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Delayed Detached-Eddy Simulation and Particle Image Velocimetry Investigation of S-Duct Flow Distortion

03 Apr 2017-AIAA Journal (American Institute of Aeronautics and Astronautics)-Vol. 55, Iss: 6, pp 1893-1908

Abstract: The dynamic flow distortion generated within convoluted aeroengine intakes can affect the performance and operability of the engine. There is a need for a better understanding of the main flow mech...

Summary (5 min read)

Introduction

  • Delayed Detached-Eddy Simulation and Particle Image Velocimetry Investigation of S-Duct Flow Distortion Daniel Gil-Prieto,∗David G.MacManus,† Pavlos K. Zachos,‡Geoffrey Tanguy,§ FrançoisWilson,¶ and Nicola Chiereghin¶ Cranfield University, Cranfield, England MK43 0AL, United Kingdom DOI: 10.2514/1.J055468.
  • The flowfieldmechanisms responsible for the main perturbations at the duct outlet are identified.
  • Complex intake configurations promote high levels of dynamic total pressure and swirl distortion, which can adversely affect the engine stability [3].
  • §Ph.D. Student, Propulsion Engineering Centre, Building 52.
  • The switching mode promoted the swirl-switching mechanism, by which one of the Dean vortices observed in the mean flow alternately dominates the flowfield [17].

A. Studied Case

  • The S-duct geometry is a scaled-down version of the geometry investigated by Garnier [13].
  • The S-duct has a circular cross section, and the main geometrical parameters are an area ratio ofAR 1.52, an axial length of L∕Din 4.95, a centerline offset ofH∕L 0.50, and an outlet diameter of Dout 150 mm (Fig. 1).
  • The S-duct centerline is composed of two consecutive 52 deg arcs with curvature ratios Rin∕Rc of γ 0.16.
  • The flow condition is determined by the Mach number at the reference plane, which is located 0.9Din upstream of the S-duct inlet.
  • The computational and experimental results presented in thiswork correspond to a referenceMach number of Mref 0.27, which is associated with a ReD 7.1 × 105.

B. Stereo Particle Image Velocimetry Experiment

  • A detailed description of the experimental facility is reported by Zachos et al. [14], and only the key aspects of the experiment are reported here.
  • The rig is calibrated to provide the requiredMach number at the reference plane (0.9Din upstream of the S-duct inlet).
  • The laser light sheet was delivered by an articulated light arm, which provides a light sheet with a thickness of approximately 2 mm.
  • TSI Insight 4G software was used for the calibration of the cameras, the acquisition, and the processing of the images.
  • The overall uncertainty was approximately 6 and 8% for the in-plane and out-of-plane components of the velocity, respectively.

C. Delayed Detached-Eddy Simulation

  • The numerical computation is performed using a detached-eddy simulation (DES), for which the unsteady Reynolds-averaged Navier–Stokes equations are applied in the boundary layer, whereas the large-eddy simulation (LES) method is employed in the highly unsteady regions away from the wall [21].
  • This profile could not be applied directly as the inlet boundary condition for the computational domain because this region was affected by the pressure gradient established in the first bend of the S-duct.
  • For the mesh used in this investigation, the determinant 2 × 2 × 2 was greater than 0.83 over the domain, which indicates a good quality mesh.
  • The corresponding values of SIstd were 1.9, 1.9, and 1.5 deg, whereas for SImax, the values were 17.5, 16.8, and 15.7 deg.
  • The impact of the time-step choice was also assessed atMref 0.60, and the DDES simulation with the medium mesh was computed at a doubled time step of Δt 1.2 × 10−5 s, which equates to Δt∕tc 3.72 × 10−3.

D. Proper Orthogonal Decomposition

  • Turbulent flows are characterized by the presence of coherent structures that are obscured by small-scale turbulent fluctuations.
  • Therefore, ai t represents the instantaneous weight of each flow feature at the different instants of time.
  • The temporal coefficients are uncorrelated to each other, so that the different flow features described by the POD modes occur uncorrelated in time [26].
  • Themodes are then ordered by the associated hKEi contribution.
  • This permits an optimum representation in terms of kinetic energy in the sense that, for a given number of terms in the series, the POD maximizes the kinetic energy content in the reconstruction [Eq. (2)] [28].

A. Experimental Validation

  • The mean velocity field for the DDES solution is compared with the SPIV results at the same inlet Mach number of Mref 0.27 (Fig. 4).
  • The DDES also predicts a pair of regions of high lateral velocity near the wall at the top of the AIP (Fig. 4c), which results in a secondary pair of vortices (Fig. 4d).
  • The maximum values are σu∕h wAIPi 0.28 and 0.22 for DDES and SPIV, respectively.
  • To quantify the discrepancies between the DDES and SPIV results in terms of fluctuating flowfield, the profile of the standard deviation of the three components of the velocity is compared along the symmetry axis of the AIP (Fig. 5).
  • Therefore, the instantaneous SI predicted in the DDES solution shows similar mean and peak values as well as similar probability distributions as indicated by the standard deviation, skewness, and kurtosis, compared to the SPIV measurements.

B. Coherent Structures at the Aerodynamic Interface Plane

  • POD [26] is applied to the three-component velocity vector at the AIP for both the DDES and SPIV data.
  • For a consistent comparison, the DDES solution is linearly interpolated using the Delaunay triangulation method into the loci of the SPIV data points before the POD computation.
  • The POD permits the identification of the flow coherent structures.
  • The temporal coefficients associated with the higher modes oscillate around the null mean value.
  • Therefore, the PODmodes are ordered by hTKEi content.

1. Delayed Detached-Eddy Simulation and Stereo Particle Image Velocimetry Coherent Structures

  • The fourmost-energetic coherent structures for the streamwise and in-planevelocity fields as predicted byDDESare similar compared to SPIV data (Fig. 7).
  • This inplane velocity perturbation is associated with a circumferential oscillation of the low-streamwise-velocity region that follows the swirl switching (Figs. 8a and 8b).
  • When aFVM t is positive, the pair of vortices becomes stronger and moves into a more centered position in the AIP (Fig. 8g).
  • The effect of this perturbation is to modulate the streamwise velocity distortion between the high- and low-streamwise-velocity regions.
  • In contrast, the DDES underpredicts the energetic content of the first vertical mode (FVM) and second vertical mode (SVM), which show values of 0.76 and 0.38%, respectively, compared to the 0.93 and 0.46% obtained for the SPIV data.

2. Spectral Analysis

  • The DDES simulations are time-resolved and therefore can be used to further develop the understanding of the temporally underresolved SPIV results through a spectral analysis of the POD temporal coefficients (Fig. 9).
  • The FVM and SVM show a more broadband spectrum, even though a distinct peak can be identified around 1.06 (Figs. 9b and 9d).
  • The POD analysis of the velocity field at the AIP has identified the main coherent structures that are responsible formost of the flowfield unsteadiness.
  • In addition, the unsteady swirl distortion pattern deviates from the well-known symmetric vortex pair, and multiswirl structures as well as single rotating cells are promoted [16].
  • The design of an efficient flow control system depends on a good understanding of the origin of the AIP perturbations upon which the flow control device has to act.

C. Symmetry Plane Flowfield

  • The mean flow at the symmetry plane is characterized by the presence of a separated flow region at the inner bend, as indicated by the reversed flow (Fig. 10a).
  • The mean position of the separation and reattachment points corresponds to saddle points, where the wall shear stress is null [33].
  • The separation bubble length is slightly underpredicted by the DDES solution compared to the experimental value of 1.95Din.
  • The computed mean vertical velocity field shows positive values near the lower wall, which is associated with the presence of the symmetric vortices (Fig. 10c).
  • Fluctuations as high as σv∕h wAIPi 0.36 are also observed for the vertical velocity field downstream of the separation bubble (Fig. 10d), at the region where the mean-flow shear layer is located (Fig. 10a).

D. Multiplane Proper Orthogonal Decomposition

  • POD is applied to the three-component velocity vector at the AIP and symmetry plane simultaneously.
  • This multiplane POD permits the identification of coherent structures at the AIP and their relationship with the upstream flowfield.
  • Therefore, this technique establishes a link between the upstream flow and the perturbations at the AIP.
  • To the authors’ knowledge, this is the first attempt to relate AIP and symmetry plane flow characteristics using POD in S-duct research.
  • Because this multiplane POD is now based on the hTKEi of both the AIP and the symmetry plane, a change in the modal distributions could be expected relative to the case where only the AIP was considered (Sec. III.B).

1. Swirl Switching

  • The first switching mode (FSM) does not show any perturbations either in the vertical or streamwise velocity components at the symmetry plane.
  • The FSM shows a series of alternate positive and negative lateral velocity regions along the symmetry plane, which are tilted by about 25–30 deg relative to the streamwise axis.
  • This indicates the dominance of one of the two secondary flow vortices, which migrate toward a more central position in the cross section, whereas the other vortex is confined to the opposite wall, as observed in Sec. III.
  • This perturbation shows the same periodic behavior at St 0.53 as the FSM (Fig. 11f).
  • The swirl switching is accompanied by a lateral oscillation of the low-streamwisevelocity region (Figs. 13a, 13d, 13g, 13j, and 13m).

2. Shear-Layer Oscillations

  • The AIP perturbation promoted by the first vertical mode (FVM) of the multiplane POD (Fig. 12a) is similar to that obtained with the POD applied just at the AIP (Fig. 7e), even though in the multiplane POD the central region of the modal shape is more spread vertically.
  • The vortex shedding occurs mainly at a frequency of about St 1.06 (Fig. 12i), which is exactly twice the value for the swirl-switching mechanism (Figs. 11e and 11f).
  • The AIP perturbation associated with the SVM (Fig. 12b) is similar to that obtained when only the AIP was considered (Fig. 7d).
  • Therefore, the AIP perturbations represented by the FVM and SVM are promoted by the same flow mechanism, which is the roll-up of alternating D ow nl oa de d by C ra nf ie ld U ni ve rs ity ( A K A D E FE N C E A C A D E M Y O F T H E U K ) on A pr il 10 , 2 01 7 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .J 05 54 68 spanwise vortices through the shear layer.
  • D ow nl oa de d by C ra nf ie ld U ni ve rs ity ( A K A D E FE N C E A C A D E M Y O F T H E U K ) on A pr il 10 , 2 01 7 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .J 05 54 68.

IV. Conclusions

  • The unsteady flowfield in an S-duct with a centerline offset of H∕L 0.50, area ratio ofAR 1.52, and lengthL∕Din 4.95 has been simulated atMref 0.27 andReD 7.1 × 105 using a delayed detached-eddy simulation (DDES) approach.
  • Very good agreement has been found between computational and Fig. 13 FVM and SVM of the combined AIP and symmetry plane velocity field POD (DDES,Mref 0.27).
  • Therefore, the capability ofDDES simulations to capture the main unsteady characteristics of flows within S-duct intakes has been demonstrated.
  • The streamwise vortices are then convected downstream and promote a swirl-switching oscillation in the AIP velocity field.
  • The identification of the source of theAIP perturbations may facilitate the design of more efficient flow control systems.

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Delayed Detached-Eddy Simulation and Particle Image
Velocimetry Investigation of S-Duct Flow Distortion
Daniel Gil-Prieto,
David G. MacManus,
Pavlos K. Zachos,
Geoffrey Tanguy,
§
François Wilson,
and Nicola Chiereghin
Cranfield University, Cranfield, England MK43 0AL, United Kingdom
DOI: 10.2514/1.J055468
The dynamic flow distortion generated within convoluted aeroengine intakes can affect the performance and
operability of the engine. There is a need for a better understanding of the main flow mechanisms that promote flow
distortion at the exit of S-shaped intakes. This paper presents a detailed analysis of the main coherent structures in an
S-duct flowfield based on a delayed detached-eddy simulation. The capability of this numerical approach to capture
the characteristics of the highly unsteady flowfield is demonstrated against high-resolution, synchronous stereoscopic
particle image velocimetry measurements at the aerodynamic interface plane. The flowfield mechanisms responsible
for the main perturbations at the duct outlet are identified. Clockwise and counterclockwise streamwise vortices are
alternately generated around the separation region at a frequency of St 0.53, which promote the swirl switching at
the duct outlet. Spanwise vortices are also shed from the separation region at a frequency of St 1.06 and convect
downstream along the separated centerline shear layer. This results in a vertical modulation of the main loss region
and a fluctuation of the velocity gradient between the high- and low-velocity flow at the aerodynamic interface plane.
Nomenclature
AR = area ratio
a = proper orthogonal decomposition temporal coeffi-
cient, ms
D = S-duct cross-section diameter, mm
f = frequency, Hz
H = S-duct centerline offset, mm
KE = kinetic energy, Jkg
L = S-duct axial length, mm
L
s
= S-duct length measured along the centerline, mm
M = Mach number
R = S-duct cross-section radius, mm
R
c
= curvature radius of the S-duct bend, mm
Re
D
= Reynolds number based on the inlet diameter
SI = swirl intensity distortion descriptor, deg
St = Strouhal number, fD
AIP
h
w
AIP
i
s = S-duct centerline coordinate, mm
TKE = turbulent kinetic energy, Jkg
t
c
= S-duct convective time, s, L
s
w
in
u, v, w = velocity vector Cartesian components, ms
V
ip
= in-plane velocity modulus, ms,

u
2
v
2
p
v
θ
= circumferential velocity component, ms
α = swirl angle, deg, arctanv
θ
w
γ = curvature ratio based on the inlet-section radius,
R
in
R
c
Δt = delayed detached-eddy simulation time step, s
Φ = proper orthogonal decomposition nondimensional
modal distribution
hi = time average
= area average
σ = standard deviation
Subscripts
AIP = aerodynamic interface plane (0.41D
out
downstream of
the S-duct outlet plane)
FSM = first switching mode
FVM = first vertical mode
in = S-duct inlet plane
max = maximum value of a temporal distribution
mean = time-averaged value of a temporal distribution
MFM = mean-flow mode
out = S-duct outlet plane
ref = reference plane (0.9D
in
upstream of the S-duct inlet
plane)
SSM = second switching mode
SVM = second vertical mode
std = standard deviation value of a temporal distribution
Superscripts
u = lateral velocity field
v = vertical velocity field
V
ip
= in-plane velocity field
w = streamwise velocity field
I. Introduction
C
ONVOLUTED aeroengine intakes are used in embedded
engine systems, which are expected to power the next
generation of aircraft. Integrated engine configurations allow for
more compact and efficient aircraft designs and are of interest to
novel civil configurations [1,2]. However, complex intake
configurations promote high levels of dynamic total pressure and
swirl distortion, which can adversely affect the engine stability [3].
Unsteady total pressure and swirl distortion are generated as a result
of flow separations and secondary flows within the intake. The
detrimental effect of total pressure distortion on the engine
operability has been widely investigated [48]. The effect of swirl
distortion has received relatively less attention because historically
swirl-related issues were implicitly mitigated with the utilization of
inlet guide vanes and relatively simple intake designs [3]. However,
the adverse effect of swirl distortion on the compression system
stability margin was demonstrated during the development of several
air vehicles [3]. Previous studies highlighted the importance of
dynamic distortion and, in particular, the local peak values upon the
onset of engine instabilities [6,9,10].
Received 29 June 2016; revision received 23 November 2016; accepted for
publication 3 January 2017; published online 31 March 2017. Copyright ©
2016 by the authors. Published by the American Institute of Aeronautics and
Astronautics, Inc., with permission. All requests for copying and permission
to reprint should be submitted to CCC at www.copyright.com; employ the
ISSN 0001-1452 (print) or 1533-385X (online) to initiate your request. See
also AIAA Rights and Permissions www.aiaa.org/randp.
*Ph.D. Student, Propulsion Engineering Centre, Building 52.
Professor, Propulsion Engineering Centre, Building 52. Member AIAA.
Lecturer, Propulsion Engineering Centre, Building 52. Member AIAA.
§
Ph.D. Student, Propulsion Engineering Centre, Building 52.
Researcher, Propulsion Engineering Centre, Building 52.
Article in Advance / 1
AIAA JOURNAL
Downloaded by Cranfield University (AKA DEFENCE ACADEMY OF THE UK) on April 10, 2017 | http://arc.aiaa.org | DOI: 10.2514/1.J055468
, 2017, Vol. 55, Iss. 6, pp1893-1908
Published by AIAA. This is the Author Accepted Manuscript issued with:
Creative Commons Attribution Non-Commercial License (CC:BY:NC 3.0).
The final published version (version of record) is available online at DOI:10.2514/1.J055468.
Please refer to any applicable publisher terms of use.

Previous research has investigated the distorted flowfield
associated with S-shaped intakes. Wellborn et al. [11] studied
the flow through a diffusing S-duct (AR 1.52, LD
in
5.0,
HL 0.27, Fig. 1) with low-bandwidth instrumentation. A total
pressure deficit was identified in the lower sector of the aerodynamic
interface plane (AIP), where a symmetric pair of counter-rotating
vortices was observed. Berens et al. [12] performed a detached-eddy
simulation (DES) of the flowfield in an S-duct with similar offset
ratio HL 0.28 (AR 1.4, LD
in
3.76) and highlighted the
limitations of time-averaged data for the intake/engine compatibility
assessment. Garnier [13] investigated the performance of active flow
control in an S-duct (AR 1.52, LD
in
4.95, HL 0.50) using
40 high-bandwidth transducers. Separated flow was detected at the
inner bend of the S-duct for the uncontrolled flow case. For a flow
condition of M
AIP
0.20, the separation point was identified at a
centerline coordinate of sD
in
2.17, and the separation-bubble
length of approximately 1.35D
in
was estimated based on the static
pressure distribution along the walls. The unsteady reattachment
point was associated with frequencies between St 0.48 and 1.20.
Zachos et al. [14] first applied stereo particle image velocimetry
(SPIV) to characterize the swirl distortion at the outlet of two
S-shaped intakes with the same nondimensional geometrical
parameters (HL, AR, LD
in
) as the configurations investigated by
Garnier [13] and Wellborn et al. [11], respectively. The main
difference between these two configurations was the centerline
offset, which was HL 0.50 and HL 0.27, respectively. The
inlet Mach number ranged from 0.27 to 0.60, with a concomitant
variation of Re
D
between 5.9 × 10
5
and 13.8 × 10
5
. The maximum
fluctuations of the streamwise velocity were found in the upper
bounds of the mean-flow main loss region and were linked to the
unsteadiness of the separated shear layer. The swirl angle maximum
fluctuations were found in the lower sector of the AIP, where the
mean flow was relatively swirl-free, and were linked to the unsteady
secondary-flow vortices. The inlet Mach number showed a modest
effect on the overall characteristics of both steady and fluctuating
flowfields. The highly unsteady nature of the flowfield resulted in
significant levels of dynamic flow distortion. Peak values of swirl
intensity (SI) as high as twice the mean value were reported. Notable
excursions from the mean-flow twin swirl pattern were observed
toward single swirling flow patterns rotating in either the clockwise
or counterclockwise direction.
The importance of the dynamic flow distortion on the engine
performance and operability [6] highlights the need for a better
understanding of the flow features that promote deviations from the
steady-state distortion levels. Proper orthogonal decomposition
(POD) has been recently applied to identify the most energetic
coherent structures in the flow within complex aeroengine intakes.
MacManus et al. [15] performed a delayed detached-eddy simulation
(DDES) of the flowfield in two S-ducts with different centerline
offsets, which corresponded to the geometry investigated by Garnier
[13] (HL 0.50) and a scaled version of the geometry investigated
by Wellborn et al. [11] (HL 0.27). Two Mach numbers were
simulated for each configuration, M
AIP
0.18 and M
AIP
0.36,
which resulted in Re
D
of approximately 1.1 × 10
6
and 1.7 × 10
6
,
respectively. The POD was applied to the computed total pressure
field at the AIP. For both configurations, the dominant coherent
structures consisted of a lateral and a vertical oscillation of the main
loss region. It was proposed that the lateral oscillation was associated
with the secondary flows, whereas the vertical perturbation was
related to the unsteadiness of the centerline diffusion-driven
separation. For the low-offset duct (HL 0.27), the spectral
analysis showed that the lateral and vertical perturbations were
associated with frequencies of St 0.35 and St 0.70,
respectively, for both M
AIP
0.18 and M
AIP
0.36. For the high-
offset duct ( HL 0.50)atM
AIP
0.18, the frequencies associated
with the lateral and vertical perturbations were St 0.55 and
St 0.85, respectively. At high Mach number (M
AIP
0.36), the
spectrum associated with the vertical oscillation showed a more
broadband spectral content.
Gil-Prieto et al. [16] used SPIV to characterize the distorted swirl
pattern at the outlet of the same S-duct configurations investigated by
Zachos et al. [14], with two different centerline offset values of
HL 0.50 and 0.27. POD was applied on the three-component
velocity vector at the AIP to identify the most-energetic coherent
structures of the flow. The dominant coherent structures were the
so-called switching and vertical perturbation modes. The switching
mode promoted the swirl-switching mechanism, by which one of the
Dean vortices observed in the mean flow alternately dominates the
flowfield [17]. The swirl-switching mode was previously observed
by Kalpakli Vester et al. [18], who used time-resolved SPIV for the
measurement of the airflow velocity field downstream a 90 deg
nondiffusing bend for two geometries with different curvature ratios
of γ 0.14 and γ 0.39,atRe
D
2.3 × 10
4
. The associated
modal distribution for the streamwise velocity resembled the lateral
perturbation reported by MacManus et al. [15] for the total pressure
field and represented a lateral modulation of the primary loss region,
which followed the movement of the dominant vortex [16]. The
vertical mode predominately represented a perturbation of the
vertical velocity field. This mode also described a vertical modulation
of the main loss region, which resembled the vertical perturbation of
the total pressure field reported by MacManus et al. [15]. Gil-Prieto
et al. [16] also assessed the impact of the most-energetic coherent
structures on the dynamic swirl distortion characteristics. The
switching mode was found to be responsible for most of the bulk swirl
events associated with the peak SI values, particularly in the high-
offset duct (HL 0.50). The vertical mode was associated with
most of the twin swirl events for both configurations. This indicated
the importance of these coherent structures in the swirl distortion
pattern.
The aim of the present investigation is to use DDES simulations to
expand the understanding of the most-energetic coherent structures
in the S-duct flowfield. The present study follows on from the
experimental work by Gil-Prieto et al. [16] with a more detailed
investigation of the flowfield coherent structures. The DDES results
are validated against SPIV measurements. The DDES simulations are
time-resolved and therefore permit the spectral analysis of the
coherent structures observed with the temporally underresolved
SPIV results. The symmetry plane velocity field is investigated to
identify the origin of the perturbations observed at the AIP, which are
responsible for the flow distortion characteristics. This is of prime
importance for the design of flow control devices. A novel multiplane
POD based on both the AIP and symmetry plane velocity fields is
conducted for this purpose.
II. Methodology
A. Studied Case
The S-duct geometry is a scaled-down version of the geometry
investigated by Garnier [13]. The S-duct has a circular cross section,
and the main geometrical parameters are an area ratio of AR 1.52,
an axial length of LD
in
4.95, a centerline offset of HL 0.50,
and an outlet diameter of D
out
150 mm (Fig. 1). The S-duct
centerline is composed of two consecutive 52 deg arcs with curvature
ratios R
in
R
c
of γ 0.16. The flow condition is determined by the
Mach number at the reference plane, which is located 0.9D
in
upstream of the S-duct inlet. The computational and experimental
results presented in this work correspond to a reference Mach number
of M
ref
0.27, which is associated with a Re
D
7.1 × 10
5
. The
Fig. 1 Schematic definition of the S-duct geometrical parameters.
2
Article in Advance / GIL-PRIETO ET AL.
Downloaded by Cranfield University (AKA DEFENCE ACADEMY OF THE UK) on April 10, 2017 | http://arc.aiaa.org | DOI: 10.2514/1.J055468

same S-duct geometry at M
ref
0.27 was tested by Zachos et al.
[14], Gil-Prieto et al. [16], and Tanguy et al. [19].
B. Stereo Particle Image Velocimetry Experiment
A detailed description of the experimental facility is reported by
Zachos et al. [14], and only the key aspects of the experiment are
reported here. A borosilicate glass, transparent section is placed
downstream of the S-duct to permit optical access for both laser and
cameras. The measurements are performed at the AIP, which is
located 0.41D
out
downstream of the S-duct outlet. A single-stage
centrifugal fan is used to control the mass flow rate. The rig is
calibrated to provide the required Mach number at the reference plane
(0.9D
in
upstream of the S-duct inlet). The Mach number uncertainty
at the flow condition considered in the present work is 0.27 0.01.
The boundary layer measured at the reference plane showed values of
displacement thickness and shape factor of 8.2 × 10
3
D
in
and 1.43,
respectively.
The SPIV system and methods used to obtain the three
components of the velocity are the same as reported by Tanguy et al.
[19]. The seeding particles were illuminated with a dual-cavity,
frequency-doubled Nd:YAG laser with a wavelength of 532 nm and a
maximum power of 200 mJ per pulse. The laser light sheet was
delivered by an articulated light arm, which provides a light sheet
with a thickness of approximately 2 mm. The seeding particles were
made of diethyl-hexyl sebacate, and the estimated diameter of the
particles was 1 μm. Two TSI PowerView Plus 8 megapixel cameras
were used in a stereoscopic configuration with an approximately
45 deg off-axis arrangement. The acquisition rate was approximately
3.5 Hz. TSI Insight 4G software was used for the calibration of the
cameras, the acquisition, and the processing of the images. About
14,000 velocity vectors were obtained at the AIP, which resulted in a
spatial resolution of 1.1 mm (0.007D
out
). A disparity correction was
applied to account for the potential misalignment between the laser
light sheet and the calibration target. The SPIV measurements
uncertainty was estimated with the procedure proposed by Raffel
et al. [20], which takes into account the particle image displacement,
particle image diameter, seeding density, quantization level, and
background noise. The overall uncertainty was approximately 6 and
8% for the in-plane and out-of-plane components of the velocity,
respectively. A data set of 1000 snapshots was considered to be
sufficient to provide statistically converged results, as reported by
Zachos et al. [14].
C. Delayed Detached-Eddy Simulation
The numerical computation is performed using a detached-eddy
simulation (DES), for which the unsteady Reynolds-averaged
NavierStokes (URANS) equations are applied in the boundary
layer, whereas the large-eddy simulation (LES) method is employed
in the highly unsteady regions away from the wall [21]. The delayed
version of the DES (DDES) ensures that the boundary layer is
resolved with the URANS formulation and is used to prevent grid-
induced separation problems [22]. The k ω SST model was chosen
for the URANS turbulence modeling. A pressure-based solver with a
segregated Pressure-Implicit with Splitting of Operators scheme was
used. The momentum, density, energy, and turbulence equations
were spatially discretized with a third-order Monotonic Upstream-
Centered Scheme for Conservation Laws scheme, whereas the
pressure equations were solved with a second-order discretization
scheme. The temporal formulation was based on a second-order
implicit scheme. The ideal gas equation was used, and the Sutherland
law was chosen to model the air viscosity dependence upon the
temperature.
The inlet total pressure profile was measured at the reference plane
located 0.9D
in
upstream of the S-duct inlet, using low-bandwidth
pressure probes. However, this profile could not be applied directly as
the inlet boundary condition for the computational domain because
this region was affected by the pressure gradient established in the
first bend of the S-duct. A total pressure profile was applied 2D
in
upstream of the S-duct inlet to match the experimental profile
measured at the reference plane. The experimental boundary layer
showed a displacement thickness of 8.2 × 10
3
D
in
and a shape factor
of 1.43. The DDES solution predicted a boundary layer with similar
values of displacement thickness and shape factor of 8.4 × 10
3
D
in
and 1.42, respectively. The experimental total temperature value of
approximately 290 K was also imposed at the inlet of the
computational domain. A uniform static pressure boundary condition
was applied at the outlet of the domain to match the experimental
mass flow rate. The outlet of the domain was extended 3D
in
to
remove any influence of the uniform boundary condition assumption
on the solution.
A baseline structured mesh of 5 milli on nodes was generated with
an H-grid structure in the center of the S-duct section and an O-grid
structure around the walls (Fi g. 2). The mesh was refined n ear the
walls to ensure that the y
was smaller than 1 over the full domain,
with an expansion ratio off the wall of 1.05. The number of nodes in
each cross section is approximately 11,000, and the number of cross
sections along the domain is approximately 450. The 2 × 2 × 2
determinant is obtained at each mesh cell as the normalized
determinant of the Jacobian matrix. Avalue of 1 represents a perfect
cube, whereas a value of 0 reflects a totally inverted cube with
negative volum e, and values above 0.3 are usually recommended
[23]. For the mesh used in this investigation, the determinant
2 × 2 × 2 wa s greater than 0.83 over the domain, which indicates
a good quality mesh. The time step was set to Δt 1.2 × 10
5
s
for the M
ref
0.27 case considered in the present work, which
corresponds to a nondimensional time step of approximately
Δtt
c
1.53 × 10
3
. The convective time t
c
is based on the S-duct
centerline length and the inlet centerline streamwise velocity. The
DDES computation was initialized from a converged Reynolds-
averaged NavierStokes (RANS) simulation. Each time step was
solved with 20 subiterat ions, which resulted in maximum residuals
of the order of 10
6
for the continuity equation at the end of each
time-step computation. The first 115t
c
of the unsteady D DES
simulation are not considered for t he analys is to remove any effect
of the transition between the RANS and DDES solutions [15]. This
is a conservative approach compared to the 10t
c
discarded by
Berens et al. [12]. The statistical convergence of the flowfield was
assessed for different simulated times, which ranged from 20t
c
to
50t
c
.TheSI
mean
, SI
std
,andSI
max
values were approximately the
same for 20t
c
and 50t
c
, w ith diffe rences of the order of 0.01 deg.
The results presented in this work are based on 50t
c
.
Three meshes of 2.5, 5, and 10 million nodes respectively were
considered to assess the sensitivity of the DDES unsteady solution to
the mesh spatial resolution. The number of nodes in each direction
was multiplied by a constant factor of 1.3 to generate the different
meshes. The number of nodes in each cross section was about 7,000,
11,000, and 18,000 for the coarse, medium, and fine meshes,
respectively. The number of cross sections along the domain was
approximately 350, 450, and 550, respectively. A mesh sensitivity
study was available for the same geometry at a flow condition of
M
ref
0.60. The conclusions from that study are presented here and
are expected to be also appropriate for the M
ref
0.27 simulation
used in the present investigation, where the requirements are
generally less stringent. Hence, the mesh sensitivity was done with
Fig. 2 Cross-section mesh topology.
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the results of the DDES simulation for these three meshes at
M
ref
0.60, with a time step of Δt 6 × 10
6
s, which equates to
Δtt
c
1.86 × 10
3
. The same values of PR
mean
and PR
std
were
obtained for the three meshes considered. The SI
mean
value was 10.2,
9.9, and 9.3 deg for the coarse, medium, and fine meshes,
respectively. The corresponding values of SI
std
were 1.9, 1.9, and
1.5 deg, whereas for SI
max
, the values were 17.5, 16.8, and 15.7 deg.
This indicates a limited impact of the mesh spatial resolution on the
swirl distortion characteristics. The impact of the time-step choice
was also assessed at M
ref
0.60, and the DDES simulation with the
medium mesh was computed at a doubled time step of
Δt 1.2 × 10
5
s, which equates to Δtt
c
3.72 × 10
3
. For this
coarser time step, the SI
mean
, SI
std
, and SI
max
values are
approximately 9.8, 1.8, and 16.5 deg, respectively. This indicates a
relatively minor dependency of the swirl distortion characteristics
upon the time-step choice. The results presented in this work are at
M
ref
0.27 and are obtained using the 5 million nodes medium
mesh with Δt 1.2 × 10
5
s (Δtt
c
of 1.53 × 10
3
).
The DDES approach switches between RANS and LES methods
based on the value of a blending function f
d
[24], so that RANS is
activated when f
d
0, whereas the LES formulation is applied when
f
d
1. Ideally, RANS should be applied within the boundary layers,
whereas LES should be activated in those regions away from the wall
where large-scale structures are expected to occur [22]. This has been
checked for all the simulations performed in this investigation,
including those required for the grid and time-step sensitivity. An
example of the blending function distribution at the AIP and
symmetry plane is provided in Fig. 3, for the simulation at M
ref
0.27 with the medium mesh.
D. Proper Orthogonal Decomposition
Turbulent flows are characterized by the presence of coherent
structures that are obscured by small-scale turbulent fluctuations.
Coherent structures are large-scale flow features that often account
for most of the essential flow mechanisms [25]. The POD permits the
identification of the most-energetic coherent structures of the
flowfield [26] and has been applied in a wide range of applications
including the flow in curved pipes [18] and S-ducts [16,27]. The POD
of the velocity vector field V, finds an orthonormal set of bases
Φ
i
fΦ
u
i
; Φ
v
i
; Φ
w
i
g, which are invariant with time. These functions
are usually referred to as POD modes and represent flow features that
are orthonormal to each other [26]. Each of the POD modes has an
associated temporal coefficient a
i
t, so that the contribution from
each flow feature to the original flowfield is a
i
tΦ
i
. Therefore, a
i
t
represents the instantaneous weight of each flow feature at the
different instants of time. The temporal coefficients are uncorrelated
to each other, so that the different flow features described by the POD
modes occur uncorrelated in time [26]. The POD representation of
the original velocity field can be obtained as the linear sum of a finite
number k of modal contributions [28] [Eq. (1)]:
V
k
X
k
j0
a
j
tΦ
j
x; y (1)
The variance of the temporal coefficients, ha
2
j
i, represents the
contribution of each POD mode to the area-averaged mean kinetic
energy h
KEi[28]. The modes are then ordered by the associated hKEi
contribution. This permits an optimum representation in terms of
kinetic energy in the sense that, for a given number of terms in the
series, the POD maximizes the kinetic energy content in the
reconstruction [Eq. (2)] [28]. The kinetic energy of the original
flowfield h
KEi can be obtained as the sum of the contribution from all
themodes. Inthe present investigation, the POD has been implemented
with the method of snapshots, developed by Sirovich [29]:
h
KEi
k
X
k
j0
ha
2
j
i (2)
III. Results
A. Experimental Validation
The mean velocity field for the DDES solution is compared with
the SPIV results at the same inlet Mach number of M
ref
0.27
(Fig. 4). The DDES solution has been linearly interpolated, using the
Delaunay triangulation method, into the loci of the SPIV data points
for a consistent comparison. The region of low streamwise velocity is
well captured in the DDES solution (Fig. 4a) compared with the SPIV
data (Fig. 4e). The minimum values of streamwise velocity in the loss
region are hwih
w
AIP
i0.76 and 0.75 for DDES and SPIV,
respectively. The DDES mean vertical velocity distribution (Fig. 4b)
is also well predicted compared to the SPIV results (Fig. 4f). The
pitch-down regions near the walls at both sides of the symmetry plane
are slightly underpredicted by the DDES. The minimum values are
hvih
w
AIP
i0.13 and 0.20 for DDES and SPIV, respectively.
The pitch-up central region is well matched, with a maximum value
of hvih
w
AIP
i0.12 and 0.13 for DDES and SPIV, respectively.
The DDES mean lateral velocity field (Fig. 4c) agrees well with the
SPIV measurements (Fig. 4g). The two opposite-sign regions of high
lateral velocity at the bottom and top of the AIP are well predicted by
the DDES. The maximum absolute values of lateral velocity at the
lower sector are huih
w
AIP
i0.11 and 0.15 for DDES and SPIV,
respectively. The corresponding values at the top regions are
huih
w
AIP
i0.06 and 0.07. The lateral and vertical velocity fields
result in the well-known symmetric pair of vortices, observed for both
DDES (Fig. 4d) and SPIV (Fig. 4h) data. The DDES also predicts a
pair of regions of high lateral velocity near the wall at the top of the
AIP (Fig. 4c), which results in a secondary pair of vortices (Fig. 4d).
These small vortical structures are, however, not revealed by the
SPIV data (Fig. 4h). One of the main flow variables of interest in
S-duct research is the swirl angle, due to the destabilizing effect that
the swirling flow can have on the downstream components of the
engine [3]. The characteristic mean-flow pair of swirling regions at
the AIP, which are associated with the presence of the two counter-
rotating vortices, is observed for both DDES (Fig. 4d) and SPIV
(Fig. 4h). In general, the measured data have very low noise levels.
Measurement noise is only present for the lateral velocity
measurements in regions very close to the wall (Fig. 4g) and are due
to reflections of the laser light sheet. Overall, there is a good
Fig. 3 Sample time step showing the DDES blending function distribution: f
d
0 (black), and f
d
1 (white).
4
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agreement between numerical and experimental time-averaged data.
To further quantify the agreement between DDES and SPIV data,
the mean flow profiles of the three components of the velocity along
the symmetry axis of the AIP are compared (Fig. 5). Both DDES
and SPIV results show similar mean flow profiles for the three
components of the velocity (Fig. 5).
The highly unsteady nature of the S-duct AIP flowfield is well
recognized [12,1416]. Therefore, it is also of interest to compare the
calculated DDES fluctuating velocity field with SPIV data. The
standard deviation of the three components of the velocity and the
swirl angle at the AIP for DDES and SPIVare compared (Fig. 6). It is
important to highlight that the DDES flowfield was acquired at a
frequency of 27.8 kHz for approximately 50t
c
(0.40 s), which is
sufficient to provide statistically converged results (see Sec. II.C). In
contrast, the SPIV measurements are temporally underresolved with
an acquisition frequency of 3.5 Hz for 286 s to provide 1000
snapshots for the statistical analysis, which ensures statistically
converged results [14]. For statistically converged data sets, the
flowfield statistics should be independent of the acquisition
frequency, and therefore the DDES and SPIV statistics are
comparable. The extent of the region of greatest streamwise velocity
fluctuations is in good agreement between DDES (Fig. 6a) and SPIV
data (Fig. 6e). This region corresponds to the upper boundary of the
mean-flow shear layer. The maximum value is approximately
σ
w
h
w
AIP
i0.23 and 0.22 for DDES and SPIV, respectively.
However, DDES data do not show the small region of high
streamwise velocity fluctuations observed in the SPIV measurements
at the top of the AIP (Fig. 6e). The greatest vertical velocity
fluctuations occur at the center of the section for both DDES (Fig. 6b)
and SPIV data (Fig. 6f). However, the fluctuation levels are slightly
overpredicted in the DDES solution, for which the maximum values
are σ
v
h
w
AIP
i0.25 compared to the SPIV value of 0.22. The
maximum lateral velocity fluctuations occur at the lower sector of the
AIP for both DDES (Fig. 6c) and SPIV data (Fig. 6g). As for the
vertical component of the velocity, the lateral velocity fluctuations
are overpredicted by the DDES. The maximum values are
σ
u
h
w
AIP
i0.28 and 0.22 for DDES and SPIV, respectively. The
regions of maximum lateral and vertical fluctuations occur as a result
Fig. 4 Time-averaged flowfield at the AIP at M
ref
0.27.
Fig. 5 Velocity profiles along the vertical symmetry axis of the AIP: DDES (solid line), SPIV (dashed line), unsteady σV
i
(white circles), and time-
averaged hV
i
i (black circles).
Article in Advance / GIL-PRIETO ET AL. 5
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Citations
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Journal ArticleDOI
Abstract: Some types of aero-engine intake systems are susceptible to the generation of secondary flows with high levels of total pressure fluctuations. The resulting peak distortion events may exceed the tolerance level of a given engine, leading to handling problems or to compressor surge. Previous work used distortion descriptors for the assessment of intake-engine compatibility to characterise modestly curved intakes where most of the self-generated time-dependent distortion was typically found to be dominated by stochastic events. This work investigates the time-dependent total pressure distortion at the exit of two high off-set diffusing S-duct intakes with the aim of establishing whether this classical approach, or similar, could be applied in these instances. The assessment of joint probability maps for time dependent radial and circumferential distortion metrics demonstrated that local ring-based distortion descriptors are more appropriate to characterise peak events. Extreme Value Theory (EVT) was applied to predict the peak distortion levels that could occur for a test time beyond the experimental data set available. Systematic assessments of model sensitivities to the de-clustering frequency, the number of exceedances and sample time length were used to extend the EVT application to local distortion descriptors and to provide guidelines on its usage.

18 citations


Cites methods from "Delayed Detached-Eddy Simulation an..."

  • ...The use of proper orthogonal decomposition (POD) applied to the S-PIV measured velocity data [9] and unsteady CFD simulations [19] revealed that the velocity flow field unsteadiness was dominated by the swirl switching mechanism [28]....

    [...]

  • ...Previous Stereoscopic Particle Image Velocimetry (PIV) and CFD analysis [9][19] found that the unsteady distortion characteristics of the velocity field were associated with different flow modes....

    [...]

  • ...Duct B was also evaluated through steady and unsteady CFD simulations [11,19] as well as with S-PIV measurements [8,9]....

    [...]


Journal ArticleDOI
Abstract: The unsteady distorted flow fields generated within convoluted intakes can have a detrimental effect on the stability of an aero-engine. The frequency signature in the distorted flow field is of key importance to the engine's response. In this work, time-resolved particle image velocimetry is used to obtain the three-component velocity field at the outlet plane of two S-duct intake configurations for a range of inlet Mach numbers. Proper orthogonal decomposition of the time-resolved velocity data allows the identification of the main frequencies and coherent structures in the flow. The most energetic unsteady structures comprise an in-plane vortex switching mode, associated with a lateral oscillation of the main loss region, and a vertical oscillation of the main loss region. The switching structure occurs at a frequency of St = 0.42 and 0.32 for the high and low offset ducts, respectively. The vertical perturbation is associated with a more broadband spectrum between approximately St = 0.6 – 1.0 and St = 0.26 – 1.0 for the high and low offset configurations, respectively. The determined frequencies for these main unsteady flow structures are within the range, which is expected to be detrimental to the operating stability of an aero-engine. The results provide a novel, time-resolved dataset of synchronous velocity measurements of high spatial resolution that enables analysis of the unsteady flows at the exit of complex aero-engine intakes.

16 citations


Journal ArticleDOI
Abstract: Peak events of unsteady total pressure and swirl distortion generated within S-duct intakes can affect the engine stability, even when within acceptable mean distortion levels. Even though the swirl distortion descriptors have been evaluated in S-duct intakes, the associated flow field pattern has not been reported in detail. This is of importance since engine tolerance to distortion is usually tested with representative patterns from intake tests replicated with steady distortion generators. Despite its importance in intake/engine compatibility assessments, the spectral characteristics of the distortion descriptors and the relationship between peak unsteady swirl and both radial and circumferential total pressure distortion has not been assessed previously. The peak distortion data is typically low-pass filtered at a frequency associated with the minimum response time of the engine. However the engine design is not always known a priori in intakes investigations and a standard approach to reporting peak distortion data is needed. In addition, expensive and time-consuming tests are usually required to capture representative extreme distortion levels. This work presents a range of analyses based on Delayed Detached-Eddy Simulation and Stereo Particle Image Velocimetry data at the outlet of a representative S-duct intake to assess these aspects of the unsteady flow distortion. The distorted pattern associated with different swirl distortion metrics is identified based on a conditional averaging technique, which indicates that the most intense swirl events are associated with a single rotating structure. The main frequencies of the flow distortion descriptors are found to lie within the range in which the engine stability may be compromised. The peak total pressure and swirl distortion events are found to be not synchronous, which highlights the need to assess both types of distortion. Peak swirl and total-pressure distortion data is reported as a function of its associated time scale in a more general way that can be used in the assessment of intake unsteady flow distortion. Extreme Value Theory has been applied to predict peak distortion values beyond those measured in the available dataset, and whose measurement would otherwise require testing times two orders of magnitude longer than those typically considered.

15 citations


Cites background or result from "Delayed Detached-Eddy Simulation an..."

  • ...3° for the fine, medium and coarse meshes, respectively, and similar results were obtained for std(S?̅?) and max(S?̅?) [29]....

    [...]

  • ...[29], and the time-averaged and fluctuating velocity fields at the AIP are only briefly described in this section for completeness....

    [...]

  • ...22, for DDES and SPIV, respectively [29]....

    [...]

  • ...9Din upstream of the S-Duct inlet plane was matched in the DDES [29]....

    [...]

  • ...2 Flow field statistics at the AIP for DDES (top) and SPIV (bottom), including the time-averaged w-velocity (left), timeaveraged swirl angle (centre) and standard-deviation of the w-velocity (right) [29]...

    [...]


Journal ArticleDOI
12 Oct 2018
TL;DR: The design parameters describe the 3D geometrical changes to the shape of the S-Duct and the improvements to the aerodynamic behavior are assessed by considering two objective functions: the pressure losses and the swirl.
Abstract: In this work, we investigate the computational design of a typical S-Duct that is found in the literature. We model the design problem as a shape optimization study. The design parameters describe the 3D geometrical changes to the shape of the S-Duct and we assess the improvements to the aerodynamic behavior by considering two objective functions: the pressure losses and the swirl. The geometry management is controlled with the Free-Form Deformation (FFD) technique, the analysis of the flow is performed using steady-state computational fluid dynamics (CFD), and the exploration of the design space is achieved using the heuristic optimization algorithm Tabu Search (MOTS). The results reveal potential improvements by 14% with respect to the pressure losses and by 71% with respect to the swirl of the flow. These findings exceed by a large margin the optimality level that was achieved by other approaches in the literature. Further investigation of a range of optimum geometries is performed and reported with a detailed discussion.

10 citations


Journal ArticleDOI
Zhaoyang Xia1, Xingsi Han1, Junkui Mao1Institutions (1)
Abstract: Strongly swirling flow is widely encountered in engineering applications. However, accurate prediction of the flow is still challenging for turbulence modeling. The present study reports the assess...

6 citations


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"Delayed Detached-Eddy Simulation an..." refers methods in this paper

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1,788 citations


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    [...]

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1,131 citations


"Delayed Detached-Eddy Simulation an..." refers background in this paper

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    [...]

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