finite element radiative and conductive module for use with phoenics department of materials...
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Finite Element Radiative and Conductive Module for use with PHOENICS
† Department of Materials Engineering, University of Swansea, Swansea , SA2 8PP, UK‡ DERA (Defence and Evaluation Research Agency) Farnborough, Hampshire, UK
Nick Lavery †
S.Brown & J.Spittle †L.Hayward & S. Rooks ‡
Structure of this presentation
1. Introduction
2. Governing equations & finite element solution
3. Numerical examples and validation of model
4. PHOENICS Interfacing
5. Conclusions & future work
The transient heat conduction equation:
The Stefan-Boltzmann equation:
The view factor equation:
2.1 Governing Equations
Qz
TK
zy
TK
yx
TK
xt
Tc zzyyxxp
JI
A A
JI
IIJ dAdA
rAF
I J
2
coscos1
(3)
)( 44JIJIIJI TTFAq (2)
(1)
2.2 Finite Element Solution
dSqNdVQN
dVz
N
z
N
y
N
y
N
x
N
x
N
dVNN
BS
i
V
i
V
jijiji
V
ij
F
K
M
FKTTM
Using 8 noded linear hexahedral elements, and the standard
Galerkin finite element discretisation:
(4)
(5)
3.1 View factor verification
Фa
cb
A2
A1
c
b
A1
a
A2
3.2 Transient heat conduction
3.3 Experimental rig for radiative heat transfer
Thermocouple 1Thermocouple 2
Thermocouple 3
3.3.1 Finite element prediction of experimental rig
Thermocouples
12
3
3.3.2 Experimental and numerical comparison
12
3
Position of fire rod
Temperature contours at t=10 s
3.7 Gnome exhaust nozzle
4. Integration with PHOENICS
• Create a coupled fluid/solid mesh (e.g. with FEMSYS)
• Solve for steady state fluid/gas flow equations PHOENICS
• Read in fluid FE mesh with boundary conditions (b.c.)
• Read in run parameters and material properties
• Calculate view factors for radiative heat transfer
• For each time step– Calculate F from equation (5) – Solve matrix equation (4) *– Update temperature, Tn+1
* The thermal conduction equation (1) is modified to include velocities for the gas/fluid
4. Conclusions and future work
• A finite element solver of radiative and conductive heat
transfer has been created
• The solver is accurate when compared to other numerical
and experimental results
• The solver is suitable for application to geometry of varying
complexity
• Fluid flow will be incorporated by the end of this year in the
form of flow fields from Phoenics
3.3.3 Animation of conducted temperature
Position of fire rod