루우버 휜을 가지는 컴팩트 열교환기에 대한 열다공성 모델 연구

Abstract

Due to the peculiar geometry of louvered fin and its complicated nearby heat and flow distribution, the 3D numerical analysis of a compact heat exchanger containing a louvered fin had been a difficult analysis task. In this study, an empirical equation for friction coefficient of a louvered fin was proposed by assuming it to be a porous medium, in order to enable the 3D numerical analysis of a compact heat exchanger containing it. In the empirical equation for friction coefficient, the intrinsic permeability and Ergun constant of the louvered fin were derived as a function of parameters for the louvered fin. In order to determine the intrinsic permeability and Ergun constant of the louvered fin, a database of friction coefficient at Reynolds number from 0.001 to 30,000 was established for 14 different types of louvered fin models that are magnified by a factor of three. For Reynolds number from 100 to 1000, the friction coefficient data was obtained from previous works, and for Reynolds number less than 100 or greater than 1000, the friction coefficient data was obtained from a 3D numerical analysis of two-pitch louvered fin. The aim of obtaining the friction coefficient value for louvered fin at Reynolds number less than 100 or greater than 1000 is to determine the intrinsic permeability for the Darcy term, which governs viscous force at very low Reynolds number, and to determine the Ergun constant for the non-Darcy term (or Forchiemer term) that governs the inertial force at high Reynolds number. To determine the intrinsic permeability and Ergun constant from the database established through experiment and numerical analyses, nonlinear and linear regression analyses were performed consecutively, and a new friction coefficient of louvered fin suitable for the properties of a porous medium was proposed. By comparing the newly proposed friction coefficient to the coefficients of the modified Darcy equation, which governs the momentum within a porous medium, the intrinsic permeability and Ergun constant of the louvered fin are obtained. For verification, the friction coefficients obtained from the database of 14 louvered fin models using the empirical equation were compared, showing the error within 10% on average. Furthermore, when the intrinsic permeability value is obtained for 14 different types of model and different Reynolds number, while the permeability of the louvered fin is constant for Reynolds number less than 1, it is not constant for Reynolds number greater than 1. This accurately corresponds to the theory of porous medium. In the theory of porous media, the pressure drop in the fluid passing the porous medium is linearly proportional to the Darcy speed when Reynolds number is less than 1, with the proportionality constant being the permeability, that is constant. However, if the Reynolds number is greater than 1, the pressure drop within the porous medium varies nonlinearly with Darcy speed, with the permeability thereof being no longer constant. Therefore, it is observed that assuming louvered fin to be a porous medium is very appropriate. For 3D performance prediction of a compact heat exchanger, the permeability and Ergun constant proposed in this study, and Colburn j factor from Kang and Jun (2011) were used. First simulation compared the 3D numerical analysis of two-pitch louvered fin and the one where thermodynamic porous medium model was applied. The comparison showed that while the predicted outlet temperature differs by less than one Celsius, the size of the volume element of the analysis with porous medium model decreases to about 1/200 of the usual method. Second simulation performed a numerical analysis of a compact heat exchanger containing louvered fin. Compared to the experimental results, it was observed that the error in the outlet temperatures of cooled air and coolant is within 2 degrees, and that the error in the pressure drop in the cooled air is less than 10%. Interestingly, if the compact heat exchanger used for verification of this study is modeled using previous method without applying the thermodynamic porous medium model, around 24.4 billion volume elements are required for louvered fin alone, while the application of thermodynamic porous medium model requires 2 million volume elements only. Moreover, since less than 10 million volume elements are required for a 3D numerical analysis of louvered fin, the performance prediction of compact heat exchanger with louvered fin is now possible using a 3D analysis. For future research, the permeability and Ergun constant can be determined for other fins that are commonly used in compact heat exchangers, so that these can correspond to the properties of porous medium. This will allow the field engineers to easily design heat exchangers or car air-conditioning and heating units with reduced design cost and development time, through free selection of fins and easy performance prediction through simulation.