Numerical modeling of heat transfer phenomena during quenching of steel

Resumo

In this thesis, the heat transfer phenomena that take place during the industrial process of quenching are studied and modeled. This work incorporates into the modeling scheme of quenching the dynamics of the quenching bath, specially, the resolution of the flow near the treated piece and the thermal interaction of the fluid with the piece. Due to the high initial temperatures involved during the process, a multiphase liquid/vapor flow has to be taken into consideration. The vaporization of the fluid is incorporated in the heat transfer mechanisms and in the fluid dynamics of the flow. To describe the cooling of the piece, the thermal problem of the solid has to be solved coupled along the evolution of the multiphase flow. This approach requires the resolution of a much more complex problem than the heat equation of a solid. The increased complexity of the pursued approach affects the modeling, implementation and numerical aspects of the simulation. In order to select the most convenient multiphase flow model, the analysis of characteristic times, couplings between phases and non-dimensional numbers, was performed. The model that retains all the relevant dynamics of the problem at an affordable numerical and modeling cost, is the drift-flux mixture model. For this model, the multiphase flow is treated as a mixture of both phases with a kinematic relationship to describe the relative velocities between phases. In addition to the multiphase approach to describe the bath dynamics, a heat partition model is proposed to incorporate all the different heat transfer mechanisms. The model is set up based on different models independently generated. In this work, a variety of models are combined to describe the heat transfer from the very high temperature conditions (film boiling) up to single phase convection. The heat transfer models were adapted and/or fitted to be applied for oil as quenching liquid. To calibrate the models, a set of physical experiments over a standard probe was performed. The cooling rates and total heat fluxes were obtained from the tests, and based on these results, the heat transfer models were calibrated. To obtain the cooling rate curves from the rather scattered experimental measures, a non-linear diffusion filter was implemented. The use of this type of filter is a novel application for this type of problems and the obtained results are smoother than the ones obtained by current techniques. The total heat flux was obtained from the resolution of the inverse heat transfer problem for the standard tests. The inverse problem was solved by the iterative resolution of the direct problem with a correction function obtained from the comparison of the experimental and numerical cooling rate curves. The cost function of the inverse problem is based on the error of the cooling rate curves instead of temperature records. The iterative method to solve the inverse heat transfer problem and the use of the error of the cooling rate as cost function are two novel methods developed in this work. Once the experimental total heat flux was obtained for the set of tested conditions, the calibration of the heat transfer model was performed. The models for each mechanism and the blending functions responsible to generate transitions between them were fitted based on nominal values of the flow. This calibration gave place to a set of correlations sensitive to nominal (non local) conditions of quenching (mainly oil temperature and velocity), therefore any condition among the tests can be interpolated from these results. The model was setup for a given oil. For the standard tests performed over a vertical cylinder, the comparison between the numerical and experimental results is very satisfactory. The heat partition model was adapted to be sensitive to local values of the flow, in addition to the vapor fraction that surrounds the piece, being this feature a novel approach in this type of model. This model was incorporated into the multiphase simulation framework and some conditions were tested. For the standard tests, it was observed that both models (correlations and multiphase) yield similar results. Tests performed on non-standard probes were performed. The probe contained a stagnation point at its middle height. The tests consisted on the immersion of the probe in two different positions of the stagnation point compared to the flow direction. Experimentally, noticeable differences between orientations were found. The correlation models weren't able to capture this difference, while the multiphase heat transfer model capture it in a qualitative way. This is one of the first (if not the first one) application of a multiphase model to describe the heat transfer during quenching of pieces of complex geometries. A deep understanding of the involved physics and limitations of the applied models and numerical implementation are discussed. Several proposals to improve the behavior of the developed model are presented as future work.