Thermo-mechanical simulation of a cast copper furnace

9 September 2014

by Lluis Martinez Biscarri, Biscarri Consultoria, member of Code_Aster ProNet

Biscarri is committed to the use and dissemination of open source CAE tools.
The solver employed in the thermo-mechanical analyses is Code_Aster. Meshing is done using SALOME combined with Python scripting. Results are processed using SALOME (ParaViS module).

Biscarri Consultoria conducted a thermo-mechanical simulation of a cast copper furnace for La Farga Group [1].


  • The numerical model consists of a structure mesh (with shell elements applied) and an inner refractory brickwork mesh (with solid elements applied) ;
  • The model is built by a parameterized Python Script - designed by Biscarri Consultoria for this project’s requirements - so that design geometric variables can be modified and the mesh rebuilt automatically very quickly. Python scripting increases productivity dramatically, easily changing mesh density to find a compromise between accuracy and solving time ;
  • Steel structure and refractory brickwork are two separate bodies in the model. They are connected through contact pairs and preloaded through springs between them, which provide the brick wall with the needed stiffness to retain copper casting. The resolution of the contact problem is non-linear and requires an iterative algorithm, which is a critical step in the solving procedure ;
  • Firstly, a linear thermal analysis calculates the temperature distribution of the whole model (refractory brickwall and steel structure) arising from the working temperature inside the furnace ;
  • Then a non-linear static analysis calculates stress and strain distribution on the model subjected to gravitational loads and the effect of thermal expansion, which are applied in an incremental way through 100 load steps.
  • This analysis is highly non-linear because of :
    • the presence of contacts,
    • the use of an elasto-plastic material law for the steel,
    • material properties being temperature dependent, such as Young’s modulus and the coefficient of thermal expansion.
  • The iterative solution of this non-linear system requires to fine tune the solver parameters in order for the model to converge properly.

Numerical results

The figures show stress distribution in the structure and the refractory brickwork as well as the deformed geometry from gravitational loads.

Figure 1 : Von Mises equivalent stress in the steel structure
Figure 2 : deformation of the refractory brickwall

Thermal expansion is of very high interest in the engineering process of this structure.

  • The furnace’s structure most stressing loading is by far thermal expansion ;
  • The structure’s cradle has to be stiff enough to ensure brickwork sealing. The thermal expansion of this part of the structure is higher than the rest, because of the contact with the lower and hottest part of the brickwork. Since the roof structure is much more flexible, but does not dilate so much, it is pulled and forced to bend, as shown in figure 3.
Figure 3 : deformed geometry resulting from gravitational load

[1] La Farga is a family-run holding group with over 200 years of history that manufactures and sells semi-finished copper products and theirs alloys for the electrical, metal packaging, railway, piping, automotive, billets and special conductors markets.