On the Use of Periodic Boundary Condition for Large Eddy Simulation of Trailing Edge Cutback Film Cooling With Internal Ribs
Authors: Aillaud Pierre , Duchaine Florent , Gicquel Laurent , Koupper Charlie 
Published: August 2018

One of the state-of-the-art system for turbine blade trailing edge cooling consists in blowing air, coming from the internal cooling system of the blade, through slots over a cutback on the pressure side. To increase the stiffness, this cutback is commonly equipped with internal ribs. The classical RANS method is widely used in industry to design such a system. However, it has been shown that the accuracy of such a stationary formalism is limited for the prediction of the adiabatic effectiveness due to the fact that the flow is driven by large-scale unsteadiness. In this context, Large Eddy Simulation (LES) appears as a good alternative to improve the quality of the predictions. However, the LES formalism has been scarcely used for trailing edge cooling configuration mainly because of the computational effort associated with such a problem as well as the need to deal with real complex geometries. To reduce costs, most of the time LES studies assume a periodic flow in the spanwise direction. Using this hypothesis, only one cooling passage is simulated making use of a lateral periodic boundary condition. The flow is however likely to be forced by this assumption while the side effects due to the end walls are neglected. In practice, the applicability of this periodic boundary condition has been rarely investigated in past studies. In the case of a trailing edge cutback equipped with internal ribs, there are several phenomena, e.g. coalescence of adjacent jets, which should be considered before using a lateral periodic boundary condition. In the present study, the relevance of such a periodic boundary condition is investigated. To do so, a transonic vane trailing edge equipped with a pressure side cutback and internal ribs is simulated using LES. The chosen setup was studied experimentally at DLR within the framework of the European project AITEB-2. The cooling air is blown through a channel, which is equipped with 2 rows of ribs in an inline arrangement to increase the stiffness of the thin trailing edge region. From the experimental results, it is reasonable to assume that several jets merge if looking at the adiabatic effectiveness results. Therefore, this configuration appears as a good candidate to investigate the relevance of lateral periodic boundary condition for trailing edge cutback flows. To achieve this, two LES are performed for two different computational domain sizes using lateral periodic boundary conditions. Merging of adjacent jets, expected from the experimental results, is highlighted in the simulations. This regrouping mechanism is shown to be dependent on the size of the computational domain. A strong sensitivity of the local adiabatic effectiveness to the computational domain size is highlighted while the global adiabatic effectiveness shows little sensitivity. Finally, it is shown that state-of-the-art RANS modeling is unable to reproduce correctly the local distribution of the adiabatic film effectiveness as well as the decrease of the laterally averaged effectiveness.