Case Studies for Uncertainty Quantification of a High-fidelity Spacecraft Oriented Break-up Tool Bent Fritsche, HTG Stijn Lemmens, ESA 8th European Symposium on Aerothermodynamics for Space Vehicles Lisbon, March 5, 2015
Re-entry Analysis Tools Object oriented approach S/C oriented approach Modeling the S/C as a set of simple geometric objects (spheres, cylinders, plates, and boxes), parent object as a container for the internal S/C components Modeling the S/C as close as possible to the real design as one consistent object with a panelized geometry model Aerodynamic analysis based on the aerodynamic parameters of the simple geometric shapes Aerodynamic analysis based on the actual aerodynamic parameters of the real geometry Dynamic analysis simplified to assumed stable attitude motion (3 DoF equations of motion), ballistic re-entry Full dynamic analysis for re-entry trajectory and attitude motion (6 DoF equations of motion) Aerothermal analysis for each object separately, heating based on shape specific heat transfer coefficients Aerothermal analysis for the complete panelized geometry, panel-wise melting analysis Fragmentation analysis with assumed break-up altitude or subsequently calculated exposure altitudes for internal objects Fragmentation analysis based on stress and structural integrity checks Page 2
Simulation uncertainties (selection) Model uncertainties (systematic/epistemic) Modeling: Considered details Flight dynamics: Integrator (step size, order) Aerodynamics: Force/torque coefficients Aerothermodynamics: Heat transfer coefficients Thermal analysis: Material data, heat exchange modeling Structural analysis: Material data, Stress calculation Tank analysis: Material data, sloshing Input uncertainties (statistical/aleatoric) Initial conditions (position, velocity, attitude) Environment (atmospheric conditions, solar activity, wind) Page 3
Case studies Three of our studies in the past were concerned with uncertainty quantification: 1. RADR: Risk Assessment for Destructive Re-entry 2. UQ4AERO: Uncertainty Quantification for Aerospace Applications 3. CLUINT: Cluster/Integral re-entry study Page 4
RADR Risk Assessment for Destructive Re-entry Influence determination of uncertainty parameters on risk prediction Atmospheric density and wind models (and related influence parameters such as date, daytime, solar activity) Aerodynamic (drag and lift) and aerothermodynamic (convective heating) models Dynamic models (attitude motion) Thermal models (convective/solar radiation heating and melting) Fragmentation models Other parameters (e.g. orbit inclination, fuel loading) Identification of possible risk mitigation measures Recommendations for the risk assessment process within ESA Page 5
RADR: Method Simulation codes: SCARAB (6D) and SESAM (3D) Modeling of three spacecraft (to be representative for uncontrolled (UNC) and controlled (CON) re-entry plus a rocket upper stage (Delta)) Simple sensitivity study for selected parameter (few samples/parameter) Page 6
SCARAB UNC Model Mass budget and subsystem composition based on available data for GOCE, BeppoSAX, and TerraSAR-X (all scientific satellites in the 1 ton class) Page 7
SCARAB CON Model Mass budget and subsystem composition based on available data for GOCE, BeppoSAX, and TerraSAR-X (all scientific satellites in the 1 ton class) with scaling factors according to ROSAT (2.4 tons) Initial fuel loading: 720 kg (270 kg MMH, 450 kg NTO) Final de-orbit fuel: 103 kg (39 kg MMH, 64 kg NTO) Main engine: thrust 400 N, specific impulse ~285 s Final thrust maneuver: 720 s firing (after perigee lowering, deorbit firing until tanks are empty) Page 8
SCARAB Delta-II Second Stage Model Dry mass: 925 kg Length: 6.3 m Diameter: 1.7 m (main tank) 2.4 m ( mini-skirt ) Page 9
Variation Cases (SCARAB) Page 10
Results: Ground Risk Standard Deviation Matrix Page 11
Results: Influence Factor Categories 4 categories for the influence factors were introduced: Negligible Small (<5% margin of deviation w.r.t. ground risk) ( 5% <10% margin of deviation w.r.t. ground risk) Medium ( 10% <35% margin of deviation w.r.t. ground risk) Large ( 35% margin of deviation w.r.t. ground risk) Page 12
UQ4AERO Uncertainty Quantification for Aerospace Applications Simulation code: SCARAB Implementation of a multi-level driver link to the DAKOTA UQ S/W Modeling of two satellites (1 burning up and 1 surviving re-entry) Assessment of uncertainty for selected parameters, using - Parameter variation, Monte-Carlo analysis, Polynomial chaos for selected aleatoric parameters - Parameter variation for selected epistemic parameters Page 13
Satellite models Model 1: CubeSat 2U Small satellite (Dimensions: 20x10x10cm, 2kg) Burning up during re-entry (no surviving fragments) Model 2: TestSat Generic type of medium-sized satellite (1 ton class) Some fragments survive the re-entry Page 14
SCARAB CubeSat Model CubeSat: External shape and dimensions fixed by CubeSat specifications Internal structure variable, only limited by total weight For the analysis some arbitrary contents were defined: - 8 printed circuit boards - 2 payload blocks Page 15
SCARAB test case satellite model TestSat: Generic type of medium-sized satellite (1 ton class) Used as tutorial case for learning satellite modelling with SCARAB Consist all major types of elements of such a satellite: - External structure - Internal (web) structure - Solar panels - Antennas - Electronic boxes - Fuel and gas tanks Page 16
Parameter variation methods CubeSat: Aleatoric parameters (Initial conditions) Parametric variation Monte-Carlo analysis Polynomial Chaos Expansion Epistemic parameters (Aero/thermal settings): Parametric variation TestSat: Aleatoric parameters (Initial conditions): Polynomial Chaos Expansion Epistemic parameters (Aero/thermal settings): Parametric variation Page 17
Distributions of initial orbital elements Page 18
Parametric variation: Parameter selection summary 1. Semi-major axis: Computed 2. Eccentricity: Prescribed/Computed 3. Inclination: Fixed at 79 4. RAAN: Varied from 0 to 360 in steps of 15 5. AoP: Varied from 0 to 360 in steps of 15 6. True Anomaly: Fixed at 210 Total number of simulations: 576 (24x24) Page 19
Parametric variation: Time of first fragmentation Page 20
Parametric variation: Time of first fragmentation Page 21
Monte-Carlo analysis: Parameter selection summary 1. Semi-major axis: Sampled from PDF 2. Eccentricity: Computed 3. Inclination: Fixed at 79 4. RAAN: Sampled from uniform distribution 5. AoP: Sampled from PDF 6. True Anomaly: Fixed at 210 Total number of simulations: 576 (t.b. consistent with parametric variation) Page 22
Monte-Carlo analysis: Altitude of first fragmentation Page 23
Monte-Carlo analysis: Altitude of first fragmentation Page 24
Monte-Carlo analysis: Altitude of demise Page 25
Monte-Carlo analysis: Shape parameters and correlations Page 26
Polynomial chaos: Parameter selection summary 1. Semi-major axis: Sampled from PDF 2. Eccentricity: Computed 3. Inclination: Fixed at 79 4. RAAN: Sampled from uniform distribution 5. AoP: Sampled from uniform distribution 6. True Anomaly: Fixed at 210 Total number of simulations: 64 Page 27
Polynomial chaos: Shape parameters for nodes and samples, Sobol indices Page 28
Epistemic parameters Four parameters were selected for the epistemic analysis: 1. Argument of perigee: 30, 120 2. Aerodynamic force factor: 0.8, 1, 1.2 3. Aerodynamic heating factor: 0.8, 1, 1.2 4. Thermal fragmentation model (standard, modified) Total number of simulations: 36 Page 29
Epistemic parameters: Total and partial correlation coefficients Page 30
TestSat simulations Initial state: As for CubeSat, but only PCE (due to higher computational effort) Variation of epistemic variables: As for CubeSat: Aerodynamic force coefficients (80%-120%) Aerodynamic heating (80%-120%) Thermal fragmentation model (standard, modified) Objective functions: First fragmentation: time and altitude Ground impact: Mass and casualty area Page 31
Variation of initial conditions: Mass at ground impact Page 32
Variation of initial conditions: Shape parameters for nodes and samples, Sobol indices Page 33
Variation of epistemic parameters: Total and partial correlation coefficients Page 34
CLUINT Cluster/Integral re-entry study SCARAB re-entry simulations for two satellites on highly eccentric orbits: Cluster (4 satellites), dry mass: 525 kg each Integral, dry mass: 3.3 t Parametric studies for Cluster: Variation of initial attitude (rate) Extra study: 2D variation of initial semi-major axis and perigee height Parametric studies for Integral (a few, not expatiated here) Variation of initial state vector Variation of perigee height Page 35
SCARAB CLUSTER Model Page 36
Re-entry Break-up analysis Simulation procedure 1. Initial orbit states provided by ESOC 2. SCARAB simulation by HTG 3. Final orbit states provided by HTG 4. Orbit propagation by ESOC New perigee pass simulations with final geometry of escaping fragment Page 37
Cluster-II Spin rate analysis Initial conditions Initial orbital conditions: S/C # a [km] e i [ ] RAAN [ ] LOP [ ] 1 71626.8859 0.9093046 125.36463 194.15743 43.52813 2 71588.0310 0.9093638 150.44198 40.47483 257.09064 3 69404.7470 0.9066141 150.37212 51.56964 268.96814 4 72125.8143 0.9099806 150.34353 52.44826 269.86229 Case # Pitch angle [ ] / rate Initial 1 S/C attitude: 64.7 / 0 2 64.7 / 0 Yaw angle [ ] / rate Spin rate [ /s] 102 / 0 116.4 (19.4 rpm) 102 / 0 84 (14 rpm) Page 38
Cluster-II Spin axis pointing analysis Spin axis pointing Sample combinations for spin axis pointing: Right ascension [ ] Declination [ ] 83-56.7 83-64.7 83-72.7 102-56.7 102-64.7 102-72.7 121-56.7 121-64.7 121-72.7 Page 39
Re-entry Break-up analysis Cluster-II Summary 461 SCARAB simulations S/C #1 and #2: final re-entry at 2nd simulated perigee pass S/C #3: complete demise during 6th and 7th perigee pass S/C #4: final re-entry at 121st to 143rd perigee pass Spin axis pointing: S/C #1 & #2: no distinct correlation for particular spin axis orientation & #4: notvelocity relevant at S/C S/C # #3 Avg. max. final re-entry [km/s] Avg. ground fragments Avg. total ground fragment mass [kg] Avg. Casualty area [m²] 1 11.12 6 4.756 3.883 2 11.25 4 1.571 2.943 3 10.4 / 9.7 0 0 0 4 8.55 6 34.850 7.345 Page 40
Second Cluster analysis: Orbit parameter variation Altitude of perigee: 0 km, 5 km,, 100 km Semi-major axis: 6,600 km, 10,000 km, 15,000 km,, 75,000 km 315 SCARAB cases Page 41
Cluster orbit parameter variation Fragment types and demised mass Page 42
Outlook Ongoing studies related to uncertainty quantification with HTG contribution: D4D: Design for demise 3 parallel contracts, lead by Thales-Alenia, Astrium, Deimos HTG is involved in all three studies for re-entry analyses CHARDEM: Characterization of demisable materials Consortium headed by DLR Cologne RADID: Rapid assessment of Design Impact on Debris Generation Contractors: ASTOS and HTG Page 43