-The generalized integral transform technique (GITT)is employed to obtain a hybrid numericalanalytical solution of natural convection in a cavity with volumetric heat generation. The hybrid nature of this approach allows for the establishment of benchmark results in the solution of non-linear partial differential equation systems, including the coupled set of heat and fluid flow equations that govern the steady natural convection problem under consideration. Through performing the GITT, the resulting transformed ODE system is then numerically solved by making use of the subroutine DBVPFD from the IMSL Library. Therefore, numerical results under user prescribed accuracy are obtained for different values of Rayleigh numbers, and the convergence behavior of the proposed eigenfunction expansions is illustrated. Critical comparisons against solutions produced by ANSYS CFX 12.0 are then conducted, which demonstrate excellent agreement. Several sets of reference results for natural convection with volumetric heat generation in a bi-dimensional square cavity are also provided for future verification of numerical results obtained by other researchers.
A mass transfer study in a lithium production electrolysis cell is carried out. The numerical domain is a 2D axis-symmetric wedge of 5 o. The bulk of the cell is filled with an electrolytic solution consisting of an eutectic mixture of LiCl − KCl. Lithium ions reduce at the cathode while Cl − oxidize at the anode releasing bubbles of chlorine gas. Those are moving upward due to their light density dragging the nearby electrolyte. The induced convection is responsible for the transport of ions, together with the migration and diffusion mechanisms. The result is a turbulent two-phase flow accounting for the transport of ions, potential drop and polarization concentration. The highly non-linear coupled mathematical model is solved using an OpenFOAM solver designed to use predictor-corrector loops for both the fluid dynamics and the electrochemistry coupling. Non-linear mixed boundary conditions complete the set of governing equations.
This work aimed to analyze the turbulent natural convection in a volumetrically heated fluid with Prandtl number equal to 0.6, representing the oxide material layer of a corium. Four turbulence models were scrutinized in order to select the most appropriate one for turbulence modeling based on Reynolds Averaged Navier-Stokes equations (RANS) of natural convection in a molten core. The turbulence models scrutinized are the standard k-ε, Shear Stress Transport (SST), low-Reynolds-k-ε (Launder-Sharma) and also an elliptic blending model ν2-f. The simulations were carried out in a square cavity with isothermal walls, for Rayleigh numbers (Ra) ranging from 109 to 1011. The numerical simulations, performed in an open-source of Computational Fluid Dynamics (CFD) - OpenFOAM (Open Field Operation and Manipulation), provided outcomes of average Nusselt number as function of Ra number, which were in a reasonable agreement with an experimental correlation and other authors’ simulations. It was also possible to observe the limitations and robustness of each model analyzed, enabling to conclude that the most adequate turbulence models for the present physical problem were SST and ν2-f.
A new solver named POTisoFOAM is presented to predict and investigate the performance of electrochemical reactors. Its mathematical model is developed and implemented through finite volume methods and exploits the flexibility of the open source package OpenFOAM. The solver consists of two consecutive predictor-corrector loops. The first solves the pressure and velocity fields accounting for turbulence, while the second handles the ions transport and current conservation. The equations' system is further complicated by means of the non linear Buttler-Volmer boundary conditions. Despite the strong coupling between the charged ions and the electric potential, the reconstruction of the tertiary current density distribution is achieved. This study simulates the electrodeposition of copper, where changes in the electrodes geometry due to material deposition and corrosion are taken into account with the intent to predict the electrodes' replacements and the productivity of the reactor.
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