Turbine design combining shaping and flow injection by using multiscale methodology
Keywords: turbine design
multi-scale method
film cooling
optimization

Recent research suggests that the over tip leakage (OTL) flow at the transonic turbine tip exhibits several unique flow features such as the interaction with the cooling flow, the acceleration at the divergent duct, the shock-boundary layer interaction and the choking at the rear portion of the tip. These flow features require the tip geometry optimization (shaping) to be considered together with tip cooling design (flow control). The blade designs that are generally used in the open literature suggest the shaping and the cooling flow control to be conducted sequentially: first, the shape of the blade is optimized, then the cooling holes are added to the uncooled blade for further optimization. However, because of the interactions between the cooling flow and the main flow, the non-linear nature of the flow in the turbine tip suggests that a potential gain may be obtained by combining blade shaping and cooling flow control.
Due to the significant disparity of the length scales between the cooling holes and the turbine blade, the combination of the cooling design and the tip geometry shaping tends to be too computationally expensive to be employed. The multi-scale method is adopted in a commercial solver to provide a fast and accurate solution for the turbine tip cooling optimization. The method uses source terms added to the coarse mesh to generate the solution close to the one obtained with a well-resolved mesh. The source terms are found to present not only the influence of mesh resolution but also the flow injection. The multi-scale results have been validated against the experimental data and the fine mesh results. The agreement shows the potential for this method to be used in cases with large length scale disparity. It is also the first-of-its-kind work to implement the multi-scale methodology in a commercial solver.
Following up the multi-scale method, a parameterization system and an optimization system are built to optimize the turbine cascades and the turbine stages using the multi-objective genetic algorithm (MOGA). Two optimization approaches are compared: a) a sequential method that optimizes an uncooled shape first and then the cooling configuration, and b) a method that optimizes shaping and cooling concurrently. The concurrent method is found to obtain the aerothermal performance that cannot be achieved by sequential optimization. Moreover, by adding the cooling, the performance ranking of the uncooled blades in terms of the aerodynamic efficiency is changed. These observations are due to the interaction between the coolant and the tip leakage flow. They indicate that the coolant injected at the tip is not passive. By altering the tip leakage flow structure, the coolant can reduce the tip leakage loss. More detailed observations of the flow field indicate that the influence of the squealer height towards the aerodynamic efficiency is caused by two competing effects: the blockage effect to reduce the tip leakage mass flow rate and the sudden expansion loss effect to generate additional losses.
By identifying the vortices in the uncooled turbine stage and the 'equivalent cascade case', a unique vortex structure is found in the squealer cavity due to the relative movement of the casing. The moving casing forms a Casing-driven Cavity Vortex (CCD) along the cavity suction side and induces a counter-rotating Pressure-side Separation Vortex (PSV). The vortex pair changes the flow path of the OTL flow and thus influences the leakage mass flow rate. Furthermore, between the two counter-rotating vortices, the vortex pair entrains the base flow, which induces a high heat flux strip.
In the cooled turbine stage, the vortex pair blocks the leakage flow and makes the blockage effect brought by the cooling flow less effective. Thus in the optimization of the turbine stage, only in the flat tip, the cooling injection is found to improve the efficiency. As the squealer height increases, the vortices divert the original path of the cooling flow and entrain the hot leakage flow to attach to the tip surface. Thus, unlike the cases in the turbine cascade where the cooling effectiveness increases with the squealer height, in the turbine stage, as the squealer height increases, the cooling performance may reduce.