Numerical study of heat transfer coefficient of titanium reactor wall at air cooling

This paper is concerned with a numerical study of the thermal regime of the retort surface in an apparatus for the production of titanium. The problem of conjugate heat transfer between the outer wall of a cylindrical retort and the wall of a furnace with heaters, with an air gap between them, is considered. The aim of the work is to obtain estimates for the temperature regime of the retort wall and its surface heat transfer coefficient at different heating and cooling regimes. Data on the distribution of heat flows on retort walls are needed to calculate the turbulent convective flows of liquid magnesium inside the retort, since the non-uniformity of temperature can have a significant impact on the processes occurring inside the retort. The computational domain consists of solid walls with moving air between them. The mathematical model is based on a system of axially symmetric non-stationary Navier-Stokes equations, and the RANS (Reynolds-averaged Navier-Stokes equations) approach is used to describe turbulent fields. Along with the mechanisms of forced convection and thermal conductivity, the model also takes into account the radiation heat transfer between two opposite walls. Four heating modes representing different possible variants of the device operation are considered. Estimates have been obtained for the required blowing rate, which allows keeping retort walls in the working range from 750 to 950 ºС in all modes. It is shown that the temperature along the considered wall section is essentially heterogeneous. Dependencies for the heat transfer coefficient at the side surface of the retort on the vertical coordinate are constructed. Comparison with known formulas for calculation of the heat transfer coefficient obtained for flat infinite surface with uniform heat flux is carried out. It has been established that, in the case under discussion which is more complex, the calculated coefficients are close to those predicted by the known engineering formulas only in part of the regimes examined in this study. In a large range of considered parameters, there are noticeable differences between the obtained dependencies and the simplified estimates; the greatest difference occurs near the channel entrance, where the temperature gradients reach their maximum.