Simulations of flow and heat transfer in a serpentine heat exchanger having dispersed resistance with porous-continuum and continuum models

Abstract

Numerical simulations of flow and heat transfer in a serpentine heat exchanger configuration are presented to demonstrate application of porous media techniques in heat exchanger analyses. The simulations are conducted using two different approaches. In the first approach, a porous continuum homogeneous model (PCM), or macroscopic model, is applied. The solid and fluid phases are modeled as a single, homogeneous medium having anisotropic effective properties that are calculated separately from unit cell scale analyses and are made available to the macroscopic analysis. In the second approach, a continuum heterogeneous model (CM), or microscopic model, is employed to solve the momentum and energy equations for the fluid phase. The solid phase, a regular interruption to the flowfield, is, in this example, composed of square rods in a spatially periodic pattern. Because the microscopic model includes computation of all the flow features, computation time is considerable. A comparison shows the advantage of using the porous-continuum model, a large savings of computation time. This is particularly valuable in parametric studies. The effective properties in the macroscopic model include permeability values, Forchheimer coefficients, thermal dispersion coefficients, and heat transfer coefficients, constructed from results of periodic unit cell scale analyses, done separately. The results from the microscopic model are volume averaged over the porous medium representative elementary volume (REV) in order to generate averaged values for comparison to the results of the macroscopic model. Profiles of average velocity and temperature at various axial and longitudinal locations within the serpentine section of the example heat exchanger show agreement between the volume-average of the microscopic model results and the macroscopic model results. Further, comparisons are discussed in terms of local and global residuals from the models. It is found that local residuals of the calculations correlate well with the dimensionless product of the streamline curvature (the inverse of the curvature radius) and the scale of the unit cell. Global residuals, which are local residuals averaged over REVs, correlate with packing number (number of unit cells within the serpentine section). The packing number is used for estimating the global residual errors incurred when using the macroscopic model.