Second, the available turbulence models cannot meet the requirements of modern turbine design.

First, the appropriate flow experiments are difficult to carry out. However, this is not so for the flow characteristics, for two reasons. Research into heat transfer characteristics has now reached a mature stage. In studies of blade cooling, the middle chord is usually modeled as a U-shaped channel, and the investigation of heat transfer and flow field characteristics is focused on the bend section of the channel. Therefore, an optimized design of the middle chord is important to improve the cooling efficiency of turbine blades. As one of the effective types for internal cooling, serpentine passage in the middle chord has been investigated and applied in the turbine blades for more than 30 years. Turbine blade cooling can generally be classified into external and internal cooling. The flow in the bend section is complex, there is a relatively high proportion of turbulent kinetic energy in the low-order modes, and there is an obvious stripe-like structure in the bend section of the channel in which the bend has both inner and outer circular walls, which matches the velocity field from the POD. It can be seen from the clear differences in the Reynolds stress for different bend sections that the fluctuations caused by the mixing of the main flow and the vortices are significantly stronger than those at the boundary. The size and number of vortices in the corner area are significantly reduced because the increase in the Reynolds number makes the impact of the influx stronger. For the main flow, the structure of the bend section has an obvious influence on the flow field characteristics. A series of important conclusions are drawn from the results. The mean flow and Reynolds stress are considered, and proper orthogonal decomposition (POD) is used to investigate the flow characteristics. The Reynolds number based on the hydraulic diameter of the channel is 8888, 13 333, or 17 777. Time-resolved particle image velocimetry is used to study internal flow field characteristics in U-shaped channels of square cross section and different structures of the bend section.

Pod using tecplot