Numerical study on flow rate limitation of open capillary channel flow through a wedge

Introduction

Open capillary channel is a structure that contains a liquid with one or more gas–liquid interfaces, which plays an important role in a number of applications in liquid management in space science, such as heat pipes and propellant management devices (PMD) in on-orbit refueling tanks of satellites.^1,2 Under the condition of microgravity, the gravity is negligible and the flow in the channel is dominated by convection, viscous stress, and surface tension. With the increase in flow rate, the pressure difference across the gas–liquid interface gradually increases, and the free surface has to bend inward to balance it. The subcritical phenomenon is observed when the interface is stable. Once the growth rate of pressure difference exceeds the surface curvature change rate, the surface collapses and gas ingests into the channel. This phenomenon is called choking, and we also call it as supercritical phenomenon, which is undesired for many applications. In critical state, the maximum flow rate is reached before the free surface becomes unstable. Thus, the study of flow rate limitation and behavior of the free surface in capillary channel is critical for efficient tank design and liquid management in certain fields.

Early research on capillary channel flow (CCF) under microgravity conditions began with the liquid flow experiments between parallel plates in drop tower.³ Jaekle¹ presented the governing equation for theoretical analysis but the errors of analytical solution are too high due to the neglect of curvature along the flow direction. Rosendahl et al.^4–6 proposed the steady one-dimensional (1D) momentum equation to investigate forced flow between parallel plates and validated with drop tower and sounding rocket flights. The unsteady flow in parallel plates is studied theoretically, numerically, and experimentally by Grah and colleagues.^7–9 Haake et al.¹⁰ expanded 1D theory to groove-shaped channel and verified the numerical solution in the Bremen drop tower.

The wedge-shaped channel (Figure 1) has also been investigated with numerical and experimental methods. The geometry is verified for its good performance in experiment of positioning the liquid¹¹ in PMD. Klatte et al.¹² developed an iterative procedure with surface evolver (SE) algorithm to calculate the critical flow in wedge channel and validated it with drop tower experiments. Wei et al.¹³ also performed theoretical...