## 1 Introduction  
The nine ventilation system plays a crucial role in the safety and efficient production of coal mines, and the fan, as an indispensable power equipment of the mine ventilation system, directly determines whether the ventilation system can operate efficiently and stably [1, 2, 3]. The mine counter-rotating axial flow fan consists of two impellers rotating in opposite directions and has the advantages of compact structure, high air pressure, and large flow rate, which has been widely used in mines and tunnels [4, 5, 6]. In axial flow fluid machinery, there is a certain clearance between the impeller tip and the shroud, leading to the phenomenon of tip leakage flow. The tip leakage flow interferes with the mainstream, seriously affecting the flow characteristics in the impeller. Moreover, the complex flow in the impeller inevitably leads to energy loss, which in turn reduces the working capacity and operating efficiency of the fan [7; 8; 9; 10]. Therefore, studying the flow characteristics and loss mechanism of the tip leakage flow is of great significance for expanding the range of efficient operation of the fan and improving its stability. Scholars both domestically and internationally have conducted numerous studies on the tip leakage flow of fans and have achieved certain results. Currently, researchers mostly explore the flow characteristics of tip leakage flow through experimental and numerical calculation methods. [PERSON] et al. [11] used particle image velocimetry (PIV) to study the tip leakage flow in low-speed axial flow fans and observed the tip leakage vortex (TLV) structure. [PERSON] et al. [12] studied the evolution of the tip leakage vortex in low-pressure axial flow fans using PIV. They found that when the velocity is high, the leakage vortex moves downstream, but its intensity decreases. [PERSON] et al. [13] studied the tip leakage flow of the circumferentially skewed axial flow fan through numerical simulation and experiments. They found that the forward skewed blade is effective in controlling the tip leakage flow to expand the stall-free operation range under off-design conditions. [PERSON] et al. [14] conducted research on the flow characteristics of leakage under different tip clearances and found that although leakage flow occurs when the tip clearance is small, a leakage vortex does not necessarily form. As the tip clearance increases, the leakage flow becomes less apparent, being replaced by a leakage vortex, and the intensity and affected region of the leakage vortex increase with the enlargement of the clearance. [PERSON] et al. [15] investigated the effect of tip clearance on the performance of an axial fan and found that tip clearance was the main source of flow loss in the impeller. As the clearance increases, the influence region of the leakage flow will further increase, enhancing the blockage of the mainstream and resulting in greater energy loss. [PERSON] et al. [16] investigated the effect of rotor-stator interaction on the tip leakage vortex of a low-speed axial fan. The evolution of the tip vortex was observed in the tip region of the fan rotor passage, and the vortices were rolled up at different chordwise positions. As the flow rate decreased, there was a noticeable trend for the vortices to move towards the leading edge of the blade. [PERSON] et al. [17] discussed the impact of different tip clearance shapes on leakage flow. A converging clearance altered the distribution of the vorticity field within the clearance, reducing tip leakage losses and enhancing the work capacity of the upper part of the blade. In contrast, using a diverging clearance led to a decrease in work capacity, with the fan performance being inferior to that of a uniform clearance. Additionally, the vorticity intensity of the tip leakage vortex decreased along the vortex line and reduced with the decrease in flow rate. [PERSON] et al. [18] investigated the effect of the shroud fence on the tip leakage flow of an axial fan.