Friction correlation of an offset strip fin modeled as porous medium for application to a geothermal heat exchanger

Abstract

Accelerated global warming caused by the use of fossil fuels has resulted in an elevated demand for renewable energy such as geothermal energy, which exploits the constancy of ground temperature throughout the year to achieve cooling or heating. Standing-column-well geothermal systems provide high quantities of heat but are affected by decreases of the natural water level due to drought, depletion of underground water, and geo-graphical specificities, which complicates the steady and reliable operation of these systems. To address this problem, we herein propose a novel geothermal heat exchanger equipped with an offset strip fin (OSF) and investigate OSF friction correlation modeled in terms of porous media in this heat exchanger. The reference friction factor, which is assumed to be a function of the Reynolds number (Re) and a characteristic coefficient, is calculated by computational fluid dynamics (CFD) in the Re range of 100-20,000 for a unit geothermal heat exchanger with OSFs and for 16 types of variable-dimension OSFs. The independent friction factor for these OSFs is obtained by nonlinear regression analysis. Next, by assuming that the characteristic coefficient is a function of OSF parameters, the generalized friction factor correlation for OSF is obtained by multiple regression analysis and it is verified by comparing existing friction factor correlations with the proposed values for 50 < Re < 1,000. In the case of a low (<200) Re, the maximum error is found to be 8 %, whereas in the case of a high ( > 500) Re, the maximum error is within 2 %, which confirms that the proposed friction factor correlation is consistent with existing data. On the other hand, the friction factor decreases with increasing OSF fin length, which is in a good agreement with the results of previous studies. In addition, the friction factor is analyzed for various working fluids (air, water, and antifreeze) by using the proposed correlation, where it is found to be independent of fluid type. The proposed friction factor correlation in the present study provides a quick assessment of calculating the pressure drop of OSF for a geothermal applications, which obviates the need for complicated and costly computational analysis.