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 (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) at design point, around 60–70% of losses are generated in the blade boundary layers far from end walls, while the remaining 30–40% is controlled by the interaction of the blade profile with the end-wall boundary layer. Increasing attention is devoted to these flow regions in industrial design processes. This paper discusses the end-wall flow characteristics of the T106 profile with parallel end walls at realistic LPT conditions, as described in the experimental setup of Duden, A., and Fottner, L., 1997, “Influence of Taper, Reynolds Number and Mach Number on the Secondary Flow Field of a Highly Loaded Turbine Cascade,” Proc. Inst. Mech. Eng., Part A, 211(4), pp.309–320. Calculations are carried out by both Reynolds-averaged Navier–Stokes (RANS), due to its continuing role as the design verification workhorse, and highly resolved large eddy simulation (LES). Part II of this paper focuses on the loss generation associated with the secondary end-wall vortices. Entropy generation and the consequent stagnation pressure losses are analyzed following the aerodynamic investigation carried out in the companion paper (GT2018-76233). The ability of classical turbulence models generally used in RANS to discern the loss contributions of the different vortical structures is discussed in detail and the attainable degree of accuracy is scrutinized with the help of LES and the available test data. The purpose is to identify the flow features that require further modeling efforts in order to improve RANS/unsteady RANS (URANS) approaches and make them able to support the design of the next generation of LPTs.

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.

In low-pressure turbines (LPTs), 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 computational fluid dynamics (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 = 120 K 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, and its impact on the blade load variation along the span and end-wall flow visualizations are analyzed. The ability of LES and RANS to accurately predict the secondary flows is discussed together with the implications this has on design.