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 (3) (2) (1)
2.2 Finite Element Solution Using 8 noded linear hexahedral elements, and the standard Galerkin finite element discretisation: (4) (5)
3.1 View factor verification Ф a c b A2A2 A1A1 c b A1A1 a A2A2
3.2 Transient heat conduction
3.3 Experimental rig for radiative heat transfer Thermocouple 1 Thermocouple 2 Thermocouple 3
3.3.1 Finite element prediction of experimental rig Thermocouples 1 2 3
3.3.2 Experimental and numerical comparison 1 2 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, T n+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