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This paper presents a Computational Fluid Dynamics (CFD) simulation of the quenching process based on ISO 9950, focusing on the heat flux and heat transfer coefficient integrated over a metal specimen. The numerical method, which employs the two-fluid VOF method and frozen turbulence approach (Cukrov et al., Appl. Sci. 2023, 13, 9144), is used for the transient simulation. Since quenching processes involve complex boiling phenomena shifting from film boiling to nucleate boiling, a standard method based on VOF cannot be applied. The comparison of the simulation results with the ones obtained using correlation, and the data obtained using the Inverse Heat Transfer Analysis (IHTA) method have revealed that the proposed method can accurately predict the heat flux and heat transfer coefficient in the film boiling regime of the immersion quenching process. Note that the previous paper (Cukrov et al., Energies. 2023, 16, 7926.) presented the immersion process modeling and the temperature distribution, while the current paper examines the heat transfer characteristics of the immersion quenching process.

The computational model that is able to estimate the temperature distribution inside a solid specimen during the film boiling phase of immersion quenching (water entry) process has been presented in this paper. It is based on the prescribed initial temperatures of the solid specimen and the liquid quenchant. In addition, the turbulence effects have to be considered using the assumed turbulence kinetic energy value, i.e., the “frozen turbulence” approach, that remains constant thorough the simulation. The studied material is nickel alloy, Inconel 600, for which extensive experimental data are available. The work has been carried out using ANSYS Fluent computational fluid dynamics software and the methods for solution of Stefan problem by Eulerian two fluid VOF model. A satisfactory agreement between the experimental and the calculated data has been achieved, yielding thereby the computationally obtained data that fit to a great extent the prescribed error band of ±10% during the estimated film boiling phase of the immersion quenching process itself. It was, however, found that the temperature calculated in the center of a specimen fits this error band until reaching somewhere t < 6 s due to low presumed turbulence level in the domain. In addition, the explosion of the vapor phase after the body reaches the free surface of the quenchant has also been successfully tracked using the numerical simulation model proposed herein. The major novelty of the present research lies in the fact that a moving boundary problem has been successfully resolved in conjunction with, to a great extent, basic-principle-based heat and mass transfer in a turbulent flow conjugate heat transfer (CHT) numerical simulation using moderate computational resources.

The DNS of film boiling requires strong computational resources that are difficult to obtain for daily CFD use by expert practitioners of industrial R&D. On the other hand, film boiling experiments are associated with the usage of expensive and highly sophisticated apparatus, and research to this end is relatively difficult due to high heat flow rates that are present in the process itself. When combined with transient heat conduction in a solid, the problem becomes significantly difficult. Therefore, a novel method in computation of conjugate heat transfer during film boiling in a quiescent liquid is proposed in this paper. The method relies on the solution of mass, momentum and energy conservation equations in a two-fluid framework, supplemented with the appropriate closures. Furthermore, turbulent flow was determined as an important parameter in obtaining an accurate solution to temperature field evolution in a solid specimen, via the proper modeling of the turbulent kinetic energy (TKE) value, that was imposed as a constant value, i.e., the frozen turbulence approach. It was found, in addition, that the appropriate TKE value can be obtained by use of Kelvin–Helmholtz instability theory in conjunction with boundary layer theory. The obtained results show excellent agreement with the experimental data within the first 15 s of the experiment, i.e., the first ca. 10% of the total duration of the film boiling mode of heat transfer. Furthermore, the heat transfer coefficient matched the error bands prescribed by the authors of this paper, which presented the correlations, whilst the averaged values are far beyond this band, i.e., are slightly more than 30% higher. Further inspection revealed a measure of similarity between the computational result of the volume fraction field distribution and the experiment, thus confirming the capability of the method to obtain realistic interface evolution in time. The method shows full capability for further pursuing industrial-scale film boiling problems that involve turbulent flow and the conjugate heat transfer approach.

A novel approach for the solution of Stefan problem within the framework of the multi fluid model supplemented with Volume of Fluid (VOF) method, i.e. two-fluid VOF, is presented in this paper. The governing equation set is comprised of mass, momentum and energy conservation equations, written on a per phase basis and supplemented with closure models via the source terms. In our method, the heat and mass transfer is calculated from the heat transfer coefficient, which has a fictitious function and depends on the local cell size and the thermal conductivity, and the implementation is straightforward because of the usage of the local value instead of a global parameter. The interface sharpness is ensured by the application of the geometrical reconstruction scheme implemented in VOF. The model is verified for three types of computational meshes including triangular cells, and good agreement was obtained for the interface position and the temperature field. Although the developed method was validated only for Stefan problem, the application of the method to engineering problems is considered to be straightforward since it is implemented to a commercial CFD code only using a local value; especially in the field of naval hydrodynamics wherein the reduction of ship resistance using boiling flow can be computed efficiently since the method handles phase change processes using low resolution meshes.