Supersonic Retro Propulsion Flight Vehicle Engineering of a Human Mission to Mars

Hanna Marklund

Space Engineering, master's level 2019

Luleå University of Technology Department of Computer Science, Electrical and Space Engineering Supervisor Dr. R. Schwane - European Space Agency, Noordwijk, The Netherlands

Examiner Dr. S. Larsson - Lule˚aUniversity of Technology, Lulea, Sweden Abstract

A manned Mars mission will require a substantial increase in landed mass compared to previous robotic missions, beyond the capabilities of current Entry Descent and Landing, EDL, technologies, such as blunt-body aeroshells and supersonic disk-gap-band parachutes. The heaviest payload successfully landed on Mars to date is the Mars Science Laboratory which delivered the Curiosity rover with an approximate mass of 900 kg. For a human mission, a payload of magnitude 30-50 times heavier will need to reach the surface in a secure manner. According to the Global Exploration Roadmap, GER, a Human Mission to Mars, HMM, is planned to take place after year 2030. To prepare for such an event several technologies need maturing and development, one of them is to be able to use and accurately asses the performance of Supersonic Retro Propulsion, SRP, another is to be able to use inﬂatable heat shields.

This internal study conducted at the European Space Agency, ESA, is a first investigation focusing on the Entry Descent and Landing, EDL, sequence of a manned Mars lander utilising an inflatable heatshield and SRP, which are both potential technologies for enabling future landings of heavy payloads on the planet. The thesis covers the areas of aerodynamics and propulsion coupled together to achieve a design, which considers the flight envelope constraints imposed on human missions. The descent has five different phases and they are defined as circular orbit, hypersonic entry, supersonic retropropulsion, vertical turn manoeuvre and soft landing. The focus of this thesis is on one of the phases, the SRP phase. The study is carried out with the retro-thrust profile and SRP phase initiation Mach number as parameters. Aerodynamic data in the hyper and supersonic regime are generated using Computational Fluid Dynamics, CFD, to accurately assess the retropropulsive performance. The basic concept and initial sizing of the manned Mars lander builds on a preliminary technical report from ESA, the Mission Scenarios and Vehicle Design Document [1]. The overall optimisation process has three parts and is based on iterations between the vehicle design, CFD computations in the software DLR-Tau and trajectory planning in the software ASTOS. Two of those parts are studied, the vehicle design and the CFD, to optimise and evaluate the feasibility of SRP during the descent and test the design parameters of the vehicle. This approach is novel, the efficiency and accuracy of the method itself is discussed and evaluated. Initially the exterior vehicle Computer Aided Design, CAD, model is created, based on the Mission Scenarios and Vehicle Design Document [1], however updated and furthered. The propulsion system is modelled and evaluated using EcosimPRO where the nozzle characteristics, pressure levels and chemistry are defined, and later incorporated in the CAD model. The first iteration of the CFD part has an SRP range between Mach 7 and 2, which results in an evaluation of five points on the trajectory. The thrust levels, the corresponding velocity, altitude and atmospheric properties at those points can then be evaluated and later incorporated in ASTOS. ASTOS, in turn, can simulate the full trajectory from orbit to landing including the CFD data of the SRP phase. Due to time limitation only one iteration of the vehicle design and the SRP range was completed. However, the goals of the study were reached. A first assessment of SRP in Mars atmosphere has been carried out, and the aerodynamic and propulsive data has been collected to be built on in the future. The results indicate that the engines can start at a velocity of Mach 7. They also show consistency with similar studies conducted in Earths atmosphere. The current vehicle design, propulsion system and SRP range can now be furthered, updated and advanced in order to optimise the different descent phases in combination with future results from ASTOS. Acknowledgements

I would ﬁrst and foremost like to thank my supervisor at ESA, Dr. Richard Schwane, for making this thesis happen. His support, his help, his knowledge and enormous experience within this ﬁeld has been invaluable to me. This thesis has been carried out at ESA and ESTEC at the section TEC-MPA supervised by Section Head Dr. Guillermo Ortega who supported my work and made me feel right at home in his section, thank you.

I would also like to thank my colleague at TEC-MPA, Mr. Csaba Jeger, for his very appreciated help and encouragement during my time at ESA, it has been valuable to have such a knowledgeable and professional person to work with. Another thanks to the Space Engineering Department and Fluid Mechanics Section at Lule˚aUniversity of Technology for giving me such good preparations, which eased my ﬁrst working experience. My family deserves a special thank you for supporting me and helping me realise this dream of moving to the Netherlands to do my Master Thesis at ESA, especially my father Mr. M˚ansMarklund for his never ending encouragement and patience. Contents

1 Glossary ...... 1 1.1 List of acronyms ...... 1 1.2 List of symbols ...... 2 1.3 Sub and superscripts ...... 2 1.4 List of ﬁgures ...... 3 1.5 List of tables ...... 4

2 Introduction ...... 5

3 Theory ...... 6 3.1 Fluid dynamics ...... 6 3.1.1 Aerodynamic parameters ...... 6 3.1.2 Mach number and shock wave formation ...... 6 3.1.3 Rocket nozzle ﬂow ...... 6 3.1.4 SRP ﬂow ...... 8 3.1.5 Computational Fluid Dynamics ...... 8 3.2 Orbital dynamics ...... 10 3.2.1 Entry, descent and landing ...... 10

4 Background ...... 11 4.1 Heavy payload entry vehicles ...... 12 4.2 Supersonic Retropropulsion ...... 12 4.3 Inﬂatable heat shields ...... 13

5 Method and objectives ...... 14 5.1 Method ...... 14 5.2 Objectives ...... 14

6 Validation of CFD tool DLR-TAU ...... 15 6.1 DLR-TAU ...... 15 6.1.1 Bow shock location ...... 15 6.1.2 Pressure distribution over the cone ...... 17 6.1.3 3D simulation ...... 18

7 Mission description ...... 21 7.1 Vehicle design ...... 21 7.2 Propulsion system ...... 23 7.3 Atmosphere of Mars ...... 24 7.4 Simpliﬁcations and parameters not taken into account ...... 25

8 Trajectory planning in ASTOS ...... 26

9 CFD simulations ...... 27 9.1 Start-up conditions ...... 27 9.1.1 Geometry, model and mesh ...... 27 9.1.2 Simulations - Jet oﬀ ...... 28 9.2 Retro propulsive phase ...... 31 9.2.1 Geometry, model and mesh ...... 31 9.2.2 Simulations - Jet on ...... 32 9.2.3 180 degree model ...... 37 9.2.4 Similar studies ...... 39

10 Discussion ...... 41 10.1 Future work ...... 42

11 Cited Literature ...... 44

4 Appendices ...... 46

A ...... 46 I General 1D rocket nozzle equations ...... 46 II Validation case data ...... 47

B ...... 48 I Reference atmospheric conditions ...... 48 II Collected data ...... 49 1 Glossary

1.1 List of acronyms ASTOS - Analysis, Simulation and Trajectory Optimisation Software CAD - Computer Aided Design

CFD - Computational Fluid Dynamics CFL - Courant Freidrichs Lewy CO2 - Carbon dioxide DES - Detached Eddy Simulation

DLR - Deutsches Zentrum f¨ur Luft- und Raumfahrt DNS - Direct Numerical Simulations EDL - Entry, Descent and Landing ESA - European Space Agency

ESPSS - European Space Propulsion System Simulation ESTEC - European Space Research and Technology Centre EV - Entry vehicle

GER - Global Exploration Roadmap GNC - Guidance, Navigation and Control HMM - Human Mission to Mars ISECG - International Space Exploration Coordination Group

LES - Large Eddy Simulation LH2 - Liquid Hydrogen LOX - Liquid Oxygen

MOLA - Mars Orbiter Laser Altimeter MSL - Mars Science Laboratory RAAN - Right Ascension of the Ascending Node RANS - Reynolds-Averaged Navier-Stokes

SRP - Supersonic Retro Propulsion SST - Shear Stress Transport TPS - Thermal Protection System

1 1.2 List of symbols Symbol Description Unit Value A Area m2 - BC Ballistic coeﬃcient kg/m2 - c Speed of sound m/s -

CD Coeﬃcient of drag - -

CL Coeﬃcient of lift - - F Force N - g Gravity m/s2 -

Isp Speciﬁc impulse s - L Characteristic length m - M Mach number - - m Mass kg - m˙ Mass ﬂow rate kg/s - p Pressure P a - q Dynamic pressure P a - Re Reynolds number - - T Temperature K - u Velocity m/s - w Thermodynamic work J - α Angle of attack ◦ - ρ Density kg/m3 - µ Dynamic viscosity N · s/m2 - γ Flight path angle ◦ -

1.3 Sub and superscripts e - Exit t - Throat T - Thrust ∞ - Ambient conditions D - Drag L - Lift

2 1.4 List of ﬁgures

1 Rocket nozzle parts and parameters. [2] ...... 7 2 Rocket nozzle design parameters [3], comparison of Bell and 15◦Cone contours...... 7 3 Supersonic retropropulsion flow characteristics. [4] ...... 8 4 Entry parameters such as flight path angle, lift, drag, height above ground, radius etc...... 10 5 Figure summarising the Global Exploration Roadmap, GER. [5]. . . . 11 6 Overview of possible entry mass and diameter criterion’s for a HMM. [6] 12 7 Definition of bow shock stand off distance, l. [7] ...... 16 8 Results from 2D inviscid simulations of bow shock location...... 16 9 CFD results of bow shock location of a higher vs. lower thrust coefficient, M∞ =3...... 17 10 Experimental set up by McGhee[7]...... 17 11 Result comparison between CFD and experimental data of pressure coefficient along the cone for maximum pressure ratios at different Mach numbers ...... 18 12 3D CFD results of bow shock location for CT = 1.4, M∞ = 3...... 19 13 Comparison of bow shock location between experimental, 2D simulations and 3D simulations...... 19 14 CFD results of bow shock location for CT = 1.4, M∞ = 3...... 20 15 Vehicle design of HMM vehicle proposed by ESA. [1] ...... 21 16 Updated vehicle design with the nozzles integrated in the heat cap. . . 22 17 Schematic of liquid propulsion system in EcosimPro...... 23 18 Atmosphere levels of temperature and pressure above 7 km...... 24 19 Atmosphere levels of temperature and pressure below 7 km...... 25 20 CAD model for simulating start-up conditions, nozzles are sealed. . . . 28 21 2D snapshots of the 45 degree slice of the 3D geometry and the finest mesh used including adaptation, in total 12e6 nodes...... 28 22 Pressure outside and inside bow shock, M∞ = 7...... 29 23 Comparison of bow shock location vs. total free stream pressure upstream of the bow shock, M∞ = 7...... 29 24 Comparison of surface pressure on the heat shield behind the bow shock, M∞ =7...... 30 25 CAD model and example of adapted mesh for jet on simulations. . . . 31 26 Pressure and Mach number curve extending along the tilted nozzle axis from the throat of the nozzle and forward, M∞ = 7...... 32 27 Pressure and Mach number plumes extending along x [mm] from the nozzle and forward, M∞ = 7...... 32 28 Mach number and velocity contour, M∞ = 6...... 33 29 Mach number plumes, M∞ = 5...... 34 30 Pressure and Mach number plumes extending along x from the nozzle and forward, M∞ =4...... 34 31 Chemistry difference and distribution between exhaust gases and the ambient CO2 dominant atmosphere , M∞ = 4...... 35 32 Mach number and pressure, M∞ = 3...... 35 33 , M∞ =2...... 36 34 Mach number plume and stream traces of the flow field, M∞ = 7. . . . 37 35 Pressure and temperature contours, M∞ = 7...... 37 36 Mach number and temperature, M∞ = 7...... 38 37 Comparison of nozzle temperature between this study and the study carried out by DLR of a Falcon 9 re-entry scenario...... 39

3 38 Comparison of Mach number levels in the nozzle between this study and the study carried out by DLR of a Falcon 9 re-entry scenario. . . 39 39 Comparison of temperature levels around the vehicles between this study and the study carried out by DLR of a Falcon 9 re-entry scenario in Earths atmosphere [8] ...... 40 40 Mach and temperature contours from this study and the study carried out by DLR of a Falcon 9 re-entry scenario in Earths atmosphere [8] . 40

1.5 List of tables

1 Summary of size parameters for the updated vehicle design...... 22 2 Parameters of the liquid propulsion system simulation in EcosimPro. . 23 3 Chemistry data file parameters for the exhaust gases in DLR-TAU. . . 24 4 Chemistry data file parameters in DLR-TAU for Mars atmosphere. . . 24 5 Circular orbit elements of phase 1 implemented in ASTOS...... 26 6 Summary of outputs from the inflatable heat shield simulations. . . . . 26 7 Atmospheric reference values of the first point in the SRP phase, start- up of the engines...... 27 8 Summary of outputs from the simulations of the start-up conditions in DLR-TAU...... 30 9 Difference in atmospheric conditions for the points of interest at different altitude and velocity...... 33 10 Summary of outputs of CFD simulations for the retropropulsive phase of 45 degree model...... 36

4 2 Introduction

A manned Mars mission will require a substantial increase in landed mass compared to previous robotic missions, beyond the capabilities of current EDL, Entry Descent and Landing, technologies, such as blunt-body aeroshells and supersonic disk-gap-band parachutes. The heaviest payload successfully landed on Mars to date is the Mars Science Laboratory which delivered the Curiosity rover with a mass of 900 kg. For a human mission, a payload of magnitude 30-50 times heavier will need to reach the surface in a secure manner. According to the GER, Global Exploration Roadmap, a HMM, human mission to Mars, is planned to take place after the year 2030. To prepare for such an event several technologies need maturing and development, one of them is to be able to use and accurately asses the performance of SRP, supersonic retro propulsion. This internal study carried out at ESA is conducted as a first investigation of SRP in a low density atmosphere. SRP is a technology for braking a spacecraft by firing rocket thrusters in the opposite direction of the velocity vector of the vehicle. The usage of SRP rockets is still a novel, but promising, technology for slowing down through an atmosphere in an efficient way, which has been shown by SpaceX in recent years [9] for applications here on Earth. While the SRP technology is making progress here on Earth with re-usability and reduced cost as its main objectives, it is also a critical area of development for further exploration of the solar system. Mars has a very low density atmosphere compared to Earth, additionally the payload of a human mission is large. This in combination with the difficulties in handling large parachutes have led to the conclusion that SRP is one of the critical technologies to study further when aiming to carry out pin point landings of heavy payloads on the red planet. The goal of this study is to introduce a first set of results of SRP from CFD in DLR-TAU as a reference to build on. The task is focused on the EDL sequence of a manned Mars lander utilising an inflatable heatshield and supersonic retro propulsion, which are both potential technologies for enabling future landings of heavy payloads on the planet. The parameters used for the optimisation are the SRP initiation Mach number, the retro-thrust profile and the design of the vehicle. The initial design and concept of the mission is based on a technical note from ESA [1] which comprises a payload of 23 metric tonnes, an inflatable heat shield surface area of 240 square meters and four main engines and nozzles for SRP.

5 3 Theory

3.1 Fluid dynamics Fluid dynamics is a subarea within fluid mechanics and describes the motion of liquids and gases. Included in the fluid dynamics discipline is the area of aerodynamics, which traditionally described only the flow of air, but was later extended to the flow of other mediums as well. The basic fluid and aerodynamic concepts used in this study will be shortly described in this chapter.

3.1.1 Aerodynamic parameters

The lift force, FL, is defined as the force perpendicular to the flow direction, while the drag force, FD is defined in the direction parallel and opposite to the flow direction. For a zero angle of attack the generated lift force of a symmetric body is zero, since the flow then surrounds the body with an even pressure. Together, the perpendicular forces FD and FL, expressed below in their respective aerodynamic coefficients, make up the total aerodynamic force on a vehicle. 2 · F C = D (1) D ρu2A 2 · F C = L (2) L ρu2A

3.1.2 Mach number and shock wave formation The Mach number is a dimensionless quantity which is used for high velocity flows. It is defined by the speed of sound, c, in the medium that it is travelling through. The different regions defined by the Mach number are subsonic M < 1 , sonic M = 1, supersonic M > 1 and hypersonic M > 5. u M = (3) c Shock waves appear when an object propagates faster than the speed of sound in a medium. The properties of the shock varies depending on the object shape and the medium. Commonly used terms for different parts of a shock waves include normal shock and oblique shock, an oblique shock is inclined with respect to the direction of the free stream and the normal shock is not. An example of shock waves present in a supersonic retro propulsion scenario is shown in Figure 3.

3.1.3 Rocket nozzle flow Rocket nozzles are designed to create large amounts of thrust which implies a high velocity increase through the nozzle and a high mass flow,m ˙ , at the exit, equation 4 shows Tsiolkovsky’s rocket equation [10]. This study only considers liquid propulsion, and hence only liquid fuel turned gaseous in the process flows through the nozzles. Figure 1 shows a schematic of a rocket nozzle, the design variables of the nozzle determines the flow acceleration, Mach number, mass flow rate etc. The complete 1D rocket nozzle equations which determines the basic characteristics of the flow can be found in Appendix A.

F =mu ˙ e + Ae(pe − p∞) =mI ˙ sp (4)

6 Figure 1: Rocket nozzle parts and parameters. [2]

The rocket nozzle contour can be calculated for a specific pressure or area ratio between the chamber, throat and the exit, or for a desired thrust level. One problem that often arises when trying to maximise the thrust and mass flow, such as for rocket applications, is that the ideal equations may result in an inadequately long nozzle which then has to be cut short to fit with the sizing of the spacecraft. An overview of nozzle performance and the full set of equations deciding the nozzle shape can be found in Sutton [3]. Two commonly used shapes are the Bell nozzle and the 15◦ cone nozzle, described in Figure 2.

Figure 2: Rocket nozzle design parameters [3], comparison of Bell and 15◦Cone contours.

7 3.1.4 SRP flow SRP is defined as when a rocket engine is fired into an opposing supersonic free stream. Hence, SRP flow consists of the combined characteristics of the the ambient supersonic retro flow and the rocket plume flowing in the opposite direction. The plume pushes the bow shock away from the body and enlarges it, which in turn increases the braking force. A fully developed jet plume extending from a nozzle which is integrated in a vehicle body and travelling through a flow at supersonic speeds is schematically explained in Figure 3. The general flow properties to recognise is the bow shock, jet shock, re-circulation regions and the jet plume.

Figure 3: Supersonic retropropulsion ﬂow characteristics. [4]

3.1.5 Computational Fluid Dynamics To model and analyse a flow field and its behaviour, a computational software can be used. This is a relatively new field witch needs maturing and further advancement to keep up with the applications it can be used for. One of those applications are SRP for spacecrafts landing on Earth or other bodies such as the Moon or Mars. There are several different computational schemes that can be used for a CFD simulation and it is important to choose and customise it according to the application studied. When inviscid cases are simulated in this study the solution is computed using the Euler equations, shown below. An inviscid solution is simplified and contains many assumptions, however it can still be useful to understand the basic flow field. The letter u denotes the velocity, t the time, w stands for work and g describes the gravity (or other acceleration).

∂~u + ~u · ∇~u = −∇w + ~g (5) ∂t ∇ · ~u = 0 (6) Other computational schemes that can be used are for example a Direct Numerical Simulation, DNS, which relies on the Navier-Stokes equations and does not include a turbulence model. Another widely used computation in engineering applications is the Large Eddy Simulations, LES, which is a model for simulating turbulent ﬂows. Yet another is the Detached Eddy Simulation, DES, which is a hybrid model

8 combining the LES and the Reynolds Averaged Navier Stokes, RANS, equations. These simulations each have their benefits, and are appropriate for different applications. However, for computing the solution of the viscous and turbulent simulations in this study the RANS equations are used alone. It is a well tested and straight forward computation, feasible to use in a first study of a partly unknown flow field as in this thesis. Below, the compressible RANS equations for ideal gas are described. Equation 7 shows the RANS equations for conservation of mass, equation 8 shows the conservation of momentum and equation 9 shows the conservation of energy. P is the stress tensor, ρ the density, q is the heat flux and E is the energy density. ∂ρ ∂ + (ρui) = 0 (7) ∂t ∂xi ∂ ∂ (ρuj) + (ρuiuj − Pij) = 0 (8) ∂t ∂xi ∂E ∂ + (uiE − ujPij + qi) = 0 (9) ∂t ∂xi The RANS equations are time averaged solutions of the Navier-Stokes equations. To complete the solution a turbulence model is required, many different turbulence models exists today and can be chosen depending on the application. Further calibration and development of turbulence modelling is a critical step in the advancement and reliability of CFD tools.

In this thesis, hyper and supersonic flows are studied and the CFD code used is called DLR-Tau, developed by DLR - the German Aerospace Center. To run a CFD simulation a geometry, a mesh and a CFD code calculating the viscid or inviscid equations are needed. The geometry and enclosure around the geometry is specified by boundary conditions on all surfaces. Examples of common boundary conditions are walls, inlets, symmetries and outlets. The boundary conditions apply rules in terms of equations to the computational domain and enables a solution. CFD of very high velocities are more uncertain and require more computer power, or computation time, than low velocity flow simulations. This is due to the mesh which has to be made up of smaller elements, compared to low velocity applications, in order to be able to capture the flow field of the high velocity flow. To check if the mesh is fine enough to catch the boundary layer near the walls, a measurement called y+ describing a dimensionless wall distance is often used. It is defined in equation 10 where u∗ is the velocity at the wall, y∗ is the cell length at the wall and ν is the kinematic viscosity. In this study the aim was to obtain a y+ of approximately 1 or lower. u y y+ = ∗ ∗ (10) ν It should be noted that all CFD simulations contain approximations. Quality and trust in CFD is an important topic to be discussed in order to evaluate how far from a ’real life’ solution, an experimental result, the outputs are. The errors, or deviations from experimental results, can arise from incomplete problem definition, turbulence modelling, numerical differences and discretization etc. When running a CFD simulation, error residuals of certain parameters can be monitored to check if the errors of those parameters are decreasing or increasing. If the monitored residuals reach a low value after a certain amount of iterations it is an indication that the solution is correct, how low below one that residual value should be differs from case to case. The grid quality, as mentioned above for y+, is another important measurement. The wall boundary layer, for viscous simulations, should be meshed according to the y+ equation and is the finest meshed area in the grid. In this thesis, a study of quality and trust in CFD is carried out to some extent. The main focus is validation and verification based on the best practice guidelines described

9 by the ﬂuid dynamics laboratory at Sulzer Innotech [11]. Since SRP in Mars atmosphere has not been done yet outside of simulations, no experimental data can be used as a comparison. However, a validation case with experimental data of a similar case is set up prior to continuing with the CFD simulations of the spacecraft of interest in this study. This is done to validate the DLR-Tau code for SRP ﬂows.

3.2 Orbital dynamics Orbital dynamics is a ﬁeld that describes the ballistic motion of a body which can be propelled or in relation to another body’s gravity, such as trajectories for spacecrafts. Some of the key variables and concepts concerning the descent trajectory planning relevant for this mission will be shortly described in this chapter.

3.2.1 Entry, descent and landing From orbit to landing there are several phases that needs to be specified and designed to ensure that the braking procedures are efficient, safe and powerful enough. The ballistic coefficient is a size to mass measurement of how a body behaves in a flow in terms of negative acceleration, the value of the ballistic coefficient impacts the entry corridor and the flyable domain for the spacecraft. For a vehicle with a high ballistic coefficient, more forceful braking capabilities are needed, such as SRP, since it does not slow down enough due to its shape, which determines CD, and high mass when travelling through the medium. m BC = (11) CD · A For a human mission, which has a large mass m, the ballistic coefficient is high compared to robotic missions. To have enough time to slow down during the descent, the entry angle, or flight path angle γ, can be chosen as shallow to extend the trajectory length. Both these features are included in the characteristics of a ballistic entry. For a ballistic entry of a axisymmetric vehicle, the local angle of attack is zero and there is only forces directed in parallel to the velocity vector. However, that is only exactly true if the center of pressure coincides with the center of mass, which may not always be the case, but could be used as a general assumption for a generic ballistic entry case.

Figure 4: Entry parameters such as ﬂight path angle, lift, drag, height above ground, radius etc.

10 4 Background

Spacecrafts have been sent towards Mars since the 1960’s, initially to orbit the planet but early on some spacecrafts carried probes to be deployed towards the surface. The first successful orbiter around Mars was Mariner 9 in 1971 sent by NASA, and the first successful landing took place only weeks after by the spacecraft called Mars 3, sent by the Soviet Union [12][13]. The Mars 3 descent module had a total wet mass of about 1200 kg which comprised the spherical landing capsule of about 350 kg, the braking aids of the vehicle consisted of a 2.9 m conical shield, parachute system and retrorockets [12]. The first European mission to Mars was called Mars Express, launched in 2003, consisting of both an orbiter and a lander. The orbiter was inserted in its desired trajectory around the planet without faults, the lander was however not able to send out any signals after arriving at the surface [14]. The latest successful landing on Mars to date is NASAs InSight lander which had a wet mass of about 600 kg entering the atmosphere, the braking system consisted of a parachute and retrorockets to obtain a soft pinpoint landing [15]. The Global Exploration Roadmap [5] is a document where 14 Space Agencies, including ESA, summarise their common goals for future space exploration. A clear goal stated in the 3rd Edition is to put humans on the surface on Mars after year 2030. In the GER, one critical technology gap highlighted to investigate is how to safely descent and land large robotic missions with a payload of more than 1000 kg and human missions of about 40 000 kg, i.e when parachutes and aero-braking are no longer viable EDL technologies. As a step in that direction it was decided to start evaluating and prepare the capabilities at ESA ESTEC for assessment of SRP in combination with an inflatable heatshield for such a human mission to Mars.

Figure 5: Figure summarising the Global Exploration Roadmap, GER. [5].

11 4.1 Heavy payload entry vehicles The mission with highest payload mass which has successfully landed on the surface of Mars is the MSL, which reached the planet in 2012. The MSL contained the Curiosity Rover as payload, which had a mass of about 900 kg. The MSL entry vehicle was slowed down from 5.8 km/s in orbit to 400 m/s by aero-braking with its 70 degree cone shape during 259 seconds. The MSL Entry Vehicle, EV, comprised the largest disk gap-band parachute ever made, which was deployed at a velocity of 400 m/s, 1.7 Mach, and at an altitude of 12 km. The powered descent was initiated 250 meters above ground in a vertical manner and ended with a procedure named the sky crane, where the rover was lowered down with wires to the ground from the hovering EV module 20 meters above ground [16]. For future Human Mars missions the payload will need to contain a habitat and a crew, and the mass of that payload will increase from Curiosity’s 900 kg up to 20-40 tonnes. A study at the Department of Aeronautics, Imperial College of London, have presented a paper highlighting the technology gaps between today’s missions and future heavy human or robotics missions [6], this is envisioned in ﬁgure 6 below.

Figure 6: Overview of possible entry mass and diameter criterion’s for a HMM. [6]

4.2 Supersonic Retropropulsion In 2013, SpaceX was the first company to fire a rocket engine into an opposing supersonic free stream, in this case Earths atmosphere, and in 2015 the first successful vertical landing of the first stage of the Falcon 9 rocket was achieved [9]. This became the start of the re-usable era in space exploration, and since then the boosters and rocket stages of Falcon Heavy have also been successfully landed with SRP, and re-used on Earth. SRP has been a technology of interest for future human Mars missions since the 1960’s, hence the need and interest to accurately assess and simulate the performance of SRP only grew once it was shown to be a game changer on Earth. A study carried out in 2017 by NASA and partners [17] compares flight data with CFD codes from Falcon 9’s first stage at re-entry at Mars relevant conditions in Earths atmosphere. The study shows that CFD of SRP is an important tool and gives sufficiently correct solutions in many cases, but the methods needs further advancing. Since SRP is such a novel technology there is not yet a large amount of gathered flight data. Especially not for different vehicles and nozzle configurations, since Falcon 9 and Falcon Heavy are the only large scale

12 spacecrafts successfully using this technology at present. The study comparing ﬂight data and CFD [17] is an important step to establish a base to build on, in a similar manner as this ESA study gathers and validates CFD data for SRP.

4.3 Inflatable heat shields Since the size of the descent module is restricted by the fairing diameter of the launch vehicle, there is a design limit for spacecrafts and their heat shields. In addition parachutes are no longer an option due to the mass. Larger spacecrafts in this sense indicate future robotic missions with payloads above 1000 kg or human missions. However, the development of inflatable heat shields could solve the size restriction of the launch vehicle fairing by being deflated until needed for descent [18]. An inflatable structure can utilise a flexible TPS which can withstand re-entry heats, as shown by NASA [19], and have a sufficient size once deployed to slow down a large and heavy spacecraft in its initial descent trajectory. The inflation of the heat shield would take place in orbit prior to the initiation of the descent. To combine SRP and an inflatable heat shield in an EDL sequence on Mars has been suggested by both ESA and NASA as a feasible approach for future heavy missions [20] [1].

13 5 Method and objectives

5.1 Method The overall optimisation process is iterative between CFD simulations in DLR-Tau, trajectory planning in ASTOS and updates of the vehicle model using the CAD software CATIA. In this thesis two parts of the optimisation process are featured, the vehicle design and CFD simulations. The general goal is to start up the iteration process by creating an initial vehicle design and to collect data from CFD simulations of the complex aerothermodynamics during the retro propulsive phase. The results from this thesis could then serve as a base for continuing to complete the whole optimisation process, including ASTOS simulations. The CFD results of the SRP phase determines the available SRP range of the engines and the operating conditions, therefore a range of Mach numbers are tested. A critical aspect is determining when and where the SRP phase can begin, the start up behaviour of the engines in high Mach number retro ﬂows is one of the parameters studied in detail. After there is an initial vehicle design and corresponding CFD results, the SRP performance can be incorporated in ASTOS to complete the ﬁrst iteration of the full process and further evaluate the results. The combined results can then be assessed, and the vehicle design updated for the next iteration.

5.2 Objectives The objectives and expected outputs of this master thesis are summarised below. • Deliver internal study, preliminary to a phase A, of the SRP part of an EDL sequence for a HMM.

• Create ﬁrst design of the vehicle and propulsion system. • Gather aerodynamic data of SRP phase in Mars atmosphere. • Find the preliminary thrust proﬁle.

14 6 Validation of CFD tool DLR-TAU

The complex flow fields of SRP and nozzle exhausts are a challenge to predict and describe precisely. The lack of a exact mathematical description of turbulence in combination with the said complexity of the flow field results in a problem set up with many uncertainties. Initially, the CFD software ANSYS Fluent was used in comparison to DLR-TAU for a nozzle flow problem. It was shown that the DLR-TAU code was more sophisticated for these particular cases, and that ANSYS Fluent was more time consuming. Hence, it was decided to continue only with DLR-TAU. In agreement with the Best Practice Guidelines in CFD [11], a validation case is set up. Due to the lack of experimental data of SRP in Mars atmosphere, the flow field investigated for the SRP phase of the the EDL sequence in this study can not be fully validated. However, a similar experimental set up was chosen to validate SRP flows in DLR-Tau.

6.1 DLR-TAU DLR-TAU is a code developed by the German space agency, DLR, especially focused towards the aerospace sector. To verify the CFD tool DLR-Tau for SRP applications a validation case was conducted. The experimental data can be found in a technical note from NASA Langley Research Centre by Robert J. McGhee [7], where a nozzle plume situated at the apex of a 140 ◦ cone is studied in retro flows of Mach 3.0, 4.5 and 6.0. This particular experimental study was chosen both since it has a reasonable SRP interval and since it includes a cone body similar to a heatshield. The experimental set up, which is thoroughly described in McGhee, was translated into an axisymmetric 2D model in the CAD software CATIA which were used in the verification simulations. The following validation case aims to highlight the problematic areas and to find the most valid approach. To ensure the correctness of the solution and set up of the 2D cases, a final step was to create a 3D model and repeat one of the simulations. The result parameters chosen for comparison were bow shock location and pressure coefficient distribution over the cone surface. The general flow field of the simulations should contain the features shown in figure 3. In McGhee, several cases per opposing Mach number were tested, to scale down the validation case amount two pressure ratios per Mach number were chosen. Expressed in thrust coefficients the first area is around CT = 0.4 and the second around CT = 1.4. Both areas of interest were found to be stable by McGhee, since the jet pressure is higher than the ambient. The simulations were set up as inviscid and steady with the Euler equations to minimise the calculation time, and also to compare how well the inviscid cases could compare to the experimental data. The mesh were created as unstructured in the software Centaur, and contained about 600 000 nodes and no boundary layer refinement due to in inviscid solver. A coarse outer mesh enclosed a refined area around the nozzle and cone which had a cell length limit of 0.4 millimetres. The boundary conditions used were Euler walls, supersonic inflow, supersonic outflow and farfield.

6.1.1 Bow shock location Figure 7 shows the deﬁnition of bow shock location in reference to the cone body and nozzle plume. The paper states that the experimental measurements are accurate within 2 %, and the 2D simulations show results within 5 % of the experimental results. All error bars in the following plots indicate 2 % deviation and the angle of attack is 0 degrees.

15 Figure 7: Deﬁnition of bow shock stand oﬀ distance, l. [7]

Figure 8 shows the comparison of bow shock stand oﬀ distance, l, over the cone base diameter, Db, as a function of thrust coeﬃcient, CT , and can be compared to Figure 12 in McGhee, which can also be found in appendix B section I. To compare the CFD results with the experimental results the Mach number distribution was extracted along the symmetry axis and the distance from the exit of the nozzle to the bow shock front was measured.

FT CT = (12) q∞A

Figure 8: Results from 2D inviscid simulations of bow shock location.

Figure 9 shows the difference in bow shock location when applying a different inlet pressure at the nozzle, different thrust coefficient. As expected, and seen in the experimental data, the bow shock location moves further away from the nozzle exit when the thrust is increased. Figure 9 shows the difference in bow shock location between a higher and a lower thrust coefficient. Due to the inviscid simplification and the mesh refinement the CFD figures show some discrepancy and unsteadiness in the flow field, which can be expected. However, the general flow properties are well represented with the bow shock, jet shock and re-attachment shock.

16 (a) CT = 1.4 (b) CT = 0.4

Figure 9: CFD results of bow shock location of a higher vs. lower thrust coeﬃcient, M∞ = 3.

Figures 9a and 9b can be compared with figure 3d in McGhee [7], where additional cases of different pressure ratios and thrust coefficients are represented as well.

6.1.2 Pressure distribution over the cone The pressure distribution over the cone is experimentally measured at orifices along the surface. The results are then translated into dimensionless quantities Cp and r/Db, where r is the radius to each orifice and Db is the length of the cone base. The simulated results were obtained by extracting the pressure along a line at the cone surface, then interpolated linearly and plotted against a length axis and made non dimensional. The experimental set up can be seen in figure 10.

P − P∞ Cp = (13) q∞

Figure 10: Experimental set up by McGhee[7].

17 (a) M∞ = 3 (b) M∞ = 4.5

Figure 11: Result comparison between CFD and experimental data of pressure coeﬃcient along the cone for maximum pressure ratios at diﬀerent Mach numbers

The simulated results plotted together with the experimental data can be seen in Figure 11. The full set of experimental results of pressure distribution can be found in Figures 3a, 4a and 5a in McGhee [7]. To be able to compare the data in an eﬃcient and more exact way the ﬁgures given in McGhee were converted to digital form, and the desired data could be extracted. Experimental data of the validation case can be found in Appendix A.

6.1.3 3D simulation The results of the 3D simulation, shown in Figure 12, for a quarter axisymmetric domain of the CT = 1.4 case shows a similar bow shock location and pressure distribution as the 2D case. Additionally Figure 12b roughly shows the pattern of SRP flow fields, which is schematically explained in figure 3.

18 (a) (b)

Figure 12: 3D CFD results of bow shock location for CT = 1.4, M∞ = 3.

Due to boundary effects of a supersonic outflow there is an incorrect increase in velocity and Mach number behind the shield, which can be seen in Figure 12a. This could be corrected by changing the boundary condition to an inviscid wall, Euler wall, in the future. The general flow field is correct but not resolved with a good resolution, which could be fixed with a finer mesh and adaptation in future simulations.

Figure 13: Comparison of bow shock location between experimental, 2D simulations and 3D simulations.

The bow shock location is similar between the experimental, 2D and 3D results,

19 which is expected since the experimental data and the 2D data agreed well. Figure 14 shows that a 3D simulation may catch the spectrum of pressure levels of the cone surface more precisely than a 2D simulation.

Figure 14: CFD results of bow shock location for CT = 1.4, M∞ = 3.

In conclusion the validation case indicates that a finer mesh, mesh adaptation and more iterations could help to sharpen the results of future SRP simulations. The inviscid simulations show good agreement with the experimental data for the parameters that were compared, however an even better agreement is of course expected for viscous simulations. Between 2D and 3D there is no large difference between the results, however a 3D model in a quarter enclosure gives a more correct pressure curve, and is perhaps to prefer in order to visualise the results in a nice way. The general flow field agrees with the theory, but should be resolved more clearly in the coming simulations.

20 7 Mission description

7.1 Vehicle design This study considers the retro propulsive phase of an EDL sequence of a manned Mars lander. The design of the Mars crew transfer vehicle is based on a technical note from ESA [1], section 5.1.7, where the payload is estimated to 23 metric tonnes consisting of the habitat and the crew. The suggested design from the technical note can be seen in ﬁgure 15 which has a cylindrical structure, contains four tanks, four rocket nozzles, an inﬂatable unit, a solid front heat cap and a parachute. In the early stages of this investigation it was concluded that a parachute wont be appropriate for such a heavy vehicle, and it was hence removed from the study. To avoid a 180 degree turn in the descent trajectory, it was also concluded that the propulsion system and nozzles must be located behind the solid heat cap and not at the top part of the vehicle.

Figure 15: Vehicle design of HMM vehicle proposed by ESA. [1]

To begin the first iteration of the design process, the initial guess of the vehicle design was created in CATIA. The inflatable heat shield has a diameter of 17.5 meters and the cylinder is 8.2 meters long, which corresponds to the proposed size by ESA [1]. The four nozzles are conical with an area ratio of 16, has an initial length of 1.5 meters and are tilted with a 7 degree angle outwards. The nozzles do not protrude but are flush against the curvature of the heat cap, this makes the length of the nozzle differ in different sections between 1.3-1.5 meters. The nozzles are treated as sealed until ignition when the protective caps are blown off by the jets and the retro propulsive phase is initiated. Once the retropropulsive phase is initiated the shield is no longer affecting the braking of the vehicle. It can then either be deflated and lie flat against the cylinder surface as an extra heat protection layer, or it can stay inflated during the thrust phase which is the chosen method in this case.

21 (a) Tilted view. (b) Side view.

Figure 16: Updated vehicle design with the nozzles integrated in the heat cap.

Figure 16 shows the updated design used in this study with the nozzles situated in the rigid heat cap. The size parameters of the spacecraft model are summarised in table 1.

Table 1: Summary of size parameters for the updated vehicle design.

Spacecraft size parameters Shield radius [m] 8.750 Cylinder radius[m] 2.580 Cylinder length [m] 8.260 Shield area [m2] 240 Total estimated mass [kg] 35000 Nozzle shape [-] Conical Nozzle tilt angle [◦] 7 Nozzle length [m] 1.3 - 1.5 (Curved surface) Nozzle throat radius [m] 0.089 Nozzle exit radius [m] 0.87

The moment of inertia matrix and the centre of gravity position for the conﬁguration is presented in Equation 14 and 15 respectively.   Ixx = 7.7e5 −Ixy = 9.5 −Ixz = −48.7  −Ixy = 9.5 Iyy = 6.9e5 −Iyz = 0  (14) −Ixz = −48.704 −Iyz = 0 Izz = 6.9e5   Gx = 0.064  Gy = 0  (15) Gz = −0.762

22 7.2 Propulsion system The propulsion system was assumed to use liquid hydrogen, LH2, as fuel and liquid oxygen, LOX, as oxidiser. It is known that it is a difficult task to start a cryogenic engine, and that it requires flushing with LH2. However it was discussed that a liquid cryogenic engine would be the only option for this study, and it had to be assumed that the engines would start. A model of such a propulsion system was realised in the software ECOsimPro and ESPSS, ESPSS is a toolkit within EcosimPro developed by ESA. The main parameters to analyse was the weight and size to ensure that the dimensions agreed with the size and mass estimations of the spacecraft stated in the technical note. The schematic created in ECOsimPro is shown in figure 17 below.

Figure 17: Schematic of liquid propulsion system in EcosimPro.

Table 2 shows the inputs and outputs of the simulation in EcosimPro. The total mass of payload and propulsion system is estimated to 33 tonnes, which is then not inclusive of the spacecraft structure mass. As stated earlier a total mass of about 35-45 tonnes is expected and it can be concluded that the propulsion system mass ﬁts that estimation.

Table 2: Parameters of the liquid propulsion system simulation in EcosimPro.

Propulsion system estimations P0 [Pa] 50e5 LOX mass fraction [%] 85.7 LH2 mass fraction [%] 14.3 Payload mass [kg] 23000 Fuel + Oxidiser mass [kg] 8540 Propulsion structure mass [kg] 1450 Nozzles + chambers mass [kg] 266 Propulsion + PL total mass [kg] 33256 Thrust/nozzle [N] 7.3e4

To be able to simulate the correct exhaust mix of the LOX and LH2 in DLR-TAU, a chemical file was created and added to the set up of the chamber in the simulations. The data was obtained in EcosimPro and re-calculated to fit the input variables for chemistry files, the used parameters for the exhaust gas can be found in Table 3.

23 Table 3: Chemistry data ﬁle parameters for the exhaust gases in DLR-TAU.

Exhaust chemical parameters Molecular weight [kg/mol] 0.027 Gas constant gamma [-] 1.3967 Prandtl number [-] 0.64 Sutherland constant [-] 119.14 Sutherland viscosity [kg/m s] 8.1135e-5 Sutherland temperature [K] 3000

7.3 Atmosphere of Mars The atmosphere of Mars consists mostly of CO2 and is very thin compared to the Earths. The chemistry ﬁle incorporated in DLR-TAU as a reference of the general atmosphere is used in the simulations to make the ambient environment as realistic as possible, values can be found in table 4. The atmosphere has a strong exponentially decreasing pressure curve, and hence density curve, while the temperature decreases linearly with height above the surface. Graphs showing the levels of pressure and temperature above and below 7 km altitude is shown in ﬁgures 18 and 19.

Table 4: Chemistry data ﬁle parameters in DLR-TAU for Mars atmosphere.

Atmospheric input parameters Molecular weight [kg/mol] 0.044009 Gas constant gamma [-] 1.298 Gas constant R [J/K mol] 188 Prandtl number [-] 0.7 Sutherland constant [-] 240 Sutherland viscosity [kg/m s] 8.17e-6 Sutherland temperature [K] 164

Figure 18: Atmosphere levels of temperature and pressure above 7 km.

24 Figure 19: Atmosphere levels of temperature and pressure below 7 km.

7.4 Simplifications and parameters not taken into account The flush surface of the heat cap gives slanted nozzles with different length segments. This will result in different side loads and may cause problems for stability and separation. The reason for angling the nozzles with a 7 degree angle is to separate the plumes slightly and increase stability of the vehicle. These side loads and the issue of the different length segments has not been studied and is not included in the current scope.

The engines are set as cryogenic, operating with liquid oxygen as oxidiser and liquid hydrogen as fuel. This requires ﬂushing with LH2 before start up. That is not possible if the nozzles are sealed until ignition, which is how they are treated in this study to simplify the start up conditions.

Throttling of the engines is a necessity, but not included in this first study, and the engine performance parameters and estimations at steady state are simplified. It is not investigated how to recover from an angle of attack, since a ballistic path is used for the majority of the trajectory. The possibility of gimbaling the engines, putting the system on a pivoted support to be able to change the thrust direction of the nozzles has not been investigated, but could be beneficial. The overall GNC has not been studied and would have to be included in future iterations of the design process. The idea of a four nozzle vehicle in a propelled descent has however been discussed and approved as a first geometry by a GNC expert at ESA.

25 8 Trajectory planning in ASTOS

To envision the descent from a circular orbit around Mars to touchdown using the trajectory software ASTOS, the diﬀerent descent phases has to be deﬁned. The only phase studied in detail in this thesis is the SRP phase. However, to decide on the constraints and set up of the SRP phase a preliminary trajectory was used as a base line for the altitude vs. velocity range and the corresponding atmospheric properties etc. This trajectory could then serve as a guide when choosing SRP initiation Mach number and Mach number range.

• Phase 1: Circular orbit

• Phase 2: Hypersonic entry • Phase 3: Supersonic Retro Propulsion • Phase 4: Manoeuvre to vertical position • Phase 5: Soft pinpoint landing

The orbit is set as circular, the orbital elements are described below.

Table 5: Circular orbit elements of phase 1 implemented in ASTOS.

Orbital parameters Apoapsis altitude [km] 500 Periapsis altitude [km] 500 Inclination [deg] 27 RAAN [deg] 120 Mean anomaly [deg] 70 Argument of periapsis [deg] 0

A short CFD evaluation of the inflatable heat shield properties at three different points were initially computed to get some preliminary data of the aerodynamics of the shield. These values can then be insert into the ASTOS set up file of phase 2, depending on where the SRP phase is set to begin.

Table 6: Summary of outputs from the inﬂatable heat shield simulations.

CFD results of the inﬂatable heat shield Mach number [-] 15 10 5 Altitude [km] 45 40 28

Cd [-] 1.551 1.564 1.618

The third phase is the SRP phase which is defined by the CFD simulations. The results of the CFD, especially the thrust levels at each point between Mach 7 and 2, can then be incorporated in ASTOS together with the propulsion system parameters. The fourth phase is specified to be a manoeuvre to position the spacecraft vertically above the surface, unfold landing legs or other gear, and descent the very last bit of the trajectory and finally, phase five, touch down gently.

26 9 CFD simulations

To set up and run a CFD simulations a geometry, a mesh and a CFD code is needed. In this study, the mesh surrounding the spacecraft and its enclosure is set up using CENTAUR, developed by CentaurSoft. The mesh is then converted into a DLR-Tau readable grid file where the boundary conditions can be re-specified in the DLR-Tau language. The CFD simulations are computed with the DLR-Tau code developed by the German Aerospace Center, DLR, and used at ESA. The program has no interface and is user controlled by programming in python and by manipulation of text files which the software can read and compute. All parameters, including files of boundary conditions and chemistry, are specified in an extensive parameter file. The parameter file containing all the information can the be run in a Linux terminal. The general approach during the viscous CFD simulations is starting the computation with a first order upwind scheme and stepping up from a low CFL number, sometimes as low as 0.01, up to 1 during a few thousand iterations. After obtaining low and steady residuals with the initial first order solution, the upwind scheme is switched to second order. The second order computation is the run for over 100 000 iterations in total. The results from DLR-Tau are converted into readable files and the post processing is done in Tecplot and Matlab.

9.1 Start-up conditions One of the most interesting phases to investigate is the start up of the engines in a high Mach number retro flow. The first assessment of the SRP phase had a Mach range of 7 to 2, where Mach 7 indicates ignition of the engines and Mach 2 indicates that the vehicle has slowed down enough to perform a vertical manoeuvre and later softly land. Mach 7 in the Martian atmosphere and at an altitude of 35 km corresponds to a velocity of about 1400 m/s, the full set of atmospheric properties at this altitude can be found in table 7. The nozzles are treated as sealed until ignition, when the protective caps covering the nozzles are blown of by the jet. The main issue is to identify if the jet flow is pushed back into the nozzle, or if the jet stream can overcome the ambient pressure caused by the retro flow of the atmosphere and brake the spacecraft in a steady manner. The reference atmospheric conditions were given by a previous trajectory calculated at ESA, the data can be found in Appendix B.

Table 7: Atmospheric reference values of the ﬁrst point in the SRP phase, start-up of the engines.

Atmospheric start-up conditions Mach number [-] 7 Altitude [km] 35 Ambient static pressure [Pa] 26 Temperature [K] 164 Density [kg/m3] 8.4e-4 Velocity [m/s] 1400 Speed of sound [m/s] 203

9.1.1 Geometry, model and mesh To evaluate the jet off conditions, a CAD model with a flushed heat cap and hence sealed nozzles, shown in figure 20, was simulated in a flow of Mach 7.

27 (a) Tilted view. (b) Side view.

Figure 20: CAD model for simulating start-up conditions, nozzles are sealed.

The simulations were carried out with a 3D axisymmetric 45 degree slice of the 3D model enclosed in a cylindrical wedge domain. 2D snapshots of the 45 degree model enclosed in the domain with and without mesh are shown in ﬁgure 21.

(a) Geometry used in DLR-TAU. (b) Fine mesh with adaptation.

Figure 21: 2D snapshots of the 45 degree slice of the 3D geometry and the ﬁnest mesh used including adaptation, in total 12e6 nodes.

9.1.2 Simulations - Jet off To determine the jet off conditions four cases were compared in DLR-TAU, one inviscid case and 3 viscous cases with increasing mesh size from 1 million nodes to 12 million nodes, the turbulence model used for the viscous jet off cases were k-w SST. The parameters of interest were the pressure and the bow shock location. The bow shock location determines how far the jet plume will travel in the lower pressure environment behind the bow shock once ignition is initiated, before hitting the largely increased pressure upstream of the bow shock. Figures 22a and 22b shows the solution of the overall dynamic pressure and the pressure on the heat shield behind the bow shock.

28 (a) Pressure distribution. (b) Surface pressure over the heat shield.

Figure 22: Pressure outside and inside bow shock, M∞ = 7.

The results shows a decreasing bow shock stand off distance with increasing number of mesh nodes, the difference between the cases are approximately 10 cm as seen in figure 23. The free stream pressure does not show large differences between the tested cases, which can also be seen in figure 23. The maximum total pressure of the free stream at a velocity of Mach 7 was determined to 2.88e5 Pa, which then gives the minimum jet pressure needed to extend a plume in the opposite direction of this flow measured in the next chapter.

Figure 23: Comparison of bow shock location vs. total free stream pressure upstream of the bow shock, M∞ = 7.

29 The surface pressure, figure 24, shows less difference between the cases. The different mesh size of the viscous cases does not seem to have a significant effect on the shield surface pressure behind the bow shock. This is due to a similarly meshed wall region. The only exception is shown at the very nose, x = 0, of the shield where the pressure varies from 1450 Pa to 1550 Pa with increasing mesh density, and this is in correlation with a more closely located bow shock. All simulations converged to a maximum density residual of 1e-3.

Figure 24: Comparison of surface pressure on the heat shield behind the bow shock, M∞ = 7.

Table 8 shows the obtained outputs of the start-up simulation of the viscous case with the finest grid, that will be used with the jet on case at the Mach 7 trajectory point. Moving forward, the boundary layer mesh of the viscous and finest meshed case will be used. The y+ value of the viscous and finest meshed cased varied between 1e-3 and 1. However, since the results of this mesh study did not vary much in terms of flow field, the mesh of the domain will initially be set as coarse and then refined heavily in areas with sharp Mach number changes and pressure gradients to save computational time in future simulations.

Table 8: Summary of outputs from the simulations of the start-up conditions in DLR-TAU.

Simulation results of start-up conditions Bow shock stand off distance [m] 0.52 Ambient dynamic pressure [Pa] 2.8e5 Heat shield surface pressure [Pa] 1600 Lift coefficient [-] 0 Drag coefficient [-] 1.56 Ballistic coeff. [-] 93 Force x-direction (Drag force) [N] 3.9e4

30 9.2 Retro propulsive phase The retro-propulsive phase starts at ignition of the engines and ends when the spacecraft has reached a velocity of Mach 2 where a soft landing is within reach. To simplify the task, the nozzles are treated as sealed until ignition, even though this is a method used for solid rocket engines and not liquid ones which requires flushing with cold hydrogen to start. The covers sealing the nozzles are blown off by the jet plume once ignited, and the plumes travel through the bow shock located approximately half a meter upstream of the centre of the heat cap and starts the braking. To ensure that the jet plume is powerful enough to develop in the retro flow of maximum pressure 2.88e5 Pa as shown in the previous section, and not be pushed back into the nozzle, the jet on conditions in Mach 7 at an altitude of 35 km in Mars atmosphere was initially studied before continuing with the rest of the retro propulsive phase. The ambient atmospheric parameters described in table 7 are used again, since the point of ignition and development of an exhaust plume is modelled as instant.

9.2.1 Geometry, model and mesh The jet on simulations are using a cylindrical enclosure which contains an 45 degree slice of the 3D axis-symmetric vehicle model and one of the nozzles. The nozzles are now open, and the model used is shown in figure 25a. The chemical files of the composition of the exhaust and the atmosphere of Mars, shown in section 7.2, were incorporated in the set up of the DLR-TAU code to get the correct species in the chamber and in the ambient flow. The boundary conditions of the set up were as follows, supersonic inflow at the inlet of the ambient atmosphere, farfield and supersonic outflow as surrounding walls, symmetry at the two wedge planes creating the quarter geometry, pressure inflow at the nozzle inlet and viscous walls for all remaining parts of the spacecraft. The simulations are viscous using the Spalart-Allmaras one equation turbulence model, which is specially designed for aerospace applications. The initial mesh contains 6e5 nodes, it is refined using DLR-TAU several times during each simulation according to the current flow field to get a more accurate solution, ending up with a final mesh containing approximately 1.3e6 nodes. The refinement tool is set to refine areas with a high pressure gradient or areas with a large difference in Mach number, the result can be seen in figure 25b. The wanted y+ value is set to one but ranges between 7e-4 to 7.7 between the different simulations.

(a) CAD model with uncovered nozzles. (b) Mesh with adaptation for SRP ﬂow.

Figure 25: CAD model and example of adapted mesh for jet on simulations.

31 9.2.2 Simulations - Jet on The initial jet on case at a velocity of Mach 7 was set up as a steady state, viscous simulation. All atmospheric parameters such as altitude, pressure and density etc. are equal to the jet off simulation. The most interesting parameters are the pressure of the plume and the distance the high pressure extends, since those values can be compared with the jet off results and determine if the jet flow will be pushed back into the nozzle or if it can overcome the dynamic pressure of the atmosphere.

(a) Mach number curve. (b) Pressure curve.

Figure 26: Pressure and Mach number curve extending along the tilted nozzle axis from the throat of the nozzle and forward, M∞ = 7.

In figure 26, the pressure which extends from the throat is shown to be of a magnitude 10 higher than the ambient dynamic pressure of 2.8e5 Pascals at jet off conditions. The jet pressure can also be seen to extend for approximately 32 meters, which is the jet shock location and stagnation point at a velocity of Mach 7. The bow shock location is 40 meters measured from the exit of the nozzle. In summary these results show that the pressure force of the engines is high enough to operate at steady state, in a retro flow of Mach 7. The question the actual ignition and start up moment is more complicated but these results are seen as a positive indicator.

(a) Mach number plume contour, [-]. (b) Pressure plume contour, [Pa].

Figure 27: Pressure and Mach number plumes extending along x [mm] from the nozzle and forward, M∞ = 7.

32 To initiate the ﬁrst iteration of the design of the retropropulsive phase, points between 36 and 8 kilometer in altitude on the trajectory were chosen to be examined further. The last point was set as close to ground level as possible to test a worst case scenario with the available fuel, at an altitude of 8 kilometer and with a velocity of 475 meters per second. The atmospheric properties at the diﬀerent points of interest are presented in table 9 below.

Table 9: Diﬀerence in atmospheric conditions for the points of interest at diﬀerent altitude and velocity.

Atmospheric parameters Mach number [-] 7 6 5 4 3 2 Velocity [m/s] 1400 1252 1069 875 700 475 Altitude [km] 36 32 28 24 12 8 Density [kg/m3] 8.4e-4 1.14e-3 1.6e-3 2.1e-3 5.6e-3 7.6e-3 Temperature [K] 169 179 188 197 223 232 Pressure [Pa] 26 38 56 81 237 340 Dynamic pressure [Pa] 2.8e5 1.3e5 5.2e4 1.6e4 9.5e3 2.6e3 Speed of sound [m/s] 203 209 214 219 233 238

(a) Mach number plume and bow shock, [-]. (b) Velocity contour, [m/s].

Figure 28: Mach number and velocity contour, M∞ = 6.

Figure 28 shows the Mach number and velocity contour at a velocity of Mach 6. The angled nozzle gives a tilted plume from the x axis.

33 (a) Mach number plume contour, [-]. (b) Mach number plume and bow shock, [-].

Figure 29: Mach number plumes, M∞ = 5.

Figure 29 shows the Mach number plume and contour at the trajectory point with velocity Mach 5. The results does not vary much from the previous trajectory point at a velocity of Mach 6.

(a) Mach number plume and bow shock, [-]. (b) Pressure plume contour, [Pa].

Figure 30: Pressure and Mach number plumes extending along x from the nozzle and forward, M∞ = 4.

Figure 30 shows the Mach number and pressure contour at the trajectory point with velocity Mach 4. The bow shock is moving further away from the spacecraft since the pressure of the opposing ﬂow is decreasing with the velocity.

34 (a) Mass fraction of exhaust gases. (b) Mass fraction of ambient atmosphere.

Figure 31: Chemistry diﬀerence and distribution between exhaust gases and the ambient CO2 dominant atmosphere , M∞ = 4.

Figure 31 shows the difference in the boundary conditions of the nozzle inlet and enclosure inlet, which are modelled with different chemistry files.

(a) Mach number plume and bow shock,[-]. (b) Pressure plume contour, [Pa].

Figure 32: Mach number and pressure, M∞ = 3.

Figure 32 shows the Mach number and pressure contour at a velocity of Mach 3. The bow shock distance from the spacecraft is further increasing which allows the plume to become more elongated since the dynamic pressure against it is decreasing.

35 (a) Mach number plume and bow shock,[-]. (b) Temperature distribution, [K].

Figure 33: , M∞ = 2.

Figure 33 shows the Mach number and temperature contour at the last point in the SRP range. The results at the diﬀerent points shows an increasing bow shock stand oﬀ distance together with a more elongated plume shape and distance with decreasing velocity, as expected. The results of the six points are summarised in table 10.

Table 10: Summary of outputs of CFD simulations for the retropropulsive phase of 45 degree model.

CFD results of retropropulsive phase Mach number [-] 7 6 5 4 3 2 Altitude [km] 36 32 28 24 12 8 Drag force [N] 3.48e5 3.19e5 3.11e5 3.59e5 2.14e5 3.45e5 Total axial force [N] 4.52e4 4.50e4 4.49e5 4.56e4 4.57e4 4.69e4 Bow shock dist. [m] 40 40 40 50 55 65

Ct [-] 1.831 1.674 1.635 1.892 1.124 1.815

The y plus values of the diﬀerent cases varies between 7e-4 to 7.7, the desired y plus is set to 1 in all cases. In table 10 the total axial force, Fx, is aligned with the center axis of the spacecraft. As mentioned the nozzles are however tilted with an angle of 7 degrees outwards from the center axis and have a thrust of 7.3e4 N per engine along the nozzle axis. All values are for one nozzle.

36 9.2.3 180 degree model To start an investigation of plume interaction between the nozzles, and to better asses the flow field, a 180 degree case were set up. The figures below shows the vehicle at the Mach 7 point in the trajectory with two nozzles active. These simulations with two active nozzles confirmed the output data in table 10.

(a) Mach number plume, [-]. (b) Stream traces of the ﬂow ﬁeld.

Figure 34: Mach number plume and stream traces of the ﬂow ﬁeld, M∞ = 7.

Figure 34 shows the Mach number plume and stream traces of the flow field with two active nozzles. Figure 34b shows the characteristic SRP flow field including the bow shock, plume shape and re-circulation regions also mentioned in the Theory Chapter.

(a) Pressure contour, [Pa], with bow shock. (b) Temperature distribution, [K].

Figure 35: Pressure and temperature contours, M∞ = 7.

Figure 35 shows the pressure and temperature contours with two active nozzles. Figure 35a shows the bow shock contour in 3D surrounding the spacecraft like a bowl. Figure 35b shows the temperature distribution with two active nozzles at a velocity of Mach 7. The walls of the spacecraft appears to be at very high temperatures, which is noted as an error to be discussed in terms of Quality and Trust in CFD.

37 (a) Mach number slice, [-]. (b) Temperature slice, [K].

Figure 36: Mach number and temperature, M∞ = 7.

Figure 36 shows contour slices of Mach number and temperature at a velocity of Mach 7 with two active nozzles. It can be seen in ﬁgure 36a that the plume of two nozzles has a diﬀerent shape compared to the results using one nozzle. The combined plume is more elongated and has a shape more similar to a large centred nozzle than a single tilted, which is expected.

38 9.2.4 Similar studies Since SRP is a technology not yet used in any other atmosphere other than the Earth’s, experimental data for low density and pressure environments is difficult to come by. However, one study conducted by Karl T. Edquist et al. [17] have done a comparative CFD study including flight data from the first stage of Falcon 9 in Mars relevant conditions. However, this study has the interesting and meaningful data edited out and only flow characteristics of SRP can be compared. Another, even more relevant CFD study is from the German Aerospace Center [8] also analysing Falcon 9 at re-entry, using the CFD code DLR-TAU. It should be noted that similarity between this study and other studies in Earths atmosphere is not the goal of the comparison. It is a comparison to show differences and similarities alike, since no experimental data of SRP is available from Mars atmosphere at this time.

(a) Nozzle temperature, [K] . (b) Nozzle temperature - study by DLR [8].

Figure 37: Comparison of nozzle temperature between this study and the study carried out by DLR of a Falcon 9 re-entry scenario.

Figure 37a shows the temperature distribution in the converging-diverging nozzle used by DLR in their Falcon 9 study [8]. The conical nozzle used in this study shows a similar temperature distribution in the nozzle.

(a) Nozzle mach number, [-]. (b) Nozzle Mach number - study by DLR [8].

Figure 38: Comparison of Mach number levels in the nozzle between this study and the study carried out by DLR of a Falcon 9 re-entry scenario.

39 Figure 38a shows the Mach number distribution in the converging-diverging nozzle simulated by DLR [8] compared to the Mach number distribution in the conical nozzle of this study. The study from DLR [8] focuses on the flow field from 3, of the total 9 nozzles, on Falcon 9. None of the nozzles in the Falcon 9 configuration are angled, and the studied Mach number SRP range by DLR is 9.45 to 5.09.

(b) Temperature, [K], 3 nozzles at Mach 5 - (a) Temperature, [K], at Mach 5. study by DLR [8].

Figure 39: Comparison of temperature levels around the vehicles between this study and the study carried out by DLR of a Falcon 9 re-entry scenario in Earths atmosphere [8] .

Figure 39 shows plume shape and temperature distribution of this study and the one from DLR [8]. The influence of the inflated heat shield can be noted, even though the temperatures of this study seems to be higher at the back body/cylinder either way. Figure 40 shows the plume shape of the two nozzles in this study and the shape from three nozzles on the Falcon 9. It can be seen that the plume shapes are more similar between two and three nozzles, than for one and three which is seen to be quite different in the previous figure, figure 39, however an expected observation.

(a) Mach contour with 2 active nozzles, (b) Temperature, [K], 3 nozzles at Mach 5- M∞ = 7. study by DLR [8].

Figure 40: Mach and temperature contours from this study and the study carried out by DLR of a Falcon 9 re-entry scenario in Earths atmosphere [8] .

40 10 Discussion

This study has the main focus of obtaining aerodynamic data of SRP in Mars atmosphere, and this goal has been achieved. It was clear after the literature study that the research within this field is about to grow exponentially, there are many new ideas on how to model and simulate SRP in the most accurate and efficient way. The fact that SRP is making waves on Earth right now with re-usability and higher profit as main objectives is of course a reason why this technology is making a comeback in the discussions of future space exploration. The initial challenge of this project was to scale down the mission, make reasonable assumptions and set up mission constraints to be able to begin the process. First up was the design, which is based on a vehicle design in a previous study by ESA [1] in 2002, but it had to be redone to ensure a safer and more simple descent trajectory. The old vehicle had the SRP engines positioned at the opposite end of the inflatable heatshield, which would indicate that a 180 degree turn would have to happen somewhere along the descent trajectory, this option was ruled out in discussions with ESA experts for such a heavy vehicle. The design created in this study is geometrically simple and could be furthered to be much more detailed in future iterations. The new design of the vehicle in this thesis, however, gave new questions such as the slanted nozzles positioned in the heat cap, which may give rise to undesired side loads. The side loads were not studied in this thesis but should be noted as a possible future problem. Perhaps there would be smaller side loads with 8, 12 or 16 smaller engines tilted with less than 7 degrees as in this study, or with no angle at all. The chosen configuration is just one of many imaginable, but the scope was to start as simple as possible not to rule anything possibilities or problems too soon. To ensure that the lander created in this study was not impossible from a Guidance, Navigation and Control, GNC, point of view. A GNC expert at ESA was shortly consulted and gave the green light of the design with SRP capabilities as a first configuration. Another issue early on was deciding on how to model the cryogenic propulsion system and the nozzles, which in the end had to be simplified in order to speed up the process due to the time limitation. As seen in section 8.2.4, using conical nozzles does not give a significantly different nozzle flow even though it is not likely to be used in a real scenario. The simplification of treating the nozzles as sealed until ignition worked well for the steady state cases, which was the goal. Even though it is well known that the nozzles would need to be flushed with LH2 before igniting the cryogenic engine, it was not in the scope to investigate the start up in a more detailed manner than on/off conditions. It was discussed what to do with the inflatable heat shield after the SRP phase begins, it could still be attached but deflated and folded flat against the cylinder, or it could stay inflated or it could be blown off. It was decided to keep it inflated as this is a simple solution and since it was seen as extra protection. Additionally, it was discussed that it might not interfere much once the SRP phase begins and the rocket engines take over the braking. Some problematic areas that should be noted and improved in the set up of the CFD simulations is first of all the wall temperature of the spacecraft which is not specified in this study, but which could be set to some reasonable value to avoid high wall temperatures in the results. Secondly, the symmetry boundary condition for the 45 degree model has to be meshed finer along the symmetry axis to avoid clustering of heat which can be seen in some temperature contours, or other discrepancies that should not appear there, it also affects the convergence and can cause a simulation to crash in some cases. This was done later on in the CFD process when the problem was identified, and should be noted for future mesh

41 generation of similar bodies. The results of the CFD simulations are deemed correct enough for this initial study. Some quality and trust parameters of the CFD can be discussed, the y+ value increases with the Mach number as expected but is still within reasonable limits at the highest flow velocity which indicates a well meshed boundary layer. As mentioned before, the discretization of the rest of the domain should be studied in more detail, especially close to the nozzle around the symmetry axis. Misunderstandings or mistakes in the setup can be a source of error since this is a very complex task. The lack of previous experience in DLR-Tau is also a factor that should be taken into account. The data obtained can be compared to CFD studies of SRP in Earth atmosphere, such as the DLR study mentioned [8] in section 8.2.4, where comparable results in terms of flow fields etc. can be found even though the atmospheres are very different. Since there is very limited amounts of published flight data for SRP available, it is difficult to find experimental data to compare with. The paper from NASA in collaboration with SpaceX [17] claims to examine flight data from Falcon 9 in Mars relevant conditions, in the Earths atmosphere, but since the actual data is edited out in that particular paper not many conclusions can be drawn. The work process has to a large content consisted of CFD set up and simulations, and due to the complex flow and high velocities it has taken large amounts of both time and computer power to get correct results. Many attempts finally resulted in a work flow where one steady simulation of a point on the trajectory could be fully calculated within 24 hours. The thrust level and outputs of the CFD, which can be found in table 10, can for example be updated by changing the velocity at a point and running the simulation again. The method of iterating between CFD in DLR-TAU, trajectory calculations in ASTOS and CAD design updates in CATIA has worked well even though the ASTOS part was minimal in this case due to the time limitation. However, since the set up and simulation of the CFD part is the most extensive and time consuming it took quite some time and research just to obtain the first results. Since there was no real trajectory to follow from the beginning, a lot of assumptions and good guesses had to be set in order to move forward and start running the tests. Now, that there is a more clear understanding of the problematic areas in the set up of the CFD, and the first set of results are done, the process can be accelerated. All data, results, set ups of simulations, vehicle designs, propulsion models etc. are stored at ESA and used as a stepping stone for continuing this optimisation process. The first iteration is the most difficult due to the many mission constraints and ideas that need to be discussed and decided on. Since this was first and foremost an aerodynamic study, simplifications at the expenses of other areas had to be made.

10.1 Future work The engine start up is the most critical stage, and it would therefore be the most useful and interesting part to investigate in more detail. More results of engine start up conditions would also affect the available SRP range, which could be altered in a future study. It would also be useful to further the model in EcosimPRO, test different parameters of the propulsion system to optimise the fuel, mass and pressure levels in the chamber to minimise the weight. The CAD model could then be refined with a more detailed propulsion system integrated in the body, with chambers, tanks etc. This would make it possible to simulate sloshing and other engine properties in both the CFD environment and in EcosimPRO. The next thing to add in the optimisation process, after ASTOS is completed for this iteration, is input from GNC is some way. The question of gimbaling of the nozzles must be addressed. Also, the configuration of the engines and nozzles would have to be looked into, maybe a set of 12 or 16 smaller nozzles are advantageous in terms of steering, recovering from angle of attack and safety. The GNC requirements will

42 have a large influence on the vehicle design and propulsion system. The heat shield could both be put in the design optimisation, to optimise the diameter, or it could be held constant and instead investigate how to deflate or jettison it once the SRP phase begins, or conclude that it should be kept inflated until landing.

43 11 Cited Literature

References

[1] Guillermo Ortega Hernando. Mission Scenarios and Vehicle Design Document - 2002. ESA ESTEC. [2] Jan Ostlund. SUPERSONIC FLOW SEPARATION WITH APPLICATION TO ROCKET ENGINE NOZZLES - 2004. Stockholm Royal Institute of Technology. [3] George P. Sutton and Oscar Biblarz. Rocket Propulsion Elements. 7th Edition. [4] Ashley M. Korzun1, Robert D. Braun1, and Juan R. Cruz2. Survey of Supersonic Retropropulsion Technology for Mars Entry, Descent, and Landing - 2008. (1) Georgia Institute of Technology and (2) NASA Langley Research Center. [5] ISECG International Space Exploration Coordination Group. Global Exploration Roadmap - 3rd Edition - 2018.

[6] Max Braun, Paul Bruce, and Errikos Levis. Strategies to Utilise Advanced Heat Shield Technology for High-Payload Mars Atmospheric Entry Missions - 2017. Imperial College London. [7] Robert J. McGhee. EFFECTS OF A RETRONOZZLE LOCATED AT THE APEX OF A 140 BLUNT CONE AT MACH NUMBERS OF 3.00, 4.50, AND 6.00 - 1971. NASA Langley Research Center. [8] Tobias Eckery 1, Franziska Zilkery 1, Etienne Dumont 1, Sebastian Karly 1, and Klaus Hannemanny 1. AEROTHERMAL ANALYSIS OF REUSABLE LAUNCHER SYSTEMS DURING RETRO-PROPULSION REENTRY AND LANDING - 2018. (1) German Aerospace Center (DLR). [9] Robert D. Braun1, Brandon Sforzo2, and Charles H. Campbell3. Advancing Supersonic Retropropulsion Using Mars-Relevant Flight Data: An Overview - 2017. (1)University of Colorado at Boulder, (2) Georgia Institute of Technology, (3) Lyndon B. Johnson Space Center. [10] Jan Ostlund¨ 1. Flow Processes in Rocket Engine Nozzles with Focus on Flow Separation and Side Loads. - 2002. (1) KTH Royal Institute of Technology. [11] Torsten Wintergerste 1 Michel Casey 1. Flow Processes in Rocket Engine Nozzles with Focus on Flow Separation and Side Loads. - 2002. (1) Fluid Dynamics Laboratory Sulzer Innotech. [12] V.G Perminov. The diﬃcult road to Mars - A brief history of Mars exploration in the Soviet Union - 1999. NASA History division. [13] Robert J. Parks. Astronautical Research - Mariner 9 and the Exploration of Mars - 1972. NASA - Jet Propulsion Laboratory. [14] A. Chicarro, P. Martin, and R. Trautner. The Mars Express Mission: An Overview - 2003. ESA ESTEC.

44 [15] NASA. InSight - Entry, Descent and Landing. https://mars.nasa.gov/insight/timeline/landing/entry-descent-landing/.

[16] David W. Way1, Richard W. Powell1, Allen Chen2, Adam D. Steltzner2, A. Miguel San Martin2, P. Daniel Burkhart2, and Gavin F. Mendeck3. Mars Science Laboratory: Entry, Descent, and Landing System Performance - 2006. (1)NASA Langley Research Center, (2) NASA Jet Propulsion Laboratory, (3) NASA Johnson Space Flight Center .

[17] Karl T. Edquist1, Ashley M. Korzun1, Karen L. Bibb1, Daniel G. Schauerhamer 2 Edward C. Ma3, Peter L. McCloud 4, Grant E. Palmer 5, and Joshua D. Monk5. Comparison of Navier-Stokes Flow Solvers to Falcon 9 Supersonic Retropropulsion Flight Data - 2017. (1)NASA Langley Research Center, (2) MRI Technologies, (3) Jacobs Technology, (4) ERC Inc., (5) Analytical Mechanics Associates Inc. [18] Dr. Guillermo Ortega Hernando1, Alvaro Martinez Barrio1, and Michael Khan2. TRAJECTORY ANALYSIS OF MARTIAN ENTRY PROBES FOR THE ESA EXPLORATION PROGRAM - 2002. (1) ESA ESTEC, (2) ESA ESOC.

[19] Walter E. Bruce1, Nathaniel J. Mesick1, Paul G. Ferlemann1, Paul M. Siemers2, Joseph A. Del Corso1 Stephen J. Hughes1, Steven A. Tobin1, and Matthew P. Kardell3. AEROTHERMAL GROUND TESTING OF FLEXIBLE THERMAL PROTECTION SYSTEMS FOR HYPERSONIC INFLATABLE AERODYNAMIC DECELERATORS - 2012. (1) NASA, (2) Analytical Services and Materials, Inc., (3) Boeing Technology Services. [20] Alicia D. Cianciolo1, Thomas A. Zang1, Ronald R. Sostaric2, and M. Kathy Mcguire3. OVERVIEW OF THE NASA ENTRY, DESCENT AND LANDING SYSTEMS ANALYSIS EXPLORATION FEED-FORWARD STUDY - 2011. (1)NASA Langley Research Center, (2)NASA Johnson Space Center, (3) NASA Ames Research Center.

45 Appendices

A I General 1D rocket nozzle equations

Ae Expr = At r Atp0 γ γ + 1 − γ+1 m˙ = √ ( ) 2(γ−1) T0 R 2

γ−1 2 Ae γ + 1 − γ+1 1 + Me γ+1 = ( ) 2(γ−1) ( 2 ) 2(γ−1) At 2 Me

Te γ − 1 2 −1 = (1 + Me ) Ttot 2

pe γ − 1 γ 2 − γ−1 = (1 + Me ) ptot 2 p ue = Me γRTe

F =mu ˙ e + (pe − p∞)Ae

F I = sp mg˙

Z landing Ft mfuel = dt ignition Isp · g

46 II Validation case data

47 B I Reference atmospheric conditions

48 II Collected data

49 50 Inertia matrix and axis system in relation to the body.