In the present work, the evolution of the boundary layer over a low-pressure turbine blade is studied using direct numerical simulations, with the aim of investigating the unsteady flow field induced by the rotor-stator interaction. The freestream flow is characterized by the high level of freestream turbulence and periodically impinging wakes. As in the experiments, the wakes are shed by moving bars modeling the rotor blades and placed upstream of the turbine blades. 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. In particular, the flow separation in the rear part of the blade is suppressed. Moreover, the presence of the wake introduces alternating regions in the streamwise direction of high- and low-velocity fluctuations inside the boundary layer. These fluctuations are responsible for significant variations of the shear stress. The analysis of the velocity fields allows the characterization of the streaky structures forced in the boundary layer by turbulence carried by upstream wakes. The breakdown events are observed once positive streamwise velocity fluctuations reach the end of the blade. 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. The amplification of the boundary layer disturbances associated with different spanwise wavenumbers has been computed. 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.

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 set-up of the simulations follows the experiments by [1], aiming to investigate the unsteady flow field induced by the rotor-stator interaction. The free-stream flow is characterized by high level of free-stream turbulence and periodically impinging wakes. As in the experiments, the wakes are shed by moving bars modeling the rotor blades and placed upstream of the turbine blades. 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. In particular, the flow separation in the rear part of the blade is suppressed. Moreover, the presence of the wake introduces alternating regions in the streamwise direction of high- and low-velocity fluctuations inside the boundary layer. These fluctuations are responsible for significant variations of the shear stress. The analysis of the velocity fields allows the characterization of the streaky structures forced in the boundary layer by turbulence carried by upstream wakes. The breakdown events are observed once positive streamwise velocity fluctuations reach the end of the blade. 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. The amplification of the boundary layer disturbances associated with different spanwise wavenumbers has been computed. 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. 

In the present work, high-fidelity direct numerical sim- ulation (DNS) data has been adopted in conjunction with an extensive post-processing to provide a detailed descrip- tion of the turbulence characteristics and its production within a low pressure turbine (LPT) cascade blade pas- sage operating with unsteady inflow. Proper orthogonal decomposition is used at first to provide the statistical rep- resentation of the flow structures that occur in the blade passage. Different inlet turbulent scales are isolated and a representation of the turbulence produced in the passage is also provided. Principal axes of the Reynolds stress and the strain tensors have been analyzed to provide further insight on the turbulence production. Since each spatial POD mode captures a quota of the Reynolds stress ten- sor, the POD modes are well suited to provide reduced order models (ROMs) that represent the different scales of turbulence. Namely, four different scales are defined, and the eigenvectors of the stress tensor for each reduced model are discussed. The discussion includes the compar- ison with the principal axis of the strain rate tensor. It is shown that the spatial locations where the eigen- vectors of the strain and stress tensors are aligned lead to the largest production of turbulent kinetic energy. The de- terministic periodic perturbations induced at the inlet by the unsteady incoming wakes lead to the largest produc- tion of turbulence in the passage region where the highest strain is detected and where the eigenvectors of the two tensors are aligned. In the suction side boundary layers, the highest production is related to the local maximum of the Reynolds shear stress due to the stochastic perturba- tions. The deterministic perturbations do not contribute to the production of turbulence in the suction side bound- ary layer, even though their induced stress is not negli- gible, because the eigenvector directions have a maximum misalignment. 

In the present work, the laminar-turbulent transition of the flow evolving around a low-pressure turbine blade has been investigated. Direct numerical simulations have been carried out for two different free stream turbulence intensity (FSTI) levels to investigate the role of free stream oscillations on the evolution of the blade boundary layer. Emphasis is placed on identifying the mechanisms driving the formation and breakup of coherent structures in the high FSTI case and how these processes are affected by the leading-edge receptivity and/or by the continuous forcing in the blade passage. Proper orthogonal decomposition (POD) has been adopted to provide a clear statistical representation of the shape of the structures. Extended POD projections provided temporal and spanwise correlations that allowed us to identify dominant temporal structures and spanwise wavelengths in the transition process. The extended POD analysis shows that the structures on the pressure side are not related to what happens at the leading edge. The results on the suction side show that the modes defining the leading edge and the passage bases correlate with coherent structures responsible for the transition. The most energetic mode of the passage basis is strongly related to the most amplified wavelength in the boundary layer and breakup events leading to transition. Modes with a smaller spanwise wavelength belong to the band predicted by optimal disturbance theory, they amplify with a smaller gain in the rear suction side, and they show the highest degree of correlation between the passage region and the rear suction side.

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 toward a turbulent state. The present study uses direct numerical simulation as the primary tool to investigate the flow behavior of the low-pressure turbine blade. 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 super-position 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 the 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 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 Orlu 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.

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. 

In the present work the evolution of the boundary layer over a low-pressureturbine blade is studied by means of direct numerical simulations. The set-upof the simulations follows the experiments by Lengani et al. (2017), aimingto investigate the unsteady flow field induced by the rotor-stator interaction.The free-stream flow is characterized by high level of free-stream turbulenceand periodically impinging wakes. As in the experiments, the wakes are shedby moving bars modeling the rotor blades and placed upstream of the turbineblades. 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 respectiveframes of reference and the coupling of the two domains is done throughappropriate boundary conditions. The presence of the wake mainly affects thedevelopment of the boundary layer on the suction side of the blade. In particular,the flow separation in the rear part of the blade is suppressed. Moreover, thepresence of the wake introduces alternating regions in the streamwise direction ofhigh- and low-velocity fluctuations inside the boundary layer. These fluctuationsare responsible for significant variations of the shear stress. The analysis of thevelocity fields allows the characterization of the streaky structures forced inthe boundary layer by turbulence carried by upstream wakes. The breakdownevents are observed once positive streamwise velocity fluctuations reach theend of the blade. Both the fluctuations induced by the migration of the wakein the blade passage and the presence of the streaks contribute to high valuesof the disturbance velocity inside the boundary layer with respect to a steadyinflow case. The amplification of the boundary layer disturbances associatedwith different spanwise wavenumbers has been computed. It was found thatthe migration of the wake in the blade passage stands for the most part of theperturbations with zero spanwise wavenumber. The non-zero wavenumbers arefound to be amplified in the rear part of the blade at the boundary betweenthe low and high speed regions associated with the wakes.