Atomisation and Heat Loads
BORBALA BERNUS
Master’s Degree Project
Stockholm, Sweden September 2020
Liquid Oxygen Vaporisation Systems: Atomisation and Heat Loads
BORIKA (BORBALA) BERNUS
Master of Science Thesis ITM completed as part of Degree Project in the Master’s of Aerospace: Space Track 30 Credits
Energy Technology
Report Number:TRITA-ITM-EX 2020:475 Date: September 4, 2020
Supervisor: Jens Fridh Examiner: Bjorn Laumert
KTH ROYAL INSTITUTE OF TECHNOLOGY Host company: Gilmour Space Technologies
Swedish title: Designundersökning av system för flytande syreförångning: Atomisering och värmebelastningar
Abstract
Computational Fluid Dynamics (CFD) simulations are presented within this study for super-cooled liquid oxygen atomisation and gasification in a sub- critical chamber operating at 1 MPa.
Relatively low cost simulation techniques have been used and their accu- racy evaluated. Gasification efficiency expected from theory is compared with simulation results and physical limitation in addition to modelling limitations are discussed. Impinging jets have been used within the simulations with the intent of atomising the incoming liquid oxygen, followed by injection of hot water vapour perpendicularly, to increase turbulent mixing, residence time and in turn expected gasification efficiency.
A computational fluid dynamics heating analysis is also included in order to highlight constraints on the chamber geometry imposed by transient rapid oxidation material limits. 316 stainless steel and 3D printed Inconel 718 were investigated experimentally to identify their transient macroscopic rapid oxi- dation limits. This information supplements existing published literature for operation at high temperatures for a transient period of time in oxygen rich environments.
ANSYS Fluent 2020R1, and its newly included Volume of Fluid to Dis- crete Particle (VOF-DPM) Model, is used for CFD simulation of LOx atomi- sation and vaporisation. The CFD simulation technique is discussed in detail in order to allow the reader to gain knowledge into areas where computational power can be saved while still allowing assessment of trends for conducting relatively quick feasibility reviews e.g. for different chamber configurations.
The CFD simulation results are compared with published experimental data and its accuracy when extended to this application is discussed.
Results indicate that gasification of LOx within a compact chamber may be feasible if sufficient turbulence, resulting in longer residence times is present providing sufficient time for heat and mass transfer from the continuous phase.
Simulations indicate that due to the mixing and gasification process the LOx particles within the chamber that have not entered the gaseous phase are smaller than that from pure atomisation and therefore more susceptible to gasification if injected into the main motor combustion chamber. Results hint at the po- tential benefit of swirl injection of hot gases to increase residence time and in turn the gasification efficiency, therefore, this is recommended for the topic of future research.
Keywords: LOx, gasification, two-phase CFD simulation, rapid oxidation, rocket, cryogenic, hybrid, atomisation
Sammanfattning
Computational Fluid Dynamics (CFD) simuleringar presenteras i denna stu- die för superkyld flytande syreförstoftning och förgasning i en underkritisk kammare som arbetar vid SI 1 MPa.
Relativt billiga simuleringstekniker har använts och deras noggrannhet ut- värderats. Förgasningseffektivitet som förväntas från teorin jämförs med simu- leringsresultat och fysisk begränsning utöver detta diskuteras modelleringsbe- räkningarna. Stötstrålar har använts inom simuleringarna med avsikt att fin- fördela det inkommande flytande syret, följt av injektion av varm vattenånga vinkelrätt, för att öka turbulent blandning, uppehållstid och i sin tur förväntad förgasningseffektivitet.
En beräkningsenhetsanalys för uppvärmningsdynamik ingår också för att belysa begränsningar för kammargeometri som införs genom övergående grän- ser för snabb oxidation. 316 rostfritt stål och 3D-printad Inconel 718 undersök- tes experimentellt för att identifiera deras övergående makroskopiska snabba oxidationsgränser. Denna information kompletterar befintlig publicerad litte- ratur för drift vid höga temperaturer under en kort tid i syrgasrika miljöer.
ANSYS Fluent 2020R1, och dess nyligen inkluderade volym av vätska till diskret partikel (VOF-DPM) -modell, används för CFD-simulering av LOx- atomisering och förångning. CFD-simuleringstekniken diskuteras i detalj för att göra det möjligt för läsaren att få kunskap om områden där beräkningskraft kan sparas medan man fortfarande tillåter bedömning av trender för att göra relativt snabba genomförbarhetsgranskningar, t.ex. för olika kammarkonfigu- rationer. CFD-simuleringsresultaten jämförs med publicerade experimentella data och dess noggrannhet när den utvidgas till denna applikation diskuteras.
Resultaten indikerar att förgasning av LOx i en kompakt kammare kan va- ra möjlig vid tillräcklig turbulens, vilket resulterar i längre uppehållstider är närvarande som ger tillräcklig tid för värme och massöverföring från den kon- tinuerliga fasen. Simuleringar indikerar att på grund av blandnings- och förgas- ningsprocessen är LOx-partiklarna i kammaren som inte har gått in i gasfasen mindre än den från ren förgasning och därför mer mottagliga för förgasning om de injiceras i huvudmotorns förbränningskammare. Resultat antyder den potentiella fördelen med virvelinjektion av heta gaser för att öka uppehållsti- den och i sin tur förgasningseffektivitet, därför rekommenderas detta för ämnet för framtida forskning.
Nyckelord: LOx, förgasning, 2-fas CFD-simulering, snabb oxidation, raket, kryogen, hybrid, atomisering
1 FOREWORD 1
2 Introduction 5
2.1 Background . . . 5
2.2 Purpose . . . 6
2.3 Scope . . . 6
2.4 Method Overview . . . 8
2.4.1 ANSYS Fluent Resources . . . 9
2.4.2 ANSYS Fluent Two-Phase Flow Simulation Overview 10 2.4.3 ANSYS Fluent Thermal Simulation Overview . . . 10
2.4.4 Confidentiality . . . 10
3 Literature Review 11 3.1 Hybrid rockets . . . 11
3.2 Oxidiser Gasification in Hybrid Rockets . . . 13
3.2.1 Geometric Influence . . . 14
3.2.2 LOx Injector Plate Design . . . 15
3.2.3 Fluid Sheet Break-up / Atomisation . . . 16
3.2.4 Droplet Size . . . 18
3.3 Two-phase CFD Simulation . . . 18
3.3.1 VOF-DPM Modelling . . . 20
3.4 Heat Transfer . . . 23
3.4.1 Rapid Oxidation of SS and Inconel . . . 23
3.4.2 Materials Testing with Oxyacetylene Torch . . . 24
4 Method 27 4.1 Two-Phase CFD for Atomisation and Vaporisation of Liquid Oxygen . . . 29
4.1.1 Boundary Conditions / Domain . . . 31
4.1.2 Fluid Properties . . . 34
v
4.1.3 Meshing . . . 38
4.1.4 Numerical Models . . . 39
4.1.5 Chemistry / Thermodynamics . . . 40
4.1.6 Volume of Fluid Model . . . 40
4.1.7 Discrete Particle Model . . . 41
4.1.8 Convergence/ Stability Criteria . . . 42
4.2 Thermal Investigation (numerical) . . . 43
4.3 Thermal Investigation (experimental) . . . 45
5 Atomisation and Gasification Results 47 5.1 Theoretical calculations . . . 47
5.1.1 Enthalpy Calculation . . . 49
5.2 Single Phase Qualitative Simulation Results . . . 51
5.3 Two-Phase Simulation Results . . . 51
5.3.1 Influence of Jet Velocity on Atomisation . . . 52
5.3.2 Vaporisation Impact on Atomisation . . . 56
5.3.3 Influence of High Temperature Gas Injection on Mix- ing and Gasification Characteristics of LOx . . . 58
5.4 Two-phase Simulation Discussion . . . 63
6 Start-up Thermal Considerations 66 6.1 Simulation Results . . . 67
6.2 Heat Flux Results Converted to Transient Temperature Profile 69 6.3 Rapid Oxidation Experimental Test Results . . . 70
6.4 Thermal Discussion . . . 74
7 Discussion 75
8 Conclusions 77
9 Recommendations and Future Work 79
Bibliography 82
A Full Case Summary for Easy Reference 86
B Ansys Fluent Text User Interface (TUI) Script to initialise two- phase flow mixture in VOF and DPM models 89 C Matlab and Python code extracts for pressure drop calculations 92
D LOx Properties 95
E Theoretical calculations 96
E.1 Heat transfer coefficient calculation . . . 96 E.2 Boundary Layer Thickness . . . 97 F Thermocouple and Thermal Camera Vendor Data 98 G LOx fluid sheet break-up parameters estimated from theory for
comparison 99
H Rapid Oxidation Test Detailed Photographic Summary and Ex-
perimental Temperature plots. 101
I Case 1-4 CFD Analysis Results Extended 105
J Confidential material produced during thesis for Gilmour Space
Technologies 113
2.1 Mixing Chamber (modelled in CFD as half chamber with sym- metry plane) . . . 7 2.2 Mixing chamber overview (modified for thermal analysis to
only have two injectors) . . . 8 3.1 Hybrid Rocket Engine Basics . . . 11 3.2 Combustion of a LOx jet at subcritical (a) and supercritical
(b) pressures. Reprinted with permission from Oschwald et al. [10]. . . 14 3.3 Jet break-up Regimes: (a) Rayleigh, (b) 1st Wind-Induced, (c)
2nd Wind-Induced, and (d) Atomisation (used from [18] with permission) . . . 16 3.4 Jet break-up regimes as a function of Reynolds and Weber
Numbers (used from [18] with permission) . . . 17 3.5 Schematic of VOF-DPM modelling transition. . . 21 3.6 Temperature gradient expected in a neutral welding flame (re-
produced from [31] with permission. . . 25 3.7 Heat flux values measured for oxidising, neutral and reducing
flames at a distance of 10-150 mm for various gas flow rates of acetylene:oxygen (figure included from [31] with permission). 26 4.1 Isometric view of Mixing Chamber (a) initial structured mesh,
(b) adapted mesh in VOF regions during Case 4 simulation. . 28 4.2 Mixing Chamber (modelled in CFD as half chamber with sym-
metry plane) . . . 31 4.3 Water sheet structures at different water jet velocities. (A)
Presheet formation regime; (B) smooth sheet regime; (C) ruf- fled sheet regime; (D, E) open-rim sheet regime. (a) 2θ = 60◦ (b) 2θ = 90◦ (figure used with permission [20]). . . 32
viii
4.4 Momentum flux vector calculations to determine the hot gas inlet effect on each impinging LOx stream. . . 32 4.5 Pressure-temperature phase diagram with the the dotted lines
representing the anomalous behaviour of water. . . 35 4.6 Oxyacetylene test bench for materials testing (reproduced with
permission from Gilmour Space Technologies). . . 46 5.1 Jet break-up regimes as function of Reynolds and Weber Num-
bers. Green dots representing cases 1/1b and orange ovals rep- resenting the range due to variation in assumed surface tension (background figure used with permission [18]). . . 49 5.2 Flow of LOx fluid sheet break-up visualised by 10% isosurface
(left) and LOx percentage on the centre line (right) (a,b) Case 1; 7 m s−1 inert (c,d) Case 1b; 11.85 m s−1inert . . . 53 5.3 LOx atomisation with inert particles showing LOx and DPM
mass in the mixing chamber as a function of time during the transient simulation. . . 54 5.4 Development during the transient simulation of the portion of
DPM particles as a percentage of LOx within the chamber. . . 55 5.5 The mean and max particle diameters compared between Cases
1-4, normalised by the number of injectors activated. Note:
the anomalously high outlet max diameter shown for Case 1b is due to one spurious particle without which it would have a similar outlet max diameter as Case 1 and DPM particles were not tracked at the outlet in Case 4. . . 55 5.6 DPM mass present in the mixing chamber for various cases
(normalised by the number of injectors activated). . . 56 5.7 Flow of LOx visualised by a 10% isosurface showing the in-
creased definition of the fluid sheet with increasing refinement levels. (a) Case 3b Level 2, (b) Case 3 Level 3, (c) Case 3c Level 4. . . 57 5.8 Flow of LOx through six sets of impinging injectors with droplet
break-up initiated and hot water vapour injection. Visualised on the left by a 50% and 10% isosurface and on the right by a chamber temperature profile with a boiling point isosurface at 119.6 K (Case 4; Velocity=11.85 m s−1. . . 58
5.9 Gasification Case 4 with LOx and hot water vapour injection showing the interaction of the LOx fluid sheet visualised by the mesh refinement in VOF fluid locations automated by the adaptive mesh refinement feature. . . 59 5.10 Case 4- Species flowrate shown progressing over transient sim-
ulation. Pressure driven inlets result in variable LOx injection depending on local pressure fluctuations in the chamber. . . . 60 5.11 Velocity magnitude and direction shown on half the chamber
(for clarity). . . 60 5.12 LOx volume fraction: composition at various cross sections
along the length of the mixing chamber. . . 61 5.13 Oxygen mass fraction: composition at various cross sections
along the length of the mixing chamber (Note a small por- tion of this is volumetric replacement for dpm particles in the chamber). . . 61 5.14 Case 4- Species mass in chamber shown progressing over tran-
sient simulation. Dotted lines represent predicted/ expected results if simulation were continued. . . 62 5.15 The minimum particle diameters compared between Cases 1-
4 (normalised by the number of injectors activated). Note:
DPM particles were not tracked at the outlet in Case 4. . . 63 5.16 Number of DPM particles present in the mixing chamber for
various cases (normalised by the number of injectors activated). 64 5.17 Combustion of a LOx jet at subcritical (a) pressures showing
similarities to CFD predicted fluid sheet break-up within this study. (Background reprinted with permission from Oschwald et al. [10]). . . 65 6.1 Total surface heat flux in W/m2 shown on the chamber walls
indicating location of maximum flux is perpendicular to the hot gas inlet both horizontally and vertically to the centre of where the LOx would be injected. . . 68 6.2 Maximum total surface heat flux (vertex min) in steady state
simulations compared for different mesh refinements. The progression of the simulations are shows from low relaxation factors to high relaxation factors and then a transient simula- tion to show that the simulation is inherently unsteady. . . 69
6.3 Mixing chamber transient surface temperature profile for Stain- less Steel and Inconel. Reference temperature of 800◦C, 2.8 MW m−2 average and 9 MW m−2 total surface heat flux. . . . 70 6.4 Materials testing in progress of the SS316 plate using an oxy-
acetylene torch tuned to an oxidising flame. . . 71 6.5 Plate transient temperature profile estimates (based on 0.7 MW m−2,
1700◦C flame) compared with experimental data for 316 Stain- less Steel . . . 72 6.6 Plate transient temperature profile estimates (based on 0.6 MW m−2,
1260◦C flame) compared with experimental data for Inconel 718 . . . 72 6.7 Photographs of a range of plate samples where the degree of
macroscopic rapid oxidation can be qualitatively seen (see full set of photographs in Appendix H). Maximum temperatures reached at a depth of 0.5 mm are shown. . . 73 9.1 Possible testing configuration for experimental chamber. . . . 80 D.1 Variation of LOx density and dynamic viscosity with temper-
ature and pressure. . . 95 F.1 TG-297 thermal camera from FLIR used for thermocouple
spot testing/ verification. . . 98 H.1 Photographic summary of all test completed on SS316, In-
conel 625 and Inconel 718. . . 102 H.2 316 stainless steel transient temperature from experimental
readings taken by a thermocouple placed 0.5 mm under the surface. . . 103 H.3 Inconel 718 stainless steel transient temperature from experi-
mental readings taken by a thermocouple placed 0.5 mm under the surface. . . 103 H.4 Inconel 625 stainless steel transient temperature from experi-
mental readings taken by a thermocouple placed 0.5 mm under the surface. . . 104 I.1 Case 1: 7 m s−1inert LOx. LOx flow visualised through 10%
Isosurface (a), centreline LOx percentage (b,e) and DPM par- ticles in domain (c,d). . . 106
I.2 Case 1b: 11.85 m s−1inert LOx. LOx flow visualised through 10% Isosurface (a), centreline LOx percentage (b,e) and DPM particles in domain (c,d). . . 107 I.3 Case 2: 7 m s−1droplet model activated. LOx flow visualised
through 10% Isosurface (a), centreline LOx percentage (b,e) and DPM particles in domain (c,d). . . 108 I.4 Case 3: 11.85 m s−1 droplet model activated. LOx flow visu-
alised through 10% Isosurface (a), centreline LOx percentage (b,e) and DPM particles in domain (c,d). . . 109 I.5 Case 3b: 11.85 m s−1 droplet model activated. Mesh refine-
ment Level 2. LOx flow visualised through 10% Isosurface (a), centreline LOx percentage (b) and DPM particles in do- main (c,d). . . 110 I.6 Case 3c: 11.85 m s−1 droplet model activated. Mesh refine-
ment level 4. LOx flow visualised through 10% Isosurface (a,e), centreline LOx percentage (b) and DPM particles in do- main (c,d). . . 111 I.7 Case 4: All LOx injectors activated with a pressure inlet achiev-
ing approximately 11.85 m s−1in addition to hot water vapour injection. LOx flow visualised through 10% Isosurface (a,e), centreline LOx percentage (b) and DPM particles in domain (c,d). . . 112
4.1 Two-phase model flow parameters (for half the chamber) for simulation of atomisation and gasification (extended table can be found in Appendix A). . . 28 4.2 Summary of Thermal Model Parameters (extended table can
be found in Appendix A). . . 29 4.3 Scaling parameters calculated and one suggested full scale
chamber presented. . . 30 4.4 Fluid critical temperatures and pressures. . . 35 4.5 Meshing for thermal cases. . . 44 4.6 Relaxation factors used through thermal simulation to account
for sudden temperature gradients during hot gas injection. . . . 45 5.1 Estimated fluid sheet break-up length and mean particle di-
ameter based on theory of one impinging LOx pair injected into a chamber filled with air at 1 MPa (see Appendix G for expanded table including comparison to water jet). . . 48 5.2 Maximum vaporisation effect on LOx at 1 MPa of hot gas at
1 MPa allowed to cool to 454 K assuming perfect mixing and heat transfer. Calculations are presented for one impinging jet and its hot gas inlet pair. . . 50 5.3 Maximum possible vaporisation due to initialised air in mix-
ing chamber if 100% mixing and heat transfer efficiency (re- verse flow in simulations may provide additional enthalpy from incoming air). . . 50 5.4 Summary of two-phase flow model parameters. . . 52 6.1 Hot gas inlet parameters described for the full chamber in or-
der to investigate flow rate, prevent choked flow and assess velocity. . . 67 6.2 Maximum total surface heat flux and mass balance results. . . 68
xiii
A.1 Two-phase model parameters for modelling of Atomisation and Gasification. . . 87 A.2 Model parameters for heating of mixing chamber walls. . . . 88 G.1 Liquid oxygen injection into an air chamber at 1 MPa (unless
otherwise specified). Note; fluid sheet break-up length theory provides an overestimation. . . 100
FOREWORD
This research was conducted as part of a Masters Degree in Aerospace Engi- neering at KTH Royal Institute of Technology. The work was completed at Gilmour Space Technologies in Queensland, Australia, under the direction of Mathew Bricalli (Head of Propulsion).
I would like to thank Mathew Bricalli for his patience and willingness to mentor and guide me in the development of this body of work and for Jan-Erik Ronningen for bringing me on board and giving me this opportunity. I would also like to thank Joshua Keep for the in-depth discussion on CFD simulation techniques and his academic guidance as well as the ANSYS LEAP personnel for their invaluable feedback and suggestions.
Thank you to Gilmour Space Technologies for this opportunity and to ev- eryone at the company for their support. It was a privilege to work with a group with such a breath of talent and passion.
Finally I would like to thank my KTH supervisor Jens Fridh for supporting me and guiding me to completion and of course my family for their constant love and support.
Borika (Borbala) Bernus Australia; September 2020
1
Abbreviations
CFD Computational Fluid Dynamics CSF Continuum Surface Force DES Diffusion Energy Source Droplet Particle which can vaporise DRW Discrete Random Walk EOS Equation of State
FLOx Mixture of liquid fluorine and liquid oxygen Gilmour Space Gilmour Space Technologies GOx Gaseous Oxygen
In Inconel
LES Large-Eddy Simulation LOx Liquid Oxygen
SBES Stress Blending-Shielded
SC Stage Combustor/ Mixing Chamber SS Stainless Steel
VOF-DPM Volume of Fluid-Discrete Particle Method List of Variables (SI units)
αv Vapor volume fraction
2
¯¯
τ stress tensor
D¯θ Droplet size produced by impinging injectors at θ◦
˙
m Mass flowrate µ Dynamic viscosity ρ~g Gravitational body force
ρ Density
σ Surface tension θ Impingement angle εp Particle emissivity F~ External body forces
~
v Velocity vector
A Area
Cp Specific heat capacity
D Diameter
d Inlet/orifice diameter fv,o Volatile fraction H Enthalpy
h Convective heat transfer coefficient hf g Latent heat
k∞ Thermal conductivity W/m-K L Fluid break-up length
P Pressure
p Momentum
P r Prandtl number
r Radius
Sm Mass added to the continuous phase from the dispersed second phase
t Time
Tp Particle temperature T∞ Bulk temperature
Tbp Boiling point temperature Tvap Vaporisation temperature V Velocity
Re Reynolds number We Weber number
Introduction
This chapter describes the background, purpose, scope and overall methodol- ogy used to produce this body of work.
2.1 Background
This thesis was conducted at Gilmour Space Technologies. Gilmour Space is a “venture-backed rocket company in Queensland, Australia that is developing new launch vehicles powered by lower-cost hybrid propulsion technologies”
[1]. This work aims to improve the body of knowledge in regards to liquid oxygen (LOx) atomisation and gasification with possible application in staged combustor design: partial or full gasification prior to combustion within a hy- brid motor or for increasing upper stage liquid combustion efficiencies. Simu- lation techniques that can be used to compare design configurations in indus- try applications are of importance to assist early and iterative design decisions when experimental data cannot be obtained. Start-up heating considerations and material limitations are discussed to ensure practicality of reviewed con- figurations.
Previous work on hybrid combustion has noted that the oxidiser must be in- jected into the combustion chamber in a gaseous state for stable combustion to occur. When a liquid oxidiser, such as LOx is used, a suitable method must be employed to gasify the fluid before primary combustion occurs within the mo- tor. If the oxidiser is injected into the combustion chamber whilst still in liquid form, or even a gas/liquid mixture, significant low pressure oscillations within the combustion chamber can occur [2]. As the primary means of fuel vapori- sation is conductive heat transfer to the fuel surface from a combustion zone residing in the boundary layer, a reduction in the heat transfer or temperature
5
of the zone will result in a reduction in the amount of gaseous fuel available for burning or even its elimination (quenching). Due to various processes, this can result in low frequency pressure oscillations that will reduce the perfor- mance and efficiency of the hybrid motor [3]. An example system has been previously used on the Hybrid Propulsion Development Program (HPDP) [2]
and demonstrated stable combustion over a series of ground tests. Although tested before in a limited capacity, minimal knowledge and data on the physical mixing and gasification processes of cryogenic liquid oxygen is known. Fur- ther development is essential to ensure successful and efficient rocket motor ignition.
2.2 Purpose
The aim of this study is to increase the understanding of super-cooled liquid oxygen atomisation and gasification and in order to allow rapid design devel- opments in initial prototyping and proof of concept applications. The scaled design has been chosen in order to allow analysis to be conducted with limited computational resources while allowing for scaled comparisons (see Section 4.1). The main areas of focus include:
• The influence of jet velocity on atomisation.
• The vaporisation impact on atomisation.
• The influence of high temperature gas injection on mixing and gasifica- tion characteristics of LOx.
A fundamental part of this analysis is to provide insight into the strengths and weaknesses of the developed two-phase flow model to predict atomisation, mixing and gasification and the parametric effect of hot gas injection. In ad- dition, the aim of this study is to highlight critical heat load considerations on the chamber walls during start-up, and supplement available material data for 316 stainless steel, Inconel 625 and 3D printed Inconel 718 currently available for these applications.
2.3 Scope
A 6.28 cm3 mixing chamber, shown in Figure 2.1, is the focus of this scaled analysis. Super-cooled liquid oxygen at 77 K enters at the top of the chamber
and mixes with hot water vapour at 2800 K injected perpendicular to the flow with a nominal operating chamber pressure of 1 MPa.
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In order to first validate the two-phase model and investigate the LOx atom- isation characteristics at varying injector velocities only one of the 6 pairs of injectors is activated to inject LOx into an air filled chamber. All LOx and hot gas injectors are later activated to investigate mixing and gasification at an oxidiser to hot gas ratio of approximately 26:1.
A modified chamber geometry, as shown in Figure 2.2, is used to inves- tigate the heat loads that could be seen on the chamber walls during start-up conditions when hot carbon dioxide is injected at 2800 K and 1.3 MPa into a chamber containing air at one atmosphere. The full hot gas flowrate is directed through two larger diameter injector holes. The use of 316 stainless steel and Inconel 625 and 718 are experimentally investigated for transient macroscopic rapid oxidation events which would limit the temperatures to which they are suitable.
The reasoning behind the fluid selections is further detailed in Section 2.4.
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Figure 2.2: Mixing chamber overview (modified for thermal analysis to only have two injectors)
2.4 Method Overview
The high level method used to produce this body of work is outlined below. A detailed methodology is provided in Section 5.
1. Literature review and theoretical calculations to predict atomisation and vaporisation of LOx using water vapour and define boundary conditions.
2. Conduct single phase CFD simulation of the mixing and gasification of LOx with hot gas, with LOx modelled as high density gas to qualitatively answer the following questions:
• Excluding two-phase effects is mixing efficiency greatly affected by hot gas inlet configurations?
• Based on initial mixing analysis qualitatively assess impact on cham- ber wall heating during start-up.
3. Conduct two-phase CFD simulations of the atomisation, mixing and gasification of LOx.
• Case 1/1b: Comparison of the results from the CFD atomisation portion of the model (excluding vaporisation) with experimental data at varying inlet velocities with one impinging jet pair acti- vated.
• Case 2/3: Review results of the CFD simulation with atomisation and vaporisation activated. Model is still reserved to analysis of only one impinging LOx jet pair injected into a mixing chamber
initialised with air. These simulations allow increased understand- ing in regards to the modelling of super-cooled liquid oxygen un- dergoing small amounts of vaporisation at different jet velocities.
• Case 4: Review results of the CFD simulation with all six LOx impinging jet pairs and hot gas inlets activated. This model aims to assess affect on both overall mixing and gasification efficiency.
• Conduct thorough comparison of CFD outputs with literature to assess the strengths and weakness of the low computational cost ANSYS Fluent simulations in determining LOx atomisation, mix- ing and gasification.
4. Conduct CFD simulation (Case T) of start-up process, injecting carbon dioxide into the mixing chamber in order to indicate the maximum total surface heat flux, and therefore temperature profile, that could be seen on the chamber walls in these types of mixing chambers. An experiment to determine the transient macroscopic rapid oxidation point of SS316 and Inconel is conducted as part of this study in order to recommend maximum start-up timeframes.
Carbon dioxide, water and oxygen are standard reinjection combustion products in rocket engines. These have been selectively chosen according to simulation requirements. Water vapour has been selected for atomisation and gasification models as its properties are well documented over a range of pres- sures and temperatures and is found to be stable in Fluent. Carbon dioxide is used for thermal simulation to provide a more general analysis of heat loads expected on the chamber walls.
2.4.1 ANSYS Fluent Resources
ANSYS Fluent was used for Computational Fluid Dynamics simulations (Ver- sion 2020R1).
Due to the lack of availability of HPC (High Performance Computing) resources the CFD calculations were performed on:
• Intel CoreR TM i7-9750H CPU @ 2.6GHz using 4 Cores.
• Intel CoreR TMi7-87550 CPU @ 1.8GHz using 6 Cores limited to 500k Cells on academic licence.
This was taken as an opportunity to showcase the areas in which limited computing power can still provide valuable insights during proof of concept design assessments.
2.4.2 ANSYS Fluent Two-Phase Flow Simulation Overview
The CFD analysis of LOx atomisation and gasification uses a transient analysis with incompressible liquid oxygen injected into a chamber of air using the k- omega SST model with the VOF-DPM coupled model activated for droplet formation and vaporisation. Gasification occurs due to heat transfer from air initialised in the chamber and injected hot water vapour.
2.4.3 ANSYS Fluent Thermal Simulation Overview
The CFD analysis of thermal heating of the chamber walls uses a steady state analysis of compressible hot gas injection, modelled as ideal gas, using the k-omega SST model. The heat transfer to the wall is investigated to determine the transient temperature of the wall during start-up. The simulation is based on the injection of carbon dioxide.
2.4.4 Confidentiality
Due to the sensitive nature of this research with Gilmour Space Technologies specific commentary on a scaled chamber is not discussed within this thesis.
Other analysis and commentary on preferred mixture and source of hot gases, exact supply pressures and engineering design including start-up timeframe requirements for solid fuel grain ignition remains confidential.
Literature Review
This chapter provides a literature review into hybrid rocket design in brief and delves more deeply into atomisation and gasification simulation techniques and available experimental data that can also be applied to upper stage com- bustion chambers to improve gasification efficiencies. Current knowledge on rapid oxidation limits of SS and Inconel are included, as are the fundamental theoretical equations governing the work within this study.
3.1 Hybrid rockets
Hybrid rockets combine the use of solid fuel with either gas or liquid. The preference is for any liquid to be gasified prior to entering the solid fuel grain which ignites once a sufficient temperature is reached (see Figure 3.1).
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Figure 3.1: Hybrid Rocket Engine Basics
11
Hybrid rocket thrusters provide inherent safety features and simplicity tra- ditionally found in cold gas thrusters but can also provide specific impulse values which are comparable with hydrazine thrusters [4]. With the impend- ing ban of hydrazine, hybrid thrusters offer a green alternative to monopro- pellant hydrazine. In addition, they have the capability to throttle, shut-down, restart while benefiting from cost and operational benefits of a solid propul- sion system with minimal maintenance requirements [5]. Hybrid Rockets have been used in only one flight production application (Teledyne Ryan AQM-81A
‘Firebolt Supersonic Aerial Target) [5] and are not yet commercialised. The ability to throttle the fuel regression rates directly by the oxidizer flux is one of the allures of this technology, as well as the ability to restart.
The main hurdle for hybrid rockets to successfully enter the aerospace mar- ket is achieving regression rates within the motors which remove the require- ment for excessively long and slender fuel ports. Traditionally cylindrical fuel ports have had very long length to diameter ratios to increase the combus- tion area. Therefore, the efficiency of combustion within the motor has been of interest for many years. Liquid oxygen is one of several oxidisers used in hybrid rockets. AMROC’s LOx hybrid motor test programs [6] suggest that
“the degree of liquid oxygen atomisation and vaporisation prior to entering the fuel ports has a strong influence on hybrid rocket combustion stability”.
Low combustion completeness has been the main defect of hybrid rockets [7].
Lung Lin [7] have completed testing using a pre-combustion chamber with liquid oxidizer sent through a chamber lined with fuel to ensure liquid oxi- dizer vaporises before entering the combustion chamber. Lung Lin [7] has noted that liquid oxidizer entering the fuel can prevent the endothermic effect of the liquid oxidizer which can block the chemical reaction as well as the fuel regression.
Mechentel, Coates, and Cantwell [8] and Boardman, Carpenter, and Claflin [9] present work completed on small-scale gaseous oxygen hybrid rocket test- ing and the effect of liquid versus gaseous injection on combustion stability respectively. Mechentel, Coates, and Cantwell [8] iterate that oxygen and FLOx are the most energetic oxidizers of the oxidiser commonly used in rocket propulsion. As FLOx comes with concerns related to toxicity and material compatibility oxygen is a favourable choice. As gaseous oxygen has such a low density the ability to package the oxygen in a smaller volume at higher pressures as LOx is desired. The challenges however come from the cryogenic service which is now imposed on the vehicle. Successful regression rates and combustion efficiencies seen are believed to be applicable to systems using liquid oxygen storage if complete vaporisation was present [8].
3.2 Oxidiser Gasification in Hybrid Rockets
A large amount of literature is available investigating ways in which to improve combustion efficiency. The upstream separation bubble which is unobvious for the case with no prevaporised zone can increase the mixing of reactants, and thus increase the combustion completeness [7]. Story et al. [5] states that “ox- idizer dump plenum configurations that produced flow recirculation of com- bustion gas at the leading edge of the diffusion flame sheet resulted in stable operation.” This indicates that recirculation and extended residence time can enhance the combustion completeness and in non-combusting products simply improve the gasification completeness.
No open literature study has has been found investigating gasification of LOx using a hot non-combustible gas as provided in this body of work. There is a particular lack of literature published for subcritical pressure applications of LOx gasification. Various studies can, however, provide some point of ref- erence. These include Oschwald et al. [10] who present liquid nitrogen in- jected into gaseous nitrogen at ambient temperature with results showing that at lower fluid inlet velocities the liquid oxygen to continuous phase boundary is more blurry. These results are applicable to similar Reynolds numbers of approximately 40,000 to 60,000, which are applicable in this study (see Figure 5.1).
Yang, N., and Shuen [11] presents work that shows a strong pressure de- pendence of the vaporisation of liquid oxygen droplets in supercritical hydro- gen environments (specifically the square of the final to initial diameter ratio).
These results are relevant to an ambient temperature of 1000 K with 100 µm as the initial injected diameter of LOx at 90K. The results indicate that the droplet surface is heated and vaporisation occurs with minimal energy trans- ferred into the droplet interior. In addition only approximately 6 ms is required for the droplet diameter to reduce to 10 µm at 1 MPa.
Hydrogen and water environments have also been modelled under sub- critical and super-critical conditions by Lafon et al. [12]. This work can pro- vide more indication of droplet lifetimes that can be expected in application of LOx vaporisation. At approximately 1 MPa and 2000 K, liquid oxygen injected at 90 K (100 µm) with a droplet lifetime of approximately 4 ms. Con- sideration of water vapour condensing at the droplet surface is also discussed and is shown to have a limited effect during the entire lifetime of droplets at 10 MPa and 50% water vapour composition.
Several pieces of literature provide details of combustion applications such as supercritical injection and mixing characteristics of liquid oxygen and kerosene
bi-swirl injectors [13] or combustion of LOx with gases such as methane [14].
These types of work often focus on the combustion effects and the injection of fuel and oxidiser are often in a swirl or coaxial configurations, therefore they do not provide an appropriate comparison for the work completed in this the- sis. Kim, Son, and Koo [15] provides details of the ignition transition of coax- ial kerosene/ gaseous oxygen jet and shows that the atomisation and oxidiser injection flow field is fairly non-uniform until ignition occurs. The ignition occurring during combustion also results in rapid vaporisation in the order of 0.4 ms which again is not applicable to this study.
Some information can however be used to inform an expected flow pat- tern. Figure 3.2 shows the development of LOx injected and vaporising during combustion. This figure can be used to qualitatively show that at subcritical pressures a more defined boundary between the continuous phase and the liq- uid oxygen is present and the figures show the fluid ligaments detaching from the main fluid jet, forming droplets which undergo vaporisation. The work completed by Oschwald et al. [10] states that the droplet number density in this work was found to be much smaller than cold flow conditions due to the rapid vaporisation of small droplets in a burning spray. They also state that subcritical flows, as present within this study, are driven by surface tension effects.
Figure 3.2: Combustion of a LOx jet at subcritical (a) and supercritical (b) pressures. Reprinted with permission from Oschwald et al. [10].
Specific literature which will be used for LOx break-up and mean droplet diameter comparisons are described later in this chapter.
3.2.1 Geometric Influence
The mixing chamber is the focus of this study in regards to its use as a gasifica- tion chamber prior to combustion in either hybrid or upper stage liquid engines.
Boardman, Carpenter, and Claflin [9] states that hot-gas recirculation zones adjacent to the combustion port entrance tended to stabilize combustion and that high-gas temperatures in this zone enhanced combustion stability. The passage of gasified LOx into the combustion chambers should be through an injector which promotes recirculation both before and after the injector. Gas expansion during the phase change process diffuses the core flow and are indi- cated to make establishment of strong recirculation zones in the vaporisation chamber more difficult than with gaseous injection [9]. Boardman, Carpen- ter, and Claflin [9] notes the presence of acoustic oscillations, harmonics etc.
that have been seen at low pressures around 3 MPa in the chamber. They stated that “spontaneous increases in mean chamber pressure due to the onset of high-amplitude acoustic oscillations were also observed in both test series”
[9].
3.2.2 LOx Injector Plate Design
The injector design is known to have an impact on the atomisation of the in- jected fluid and its spatial location impacts the chamber coverage. Papers re- port that as the pressure drop across the face of the injector is increased, and as a result the jet velocity, a finer LOx droplet size will be obtained, how- ever, the residence time will be reduced [6]. AMROC [6] used a centralised showerhead injector design for their successful hybrid motor tests however it is mentioned that each injector type is likely to have difference preferred op- erating parameters. Triethylaluminum (TEAl) was injected with the LOx to initiate combustion. As their test set-up relied on pre-combustion of the LOx and operation was above critical pressure > 5 MPa, variation of results will be seen at sub-critical pressures.
Impinging injectors are often used when atomisation of fluids is required.
Rocketdyne published a large amount of data on the atomisation and mix- ing characteristics of impinging jets and characterised droplet sizes via ex- periments completed by injecting molten wax and determining final droplet size based on the velocity of jet injection [16][17]. Boardman, Carpenter, and Claflin [9] also indicates that when simulating two-phase flow with liq- uid oxygen injection “The differences resulting from volumetric displacement of evaporating droplets made overall motor stability characteristics somewhat less sensitive to the initial liquid oxygen injection pattern than to the gaseous- oxygen injection pattern.” A simplified jet impingement pattern has therefore been chosen to allow for experimental comparison. The downstream injection device used to feed gaseous oxygen into the hybrid motor or main combustion
chamber will assist in final mixing and gasification however will be enhanced by increased mixing and gasification upstream.
3.2.3 Fluid Sheet Break-up / Atomisation
Sweeney [18] presents a method of predicting the jet-break-up regime based on Reynolds number (Re) and Weber number (We). The work was not specifically based on liquid oxygen however the break-up length formulation developed for water is assumed to be a reasonable approximation for comparison to liquid oxygen fluid break-up particularly if the liquid oxygen is modelled as an inert fluid.
The Reynolds number and Weber number equations are shown below.
Re = ρLV D
µ (3.1)
W e = ρLV2D
σL (3.2)
where σ is the surface tension between the fluid injected and the chamber fluid, ρL is the density of the fluid, µ is the viscosity and V and D are the velocity and diameter.
Figure 3.3 shows the jet break-up regimes with Figure 3.4 showing their dependence on the Reynolds number and Weber number.
Figure 3.3: Jet break-up Regimes: (a) Rayleigh, (b) 1st Wind-Induced, (c) 2nd Wind-Induced, and (d) Atomisation (used from [18] with permission)
It is important to consider which jet-break-up regime is activated during injection and Cordesse, Massot, and Murrone [19] reiterates that “In partic- ular, the stability and the efficiency of the engine are extremely correlated to the way the liquid oxygen is injected and its primary atomisation”.
Figure 3.4: Jet break-up regimes as a function of Reynolds and Weber Num- bers (used from [18] with permission)
An estimate of the fluid break-up length is provided by Yakang et al. [20]
for two liquid impinging jets when the Weber number is larger than 200. The formulation is described in Equation 3.3, however it provides only a relative approximation of the break-up length which can be used for comparative pur- poses. The absolute values calculated are shown to overestimate the break-up length compared to experimental data.
L
D = 5.451 ρa ρL
−23
(W e ∗ f (θ/2))−13 (3.3) where,
f (θ/2) = (1 − cos (θ/2))2
sin3(θ/2) (3.4)
and ρais the density of the chamber fluid, ρLis the density of incoming fluid, θ is the impingement angle and L/D is the fluid break-up length to inlet diameter.
Many researchers have worked on the atomisation of fluids in order to achieve efficient combustion. In 1996 a 10,000 lb(f) thrust was generated on a hybrid motor testbed at Stennis Space Center [6]. Results indicated that as the pressure drop across the face of the injector is increased, a finer LOx droplet size is obtained. An increase in pressure drop however also results in an in- crease in jet velocity. Especially for small chamber lengths the resulting in- crease in velocity can have a noticeable impact on reducing the residence time and resulting timeframe for heat transfer and vaporisation. For the work com- pleted in this paper a balance is sought to achieve sufficiently small droplets with a residence time sufficient for droplet heating and gasification without
the requirement for high inlet velocities. Small droplets, resulting from atom- isation, is also desirable in order to reduce the requirements for convection of heat across the liquid oxygen surface in order to allow the hot gases to more effectively gasify the same quantity of LOx. Previous papers have indicated that longer residence assist for example in the case of oxygen heated by a fuel lining in a pre-combustion chamber [6]. Longer residence times are therefore believed to assist in mixing and gasification using hot gas injection into the chamber.
3.2.4 Droplet Size
Droplet sizes resulting from impinging jets are presented by Zajac [17, 21]
and Burick [22]. The calculations are based on experimental data that was conducted by injecting molten wax into the air and measuring the particle sizes once they cooled and hardened. They discuss how the droplet mean diameter should be corrected for the difference between physical properties of molten wax and the oxidiser of interest, in this case LOx. It is however noted that except for absolute viscosity and density, molten wax simulates LOx and other oxidisers fairly well [22] and is therefore used for CFD comparisons.
Equations 3.5 and 3.6 are used to provide an estimate of the mean droplet diameter that can be expected based on impingement angle, inlet diameter and velocity.
D¯60 = 15.9e4d0.58/VL (3.5) where d is the orifice diameter (in inches) and VL the injection velocity (in ft/sec)
D¯60provides the droplet size produced by an impinging injector at a given liquid velocity into a static environment i.e. no gas flow at an impingement angle of 60 degrees. The below conversion is then provided to account for varying impingement angles.
D¯θ = (1.42 − 0.0073θ) ¯D60 (3.6) whereD¯θ is the dropsize (in microns) obtained at an impingement angle of θ degrees.
3.3 Two-phase CFD Simulation
Simulating two-phase flow characteristics is understood to be a computation- ally expensive exercise as well as comprising a high number of degrees of
freedom with respect to assumed properties all of which can play an impor- tant role in producing realistic simulations. There are several commercially available Computational Fluid Dynamics (CFD) softwares and open source softwares such as OpenFoam.
ANSYS Fluent was chosen for simulation purposes. It allows for complex fluid dynamics simulation and provides support for its users. Its main interface runs through a Graphical User Interface (GUI) interface and detailed docu- mentation is available explaining the theoretical basis of the available models.
It can also be run via Text User Interface (TUI) commands, an extract of which is provided in Appendix B as was used in this study.
In ANSYS Fluent simulations, Faber Navier-Stokes equations are solved using the general conservation of mass, momentum and energy equations while turbulence can be handled through the SST k-omega model.
The general form of the continuity equation (conservation of mass) is:
δρ
δt + ∇ · (ρ~v) = Sm (3.7)
where Sm is the mass added to the continuous phase from the dispersed second phase, ~v is the velocity vector and δt is the time.
The conservation of momentum in an inertial (non-accelerating) reference frame is represented as:
δ
δt(ρ~v + ∇ · (ρ~v~v) = −∇P + ∇ · (¯τ ) + ρ~¯ g + ~F (3.8) where P is the static pressure, ρ~g and ~F are the gravitational body force and external body forces and ¯τ is the stress tensor described further in Fluent doc-¯ umentation.
In ANSYS Fluent, thermodynamic properties, including density, enthalpy, and specific heat at constant pressure, etc., are evaluated according to the mod- ified Soave-Redlich-Kwong equation of state and the fundamental thermody- namic theory. Transport properties can be (thermal conductivity and dynamic viscosity) estimated by an extended corresponding-state principle along with the 32-term Benedict-Webb-Rubin equation of state.
Historically speaking, the pressure-based approach was developed for low- speed incompressible flows, while the density-based approach was mainly used for high-speed compressible flows.
Banuti et al. [23] describes an efficient multi-fluid-mixing model for real gas reacting flows in liquid propellant rocket engines when “real fluid be- haviour only occurs in the cryogenic oxygen stream, this is the only place where a real gas equation of state (EOS) is required”. It describes the use
of the Euler-Euler approach with VOF modelling. The VOF model can be used for two or more immiscible fluids where the interface between the fluids is of interest. The default VOF method cannot simulate heat and mass transfer through the phase interface.
Turbulent closure via large-eddy simulation (LES) technique was used by Wang and Yang [13] to model LOx and kerosene via swirl injection: Favre- filtered transportation equations of mass, momentum, energy, and mixture fraction in a conservative form where non-linearity of viscous terms and heat flux terms are neglected, Prandtl number and Schmidt number were taken as 0.7 and 0.4 respectively. The A60 is also a popular reference case for real fluid CFD validation [23].
3.3.1 VOF-DPM Modelling
Existing literature currently focuses on simulation of two phase flow develop- ment in two parts:
• Main fluid development and evaporation
• Droplet development, evaporation etc.
Simulations often either ignore the droplet development process and model fluid flow via Volume-of-Fluid methods however this requires high levels of computational power due to the high mesh fidelity required for accuracy of results operating in the Eulerian frame. Others use theoretical calculations or experimental data to estimate the atomisation process and droplet size and utilise Discrete Particle Modelling (DPM) to inject these particles and follow their development. DPM operates in the Lagrangian frame. It is weakly mesh dependent due to coupling and can therefore be run on a coarser mesh with cor- respondingly reduced computational time. The use of the DPM model results in an assumed interface where droplets are formed and provides difficulties in allowing the droplet formation and turbulence within a small domain to be evaluated.
A recent addition to the Fluent suite of options now includes the VOF-DPM model which allow both of these functions to be simultaneously modelled.
The Eulerian-Lagrangian VOF-DPM model has the potential to provide more realistic particle distributions and resolution of the VOF to DPM interfaces.
This process is shown in the schematic in Figure 3.5. Liquid lumps which are separated from the main liquid body are converted into Discrete Particle Model particles (point masses) for further tracking. These point masses carry
information with them in regards to momentum and mass but avoid the need to track interfaces of small liquid drops. The volumetric impact is accounted for by the replacement of the liquid drops with an equivalent volume of gas to maintain pressure balance. The VOF-DPM model also allows the VOF phase to be used when the volume fraction of dispersed phase is higher than approx- imately 10%.
Figure 3.5: Schematic of VOF-DPM modelling transition.
A reduction in computational power is seen when the fluid is converted to DPM particles as the mesh can be coarsened when moving into the Lagrangian frame.
Volume of Fluid Modelling
Interaction of immiscible gas and liquid phases in Fluent is modelled using the VOF method.
• A single set of conservation equations is shared by the phases.
• The volume fraction of each phase is calculated in each cell in the do- main.
• VOF method can locate the surface of one of the fluids and its concen- tration (uses regions not surfaces).
• Continuum surface force (CSF) model proposed by Brackbill et al. can be used to compute the surface tension force for cells containing the gas-liquid interface.
ANSYS Fluent uses one of two models to represent evaporation and con- densation; Lee’s model or the Thermal Phase Change Model. For the mix- ture multiphase model required for this analysis Fluent recommends the use of Lee’s model for the liquid-mass transfer. It is governed by the vapor trans- port Equation 3.9 reproduced from the Fluent manual.
δ
δt(αvρv) + ∆ · (αvρvV~v) = ˙mlv− ˙mvl (3.9) where αv is the vapor volume fraction, ρv is the vapor density,V~v is the vapor phase velocity and ˙mlv and ˙mvl are the mass transfer due to evaporation and condensation respectively.
DPM Modelling
The Discrete Particle Model in Fluent allows for both particles which are inert to be modelled as well as particles which allow both heat and mass transfer with the surrounding environment (also referred to as droplets throughout this study). Standard models for interfacial exchange terms [24] are detailed in the Fluent manual. The formulas covering the property inputs for particles are also detailed in the Fluent manual and where necessary discussed in further detail in Section 4. These include density, specific heat, thermal conductivity, viscosity, latent heat, vaporisation temperature, boiling point, saturation vapor pressure and particle surface tension.
The mass transfer from DPM to continuous phase is termed the evaporated mass in ANSYS Fluent and is driven by heat and mass exchange to and from the DPM particles. This is controlled by several heat and mass transfer rela- tionships. A droplet is a liquid particle in a continuous-phase gas flow that obeys the force balance, experiences heating and cooling via Law 1 and 6 (as does an inert particle) but in addition experiences vaporisation and boiling ac- cording to Laws 2 and 3. A selection of these is reproduced from the Fluent Manual (Section 16.4). Law 1 and 6 for heating and cooling are defined as:
Tp < Tvap (3.10a)
mp ≤ (1 − fv,o)mp,0 (3.10b)
where Tp is the particle temperature,Tvapis the vaporisation temperature, mp is its current mass of the particle, mp,0 is the initial mass of the particle and fv,0 is the volatile fraction.
ANSYS Fluent uses a heat balance to relate the particle temperature to the convective heat transfer and radiation at the particle surface.
Law 2 is partial pressure driven and is activated when the temperature of the droplet reaches the vaporisation temperature Tvap and continues until the droplet reaches its boiling point Tbpor the volatile fraction is consumed.
During slow vaporisation rate a diffusion controlled model is implemented while a convective/diffusion controlled model is used for high vaporisation rates. Once the boiling temperature is reached the boiling rate (excluding heat transfer) is described by Law 3 which is believed to dominate in this study:
d(dp)
dt = 2k∞
ρpcp∞dp(2 + 0.6Re12P r13)In(1 + cp∞(T∞− Tp)
hf g ) (3.11) where dp is the particle diameter, cp,∞ is the heat capacity of the gas in J/kg-K, ρpis the particle density, Re is the Reynolds number, Pr is the Prandtl number of the continuous phase, k∞is the thermal conductivity of the gas in W/m-K, hf g is the latent heat in Joules, T∞is the bulk temperature and Tp is the particle temperature.
3.4 Heat Transfer
Hot gases impinging on the mixing chamber walls should be considered in the construction and geometry of the chamber. Degenève et al. [25] notes that high concentrations of carbon dioxide are known to significantly enhance radiative heat transfer, similar impact would be seen with water vapour which has an even higher specific enthalpy.
3.4.1 Rapid Oxidation of SS and Inconel
The choice of material is of particular importance when exposed to high levels of oxygen content during its heated state in order to avoid failure due to rapid oxidation degradation of the material. Rapid oxidation is the process by which a metal combusts or burns. It happens rapidly and produces light, noticeable heat and mass loss. It occurs more readily in an oxygen rich atmosphere at high temperatures which is why care must be taken when hot gases and oxygen are present in the mixing chamber particularly during start-up when pressure are
close to atmospheric. Shao et al. [26] investigated the combustion of metals in oxygen enriched atmosphere in 2020. They note that 316 stainless steel is regularly used in pressure vessels and piping up to 816◦C. Points of reference are provided by Shao et al. [26] showing the relationship of temperature to burning pressure under 100% oxygen environments.
• At ambient temperature, combustion of SS316 at 3.45 MPa
• At 875◦C, combustion of SS316 at 0.2 MPa
No specific data is readily accessible in regards to the transient macro- scopic oxidation for SS316 or Inconel at 1 atm (approximate mixing chamber start-up pressure) or 1 MPa (nominal mixing chamber operating pressure) or a numerical relationship relating combustion temperature and pressure there- fore experimentation to provide comparative rapid oxidation results would be useful at atmospheric pressure.
Greene [27] conducted a series of experiments which show that a parabolic, diffusion controlled oxidation rate dependence in air is present from 1223 K.
Below 1173 K only minimal oxidation is indicated for a period of 24 hrs. They also state that for superalloys such as Inconel the rate of oxidation is not sen- sitive to the oxygen partial pressure.
Brady et al. [28] provides 310SS as another option for replacement of SS316 highlighting its better resistance to oxidation. Comparisons between 310SS and SS316 are provided by Graham et al. [29] with samples exposed to 1250◦C at atmospheric pressure with experimental results showing that the alloy composition was affected to a depth of 5 µm and 26 µm respectively dur- ing heat testing. In addition, no spallation was observed upon cooling 310SS as compared to a large amount due to the thick outer layer of Fe based on the oxide grown on the SS316 sample. Inconel is also known to have increased oxidation resistance.
3.4.2 Materials Testing with Oxyacetylene Torch
Oxyacetylene torches are normally operated in three regimes and are able to produce flame temperatures of approximately 3000◦C [30]:
• A neutral flame; named as such as it will have no chemical effect on the metal being welded
• A carburising flame (rich flame); where an excess of acetylene to oxygen is fed to the torch
• An oxidising flame (lean flame); where an excess of oxygen is fed to the torch and produces a hotter flame.
Flame temperatures can vary based on the type of flame and location within the flame. Flame temperature can vary between about 3300◦C and 1260◦C as shown in Figure 3.6.
!""#$%&'"#
()*)+(())%!,%
-./)%!,%
.-))%!,%
012#$%#"3#4'5#
Figure 3.6: Temperature gradient expected in a neutral welding flame (repro- duced from [31] with permission.
Paul et al. [31] has published data correlating the heat flux of various flames to the distance from the torch that is show in Figure 3.7. At distances
≤20 mm from the nozzle and more than ≈100 mm from the nozzle the varia- tion due to exact composition of flame varies minimally. During experimenta- tion, this fact can be used to estimate heat flux when instrumentation to mea- sure the exact heat flux or composition is not available.
Figure 3.7: Heat flux values measured for oxidising, neutral and reduc- ing flames at a distance of 10-150 mm for various gas flow rates of acety- lene:oxygen (figure included from [31] with permission).
Method
CFD simulations have been performed in order to; 1) investigate the atomisa- tion and gasification of LOx and; 2) investigate the heat flux loading that could be expected on the chamber walls.
The atomisation and gasification of LOx was investigated using a cylin- drical chamber with super-cooled LOx at 77 K injected at the top through im- pinging injectors 0.686 mm in diameter with hot water vapour gas at 2800 K injected half way down the mixing chamber through 0.85 mm diameter inlets.
Cases 1-4 were created as part of the investigation and a summary of the main model parameters are provided in Table 4.1 with the aim of:
• Case 1 and 1b (inert fluid) providing comparison to experimental pub- lished data on particle formation, impinging jet sheet break-up and atom- isation with 77 K LOx injected into a 300 K, 1 MPa chamber filled with air.
• Case 2 and 3 provides comparison of impact of jet velocity with 77 K LOx injected into a 300 K, 1 MPa chamber filled with air.
• Case 3, 3b, 3c provides comparison of impact of mesh adaption/ refine- ment level on fluid sheet and droplet formation.
• Case 4 allows evaluation of the impact of additional heat/ enthalpy in- put to the rate and quantity of vaporisation with 77 K LOx injected into a 1000 K, 1 MPa chamber filled with air (initialised with VOF-DPM model disabled until simulation stabilised).
An overview of the chamber configuration is provided in Figure 4.1 and dimensions detailed in Figure 4.2.
27
Table 4.1: Two-phase model flow parameters (for half the chamber) for simula- tion of atomisation and gasification (extended table can be found in Appendix A).
Case Jet pairs Inlet flow velocity Surface tension Evaporation Mesh adaption
- [m s−1] [N m−1] [Y/N] [-]
1 1 7 0.0132 N 3
1b 1 11.85 0.0132 N 3
2 1 7 0.004 : 0.0144 Y 3
3 1 11.85 0.004 : 0.0144 Y 3
3b 1 11.85 0.004 : 0.0144 Y 2
3c 1 11.85 0.004 : 0.0144 Y 4
4 3 ≈11.85 0.004 : 0.0144 Y 3
a) b)
Figure 4.1: Isometric view of Mixing Chamber (a) initial structured mesh, (b) adapted mesh in VOF regions during Case 4 simulation.
A variation on the above geometry was used, as shown in Figure 2.2. The hot gas injectors were reduced from six to two and their size increased to 2.55 mm in diameter. This results in a conservative heat flux estimate on the chamber walls. Single phase analysis informed this selection considering an evenly distributed hot gas injection will result in a lower maximum heat flux with the fan of hot gas impinging on the mixing chamber walls when two op- posing streams interact. In order to minimize the impact of reverse flow on the thermal models the chamber length was increased and tapered to add out- let pressure control. A summary of the main model parameters are provided in Table 4.2.
Table 4.2: Summary of Thermal Model Parameters (extended table can be found in Appendix A).
Model Mesh Refinement Inlet Pressure/ Flowrate Initialisation Pressure/
- Level Temperature - Temperature
- - MPa / K kg s−1 atm / K
T1 2 1.3 / 2800 5.84 × 10−3 1 / 300
T2 3 1.3 / 2800 5.84 × 10−3 1 / 300
T3 4 1.3 / 2800 5.84 × 10−3 1 / 300
4.1 Two-Phase CFD for Atomisation and Va- porisation of Liquid Oxygen
When selecting the chamber geometry for two-phase investigations several pa- rameters were considered, in particular the available computational power. A scaled geometry was thus chosen with inlet parameters selected in order to allow for possible full scale testing in the future. The main non-dimensional scaling factors considered include:
• Estimated mean particle diameter, described in Section 3.2.4, is propor- tional to d0.58/v.
• Momentum flux can have an impact on the penetration and therefore mixing and LOx fluid break-up into particles.
• Mass flowrate ratio between LOx and hot gas impacts the enthalpy ra- tio which drives vaporisation. Dimensions were also chosen to prevent choked flow during normal operation.
