Representation of 3D phenomena of laminar flow and heat transfer in a helically coiled tube using a 2D geometry

Abstract

The coiled tube geometry has different industrial applications whereby heating and cooling operations are required. In this work, a 2D semi-empirical model based on a straight tube is proposed to represent the 3D phenomena of flow and heat transfer in a coiled tube. The model considers a modified velocity profile based on residence time distribution (RTD) experiments and a heat transfer enhancement factor based on heating and cooling experiments. For testing and validating the model, experiments were performed using a Newtonian fluid (glycerin/water mixture) and a non-Newtonian fluid (carboxymethylcellulose CMC solution) at flow rates from 0.5 to 2.0 L/min in a coiled tube with 9 turns. The y-laminar RTD model was successfully adjusted to experimental E-curves and its parameter y was correlated with flow rate. Heating and cooling experiments with the coil provided outlet temperatures at different conditions of flow rate and temperature. The model was adjusted to match the outlet temperatures, providing the heat transfer enhancement factor F, the second empirical parameter of the model. This factor was linearly correlated with Reynolds number in a log-log plot and showed a threshold for negligible enhancement (F = 1). The model was numerically solved the finite difference method after a mesh dependency study. Good outlet temperature predictions were obtained with computational time of about 1 min, which is much smaller than usual computational times for a 3D coil geometry, and model provides velocity and temperature fields useful for further simulation of non-isothermal laminar flow reactors, such as bacterial inactivation in thermal processing of liquid foods.