基于定涡黏性连续伴随的叶栅气热优化方法研究

Study on Continuous Adjoint Method for Turbine Cascade Aerodynamic and Heat Transfer Optimization Design Based on the Constant Eddy Viscosity Assumption

本文基于网格节点位置坐标变分技术及流动通量雅克比矩阵,在定涡黏性假设下推导了适用于透平叶栅的连续伴随优化系统,降低了RANS方程下伴随系统的推导难度。针对透平叶栅气动换热优化问题,从质熵流和热熵流的角度定义了熵增目标函数,以综合衡量叶栅的气动和换热性能,其中质熵流对应流动损失,热熵流对应叶片表面换热损失。与定涡黏性假设下的连续伴随系统结合,详细推导了伴随方程及边界条件,建立了气动换热伴随优化系统。选取SST k-ω湍流模型及Gamma-Theta转捩模型进行流场和温度场模拟,配合伴随梯度值,使用最速下降法对无冷却结构的MarkⅡ叶栅和GE-E^3静叶进行了气动换热伴随优化分析。优化后总目标函数分别下降了32.95%和8.81%,验证了连续伴随优化系统的有效性。

In this paper, the continuous adjoint system for turbine cascade aero-thermal optimization based on the constant eddy viscosity(CEV) assumption was established by using the variation technique in the grid node coordinates combined with Jacobian Matrics of flow fluxes, which reduced the derivation difficulty of the RANS equations. For turbine cascade aerodynamic and heat transfer optimization problem, the aerodynamic and heat transfer performances were evaluated comprehensively through the objective of system entropy generation, in which the mass entropy flow represents the flow loss and the heat entropy flow corresponds to the heat transfer loss on the blade surface. Combined with the continuous adjoint method under the CEV assumption, the specific adjoint equations and relative boundary conditions were deduced in detail, and the corresponding aerodynamic heat exchange optimization system was established. The SST κ-ω turbulence model and Gamma-Theta transition model were selected to simulate the internal flow and temperature field.Then the flow and heat transfer performance analysis of Mark II cascade without cooling structure and the GE-E^3 vane were calculated using the adjoint gradients and steepest descent method. The total objective function after optimization was decreased by 32.95% and 8.81% respectively. The effectiveness of the continuous adjoint optimization system was verified.