Rotating cavities with axial throughflow are found inside the compressor rotors of turbo-machines. The flow pattern and heat transfer in the cavities are known as sophisticated problems. Because of the numerical errors and model errors, as well as the stiffness introduced by low-Ma number, prediction of 3D unsteady flow and heat transfer in rotating cavity is still a challenge for modern CFD technology.
An in-house 3D unsteady CFD code was developed in this study. The discontinuous galerkin method, which can fulfill any high-order accuracy on the unstructured grid, was applied to reduce the discretization errors. The SST-γ-Reθ transition model proposed by Menter was applied to reduce the model errors. To overcome the stiffness and achieve good convergence characteristics and solution quality, the preconditioning matrix technique combined with DG method was introduced for low-Ma number viscous flow. First, natural convection of air in a square cavity was studied to test the code. The feasibility and credibility, of applying the DG method and the preconditioned matrix technique for buoyancy–induced Rayleigh-Bénard like flow, were further verified. Second, the 3D compressible flow field in a rotating cavity was investigated numerically using the FV method, DG method and laminar/SA/SST-transition turbulence model. It is demonstrated that the whole flow structure of all calculated cases was similar after comparing the calculated results with the available experimental data. But, the transition turbulence model fitted the experimental data better. On the other hand, the performance of high-order method was much better for both the rotating cavity flow and natural convection, in terms of heat transfer.
To better understand this phenomenon, an accuracy analysis of heat flux using DG method and FV method was performed. It showed the DG method could realize arbitrary precision of viscous stress and heat fluxes on irregular unstructured grids, while the FV method could only realize the first-order accuracy of the heat fluxes at the boundary faces and may exhibit erroneous behaviors. It also demonstrated that the high-order accuracy of gradients was needed to decrease errors of heat fluxes and viscous stresses, and that DG method was a promising method.
A Sub-element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods
