The application of discontinuous Galerkin methods in conjugate heat transfer simulations of gas turbines

Abstract

The performance of modern heavy-duty gas turbines is greatly determined by the accurate numerical predictions of thermal loading on the hot-end components. The purpose of this paper is: (1) to present an approach applying a novel numerical technique-the discontinuous Galerkin (DG) method-to conjugate heat transfer (CHT) simulations, develop the engineering-oriented numerical platform, and validate the feasibility of the methodology and tool preliminarily; and (2) to utilize the constructed platform to investigate the aerothermodynamic features of a typical transonic turbine vane with convection cooling. Fluid dynamic and solid heat conductive equations are discretized into explicit DG formulations. A centroid-expanded Taylor basis is adopted for various types of elements. The Bassi-Rebay method is used in the computation of gradients. A coupled strategy based on a data exchange process via numerical flux on interface quadrature points is simply devised. Additionally, various turbulence Reynolds-Averaged-Navier-Stokes (RANS) models and the local-variable-based transition model γ-Reθ are assimilated into the integral framework, combining sophisticated modelling with the innovative algorithm. Numerical tests exhibit good consistency between computational and analytical or experimental results, demonstrating that the presented approach and tool can handle well general CHT simulations. Application and analysis in the turbine vane, focusing on features around where there in cluster exist shock, separation and transition, illustrate the effects of Bradshaw's shear stress limitation and separation-induced-transition modelling. The general overestimation of heat transfer intensity behind shock is conjectured to be associated with compressibility effects on transition modeling. This work presents an unconventional formulation in CHT problems and achieves its engineering applications in gas turbines.