Direct numerical simulation of flow and heat transfer in a turbine cascade with incoming wakes

Direct numerical simulations (DNS) of flow in a turbine cascade with heat transfer have been performed. The set-up of the simulations was chosen in close accordance with previous experiments. Three of the experimental situations were simulated: one without free-stream turbulence and two with periodically incoming wakes of different frequency and with different levels of background fluctuation. Hence, the calculations allow us to study the influence of impinging wakes and background fluctuations on the development of the boundary layers and the local Nusselt number along the surfaces of the heated blade. Along the suction side, the pressure gradient is first favourable and then turns adverse near the trailing edge and the boundary layer remains laminar for the case without free-stream turbulence with the Nusselt number showing the typical decay from the leading to the trailing edge. With periodic wakes and background turbulence, transition occurs when the pressure gradient turns adverse, but intermittency persists so that the boundary layer is not fully turbulent when the trailing edge is reached. In this region, the heat transfer is increased significantly by an amount comparable to that found in the experiments. In the pre-transitional region with favourable pressure gradient, the flow acceleration stretches the free-stream vortices, aligning their axis with the flow direction, thereby forming streamwise vortical structures. These increase the laminar heat transfer in this region by 20–30%, which is, however, much less than observed in the experiments. On the pressure side, the pressure gradient is favourable along the entire blade so that the boundary layer remains laminar. Here, the wakes, through their impingement, also generate streamwise vortical structures which, because of the low convection speed on this side, have a very long lifetime compared to the structures along the suction side. Also these structures increase the laminar heat transfer by about 30%, which for the case with the highest wake frequency is again much less than in the experiments. The simulated average level of fluctuations in the laminar parts of the boundary layers is comparable or even higher than that in the experiments so that it seems likely that a difference in the spectral contents causes the discrepancies. The wake turbulence entering the calculation domain corresponds to that in far wakes with relatively small-scale structures, whereas in the experiments the wakes most probably still carried some large-scale fluctuations of the size of the wake width, which have been found to be more effective in increasing laminar heat transfer.