基于标量扩散方程的气膜冷却二维分布理论模型

2-D Scalar Diffusion Equation Based Model for Predicting Film Cooling Effectiveness

气膜冷却效率的参数化方法对燃机透平的冷却设计具有重要作用,已有关联式多集中于拟合横向平均的冷却效率分布,而对二维参数化拟合方法关注很少。本文引入了标量扩散方程,并在已有一维横向平均有效度分布基础上,模拟气膜孔出口下游冷气的横向分布规律,考虑时均后的湍流度影响,用有效扩散系数描述在不同吹风比下冷气的横向扩散效果。研究结果表明,随着射流吹风比的提高,有效扩散系数先减小后有所回升。误差分析表明,标量输运方程能够很好地模拟冷气的二维分布,有效度偏差均值小于0.05,满足工程设计需求。

Methods for film cooling effectiveness predictions are widely employed in gas turbine cooling design.There have existed some correlations for the laterally averaged cooling effectiveness along the streamwise direction,but few paid attentions to the 2-D prediction methods.The current work introduces the scalar diffusion equation to simulate the coolant lateral expansion,extending the 1-D equation into 2-D.The effective diffusion coefficient is modelled,considering effects of the turbulence transportation and molecular diffusion under varying blowing ratios.Results come that with increasing blowing ratios,the effective diffusion coefficient presents a down-and-up trend.The diffusion equation is validated to be able to well predict the 2-D effectiveness distributions,and the error is within 0.05.