Work conjugate principle-constrained volume averaging technique for multiphase porous media

Volume averaging is a standard method for the development of macroscopic balance equations for modelling the thermodynamic behaviors of multiphase porous media. However, work conjugate principle which is a common practice in continuum mechanics is not emphasized by the volume averaging technique resulting in the macroscopic balance equations are not capable of comprehensively describing the kinematic behaviors of multiphase porous media due to the loss of essential macroscopic variables. This study derives the macroscopic mass and momentum balance equations for the pore fluid of a fluid-solid porous medium by use of the volume averaging technique. We show(1) if the procedure of the volume averaging is implemented in its traditional manner, only the average flux of the pore fluid described by its mass average velocity is captured;(2) if the work conjugate principle is employed to define a work-conjugate velocity for the pore fluid at the macroscale, both the average flux(described by the mass average velocity) and the dispersive flux(described by the deviation of the mass average velocity from the work-conjugate one) are reproduced. This theoretical analysis demonstrates that the work conjugate principle is an essential thermodynamic constraint to improve the volume averaging technique, in the sense that the macroscopic balance equations are required to be capable of comprehensively describing the macroscopic kinematic behaviors of multiphase porous media.

Advances in porous volumetric solar receivers and enhancement of volumetric absorption

Porous volumetric solar receivers are one type of solar receivers that can volumetrically absorb solar radiation and achieve efficient solar-to-thermal energy conversion.Porous volumetric solar receivers have been developed since 1980s.In this review,we focus on the development progress of the atmospheric and pressurized porous volumetric solar receivers,in which the structural designs,the material selections,the experimental research methods,the comparison of thermal performance,and the transient response characteristic of the receivers were reviewed.On the other hand,the theoretical research methods including the direct pore-scale and volume averaging simulations were introduced.The pore-scale reconstruction method and the procedure to investigate the fluid flow and heat transfer processes at the pore-scale were presented.For the volume averaging method,detailed descriptions for the selection of empirical parameters in the governing equations to be solved were summarized.Typical research results based on these methods were presented and research limitations were also pointed out.Furthermore,the methods for the enhancement of volumetric absorption and the improvement of thermal efficiency of the receivers have been comprehensively reviewed.Two methods including geometrical parameters optimization and spectrally selective absorption were presented in detail.This review will provide a better understanding of the development and research methods for porous volumetric solar receivers,and inspire future studies for the performance improvement of the receivers.

THE STRUCTURAL FLOW IN PIPE CONTAINING POROUS MEDIUM SATURATED WITH POWER-LAW FLUID

In this article,the method of volume averaging of flow in porous media and averaging theorem was employed to the Navier-Stokes equations.The total drag force per unit volume was considered as the bulk damping resistance due to the porous structure（i.e.,the Darcy resistance）and the resistance due to the inertia force（i.e.,the Forchheimer resistance）,then the Brinkman-Forchheimer extended Darcy model was obtained from average momentum equation.The structural flow in a pipe containing porous medium saturated with power law fluid was applied in the present study.A new theoretical analysis of fully developed non-Darcy flow in a pipe containing a fibrous medium saturated with power law fluid was conducted.Using the integration method,the boundary layer solutions were obtained for flow core velocity and its radius.These theoretical solutions were used to analyze the effects of the Darcy number and inertia parameter on the axial velocity profile in the porous medium pipe.