A three-equation model has been applied to the prediction of separation-induced transition in high-lift low-Reynolds-number cascade flows. Classical turbulence models fail to predict accurately laminar separation and turbulent reattachment, and usually overpredict the separation length, the main reason for this being the slow rise of the turbulent kinetic energy in the early stage of the separation process. The proposed approach is based on solving an additional transport equation for the so-called laminar kinetic energy, which allows the increase in the nonturbulent fluctuations in the pretransitional and transitional region to be taken into account. The model is derived from that of Lardeau et al. (2004, “Modelling Bypass Transition With Low-Reynolds-Number Non-Linear Eddy-Viscosity Closure,” Flow, Turbul. Combust., 73, pp. 49–76), which was originally formulated to predict bypass transition for attached flows, subject to a wide range of freestream turbulence intensity. A new production term is proposed, based on the mean shear and a laminar eddy-viscosity concept. After a validation of the model for a flat-plate boundary layer, subjected to an adverse pressure gradient, the T106 and T2 cascades, recently tested at the von Kármán Institute, are selected as test cases to assess the ability of the model to predict the flow around high-lift cascades in conditions representative of those in low-pressure turbines. Good agreement with experimental data, in terms of blade-load distributions, separation onset, reattachment locations, and losses, is found over a wide range of Reynolds-number values.

In low-pressure-turbines (LPT) around 60–70% of losses are generated away from end-walls, while the remaining 30–40% is controlled by the interaction of the blade profile with the end-wall boundary layer. Experimental and numerical studies have shown how the strength and penetration of the secondary flow depends on the characteristics of the incoming end-wall boundary layer. Experimental techniques did shed light on the mechanism that controls the growth of the secondary vortices, and scale-resolving CFD allowed to dive deep into the details of the vorticity generation. Along these lines, this paper discusses the end-wall flow characteristics of the T106 LPT profile at Re = 120K and M = 0.59 by benchmarking with experiments and investigating the impact of the incoming boundary layer state. The simulations are carried out with proven Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulation (LES) solvers to determine if Reynolds Averaged models can capture the relevant flow details with enough accuracy to drive the design of this flow region. Part I of the paper focuses on the critical grid needs to ensure accurate LES, and on the analysis of the overall time averaged flow field and comparison between RANS, LES and measurements when available. In particular, the growth of secondary flow features, the trace and strength of the secondary vortex system, its impact on the blade load variation along the span and end-wall flow visualizations are analysed. The ability of LES and RANS to accurately predict the secondary flows is discussed together with the implications this has on design.

This paper discusses the application of different transition-sensitive turbulence closures to the prediction of low-Reynolds-number flows in high-lift cascades operating in low-pressure turbine (LPT) conditions. Different formulations of the well known γ-R˜eθt model are considered and compared to a recently developed transition model based on the laminar kinetic energy (LKE) concept. All those approaches have been coupled to the Wilcox k-ω turbulence model. The performance of the transition-sensitive closures has been assessed by analyzing three different high-lift cascades, recently tested experimentally in two European research projects (Unsteady Transition in Axial Turbomachines (UTAT) and Turbulence and Transition Modeling for Special Turbomachinery Applications (TATMo)). Such cascades (T106A, T106C, and T108) feature different loading distributions, different suction side diffusion factors, and they are characterized by suction side boundary layer separation when operated in steady inflow. Both steady and unsteady inflow conditions (induced by upstream passing wakes) have been studied. Particular attention has been devoted to the treatment of crucial boundary conditions like the freestream turbulence intensity and the turbulent length scale. A detailed comparison between measurements and computations, in terms of blade surface isentropic Mach number distributions and cascade lapse rates will be presented and discussed. Specific features of the computed wake-induced transition patterns will be discussed for selected Reynolds numbers. Finally, some guidelines concerning the computations of high-lift cascades for LPT applications using Reynolds-averaged Navier–Stokes (RANS)/unsteady RANS (URANS) approaches and transition-sensitive closures will be reported.

The paper describes the development and validation of a novel CFD-based throughflow model. It is based on the axisymmetric Euler equations with tangential blockage and body forces and inherits its numerical scheme from state-of-the-art CFD solver (TRAF code), including real-gas capabilities. A crucial aspect of the numerical procedure is represented by an adaptive approach for the meridional flow surface, which employs a new time-dependent equation to accommodate incidence and deviation effects, and which allows the explicit calculation of the blade body force. A realistic distribution of entropy along the streamlines is proposed in order to compute dissipative forces on the basis of a distributed loss model. The throughflow code is applied to the investigation of the NASA rotor 67 transonic fan and of a four stage low-pressure steam turbine at design conditions. The performance of the method is evaluated by comparing predicted operating characteristics and spanwise distributions of flow quantities with the results of CFD, steady, viscous calculations and experimental data.

This paper presents the development of accurate turbulence closures for low-pressure turbine (LPT) wake mixing prediction by integrating a machine-learning approach based on gene expression programming (GEP), with Reynolds Averaged Navier-Stokes (RANS) based computational fluid dynamics (CFD). In order to further improve the performance and robustness of GEP-based data-driven closures, the fitness of models is evaluated by running RANS calculations in an integrated way, instead of an algebraic function. Using a canonical turbine wake with inlet conditions prescribed based on high-fidelity data of the T106A cascade, we demonstrate that the ‘CFD-driven’ machine-learning approach produces physically correct non-linear turbulence closures, i.e., predict the right down-stream wake development and maintain an accurate peak wake loss throughout the domain. We then extend our analysis to full turbine blade cases and show that the model development is sensitive to the training region due to the presence of deterministic unsteadiness in the near-wake. Models developed including the near-wake have artificially large diffusion coefficients to over-compensate for the vortex shedding steady RANS cannot capture. In contrast, excluding the near-wake in the model development produces the correct physical model behavior, but predictive accuracy in the near-wake remains unsatisfactory. This can be remedied by using the physically consistent models in unsteady RANS. Overall, the ‘CFD-driven’ models were found to be robust and capture the correct physical wake mixing behavior across different LPT operating conditions and airfoils such as T106C and PakB.