fmiFinal

ARTICLE IN PRESS
Flow Measurement and Instrumentation ( ) –
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation
journal homepage: www.elsevier.com/locate/flowmeasinst
Experimental and numerical study of the sweep effect on three-dimensional
flow downstream of axial flow fans
J. Huraulta
, S. Kouidrib,∗
, F. Bakira
, R. Reya
a
LEMFI, Arts et Metiers Paristech, 151 Boulevard de l’Hopital 75013 Paris, France
b
LIMSI-CNRS/UPMC, B.P. 133, 91403 Orsay CEDEX, France
a r t i c l e i n f o
Article history:
Received 15 March 2009
Received in revised form
13 August 2009
Accepted 5 February 2010
Keywords:
Axial flow fan
Sweep
Hot-wire anemometry
Reynolds stress model
a b s t r a c t
The purpose of this work is to study the influence of the axial flow fan sweep on the downstream
turbulent flow. The fans studied are three low-pressure and low-Mach-number axial flow fans, with
respectively a radial, a forward and a backward sweep. Experimental and computational fluid dynamics
(CFD) investigations are carried out on three fans, and the results are compared. The CFD method is a three-
dimensional (3D) Reynolds average Navier–Stokes (RANS) numerical simulation with the Reynolds stress
model (RSM) as the turbulence model. It allows us to compute the Reynolds stress tensor components.
Unsteady velocity measurements are carried out downstream of the fans with hot-wire anemometry. The
values of the three velocity components of the flow and the six components of the Reynolds stress tensor
obtained from experiments and simulations are compared. Overall performances are also measured to
validate the design and fan simulation. It appears that a forward sweep decreases the radial component of
the velocity whereas a backward sweep increases this component. Moreover, the sweep has a significant
influence on the turbulent kinetic energy downstream of the fan.
© 2010 Elsevier Ltd. All rights reserved.
1. Introduction
The flows in turbomachinery are very complex. They are charac-
terised by three-dimensional (3D), viscous and unsteady elements.
Geometric characteristics and operating conditions have a strong
influence on the flows. The unsteady aerodynamic phenomena
often appear in the form of a decrease of the aerodynamic specifica-
tions and they are the cause of acoustic inconvenience and aeroe-
lasticity phenomena. Therefore unsteady flows in axial flow fans
are an important topic for investigation. Numerical simulations
with different turbulence models are used to study these complex
flows. Computational fluid dynamics (CFD) tools using the resolu-
tion of the averaged Navier–Stokes equations do not give the un-
steady aerodynamic characteristics of the flow. In addition, tools
using direct numerical simulation or large eddy simulation (LES)
are still expensive for industrial users in the case of a complex ge-
ometry such as turbomachinery.
The aim of this paper is to determine the sweep effect on the
velocity components downstream of the trailing edge. This un-
steady component can be separated into a deterministic part and a
random one. The deterministic part is the discrete component ap-
pearing at the blade passage frequency and its harmonics. It orig-
inates from the periodic unsteady forces owing to the interaction
∗ Corresponding author.
E-mail address: kouidri@limsi.fr (S. Kouidri).
between the rotor blades and their environment. The random com-
ponent is mainly because of turbulence phenomena around the
blade airfoil, and contributes to all frequencies over a frequency
band ranging from 5 to 20 000 Hz.
The work presented in this paper is preliminary work on noise
prediction. The turbulent kinetic energy will be used as the input
for a noise prediction model [1,2]. The Reynolds stress model
(RSM) turbulence model allows us to compute turbulent kinetic
energy with high accuracy (Section 4.3).
Axial flow fans used in automotive cooling systems provide
the case study. They are often subject to poor inflow conditions.
From this inflow result periodic and random forces that cause tonal
and broadband interaction noise. Moreover, the force fluctuations
owing to the turbulent boundary layer on the blade surfaces and
their interaction with the trailing edge cause the self-noise of the
fan, which is broadband.
The use of blade sweep for noise reduction appears to be
effective. Hanson [3] studied the problem primarily in terms of
reduction of blade tonal noise through phase-shift cancellation of
the noise generated at different radial locations. He also studied
blade-to-blade interference. While his work shows that very large
angles of blade sweep may be required, particularly for low-speed
rotors, the works of Fukano et al. [4], Cummings et al. [5], and
Fujita [6] have shown experimentally that reasonable amounts of
sweep may be very beneficial in reducing the noise.
In particular, the works of Kerschen [7] and Envia and
Kerschen [8] seem to provide a theoretical basis for selecting a
0955-5986/$ – see front matter © 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.flowmeasinst.2010.02.003
Please cite this article in press as: Hurault J, et al. Experimental and numerical study of the sweep effect on three-dimensional flow downstream of axial flow fans. Flow
Measurement and Instrumentation (2010), doi:10.1016/j.flowmeasinst.2010.02.003

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2 J. Hurault et al. / Flow Measurement and Instrumentation ( ) –
Nomenclature
uiuj Components of the Reynolds stress tensor (m2
/s2
)
Ca, Cr , Ct Components of the velocity in the fan coordinate
system (m/s)
h1, h2 Pitch factor of wire 1 and wire 2 [-]
k Turbulent kinetic energy (m2
/s2
)
k1, k2 Yaw factor of wire 1 and wire 2 [-]
Rext Outer radius of the fan (mm)
Rint Inner radius of the fan (mm)
U1, U2, V Components of the velocity in the wire coordinate
system in position 2 (m/s)
U1eff, U2eff Effective cooling velocities of wire 1 and wire 2 in
position 2 (m/s)
U1, U2, W Components of the velocity in the wire coordinate
system in position 1 (m/s)
U1eff, U2eff Effective cooling velocities of wire 1 and wire 2 in
position 1 (m/s)
U90 Velocity in the axis of the probe in position 2 (m/s)
U, V, W Components of the velocity in the probe coordinate
system
β Angle between the axis of the probe and the fan
plane (°)
η Static efficiency of the fan [-]
ϕn Nominal flow rate coefficient of the fan [-]
1.3ϕn 30% higher nominal flow rate coefficient [-]
distribution of sweep angles along a blade, which provide sharp
reductions in the noise associated with turbulence ingestion.
Applied to low-speed axial fans, the backward and forward sweeps
alter the spatial distribution of the elementary noise sources so
that they are not generated simultaneously at each blade radius.
The phase shift thus produced results in destructive or constructive
interferences of the spanwise components of the pressure and
velocity, and consequently in a modification of the radiated noise.
Complete literature on the aerodynamic and acoustic properties of
axial fans with swept blades is presented in reference [9].
URANS numerical simulation yields steady and unsteady
loading on the blades and the Ffowcs Williams & Hawkings
formulation could be used to derive the tonal part of the acoustic
spectra of impellers [10]. For a spatially uniform but temporally
unsteady inflow, however, the URANS method fails as regards
broadband noise prediction. The prediction of broadband noise
sources requires a numerical method with high accuracy. Carolus
et al. [11] used hot-wire anemometry to obtain a database
of the turbulence statistics for a variety of different inflow
configurations. These results are compared with an LES simulation.
The LES predicted the effects of the ingested turbulence on the
fluctuating blade forces and the fan noise compares favourably
with experiments. LES is still expensive for industrial users and
a prediction with the turbulent kinetic energy from Reynolds
average Navier–Stokes (RANS) computation can be useful [1,2].
The experimental set-up used to measure the 3D unsteady
velocity components downstream of the fans is presented in
Section 2. The measurements are performed along the radius of the
turbomachinery by means of hot-wire anemometry. Data analysis
yielding the turbulent velocity fluctuations, the components of
the Reynolds stress tensor and the turbulent kinetic energy is
described. Then a simulation for the three different sweep fans
(Section 3) is modelled and computed. Finally, the results are
compared and analysed in Section 4.
2. Experimental set-up
The fans used in this study are three prototypes of axial flow
type. The blades are radially swept on the leading edge in three
ba c
Fig. 1. Front view of the three fans, G2rad (a), G2for (b) and G2back (c).
Table 1
Working flow rate coefficient for the three fans.
G2for G2rad G2back
ϕn 0.223 0.248 0.247
1.3ϕn 0.289 0.330 0.314
different ways, as shown in Fig. 1. The first fan presents a radial
sweep (G2rad), the second one is swept in the direction of rotation
(G2for) and the third is swept in the inverse direction of rotation
(G2back). The law of the sweep is symmetric between G2for and
G2back. The other geometrical characteristics are, however, the
same. Each of these fans has eight blades. The design characteristics
of the three axial fans are as follows: an external radius Rext =
187.5 mm, an internal radius Rint = 85 mm and a stagger angle
75° at mid-span. The shroud has a thickness of 2.5 mm. The rotor is
built up from blades of NACA0065, with a thin profile of maximum
thickness 5.5 mm along the camber lines, rounded at the leading
and trailing edges. The rotation speed is 45 Hz.
All the measurements are performed at the nominal flow rate
(ϕn) and at 130% of the nominal flow rate (1.3ϕn) for the three fans,
according to Table 1.
2.1. Test facility
In this study, it was decided to use constant temperature
anemometry (CTA) because of its rapidity, and its ability to deliver
accurate time series and broadband spectral signals. According
to the radial equilibrium hypothesis, an axial fan should present
a 2D flow and the radial component of the absolute velocity
should be negligible. This situation is rarely observed, since an
energy transfer occurs between the concentric air tubes, so a
3D description of the axial fan flow field is needed. The axial,
tangential and radial components of the velocity have to be
measured and compared with those obtained by computation.
A 2D Dantec 55R51 hot fiber film probe was used to measure
the components of the instantaneous velocity. Measuring two
different angular positions enables the measurement of the three
velocity components. To do that, a rotation at an angle of 90°
around the axis probe is performed. The detailed methodology to
get the complete 3D structure of the flow field using a 2D probe
is described later. The complete measuring system is composed of
a 5H24 probe support, a 54T30 miniCTA anemometer per wire, a
National Instrument PCI6048-E A/D converter board, a tachometer
trigger and Dantec CTA v3.4 software which enables sampling of
the signals up to 250 kHz. Figs. 2 and 3 show the experimental
facility. The air test bench, designed and built according to ISO 5801
standard [12], enables a controlled air flow rate to operate at the
design point, choosing the adequate orifice plate diameter.
The hot-wire probe is positioned spanwise at 11 uniformly
spaced points in the radial direction downstream of the fan, 10 mm
away from the trailing edge at the hub, at angle β to the fan plane
(Fig. 4). This β angle corresponds to the absolute velocity angle in
the measurement plane at mid-span. The absolute velocity angle
is dependent on the fan and the flow rate, so it is different for
each measurement. Moreover, this angle varies along the radius

ARTICLE IN PRESS
J. Hurault et al. / Flow Measurement and Instrumentation ( ) – 3
Fig. 2. ISO 5801 test bench.
Fig. 3. Hot-wire probe and support downstream of the fan, with coordinate system
of the fan.
Fig. 4. Location of the probe.
of the fan. The absolute velocity angle at mid-span is chosen for all
measurement points.
The CTA system is configured with a sampling frequency of
45 kHz, which allows 1000 samples per revolution. The data are
gathered for 20 revolutions of the fan.
2.2. Calibration and uncertainty analysis
Calibration establishes a relation between the voltage output
and the flow velocity by exposing the probe to a set of known ve-
locities, U, and then records the voltages, E. A curve fit through the
points (E, U) represents the transfer function to be used when con-
verting data records from voltages into velocities. For a better accu-
racy a logarithmic distribution of 20 velocity points between 1 and
25 m s−1
is chosen. Then the software computes a transfer function
in the form of a fourth-order polynomial.
The probe is calibrated in a free wind jet before and after the
test in order to control its drift. The calibration bench is composed
of a big volume at a constant pressure and a small hole where a free
wind jet goes outside of the volume to reach atmospheric pressure.
The velocity of the jet is computed with the Bernoulli equation
and is equal to V = 2∗∆P
ρ
, where ρ is the density of the air and
∆P is the relative pressure between the pressure in the box and
atmospheric pressure.
After 20 calibrations it appears that the error of repeatability is
negligible compared to the two errors listed below. The first one
is the determination of the velocity of calibration: the accuracy
of the manometer is 0.1 Pa, which is equal to an accuracy of the
calibration bench of 0.407 m s−1
. The second is the difference
between the computed fourth-order polynomial and the real
transfer function. The maximum relative error between the fourth-
order polynomial curve and the measured point is 3% and is for
the low velocities (up to 4 m s−1
). For higher velocities the error is
about 1%.
For example, this leads to an acceptable relative error of 3% for
a velocity of 20 m s−1
and a relative error of 13% for a velocity of
4 m s−1
.
2.3. Measurement procedure
A 2D probe is specifically designed for measurements of
2D flow fields since two velocity components are measured
simultaneously. Measurement of three components has to take
into account the influence of the third component and involves
placing the probe at another orientation with respect to the flow.
Figs. 4 and 5 present the 2D probe and fan coordinate systems, and
the wire location. The wires are perpendicular to one another so
that the flow in the axis of the probe (x) is at 45° of each wire.
They form one X-wire array parallel to the (u, v) plane, which is
designated as Position 1. Position 2 corresponds to a 90° rotation
of Position 1 around the probe axis (Fig. 5). In a highly turbulent 3D
flow, which is the case for measurements downstream of axial flow
fans, the velocity binormal component (perpendicular to the probe
plane) is important. In order to take its influence into account,
equations similar to those for tri-sensor probes or four-sensor
probes have been developed [13].
The 3D flow in the probe coordinate system is characterised by
its velocity components (U, V, W). Measurements are performed
to get the wire coordinates (U1, U2) and binormal component W
in Position 1. After rotation, the wire coordinates (U1, U2) and
binormal component V are measured in Position 2 (Fig. 5). The wire
coordinates (U1, U2, U1, U2) are linearly dependent on the probe
coordinates (U, V, W), so the four equations can be expressed in
terms of components (U, V, W) with three unknowns (Eqs. (1) and
(2)). In Positions 1 and 2, the binormal components correspond
to velocity components W and V, respectively. The tangential
components will perturb the measurement of the effective cooling
velocities (U1eff, U2eff) and (U1eff, U2eff). These perturbations are
taken into account using yaw factors (k1, k2) with tangential
components (U1, U2) and (U1, U2) and pitch factors (h1, h2) with
binormal components W and V, so that the general expressions in
3D flows for the two wires before and after rotation are [13]
U2
1eff = k2
1U2
1 + U2
2 + h2
1W2
; U2
2eff = U2
1 + k2
2U2
2 + h2
2W2
(1)
U 2
1eff = k2
1U 2
1 + U 2
2 + h2
1V2
; U 2
2eff = U 2
1 + k2
2U 2
2 + h2
2V2
. (2)
The direct 2D measurement procedure that neglects the
influence of the velocity binormal component is used, evaluating
the error at 15%. The CTA software provides velocity components

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Fig. 5. Position 1 and Position 2 of the probe with associated coordinate systems.
U and V in Position 1. Components U90 and W are then obtained
in Position 2. Components U and U90 are supposed to be close,
so the components of instantaneous velocity are expressed from
(U, V, W) in the fan coordinate system using the following
formulation [13]:
Ca = U cos β − W sin β
Cr = V
Ct = U sin β + W cos β
(3)
where Ca, Cr and Ct are respectively the axial, radial and tangential
components of the velocity in the fan coordinate system (Fig. 3).
3. Numerical simulations
The 3D simulations are performed with the commercial CFD
code Fluent 6.3. The Fluent flow solver is based on the multiple
element (hexahedral, tetrahedral, wedge, pyramid) finite volume
method. Structured, unstructured, and hybrid (mixed) element
meshes are implemented in the pre-processor Gambit 2.4. Due to
the complexity of the blade geometry, unstructured tetrahedral
meshes are used. Primitive variables for velocity, pressure, and
enthalpy are defined at nodes at the corners of each element.
Conservation equations are obtained by integration over the
element mesh-dual. First-order integrations and flux discretisation
are used. A fully implicit solution strategy is employed.
3.1. Geometry and meshing
In order to compare the predicted results with the experiments,
a test bench is designed with CAD software. The test bench shown
in Figs. 2 and 3 is considered in its entirety for the numerical
simulation. Fig. 2 shows an overview of the modelled test bench
following ISO 5801 [12], including the fan location. The fans are
rotating at 2700 rpm (45 Hz). In the experimentation, orifice
plates with different diameters are used to fit the flow rate. In the
simulation, the velocity inlet boundary condition sets the flow rate.
The numerical modelling comprises three domains. The fan
sucks the airflow from inside the box to the atmospheric conditions
outside the box. Therefore, the boundary conditions imposed are
mass flow at the inlet and static pressure at the outlet. Modelling is
focused on details which are very important for measurement and
simulation results, such as the tip clearance between the shroud
and box wall and the inlet orifice plate’s chamfer.
Fig. 6. Fluid domain and boundary conditions for the G2for modelling. (For
interpretation of the references to colour in this figure legend, the reader is referred
to the web version of this article.)
Fig. 7. Mesh of the fan (top) and the numerical domain (bottom) with refined mesh
near the fan.
One-eighth of the domain is modelled with periodic boundary
conditions in order to minimise the computing time. The
periodicity is defined in rotation around the rotation axis of the fan
(Fig. 6). A tip clearance of 4 mm is modelled between the shroud
and the wall of the test bench as in the experimental set-up. Three
different geometries are created for the three different sweep fans.
The boundary conditions are defined in Fig. 6 as the blue, grey,
yellow and red colours corresponding to the inlet, the walls, the fan
interfaces with the box and the outlet, and the outlet, respectively.
The box has the same dimensions as the experimental box but
is rounded to respect the periodicity in rotation. The velocity
inlet boundary conditions could be used because of the very low
Mach number (<0.3). The pressure outlet boundary conditions are
set at atmospheric conditions. The total number of cells for the
computing domain is four million. This corresponds to 32 million
cells for the domain without periodic boundary conditions. The
mesh size is very small close to the blade wall, about 1 mm,
and becomes progressively bigger far away from the fan. Fig. 7
illustrates the mesh overview for a given fan.

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Fig. 8. Path-lines in the test bench coloured by velocity magnitude (m/s). (For
interpretation of the references to colour in this figure legend, the reader is referred
to the web version of this article.)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Flow Rate Coefficient
PressureCoefficient
G2for Experiment
G2for Simulation
G2rad Experiment
G2rad Simulation
G2back Simulation
G2back Experiment
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Fig. 9. Comparison of the performance between the simulation and the
experiments for the three fans. (For interpretation of the references to colour in
this figure legend, the reader is referred to the web version of this article.)
Fig. 8 shows the path-lines in the box coloured by velocity
magnitude for two different flow rates. The homogenisation grid
in the box, defined following the ISO 5801 standard, compel the
velocity profile to be constant in the measurement section of the
box upstream of the fan. The velocity magnitude in this area is close
to 0 m/s before the suction of the fan. For this type of fan, at the
nominal flow rate, the flow downstream has a high radial velocity
owing to the high centrifugation of the flow. At a higher flow rate,
the radial velocity decreases as the axial velocity increases.
3.2. Turbulence model
The Reynolds stress model involves calculation of the individual
components of the Reynolds stress tensor, uiuj, using differential
transport equations. The RSM is a RANS second-moment closure
which solves six equations for the Reynolds stress tensor. It
represents the influence of turbulence on the mean flow. The
individual Reynolds stresses are then used to obtain closure of
the Reynolds-averaged momentum equation. The exact form of
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Flow rate coefficient
Efficiency(η/ηmax)
G2for Experiment
G2for Simulation
G2rad Experiment
G2rad Simulation
G2back Simulation
G2back Experiment
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fig. 10. Comparison of the efficiency (η/ηmax) of the simulation and the
experiments for the three fans.
the Reynolds stress transport equations may be derived by taking
moments of the exact momentum equation. This is a process
wherein the exact momentum equations are multiplied by a
fluctuating property, the product then being Reynolds-averaged.
Such models naturally include the effects of streamline curvature,
sudden changes in strain rate and secondary motions, but they
increase the complexity and computational cost compared with
first-order closure models.
The Reynolds stress tensor [14] is defined for the fan as
− ρuiuj = −ρ


CaCa CaCr CaCt
· · · Cr Cr Cr Ct
· · · · · · Ct Ct


= −ρ
UUstress UVstress UWstress
· · · VVstress VWstress
· · · · · · WWstress
. (4)
The turbulent kinetic energy [14] is defined as
k = −
1
2
ρuiui = −
1
2
ρ (UUstress + VVstress + WWstress) . (5)
The convergence criterion is that the scaled residual has to
decrease to 10−5
for the 12 equations (continuity, the three
components of the velocity, k and ε, and the six Reynolds stress
tensor components). The velocity and Reynolds stress tensor
components are computed in a plane, 10 mm downstream of the
fan according to the hot-wire measurement.
4. Results and discussion
4.1. Overall characteristics
The pressure rise versus the flow rate is represented in Fig. 9.
It can be seen that the numerical RSM results with the three fans
are close to the experimental results, more especially around the
nominal flow rate. There are some discrepancies at the very high
flow rate where strong secondary flow results in difficulties in
the convergence of the simulation. Five flow rates are calculated
around the radial swept fan nominal flow rate. Very low flow
rates are not computed due to the strong secondary flow near
the hub and detachment of the flow around the blade that leads
to difficulties in the convergence. The blue curve is the result of
computation with the RSM turbulence model for G2for. Its pressure

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–2
–1
0
0
2
4
6
8
10
12
14
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
1
2
3
4
5
6
7
0
–2
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
2
4
6
8
10
12
HUB TIPRadius / Tip Radius
AxialVelocity(m/s)
RadialVelocity(m/s)TangentialVelocity(m/s)
Fig. 11. Comparison of experimental and computed velocity profiles for G2for at
two flow rates.
rise is below that of G2rad. Moreover, the performance of G2back
(green curve) is very close to that of G2rad.
The static efficiency is shown in Fig. 10. A maximum of 6%
difference is observed between the experiment and the simulation.
G2for has a nominal flow rate coefficient that is lower than that
of G2rad (ϕn = 0.223 versus 0.248). The maximum efficiency of
G2for is lower than that of G2rad. As regards G2back, the maximum
efficiency is at the same level as for G2for but at a higher flow rate
–1
0
4
2
0
6
8
10
12
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
1
2
3
4
5
6
0
–2
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
2
4
6
8
10
12
AxialVelocity(m/s)RadialVelocity(m/s)TangentialVelocity(m/s)
Fig. 12. Comparison of the computed velocity profile for the three fans.
(ϕn = 0.247). The maximum static efficiency of G2rad is better
and at a higher flow rate than for G2for, and the pressure rise is
higher. With regard to the overall behaviour, the modelling with
periodicity is validated. It allows us to compute complex flow with
a second-order closure model and obtain results comparable with
experimental results.
The sweep of the fan is known to improve the acoustic
behaviour, but the aerodynamic behaviour is quite different. Here
the forward sweep decreases the efficiency. In another study
where the fan blades are more loaded [15] the forward sweep
increases the efficiency. In [15] the fans are designed to be more
loaded, especially in the tip region. A fan with forward sweep blade
loaded in the tip region seems to improve the efficiency whereas
a fan with forward sweep blade equally loaded spanwise seems to
decrease the efficiency. The influence of the sweep relies on other
geometrical characteristics of the fan.

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0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0.5
1
1.5
2
2.5
UUstress(ms
22
/)
0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0.5
1
1.5
2
2.5
UVstress(ms
22
/)
0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0.5
1
1.5
2
2.5
HUB TIP
Radius / Tip Radius
VVstress(ms
22
/)
0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0.5
1
1.5
2
2.5
HUB TIP
Radius / Tip Radius
UWstress(ms
22
/)
0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0.5
1
1.5
2
2.5
HUB
HUBTIP
Radius / Tip Radius
WWstress(ms
22
/)
0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0.5
1
1.5
2
2.5
TIP
Radius / Tip Radius
VWstress(ms
22
/)
Fig. 13. Comparison of experimental and computed Reynolds stress tensor profiles for G2for at two flow rates.
4.2. Downstream velocity
Velocity profiles downstream of the fan are computed with
RSM simulation and compared with those obtained with hot-wire
measurement for the three fans (Eq. (3)). The experiment and
simulation are performed at the flow rate defined in Table 1. The
results for G2for are represented in Fig. 11. Those obtained for
G2rad and G2back are similar and invoke the same comment.
The shape of the computed velocity profile is close to the ex-
perimental ones. Discrepancies between the simulations and the
measurement appear near the hub at design flow rate ϕn. This is
because the mean angle of the velocity is very different from those
at the other radius owing to the design of this fan. These discrep-
ancies disappear with the 1.3ϕn flow rate, which confirms that
the position of the probe is very important for the accuracy of the
measurement. There are discrepancies for the radial component
at higher flow rate 1.3ϕn (Fig. 11). For G2for at this flow rate the
level of the radial velocity component is very low (between 2 and
−1 m s−1
) because the forward sweep decrease this velocity com-
ponent (Fig. 12) and at higher flow rate the radial velocity com-
ponent decrease. The inaccuracy of the measurement at very low
velocity could explain these discrepancies.
Considering the measurement accuracy of the procedure, the
comparison gives good agreement only for axial and tangential
data at the two flow rates, and for radial data at nominal flow rate.
The measured flow rate with the standard box and calculated
flow rate on the basis of the hot-wire axial velocity measurement
are compared in order to validate the measurement. The difference
is less than 2%.
The first comment to make is that none of the three components
of the velocity can be neglected. The flow downstream of the fan is
fully three-dimensional. When the flow rate is increased, the axial
component of the velocity increases and the radial one decreases.
The tangential velocity level remains equivalent but the spatial
distribution changes.

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0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
1.5
2
2.5
3
UUstress(ms22/)
–0.2
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0.1
0.2
0.3
0.4
0.5
UVstress(ms22/)
0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0.6
0.4
0.2
0.8
1
1.2
1.4
VVstress(ms22/)
0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0.4
0.2
–0.2
0.6
0.8
1
1.2
HUB TIP
Radius / Tip Radius
UWstress(ms22/)
0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0.5
1
1.5
2
2.5
HUB HUBTIP
Radius / Tip Radius
WWstress(ms22/)
–0.2
–0.3
–0.1
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
0
0.1
0.2
0.3
0.4
TIP
Radius / Tip Radius
VWstress(ms22/)
1
0.5
0
–0.1
Fig. 14. Comparison of the computed Reynolds stress tensor components profile for the three fans.
The agreement is quite good between the simulation and
measurement for the shape and the level of the mean velocity; on
the other hand, it appears that the measured velocities are always
slightly higher than the calculated ones. This can be explained by
the measurement procedure. With the 2D probe, a component of
the velocity cooling the wires is neglected for each measurement
position. So the other two components are measured at a higher
level than their real one. Therefore the two measured velocity
components are always higher because of the third component.
Fig. 11 shows the backflow near the hub at ϕn, which disappears
at 1.3ϕn.
Fig. 12 shows the comparison of the mean velocity profile for
the three fans. The major difference between the three fans is the
radial component. It is reduced with the forward sweep, and it
is increased for the backward sweep. The forward sweep reduces
the radial component to a very low level at 1.3ϕn, in comparison
with the other sweeps. A small backflow is observed near the hub
for G2back at 1.3ϕn. It disappears at 1.3ϕn. The tangential velocity
is close for the three fans, but G2rad has the biggest one. This is
consistent with the performance of G2rad (see 4.1).
4.3. Reynolds stress tensor
The comparison between the measured components of the
Reynolds stress tensor and those obtained with the RSM simulation
is discussed in this section (Eq. (4)). Fig. 13 shows this comparison
for the six components of the Reynolds stress tensor for G2for at
two flow rates defined in Table 1.
Three zones can be observed: the tip and the hub where the
tensor components are the highest (for both the cross-components
and the diagonal ones), and the mid-span zone where all the
components are negligible. All the components are quite different
and show the non-isotropy of the turbulence in this case. The
hypothesis of isotropic turbulence could not be assumed for 3D
flow with rotating body and flow of other curved surfaces as in
turbomachinery. The RSM is more accurate than first-order closure

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models such as k-ε or k-ω. When the prediction of the diagonal
component is consistent, there are some discrepancies in the cross-
component. The level of the cross-component is lower and it
becomes difficult to measure this very light velocity fluctuation
compared with the high mean velocity. A higher level is obtained
for the diagonal components. A higher flow rate raises the level
of the turbulence near the hub and reduces the level near the tip
for G2for. The simulations predict the difference between the three
zones, but generally underestimate the level of the Reynolds stress
tensor cross-components.
Fig. 14 shows a comparison of the components of the Reynolds
stress tensor for the three fans. The shape of the curves is very
close for the three fans. For the diagonal components the area near
the hub reaches a higher level than the area near the tip. G2back
generates more turbulent energy near the hub and less near the
tip. The levels for G2rad and G2for are very close except for the VV
stress component in the area of the tip. Here, G2rad generates more
energy. The UU and WW stresses reach a level of 2.5 m2
/s2
, which
is almost twice the level of the maximum VV stress. The cross-
components have negligible levels, except the UW stress near the
hub, where the level is 1 m2
/s2
.
It is interesting to compare the turbulent kinetic energy, k
(Eq. (5)), from an RSM and a k-ω model which is often used for
turbomachinery flow computation. Fig. 15 shows the k profile
downstream of G2for and G2rad for two computations with
the two different turbulence models. The hot-wire measurement
results are also drawn. The results with RSM simulation are closer
to those from experiments than the results with the k-ω model. The
shape is similar, with a high level near the hub, but the turbulent
kinetic energy level is overestimated with the k-ω model. This
confirms that the hypothesis of the k-ω model is not adequate for
this flow configuration.
0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.1
1
2
3
4
5
6
HUB TIP
Fig. 15. Comparison of the turbulent kinetic energy profile for two turbulence
models at ϕn. G2rad RSM simulation (—), G2rad experiment (•), G2rad k-ω
simulation (· · ·), G2for RSM simulation (– · –), G2for experiment (×), G2for k-ω
simulation (– –).
4.4. CFD results
It is interesting to present more CFD results in order to
understand the phenomenon governing the flow.
Fig. 16. k (m2
/s2
) and components of the velocity (m/s) downstream of the fans, at ϕn. (For interpretation of the references to colour in this figure legend, the reader is
referred to the web version of this article.)

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Fig. 17. Surface of iso-turbulent kinetic energy (m2
/s2
, Blue = 0.05, Green = 1, Orange = 4). (For interpretation of the references to colour in this figure legend, the reader
is referred to the web version of this article.)
In Fig. 16, the contour of k and the axial, radial and tangential
velocities are plotted at ϕn. They are represented on a plane
downstream of the fan, with the fan in translucency to show its
location. Concerning k, the level is low on almost all the surface
below <1 m2
/s2
, and we can see clearly the location of the
high level (near the hub and near the tip). G2rad, which has the
strongest backflow near the hub, also has the highest k. G2for
produces the highest level near the tip owing to the early presence
of the leading edge in this area. The contour of the axial velocity
shows the backflow in the hub and tip region. The drag of the blade
is the high level axial velocity (red area). The radial velocity level
is high at this flow rate (ϕn), almost the same level as the axial
component. For G2for and G2rad, a high level of radial velocity
is reached near the leading edge on a small area, whereas the
G2back geometry cancels this area and we see a smoother radial
component. Logically, the tangential component increases from
the hub to the tip, but with a decrease just before the tip present
in all the configurations.
In Fig. 17, three different surfaces of iso-k are represented
around the fan. The low level of 0.05 m2
/s2
is chosen because it
is present in all the domains, downstream and upstream of the fan.
The medium level of 1 m2
/s2
is generated by the rotation of the
fan, nearer the hub and the tip, as seen in Section 4.3. The high
level of 4 m2
/s2
is generated around the shroud, in the tip clearance
and at the end of the hub. The propagation of the turbulent kinetic
energy follows the direction of the flow, in a radial way at ϕn and
a more axial way at 1.3ϕn. For the three sweeps, the turbulent
kinetic energy produced at the hub appears to be higher at ϕn
than at 1.3ϕn, but the distance of propagation is shorter and more
radial. The production of turbulent kinetic energy near the tip is
lower for G2rad than the other two sweeps. The turbulent kinetic
energy generated near the hub and near the tip propagates far
downstream of the fan and generates another source of high k for
G2for. This is observed for the two flow rates.
5. Conclusion
A numerical simulation was carried out with a second-moment
closure turbulence model, RSM, in order to obtain information
on the turbulence generated by a fan and especially the radial
distribution of the components of the Reynolds stress tensor.
Three fans were designed and tested and results were compared.
These three fans with three different sweeps were described with
the same experimental procedure and numerical modelling. They
clearly indicate the influence of the sweep on the unsteadiness
of the 3D flow field for close aerodynamic characteristics. An
anisotropic character of the flow field has been observed for
the three fans and at two flow rates. This study shows that,
in addition to the axial and tangential velocity measurements,
the radial component must be collected for such turbomachinery
where the radial equilibrium hypothesis is often wrongly assumed.
The results show that the turbulence can be predicted with good

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agreements in a spatial way, but the level is predicted with a
few discrepancies. Moreover, it is shown that the RSM turbulence
model can predict the turbulent kinetic energy better than
the first-order moment-closure RANS simulation. The turbulent
kinetic energy could be very important data for the prediction of
radiated noise by a fast and efficient method in turbomachinery.
The forward sweep tends to decrease the radial component of the
velocity whereas the backward sweep tends to increase it. The
sweep must be chosen carefully, and it depends on the item to
be cooled. In our case of an automotive engine, a radial velocity
could be useful to cool all the engine block. G2back seems to be
better for low turbulent kinetic energy, and G2rad has the highest
performance and efficiency.
Acknowledgements
The authors would like to thank the Agence De l’Environnement
et de la Maîtrise de l’Energie (ADEME) for its financial support.
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