Eventos Anais de eventos
ENCIT 2020
18th Brazilian Congress of Thermal Sciences and Engineering
IMPROVED LUMPED-DIFFERENTIAL ANALYSIS OF THE FREEZING PROCESS IN A SUPERCOOLED WATER DROPLET
Submission Author:
Renato Machado Cotta , RJ
Co-Authors:
Emerson Barbosa dos Anjos, Carolina Palma Naveira Cotta, Renato Machado Cotta, Igor Soares Carvalho, Manish Tiwari
Presenter: Emerson Barbosa dos Anjos
doi://10.26678/ABCM.ENCIT2020.CIT20-0502
Abstract
This work presents a theoretical analysis of the transient freezing process of a supercooled droplet immersed in a cold air stream. The main objective is in evaluating the temperatures evolution and the time of freezing for the whole process through a proper yet simple mathematical model for the energy balance in the suspended water droplet undergoing solidification. The entire freezing process can be described by four distinct stages, namely, supercooling, recalescence, freezing and cooling. At each stage, a model reduction methodology known as the Coupled Integral Equation Approach (CIEA) is employed, which reduces the partial differential equation for the temperature distribution within the spherical droplet into a system of coupled ordinary differential equations for average temperatures and moving boundary position. The resulting lumped-differential model is expected to offer improved accuracy with respect to the classical lumped system analysis, since boundary conditions are accounted for in the averaging process through the Hermite integral approximations employed. The results of the CIEA were verified against an accurate hybrid numerical-analytical solution for the full partial differential formulation, recently advanced through the Generalized Integral Transform Technique (GITT), besides comparing against numerical and experimental results available in the literature. After verification and validation of the proposed solution, a parametric analysis was implemented, for different conditions of airflow velocity and droplet radius, highlighting that variations in these parameters cause changes in the Biot number, which has a direct effect on the accuracy of the improved lumped-differential formulation.
Keywords
Droplet freezing, heat conduction, Lumped analysis, CIEA, Moving boundary, Hybrid method, GITT, Integral Transforms
DOWNLOAD PDF VIEW PRESENTATION
