To evaluate turbulent heat transfer on rotating turbine blades, knowledge of the Reynolds stress and heat conduction moments on the blades is required. This involves solving the mean flow equations of momentum and thermal energy on the rotating blades. In this paper, the turbine blades are represented by rotating curved surfaces, and turbulent heat transfer calculations are carried out by invoking a valid Reynolds analogy because of its simplicity. The classic Reynolds analogy is defined as the ratio between the eddy and thermal diffusivity in a stationary plane flow; however, its counterpart for rotating curved flows is still not known. To derive a Reynolds analogy for rotating curved flows, appropriate turbulence models to close the Reynolds transport equations for momentum and thermal energy are required. Assuming that, in the constant flux region, advection and diffusion of Reynolds stress and heat conduction moments are negligible compared to the production of turbulent energy, the Reynolds shear stresses and heat conduction moments can be solved in terms of the mean flow gradients, a turbulent Prandtl number (Pr_t)_rc and a gradient Richardson number for rotating curved flows Ri_rc. These dimensionless numbers are dependent on mean flow properties, surface curvature, and system rotational speed. Thus derived, the classic Reynolds analogy can be recovered only when Ri_rc << 1 and (Pr_t)_rc = 1. For turbine blade heat transfer, Ri_rc is not necessary very small and (Pr_t)_rc differs from unity in the whole flow field. Therefore, using the classic Reynolds analogy to estimate turbine blade heat transfer will lead to incorrect result. The new Reynolds analogy, formulated for turbulent thermal flows on rotating curved surfaces, takes all pertinent external body force effects into account; thus, turbulent heat transfer evaluation on turbine blade surfaces can be substantially improved.

为了评估旋转涡轮机叶片上的湍流传热，需要了解雷诺应力和叶片上的热传导矩。这涉及求解旋转叶片上的动量和热能的平均流量方程。在本文中，涡轮叶片以旋转曲面表示，湍流传热计算由于其简单性而通过调用有效的雷诺类比进行。经典的雷诺兹比喻定义为固定平面流中的涡流与热扩散率之比；但是，其旋转弯曲流的对应方式仍然未知。为了得出旋转弯流的雷诺类比，需要合适的湍流模型来关闭动量和热能的雷诺输运方程。假如说，Pr _t）_rc和旋转弯曲流Ri _rc的梯度理查森数。这些无因次数取决于平均流量特性，表面曲率和系统转速。由此推论，只有在Ri _rc << 1和（Pr _t）_rc  = 1时，才能恢复经典的雷诺兹比喻。对于涡轮叶片传热，Ri _rc不必很小，而（Pr _t）_rc在整个流场中不同于统一性。因此，使用经典的雷诺比喻来估计涡轮叶片的热传递会导致错误的结果。新的雷诺类比法是针对旋转曲面上的湍流热流而制定的，它考虑到了所有相关的外力作用。因此，可以显着改善涡轮叶片表面的湍流传热评估。