numerical simulations of the apollo 4 reentry trajectory

154 Pages·2014·9.27 MB·English

ARISTOTLE UNIVERSITY OF THESSALONIKI AND
´ ´ ´
ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
MASTER THESIS
NUMERICAL SIMULATIONS
OF THE APOLLO 4
REENTRY TRAJECTORY
A thesis submitted in fulfillment of the requirements
for the degree of Master of Mechanical engineering
Author’s name:
Ermioni Papadopoulou
Supervisors:
Dr. Penelope Leyland
Nikhil Banerji
Elise Fay
Lausanne, Suisse, March 2013

Acknowledgments
During this project there have been numerous people that contributed time and thoughts
in order the present work to be fulfilled. My thanks are addressed to:
Dr. PenelopeLeyland,whoallowedmetoworkonthisprojectasamemberoftheInterdis-
ciplinaryAerodynamicsGroup(IAG)andherdedicationandhelpthroughouttheproject.
My colleagues and friends, Nikhil Banerji, for his supervision and moral support, Rik Ge-
uns, Jeremy Mora-Monteros, Elise Fay, Oleg Kotsur, Gennady Plyushchev, for the every
day support and the good times we spent in and out of the office and Angelo Casagrande
for his support and patience.
Special thanks should be addressed to my supervisor in Greece, Prof. Anestis I.Kalfas, for
giving me this opportunity to do my Master’s thesis in EPFL and for his constant control
and support for this project.
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Abstract
Sample return capsules, as the Apollo Command Module have been widely used to ad-
vance the knowledge and planning of manned lunar and planetary return missions. Such
reentry vehicles undergo extreme thermal conditions, caused by shock-heated air during
their super-orbital atmospheric re-entry. Such extreme conditions can result in failure of
the aeroshell structure and loss of important payload. This technological challenge is ad-
dressed by the use of ablative thermal protection systems (TPS), which dissipate the heat
away from the vehicles front wall via ablative products release into the boundary layer.
Additionally, such velocity and temperature magnitudes during reentry conditions intro-
duce significant radiative heat loads, filling the shock layer with radiators that react with
the ablative species injected by the capsule wall.
Therefore, accurate numerical modeling techniques are required, so that the thermophys-
ical, thermochemical environment of a reentry capsule can be successfully reproduced
and predicted. The present work aims to numerically rebuild certain significant trajectory
points, containing the peak heating points of the Apollo 4 terrestrial re-entry. This re-
quires the coupling of the resolved flow-field with radiative and ablative effects in order
to accurately predict the convective and radiative heat flux for each trajectory point. The
results will be compared to previous calculations and existing flight data.
The numerical simulations are performed in 2D thermal non-equilibrium with a compress-
ible explicit Navier-Stokes solver, coupled to a radiation database and a thermal material
responsecodetoimplementtheablativeeffects.Thecalculationsareperformedalsoin3D,
using a commercial implicit Navier-Stokes solver. The results will be used to reproduce
the capsules trajectory and verify the accuracy of the associated Modeling Tools.
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Contents
Acknowledgments iii
Abstract v
Contents vii
List of Figures xi
List of Tables xv
1 Introduction 1
1.1 The Arc Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Reentry flight missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Applied Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Scope and Overview of the present dissertation . . . . . . . . . . . . . . . . 2
I Theory 5
2 Theoretical Background 7
2.1 Hypersonic Flow-fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Stagnation flow-field properties . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 The shock-standoff distance . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Aerothermodynamics of hypersonic flights . . . . . . . . . . . . . . . . . . . 8
2.2.1 Stagnation region flow-field and thermodynamic state . . . . . . . . 9
2.3 Investigation of Reentry Shock Layers . . . . . . . . . . . . . . . . . . . . . 12
2.4 The Apollo Command Module Mission . . . . . . . . . . . . . . . . . . . . . 13
3 Equations and Methods 17
3.1 Compressible Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . 17
3.2 Implemented equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
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Contents Contents
3.2.1 Axisymmetric 2D flows- Two temperature thermodynamic model . . 19
3.2.2 Three-Dimensional Flows . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Numerical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.1 Finite volume Method . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.2 Time stepping procedure . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3.3 Time discretization method . . . . . . . . . . . . . . . . . . . . . . . 25
3.3.3.1 Explicit Method . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3.3.2 Implicit Methods . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.5 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.6 Thermochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.6.1 Chemical modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.6.2 Chemical Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.6.3 Transport properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.7 Heat transfer modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.7.1 Convection Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.7.2 Radiation Transport Modelling . . . . . . . . . . . . . . . . . . . . . 35
3.7.2.1 Radiation Source Term . . . . . . . . . . . . . . . . . . . . 36
3.7.3 Flow-field Radiation coupling . . . . . . . . . . . . . . . . . . . . . . 37
3.7.3.1 Transport models . . . . . . . . . . . . . . . . . . . . . . . 37
II Numerical Simulations in 2D 43
4 Simulations in 2D 45
4.1 Eilmer3: The code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1.1 Simulation procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 Results Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.1 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.2 Comparative results for one trajectory point. . . . . . . . . . . . . . 48
4.2.2.1 Flow-field results . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.2.2 Heat flux calculations . . . . . . . . . . . . . . . . . . . . . 51
4.2.2.3 Radiation Calculations . . . . . . . . . . . . . . . . . . . . 53
4.2.3 Trajectory points comparison . . . . . . . . . . . . . . . . . . . . . . 59
4.2.4 Validation of the results . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.4.1 Semi-empirical correlations . . . . . . . . . . . . . . . . . . 62
4.2.4.2 Bertin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.4.3 Fay-Riddel . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.4.4 Martin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2.4.5 Tauber-Sutton . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2.4.6 Results Discussion . . . . . . . . . . . . . . . . . . . . . . . 65
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Contents Contents
IIINumerical Simulations in 3D 67
5 Simulations in 3D 69
5.1 General Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.1.1 Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2.1 Geometry Configuration . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2.2 Mesh Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2.2.1 Fore-Body . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2.2.2 Whole Body . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.3 Fore-Body Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3.1 CFD++ Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.1.1 Viscous Flow- Perfect gas model . . . . . . . . . . . . . . . 86
5.3.1.2 Real 5-species equilibrium gas model. . . . . . . . . . . . . 88
5.3.1.3 Real 5-species non-equilibrium gas model . . . . . . . . . . 90
5.3.1.4 Real 11-species equilibrium gas model . . . . . . . . . . . . 93
5.3.1.5 Real 11-species non-equilibrium gas model . . . . . . . . . 95
5.3.1.6 Overview of CFD++ simulations results . . . . . . . . . . 96
5.3.2 NSMB Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3.2.1 Equilibrium gas model . . . . . . . . . . . . . . . . . . . . 99
5.3.2.2 Chemical non-equilibrium gas model . . . . . . . . . . . . . 101
5.3.2.3 Thermal and chemical non-equilibrium gas model . . . . . 105
5.3.2.4 Overview of the NSMB simulations . . . . . . . . . . . . . 106
5.3.3 Comparison of the two solvers. . . . . . . . . . . . . . . . . . . . . . 106
5.4 Whole Body Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.4.1 Equilibrium gas model . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.4.2 Thermal Non-Equilibrium gas model . . . . . . . . . . . . . . . . . . 113
IVConclusion 115
6 Conclusions and Recommendations 117
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Bibliography 121
A Contours 3D Simulations 1
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