatic mixture-ratio control.

Figure 2.2: The Black Knight rocket

Black Knight was launched 22 times from its Woomera facility in Australia between 1958 and 1965. Larger next generation vehicles named Black Arrow, Blue Streak, and Black Prince were pursued as conceptual designs. Only the Black Arrow has been actu- ally developed. The B.A. was a three stage designed powered by the Gamma 301. Eight 301s were used on the first stage with a total thrust of about 142.3 kN. The second stage used two 301 s and the third stage was a small apogee motor. Only five B.A. vehicles were ever built with the fourth flight successfully lofting a British satellite on Oct. 28, 1971. The fourth and final B.A. is on display at the science museum in Kensington. Black Prince would have been similar to the Thor vehicles launched by NASA and it should have been composed by three stages. Stage one would use four combustors based upon

5 the Stentor engine. The second stage would have used a Gamma 304, and the third stage would have used a four-barrel version of the PR 37. Black Prince would have provided the capability to launch small payloads (800 kg) into polar low earth orbit. Note that today this could have been a very attractive vehicle for small commercial and scientific payloads, as well as a few defense missions. Numerous rocket engines were developed as a part of this activity. Derivative engines such as the PR 37 and BS 605 were created as aircraft rocket engines. [3] In parallel to the Black Knight project, research and testing of HTP rocket engines was being conducted by the United States, with a particular focus on monopropellants. Test- ing had begun on monopropellant HTP thrusters for Reaction Control Systems (RCS). This culminated in the production of RCS thrusters that were used most notably on the Mercury spacecraft and the X-1 and X-15 space planes. The X-1B used hydrogen perox- ide with a silver catalyst. These were silver coated stainless steel screens, inter-dispersed with non-coated screens to add additional support. For maximum performance all RCS thrusters were preheated with a small, continuous flow of HTP. This reduced start-up time which was measured at 0.2 s from pilot input to full thrust; 0.1 s was the delay in the catalyst bed itself as the peroxide was decomposed.

Figure 2.3: The X-15

The Soviet Union developed hydrogen peroxide systems throughout the cold war era. Little is known about the progress made due to the Iron Curtain which made information transfer between the East and West almost impossible. What is known is that the work resulted in the use of hydrogen peroxide in the Soyuz launch vehicle. It continues to be used to drive the RCS thrusters and main engine turbine pump with over 1700 launches successfully completed. Although research into hydrogen peroxide had shown promising results, its use in the Eu- ropean and American space industries began to cease in the 1970’s and 1980’s. With the onset of the cold war it became clear that higher performance propellants were wanted, with little regard given to toxicity or cost. Hydrazine had been identified as one such propellant but it was not until a new catalyst, Shell 405, was developed in 1966 that its use became widespread. Monopropellant designs utilising hydrazine quickly emerged

6 followed by bi-propellant applications using hydrazine derivatives, such as monomethyl hydrazine (MMH) and unsymmetrical dimethyl hydrazine (UDMH). These bipropellants used nitrogen tetroxide (NTO) or Mixed Oxides of Nitrogen (MON) as oxidisers. The bipropellant combinations were hypergolic with low freezing points and high specific im- pulse. At the same time several publications had been produced attacking the viability of hydrogen peroxide as a propellant. These mainly focused on, amongst others, difficul- ties with storage, self-decomposition and poor physical properties such as a high freezing point (-11°C for 90% HTP and -0.5°C for 100% HTP). For over 40 years hydrazine and its derivatives have been the mainstay storable propellants of the space industry and as a result have an impressive heritage which can be matched by no other non-cryogenic propellant [2].

2.1.2 Current developments Hydrazine has proven to be an excellent monopropellant in terms of its performance with a theoretical specific impulse of 230 s [4]; However, hydrazine is a highly toxic and dan- gerously unstable substance. Importantly, its use as a propellant has been compromised by stringent laws to protect personnel who have to work with substances which are highly toxic and carcinogenic. Recently, much more benign, low toxicity (“green”) storable liquid propellants have therefore attracted considerable attention as possible replacements for hydrazine. This is due to the significant increase in the costs of production, storage and handling of toxic propellants, and has set the stage for the search for green replacement propellants. Hydrogen peroxide is one of the most attractive replacements, not only since it is non-toxic and non-carcinogenic, but also due to its many advantageous properties, such as its high density and relatively low cost. From a financial standpoint, H2O2 also promises significant cost savings due to the drastic simplifications in health and safety pro- tection procedures during the production, storage and handling of the propellant. These advantages are of special relevance in low or medium thrust rocket engines for small mis- sions, which offer strong potential as profitable opportunities for focussed SMEs [5]. In 2013, Nammo, an international aerospace and defense company headquartered in Nor- way, was selected for the development and delivery of the secondary propulsion system onboard the Ariane 5 ME second stage. The mono-propellant propulsion subsystem of- fered by Nammo is based on hydrogen peroxide as the propellant and was selected as a green propulsion alternative to replace hydrazine. After Ariane 5 ME was cancelled in favor of Ariane 6, the development contract of the system was annulled in preparation of renewed requirements to be released by the Prime Contractor during 2015 for Ariane 6. Earlier in 2015, Nammo has done extensive testing of the environmentally friendly propul- sion system under in-vacuum conditions at DLR Lampoldshausen’s high-altitude simula- tion facilities in Germany. The system functioned flawlessly for both short pulses, long duration burning at nominal thrust level of 200 N as well as throttling between 50 N and 230 N. Heat soak and chill down under vacuum conditions were the main focus during these vacuum test firings. Throttling is achieved through a newly developed Flow Control Valve from Moog Ireland Ltd. The Nammo developed secondary propulsion system has demonstrated excellent properties in throttling, pulsing, multiple restarts without igniter and excellent cold start capabilities. Long duration burns result in relatively moderate structural temperatures, which ease integration with the spacecraft. During the different tests performed, it was also demonstrated that the technology is easily scalable, providing a design flexibility which existing systems lack.

7 The test program, completed with the long term storage and compatibility tests of the flight weight storage tank, has proven the many advantages with the Nammo developed green propulsion system. An expulsion factor of more than 99% was achieved for the tank. Clean Space initiatives have made aluminum tanks for In-Space use also attractive for satellite systems which need to come apart easily during re-entry to avoid fragments reaching the surface of the Earth [6]. Nammo has been awarded a 19 million Euro development contract in the ESA VEGA- E program from Italy based AVIO to provide the next generation of Roll and Attitude Control System (RACS) for the European VEGA-E launcher using hydrogen peroxide. Once the RACS qualification program has been successfully completed the system is also a candidate for the VEGA-C and SPACE RIDER. Roll and Attitude Control Systems are used to help spacecraft such as the VEGA position itself accurately in orbit, which is crucial when deploying its payload, such as satellites. The Nammo RACS architecture for VEGA-E consists of six monopropellant thrusters in two clusters located on opposite sides on the top of the last stage of the launcher. Four thrusters will provide roll control, while the two remaining thrusters will provide pitch and yaw control as well as distancing during stage separation. All of them are fed by a single H2O2-tank capable of operating both under the heavy loads conditions during the boosted ascent phase and in micro-gravity [7]. At the end of January 2018, the Institute of Aviation successfully completed tasks under the European project “Hybrid Propulsion System for LEO, MEO and GEO transfer” (HYPROGEO) co-financed by the European Commission under the Horizon 2020 pro- gramme. The main aim of the project was to develop a satellite propulsion module based on a hybrid rocket engine that uses 98% hydrogen peroxide as the oxidizer. Within the project a laboratory-scale demonstrator of a hybrid engine with a circumferential injec- tion of decomposition products of catalytically decomposed 98% HTP was developed and tested. Additionally, a new PX-1 catalyst, developed by AIRBUS UK, was tested for operations with 98% hydrogen peroxide [8].

2.2 Theory of rocket propulsion

Rocket propulsion systems may be classified in a number ways, for example, according to energy source type (chemical, nuclear, or solar) or by their basic function (booster stage, sustainer or upper stages, attitude control, orbit station keeping, etc.) or by the type of vehicle they propel (aircraft, missile, assisted takeoff, space vehicle, etc.) or by their size, type of propellant, type of construction, and/or by the number of rocket propulsion units used in a given vehicle. Another useful way to classify rockets is by the method of producing thrust. The thermodynamic expansion of a gas in a supersonic nozzle is utilized in most common rocket propulsion concepts. The internal energy of the propellant is converted into exhaust kinetic energy, and thrust is also produced by the pressure on surfaces exposed to the exhaust gases. This same thermodynamic theory and the same generic equipment (i.e., a chamber plus a nozzle) is used for jet propulsion, rocket propulsion, nuclear propulsion, laser-thermal and solar-thermal propulsion, and in some types of electrical propulsion. Totally different methods of producing thrust are used in nonthermal types of electric propulsion. As a matter of fact, these electric systems use magnetic and/or electric fields to accelerate electrically charged atoms or molecules at very low gas densities.

8 Chemical rocket propulsion Energy from the combustion reaction of chemical propellants, usually a fuel and an oxi- dizer, in a high-pressure chamber goes into heating reaction product gases to high temper- atures (typically 2500 to 4100 °C). These gases are subsequently expanded in a supersonic nozzle and accelerated to high velocities (1800 to 4300 m/s). Since such gas temperatures are about twice the melting point of steel, it is necessary to cool or insulate all the surfaces and structures that are exposed to the hot gases. According to the physical state of the stored propellant, there are several different classes of chemical rocket propulsion devices. Liquid propellant rocket engines use propellants stored as liquids that are fed under pres- sure from tanks into a thrust chamber. The bipropellant (Fig.2.4)consists of a liquid ox- idizer (e.g., liquid oxygen) and a liquid fuel (e.g., kerosene). A monopropellant (Fig.2.5) is a single liquid that decomposes into hot gases when properly catalyzed. Gas pressure feed systems are used mostly on low-thrust, low-total-energy propulsion systems, such as those used for attitude control of flying vehicles, often with more than one thrust chamber per engine. Chemical propellants react to form hot gases inside the thrust chamber and proceed in turn to be accelerated through a supersonic nozzle from which they are ejected at a high velocity, thereby imparting momentum to the vehicle. Supersonic nozzles consist of a converging section, a constriction or throat, and a conical or bell-shaped diverging section. Some liquid rocket engines permit repetitive operation and can be started and shut off at will. If the thrust chamber is provided with adequate cooling capacity, it is possible to run liquid rockets for hours, depending only on the propellant supply. A liquid rocket propulsion system requires several precision valves and some have complex feed mechanisms that include propellant pumps, turbines and gas generators. All have propellant-pressurizing devices and relatively intricate combustion/thrust chambers.

Figure 2.4: Liquid bipropellant rocket

Figure 2.5: Liquid monopropellant rocket

In solid propellant rocket motors (Fig.2.6) the ingredients to be burned are already stored within a combustion chamber or case. The solid propellant (or charge) is called

9 the grain, and it contains all the chemical elements for complete burning. Once ignited, it is designed to burn smoothly at a predetermined rate on all the exposed internal grain surfaces. The internal cavity expands as propellant is burned and consumed and the resulting hot gases flow through the supersonic nozzle to impart thrust. Once ignited, motor combustion is designed to proceed in an orderly manner until essentially all the propellant has been consumed. There are no feed systems or valves.

Figure 2.6: Solid propellant rocket

Gaseous propellant rocket engines use a stored high-pressure gas, such as air, nitrogen, or helium, as working fluid. Such stored gases require relatively heavy tanks. These cold gas thrusters were used in many early space vehicles for low-thrust maneuvers and for attitude-control systems, and some are still used today. Heating the gas with electrical energy or by the combustion of certain monopropellants in a chamber improves their performance, and this has often been called warm gas propellant rocket propulsion.

Figure 2.7: Hybrid propellant rocket

Hybrid propellant rocket propulsion (Fig.2.7) systems use both liquid and solid pro- pellant storage. For example, if a liquid oxidizing agent is injected into a combustion chamber filled with a solid carbonaceous fuel grain, the chemical reaction produces hot combustion gases [9]. This thesis work is focused on liquid propulsion only and more specifically on monopropellant rocket engines.

10 2.2.1 Fundamental equations Two basic parameters of rocket engine design are thrust and specific impulse. Thrust, F , is the amount of force applied to the rocket based on the expulsion of gases [10]:

F =m ˙ pVe + Ae (Pe − Pa) (2.1)

where Ae is nozzle exit area, Pe is the gas pressure at the nozzle exit, Pa is the ambient pressure, Ve is propellant exhaust velocity, andm ˙ p is propellant mass flow rate. Specific impulse, Isp is the ratio of the thrust, F, to the weight flow rate,m ˙ pg, of propellant: F Isp = (2.2) m˙ p g Specific impulse describes the effective generation of thrust per unit mass of propellant. For small volume constricted spacecraft, like those where hydrogen peroxide may have the greatest benefit, another term become important; the density specific impulse. This describes the generation of thrust per unit volume of propellant by multiplying the specific impulse by the specific gravity, SG, of the propellant. F ρIsp = SG (2.3) m˙ p g The specific impulse is closely linked to the velocity change, ∆V . This is a space vehicle design parameter and can be shown using the Tsiolkovsky or ideal rocket equation:   mtot ∆V = gIsp ln (2.4) mtot − mp

The theoretical exit velocity Ve can be determined by considering an adiabatic, isen- tropic, mono-dimensional and perfect gas flow: v " γ−1 # u   γ u 2γ Pe Ve = t TcR 1 − (2.5) γ − 1 Pc As can be seen above, the gas velocity exhausting from an ideal nozzle is a function of the prevailing pressure ratio Pe/Pc, the ratio of specific heats γ, and the absolute temperature at the nozzle inlet Tc, as well as of the gas constant R [9]. The maximum thrust is achieved when exit pressure equals ambient pressure. Although 2.1 suggests that greater thrust can be obtained with an exit pressure greater than the ambient pressure, the exhaust velocity is reduced, resulting in a loss of thrust. As a result, we design rocket exhaust nozzles with an exit pressure equal to the ambient pressure whenever possible. The exit pressure is governed by the nozzle-area expansion ratio:

1 1   γ−1   γ 2 Pc Ae γ+1 Pe  = = s (2.6) At  γ−1    γ γ+1 1 − Pe γ−1 Pc

11 The characteristic velocity, c∗, is a measure of the energy available from the combustion process and is given by:

s γ+1 P A RT γ + 1 2(γ−1) c∗ = c t = c (2.7) m˙ p γ 2

where At is area of the nozzle throat, and Pc is the combustion chamber pressure. The thrust coefficient, CF is a measure of the efficiency of converting the energy to exhaust velocity and characterizes the nozzle performance: F CF = (2.8) PcAt The product of 2.7and 2.8, divided by the gravity constant, gives the specific impulse:

∗ F c CF Isp = = (2.9) m˙ p g g

2.2.2 Expansion in convergent-divergent nozzle A supersonic nozzle is a shaped pipe, first convergent and then divergent, connected by a section of minimum flow area called throat of the nozzle. Such a device, first suggested by De Laval in 1888 for a vapor turbine, is today an essential component of all aerospace propulsion systems of thermal nature and a variety of gasdynamic apparatus. In Fig.2.8 the behaviour of a convergent-divergent nozzle is sketched, by representing the trend of pressure along the axis of the nozzle. The simplest case is when ambient pressure is equal to stagnation pressure, so no fluid flow is achieved inside the nozzle. By decreasing the ambient pressure Pa, different cases can be identified.

Figure 2.8: Gasdynamic expansion in a supersonic nozzle

ˆ Subsonic throat, implying subsonic flow all along to the exit (case a).

ˆ Fully subsonic flow except at the throat (case b).

ˆ Flow becomes supersonic after the throat, but, before exit, a normal shock wave causes a sudden transition to subsonic flow (case c). It may happen that the flow detaches from the wall.

12 ˆ Flow becomes supersonic after the throat, with the normal shock wave just at the exit section (case d).

ˆ Flow becomes supersonic after the throat, and remains supersonic until de exit, but there, three cases may be distinguished: overexpanded (case e), adapted (case f) and underexpanded (case g)

2.2.3 Plume structure Plume structure is quite complex and it does not depend on mixture composition. The core flow from the nozzle exit can be divided into two sections: the inviscid inner core and the viscous outer core (mixing layer). Within the inviscid core, it is assumed that no chemical reactions occur [11]. Fig.2.9 presents a schematic of the near field plume structure. In this figure, it can also be seen that the mixing layer thickness increases with increasing distance from the nozzle exit. However, in the inviscid core, shocks and expansion waves occurs and thus, the flow structure is dominated by these gas dynamic characteristics [12].

Figure 2.9: Schematic of the plume structure in the near field

The plume can be divided into the two parts mentioned above. The flow in the inviscid core is non-reacting in contrast to the mixing layer. In the mixing layer the flow is viscid and surrounds the core flow. The reactions take place by mixing with the ambient environment [11]. An additional set of reactions can occur in the viscous mixing layer, which is known as afterburning. The occurrence of afterburning, however, depends on the altitude. The chemical reaction which leads to afterburning occurs only when the oxygen concentration is high enough. Afterburning leads to higher temperatures in the mixing zone and thus, to infrared emissions, which can be observed [13]. The plume expands as the ambient pressure decreases, as the launch vehicle accelerates and rises through the atmosphere. The turbulent mixing also decreases as the relative velocity between the exhaust and the free stream decreases. Less mixing and a decreased temperature lead to a decrease in afterburning, and thus, observed emissions. The process of afterburning ends when the velocity of the vehicle is equal to the velocity of the exhaust. That means when the exhaust is released into the atmosphere with a relative velocity of zero [11].

13 Near Field When the nozzle is overexpanded it means that ambient pressure is higher than exit pressure (low altitude condition). Oblique shock-waves appear at the exit, to compress the exhaust to the higher back pressure (Fig.2.10). On the contrary, when ambient pressure is lower than exit pressure (high altitude condition), expansion waves appear at the exit, to expand the exhaust to the lower back pressure (Fig.2.11). These waves will propagate downstream to a point where the expansion waves intercept the ambient boundary, which has a constant pressure. Due to reflections from the plume boundary, the expansion waves become compression waves, with the aim of matching the local pressure which is higher. The reflected compression waves merge further downstream because of the shape of the plume boundary. This merging leads to a barrel shock. If this barrel (or oblique) shock is strong, a normal shock (Mach disk) will appear on the centerline. A subsonic region after this Mach disc will occur. The pattern of barrel shock and Mach disk is driven by the ratio of the pressure at the exit and the ambient pressure. This pattern can repeat itself several times and in this case a diamond crystal shape pattern (“shock diamond”) occurs. This shock diamond weakens with the mixing, i. e. the further away from the nozzle exit, the weaker the shock diamond [14]. In Fig.2.12 a picture of shock diamonds structure is captured.

Figure 2.10: Overexpanded nozzle

Figure 2.11: Underexpanded nozzle

14 Figure 2.12: Shock-wave diamonds

Far Field When the pattern of barrel shocks ends, the far field begins. This means, that the mixing with the ambient environment dominates and the afterburning process can occur. After a while, the plume is completely mixed with the ambient environment and the plume is dispersed within the surrounding atmosphere. Afterburning Afterburning processes occur when the plume mixes with the ambient atmosphere. However, the afterburning reactions depend on the altitude of the plume, because with increasing altitude, oxygen content of the atmosphere decreases. The oxygen content is important because the fresh and unburnt oxygen is responsible for the further burning processes. Furthermore, the afterburning process depends also on the degree of mixing. The less the plume mixes with the ambient environment, the more unlikely afterburning will occur. The end of the afterburning process is caused either by the altitude (and hence lack of oxygen) or when the velocity of the rocket matches the velocity of the exhaust.

2.3 Hydrogen Peroxide safety, handling and storage

As previously mentioned, propellant systems for liquid rockets generally falls into two cat- egories: monopropellant and bipropellant. Monopropellant rocket uses single fluid system as propellant and the most commonly used monopropellant is hydrazine (N2H4) which is highly toxic and dangerously unstable unless handled in solution. In bipropellant rockets, two fluids system is used to form the propellant and they are categorised into fuel and oxidizer such as the most commonly use combination of monomethylhydrazine (MMH) and nitrogen tetroxide (N2O4) which are highly toxic and unstable. The above mentioned propellant combinations require special propellant handling and pre-launch preparation. Due to that, hydrogen peroxide (H2O2) have become considerably more attractive liquid as possible substitutes for hydrazines and nitrogen tetroxide. The rocket grade H2O2 (con- centration above 85%) is a non-toxic chemical that has a natural familiarity to human chemistry thus it is the best general solution for space, air, land and sea applications. Among other concerns when choosing H2O2 as a monopropellant are also the significant cost saving associated with the drastic simplification of health and safety precautions necessary during the production and the storage and handling of the propellants. These advantages have a special relevance to low or medium thrust thruster, where the above cost does not scale down proportionally with the thruster size. The governing reaction

15 equation for the decomposition process involving H2O2 is given in Eq.2.10:

catalyst 2 H2O2(l) 2 H2O(l) + O2(g) + heat (2.10) Eq.2.10 shows that only the superheated steam and oxygen are released from decom- position process. It means that no other toxic gas is released to the air [15]. The rate of decomposition of hydrogen peroxide is affected by several factors, such as rate of decomposition, including temperature, degree of contamination, surface activity, pH, and to a lesser extent concentration. For instance, the decomposition rate increases approximately 2.3 times for each 10 °C rise in temperature. However, the standard rate at which commercial grades of hydrogen peroxide stored in compatible equipment decom- poses is extremely low, usually less than 1% relative loss per year. Pure concentrated H2O2 is very stable. In fact, concentrated H2O2 is generally more stable than a dilute solution (if uncontaminated). However, the particular resistance of any grade or con- centration of H2O2 towards contamination is very dependent on the level (and type) of stabilizers used. Industrial grades of H2O2 are stabilized with different additives which provide a certain level of protection against some levels of contaminants that may be ex- perienced during transportation and storage in standard equipment, which are typically passivated 304 or 316 stainless steel. This stabilization, however, is not able to protect against “gross” contamination (which may mean levels below 1 ppm for certain contami- nants, for example, Fe, Cu, Cr, or Mn ions, particularly in combination with each other) and in such instances slow decomposition of the product will commence. In contrast, HTP required for aerospace purposes, which is in general very lightly stabilized, is much more exposed to contamination than the industrial grades because the amount of addi- tive present has to be quite limited. In order to ensure proper stability for transportation and on-site storage, the choice of acceptable materials is in general more restrictive and the use of standard equipment might be inappropriate in some circumstances. All the effects described above fall inside the case of homogeneous decomposition. In fact, it is also present heterogeneous decomposition of hydrogen peroxide that occurs entering in contact on some material surfaces. The magnitude of this effect can be quite significative depending on the particular material and the surface condition. Thus, relatively only a few materials are suitable for long term contact with H2O2 and careful attention must be paid to the preparation and conditioning of these surfaces during any tests. As an example, silver is one of the most active, making it one of the most suitable materials for decomposition catalyst systems in HTP based propulsion (Fig.2.13). On the other hand, certain grades of polyethylene and PTFE are completely inert towards HTP, thus are very suitable as material for containers (Fig.2.14), also for long term storage.

Figure 2.13: Example of pure solid silver wire catalyst screen of 20 x 20 mesh

16 Figure 2.14: HTP stored in PTFE containers

Roughness is also a factor that increases the rate of heterogeneous decomposition: in fact, a rough surface is more active than a smooth one. Hydrogen peroxide compatible metal surfaces always require to be passivated and conditioned prior to use. The most important aspect to be taken into account is the effect of the surface material on hydrogen peroxide, rather than viceversa. Being H2O2 decomposition a significantly exothermic process , the temperature of the decomposing solution will keep rising if the generated heat can not be dissipated. This increase in temperature will increase the rate of decomposition resulting in a self-accelerating system. This is in general applied to all concentrations of hydrogen peroxide, but the magnitude of the consequences of H2O2 decomposition are linked to the initial concentration, and might be quite serious if the concentration of solution is high, as in case of H2O2 used as rocket propellant. Relatively large volumes of gaseous oxygen are evolved as hydrogen peroxide decomposes. If the peroxide strength is high enough, the material will boil and large volumes of steam will also be generated. For concentrations up to 65% H2O2, the maximum adiabatic decomposition temperature that may be observed is 100 °C; i.e. there is sufficient water present to absorb the total heat of decomposition by generation of steam. For concentrations above 65%, the final adiabatic temperature that may be attained increases with increase in initial H2O2 concentration.

Continuous and emergency venting of tanks and vessels Because all solutions of hydrogen peroxide are continually decomposing, albeit at a nor- mally very low rate, a vent should always be provided for hydrogen peroxide storage and handling systems, regardless of the amount of product that is stored. For nor- mal/continuous venting, the following should be provided: ˆ a filtered vent for non pressurized systems. ˆ a pressure safety valve for pressurized or vacuum systems. For emergency venting of concentrations up to 86%, a minimum of 200 cm2 of venting for each tonne of 100% H2O2 equivalent should be provided through:

17 ˆ a free lift manway cover for tanks. ˆ a rupture (or bursting) disk on pressurized and vacuum vessels. All pipelines in which hydrogen peroxide may be locked off (i.e. between valves) must be fitted with a relief valve. The cavities of valves which could trap peroxide when in the closed position should be vented. Drilled ball valves are recommended for H2O2 service. Lines and tanks should be designed to vent at the lowest practical pressure and they should not be allowed to experience over-pressurization. [16]

Construction materials The effects associated with materials in contact with hydrogen peroxide can vary widely, thus a standard method of classification according to likely performance in service has been devised as follows: ˆ Class 1: materials that are fully compatible with hydrogen peroxide and suitable for long term contact such as storage tanks. ˆ Class 2: materials that are satisfactory for repeated short term contact with hydro- gen peroxide prior to storage or use. Contact time should be quite short prior to storage. contact time should not exceed four hours at 71°C or one week at 21°C prior to use. ˆ Class 3: materials that are suitable for short term contact only, prior to prompt use. ˆ Class 4: materials that are unsuitable or hazardous for any use with hydrogen peroxide. The requirement for class 1 materials for long term contact is not unique to concentrated H2O2 and in fact applies to all concentrations. However, a material that is rated class 1 for storage of 50% H2O2, for example, may not carry the same rating for storage of 70% or 85% H2O2. For storage of high purity 70% H2O2 or 85% H2O2, class 1 materials are PTFE lined stainless steel (304L or 316L) or 99.5% aluminium. Other aluminium alloys may be used but the exact composition of the alloy can significantly impact the rate of metal pick-up and hence have an effect on the product stability and purity.

Vapor phase explosion Hydrogen peroxide is non flammable substance. However, it can form explosive vapours under certain conditions (explosion occurring by decomposition of the vapour rather than combustion). This potential hazard is a function of temperature, pressure, and H2O2 liquid concentration. At the ambient pressure, boiling 74% hydrogen peroxide (at 130 °C) will give a vapour just at the limit of flammability. This is a kind of lower explosive limit for H2O2 vapour and its value is 26 mol% (39 wt.%) at atmospheric pressure. For liquid concentrations higher than 74%, explosive vapours can be generated at temperatures less than their normal boiling points (Fig. 2.15). As the pressure increases, flammable atmospheres are achieved at progressively lower concentrations of boiling liquid, until a pressure of 4 bar is reached. At this pressure, the limit of flammability of H2O2 vapour is 33 wt.%, which is in equilibrium with boiling 66.5% H2O2. Above 4 bar, the flammable limit of the vapour remains constant at 33 wt. % and the equilibrium liquid concentration falls very slowly as pressure increases.

18 Figure 2.15: Explosive range of hydrogen peroxide

Decomposition of hydrogen peroxide solutions can, of course, raise their temperature to boiling point and evaporate water and hydrogen peroxide (Tab. 2.1). In the absence of any other reactive substance, the concentration of the boiling peroxide always decreases. The large volumes of oxygen generated as H2O2 decomposes further add to this potential problem. Oxygen enrichment atmospheres greatly increase the fire hazards posed by flammable liquids, vapours and gases. First of all, oxygen enrichment widens the explosive limits. It does not affect the flash point significantly, so materials below the flash point remain safe. The increase is into the fuel rich area. It also greatly reduces the energy required to produce ignition and increases the rate. Even dilute hydrogen peroxide can create potential problems. For example 3% H2O2 generates 10 volumes of oxygen for each volume of H2O2 decomposed. Oxygen enrichment of confined spaces is therefore a real possibility. Dilution with copious amounts of water is the appropriate response to spillage of hydrogen peroxide. Entrapment in confined spaces must be actively avoided [17]. Another danger in the event of an upset is the mist explosion or torch effect when a mist or fine droplet spray of an organic liquid is discharged into an oxygen enriched atmosphere. Under these conditions an explosion can occur regardless of whether the organic liquid is above or below its flash point.

Fire raising potential Although hydrogen peroxide is non flammable, it is a strong oxidizer and can readily start fires when in contact with combustible materials, particularly solid natural materials such as wood, leather, cotton, etc. The mechanism of fire initiation has previously been considered to be due to concentration of H2O2 to a critical level via evaporation of water. However, a combination of decomposition of the hydrogen peroxide and oxidation of the substrate by the hydrogen peroxide may be required for effective onset of a fire. In general, the higher the strength of the peroxide, the more readily fires will initiate but fires with concentrations of H2O2 as low as 16% have been reported. Cleanliness of all areas where hydrogen peroxide is stored and handled is key to the avoidance of fires and all spills should be immediately flushed with large amounts of water. If fires involving hydrogen peroxide do occur, they should be fought with water in order to provide both cooling and dilution and because oxygen from decomposing peroxide will cause re-ignition in flame supporting environments.

19 3 H2O2 [wt.%] Tad [°C] (H2O)evap [%] vprod [dm /kg] 10 89 0 44 20 100 12,1 276 30 100 27,9 542 40 100 45,5 808 50 100 65,5 1076 60 100 88,3 1347 65 109 100 1508 70 233 100 1974 75 360 100 2439 80 487 100 2893 85 613 100 3331 90 743 100 3761 95 867 100 4179 100 996 100 4592

Table 2.1: Calculated adiabatic temperature of decomposition products and their volume for solutions of H2O2

Potential Health Effects The potential health effects of hydrogen peroxide are essentially the same for 70% and 85% concentrations. The following excerpts are taken from Solvay Interox material safety data sheets for: a) 60 - 73% H2O2 b) 84 - 86% H2O2 General

ˆ Corrosive to mucous membranes, eyes and skin

ˆ The seriousness of the lesions and the prognosis of intoxication depend directly on the concentration and duration of exposure

Inhalation

ˆ Nose and throat irritation

ˆ Cough and difficulty in breathing

ˆ In case of repeated or prolonged exposure: risk of sore throat, nose bleeds, chronic bronchitis

ˆ Risk of pulmonary oedema (for 85% H2O2)

20 ˆ Nausea and vomiting (for 85% H2O2) Eye Contact

ˆ Severe eye irritation, watering, redness and swelling of the eyelids

ˆ Risk of serious or permanent eye lesions

ˆ Risk of blindness

Skin Contact

ˆ Painful irritation, redness and swelling of the skin

ˆ Risk of severe burns

Ingestion

ˆ May be fatal if swallowed

ˆ Paleness and cyanosis of the face

ˆ Severe irritation, risk of burns and perforation of the gastrointestinal tract accom- panied by shock

ˆ Excessive fluid in the mouth and nose, with risk of suffocation

ˆ Risk of throat oedema and suffocation

ˆ Bloating of stomach, belching

ˆ Nausea and vomiting (bloody)

ˆ Cough and difficulty breathing

ˆ Risk of chemical pneumonitis from product inhalation

Whilst the effects of H2O2 vapor are generally only moderate at ambient temperature, the vapor above stable solutions in tanks can give rise to breathing difficulties. The mixture of oxygen and vaporized hydrogen peroxide given off during decomposition is highly irritating to the mucous membranes and respiratory tract and could be a major problem in a confined space if decomposition did occur [16].

2.4 Decomposition of Hydrogen Peroxide

Hydrogen peroxide (H2O2) is very similar compound to water (H2O) and it possesses similar physical properties. It occurs naturally and is found in low concentrations in streams and rivers, although it is an unstable compound and readily decomposes into water and oxygen. The decomposition reaction is exothermic and the temperature of the decomposition products is dependent upon the initial concentration of the hydrogen peroxide and the efficiency of the decomposition. The decomposition reaction of hydrogen peroxide may consist of up to twenty intermediate steps. The exhaust products are water and oxygen, as can be seen from Eq.2.10. The process of decomposition can be started catalytically or thermally [18].

21 2.4.1 Catalytic decomposition A catalyst is defined as a substance that accelerates a chemical reaction without being consumed in the process. The conversion of one substance into another requires chemical bonds to be both broken and created. Breaking bonds requires energy and making bonds releases energy. Initiation of a reaction, requires an activation energy, Ea, to break the first bonds. Introduction of a catalyst into a reaction allows this activation energy to be reduced, thereby accelerating the reaction. Fig.2.16 illustrates this, where the green path represents the catalysed pathway requiring a reduced activation energy to initiate the reaction.

Figure 2.16: The reaction pathway

The reaction illustrated is an exothermic reaction, where the energy of the products is lower than that of the reactants, with the difference in energy being released as heat. In the case of an endothermic reaction the energy of the products is higher than that of the reactants and heat is absorbed. Catalysis may be homogeneous or heterogeneous, depen- dent upon the phase of the catalyst compound in relation to the reactants. Homogeneous catalysis is when both the reactants and catalyst are in the same phase. Heterogeneous catalysis is when the reactants and catalyst are in different phases. In heterogeneous catalysis the catalyst is usually solid and the reactants either gaseous or liquid. The key advantage of using heterogeneous catalysis is that it is easier to contain, and therefore re- cycle, the catalyst material. The process of heterogeneous catalysis involves the reactants adsorbing onto the surface of the catalyst. This weakens the bonds within the reactants allowing the reaction to progress with a lower activation energy. Following the reaction the products are then desorbed from the surface and exhausted. The reaction takes place on the surface of the catalyst therefore it is pertinent to optimise the available surface area. For this reason a solid catalyst is usually in the form of a fine powder or a section of highly porous foam. There are many known catalysts for the decomposition of hydrogen peroxide. In chemistry classes low concentrations of hydrogen peroxide may be catalysed using a small piece of liver or potato. At high concentrations a catalyst with a longer lifetime is required and interest moves primarily to silver and manganese oxides. Overall silver, in the form of compressed gauzes, is the preferred catalyst for the decomposition of hydrogen peroxide in a conventional thruster. The gauzes themselves are easy to han- dle thereby facilitating installation and compression within the chamber. The primary

22 alternative is to use a manganese oxide catalyst, which will produce a faster reaction than silver, enabling a rapid start up characteristic. It may be used as either a solution or a solid catalyst supported on another surface. Use of this catalyst in solution form requires the design of injectors to spray the catalyst onto the propellant, which adds complexity to the system. It is difficult to create solid manganese oxide in any form other than a fine powder. For use as a catalyst it is therefore supported on a substrate, which provides the required structural strength [19].

2.4.2 Thermal decomposition As it has been seen in the previous chapter, heterogeneous reactions are catalyzed by material surfaces, such as walls, catalyst beds, or reactive particles in the flow. Drawbacks to this approach include catalyst poisoning due to the presence of stabilizers in HTP, and susceptibility of the metal catalyst to melting because of the intense heat release. This renders the use of catalysts not only inconvenient but also quite expensive. An alternate approach for HTP decomposition is thermal, where no catalyst is required [20]. Thermal decomposition of H2O2 is a complex process, and involves many intermediate radical species. Schumb et al. [21] describe self-sustaining thermal decomposition as follows: ”If a concentrated aqueous hydrogen peroxide solution is heated to a temperature at which the vapor produced lies within the explosive composition range, it is possible to ignite the vapor and produce a continuously-propagating flame . . . the vapor can be ignited by a spark, hot wire, or catalytically-active surface . . . heat transferred down from the flame causes continuous vaporization of the liquid, and the flame will continue to “burn” quite evenly without supply of any external heat.” Thermal decomposition is based on raising temperature at which reaction occurs in order to increase the rate of reaction. In fact, according to Arrhenius’ Law (see Eq.2.11), the reaction rate coefficient κ depends on temperature:

− Ea κ = Ae RT (2.11) The modified Arrhenius’ equation makes explicit the temperature dependence of the pre-exponential factor. The modified equation is usually of the form:

n − Ea κ = AT e RT (2.12) The important feature of the mechanism is the pressure dependence of the reaction rate. In real situation, the pressure inside the decomposer is likely to vary widely. There- fore in order to model a reacting flow accurately, the reaction rate constants must reflect their pressure dependence. The reaction mechanism in Tab. 2.2 shows that many re- actions are pressure dependent (or third-body mediated). One of the most important reactions in the list is the step number 20 [22]. This reaction represents the first step of H2O2 decomposition to produce two OH radicals. The OH radicals initiate other reactions and produce some intermediate species, such as HO2, H and O.

23 Reactions A n Ea/R ∆h 12 8 1 2 O + M O2 + M 0.120 × 10 −1.00 0.00 −4.9832 × 10 2 O + H + M OH + M 0.500 × 1012 −1.00 0.00 −4.2780 × 108 2 4 6 3 O + H2 H + OH 0.387 × 10 2.70 0.32 × 10 −8.1700 × 10 11 8 4 O + HO2 O2 + OH 0.200 × 10 0.00 0.00 −2.2237 × 10 4 4 7 5 O + H2O2 OH + HO2 0.963 × 10 2.00 0.20 × 10 −6.1392 × 10 13 8 6 O2 + H + M HO2 + M 0.280 × 10 −0.86 0.00 −2.0543 × 10 14 8 7 2 O2 + H O2 + HO2 0.208 × 10 −1.24 0.00 −2.0543 × 10 14 8 8 O2 + H + H2O HO2 + H2O 0.113 × 10 −0.76 0.00 −2.0543 × 10 14 4 7 9 O2 + H O + OH 0.265 × 10 −0.67 0.86 × 10 −7.0519 × 10 13 8 10 2 H + M H2 + M 0.100 × 10 −1.00 0.00 −4.3597 × 10 11 8 11 2 H + H2 2 H2 0.900 × 10 −0.60 0.00 −4.3597 × 10 14 8 12 2 H + H2O H2 + H2O 0.600 × 10 −1.25 0.00 −4.3597 × 10 17 8 13 H + OH + M H2O + M 0.220 × 10 −2.00 0.00 −4.9914 × 10 10 3 8 14 H + HO2 O + H2O 0.397 × 10 0.00 0.34 × 10 −2.2319 × 10 11 3 8 15 H + HO2 O2 + H2 0.448 × 10 0.00 0.54 × 10 −2.3054 × 10 11 3 8 16 H + HO2 2 OH 0.840 × 10 0.00 0.32 × 10 −1.5185 × 10 5 4 7 17 H + H2O2 H2 + HO2 0.121 × 10 2.00 0.26 × 10 −6.9562 × 10 11 4 8 18 H + H2O2 OH + H2O 0.100 × 10 0.00 0.18 × 10 −2.8458 × 10 6 4 7 19 OH + H2 H + H2O 0.216 × 10 1.51 0.17 × 10 −6.3171 × 10 8 8 20 2 OH + M H2O2 + M 0.740 × 10 −0.37 0.00 −2.1456 × 10 2 4 7 21 2 OH O + H2O 0.357 × 10 2.40 −0.11 × 10 −7.1341 × 10 11 3 8 22 OH + HO2 O2 + H2O 0.145 × 10 0.00 −0.25 × 10 −2.9371 × 10 10 3 8 23 OH + H2O2 HO2 + H2O 0.200 × 10 0.00 0.21 × 10 −1.3273 × 10 16 5 8 24 OH + H2O2 HO2 + H2O 0.170 × 10 0.00 0.15 × 10 −1.3273 × 10 9 3 8 25 2 HO2 O2 + H2O2 0.130 × 10 0.00 −0.82 × 10 −1.6097 × 10 12 4 8 26 2 HO2 O2 + H2O2 0.420 × 10 0.00 0.60 × 10 −1.6097 × 10 13 4 8 27 OH + HO2 O2 + H2O 0.500 × 10 0.00 0.87 × 10 −2.9371 × 10

Table 2.2: Reaction mechanism for H2O2 decomposition. Rate constants are expressed in Arrhenius’ form with SI unit (kilomol, meter, second). ∆h is in Joule/kilomol. The “ ” symbol represents that the backward reactions are also considered. ”M” represents third-body and reactions involving ”M” are third-body mediated pressure dependent.

24 Chapter 3

Preliminary design

3.1 Computation of operating parameters with NASA CEA code

The goal of the thesis is to design a monopropellant rocket engine, fueled with 87.5% HTP, which is able to produce a thrust of 1 N in vacuum condition. To perform the preliminary calculation the CEA code has been used. The NASA Computer program CEA (Chemical Equilibrium with Applications) calculates chemical equilibrium composi- tions and properties of complex mixtures. Applications include assigned thermodynamic states, theoretical rocket performance, Chapman-Jouguet detonations, and shock-tube parameters for incident and reflected shocks [23]. Pressure inside decomposition cham- ber has initially been set to 5 bar. Monopropellant rocket engines are mainly used for in-space application, so they should be designed to work in vacuum condition. However, since water is a product of decomposition of hydrogen peroxide, it is safer to keep the exit pressure (and consequently temperature) not too low, in order to avoid condensation inside the nozzle. With the CEA code it is possible to verify if a phase change occurs during expansion. Setting an exit pressure of 0.1 bar, the CEA code shows that the only products at nozzle exit nozzle are water and oxygen in gaseous form. Input parameters in the CEA code are summarized in Tab.3.1.

Input parameter Value Units

Decomposition chamber pressure, Pc 5 bar

Exit nozzle pressure, Pe 0.1 bar HTP concentration 87.5 %

Table 3.1: Input parameters in the CEA code

Computation has been performed by imposing continuous equilibrium adjustment dur- ing the expansion (shifting equilibrium) and infinite area combustor. The results obtained by the CEA code are resumed in Tab.3.2.

25 Output parameter Value Units

Decomposition chamber temperature, Tc 961.36 K

Throat temperature, Tt 844.29 K

Exit nozzle temperature, Te 384.33 K Area ratio,  5.8179 - Characteristics velocity, c∗ 909.8 m/s

Thrust coefficient, CF 1.5104 -

Specific impulse in vacuum, ISPvac 150.88 s

Specific impulse, ISP 140.08 s

Exit nozzle speed of sound, ce 441.1 m/s

Exit nozzle Mach number, Me 3.116 -

Exit nozzle velocity, Ve 1374.47 m/s Decomposition chamber speed of sound, c 679.90 m/s Gas constant, R 378.50 J/(kgK)

H2O mass fraction 0.58843 -

O2 mass fraction 0.41157 -

Table 3.2: Data output in the CEA code

3.2 Sizing of the thruster

The monopropellant in analysis is designed to achieve an ideal thrust of 1 N in vacuum condition. Therefore, propellant mass flow rate is computed by applying Eq.3.1: F m˙ p = = 0.68 g/s (3.1) gISPvac A decomposition diameter of 5 mm has been chosen. An important parameter for catalyst is bed loading φ: m˙ φ = p = 34.41 kg/m2s (3.2) Ac The value of φ obtained is adequate for the level of thrust of this particular application. Once the mass flow rate is known, also the throat area At can be derived:

∗ m˙ pc 2 At = = 1.23 mm (3.3) Pc Which corresponds to a throat diameter of 1.25 mm. Exit nozzle area is then now quite immediate to compute, in fact:

2 Ae = At = 7.15 mm (3.4)

26 The nozzle exit diameter is then 3.30 mm. The catalyst pack length is function of several factors, as can be seen in Eq.3.5. In order to have a complete decomposition inside the catalyst, a residence time tres of one millisecond is assumed:

Rm˙ pTctres Lcp = = 25.04 mm (3.5) AcPc Pressure drop through the catalyst pack can be computed by using the empirical 2 formula (Pc is expressed in psi and φ in lb/(in s)): 3.5 × 104 × φ1.375 ∆Pcp = 0.778 = 19.72 psi (3.6) Pc Which corresponds to 1.36 bar. Since the nozzle under exam has a particularly reduced dimension, the choice to de- sign a conical-shape nozzle is adequate. In fact, a bell-shape nozzle, which presents some advantages in terms of efficiency, does not result to be convenient for such a small appli- cation. A convergent angle of 45 degrees is chosen, while the divergent angle is 15 degrees only, since the presence of supersonic flow may lead to problems of flow separation for higher angles. Therefore, the length of convergent and divergent part is derived with simple geometric considerations:

Dc − Dt Lconv = = 1.87 mm (3.7) 2 tan(αconv)

De − Dt Ldiv = = 3.30 mm (3.8) 2 tan(αdiv) Design parameters of the thruster are summarized in Tab.3.3.

Design parameter Value Units

Thrust, F 1 N

Propellant mass flow rate,m ˙ p 0.68 g/s Bed loading, φ 34.41 kg/m2s

Residence time, tres 0.001 s

Convergent angle, αconv 45 deg

Divergent angle, αdiv 15 deg

Decomposition chamber diameter, Dc 5 mm

Throat diameter, Dt 1.25 mm

Exit nozzle diameter, De 3.02 mm

Catalyst pack pressure drop, ∆Pcp 1.36 bar

Catalyst pack length, Lcp 25.04 mm

Convergent length, Lconv 1.87 mm

Divergent length, Ldiv 3.30 mm

Table 3.3: Design parameters of the thruster

27 3.3 Feed line design

In the combustion chamber of monopropellant, a certain amount of pressure is needed to accelerate the hot gas mixture. Therefore, a feed system is needed to pressurize and transport the propellant from the tank to the thrust chamber. Due to this reason, to effectively de-link the feed system from the engine, generally about 6 bar or 10 percent of the chamber pressure, whichever is higher, is provided at the propellant injector [15] [24]. Assuming the coefficient of discharge for the orifice as 0.8, the orifice diameter Di is 3 calculated as follows (ρHTP is equal to 1350 kg/m ): s 4m ˙ p Di = √ = 0.164 mm (3.9) πCDi 2∆PiρHTP Upstream the injection system, a solenoid valve regulates the flow of the propellant. As all the components in contact with hydrogen peroxide, it is necessary to have a stainless steel valve, possibly sealed with PTFE. For the mass flow rate under exam, the orifice of the valve has to be quite small. Therefore, considering a flow coefficient Kv of 0.002, the pressure drop across the solenoid valve can be computed as follows:

SG × Qp ∆Pv = 2 = 1.11 bar (3.10) Kv

where SG is the specific gravity (of HTP) and Qp is the volumetric flow rate of the propellant, expressed in m3/h. Propellant tank pressure is a fundamental parameter for the design of the thruster. In fact, an insufficient pressurization of the tank would lead to a lower pressure inside the decomposition chamber, with serious consequences on the efficiency of the whole system. Pressurization is achieved by means of a gas, which is usually nitrogen. Being known all the pressure losses inside the feed line, the propellant tank pressure necessary to have 5 bar inside combustion chamber is:

Ppt = Pc + ∆Pcp + ∆Pi + ∆Pv = 13.47 bar (3.11) Assuming a boost time of 20 s and an ullage volume of 10 %, the propellant tank volume is evaluated as:

1.1 × m˙ ptboost −5 3 Vpt = = 1.11 × 10 m (3.12) ρHTP Design parameters of the feed line are summarized in Tab.3.4.

28 Design parameter Value Units

Injector pressure drop, ∆Pi 6 bar

Injector diameter, Di 0.164 mm

Injector discharge coefficient, CDi 0.8 -

Solenoid valve flow coefficient, Kv 0.002 -

Solenoid valve pressure drop, ∆Pv 1.11 bar

Propellant tank pressure, Ppt 13.47 bar −5 3 Propellant tank volume, Vpt 1.11 × 10 m

Boost time, tboost 20 s

Table 3.4: Design parameters of the feed line

The feed line described in this section is a standard configuration with the liquid and the gas stored in two different tanks (Fig.3.1a). A more advanced concept is the self- pressurized system and some possibilities are shown in Fig.3.1. The option showed in Fig.3.1b uses a pressure-biased tank, so that liquid is delivered above the gas pressure. This can be done with a differential area piston or an elastically-loaded diaphragm which separates the gas and liquid. Acceleration could possibly be used, e.g. gravity in a terrestrial application or centripetal acceleration on a spinning spacecraft. Alternatively, option showed in Fig.3.1c works with any tank. A pressure boosting pump provides for circulation through the gas generator and back to the tank ullage [25].

(a) Conventional (b) Self-pressurized (c) Self-pressurized pressurization (biasing tank divider) (with boost pump)

Figure 3.1: Examples of feed lines for propulsive systems

29 3.4 Example of research stand for experimental in- vestigation

Researchers of the Warsaw Institute of Aviation have built a research stand for investi- gation of thermal decomposition of HTP applied to a monopropellant thruster (Fig.3.2). Hydrogen peroxide is stored in cylindrical, low volume tank made of passivated stainless steel. It is equipped with filling valve and safety valve in the case of an undesirable de- composition. Due to the safety reasons the stored amount of HTP has to be very low (required only for few experiments at most). To deliver the medium to the decomposition chamber, the pressure fed system is used. Gaseous nitrogen is used as pressurizer delivered to the HTP tank through the valve, pressure regulator (reductor) and low pressure tank (LPT). LPT is used to lower the pressure oscillation in the system during the experiments [1]. Thermal decomposition is achieved by pre-heating the chamber using an electrical resistance. The test bench is equipped with sensors for pressure, temperature and thrust measurement.

Figure 3.2: Research stand at IoA: 1-Nitrogen valve, 2-Pressure reductor, 3-Low pressure nitrogen tank, 4-HTP filling valve, 5-Safety valve, 6-HTP filter, 7-Injection valve, 8-Heater, 9-Decomposition chamber, 10-Power supply, 11-Thrust measurement system.

30 Chapter 4

CFD Simulation and modelization

Computational Fluid Dynamics (CFD) is the simulation of fluids engineering systems us- ing modeling (mathematical physical problem formulation) and numerical methods (dis- cretization methods, solvers, numerical parameters and grid generations). Fig.4.1 resumes the fundamental steps of the process [26]:

Figure 4.1: Process of CFD

CFD is applied to a wide range of research and engineering problems in many fields of study and industries, including aerodynamics and aerospace analysis, weather simulation, natural science and environmental engineering, industrial system design and analysis, biological engineering, fluid flows and heat transfer, and engine and combustion analysis. Computational Fluid Dynamics presents many advantages with respect to experimental approach, which is usually expensive and requires a lot of time (see Tab.4.1).

31 Simulation (CFD) Experimental

Cost Cheap Expensive Time Short Long Scale Any Small/Middle Information All Measured Point Repeatable Yes Some Safety Yes Some Dangerous

Table 4.1: Comparison between simulation and experimental approach

4.1 Description and resolution of Navier-Stokes equa- tions

General conservation equations are summarized below: Continuity:

∂ρ ∂(ρu ) + α = 0 (4.1) ∂t ∂xα Momentum:

Dui ∂p ∂σiα = − + + ρgi (4.2) Dt ∂xi ∂xα Energy:

DhS ∂p ∂  λ ∂hS  = + − qcωr (4.3) Dt ∂t ∂xα Cp ∂xα Species:

DY ∂  ∂Y  = ρd + ωr (4.4) Dt ∂xα ∂xα where:

D ∂ ∂ ∂ρ ∂(ρuα) = ρ + ρuα = + (4.5) Dt ∂t ∂xα ∂t ∂xα and:   ∂ui ∂uj 2 ∂uα σij = µ + − δij (4.6) ∂xj ∂xi 3 ∂xα

Formulation is then completed by perfect gas equation:

p = ρRT (4.7)

32 4.1.1 Direct Numerical Simulation (DNS) A direct numerical simulation (DNS) is a simulation in computational fluid dynamics in which the Navier-Stokes equations are numerically solved without any turbulence model. This means that the whole range of spatial and temporal scales of the turbulence must be resolved. All the spatial scales of the turbulence must be resolved in the computational mesh, from the smallest dissipative scales (Kolmogorov scales), up to the integral scale l0, associated with the motions containing most of the kinetic energy. The Kolmogorov lk is given by:

1 ν3  4 l = (4.8) k ε where ν and ε are respectively the kinematic viscosity and the dissipation rate of turbulent kinetic energy. The minimum number of points N along a given mesh direction with increments sm necessary to perform the simulation until the Kolmogorov scales is:

Nsm > l0 (4.9) so that the integral scale is contained within the computational domain, and also

sm ≤ lk (4.10) so that the Kolmogorov scale can be resolved. Since:

u0 3 ε ≈ 0 (4.11) l0 0 where u0 is the Root Mean Square (RMS) of the velocity. The previous relations imply that for a three-dimensional simulation a number of mesh points N 3 is required, satisfying:

3 9 N ≥ Re0 4 (4.12)

where Re0 is the turbulent Reynolds number: u0 l Re = 0 0 (4.13) 0 ν Hence, the memory storage requirement in a DNS grows very fast with the Reynolds number. In addition, given the very large memory necessary, the integration of the solu- tion in time must be done by an explicit method. This means that in order to be accurate, the integration must be done with a time step, ∆t, small enough such that a fluid particle moves only a fraction of the mesh spacing sm in each step. That is, u0 ∆t C = 0 < 1 (4.14) sm where C is the Courant number. The total time interval simulated is generally pro- portional to the turbulence time scale τ given by:

l0 τ = 0 (4.15) u0

33 Combining these relations, and the fact that sm must be of the order of lk, the number of time-integration steps must be proportional to l0/(Clk). By other hand, from the definitions for Re, lk and l0 given above, it follows that:

l0 3 ≈ Re0 4 (4.16) lk and consequently, the number of time steps grows also as a power law of the turbu- lent Reynolds number. One can estimate that the number of floating-point operations required to complete the simulation is proportional to the number of mesh points and 3 the number of time steps, and in conclusion, the number of operations grows as Re0 . Therefore, the computational cost of DNS is very high, even at low Reynolds numbers. For the Reynolds numbers encountered in most industrial applications, the computational resources required by a DNS would exceed the capacity of the most powerful computer currently available. However, direct numerical simulation is a useful tool in fundamental research in turbulence. Using DNS it is possible to perform ”numerical experiments”, and extract from them information difficult or impossible to obtain in the laboratory, allowing a better understanding of the physics of turbulence. Also, direct numerical simulations are useful in the development of turbulence models for practical applications, such as sub- grid scale models for Large Eddy Simulation (LES) and models for methods that solve the Reynolds-Averaged Navier-Stokes equations (RANS).

4.1.2 RANS Equations To solve the flow field of a turbulent flow the Navier-Stokes equation can be used with direct numerical simulation (DNS). As seen in the previous paragraph, this method is computationally demanding and expensive, and is mostly used on smaller scale issues for research purposes. With the case considered in this thesis the Reynolds Averaged Navier-Stokes (RANS) equation is therefore applied instead. RANS equation are derived by applying Favre average (see Eq.4.17 and4.18) in the general conservation equations (Eqs.4.1 ∼ 4.4).

u(x, t) =u ˜(x, t) + u00(x, t) (4.17)

ρu u˜ = (4.18) ρ¯ ∂ρ¯ ∂(¯ρu ) + fα = 0 (4.19) ∂t ∂xα ˜ Du˜i ∂p¯ ∂ 00 00 = − + (σiα − ρ¯ugαui ) +ρg ¯ i (4.20) Dt˜ ∂xi ∂xα

˜ ˜S S ! Dh ∂p¯ ∂ λ ∂h 00 S = + − ρ¯ugαh − qcωr (4.21) Dt˜ ∂t ∂xα Cp ∂xα ˜ ˜   DY ∂ ∂Y 00 00 = ρd − ρ¯ugαY + ωr (4.22) Dt˜ ∂xα ∂xα

34 where:

D˜ ∂ ∂ =ρ ¯ +ρ ¯ + ufα (4.23) Dt˜ ∂t ∂xα   ∂ui ∂uj 2 ∂uα σij = µ + − δij (4.24) ∂xj ∂xi 3 ∂xα

Gradient transport models Because of the additional turbulent terms, the problem needs more equations for closure. The Boussinesq hypothesis (Eq.4.25) assumes that the turbulent transport term of a property is correlated to the gradient of the correspondant average property: ˜ 00 00 µT ∂Φ −ρ¯ugi Φ = (4.25) σΦ ∂xi

Where Φ is a reaction scalar, µT is the turbulent viscosity (still unknown) and σΦ is a Prandtl or Schmidt number. The latter is usually treated as an empirical constant. To 00 00 describe an expression for the Reynolds stress term −ρ¯ugi uj it has to be noticed that the 00 00 termsρ ¯ugi ui should note be included since since momentum transport in one direction is caused by its gradient in the normal direction with respect to it. Defining turbulent kinetic energy is defined as: 1 k˜ = ug00 u00 (4.26) 2 α α Reynolds stresses can be then expressed as:

 2   ∂u ∂u  2 ∂u 00 00 ei ej fα − ρ¯ugi uj − ρ¯ekδij = µT + − µT δij (4.27) 3 ∂xj ∂xi 3 ∂xα

One equation models: Prandtl mixing length According to diffusive transport: µ ν = T ≈ u∗l∗ (4.28) T ρ ∗ ∗ where νT is the kinematic turbulent viscosity and u and l are velocity and length scales. In analogy with molecular diffusion, Prandtl described the mixing length hypoth- ∗ izing that l is a certain mixing length lm along which the turbulent transport occurs, and its value is:

∗ ∂u˜ u ≈ lm (4.29) ∂y for 2D flows. Thus:

2 ∂u˜ νT ≈ lm (4.30) ∂y

lm should be now evaluated. For instance, for duct or channel flows, lm might be considered as proportional to the diameter of the duct or the height of the channel.

35 Two-equations models: k − ε and k − ω In two-equations models the basic concept is describing the two fundamental param- eters u∗ and l∗ by means of differential equations instead of an algebraic way as in the mixing length.

u∗ ≈ k˜1/2 (4.31)

k˜3/2 l∗ ≈ (4.32) ε˜ whereε ˜ is the dissipation rate of turbulent kinetic energy k˜, defined as:

00 00 ∂ugα∂uα ε˜ = νT (4.33) ∂xα∂xα From 4.28 is then possible to write:

ke2 ν = C (4.34) T µ ε˜

Where Cµ is a constant. From DNS studies it is approximatly 0.09. ˜ So, it is now matter of determining k andε ˜ in order to find νT [27]. In order to derive ˜ 00 00 an equation for k, 4.2 is written for i and j. Cross-product of the equations for uj and ui and Favre average are applied. Then, sum of equations is performed. By imposing i = j and summing on i, following equation for k is obtained:

D˜k˜ ∂u˜ ∂  ∂p¯  ∂ ∂u00 00 00 β 00 00 ¯00 0 00 0 α = −ρ¯ugαuβ − (¯ρugαk ) − uα − gα − (pguα) + p − ρ¯ε˜ (4.35) Dt˜ ∂xα ∂xα ∂xα ∂xα ∂xα where molecular transport has been neglected, assuming high Reynolds number flow. Reynolds stress (first term on right-hand side) can be modeled according to 4.27. Second 00 00 term involves the transport of k through ui , thus can be modeled as transport of gradient 0 00 of k. This assumption is valid for p ui also. So it is possible to write: ˜ 00 00 0 00 µT ∂k −(¯ρugαk + pguα) = (4.36) σk ∂xα

where the recommended value for σk is 1.00. So, equation for k is given by:

˜ ˜ ˜ ! Dk ∂ µT ∂k = + Pk − ρ¯ε˜ (4.37) Dt˜ ∂xα σk ∂xα where:     ∂u˜α ∂u˜β ∂uα 2 ∂u˜β ˜ ∂u˜α Pk = µT + − µT +ρ ¯k (4.38) ∂xβ ∂xα ∂xβ 3 ∂xβ ∂xα The equation for ε can be written in the same form of k using empirical constants:

˜   2 Dε˜ ∂ µT ∂ε˜ ε˜ ε˜ = + Cε1 Pk − Cε2ρ¯ (4.39) Dt˜ ∂xα σε ∂xα k˜ k˜

where σε = 1.3, Cε1 = 1.44 and Cε2 = 1.92.

36 Another two-equations model is k − ω: it is similar to k − ε model, but now the new variable ω is defined: ε˜ ω˜ = (4.40) k˜ which is the characteristic frequency of the turbulence. Turbulent kinematic viscosity can be rewritten as:

k˜ ν = C (4.41) T µ ω˜ The two equations of the model are now:

˜ ˜ ˜ ! Dk ∂ µT ∂k ˜ = + Pk − ρ¯kω˜ (4.42) Dt˜ ∂xα σk ∂xα ˜   Dω˜ ∂ µT ∂ω˜ ω˜ 2 = + Cω1 Pk − Cω2ω˜ (4.43) Dt˜ ∂xα σω ∂xα k˜ This model is frequently used to deal boundary layer flows [28].

Reynolds stress models In the gradient transport models, Reynolds stresses are are determined indirectly by turbulent viscosity coefficient, subjected to gradient transport hypothesis. The idea is now to solve model transport equations for the individual Reynolds stresses. This is also called second-order modelling. This can be achieved with a process similar for the derivation of the equation for k (without imposing i = j and summing):

D˜u00u00   gi j 00 00 ∂u˜i 00 00 ∂u˜j ∂ 00 00 00 = − ρ¯ugαuj +ρ ¯ugαui − (¯ρ(uαui uj ))− (4.44) Dt˜ ∂xα ∂xα ∂xα   00 ∂p 00 ∂p 00 00 00 ∂σiα 00 ∂σjα uj + ui + uj gi + ui gj + uj + ui ∂xi ∂xj ∂xα ∂xα The equation for the generic Reynolds fluxρ ¯ug00Φ00 is:

˜ 00 00 ˜ ! Dugi Φ 00 00 ∂u˜i 00 00 ∂Φ ∂ 00 00 = − ρ¯ugαΦ +ρ ¯ugαui − (¯ρ(uαui Φ))− (4.45) Dt˜ ∂xα ∂xα ∂xα

00 ∂p 00 00 ∂ui ∂Φ Φ + Φ gi + ui ωr + µ ∂xi ∂xα ∂xα Finally, it is also necessary an auxiliary equation in order to describe Φg002:

˜ ˜  2 D 002 00 00 ∂Φ ∂ 00 002 00 ∂Φ Φg = 2¯ρugαΦ − (¯ρugαΦ ) + Φ ωr − ρµ¯ (4.46) Dt˜ ∂xα ∂xα ∂xα

37 4.1.3 Large Eddy Simulation (LES) RANS equations have been applied successfully but, since the solution is a statistic av- erage, their limitation is that they are not sufficient to study in detail the turbulent structure. Large Eddy Simulation finds a compromise between DNS (computationally prohibitive) and RANS: they solve accurately all the large scales, but modeling also the dissipative processes of small scales. For LES implementation, all the equations are spa- tially filtered with a filter of dimension ∆ , generally equivalent to the dimension of the grid of LES simulation. The filtered variable is denoted as: Z u¯(x, t) = G(x, r)u(x − r, t)dr (4.47)

D where the integral is extended to the entire domain of flux D, and G is a certain filter function which satisfies following relation: Z G(x, r)dr = 1 (4.48)

D

Typically, G is the product of three filter functions in each spatial dimension xi, with i = 1, 2, 3. By applying the filter of Eq.4.47 to the momentum equation 4.2: ˜ Du˜i ∂p¯ ∂ = − + [¯σiα − ρ¯(ugiuα − ueiufα)] +ρg ¯ i (4.49) Dt˜ ∂xi xα which appears quite similar to RANS 4.20. The main difference is the subgrid stress term:

τij = −ρ¯(ugiuα − ueiufα) (4.50) which physically represents the turbulent dissipation for unresolved scales. Since ugiuj cannot be determined from the solution of filtered equation, this term has to be modeled. One of the most common approaches is Smagorinsky model:   1 ∂uei ∂uej ¯ τij = − δijτkk = νt + = −2νtSij (4.51) 3 ∂xj ∂xi in analogy with gradient transport model. Similarly to mixing length evaluation, subgrid viscosity νt is modeled as

2 ˜ νt = Cs∆ S (4.52)

where Cs, called Smagorinsky coefficient, has to be determined. In Smagorinsky model, Cs is predetermined as a constant value, typically 0.3 or less, according to flow configura- tion. In a more refined model, called dynamic subgrid-scale model (DSGS), Cs is part of integration process. A ’test filter’ ∆,ˆ which is typically twice the original grid dimension ∆, is applied to equation 4.49:

ˆ ˆ Tij =ρ ¯(ugdiuj − u˜iu˜j) (4.53)

38 By applying once another the filter test on equation 4.50 and then equalizing the term ugdiuj from Eqs 4.50 and 4.53, the following mathematical identity is obtained: ˆ ˆ ugdiuj − u˜iu˜j = Tij − τˆij (4.54)

which is known as Germano’s identity [29]. Cs can be now determined since it depends on ui and its gradients only. It is computed dynamically and it is in general space and time dependant.

4.2 Finite Volume Method

Once the formulation for Navier-Stokes equations is complete, they need to be discretized in order to be solved by a calculator. The typical discretization method for CFD calcu- lation is Finite Volume Method (FVM), since it is very useful for resolution of Partial Differential Equations (PDE). This is due to the fact that, with FVM, if Navier-Stokes equation is satisfied in every control volume, it will automatically be satisfied for the whole domain. Considering steady-state Navier-Stokes Equation in vectorial form:

∇ · (ρuΦ) = ∇ · (ρΓ∇Φ) + qΦ (4.55) Integrating this over the control volume Ω: Z Z ∇ · (ρuΦ − ρΓ∇Φ)dV = qΦdV (4.56)

Ω Ω recalling divergence (Gauss) theorem: Z Z ∇ · AdΩ = A · nds (4.57)

Ωv ∂Ωv and applying it on equation 4.56, the following form of N-S is obtained: Z Z (ρuΦ − ρΓ∇Φ) · nds + qΦdΩ (4.58)

∂Ωv Ωv The source term (volume integral) can be approximated by evaluating it at the cell centre (P) and multiplying by the volume of the cell. For a 2-D grid (see Fig.4.2: Z qΦdΩ = (qΦ)P ∆x∆y (4.59)

Ωv It can be demonstrated that this approximation is of second order accuracy To approximate the surface integral, an interpolation process is required. Typically, there are two types of interpolations, one is upwind interpolation, and the other one is central interpolation. Upwind Interpolation:

( Φ = Φ if(u · n) > 0 e P (4.60) Φe = ΦE if(u · n) < 0

39 Figure 4.2: 2D Structured Grid Domain

It is a very simple scheme and it is always bounded. However, it is only first order accurate Central Interpolation:

Φe = ΦEλe + ΦP (1 − λe) (4.61) where

xe − xP λe = (4.62) xE − xP The central difference scheme is a second order approximation and thus more accurate than the first order upwind scheme, although it can produce oscillatory solutions [30].

40 Chapter 5

Simulation Set-Up

5.1 Geometry

Nozzle geometry has been designed according to values reported in chapter 3. Total length is 100 mm and total height is 15 mm (Fig.5.1). Only half geometry is necessary, since in the simulation the case is going to be axisymmetric. The nozzle (Fig.5.2) has been designed with smooth throat section, since a sharp throat may generate issues in the boundary layer. Moreover, it is also more convenient for manufacturing. A certain number of Face Split has been applied in order to have a more precise mesh control, in fact inside the nozzle and in particular in throat region the mesh has to be more refined.

Figure 5.1: Global geometry

41 Figure 5.2: Detail of nozzle geometry

5.2 Mesh

The mesh consists of a large number of quadrilateral and a small number of triangular elements. As previously mentioned, the axisymmetric geometry allows to work on half geometry only, saving a significant amount of computational cost. For this reason, it has been possible to improve mesh refinement and quality. In particular, a more refined sizing has been applied to the nozzle region (see Fig.5.3 and 5.4). Mesh quality is fundamental in order to avoid divergence problem during simulation. In particular, orthogonal quality and skewness are the two most important parameters. The minimum and average values of orthogonal quality are respectively 0.672 and 0.999 (Fig.5.5). For skewness the maximum value is 0.555 and the average is 0.015 (Fig.5.6). Since skewness has to be ideally close to 0 and orthogonal quality close to 1, the values obtained for the mesh can be considered good. In the mesh modeler the named selections for the application of boundary conditions have been created also (Fig.5.7).

Figure 5.3: Global mesh

42 Figure 5.4: Detail of nozzle mesh

Figure 5.5: Orthogonal Quality

Figure 5.6: Skewness

43 (a) Inlet (b) Walls

(c) Axis (d) Outlet

Figure 5.7: Named Selections

5.3 Fluent Set-Up

All the cases have been run as a steady simulation, with the density based solver for an axisymmetric geometry. Energy equation has been enabled and the k −  Realizable has been used as turbulence model. A mixture composed by water, oxygen and air has been defined enabling Species transport. The property of the mixture are summarized in Tab.5.1.

Name Value Units

Mixture type H2O(g), O2, air - Density Ideal gas kg/m3

Specific heat (Cp) Mixing law J/(kgK) Thermal conductivity Constant; 0.0454 W/(mK) Viscosity Constant; 1.72 × 10−5 kg/(ms) Mass diffusivity Constant-dilute-appx; 2.88 × 10−5 m2/s

Table 5.1: Mixture properties

Four cases have been analyzed, changing the atmospheric condition in which nozzle is operating in order to observe adapted, overexpanded and underexpanded behaviour (Tab.5.4). Inlet and walls boundary conditions are the same for all the cases (Tab.5.2 and 5.3). 20000 iterations have been set to run the calculation. However, since residuals remain constant from about 10000 iterations, the solution can be considered converged before the end of the entire calculation.

44 BC Value Units

Gauge total pressure 500000 P a Supersonic/initial gauge pressure 499569 P a Turbulent intensity 5 % Turbulent viscosity ratio 10 - Total temperature 961.36 K

Mass fraction of H2O 0.58843 -

Mass fraction of O2 0.41157 - Mass fraction of air 0 -

Table 5.2: Boundary Conditions at inlet

BC Type

Wall motion Stationary wall Shear condition No slip Roughness models Standard Heat flux null Wall thickness null Heat generation rate null

Table 5.3: Boundary Conditions at walls

BC Case 1 Case 2 Case 3 Case 4 Units

Gauge pressure 10000 1000 20000 40000 Pa Backflow turbulent intensity 5 5 5 5 % Backflow turbulent viscosity ratio 10 10 10 10 - Backflow total temperature 220 180 220 250 K

Mass fraction of H2O 0 0 0 0 -

Mass fraction of O2 0 0 0 0 - Mass fraction of air 1 1 1 1 -

Table 5.4: Outlet Boundary Conditions

45 Chapter 6

Results

6.1 Case 1: Optimal

Results for optimal expansion are presented in this section. In this case, atmospheric pressure is set to be equal to nozzle exit pressure. With an external pressure of 0.1 bar and 220 K, it simulates an atmospheric condition for an altitude of about 14.5 km. However, because of losses inside the nozzle due to the viscosity of the fluid, the pressure at nozzle outlet results to be slightly higher. For this reason, the nozzle exhaust presents some effects of overexpansion, such as weak oblique shocks. Contour of static pressure is shown in Fig.6.1. In the convergent region, where the flow is subsonic, the variation of pressure is not very significative. When the flow reaches the throat section, where the transition in supersonic regime occurs, pressure drops significantly and keeps decreasing inside the divergent region. It is possible to appreciate the so-called ”shock-diamonds” structure, typical behaviour of overexpanded nozzles, which has already been explained in detail in Chapter 2. Contours of velocity magnitude and Mach number are presented in Fig.6.2 and 6.3. Velocity and Mach number remain quite small in the convergent zone. Inside the throat, where there should be the transition from subsonic to supersonic condition, Mach number is very close to unity. Finally, in the divergent region where the flow is supersonic, Mach number and velocity increase significantly. Since the nozzle is working in a condition close to the adapted condition (even though, as already mentioned, it is slightly overexpanded because of viscous effect) the flow gets out of the outlet quite regularly (so it is neither divergent nor convergent). Fig.6.4 shows the distribution of the mass fraction of air inside the considered domain. Inside the nozzle mass fraction of air is obviously zero since decomposition products are oxygen and water vapour. In the near region, inside the core flow, there are again water vapour and oxygen only. In fact, the mass fraction of air is zero here (blue zone). In the region surrounding the core flow, called viscous mixing layer, the mass fraction of air starts increasing. In the far-field region (red zone) there is air only. Temperature decreases along with the nozzle as can be seen in Fig.6.5. The tempera- ture keeps decreasing in the core flow region and then it increases again because of oblique shocks. Turbulent intensity (Fig.6.6) inside the nozzle remains quite low far from the walls. Close to the wall, because of the presence of the boundary layer, turbulent intensity results to be higher. Regarding the exhaust region, the turbulent intensity remains very low in the core flow. On the other hand, the viscous region, where the mixing of water and

46 oxygen with ambient air occurs, presents a significant amount of turbulence.

Figure 6.1: Contour of static pressure

Figure 6.2: Contour of velocity magnitude

Figure 6.3: Contour of Mach number

Figure 6.4: Contour of mass fraction of air

47 Figure 6.5: Contour of static temperature

Figure 6.6: Contour of turbulent intensity

6.2 Case 2: Underexpanded

In this second case the nozzle works in underexpanded condition, so ambient pressure is much lower than pressure at nozzle outlet. External pressure and temperature are respec- tively 0.01 bar and 180 K. This level of pressure and temperature are not referred to a particular altitude since the goal of this case was to simulate how the nozzle works in space and so in a condition as close as possible to vacuum. Since the equations of fluid dynamics are no longer valid in vacuum, Fluent does not permit to perform a simulation with a too low level of pressure. Therefore, being necessary to keep a small margin, 0.01 bar is a reasonable value. From pressure distribution in Fig.6.7, a Prandtl-Meyer expansion fan is observable at nozzle exit that is generated to further expand the underexpanded flow. Afterwards, since at a certain distance pressure in the core region turns lower than ambient pressure, the flow is recompressed and pressure rises up. When the nozzle works in underexpanded condition, velocity and Mach number in the exhaust plume rise significantly with respect to adapted and overexpanded cases (see Fig.6.8 and 6.9). The core flow, containing only water and oxygen (Fig.6.10), results to be enlarged too. It can also be noticed that, in underexpanded condition, the flow requires a higher lenght in order to be dissipated. Also temperature (Fig.6.11) presents the same enlarged structure. It may be observed the important difference in temperature between core flow and viscous mixing layer. Turbulent intensity (Fig.6.12) remains lower inside core flow and higher in the mixing region.

48 Figure 6.7: Contour of static pressure

Figure 6.8: Contour of velocity magnitude

Figure 6.9: Contour of Mach number

Figure 6.10: Contour of mass fraction of air

49 Figure 6.11: Contour of static temperature

Figure 6.12: Contour of turbulent intensity

6.3 Case 3: Overexpanded

The first overexpanded case has been simulated for an external pressure of 0.2 bar and an external temperature of 220 K. This condition corresponds to an altitude of about 11.5 km. The exhaust is now clearly overexpanded, how can be noticed by the alternation of oblique shocks and expansions in pressure distribution (Fig.6.13). Velocity magnitude (Fig.6.14) and Mach number (Fig.6.15) in the core are lower with respect to previous cases. From Fig.6.16 it is observable the reduction of core flow region, with mixing among air oxygen and water occurring much closer to the nozzle with respect to adapted and overexpanded cases. In general, the overexpanded case presents a shorter exhaust plume. Observing the distribution of static temperature (Fig.6.17), the cold region inside the core flow is quite reduced in size with respect to adapted and underexpanded in particular. Finally, distribution of turbulent intensity is presented in Fig.6.18.

Figure 6.13: Contour of static pressure

50 Figure 6.14: Contour of velocity magnitude

Figure 6.15: Contour of Mach number

Figure 6.16: Contour of mass fraction of air

Figure 6.17: Contour of static temperature

51 Figure 6.18: Contour of turbulent intensity

6.4 Case 4: Highly overexpanded

The last case considered is related to a higher lever of overexpansion. With ambient conditions for pressure and temperature of 0.4 bar and 250 K, it simulates an altitude of 6.2 km, which is quite unusual for this kind of application. However, it may be useful in order to understand the behaviour of the rocket engine in low altitude conditions. When external pressure is much higher with respect to outlet pressure, the risk of a normal shock inside the nozzle has to be accounted for. However, as can be seen by pressure distribution (Fig.6.19), it is still a condition with an oblique shock wave that remains confined outside the nozzle. Velocity (Fig.6.20) and Mach number (Fig.6.21) are lower with respect to the overexpanded case at 0.2 bar and the exhaust plume region is drastically reduced. Also mixing among water vapour, oxygen and air occurs much closer to the nozzle (Fig.6.22). Static temperature (Fig.6.23) is subjected to a significative increase downstream of oblique shock. Finally, turbulent intensity (Fig.6.24) is very high close to the wall where the shocks are generated.

Figure 6.19: Contour of static pressure

52 Figure 6.20: Contour of velocity magnitude

Figure 6.21: Contour of Mach number

Figure 6.22: Contour of mass fraction of air

Figure 6.23: Contour of static temperature

53 Figure 6.24: Contour of turbulent intensity

6.5 Comparison among the cases

6.5.1 Nozzle The pressure inside the nozzle is not influenced by the ambient conditions. This is due to the fact that being the flow supersonic, the nozzle is chocked and so a change of external condition has no effect on upstream flow. The physical explanation of this phenomenon is as follows: a downstream perturbation of pressure propagates at sound velocity, and so, being slower than the flow inside the divergent, it is not to able to travel inside the nozzle. Since all the properties of the nozzle depend on pressure, also all the other variables (velocity, temperature..) inside the nozzle are not influenced by downstream condition. Fig.6.25 shows the trend of static pressure and Mach number along the nozzle axis. These curves are identical in each case for the reason explained above and so they are presented for case 1 only. It can be clearly seen how Mach number is approximately equal to 1 at the throat (which in the graph is located at zero position). However, since inside the boundary layer the flow might be subsonic, conditions are not the same for each case close to the wall. Fig.6.26 shows how the change of axial velocity along radial coordinate at the nozzle exit. For the overexpanded cases, because of the presence of shocks, the region at constant velocity (null gradient) is reduced with respect to adapted and underexpanded.

54 Figure 6.25: Static pressure and Mach number along nozzle axis

Figure 6.26: dV/dy at nozzle exit

55 As it has been seen above, the thickness of the boundary layer is linked to external pressure condition. Therefore, since values on the nozzle axis are always the same, in order to evaluate the efficiency of the nozzle for each case, it is necessary to calculate the parameters across the exit plane with a mass-weighted average method (see Tab.6.1).

Parameter CEA 0.1 bar 0.01 bar 0.2 bar 0.4 bar

Pressure, Pe[P a] 10000 10898 10840 11158 13296 3 Density, ρe[kg/m ] 0.068739 0.071053 0.070814 0.071989 0.078695

Temperature, Te[K] 384.33 408.15 407.16 411.65 432.32

Velocity, Ve[m/s] 1374.2 1345.5 1347.1 1336.2 1291.4

Mach, Me 3.116 2.979 2.984 2.956 2.836

Table 6.1: Exit nozzle parameters

Thrust coefficient CF is a non dimensional coefficient which evaluates efficiency of the nozzle. CF has been computed for each case considering values obtained by the CEA (ideal case) and the CFD by applying the following equations: V P C = eid + eid  (6.1) Fideal ∗ c Pc

VeCFD PeCFD CFCFD = ∗ +  (6.2) c Pc ∗ where c and Pc are constant since they depend on chamber condition. Results are summarized in Tab.6.2.

0.1 bar 0.01 bar 0.2 bar 0.4 bar

CFideal 1.5104 1.6151 1.3940 1.1613

CFCFD 1.4894 1.5951 1.3658 1.1088

Table 6.2: Comparison between CFideal and CFCFD

The results reported in Tab.6.1 and 6.2 show that adapted and underexpanded cases are the most efficient in terms of expansion quality. Actually, the underexpanded case shows an even better performance than the adapted one. It can be explained by the fact that, due to the viscosity of the non-ideal fluid, the adapted case is actually slightly overexpanded, leading to shock at nozzle exit which reduces the overall efficiency. With a perfect match between the exit and ambient pressure, the adapted nozzle should be the most efficient one. Considering overexpanded cases, it can be observed a progressive reduction of performance with the rise of ambient pressure.

56 6.5.2 Exhaust plume In Fig.6.27 and 6.28 are plotted respectively static pressure and Mach number along the axis of exhaust plume. The different pattern of shocks and expansion waves is observable for each case. The first aspect which may be noticed is that, for overexpanded cases, the intensity of the first shock is directly proportional to external pressure. The oblique shock intercepts the axis much closer to the nozzle when the overexpansion increases and the higher the difference between nozzle and environment condition, the less is the distance at which pressure stabilizes, requiring also a smaller number of compression- expansion cycles. The underexpanded case is completely different. Once the flow exits from the nozzle, pressure keeps decreasing because of Prandtl-Meyer expansion. Once pressure becomes too low with respect to ambient, the flow is subjected to a compression fan, which is different from a shock since pressure rises smoothly. The flow becomes hypersonic since Mach number reaches a value of almost 8. Fig.6.29 shows how the external pressure influences also the mixing of the different species involved. The air starts mixing with the decomposition products at a higher distance from the nozzle when external pressure is lower. Thus, for an underexpanded case, the presence of water and oxygen may be detected also much farther from the nozzle exit.

57 Figure 6.27: Pressure along axis of exhaust plume

Figure 6.28: Mach number along axis of exhaust plume

58 Figure 6.29: Mass fraction of air along axis of exhaust plume

59 6.6 Verification of the model

6.6.1 Convergence of the solution In order to check the convergence of the model, average static pressure and temperature at nozzle exit have been monitored during the iterative process of each case (see Fig.6.30 and 6.31).

(a) 0.1 bar (b) 0.01 bar

(c) 0.2 bar (d) 0.4 bar

Figure 6.30: Convergence of pressure at nozzle exit

(a) 0.1 bar (b) 0.01 bar

(c) 0.2 bar (d) 0.4 bar

Figure 6.31: Convergence of temperature at nozzle exit

60 6.6.2 y+ verification The value of the dimensionless wall distance y+ has to be verified in order to check if the mesh sizing near the wall is adequate for the model. y+ is defined as: u y y+ = τ (6.3) ν

where uτ is the friction velocity, y is the distance from the wall and ν is the kinematic viscosity. The boundary layer is divided in different regions according to distance from the wall [28]:

ˆ Viscous sublayer: y+ < 5

ˆ Buffer layer: 5 < y+ < 30

ˆ Log-law region: 30 < y+ < 300

The k − ω is set by default in ANSYS® Fluent since it solves all the regions of the boundary layer. However, in order to be effective, it requires a very refined mesh close to the wall, implying a much larger amount of computational cost and a lower mesh quality overall. Therefore, it has been decided to use the k − ε Realizable model (a more accurate and modern version of the standard k −ε), which is absolutely adequate for the resolution of Log-law region. For verification of y+, case 1 has been considered. How can be seen from figure 6.32, the maximum value of y+ is about 38, meaning that the first mesh cell falls inside the log region. Therefore, the mesh under exam is adequate for the resolution of Log-law region, making it perfectly compatible with the used model.

Figure 6.32: Contour of y+

61 Chapter 7

Conclusions and future work

7.1 Conclusions

The present thesis work focused on the design and verification by means of CFD method of a hydrogen peroxide monopropellant for low thrust application. The design described in Chapter 3 has been done assuming an ideal expansion inside the nozzle, in order to compare the completely ideal thruster with the CFD simulation where the fluid has a real behaviour because of viscosity and turbulence. The results obtained showed how the efficiency of adapted and underexpanded nozzles are quite high and more or less comparable between them. Concerning overexpansion, the efficiency drops when the difference in pressure between the nozzle outlet and the surrounding environment becomes relevant, generating oblique shocks which are a negative factor in the economy of nozzle efficiency. For the reason explained above, the exhaust plume of the nozzle has been an object of study, in particular observing the pattern of shocks and expansion waves and how they are influenced by the altitude at which the rocket is flying. At low altitude, the intensity of the first shock resulted to be very large and the equilibrium, in pressure and gas composition, between the exhaust plume and the ambient is achieved much closer to the nozzle. On the contrary, for an underexpanded condition, the flow keeps expanding also outside the nozzle thanks to the formation of expansion waves. Inside the core flow, a hypersonic Mach number is observable.

7.2 Recommendation for future work

It would be very interesting an experimental validation of the numerical results, possibly using a vacuum chamber in order to simulate different altitude conditions. Experimental tests can be performed for the study of catalytic and thermal decomposition of hydrogen peroxide. Another suggestion for the future is the realization of a detailed project of the system in flight configuration, in order to have a more complete and realistic characterisation of the behaviour of the rocket. Concerning numerical simulation, a possible future work might be a detailed investi- gation about the boundary layer inside the nozzle, studying in particular the regions of viscous sublayer and buffer layer. However, it would be computationally more expensive, since a more refined mesh would be required. Therefore, it is suggested to focus on the nozzle region only, since the analysis of the exhaust plume is already treated inside this thesis work.

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