Direct Numerical Simulations of Transitional Flow in Turbomachinery

An overview is provided of various direct numerical simulations (DNS) of transitional flows in turbine-related geometries. Two flow cases are considered: the first case concerns separating flow over a flat plate and the second case flows in turbine cascades. In the first case, in which $Re=60,000$⁠, either an oscillating oncoming flow (1) or a uniform flow with and without oncoming turbulent free-stream fluctuations (2) is prescribed at the inlet. In both subcases (1) and (2), separation is induced by a contoured upper wall. In (1), the separated boundary layer is found to roll up due to a Kelvin-Helmholtz (KH) instability. This rolled-up shear layer is subject to spanwise instability and disintegrates rapidly into turbulent fluctuations. In (2), a massive separation bubble is obtained in the simulation without oncoming free-stream fluctuations. A KH instability is eventually triggered by numerical round-off error and is followed again by a rapid transition. With oncoming turbulent fluctuations, this KH instability is triggered much earlier and transition is enhanced, which leads to a drastic reduction in size of the separation bubble. The second case, concerning flow in turbine cascades, includes (1) flow in the T106 turbine cascade with periodically oncoming wakes at $Re=51,800$ and (2) flow and heat transfer in a MTU cascade with oncoming wakes and background turbulence at $Re=72,000$⁠. In the simulation of flow in the T106 cascade with oncoming wakes, the boundary layer along the downstream half of the suction side is found to separate intermittently and subsequently rolls up due to a KH instability leading to separation-induced transition. At times when the wakes impinge separation is suppressed. In the simulations of flow around a MTU turbine blade, evidence of by-pass transition in the suction-side boundary-layer flow is observed while the pressure-side boundary layer remains laminar in spite of significant fluctuations present. In agreement with the experiments, the impinging wakes cause the heat transfer coefficient to increase significantly in the transitional suction-side region close to the trailing edge and by about 30% on the pressure side. The large increase in heat transfer in the pre-transitional suction-side region observed in the experiments could not be reproduced. The discrepancy is explained by differences in spectral contents of the turbulence in the oncoming wakes.