One contribution of 13 to a Theme Issue 'Aerodynamics, computers and the environment' . A better understanding of turbulent unsteady flows is a necessary step towards a breakthrough in the design of modern compressors. Owing to high Reynolds numbers and very complex geometry, the flow that develops in such industrial machines is extremely hard to predict. At this time, the most popular method to simulate these flows is still based on a Reynoldsaveraged Navier-Stokes approach. However, there is some evidence that this formalism is not accurate for these components, especially when a description of time-dependent turbulent flows is desired. With the increase in computing power, large eddy simulation (LES) emerges as a promising technique to improve both knowledge of complex physics and reliability of flow solver predictions. The objective of the paper is thus to give an overview of the current status of LES for industrial compressor flows as well as to propose future research axes regarding the use of LES for compressor design. While the use of wallresolved LES for industrial multistage compressors at realistic Reynolds number should not be ready before 2035, some possibilities exist to reduce the cost of LES, such as wall modelling and the adaptation of the phase-lag condition. This paper also points out the necessity to combine LES to techniques able to tackle complex geometries. Indeed LES alone, i.e. without prior knowledge of such flows for grid construction or the prohibitive yet ideal use of fully homogeneous meshes to predict compressor flows, is quite limited today. IntroductionThe aeronautic industry faces a formidable challenge by targeting in 2050 a reduction of CO 2 and NO x 2014 The Author(s) Published by the Royal Society. All rights reserved. emissions by 75% and 90% per kilometre and per passenger, respectively (compared to the 2000 level). Ultra-high bypass ratio (BR > 20) turbofan and ultra-high overall pressure ratio (OPR > 70) core engines have the potential for such significant reductions in fuel burn. However, after many years of optimization, the design of ever more efficient gas turbines now requires understanding of the complex unsteady flow appearing within each individual component and in an integrated fashion. Among all components, the compressor remains a critical part of a gas turbine, especially regarding its efficiency and stability. Owing to the adverse pressure gradients, compressors are naturally subjected to unstable flows such as surge and rotating stall [1], which can potentially lead to mechanical failure. These aerodynamic instabilities impose serious constraints on the design (the so-called 'surge margin') and thus on performance. In this context, maximizing the efficiency of compressors remains particularly complex and the improvement of the compressor robustness and performance thus requires good understanding of the flow physics.Complementary to experimental investigations, the numerical simulation of flows, commonly referred to as computational fluid dynamics (CFD), is...

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a b s t r a c tRecent developments and demonstrations for the prediction of turbulent flows around blades point to Large Eddy Simulations (LES) as a very promising tool. Indeed and despite the fact that this numerical method still requires modeling and intense computing effort compared to Reynolds Average NavierStokes (RANS), this fully unsteady simulation technique provides valuable information on the turbulent flow otherwise inaccessible. Theoretical limits and scales of wall bounded flows are now well mastered in simple cases but complex industrial applications usually introduce unknowns and mechanisms that are difficult to apprehend beforehand especially with LES which is usually computationally intensive and bounded to code scalability, mesh quality, modeling performances and computer power. In this specific context, few studies directly address the use of fully structured versus unstructured, implicit versus explicit flow solvers and their respective impact for LES modeling of complex wall bounded flows. To partly address these important issues, two dedicated structured and unstructured computational solvers are applied and assessed by comparing the predictions of the heat transfer around the experimental high pressure turbine blade profile cascade of Arts et al. [6]. First, both LES predictions are compared to RANS modeling with a particular interest for the accuracy/cost ratio and improvement of the physical phenomena around the blade. LES's are then detailed and further investigated to assess their ability to reproduce the inlet turbulence effect on heat transfer and the development of the transitioning boundary layer around the blade. Quantitative comparisons against experimental findings show excellent agreement especially on the pressure side of the profile. Detailed analysis of the flow predictions provided by both the structured and unstructured solvers underline the importance of long stream-wise streaky structures responsible for the augmentation of the heat transfer and leading to the transition of the suction-side boundary layer.

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In the absence of instabilities, the large deterministic scales of turbomachinery flows resulting from the periodic rotation of blades can be considered periodic in time. Such flows are not simulated with enough efficiency when using classical unsteady techniques as a transient regime must be bypassed. New techniques, dedicated to time-periodic flows and based on Fourier analysis, have been developed recently. Among these, harmonic balance methods cast a time-periodic flow computation in several coupled steady flow computations. A time-domain harmonic balance method is derived and adapted to phase lag periodic conditions to allow the simulation of only one blade passage per row regardless of row blade counts. Sophisticated space and time interpolations are involved and detailed. The test case is a single stage subsonic compressor. A convergence study of the present harmonic balance is performed and compared with a reference well-resolved classical unsteady flow simulation. The results show, on one hand, the good behavior of the harmonic balance and its ability to correctly predict global quantities as well as local flow pattern; on the other hand, the simulation time is drastically reduced.