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• TRAJ, an established trajectory simula4on tool successfully modified for meteor entries • Improvements include:
• Simple mass loss equa4on of meteor physics • Time-‐varying heat transfer coefficient based on detailed flow computa4ons • Ability to specify fragmenta4on events
• Updated version of TRAJ tested against Chelyabinsk observa4ons • TRAJ can now be used to establish sensi4vity of trajectories to various meteor parameters • Leaves open the issue of verifica4on/valida4on of TRAJ and addi4onal test cases are needed
• Could tek4tes [4] be used as addi4onal test cases? • Advantages of simula4ng tek4te entries into Earth’s atmosphere
• Exo-‐atmospheric shapes are definitely spherical • Small sizes and (sub)orbital entry veloci4es • Problem is dominated by convec4ve hea4ng and mel4ng • Melted shapes are aerodynamically stable • Chemical composi4on of australite tek4tes is sta4s4cally well defined • Serve as a good founda4on for the tougher meteor entry problem
0
0.02
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0.1
0 20 40 60 80 100
Ch
Alt, km
Ch vs. AltitudeV = 16 km/sec, Base Diameter = 10 m
raw dataf(x)
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1.29e+07 1.292e+07 1.294e+07 1.296e+07 1.298e+07 1.3e+07 1.302e+07
Altit
ude,
km
Mass, kg
Mass vs. Altitude
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0 2e+06 4e+06 6e+06 8e+06 1e+07 1.2e+07 1.4e+07
Alti
tude
, km
Mass, kg
Mass vs. Altitude
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0 1 2 3 4 5 6 7 8 9 10
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ude,
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Meteor Radius, m
Meteor Radius vs. Altitude
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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Alti
tude
, km
Ch, Heat Transfer Coefficient
Heat Transfer Coefficient vs. Altitude
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0 500000 1e+06 1.5e+06 2e+06 2.5e+06 3e+06 3.5e+06
Altit
ude,
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Radiative Heat Flux, watts/cm^2
Stagnation Point Radiative Heat Flux versus Altitude
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0 5 10 15 20 25
Altit
ude,
km
Velocity, km/sec
Altitude versus Velocity for Chelyabinsk Fragmented MeteorCompared to Heat Transfer Coefficient Data PointsChelyabinsk Observed
Case 2_ACase 2_BCase 2_CCase 2_D
Heat Transfer Coef.
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0 5 10 15 20 25
Altit
ude,
km
Velocity, km/sec
Altitude versus Velocity Chelyabinsk Single Body MeteorCompared to Heat Transfer Coefficient Data Points
Stardust AeroshellChelyabinsk Observed
Case 1_ACase 1_BCase 1_C
Heat Transfer Coef.
Gary A. Allen, Jr., Dinesh K. Prabhu, and David A. Saunders ERC, Inc. at NASA Ames Research Center, MoffeC Field, CA 94035, USA
1st InternaLonal Workshop on PHA CharacterizaLon, Atmospheric Entry and Risk Assessment 7 – 9 July 2015, NASA Ames Research Center, California
Trajectory SimulaLon of Meteors Assuming Mass Loss and FragmentaLon
Trajectory Simulation Process with Meteor Physics Equations
Entry State (t = 0) (Velocity, Entry AlLtude, Entry Angles, Geographic LocaLon, Meteor Shape, Size and Mass)
Meteor Shape(s) (Tabulated or Newtonian
Aerodynamic Model, Surface Recession, Fracture and Breakup)
Heat Flux Environment (ConvecLve and RadiaLve Heat Flux Modeled as Heat Transfer
Coefficient, CH )
Mass Loss (AblaLon, SublimaLon and
MelLng)
Trajectory (Single or MulLple Bodies
traversing over an Oblate Earth with J2 harmonic and tabulated
atmospheric model)
dmm
dt= −
12ρaum
3 CHAmQ
AmA0
=mm
m0
!
"#
$
%&
2/3
Sensitivity to Basic Assumptions: Entry Mass, Fragmentation, Heat Transfer Coefficient and Heat-of-Ablation
Mass Change EquaLon Shape Change EquaLon (assuming spherical meteor)
Case 2_A: Single fragmenta4on event at 40 km, and CH = 0.1 Case 2_B: Two fragmenta4on events at 40 & 30 km, and CH = 0.1 Case 2_C: Single fragmenta4on event at 40 km, and CH 4me varying Case 2_D: Two fragmenta4on events at 40 and 30 km, and CH 4me varying For Cases 2_A – 2_D: Meteor radius: 3.5 m at 40 km alt. Revised mass: 5.93 x105 kg For Cases 2_B & 2_D: Meteor radius: 0.7 m at 30 km alt. Revised mass: 4.74 x103 kg
Conclusions, Future Work and References
References: 1. Gary A. Allen, Jr., Michael J. Wright, and Peter Gage, “The Trajectory Program (Traj): Reference Manual and User's Guide,” NASA TM-‐2004-‐212847, 2005. 2. Michael E. Tauber, Paul Wercinski, Lily Yang, and Yih-‐Kanq Chen, “A Fast Code for Jupiter Atmospheric Entry Analysis,” NASA/TM-‐1999-‐208796, September 1999. 3. Jiri Borovicka, et al., “The trajectory, structure and origin of the Chelyabinsk asteroidal impactor,” Nature, 503, 235-‐237, 14 November 2013. 4. George Baker, “Structures of Well Preserved Australite Bunons from Port Campbell, Victoria, Australia,” Meteori2cs, 3(4), December 1967.
Introduction and Objective
• NASA’s Galileo probe to Jupiter only one that experienced significant mass loss • Entry capsule was a 45° sphere-‐cone with fully-‐dense carbon phenolic as heatshield material • M. Tauber et al. [2] developed JAE code for simula4on of Galileo probe (Jupiter entry) • JAE logic incorporated into Traj
– Sphere-‐cone shape replaced by sphere – Mass loss equa4on of meteor physics used – Allow input specifica4on of heat of abla4on, Q – Allow heat transfer coefficient to vary in 4me – Time-‐varying heat transfer coefficients from detailed flow computa4ons curve fit as a func4on of al4tude, velocity, and size
Modifications Made to TRAJ for Meteor Simulation
TRAJ Features: • Program used to simulate atmospheric flight trajectories of entry capsules [1] • Includes models of atmospheres of different planetary des4na4ons – Earth, Mars, Venus, Jupiter, Saturn, Uranus, Titan, … • Solves 3-‐degrees of freedom (3DoF) equa4ons for a single body treated as a point mass • Also supports 6-‐DoF trajectory simula4on and Monte Carlo analyses • Uses Fehlberg-‐Runge-‐Kuna (4th–5th order) 4me integra4on with automa4c step size control • Includes rota4ng spheroidal planet with gravita4onal field having a J2 harmonic • Includes a variety of engineering aerodynamic and heat flux models • Capable of specifying events – heatshield jeuson, parachute deployment, etc. – at predefined al4tudes or Mach number • Has material thermal response models of typical aerospace materials integrated
Modify trajectory simulaLon tool, TRAJ, to make it suitable for meteor entries including mass loss & fragmentaLon
t = Time A0 = Cross sec4onal area at entry mm = Mass at 4me t um = Rela4ve velocity at 4me t ρa = Atmospheric density 4me t Q = Heat of abla4on CH = Heat transfer coefficient
Heat Transfer Coefficient, CH, Model
• Curve fit expressions are to be used for z > 15. 5 km • CH for different veloci4es and diameters obtained through linear interpola4on!
CH (z) = a+ b z - c( )d!"
#$ exp - z - c
f%
&'
(
)*
An example “quality of fit” plot generated with curve fit .
Test Case: Chelyabinsk [3]
Basic AssumpLons:
Hyperbolic excess velocity: 15.0 km/s Al4tude at entry: 95.0 km Rela4ve velocity at entry: 19.0 km/s Rela4ve entry angle: -‐18.5 deg Rela4ve heading angle: -‐76.6 deg Geographic la4tude at entry: 54.5 deg
Oblate rota4ng Earth Gravita4onal model includes J2 term
US-‐1976 atmospheric model Meteoroid AssumpLons:
Shape: Sphere Density of meteoric material: 3300 kg/m3 Aerodynamic model: Sphere SensiLvity study to entry mass, heat transfer coefficient, heat of ablaLon, and fragmentaLon
Case 1_A: Single body with CH = 0.1 Case 1_B: Single body with 4me varying CH Case 1_C: Time varying CH for a single body. Entry mass and heat of abla4on tuned to overlay Chelyabinsk observa4ons
Entry mass: 13 x106 kg Meteor radius at entry: 9.8 m Heat-‐of-‐Abla4on: 8 MJ/kg
Entry mass: 6.8 x104 kg Meteor radius at entry: 1.7 m Heat-‐of-‐Abla4on: 0.85 MJ/kg
Basic Plots for Variable CH and Double Fragmentation (Case 2_D)
• For Case 2_D simula4on fragmenta4on at 40 & 30 km al4tudes assumed to occur instantly
• Fragment masses tuned to overlay simulated trajectory on Chelyabinsk observa4ons.
• On a scale of 40 to 90 km al4tude, mass vs al4tude trace appears to be a straight line over the en4re mass range
• Trace is actually parabolic when mass scale is expanded
• Influence of CH model is insignificant if large changes occur in meteor mass due to fragmenta4on.
Recovered australite tek4te
The present work was supported by NASA contract NNA10DE12C to ERC, Inc.
• Myriad ways to fit observa4ons by choice of model parameters and fragmenta4on events • Problem compounded by the fact that exo-‐atmospheric dynamical mass not known precisely
https://ntrs.nasa.gov/search.jsp?R=20150022896 2018-06-30T03:20:09+00:00Z
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