<p>This paper investigates the flow characteristics in thin liquid layer through downward inclined channels. In order to analyze the flow behaviour in the developing and fully developed regions, the shallow water theory for thin film flow is performed. Computational fluid dynamics based simulation is also performed to supplement the theoretical analysis. At low channel inclination or small Reynolds number, a hydraulic jump forms during the flow. For higher channel inclination or larger Reynolds number, this jump does not occur. Although the jump and no jump regimes are identified through the regime map, the detailed analysis presented in this study is focused on the no jump operating condition. Under the no jump operating condition, the Froude number gradually decreases from its inlet value and eventually becomes constant. The liquid layer height increases along the streamwise distance from the inlet and becomes constant beyond the developing length, resulting in fully developed flow condition. It is observed that the slope of liquid height profile just after the inlet is a function of Reynolds number, whereas it is independent of inclination angle. As the Reynolds number rises, the developing length increases, while a greater angle of channel inclination results in a decrease in developing length. The developing length and the constant liquid layer height in the fully developed flow are independent of channel length. It is noted that the lower channel inclination and higher Reynolds number lead to lower skin friction coefficient, resulting in lesser energy loss. Further, it is also shown that the flow in the developing region can be regarded as locally, fully developed.</p>

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Thin Film Flow Dynamics in Down Sloping Channels: Shallow Water Analysis

  • Siddhartha Das,
  • Mrinmoy Dhar

摘要

This paper investigates the flow characteristics in thin liquid layer through downward inclined channels. In order to analyze the flow behaviour in the developing and fully developed regions, the shallow water theory for thin film flow is performed. Computational fluid dynamics based simulation is also performed to supplement the theoretical analysis. At low channel inclination or small Reynolds number, a hydraulic jump forms during the flow. For higher channel inclination or larger Reynolds number, this jump does not occur. Although the jump and no jump regimes are identified through the regime map, the detailed analysis presented in this study is focused on the no jump operating condition. Under the no jump operating condition, the Froude number gradually decreases from its inlet value and eventually becomes constant. The liquid layer height increases along the streamwise distance from the inlet and becomes constant beyond the developing length, resulting in fully developed flow condition. It is observed that the slope of liquid height profile just after the inlet is a function of Reynolds number, whereas it is independent of inclination angle. As the Reynolds number rises, the developing length increases, while a greater angle of channel inclination results in a decrease in developing length. The developing length and the constant liquid layer height in the fully developed flow are independent of channel length. It is noted that the lower channel inclination and higher Reynolds number lead to lower skin friction coefficient, resulting in lesser energy loss. Further, it is also shown that the flow in the developing region can be regarded as locally, fully developed.