finite element based analysis tool for re-entry vehicle tps … · 2005-02-25 · 18th european...

18th European Thermal & ECLS Software

Workshop, ESA-Estec, 5/10/04,

Finite Element Based Analysis Tool For ReFinite Element Based Analysis Tool For Re--entry entry

Vehicle TPS AblatorsVehicle TPS Ablators

1818thth European Thermal & ECLS Software WorkshopEuropean Thermal & ECLS Software WorkshopESAESA--Estec, Noordwijk, The Netherlands.Estec, Noordwijk, The Netherlands.

55--1010--20042004

Tom van Eekelen, Tom van Eekelen, SAMTECH s.a.SAMTECH s.a.


Workshop, ESA-Estec, 5/10/04, Page 2

• Hypersonic re-entry into the atmosphere.

• Convection (v3), Radiation

• TPS is needed to maintain low enough temperature• Speed of re-entry (slow/fast)

• Heating rate

• Heating load

Hea

ting

rate

[W/m

2 ]

Heat load [J/m2]

Ballistic entry

AURORA ERC

Apollo

Space shuttle



• Active systems• Cooling fluid (externally supplied)

• Transpiration/film cooling

• Semi passive systems• Cooling fluid (internally supplied)

• Heat pipes

• Ablators/pyrolysis

• Passive systems• Heat sink

• Insulation

• Re-radiation (hot structure)

• Trade off between:• high heat removal capacity• complexity (possible failure)



• Insulation of the structure • Maximum allowable structural temperature

• Low density (maximum TPS mass)

• Re-radiation into the environment• High allowable wall temperature

• High emissivity

• Good insulation properties

• Pyrolysis• Endothermic chemical reactions (volume)

• Blocking of boundary conditions

• Ablation• Sublimation (surface recession)

• Blocking of boundary conditions

• Low versus high density ablators:• insulation

• recession rate



• Material subjected to degradation ( )

• Density ρ varies between ρv virgin and ρc carbonized state

• Degradation will cause Gas mass flow (mig ).

• Surface ablation (removal of material) will take place ( )

Virgin material

Pyrolysis zone

Carbonized material

4

1

2

3

δ

ρ�

ρv

ρc

1 2 3 δ

ρ



• Heat balance equations:

• Darcy equation:

• Arrhénius equations:

( ) QhmTdt

dhH g

igijijiP +∂−∂∂=+− λρρ

�

( ) ρ�

=∂∂ PK jpi

( ) RTEN

cN

v eA−− −−= ρρρρ 1�



• User defines properties in « virgin » and « charred » state (dependent on temperature and pressure).

• Program calculates material properties during the analysis (as a function of ρ):

• The constitutive equations define the heat and gas mass flux respectively:

PKm jpgi ∂−=Tq jiji ∂−= λ

RT

PMK

g

g

p µβ=

( )ρ,, cv ccfc =( )ρλλλ ,, cvg=

( )ρββ ,vh=



• Three types of ablation can de defined:• Mechanical: (explicit definition of ablation speed)

• Chemical: (explicit definition of ablation speed)

• Phase change: (implicit definition of ablation speed)

• Ablation speed is found to satisfy the thermal equilibrium on the surface. qreaction

is due to maximum phase change temperature (contact)

( ) TT

m

E

ebPas−+= τ

�

( )igicc nmPTss ,,

��

=

( )[ ] reactionphwaph qsHHL =−+�

1ηρ



• Due to ablation, the external surface moves.• Ablation speed perpendicular to external surface

• Mesh moves along « master » lines

• Internal mesh distribution can depend on penetration depth of the temperature

• Two solution strategies:• Convective term added:

• Nodal values re-calculated per time step

y

Tv

x

Tu

dt

dT

Dt

DT

∂∂+

∂∂+=

s�

s�

s�



• Classical boundary conditions ( ); flux, convection,radiation, etc.• Blocking terms due to injection of material into the surrounding:

• Due to Gas flux ( )

• Due to Ablation ( )

• Gas mass flux blocking term:

• Ablation blocking term:

( ) igi nmPTgq ,−≅

( ) ρsPThq�

,−≅Virgin material

Pyrolysis zone

Carbonized material

s�



• Applied flux:• Added flux due to combustion of pyrolysis gas

• Blocking terms due to ablation material

• Convective flux (enthalpy formulation):

• Blocking terms due to ablation material and pyrolysis gas

• The enthalpy Hw(T,P) per unit of fluid mass, is automatically calculated using aMollier diagram

phphcccombigi LsHsHnmq ρρ

��

−−+

( )( )( )waphcigiii HHssnmnq −+−−=

��

ρηηα 12

Additional terms



• 2D/Axis-symmetric finite element mesh with three degrees of freedom per node:

• Temperature (T),

• Pressure (P) and

• Density (ρ)

• Triangular and quadrangular elements• Degree 1 and degree 2 elements

• Fully integrated into SAMCEF Thermal• Steady state & Transient analysis

• Coupling with other elements (3D/Controller)

SAMCEF Amaryllis



• Test specimen subjected to:• External pressure

• Convection (enthalpy form)• Radiation flux (outward)

• Undergoing:• Chemical ablation

1D thickness calculation

• Pyrolysis• N = 3• E = 99768• A = 107

( ) RTe99768327 14001650.10

−− −−= ρρ�

q

x

y 0=∂∂=

∂∂

x

P

x

T

25 N/m 10.3=P

L=10 mm



• Conductivity K and capacity C (“virgin” and “charred”)

• Pressure conductivity Kp

• βv = 7.3881 10-13

• µ = 1 10-4

• Mg = 2.8 10-2


T

P

R

MK

g

p µβ=



• Element distribution:• 25 elements

• 20 elements in a zone of 2.δ(t)

• (δ=penetration depth)

• Blocking terms taken into account:• η1 : blocking due to ablation material

• η2 : blocking due to gas mass flow

• Transient calculation between 0 and 5 seconds.

• Temperature distribution

• at t = 1.0 s




• Temperature/density evolution at ablation front

• Density distribution


• Gas mass flow

Element 1 Comp. 2

mgtime

Node 2

ρ

time

Node 2

T

time

T= 1 s

T= 5 s

ρ

x



• Influence of gas mass flow• Temperature evolution

• Large influence on ablation depth (+12.8 %) via:• Gas flow through charred material.• Blocking of convection load.


• Surface recession S

time

T

mg <> 0

mg <>0, η2 = 0

mg = 0

mg, mg <>0

mg <>0, η2 = 0

mg, mg = 0

ss�

,

s

s�

time



• Ablation of a Carbon sphere

• Material properties for Carbon:• Conductivity

• Capacity• No pyrolysis

2D thickness distribution



• Axis-symmetric mesh• Re-meshing lines

• Mechanical ablation:• Position and time dependent pressure

• A = 1 10-9

• B = 1.

• TE = 300.


10

1

1189

76

54

2

3



• Radiation with the environment + radiation load• TR = 300, σε = 5.103 10-11

• Position dependent

• Time dependent

• Convection load (enthalpy formulation)• Position dependent• Time dependent

• Blocking term η2




• Temperature in section N 176 -> 1

• Temperature distribution at t = 17 s

• Temperature at the outer surface

• Temperature distribution


S <> 0

S = 0

T

time

T

x

S <> 0

S = 0

176 1



• The test specimen subjected to:• Convection (enthalpy form)

• Re-radiation• Chemical ablation

• Combustion heat

• Blocking terms (pyrolysis/ablation)

• Analysis to prepare for material test phase• Density distribution of the virgin material

• Test specimen (ablator)• Side protection (ablator)

• Metal structure

• Moving Contact between different materials

Axis-symmetric test specimen (EADS-ST)



• Pressure at t = 80 s

• Density evolution

• Temperature at t = 80 s

• Temperature evolution

Axis-symmetric test specimen (EADS-ST)



• Ablation and pyrolysis are:• needed for material characterization

• both necessary for Ablation distribution

• SAMCEF Amaryllis:• is capable of modelling 2D/Axis-symmetric structures of practical complexity

• will be used in the AURORA program: Delta Qualification testing of TPS ablators

finite element based analysis tool for re-entry vehicle tps … · 2005-02-25 · 18th european...

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