The classical gradient-diffusion hypothesis has known deficiencies when applied to cooling applications. In this paper, the gene-expression programming (GEP) method, a machine learning approach, has been applied to develop scalar-flux models via symbolic regression. The scalar-flux, the unclosed term of the mean passive-scalar transport equation, is treated by considering the polynomial basis and scalar invariants available from computable Reynolds-averaged quantities. This method has been applied to develop and then assess a model for the test case of jet in crossflow. A high-fidelity database was first probed for insight into which of the candidate bases are the most suitable as modelling terms. The high dimensionality of the function space, spanned by the basis, was then reduced by basic statistical techniques. The resulting data-driven model is presented and tested for a range of different jet in crossflow cases. Compared with eddy-diffusivity models, the new model is shown to produce reliably more accurate results. This demonstrates that the current framework can be used for scalar-flux modelling in complex three-dimensional flows and has potential to provide generalized form closures with improved predictive accuracy for the same classes of flows they were trained on.

This paper presents a novel CFD-driven machine learning framework to develop Reynolds-averaged Navier-Stokes (RANS) models. The CFD-driven training is an extension of the gene expression programming method Weatheritt and Sandberg (2016) [8], but crucially the fitness of candidate models is now evaluated by running RANS calculations in an integrated way, rather than using an algebraic function. Unlike other data-driven methods that fit the Reynolds stresses of trained models to high-fidelity data, the cost function for the CFD-driven training can be defined based on any flow feature from the CFD results. This extends the applicability of the method especially when the training data is limited. Furthermore, the resulting model, which is the one providing the most accurate CFD results at the end of the training, inherently shows good performance in RANS calculations. To demonstrate the potential of this new method, the CFD-driven machine learning approach is applied to model development for wake mixing in turbomachines. A new model is trained based on a high-pressure turbine case and then tested for three additional cases, all representative of modern turbine nozzles. Despite the geometric configurations and operating conditions being different among the cases, the predicted wake mixing profiles are significantly improved in all of these a posteriori tests. Moreover, the model equation is explicitly given and available for analysis, thus it could be deduced that the enhanced wake prediction is predominantly due to the extra diffusion introduced by the CFD-driven model.

This paper aims at characterizing the bypass transition in boundary layers subject to strong pressure gradient and curvature effects. A series of highly resolved large-eddy simulations of a high-pressure turbine vane are performed, and the primary focus is on the effects of free-stream turbulence (FST) states on transition mechanisms. The turbulent fluctuations that have convected from the inlet first interact with the blunt blade leading edge, forming vortical structures wrapping around the blade. For cases with relatively low-level FST, streamwise streaks are observed in the suction-side boundary layer, and the instabilities of the streaks cause the breakdown to turbulence. Moreover, the varicose mode of streak instability is predominant in the adverse pressure gradient region, while the sinuous mode is more common in the (weak) favourable pressure gradient region. On the other hand, for cases with higher levels of FST, the leading-edge structures are more irregularly distributed and no obvious streak instability is observed. Accordingly, the transition onset occurs much earlier, through the breakdown caused by interactions between vortical structures. Comparing between different cases, it is the competing effect between the FST intensity and the stabilizing pressure gradient that decides the path to transition and also the transition onset, whereas the integral length scale of FST affects the scales of the streamwise streaks in the boundary layer. Furthermore, while the streaks in the low-level FST cases are mainly induced by leading-edge vortical structures, the corresponding fluctuations show a stage of algebraic growth despite the weak favourable pressure gradient and curvature.

© 2019 by ASME. 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.

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 endwall 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. This paper discusses the endwall 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 analyzed. The ability of LES and RANS to accurately predict the secondary flows is discussed together with the implications this has on design.

Author(s): Yaomin Zhao, Shiying Xiong, Yue Yang, and Shiyi ChenThere is a continued debate about the generation mechanism of turbulent spots in boundary-layer transition. We use the vortex-surface field to show that the sinuous distortion of vortex surfaces plays an important role in the rapid lateral growth of turbulent spots.[Phys. Rev. Fluids 3, 074701] Published Wed Jul 11, 2018

In this paper, the shear-improved Smagorinsky model (SISM) is assessed in a K-type transitional channel flow. Our numerical simulation results show that the original SISM model is still too dissipative to predict the transitional channel flow. Two former reported empirical correction approaches, including a low-Reynolds-number correction and a shape-factor-based intermittency correction, are applied to further promote the capability of the SISM model in simulating the transition process. Numerical tests show that the shape-factor-based intermittency correction approach can correctly improve the transition-prediction capability of the SISM model, while the low-Reynolds-number correction approach fails. Furthermore, the shape-factor-based intermittency-corrected SISM model can capture the vortical structures during the transitional process very well and possesses the grid-insensitive characteristics.