## 1 Introduction  
Deterioration, induced by operational and environmental effects, leads to a gradual decline of the performance of an aircraft engine [1, 2, 3]. Therefore, requirements for rapid full-engine simulations occur. Numerical calculation methods for aeroengines can be divided into three different types: zero-dimensional, two-dimensional/quasi three-dimensional and three-dimensional. The zero-dimensional calculation does not need detailed geometric parameters, has very low requirements in terms of computer resources and is very fast. It is suitable for scheme evaluation and preliminary design. However, the accuracy of such a calculation depends on the characteristic lines of the existing components and reliable experimental data. At the same time, the flow field of the main channel and the secondary air system (SAS) of the engine cannot be simulated, so the flow field information cannot be used in the optimization of specific components[PERSON]  
Compared with the zero-dimensional simulation, 3D simulation can describe the three-dimensional relationship between the components and the whole flow channel, and can be used to discuss the complex physical phenomena and flow field structure inside the components. However, in order to obtain such abundant flow field details, a large amount of computer resources are required[PERSON] In the current literature, there are a few published studies on 3D high fidelity simulation calculation of an aeroengine. The center for turbulence simulation (CITS) of Stanford University has carried out a series of research aimed at developing integrated high fidelity aeroengine simulation technology and has been able to achieve preliminary simulation of the whole aircraft engine [4; 5]. [PERSON] et al. [6] completed the simulation of a 20 degrees sector of a gas turbine engine including the fan, compressors, turbines, the exit nozzle and the combustor. The simulation was performed on two different meshes; one was fine, and the other was coarse. For the coarse mesh which contained 14 million cells, the simulation was performed on 700 processors and required around two weeks to converge [7; 8; 9; 10]. Three-dimensional simulation of the aeroengine main channel requires a computational speed of more than \(10^{12}\) per second [11]. Full 3D simulation requires enormous amounts of relatively accurate data such as [PERSON] conditions and initial conditions, which is not easy to obtain. [PERSON] et al. [12] pointed out that even if the current computing capabilities can meet these requirements, considering the large number of resources required for full 3D calculations, it is still difficult to use the full 3D simulation as a tool for conventional research in Aeroengine Design in the short term. In contrast with 0D and 3D simulation, quasi three-dimensional simulation exhibits unique advantages. First of all, quasi-3D simulation can provide more abundant \(\mathrm{S}_{2}\) flow field information. Secondly, quasi-3D simulation is easy to implement due to the small amount of calculation. Finally, for specific cases, the quasi-3D simulation can use empirical or semi-empirical models, such as loss and blockage models obtained from the experimental data, to modify the flow field results, so as to avoid the amplification of the flow field calculation error caused by the limitations of the turbulence model. Last but not least, the simulations of full-engine in the literature mentioned above have not included the SAS, which is known to have a considerable impact on the engine performance [13]. As a part of the SAS, seal cavity leakage flow occurs in the seal cavity at shrouded stator root (in compressors and turbines) or shrouded rotor tip (usually in turbines). Figure 1 shows the seal cavity leakage in a compressor with shrouded stator. Although the flow exchange between the main channel and the cavity below the axial gap is often suppressed by engineering measures such as a labyrinth seal, it is difficult to fully eliminate the leakage from the axial gap.