One Dimensional Approximation-Based Prediction Method for Mass Transfer Characteristics in Microtubes
Authors: ZHENG Wenpeng  , LU Xiaoge  , ZHAO Yuxin  , ZHANG Zhen  , YI Shihe  ,   School of Aerospace Science, National University of Defense Technology, Changsha 410073, China
Published: February 2025

The fundamental issues related to heat and mass transfer in microchannels have significant scientific research demands in various engineering fields, including new materials, microelectronics, and aerospace. This paper addresses the problem of predicting mass transport characteristics within microtubes by developing numerical methods, conducting experimental measurements for validation, and analyzing prediction errors.<br>A one-dimensional approximation method is employed to simplify the compressible flow equations, and a fourth-order Runge-Kutta numerical method is used to iteratively solve the governing equations. A theoretical calculation method suitable for predicting mass transport characteristics in microtubes is established. This method can calculate various flow parameters along the length of the microtube and can handle different flow conditions, such as static pressure matching at the outlet or flow choking.<br>Subsequently, by comparing the numerical calculation results with the theoretical results of the Fanuo line parameter ratio, the correctness of the numerical calculation method has been verified. Also, Schlieren experiments and a self-designed mass flow measurement device are used to qualitatively and quantitatively verify the effectiveness of physical computing models. Under typical driving pressure differences, the qualitative agreement between the calculated and schlieren results for the outlet conditions of the microtube demonstrate the rationality of the numerical method in terms of static pressure matching and flow choking calculations. Regarding mass flow prediction, comparisons between theoretical calculations and experimental measurements under different driving pressures revealed that when the flow inside the microtube is in a fully laminar state, the mass flow prediction error is within 3%. When the flow is fully turbulent, the prediction error is within 8%. However, when the flow involves a transition from laminar to turbulent, the prediction error increases to 29%.<br>During the numerical calculations, the transition Reynolds number and the turbulent friction factor formula are set as input parameters based on existing research results. However, analysis of the Reynolds numbers along the length of the microtube and the average friction factors under different conditions show that the actual transition Reynolds number in the microtube is lower than the value set in the numerical calculations. Additionally, there is a significant discrepancy between the calculated turbulent friction factor and the actual value. Moreover, during the transition from laminar to turbulent flow, the friction factor should increase continuously with the Reynolds number, but the numerical calculations directly used the turbulent friction factor to represent this process. These factors are the main reasons for the larger mass flow prediction errors when the flow involves transition and turbulence.