The Application of Discontinuous Galerkin Methods in Conjugate Heat Transfer Simulations of Gas Turbines

Zeng-Rong Hao,Chun-Wei Gu,Xiao-Dong Ren

doi:10.3390/en7127857

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.

Highlights

The continuous increase of the combustor outlet temperature has been producing incessant breakthroughs in the performance of modern aero engines and heavy-duty gas turbines
This method taking advantage of available single-filed solvers had been promptly adopted by some investigations [2,3,4,5,6], most of which used mature parabolic or elliptic equation solvers based on finite element (FE) methods in the solid domain
We present a primary framework for conjugate heat transfer (CHT) simulations applying the discontinuous Galerkin (DG) methods on unstructured grids and a corresponding code fit for general engineering problems in gas turbines is developed

Summary

Introduction

The continuous increase of the combustor outlet temperature has been producing incessant breakthroughs in the performance of modern aero engines and heavy-duty gas turbines. The thermal load of hot-end components has been steadily increasing, which necessitates the application of more complex cooling structures, such as various types of film cooling holes, impingement cooling holes, fins and serpentine-shaped channels, etc The use of these structures increases the conjugate effects of heat transfer between hot flow, cooling flow and solid. In 1999, Martin et al [1] developed a sequential conjugate strategy, by which a code for gas flow field computation and another one for solving heat conduction in solid blade was combined through an inner iteration process This method taking advantage of available single-filed solvers had been promptly adopted by some investigations [2,3,4,5,6], most of which used mature parabolic or elliptic equation solvers based on finite element (FE) methods in the solid domain. Partially aiming at enhancing the stability of the algorithm, the direct or full conjugate strategy [7,8,9,10,11] that integrates the governing equations in both fluid and solid domains using a single code began to be developed and applied

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