Prediction of Darcy Permeability and Forchheimer’s Coefficient of Porous Structures Relevant to Regenerator of a Stirling Cryocooler Using a Correlation Based Method

Abstract

A regenerative heat exchanger is the most vital component in the design of a Stirling cryocooler. Computational Fluid Dynamics (CFD) is the best technique for the design and prediction of the performance of a regenerator. The reliability of the simulation results depend on the accuracy of the Darcy permeability [Formula: see text] and Forchheimer’s inertial coefficient [Formula: see text] used for modeling the momentum transfer in porous media. Usually these coefficients are calculated from pressure drop data obtained from experiment. Because of the requirement of sophisticated equipments for the measurement and analysis of data, experimental study becomes expensive. This paper proposes a friction factor correlation-based method for the prediction of directional permeability and Forchheimer’s inertial coefficient of wire mesh structures relevant to Stirling cryocooler. The friction factor for the flow of helium through #325, #400 and #635 SS wire matrices with porosities of 0.6969, 0.6969 and 0.6312 are calculated using standard correlations and compared with the friction factor given by Clearman et al. based on steady flow experimental study. The friction factor obtained from Blass and Tong/London correlations are in agreement with that of Clearman et al. The viscous and inertial resistances are calculated from the friction factor obtained from Blass and Tong/London correlations. Using these values, the regenerator was modeled as a porous media in Fluent. From the steady flow simulation, pressure drop at different mass flow rates (0.08–1.44[Formula: see text]g/s) is obtained. The maximum deviation of predicted pressure drop from the reported experimental data is 15.14%. The Darcy permeability [Formula: see text] and Forchheimer’s inertial coefficient [Formula: see text] obtained from correlation-based method was used for modeling the oscillatory flow of helium through a #400 regenerator. The pressure amplitude and phase at regenerator exit were obtained at different frequencies. The average deviation of predicted pressure amplitude from the experimental data is 15.83%. The model could predict the phase angle also accurately. Therefore, the proposed method can be used to calculate the hydrodynamic parameters of woven wire screen matrices applied to Stirling cryocoolers.