The aerodynamic efficiency of turbomachinery blades is profoundly affected by the occurrence of laminar-turbulent transition in the boundary layer since skin friction and losses rise for the turbulent state. Depending on the free-stream turbulence level, we can identify different paths towards a turbulent state. The present study uses direct numerical simulation as the primary tool to investigate the flow behaviour of the low-pressure turbine blade. The computational set-up was designed to follow the experiments by Lengani & Simoni (2015). In the simulations, the flow past one blade is computed, with periodic boundary conditions in the cross-flow directions to account for the cascade. Isotropic homogeneous free-stream turbulence is prescribed at the inlet as a superposition of Fourier modes with a random phase shift. Two levels of the free-stream turbulence intensity were simulated (Tu=0.19% and 5.2%), with the integral length scale being 0.167c, at the leading edge. We observed that in case of low free-stream turbulence on the suction side, the Kelvin–Helmholz instability dominated the transition process and full-span vortices were shed from the separation bubble. Transition on the suction side proceeded more rapidly in the high-turbulence case, where streaks broke down into turbulent spots and caused bypass transition. On the pressure side, we have identified the appearance of longitudinal vortical structures, where increasing the turbulence level gives rise to more longitudinal structures. We note that these vortical structures are not produced by Gortler instability.

The aerodynamic efficiency of turbomachinery blades is profoundly affected by the occurrence of laminar-turbulent transition in the boundary layer since skin friction and losses rise for the turbulent state. Depending on the free-stream turbulence level, we can identify different paths towards a turbulent state. The present study uses direct numerical simulation as the primary tool to investigate the flow behaviour of the low-pressure turbine blade. The computational set-up was designed to follow the experiments by Lengani & Simoni [1]. In the simulations, the flow past only one blade is computed, with periodic boundary conditions in the cross-flow directions to account for the cascade. Isotropic homogeneous free-stream turbulence is prescribed at the inlet. The free-stream turbulence is prescribed as a superposition of Fourier modes with a random phase shift. Two levels of the free-stream turbulence intensity were simulated (Tu = 0.19% and 5.2%), with the integral length scale being 0.167c, at the leading edge. We observed that in case of low free-stream turbulence on the suction side, the Kelvin-Helmholz instability dominated the transition process and full-span vortices were shed from the separation bubble. Transition on the suction side proceeded more rapidly in the high-turbulence case, where streaks broke down into turbulent spots and caused bypass transition. On the pressure side, we have identified the appearance of longitudinal vortical structures, where increasing the turbulence level gives rise to more longitudinal structures. We note that these vortical structures are not produced by Görtler instability.p t1 − p 2 ) c pt Total pressure coefficient = (p t1 − p t2 )/(p t1 − p 2 ) g Blade pitch G θ Görtler number h Blade height H 12 Shape factor l* Viscous length L Integral length scale o Cascade throat p Static pressure p t Total pressure R Radius of curvature Re Reynolds number t Trailing edge thickness T Time Tu Turbulence intensity u Velocity vector u τ Friction velocity U in Inflow velocity x, y, z Streamwise, wall-normal, spanwise coordinate Zw Zweifel number = 2g/c x cos 2 α 2 (tanα 1 − tanα 2 ) α Absolute flow angle α m Blade metal angle δ * Displacement thickness

The instability of an incompressible boundary-layer flow over an infinite swept wing in the presence of disc-type roughness elements and free-stream turbulence (FST) has been investigated by means of direct numerical simulations. Our study corresponds to the experiments by Örlü et al. (Tech. Rep., KTH Royal Institute of Technology, 2021, http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-291874). Here, different dimensions of the roughness elements and levels of FST have been considered. The aim of the present work is to investigate the experimentally observed sensitivity of the transition to the FST intensity. In the absence of FST, flow behind the roughness elements with a height above a certain value immediately undergoes transition to turbulence. Impulse–response analyses of the steady flow have been performed to identify the mechanism behind the observed flow instability. For subcritical roughness, the generated wave packet experiences a weak transient growth behind the roughness and then its amplitude decays as it is advected out of the computational domain. In the supercritical case, in which the flow transitions to turbulence, flow as expected exhibits an absolute instability. The presence of FST is found to have a significant impact on the transition behind the roughness, in particular in the case of a subcritical roughness height. For a height corresponding to a roughness Reynolds number $Re_{hh}=461$ , in the absence of FST the flow reaches a steady laminar state, while a very low FST intensity of $Tu =0.03\,\%$ causes the appearance of turbulence spots in the wake of the roughness. These randomly generated spots are advected out of the computational domain. For a higher FST level of $Tu=0.3\,\%$ , a turbulent wake is clearly visible behind the element, similar to that for the globally unstable case. The presented results confirm the experimental observations and explain the mechanisms behind the observed laminar–turbulent transition and its sensitivity to FST.

In the present work the evolution of the boundary layer over a low-pressure turbine blade is studied by means of direct numerical simulations. The free-stream flow is characterized by high level of free-stream turbulence and periodically impinging wakes. To include the presence of the wake without employing an ad-hoc model, we simulate both the moving bars and the stationary blades in their respective frames of reference and the coupling of the two domains is done through appropriate boundary conditions. The presence of the wake mainly affects the development of the boundary layer on the suction side of the blade. The presence of the wake introduces alternating regions in the streamwise direction of high- and low-velocity fluctuations inside the boundary layer. The analysis of the velocity fields allows the characterization of the streaky structures forced in the boundary layer by turbulence carried by upstream wakes. Both the fluctuations induced by the migration of the wake in the blade passage and the presence of the streaks contribute to high values of the disturbance velocity inside the boundary layer with respect to a steady inflow case. It was found that the migration of the wake in the blade passage stands for the most part of the perturbations with zero spanwise wavenumber. The non-zero wavenumbers are found to be amplified in the rear part of the blade at the boundary between the low and high speed regions associated with the wakes.