## 2 Numerical Model and Research Object  
The governing equations of CAM are the circumferentially averaged Navier-Stokes equations. Spalart-Allmaras (S-A) one equation model is adopted for turbulence modelling. Since the Mach number is below 0.3 in the shrouded cavity and above 0.3 in the main passage, the preconditioning technique proposed by [PERSON] and [PERSON] [30] is applied to avoid the stiffness of compressible equations at low speed. A time-marching finite volume method is chosen to solve equations. The validation of CAM by NASA Rotor 67 and a high-loaded low speed fan TA36 can be found in references [31; 32]. More details for CAM can also be reviewed in references [33; 34].  
In the calculation of labyrinth leakage flow, the accuracy of CAM is validated by the data of [PERSON] [35]. [PERSON] et al. tested the straight-through labyrinth shown in Figure 2, and obtained the flow characteristics of the labyrinth under 12 working conditions (pressure ratio from 1.0031 to 1.8974). See reference [35] for details of test pieces and test equipment. For the case that the clearance between the labyrinth teeth Cl = 0.36 mm, they also calculated with Fluent. The calculation results of CAM are compared with their experimental results and Fluent calculation results.  
Figure 1: The seal cavity leakage in a compressor with shrouded stator.  
The computational mesh of CAM is shown in Figure 3. The number of grid points is 5123. The total temperature \(T_{0}^{*}\), total pressure \(p_{0}^{*}\) and flow direction (horizontal intake) are given at the inlet. The static pressure \(p_{b}\) is given at the outlet. Adiabatic no-slip condition is applied at wall surface. The relationship between mass flow parameter and inlet/outlet pressure ratio is shown in Figure 4. It can be seen that the calculated results of CAM are in good agreement with the experimental results, and the errors are basically within the range of experimental uncertainty (4.00\(-\)4.90%). When the inlet/outlet pressure ratio is in the range of 1.48 to 1.88, the calculation accuracy of CAM is higher than that of the Fluent calculation performed by [PERSON] et al.  
The throughflow program CAM has been applied to the first three stages of a high-loading transonic six-stage compressor with inlet guide vanes (IGV). The flow path with sealing cavity is shown in Figure 5, where the geometric structure of the channel, cavity and labyrinth is simplified to some extent. Table 1 provide the values of specific blade parameters. In Figure 6, the computational mesh is shown. The channel and the mainstream  
Figure 4: Relationship between mass flow parameter and inlet/outlet pressure ratio.  
Figure 3: Computational mesh of CAM.  
Figure 2: Geometry of labyrinth.  
flow path grid are matched at the junction interface. In order to study the influence of seal leakage flow on the compressor as a whole and on each row of blades, six configurations were set up to adjust the leakage flow by changing the size of the tip clearance (c) of the labyrinth. The setting of each configuration is described in Table 2. When the tip clearance is 0, the seal cavity of the corresponding stage is removed, and only the mainstream flow path grid is retained. The silhouettes for different configurations are shown in Figure 7.  
The boundary conditions are as follows: for the main flow of the compressor, the total temperature, total pressure and flow direction are given at the inlet, i.e., standard atmospheric conditions and horizontal intake. For different working conditions, given the corresponding static pressure at the outlet hub, the static pressure distribution along the spanwise direction at the outlet is obtained by using the simplified radial equilibrium equation. The numerical simulation was carried out at the design speed, i.e., 12,302 rpm. Table 3 shows the number of grid points of configuration 4, and the convergence time is about 1.5 h.