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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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.

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