## 1 Introduction  
Supercritical carbon dioxide (SCO2) has excellent physical properties and can bring outstanding compactness and high efficiency to the Brayton cycle power system [1]. In recent years, the Brayton power cycle system with SCO2 as working fluid has been widely investigated by scholars [2; 3; 4; 5]. The turbine is the core part of the power cycle system, which plays a critical role in generating power. The axial-inflow turbine becomes the best choice when large output power is required. In order to improve the vibration performance, the shrouded blades are usually utilized. The leakage of working fluid at the tip clearance causes a decrease in power and efficiency. Under these circumstances, the labyrinth seal (LS) is generally utilized for the reduction in leakage [6]. A series of research on the performance of LS has been carried out, most of which are focused on the influence of structural parameters. [PERSON] [7] numerically analyzed the performance of LS considering mushroom wear and explored the effects of seal clearance, pressure ratio, number of teeth and velocity. [PERSON] [8] investigated the performance of stepped LS under different structural parameters. The difference of leakage mechanism between the upwind and backwind structures has also been obtained. The Computational Fluid Dynamics (CFD) method was adopted to study the influence of structural and operation parameters on tangential friction coefficients by [PERSON] [9] and the leakage performance of four LS configurations was also studied [10]. [PERSON] [11] optimized the structural variables of LS with honeycomb holes and achieved a reduction in leakage. Parametric research on a type of LS with honeycomb holes was conducted by [PERSON] [12] and the influence of honeycomb size, pressure ratio and clearance on performance was obtained. [PERSON] [13] studied the effect of gap thickness on mass flow coefficient under different working conditions. [PERSON] [14] experimentally and numerically investigated the influence of the stator hole on the performance of LS. However, the above research was only carried out for LS without consideration of the blade region. The coupled analysis of LS and blade was also conducted by plenty of scholars. [PERSON] [15] studied the mixing effect of flows in leakage passage and cascade when the LS was arranged on the top of the rotor blade. The results agreed utterly with the test data. A new type of radial seal was proposed by [PERSON] [16], and the large flow resistance and low leakage were achieved compared with the traditional LS. [PERSON] [17] concluded that the LS arranged on the top of the shroud can significantly reduce the total pressure loss. Flow characteristics of LS on an axial-flow turbine were investigated with low Mach number preconditioning technique by [PERSON] [18]. [PERSON] [19] developed a type of cavity seal and greatly reduced the aerodynamic force of LS under small clearance. [PERSON] [20] proposed a multi-dimensional coupling simulation method to study the flow field characteristics of a turbine with LS under various operating conditions. The numerical study carried out by [PERSON] [21] proved that the interaction of flows mainly affects the top flow field. It is noted that although there is some research on the performance of LS arranged on the top of the blade shroud, the selected working fluid is all air or gas. However, there are major differences between the physical properties of SCO\({}_{2}\) and air, such as density, viscosity and compress factor. It is necessary to investigate the performance of LS with SCO\({}_{2}\) as a working fluid. Only [PERSON] [22] and [PERSON] [23] have carried out a preliminary investigation on SCO\({}_{2}\) LS, but comprehensive research on SCO\({}_{2}\) LS coupled with a blade is also in absence. Therefore, the investigation on a SCO\({}_{2}\) axial-inflow turbine with LS is carried out in this paper. Configurations with LS arranged on the top of the shroud of both stator and rotor blade are established.