Desenvolvimento de um modelo semiempírico bidimensional para representar o fenômeno tridimensional de escoamento laminar e transferência de calor em um tubo helicoidal.

Abstract

The high mixing rate in laminar flow in helical pipes is an important characteristic in heating or cooling processes of fluids. In this work, a two-dimensional (2D) semiempirical model based on a straight tube was proposed to represent laminar flow and heat transfer in a helical tube and a three-dimensional (3D) model was developed to study the phenomenon of secondary flow and heat exchange enhancement. To adjust the 2D model, isothermal residence time distribution (RTD) experiments were carried out in a helical tube with flow of a glycerin/water mixture and a carboxymethyl cellulose (CMC) solution at flow rates from 0.5 to 2.0 L/min. RTD models were fitted to the experimental data.Heating and cooling experiments were conducted in the helical tube with flow of both fluids under different flow and temperature conditions, immersed in an ultrathermostatic water bath. Appropriate boundary conditions were applied to the models and mesh independency studies provided the mesh for the computational domain discretization of each model. Simulations were performed using the finite difference method for the 2D model and the finite element method for the 3D model under the experimental heating and cooling conditions. The velocity profile corresponding to the 𝑦-laminar RTD model (best fit) was included in the 2D model, and the outlet temperatures from the heating and cooling experiments were specified in the 2D model simulations to determine the heat transfer enhancement factor (𝐹). This factor was correlated with the Reynolds number and had a limit value of 𝐹 = 1 when there was no enhancement of heat transfer. The 3D model simulations for a cooling case with the CMC solution allowed the identification of Dean vortices in the flow, which were more evident at the higher flow rate (1.5 L/min).The 2D model simulations were completed in about 1 minute and had low consumption of RAM memory (1 GB), while the 3D model took up to 4 days to complete simulations with high consumption of RAM (250 GB). The fast simulations and the good temperature prediction of the 2D model can be used for predictive control in thermal processes, especially when it is necessary to have the temperature profile along the tube and not just the outlet temperature; however, since it is a semi-empirical model, it requires adjustments based on experimental data.