Spanwise-averaged computational method for non-axisymmetric flow and heat transfer in rotating cavity

This is the authors' abstract. We don't add key points for this paper.

The complex three-dimensional non-axisymmetric flow within the compressor cavity requires full 360 circumferential domain to capture accurately, whereas simplified two dimension (2D) axisymmetric calculations yield substantial errors. Accurate assessment of tip clearance variations during engine transient processes necessitates transient conjugate heat transfer (CHT) calculations. However, transient CHT calculations impose substantial computational time costs. Even with time-acceleration algorithms, the large spatial grid size required for full 360° circumferential coverage of the compressor disk cavity remains a limiting factor. This paper proposes a novel dimensionality reduction computational method enabling 2D calculations to achieve equivalent results to three dimension (3D) full-circumference computations, significantly reducing computational demands. By applying a spanwise averaging process to the Navier–Stokes (N–S) equations, spanwise-averaged N–S equations are obtained. Missing spatial field information is supplemented in the form of spanwise-stress residual (SSR) tensor. Various forms of SSR suitable for different conditions are explored. This method is validated in both simple square cavity natural convection cases and compressor disk cavity cases. The difference between the 2D case with added SSR and the 3D case is small. For transient process simulations, interpolation methods can be employed to obtain the SSR at each time step. The SSR is iteratively updated until convergence is achieved. Comparison of the transient iterative calculation results with existing experimental data demonstrates the reliability of this method for transient CHT calculations. This method achieves acceleration factors approaching 100 times for transient CHT calculations, providing a pathway for accurate and rapid simulation in engineering applications.