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微通道传热传质相关基础问题在新材料、微电子、航空航天等工程领域具有重要的科研需求. 本文针对微圆管内质量运输特性预测问题开展了数值方法研究及实验测量验证. 采用一维近似处理方法简化可压缩流动方程组, 建立了适用于微圆管质量运输特性预测的数值计算方法, 结合范诺线方程及实验方法对数值计算方法的正确性和物理计算模型的有效性进行检验, 并详细分析预测误差来源. 结果表明, 依据范诺线参数比理论结果与数值计算结果证明了数值计算方法的正确性. 对比典型驱动压差条件下微圆管出口工况的计算与纹影结果, 证明了数值方法关于流动壅塞预测的合理性. 在质量流量预测方面, 全层流阶段质量流量预测误差在3%以内, 全湍流状态下的预测误差在8%以内, 而当微圆管内流动包含层流至湍流的过渡过程时, 预测误差则提高至29%, 这是由于给定的转捩雷诺数以及摩擦系数计算公式的误差引入而造成的.
The fundamental issues related to heat and mass transfer in microchannels have significant research needs in various engineering fields, such as 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. A one-dimensional approximation method is employed to simplify the compressible flow equations, and a fourth-order Runge-Kutta numerical method is also 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 or flow choking at the outlet. Subsequently, by comparing the numerical calculation results with the theoretical results of the Fanuo line parameter ratio, the correctness of the numerical calculation method is 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 reveal 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%. During the numerical calculations, based on existing research results, the formula for transition Reynolds number and the turbulent friction factor are set as input parameters . However, the analyses 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 increasing, but the in the numerical calculations the turbulent friction factor is directly used to represent this process. These factors are the main reasons for the larger mass flow prediction errors when the flow involves transition and turbulence. 
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Keywords:
- one-dimensional processing method /
- mass transfer /
- numerical prediction /
- friction coefficient
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图 3 数值计算方法与范诺线方程求解p1/p2对比
Fig. 3. Comparison of numerical calculation methods and van Gogh line equations for p1/p2.
图 9 Case 1直管内沿程Ma, p, T分布
Fig. 9. Distribution of Ma, p, and T along the tube of Case1.
图 10 Case 2直管内沿程Ma, p, T分布
Fig. 10. Distribution of Ma, p, and T along the tube of Case2.
图 12 数值计算与实验测量质量流量结果对比 (a) 系列 1 (d = 100 μm); (b) 系列 2 (d = 200 μm)
Fig. 12. Comparison of mass flow rate results of numerical calculation and experimental measurement: (a) Series 1 (d = 100 μm); (b) Series 2 (d = 200 μm).
图 13 不同滞止压力时的平均摩擦系数 (a) d = 100 μm; (b) d = 200 μm
Fig. 13. Average friction coefficient at different stagnation pressures: (a) d = 100 μm; (b) d = 200 μm.
图 14 不同滞止压力时的沿程雷诺数 (a) d = 100 μm; (b) d = 200 μm
Fig. 14. Reynolds numbers along the tube at different stagnation pressures: (a) d = 100 μm; (b) d = 200 μm.
表 1 工况条件
Table 1. Operating conditions.
Case P0/kPa T0 /K pe /kPa d/μm L/mm 1 256 298 106 200 120 2 706 298 106 200 120 
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表 2 计算与实验条件
Table 2. Calculation and experimental conditions.
Series P0 /kPa T0 /K pe /kPa d/μm L/mm 1 256—706 298 106 100 120 2 156—706 298 106 200 120
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