1. Sebastian Höfner, H. Sierks, J.B. Vincent, J. Blum
Thermal Analysis of surface and Interior A 3D Thermal model approach to Lutetia and CG
Sebastian Höfner, H. Sierks, J.B. Vincent, J. Blum
Osiris Full Team Meeting
Max-Planck-Institut für Sonnensystemforschung, Katlenburg-Lindau

2. Outline Motivation: thermophysical processes in nucleus active regions
Thermal analysis software: ESATAN TMS
Description of the modeling method
Lutetia thermal analysis
CG simple thermal analysis (without sublimation)

3. Motivation
Setup of a 3D thermophysical model of a universal comet nucleus model
Focusing on active region modelling
including surface geometry and internal/external radiative heat exchange
gas production and its contribution to dust jet formation
Structures and mass loss
First step: Nucleus thermal analysis with commercial software ESATAN-TMS

4. Thermal analysis software tool (spacecraft industry)
ESATAN TMS
Thermal analysis software tool
(spacecraft industry)
Step 1: Calculating the radiative coupling between facets and the solar irradiation via Monte-Carlo Ray Tracing
Step 2: Solving the heat balance equation via a lumped parameter model discretization
Convection and Phase-Change modeling possible
Capacity
Conduction
Radiation
Source Term: Solar Irradiation

5. Surface radiative interaction
3D Modeling Method
Surface cross-section
Model approach with differentiated depth layers
Radiative Exchange
with environment
Radiative and conductive
layer exchange
Conductive exchange
Boundary coupling
Increasing
thermal
inertia
Grains
Void
Lutetia CG
Thermophysical properties
0-10 mm
10+ mm
Albedo
[ - ]
0.073
0.032
Emissivity
0.97
Surface thermal inertia
[ J / Km²s^(-0.5) ] 25
325 10
Bulk density
[ kg / m³ ]
1020
2040
350
Heat capacity
[ J / kgK ]
1000
778
Conductivity
[ W / mK ]
0.0004
0.008
Surface roughness factor
1.2 --
Layer view factor
0.2
0.15
Surface radiative interaction
(e.g Massilia Crater)

6. Surface Thermal Wave
Temperature [K]

7. Surface Thermal Wave
Irradiation [W/m²]
30 deg steps
Temperature [K]

8. Location: Massilia Crater
Temperature wave [K] in different layer depths for a rotational period [h] Thermal gradient for seven time steps [h]
Thermal surface wave lag: 0.2h
Thermal wave lag
for 10mm depth: 4.5h
Temperature [K]
Temperature [K]
Thermal wave
amplitude in
10mm depth: 2.5 K
Rotational period [h]
Layer depth [mm]
Ruling thermal fluxes [W/m²] for one rotational period [h]
Location: Massilia Crater
Heat Fluxes [W/m²]
Rotational period [h]
Rotational period [h]

9. Ruling thermal fluxes [W/m²] for one rotational period [h]
Temperature wave [K] in different layer depths for a rotational period [h] Thermal gradient for seven time steps [h]
Temperature [K]
Temperature [K]
Rotational period [h]
Layer depth [mm]
Ruling thermal fluxes [W/m²] for one rotational period [h]
Rim near Northern Pole
Heat Fluxes [W/m²]
Rotational period [h]
Rotational period [h]

10. VIRTIS Temperature Mapping

11. Temperature wave [K] in different layer depths for a rotational period [h]
Survey of facet 3730 in the equatorial zone
2 AU
Temperature [K]
Rotational period [h]
Hot spot in crater rim: 321K (48 °C)
1.5 AU
Temperature [K]
Hot spot in crater rim: 325K (52 °C)
Rotational period [h]

12. Thank you for your Attention
Any questions?
Marc Hofmann - Granular flow in low gravity space environment

13. Emitted Radiative Intensity
Sublimation Problem
Temperature
Vapor Pressure
Sublimation Rate
Sublimation Enthalpy
Emitted Radiative Intensity T Pv Z
LZ(T) I
[ K ]
[ N / m² ]
[ kg / m²s ]
[ W / m² ]
150
5.1E-06
2.5E-10
6.9E-05
2.8E+01
160
6.7E-05
3.1E-09
8.7E-04
3.6E+01
170
6.4E-04
2.9E-08
8.1E-03
4.6E+01
180
4.8E-03
2.1E-07
5.9E-02
5.8E+01
190
2.9E-02
1.2E-06
3.5E-01
7.2E+01
200
1.5E-01
6.2E-06
1.7E+00
8.8E+01
210
6.4E-01
2.6E-05
7.3E+00
1.1E+02
220
2.4E+00
9.7E-05
2.7E+01
1.3E+02
230
8.2E+00
3.2E-04
8.9E+01
1.5E+02
240
2.5E+01
9.5E-04
2.7E+02
1.8E+02
250
7.0E+01
2.6E-03
7.3E+02
2.1E+02
260
6.6E-03
1.8E+03
2.5E+02
270
4.4E+02
1.6E-02
4.4E+03
2.9E+02
280
9.9E+02
3.5E-02
9.7E+03
3.4E+02
290
2.1E+03
7.3E-02
2.0E+04
3.9E+02
300
4.3E+03
1.4E-01
4.1E+04
4.5E+02
310
8.3E+03
2.8E-01
7.7E+04
5.1E+02
320
1.5E+04
5.1E-01
1.4E+05
5.8E+02
330
2.8E+04
8.9E-01
2.5E+05
6.5E+02
340
4.8E+04
1.5E+00
4.3E+05
350
8.0E+04
2.5E+00
7.1E+05
8.3E+02