Data reduction of friction factor, permeability and inertial coefficient for a compressible gas flow through a milli-regenerator

¹ FEMTO-ST Institute, Univ. Bourgogne Franche-Comté, CNRS, Energy Department, 90000 Belfort, France
² FEMTO-ST Institute, Univ. Bourgogne Franche-Comté, CNRS, AS2M Department, 25000 Besançon, France

^* Corresponding author: francois.lanzetta@univ-fcomte.fr

Abstract

A regenerator of a Stirling machine alternately absorbs and releases heat from and to the working fluid which allows to recycle rejected heat during theoretical isochoric processes. This work focuses on a milli-regenerator fabricated with a multiple jet molding process. The regenerator is a porous medium filled with a dense pillar matrix. The pillars have a geometrical lens shape. Two metallic layers (chromium and copper) are deposited on the polymer pillars to increase heat transfer inside the regenerator. We performed experiments on different milli-regenerators corresponding to three porosities (ε = 0.80, 0.85 and 0.90) under nitrogen steady and oscillating compressible flows (oscillating Reynolds number in the range 0 < Re_ω < 60 and Reynolds number based on the hydraulic diameter Re_Dh,max<6000) for different temperature gradients (ΔT < 100°C). Temperature, velocity and pressure experimental measurements are performed with microthermocouples (type K with 7,6 µm diameter), hotwires and miniature pressure sensors, respectively. We identified a threeterm composite correlation equation for the friction factor based on a Darcy-Forchheimer flow model that best-fit the experimental data. In steady and oscillating flows permeabilities and inertial coefficients are of the same magnitude order. Inertial coefficients decrease when the porosities increase.