Elie Hachem
Co-authors : E. Massoni and T. Coupez
Title :
Immersed volume technique for solving natural convection, conduction and radiation of a
hat-shaped disk inside an enclosure
Abstract :
The paper presents an original modelling approach of transient heat transfer by natural
convection, conduction and radiation of a hat-shaped disk (inconel 718) inside an
enclosure.
We solved three-dimensional coupled equations of conservation of mass, momentum and
energy, with the Boussinesq approximation using stabilized finite element methods. The
radiation source term is computed using the P1 model. In order to take into account the
heated disk inside the enclosure, a novel immersed volume technique for multi-component
applications is applied. The signed levelset function is used to provide us homogeneous
thermal properties. Thus, solving only one equation on the whole domain with different
thermal properties can reduce the computational costs. The originality of this immersion
technique consists in considering only one single grid for both air and solid (Fig. 1). An
anisotropic mesh adaptation is also applied in order to gain precision at the disk’s
interface.
On the other hand, using stabilized finite element for the Navier-Stokes and the heat
equations allows the control of spurious oscillations and thermal shocks giving more
accurate results.
The proposed method demonstrates the capability of the model to simulate a real
industrial application of such 3D time-dependent problem. Results are assessed by
comparing the predictions with the experimental data.
Figure 1. Hat-shaped disk inside a cold enclosure
References :
[1] E. Hachem, H. Digonnet, E. Massoni and T. Coupez, “Enriched finite element spaces for
transient conduction heat transfer,”Int. J. for Num. Methods in Engng (submitted Nov 2008)
[2] A. Mezrhab, H. Bouali, H. Amaoui, M. Bouzidi, “Computation of combined naturalconvection and radiation heat-transfer in a cavity having a square body at its center,”
Applied Energy, Vol. 83, pp. 1004-1023, 2006.
[3] Kamel Guedri, Mohamed Naceur Borjini, Habib Farhat, “Modelization of combined
radiative and conductive heat transfer in three-dimensional comple enclosures,”
International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 15, pp. 257-276,
2005
[4] T. Coupez, H. Digonnet and R. Ducloux, “Parallel meshing and remeshing,” Comput.
Methods in Appl. Mech. and Engng., Vol. 25, pp. 153-157, 2000