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Research Papers

# Adaptation of Phase-Lagged Boundary Conditions to Large Eddy Simulation in Turbomachinery Configurations

[+] Author and Article Information
Gaelle Mouret

CFD Team,
Safran-Snecma,
Villaroche 77550, France;
CFD Team,
France CERFACS,
Toulouse 31100, France
e-mail: gaelle.mouret@cerfacs.fr

Nicolas Gourdain

DAEP Team,
ISAE,
Toulouse 31055, France
e-mail: nicolas.gourdain@isae.fr

Lionel Castillon

DAAP Team,
ONERA,
Meudon 92190, France
e-mail: lionel.castillon@onera.fr

1Corresponding author.

Manuscript received October 8, 2015; final manuscript received November 2, 2015; published online December 29, 2015. Editor: Kenneth C. Hall.

J. Turbomach 138(4), 041003 (Dec 29, 2015) (11 pages) Paper No: TURBO-15-1222; doi: 10.1115/1.4032044 History: Received October 08, 2015; Revised November 02, 2015

## Abstract

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 turbomachinery flow predictions. However, these simulations are very expensive for industrial applications, especially when a $360 deg$ configuration should be considered. The objective of this paper is thus to adapt the well-known phase-lagged conditions to the LES approach by replacing the traditional Fourier series decomposition (FSD) with a compression method that does not make any assumptions on the spectrum of the flow. Several methods are reviewed, and the proper orthogonal decomposition (POD) is retained. This new method is first validated on a flow around a circular cylinder with rotating downstream blocks. The results show significant improvements with respect to the FSD. It is then applied to unsteady Reynolds-averaged Navier–Stokes (URANS) simulations of a single-stage compressor in 2.5D and 3D as a first validation step toward single-passage LES of turbomachinery configuration.

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## Figures

Fig. 1

Compression with the POD of a square wave. Signal and its PSD for (a) and (b) 50, (c) and (d) 100, (e) and (f) 200, and (g) and (h) 270 modes kept over 300.

Fig. 2

Configurations of the two simulations and position of the probe: (a) sliding no-match and (b) phase-lagged

Fig. 3

PSD of velocity fluctuation of an LES simulation around a cylinder for sliding no-match and phase-lagged simulations. The gray lines correspond to the BPF and its first 32 harmonics. VS stands for vortex shedding.

Fig. 4

TKE at the rotor–stator interface for (a) sliding no-match and (b) phase-lagged simulations

Fig. 5

Influence of the compression algorithms on an axial velocity signal: (a) temporal signal and Fourier transforms of signals with (b) no compression, (c) DFT, (d) DCT, (e) DWT, and (f) POD

Fig. 6

Evolution of the compression rate of the relative error of (a) the mean and (b) the standard deviation of a signal caused by it is compression–decompression by FSD and POD

Fig. 7

Reconstructed sector of 2π/10 obtained with POD-based phase-lagged conditions with (a) 2, (b) 3, (c) 5, and (d) 7 modes, (e) with FSD-based phase-lagged conditions, and (f) for sector simulation. Shaded with entropy.

Fig. 8

(a) Static pressure and (b) axial velocity in stator passage for sector, Fourier-based, and POD-based phase-lagged conditions at nominal operating conditions

Fig. 9

Axial velocity signals in stator passage for POD-based phase-lagged conditions with different numbers of modes kept at nominal operating conditions

Fig. 10

Operating line for sector, POD with one mode kept, and converged POD- and FSD-based simulations

Fig. 11

(a) Static pressure and (b) axial velocity in stator passage for sector and Fourier-based and POD-based phase-lagged conditions for a normalized mass flow rate of 0.74

Fig. 13

Axial velocity (a) at midspan and (b) near casing for sector and phase-lagged computations

Fig. 12

Entropy snapshot: (a) and (b) near hub, (c) and (d) at midspan, and (e) and (f) near casing for Fourier-based (left) and POD-based (right) phase-lagged simulation of the 3D case

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