The Effect of Turbulence on Momentum and Heat Transport in Packed Beds with Low Tube to Particle Diameter Ratio

Abstract

Abstract This is a theoretical study about the influence of turbulence on momentum and heat transport in a packed-bed with low tube to particle diameter ratio. The hydrodynamics is given here by the time-averaged Navier-Stokes equations including Darcy and Forchheimer terms, plus a κ-ε two-equation model to describe a 2D pseudo-homogeneous medium. For comparison, an equivalent conventional flow model has also been tested. Both models are coupled to a heat transport equation and they are solved using spatial discretization with orthogonal collocation, while the time derivative is discretized by an implicit Euler scheme. We compared the prediction of radial and axial temperature observations from a packed-bed at particle Reynolds numbers (Rep) of 630, 767, and 1000. The conventional flow model uses effective heat transport parameters: wall heat transfer coefficient (hw) and thermal conductivity (keff), whereas the turbulent flow model includes a turbulent thermal conductivity (kt), estimating hw via least-squares with Levenberg-Marquardt method. Although predictions of axial and radial measured temperature profiles with both models show small differences, the calculated radial profiles of the axial velocity component are very different. We demonstrate that the model that includes turbulence compares well with mass flux measurements at the packed-bed inlet, yielding an error of 0.77 % in mass flux balance at Rep = 630. We suggest that this approach can be used efficiently for the hydrodynamics characterization and design and scale-up of packed beds with low tube to particle diameter ratio in several industrial applications.