Numerical modeling of steel tube reheating in walking beam furnaces

Walking beam furnaces are used in seamless steel tube manufacturing plants to reheat tubes between rolling stages and to austenize and temper the tubes during heat treatments. For such furnaces, a numerical model of the heating process was developed aiming at the following objectives: 1) to assure a narrow outlet temperature range; 2) to prevent tubes from bending inside the furnace due to high temperature gradients; 3) to increase productivity. The model involves two-dimensional tube temperature descriptions in polar coordinates, corresponding to different longitudinal positions along the tube. It takes into account tube rotation during transference from one location to the following one: and requires input values from thermocouple measurements. The calculation of the radiative fluxes on the tube and hearth surfaces is divided into two parts. In the first one the radiation exchanges in the combustion chamber are modeled using a spectral zone method with combustion gas properties provided by RADCAL. In it, the tubes and underlying hearth are represented by an interface plane tangent to the tubes. In the second part, heat fluxes on the tube surface are calculated from those obtained for the interface using a detailed model of the radiative exchanges in the tube vicinity. In this article the model is used to analyze the effect of process parameters such as cycle time, zone temperature settings, tube spacing, and rotational velocity, on the average tube temperature and temperature inhomogeneity in steady state operation. Model results are validated through comparisons with plant measurements.