中文摘要：

本文在所构建的基于统一的间断Galerkin（DG）方法求解气热耦合问题的理论框架基础上，将二方程湍流模型BSL／SST和二方程转捩模型7～Re日纳入其中，并对对数形式的ω方程的源项近似隐式处理以减小其刚性带来的不利影响，进而实现了基于显式RKDG方法的RANS方程、湍流方程、转捩方程和Fourier方程的全耦合同步求解，增强了对复杂耦合传热问题的适用性。在此基础上对高压内冷透平叶栅MarkII的5411工况进行了多种模型的二维气热耦合模拟。计算得到的叶片表面压力分布与实验值吻合良好；含有转捩模式的模型计算的表面温度分布与实验值的吻合程度明显好于不含转捩模式的模型；基于RKDG的SST＋Y-Reo模型可同时捕捉到强弱激波、转捩、分离等现象。本文的工作可为DG这种未来具有相当发展潜力的高精度CFD算法进一步应用于叶轮机械内部复杂耦合传热的模拟中提供研究参考。

英文摘要：

On the basis of the pre-built unified framework for Conjugate Heat Transfer （CHT） simulations based on Discontinuous Galerkin （DG） methods, this work introduced the two-equation turbulence models BSL/SST and a two-equation transition model y - Ree into the method and the code. An approximate implicit treatment of the turbulence source terms were derived to decrease the adverse impact rooted in their stiffness on the computations to some extent. The coupled equations including RANS, turbulence, transition and Fourier equations were solved under the unified explicit RKDG algorithm and the performance of the methods for more complex CHT simulations were improved. A 2-D model of high-pressure turbine vane （named Mark II） with 10 convection cooling holes was simulated to validate the feasibility of the above methods. The results of pressure distributions on the vane surface coincided with the available experiment data well. For the temperature distributions, the models with Y - Reo transition model behaved obviously better than the ones without it and the SST＋V - Reo model can predicted the features of strong and weak shocks, transition and separation. The presented work might be viewed as an attempt towards further ap- plications of high-order accuracy numerical methods in complicated CHT problems of turbomachinery.