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Proceedings of the ASME 2017 Fluids Engineering Division Summer Meeting
FEDSM2017
July 30-August 3, 2017, Waikoloa, Hawaii, USA
FEDSM2017-69271
A CRITICAL COMPARISON OF NUMERICAL AND EXPERIMENTAL RESULTS FOR
THE EXAMINATION OF A CASCADE CONSISTING OF
NACA 65-010 1 % PROFILES
Andreas Baum∗, Constantin Berger, Christian Landfester, Martin Böhle
Institute of Fluid Mechanics and Fluid Machinery
University of Kaiserslautern, Germany
Email: [email protected]
ABSTRACT
Numerical and experimental investigations through different
spans of the rotor are a common approach in turbo machinery
design. As the aerodynamic quality of rotor blades is crucial for
turbo machinery’s efficiency, mass-averaged loss coefficients ζ¯
NOMENCLATURE
b
c1
c2
D
DF
e
H
i
l
ki, j
M
N
ptot,1
ptot,2
Re
t
t/l
x
y
z
β1
β2
∆β
γ
Γ
δ
δ
ζ
and turning angles ∆β̄ are of particular interest. Using the example of commonly used NACA-65 profiles, a comparison between
the results obtained by those methods should investigate whether
Computational Fluid Dynamics (CFD) applying the Transition
SST turbulence model delivers sufficiently accurate results regarding both 2D and 3D modeling approaches. The comparison
is supplemented by the singularity method based on the potential
theory as well as historical data provided by NACA.
While CFD produced a noticeable offset for some angle configurations, the 2D results of ∆β̄ were in good agreement for singularity method, historical data and experimental investigations on
the center line of the cascade supporting the validity of the measurement. Although significant deviations were also found for ζ¯ ,
it can be stated that CFD reproduced the qualitative course sufficiently for both variables considered. A similar picture emerges
from the 3D comparison: Despite noticeable deviations in quantitative terms, a good correspondence was found for both variables regarding local and mass-averaged values.
KEYWORDS: compressor blade cascade, loss coefficient,
corner stall / separation, NACA-65, secondary flow, five-hole
probe measurements, turbulence modeling
∗ Address
all correspondence to this author.
1
Width of the blade
Velocity upstream of the cascade
Velocity downstream of the cascade
Diffusion parameter
Diffusion factor
Maximal thickness of the blade
De Haller criterion
Incidence angle
Chord length of the blade
Coupling coefficient between points i and j
Mach number
Number of points on the contour of the blade
Total pressure upstream of the cascade
Total pressure downstream of the cascade
Reynolds number
Time
Spacing ratio
Cartesian coordinate
Cartesian coordinate
Cartesian coordinate
Inflow angle
Outflow angle
Turning angle
Vorticity per length
Circulation
Deviation angle
Boundary layer thickness
Loss coefficient
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η
λ
µ
ϕ
φ
ρ
σ
Dynamic viscosity
Stagger angle
Axial velocity ratio
Camber angle
Velocity potential
Density
Solidity
c2
c1
β2
δ
c∞
φ = 40°
c2
camber line
β2
β∞
t
chord line
λ
β1
i
c1
β1
cm
INTRODUCTION
m
00
m
1
l=
For ecological and economical reasons, turbo machines have
to cover wider loading ranges whilst guaranteeing efficient operation. Under part- and overload conditions wall-induced flow
phenomena like corner stall (resp. corner separation) and, hence,
blocking effects intensify. As those effects massively affect both
loss emergence and flow deflection, this issue has to be addressed
by research and development in order to allow efficient and stable operation.
Multiple variations and approaches in blade and cascade design
were meant to deal with separation and secondary flow effects,
e.g. side-slotted blades or sheets, variations of NACA profiles
etc. [1–3]. Other cascade studies were conducted for different
operating conditions, like transonic flows [4]. Beside experimental examinations, these issues were addressed by numerical studies investigating the outcome and validity of different modeling
approaches, e.g. the turbulence model [5].
Using the example of commonly used NACA-65 profiles, the
present study concentrates on a critical comparison between numerical and experimental methods in order to investigate whether
CFD delivers sufficiently accurate results for the specific test design. A valid model would not only allow swift and equally extensive parameter variation for future research, but also a profound investigation of near wall flow phenomena. The comparison is supplemented by the singularity method based on the potential theory as well as historical data provided by NACA [6].
For the purpose of further comparison and validation, separation
and blocking indicators are applied, e.g. two diffusion factors
(according to Lei [7] and Lieblein [8]), the Wilson’s de Haller
criterion and the axial velocity ratio. Moreover, this study is intended to provide detailed and systematic data for a broad range
of parameter variations, e.g. spacing ratios, inflow and stagger
angles. Beside general insights into the influence of these parameters on losses and turning angles, this study is meant to examine wall-induced 3D losses in both measurement and simulation.
Last but not least, it is part of a research series which will examine and compare the current blades with simple circular-arc sheet
blades regarding 2D and 3D losses.
FIGURE 1.
Nomenclature cascade flow
TEST DESIGN
The cascade consists of blades with a NACA-65 equivalent
circular arc camber line and a NACA 65-010 thickness distribution. The relative thickness amounts 8 %. Its trailing edge has
been thickened by 1 % of the chord line length l. The geometry
and kinematic relations of the cascade are shown in Fig.1. The
incidence angle i is defined as the angle between the inlet velocity vector c1 and the tangent to the camber line. It is defined
i = β1 − λ −
ϕ
2
(1)
The geometric specifications of the examined cascade as
well as the test parameters are given in Tab.1. The examination was conducted for three spacing ratios t/l = {0.5, 1.0, 1.5}
and two stagger angles λ1 = 30◦ and λ2 = 40◦ . All investigations
were performed for a Reynolds number Re = 4 · 105 . 2D calculations and line measurements at the cascade’s center line were
carried out for imin = −25◦ and imax = 12.5◦ representing both
heavy part and over load scenarios. For the investigation of near
wall phenomena caused by secondary flow and its influence on
losses, 3D calculations and field measurements were conducted
for three selected incidence angles, i.e. the optimal incidence and
the outermost angles of the operational range, where losses rise
sharply.
2
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TABLE 1.
Geometric specifications and test parameters
honeycomb Prandtl probe
Side channel
compressor
②
measuring
traverse
ṁ SC2
Parameter
Value
Unit
ρ
1.196
kg/m3
η
1.847 · 10−5
kg/(m·s)
l
0.1
m
b
0.2
m
e
0.08
ϕ
40
◦
c1
61.3
m/s
Re
4 · 105
M
0.18
ṁ
ṁ SC1
①
inflow
inlet nozzle
acceleration
two stage
cone
axial compressor
FIGURE 2.
Side channel
compressor
test section
Measurement setup
∆z = 2 · 10−3 m and ∆y = 10−3 m were chosen for the field measurements. The number of samples was reduced to 10 with an
interval of ∆t = 0.1 s. A schematic depiction of the measurement
setup is given in Fig.2.
CFD SETUP
For the discretization of the control areas, ANSYS ICEM
CFD (v15) was used. As the flow can be considered to be periodic between the spacings of the cascade, the control area was
limited to a single spacing for the benefit of less calculation effort. By means of a block structured grid, the 2D control area was
divided into three sections. Two H-grids for the in- and outlet ensure a less distorted mesh with an optimized number of cells. For
a sufficient refinement of the near wall cells, an O-grid was used
around the blade. The 3D meshes have been generated by extruding the 2D meshes. By means of a mesh independence study, a
sufficient number of cells was determined counting 5.5 · 105 for
the 2D mesh with t/l = 1 and 5.5 · 107 for the corresponding 3D
+
mesh. With y+
min ≈ 0.01 and ymax ≈ 3, it was further taken care
that the meshes meet the requirements of Menters [10] Transition
SST turbulence model which was used for a precise calculation
of the laminar-turbulent transition [11]. The calculations were
carried out with ANSYS FLUENT (v15). The 3D flow region,
its boundary conditions and characteristic dimensions are shown
in Fig.3. The velocity inlet and the measure plane were placed in
a distance of l/2 in front of the leading edge and −l/2 behind the
trailing edge of the blade. The outflow was set one chord-length
behind the blade. Assuming symmetric flow referred to the center line, a symmetry condition was set at a blade width of b/2.
Based on a free flow measurement, an user-defined function for
the velocity inlet was implemented utilizing the 1/7 potential law
and, therefore, reproducing the specific inflow conditions of the
test section. It is given by
MEASUREMENT SETUP
An in-house cascade wind tunnel has been used for the measurements, cf. [9]. It consists of an inlet nozzle according to standard DIN 1952 (inner diameter 0.71 m, length 1.575 m), a frequency controlled two stage axial compressor (diameter 0.6 m,
performance 18.5 kW per stage), a honeycomb grid (length
0.16 m, comb distance 9 · 10−3 m, thickness 2 · 10−4 m) to produce an unimpeded stream behind the compressor, an acceleration nozzle (length 1.5 m, inlet diameter 0.71 m, outflow cross
section 0.5 × 0.2 m), a smoothing segment (length 0.6 m) and a
test section. Two frequency controlled side channel compressors
are installed in front of the test section to suction the upper and
lower boundary layer of the smoothing section. They are also
used to avoid blocking and to realize periodic inflow conditions.
By means of a Prandtl probe at the center of the inflow’s cross
section, the reference values for total and static pressure are measured. The test section is pivoted to realize different inflow angles. The measurements of loss coefficients and turning angles
were carried out at a distance of l/2 behind the trailing edge using a calibrated five-hole-probe. The probe has a length of 0.25 m
and a diameter of 2 · 10−3 m. For the acquisition and processing
of raw measurement data, an in-house developed measuring box
is used containing AMSYS pressure sensors with a measurement
error of ±1. (%FS)RT and a programmable Arduino Mega 2560
microcontroller. To ensure safe operation, field measurements
were carried out up to a distance of 4 · 10−3 m from the side wall.
The aluminum-milled NACA-65 blades can be considered to be
hydraulically smooth.
A step size of ∆z = 5 · 10−4 m was chosen for line measurements.
To compensate fluctuations of the axial compressors as well as
the pressure sensors, 20 samples with an interval of ∆t = 0.1 s are
measured and averaged in each measurement point. Step sizes of
y
c1 (y) = c1 · ( )8/71
δ
if y ≤ δ
(2)
The simulations were conducted at an isotropic turbulence intensity of 2 %. This value has been determined by hot-wire mea-
3
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periodic 1
and
symmetry
1 n−1
cz,i =
∑
2t j=0
wall (blade)
velocity inlet
2Π
t (x − x j )
2Π
2Π
t (x − x j ) − cos t
cosh
!
sinh
(z − z j )
γ j ∆s j
(4)
Adding the kinematic boundary condition leads to the linear
equation for the contour integral:
M
∑ k(i, j)γ(s j )∆(s j ) = 2 · (ẋi cos(βi ) + z˙i sin(βi ))
measuring
plane
(5)
j=1
outflow
with:
wall
z
x
y
periodic 2
FIGURE 3.
2Π
Π z˙i · sinh 2Π
t (xi − x j ) − ẋi · sin t (zi − z j )
ki, j =
(6)
2Π
Π
t · N cosh 2Π
t (xi − x j ) − cos t (zi − z j ) + zi · t·N
Control volume CFD calculations
if i 6= j and
surements at the wind tunnel. The SIMPLEC-algorithm with a
skewness correction of 1 has been used. The equations of motion for pressure, momentum and viscosity have been spatially
discretized with the Second Order Upwind method, while for the
gradient calculation the ”Least Square Cell based” method has
been chosen. For solution controls, the settings were set to default. As it may not be sufficient to judge convergence only by
examining the residuals, it was additionally evaluated by monitoring the drag coefficients and the mass-averaged total pressure
on the measuring plane. The post-processing and evaluation of
the obtained data were performed with ANSYS CFD-Post (v15)
and Matlab 2016a.
ki, j = 1 +
1 (ẋi · ẍi ) − (z˙i · z¨i )
Π
2N ẋi 2 + z˙i 2 · z˙i · t·N
(7)
if i = j respectively.
Based on the velocity triangles and the coherences for c∞,x , c∞,z
and tan βi , the outflow angle can be calculated by:
β2 = arctan tan β1 +
Γ
t · cos β1
(8)
where the circulation Γ is described by:
n−1
Γ≈
POTENTIAL THEORY
The calculations for the potential theory are based on the
Martensen Method (cf. e.g. [12]) using singularities to model
the flow around the blade surfaces. The potential flow at a given
point results from the superposition of a translational flow c∞ and
the vortex distribution on the contour of the blade. Therefore, the
components of the velocity ci in a point i can be calculated by:
1 n−1
cx,i = − ∑
2t j=0
sin
cosh
2Π
t
∑ γ j · ∆s j
(9)
j=0
2Π
t (z − z j )
(x − x j ) − cos
AERODYNAMIC QUALITY
The aerodynamic quality of a cascade is characterized by its
losses:
!
2Π
t
The Kutta condition wit γ j=n−1 = 0 was imposed.
(z − z j )
γ j ∆s j
ζ (y, z) =
(3)
4
ptot,1 − ptot,2 (y, z)
ρ 2
2 c1
(10)
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Mass-averaging For comparison and evaluation purposes, it
is useful to mass-average loss coefficients and turning angles as
conclusions on the overall performance can only be drawn from
a limited extent from local values. Therefore, an integration was
carried out over one spacing t/l and, based on the symmetric
flow conditions, half of the blade width b . This leads to
c
ζ (y, z) · c2,x
(y, z)dzdy
z
1
R y=b/2 R z+t c2,x
z
y=0
c1 (y, z)dzdy
Separation and stall criteria To signify the occurrence of
stall, and measure the aerodynamic load of a three dimensional
flow, the diffusion parameter in reference to Lei et al. [7] is used.
It assumes separation for:

1
1−
D=
σ
cos β1
cos λ − ϕ2
!2 
 · (i + ϕ) ≥ 0.4 ± 0.05
(13)
R y=b/2 R z+t
ζ=


β2 = arctan 
y=0
R y=b/2 R z+t c2,z
z
c1
Another measurement is Wilson’s de Haller criterion [14]. It is
defined as the velocity ratio in front of and behind the cascade
and implies stall if:

c2,x
c1 (y, z)dzdy 

2
(y, z) ·
R y=b/2 R z+t c2,x
z
y=0
c1 (y, z)
y=0
(11)
H=
(12)
c2
(y)min < 0.7
c1
(14)
dzdy
For two dimensional flows, Lieblein’s Diffusion factor [8] is a
typical measurement to forecast separation. Therefore, the bound
for the beginning of separation is exceeded if:
For two dimensional investigations, the dependence of the
horizontal axis y disappears.
cos β1
1 cos β1
DF = 1 −
+ ·
(tan β1 − tan β2 ) > 0.6 (15)
cos β2
σ
2
Correction of loss coefficients The evaluation of a free field
measurement revealed that loss coefficients decline from the center line reaching negative values up to a point where side-wall
related effects set in. It can be assumed that this decline has to
be attributed not to flow physics, but to measurement restrictions
as the reference pressure is measured on a fixed centered position in front of the test section. Therefore, a local correction
of the measured loss coefficients is applied which based on the
measured loss coefficients of the free field. Assuming that losses
have to be zero within the free stream of the free field, the free
field loss coefficients are mass-averaged in z-direction and added
to the corresponding local values of the final measurements. To
prevent a distortion of near wall losses, the correction value at
the border line between free stream and boundary layer is perpetuated up to the side wall.
To get a comprehension about the blockage due to the increase
in boundary layer thickness, secondary flow effects and recirculation of the primary flow, the axial velocity ratio is taken into
account. It is defined as
µ(y, z) =
c2,x
c2 · cos β2 (y, z) · cos γ(y, z)
=
c1,x
c1 · cos β1
(16)
2D RESULTS
Beside some general observations regarding the dependence
of ζ¯ and ∆β̄ on t/l and λ , this section is dedicated to the comparison between the line measurements and the corresponding
2D calculations. It can be noticed that ζ¯CFD and ζ¯EXP are in best
agreement for the medium spacing ratio t/l = 1. While ζ¯CFD is
surpassed by ζ¯EXP for t/l = 0.5, the CFD results exceed the experimental values for t/l = 1.5. Regarding the turning angles ∆β̄ ,
the following picture emerges: A better accordance is generally
found for higher spacing ratios and smaller stagger angles within
the incidence angle range of linear dependency. When leaving
the interval of linear dependency, growing separation presumably leads to a smaller incline of β̄ . This effect is significantly
overvalued by CFD resulting in a pronounced deviation between
the experimental and numerical results. As smaller spacing ratios provide a better flow guidance, the operating range becomes
broader for smaller t/l. Since better guidance is attended by
Secondary flow 3D losses are highly influenced by secondary
flow phenomena like corner stall, i.e. a simultaneous back
flow on the side wall and the suction side of the blade due
to an imbalance of pressure- and dynamic forces. It evokes
secondary flow phenomena, which are highly responsible for
the losses in turbo machinery. Secondary flow is defined as the
deviation between the local- and potential flow (characterized
by ∆φ = 0) [13]. According to comparable parameters the
primary flow is defined by mass averaging the flow in the nearly
frictionless region outside the wake for both CFD calculations
and experimental investigations.
5
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FIGURE 4.
Results for ζ¯ and ∆β̄ for line measurements
higher losses, the loss curve shifts upwards for smaller t/l and
ζ¯min moves towards smaller incidence angles. However, this correlation cannot be derived from the computational results where
losses rises for higher t/l.
Within the incidence angle range of linear dependency, the occurring deviations between the experimental and numerical results
seem to have a nearly constant offset which leads to the conclusion of a systematic bias. For interpretation, the course of the
axial velocity ratio is exemplary shown for t/l = 1 in Tab.2. Due
to the highest blocking effect occurs in the homogeneous flow
field, the maximum value of µ is characteristic. As monitored,
an increase of i causes an acceleration of the axial flow component. Therefore, a separation is prevented, leading to both a
higher deflection and a decrease in losses. In contrast, the 2D
CFD results show a constant velocity upstream and downstream
of the blade.
For an additional validation the experimental results are compared with values obtained from the described singularity
method as well as a formula apparatus from Aungier [15] based
on the results made by Bullock and Johnson [6]. In Tab.3 several
6
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TABLE 2.
Maximal axial velocity ratio for σ = 1 in dependence of i
TABLE 3.
i/◦
i/◦
30
µmax
−20
0.98
−15
0.99
−10
0.98
1.10
−5
1.04
1.21
0
1.12
1.38
5
1.27
1.60
two problems: in some cases it emerged from convergence issues
during the numerical simulation and in others it was restricted by
the measuring method, or more precise, by leaving the calibration range of the five-hole probe. Due to the correction procedure
described in ’Correction of loss coefficients’, the 2D results were
also affected. The adaptation of the loss coefficient led to a systematic shifting of the data points. Subsequently, the results for
t/l = {1, 1.5} approximated the CFD values and, however, for
t/l = 0.5 the results diverged.
40
µmax
3D RESULTS
Additionally to the line measurements covering the whole
operating range, several field measurements were conducted
to examine and compare the influence of wall-induced flow
phenomena on the emergence and distribution of losses. Due
to limited space for extensive diagrams, the medium spacing
ratio t/l = 1 was taken for representation of loss distribution
and secondary flow, depicted in Fig.5 and Fig.6. The chosen
incidence angles are i = {−15◦ , −5◦ , 5◦ }. First, the distribution
of the loss coefficients on the measuring plane is compared
between measurement and calculation. Beside this comparison,
general observations regarding the cause of the specific loss
distribution are described. In the second step, a closer look is
taken at the secondary flow and its influence on loss emergence.
Comparison of turning angles for σ = 1, λ = 30◦
∆β exp /◦
∆β Sing /◦ ∆β NACA /◦
∆NACA
/% ∆Sing
rel
rel /%
−20
9.3
11.9
11.7
25.9
28.5
−15
14.4
16.8
16.3
13.2
16.5
−10
19.6
21.6
20.9
6.3
10.2
−5
24.2
26.5
25.4
4.6
9.1
0
28.4
31.3
29.8
5.0
10.1
5
31.7
36.0
34.2
7.6
13.5
Losses and turning angles 2D related losses, i.e. a clearly
separated wake and a large free-flow area, can be seen for both
measurement and calculation expanding from the center line in
direction to side wall. Depending on the inflow conditions, wallinduced 3D losses set in. With increasing incidence angles, the
influence of those losses rises as the effects of corner stall occurring on the side wall and the suction side of the blade increase.
As this effect is directly linked to secondary flow and corner stall,
its cause is described in the following section. Moreover, it can
be clearly seen that the wake is bend upwards – especially for
i = {−15◦ , −5◦ }.
The comparison shows a sufficient agreement for smaller incidence angles. Although the deviations in the loss distribution
rise, there is still a good accordance in qualitative terms for
higher incidence angles, i.e. the underlying flow phenomena are
sufficiently represented in the calculation. It can be assumed
that the increasing deviations between CFD and measurement
for larger incidence angles have to be attributed to the changes
in thickness of the side wall’s boundary layer in the experiment
and, therefore, deviation from the UDF. This guess is also confirmed by the column by column mass averaged flow parameters,
shown in the lower row of Fig.5.
The mass-averaged losses of the measurement show a pronounced decrease on the way to the side wall which has no representation in the calculation. In fact, the course of mass-averaged
values for ∆β are exemplary compared and the relative deviations are given. It is apparent that for uncritical inflow angles
(−10◦ ≤ i ≤ 5◦ ) the deviations are small, especially for NACA
results. For high overload regions, a pressure sided flow separation occurs for the experimental investigations. For regions of
partload, the results show again an earlier separation compared
to the NACA data. In contrast, the singularity method cannot
represent the phenomenon of flow separation leading to higher
calculated turning angles ∆β than achievable in the experiment.
Within the linear dependency of the turning angles, the deviation does not significantly exceed 10 % for both methods. Beside
that, there is a nearly constant offset, which can be considered to
be an acceptable result.
A comparison of the applicability for DF shows different results
for CFD and experimental investigations. While a reasonably
good agreement for the flow prediction by means of CFD can be
recognized, the experimental results differ considerably. Therefore, the flow stays attached for values significant larger than
DF = 0.6.
In some cases the amount of data points was limited due to the
possibility to obtain valid results. This limitation is based on
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3D
FIGURE 5.
SS
SS
PS
EXP
PS
PS
PS
SS
CFD
PS
EXP
SS
EXP
i = 5°
CFD
PS
CFD
SS
i = -5°
SS
i = -15°
2D
Comparison of 3D results for λ = 30◦
losses is even opposed for i = 5◦ . Even though losses clearly
increases at close distance to the side wall for every incidence
angle, there is only a good accordance in qualitative terms for
i = −15◦ . To compare the differences more in detail, again, the
changes of µ are taken into account. For experimental data, µ
rises from the center line to the inset of the boundary layer. This
increase has an influence on separation and 3D flow phenomena
resulting in lower losses. In contrast, due to idealized boundary
conditions the blocking effect is much smaller for CFD leading
to a nearly constant course of µ. Similar to the 2D results, steeper
inflow angles lead to an increase of µ for experimental investigations, and so, to a worse agreement between experiments and
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TABLE 4. Comparison of 2D and corner stall induced losses for σ =
1 and λ = 30◦
TABLE 5.
Values of D and H EXP for σ = 1 and λ = 30◦ .
i/◦
D
H EXP
i/◦
ζ 2D /%
ζ CS /%
−15
0.1344
0.696
−15
3.12
2.03
−5
0.2959
0.573
−5
2.91
4.02
5
0.5190
0.628
5
4.52
4.83
is just reached, the experimental investigation shows only a small
area of higher losses.
CFD. The same holds true for 2D and 3D simulations regarding
the agreement of the results at the center line. In general, the 2D
CFD investigations overestimate the losses at the center line due
to an exclusion of 3D flow phenomena. The overestimation of
losses are positively correlated to β1 .
A better agreement was achieved for the mass-averaged turning
angles: In both measurement and calculation ∆β̄ decreases in
direction to the side wall before it sharply increases and even exceeds the center line’s value in direct proximity to the side wall.
This effect has to be attributed to near wall secondary flows resulting in an extend curvature of the streamlines as described below. For all three incidence angles the measured turning angles
exceed the calculated ones as the evaluation of the 2D findings
has already indicated. The systematic deviation increases with
rising incidence angles reaching up to 10◦ .
To quantify the influence of corner stall, the 3D losses are considered separately. Therefore, the corner stall influenced area is
detected as the loss region exceeding ζ at the center line. Additionally, the mass averaged 2D losses are deducted. For the exemplary shown results, a comparison of 2D losses and losses induced through corner stall is given in Tab.4. In accordance with
the course of losses, the influence of corner stall is reflected in an
increase in ζ CS . Especially in regions near the 2D design point,
the losses induced by corner stall reach approximately 60 % of
the total losses.
Secondary flow Due to secondary flow, a circulation sets in
transporting low-loss fluid along the pressure side towards the
side wall. On the suction side the high-loss boundary layer of the
side wall is carried away and intermixes with the main flow. Although these opposing flows mutually weaken each other behind
the trailing edge (with an increase of friction losses), this circulation still persists on the measurement plane bending the wake
upwards and expanding the area of high losses on the suction
side. This process is highly influenced by the inflow conditions:
Increasing incidence angles trigger higher pressure gradients between the suction and pressure side. Higher pressure gradients
foster the curvature of the near wall streamlines. This intensifies,
in turn, secondary flow due to continuity requirements (cf. [16]).
For high incidence angles, such as i = 5◦ , these secondary flows
transport considerable parts of near wall fluid expanding highloss areas up to one quarter of the blades’ width.
Regarding the secondary flow under qualitative aspects, the accordance between experiment and CFD is good. The circulation
area is precisely depicted and consistent. In both measurement
and calculation, the level of secondary flow clearly increases with
smaller distances to the side wall. In contrast to the measurement, the calculation shows a strong secondary flow pointing
downwards from the pressure side of the adjacent blade. Moreover, the calculated secondary flow on the left edge of the highloss area heads in south-west direction while the measured secondary flow points almost horizontally to the blade’s center line.
Separation and corner stall Alike for two-dimensional investigations, a comparison between literature parameters and the investigation results is considered. The values for D and H EXP are
exemplary shown for t/l = 1 and λ = 30◦ in Tab.5. As mentioned before, all investigations show typical corner stall phenomena, while D predicts the formation only for an incidence
angle of i = 5◦ . This discrepancy can be explained by the thickness distribution of the side-wall boundary layer, as this parameter highly influences the occurrence of corner stall. Since it is
not considered in the diffusion parameter, the prediction of corner stall formation is delayed. In contrast, the results are totally
in accordance with the de Haller criterion. While for small incidence angles the boundary condition for corner stall occurrence
CONCLUSION
For a cascade, consisting of NACA-65 blades, experimental
and numerical findings for three spacing ratios and two stagger
angles were compared with regard to its losses and turning angles. Additionally, the prediction of the occurrence of separation
for both 2D and 3D flows was examined.
It can be stated that prediction of the real flow behavior by
means of CFD is only useful in qualitative terms, while for precise findings an experimental investigation is indispensable. A
forecast of the turning angles for 2D consideration using the sin-
9
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0.5
0.9
0.75
0.98
REFERENCES
[1] Ma, W., 2012. “Experimental investigation of corner stall
in a linear compressor cascade”. Phd thesis, Ecole Centrale
de Lyon.
[2] Roche, R. F., and Thomas, L. R., 1954. “The effects of
slotted blade tips on the secondary flow in a compressor
cascade”.
[3] Beselt, C., 2016. “Experimental investigation of secondary
flow phenomena in a compressor stator cascade”. PhD thesis, Technische Universität Berlin.
[4] Weber, A., Schreiber, H. A., Fuchs, R., and Steinert, W.,
2002. “3-D Transonic Flow in a Compressor Cascade With
Shock-Induced Corner Stall”. ASME Journal of Turbomachinery, pp. 358–366.
[5] Liu, Y., J. L. H. Y., 2016. “Numerical study of corner separation in a linear compressor cascade using various turbulence models”. Chinese Journal of Aeronautics, 29(3),
pp. 639–652.
[6] Bullock, R. O., J. I. A., 1965. Aerodynamic Design of
Axial-Flow Compressors. Tech. rep., NASA, Washington,
7. An optional note.
[7] Lei, V.-M., Spakovszky, Z., and Greitzer, E., 2008. “A criterion for axial compressor hub-corner stall”. Journal of
Turbomachinery, 130(3).
[8] Abbott, Ira. A., v. D. A. E. S. L. S. j., 1945. Summary of
Airfoil Data. Tech. rep., National Advisory Committee for
Aeronautics.
[9] Böhle, M., T. F. “Three-dimensional near wall flow phenomena of a tandem cascade”. 10th European Conference
on Turbomachinery Fluid dynamics & Thermodynamics,
2013, pp. 1–12.
[10] Menter, F. R. “Two-Equation Eddy-Viscosity Turbulence
Models for Engineering Applications”. pp. 1598–1605.
[11] ANSYS, 2013. Ansys fluent theory guide. release 15.0.
[12] Lewis, R. I., 1996. Turbomachinery Performance Analysis.
Butterworth-Heinemann.
[13] Detra, R. W., 1953. “The Secondary Flow in Curved
Pipes”. Dissertation, The Swiss Federal Institute of Technology, Zurich.
[14] Wilson, D. G., T. K., 2014. The Design of High-Efficiency
Turbomachinery and Gas Turbines, 2. edition ed. The MIT
Press.
[15] Aungier, R. H., 2003. Axial-Flow Compressors - A Strategy for Aerodynamic Design and Analysis. ASME Press.
[16] Frey, T., 2014. “Numerische und experimentelle Untersuchungen der 3D-Grenzschichtströmung in Wandnähe
hochumlenkender Tandem-Gitter”. PhD thesis.
C2 / C1
0.1
1
z/t
CFD
0.5
0
1
z/t
EXP
0.5
0
0.5
y/b
FIGURE 6.
Secondary flow for i = −5◦ and λ = 30◦
gularity method as well as the historical NACA data is in good
accordance to the experimental results. Hence, the validity of the
measurement was guaranteed.
It has been shown that the prediction for flow separation by
means of Lieblein’s diffusion factor and Lei’s diffusion parameters differs significantly from the experimental results. In contrast, DF corresponds to the results made by CFD, while D shows
qualitatively the same difference as for the experimental investigations. Merely, the de Haller criterion is in a good agreement
with both types of investigations. To get a comprehensive prediction of 3D flow separation, Lei’s diffusion factor needs to be
extended by a parameter involving the boundary layer thickness,
which has to be addressed by future research.
10
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