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Research Papers: Flows in Complex Systems

# Corner Separation Dynamics in a Linear Compressor Cascade

[+] Author and Article Information
Gherardo Zambonini

Laboratoire de Mécanique des Fluides et
d’Acoustique (LMFA),
Ecole Centrale de Lyon (ECL),
Ecully 69130, France
e-mail: gherardo.zambonini@ec-lyon.fr

Xavier Ottavy

Laboratoire de Mécanique des Fluides et
d’Acoustique (LMFA),
Ecole Centrale de Lyon (ECL),
Ecully 69130, France
e-mail: xavier.ottavy@ec-lyon.fr

Jochen Kriegseis

Institute of Fluid Mechanics (ISTM),
Karlsruhe Institute of Technology (KIT),
Karlsruhe D-76131, Germany
e-mail: kriegseis@kit.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 29, 2016; final manuscript received January 18, 2017; published online March 22, 2017. Assoc. Editor: Hui Hu.

J. Fluids Eng 139(6), 061101 (Mar 22, 2017) (13 pages) Paper No: FE-16-1409; doi: 10.1115/1.4035876 History: Received June 29, 2016; Revised January 18, 2017

## Abstract

This paper considers the inherent unsteady behavior of the three-dimensional (3D) separation in the corner region of a subsonic linear compressor cascade equipped of 13 NACA 65-009 profile blades. Detailed experimental measurements were carried out at different sections in spanwise direction achieving, simultaneously, unsteady wall pressure signals on the surface of the blade and velocity fields by time-resolved particle image velocimetry (PIV) measurements. Two configurations of the cascade were investigated with an incidence of 4 deg and 7 deg, both at $Re=3.8×105$ and Ma = 0.12 at the inlet of the facility. The intermittent switch between two statistical preferred sizes of separation, large, and almost suppressed, is called bimodal behavior. The present PIV measurements provide, for the first time, time-resolved flow visualizations of the separation switch with an extended field of view covering the entire blade section. Random large structures of the incoming boundary layer are found to destabilize the separation boundary. The recirculation region, therefore, enlarges when these high vorticity perturbations blend with larger eddies situated in the aft part of the blade. Such a massive detached region persists until its main constituting vortex suddenly breaks down and the separation almost completely vanishes. The increase of the blockage during the separation growth phase appears to be responsible for this mechanism. Consequently, the proper orthogonal decomposition (POD) analysis is carried out to decompose the flow modes and to contribute to clarify the underlying cause-effect relations, which predominate the dynamics of the present flow scenario.

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## Figures

Fig. 1

Compressor cascade configuration: (a) blade geometry sketch, (b) unsteady coupled PIV-pressure measurements on the linear compressor cascade, and (c) sketch of measurement configuration representing the planes and the position of PIV instrumentation

Fig. 2

Statistical significance of the PIV data at characteristic locations for the section z/h=1.35%: sketch of sample locations and convergence diagram of relative standard deviations σU/Utot¯. Vertical dashed line: single-set measurement, N1=2781.

Fig. 3

Total pressure losses at xc/ca=36.3% downstream the TE and velocity RMS at section z/h=1.35%. Configuration i=4 deg: (a) and (c); configuration i=7deg: (b) and (d). Localization of positions p1, p2, and p3 utilized for the bimodal analysis in Sec. 4.2.

Fig. 4

Three-dimensional visualization of 2D sections characterized by normalized absolute velocity and streamlines. Sections at z/h=1.35%, z/h=5.4%, z/h=10.9% and z/h=50% from the endwall.

Fig. 5

Bimodal behavior presented for the measurement case i=7deg, z/h=1.35% at half of the blade profile s*=0.5. Comparison of velocity distributions, time signals, and spectra between bimodal point (middle plots, n/c=6% from the surface of the blade) and not-bimodal points (n/c=1.7% and n/c=13%). Vertical lines in time plots: instants from t1 to t6 selected for flow visualizations in Fig. 6.

Fig. 6

Visualization of main dynamics of the development of the separation, case i=7deg, z/h=1.35%. Closed separation at t1, propagation of perturbations from LE to separation at t2, separation-backflow collision at t3, large recirculation at t4, vortex sweep at t5, and re-establishing of closed separation at t6.

Fig. 7

(a) Unsteady flow angle map αb of the extracted line in front of the LE, as labeled in Fig. 6 and (b) displacement thicknesses calculated at LE and across the separation. The filtered results δf are superposed to the unfiltered signals. Below: position of the extraction lines and associated correlation.

Fig. 8

Time pressure signals for the selected channels, highlighted suction surface points in Fig. 6: (a) 3 Hz low-cut signals and (b) 50 Hz low-cut signals with indication of LDPI and HDPI region. Vertical lines represent the time instants selected in Figs. 6 and 7(a).

Fig. 10

Energy of the first six modes of POD, cumulated energies of the six modes are represented in the first left column

Fig. 11

Interpretation of Fig. 9: sketch of the direction of the most extended vectors for the first four modes of POD applied to 2D velocity field, configuration i=7deg at z/h=1.35%

Fig. 12

POD time coefficients aj(t) (j=1:6) corresponding to the first six modes obtained by global POD field calculation for 1 s of acquisition, N1=2781

Fig. 9

First six modes of the POD performed on the whole field of data-set i=7deg at z/h=1.35%, time data-set 1 s (N1=2781 samples)

Fig. 13

First four modes of POD on cut sections of the original field: LE and separation

Fig. 14

Energy of the first four modes of local POD applied to cut sections of the original field: (a) leading edge region (LER), and (b) separation region (SR). Cumulated energy is represented in the first left column of each diagram.

Fig. 15

Highest correlations between different modes of the two selected regions, LE and separation. dot-dash lines: auto-correlation of separation region modes; dotted lines: autocorrelation of LE region modes. Solid lines: cross correlations between LE and separation. Corresponding selected modes for correlations are sketched below each correlation figure.

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