Abstract: A two-dimensional convective turbine blade cooling model is presented, considering the heat conductivity both in the radial direction and in the direction normal to the blade wall for improved prediction accuracy. This model divides the blade wall into small elements in the chord wise direction, neglecting the temperature variation in that direction. In each element, 2D heat conductivity equation is established in the radial direction and in the direction normal to the blade wall as governing equation for the temperature field of the blade solid wall. Boundary conditions for the equation include the adiabatic temperature and heat transfer coefficient of the gas-side blade wall, and the heat flux through the blade tip and root. The 2D heat conductivity equations with conditions for the model and the corresponding differential solving method are all provided. This model is then applied to a high-pressure turbine vane of E ³. The comparison between the gas-side wall temperature results of the model and CFD is conducted. It shows that with the given coolant mass, the blade gas-side wall temperature distribution predicted by the model is similar to that by the CFD and the maximum error is less than 6.5% with a reduction of 95% in simulation time. It is proved that this model can be employed to obtain the turbine blade convective coolant flow requirement quickly and accurately.

Key words: Turbine;Blade;Convective cooling;Heat transfer;Temperature distribution;Calculation model

摘要： 为了提高涡轮叶片对流冷却模型预测精度，提出了一种在叶片固壁内同时考虑叶片径向和垂直于壁面方向（法向）导热的二维对流冷却模型。该模型在弦长方向划分多个元素，忽略元素内弦长方向叶片温度变化，在元素内的径向和法向建立二维导热方程作为叶片固壁温度场的控制方程，其边界条件包括叶表燃气绝热温度、燃气侧对流换热系数和叶片叶根、叶顶热流密度等。给出了该模型二维导热方程和边界条件的差分求解方法。以E ³涡轮高压导叶为例，将模型与CFD计算的叶片外壁面温度分布进行了对比。结果表明，该模型在给定冷气量下预测的叶片温度分布变化趋势与CFD相近，最大温度误差不超过6.5%，计算时间与CFD相比缩短了95%，能够快速、准确预测涡轮对流冷却叶片的冷气需求量。

关键词: 涡轮;叶片;对流冷却;热传导;温度分布;计算模型