Jtam-A4.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

56, 4, pp. 1083-1095, Warsaw 2018
DOI: 10.15632/jtam-pl.56.4.1083

NUMERICAL LOSS ANALYSIS IN A COMPRESSOR CASCADE WITH

LEADING EDGE TUBERCLES

Tan Zheng, Xiao-Qing Qiang, Jin-Fang Teng, Jin-Zhang Feng

School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, China

e-mail: qiangxiaoqing@sjtu.edu.cn

A numerical analysis of loss has been carried out to explore the loss mechanism of leading
edge tubercles in a high speed compressor cascade. Taking the lead from flippers of the
humpback whale, tubercles are passive structures of a blade for flow control. Evaluation
of the overall performance in terms of entropy increase shows that the loss reduction is
achieved both at high negative and high positive incidence angles, while a rise in the loss is
obtained near the design point. And a smaller wave number as well as a smaller amplitude
results in lower additional losses at the design point. Spanwise and streamwise distributions
of pitchwise-averaged entropy increase combined with flow details have been presented to
survey the lossdevelopmentand, subsequently, to interpret the lossmechanism.The tubercle
geometry results in the deflection flow and the consequent spanwise pressure gradient. This
pressure gradient induces formationof counter-rotating streamwisevortices, transports away
the low-momentum fluid near wall from crests towards troughs and leads to local high loss
regions behind troughs as well as loss reduction behind the crests in comparison to the
baseline. The interaction between these vortices and flow separation bymomentum transfer
leads to separation delay and the consequent loss reduction at the outlet.

Keywords: compressor cascade, flow separation, passive flow control, leading edge tubercles,
streamwise vortices, loss analysis

Nomenclature

c,cz – blade and axial blade chord [mm]
H,t,l – blade span, pitch and camber length, respectively [mm]
β,γ – flow angle and stagger angle with respect to axial direction [◦]
∆β – deflection angle [◦]
ω – total pressure loss coefficient [–]
∆s – specific entropy increase relative to incoming flow [J/(kg·K)]
∆sref – reference specific entropy increase [J/(kg·K)]
p,pt – static and total pressure [Pa]
Cp – pressure coefficient [–]
M – Mach number [–]
i – incidence angle [◦]
A,W – amplitude and wavelength of leading edge tubercles [mm]
N – wave number of leading edge tubercles [–]
X,Y,Z – spanwise, pitchwise and axial direction
S – camber length direction
ξz – streamwise vorticity [s

−1]
V – velocity [m/s]
LE, TE – leading edge and trailing edge [–]



1084 T. Zheng et al.

1. Introduction

Flow separation is a common phenomenon in the axial compressors that occurs near the blades.
Severe separation contributes greatly to passage blockage and to aerodynamic losses. Worse
yet, compressor stall may be induced, which subsequently leads to a sharp decrease in the
aerodynamic performance.

Studies of active and passive flow control have been carried out with the aim of depressing
flow separation. An overview of possible flow control methods in gas turbine engines is given by
several researchers (Lord et al., 2000).Active flowcontrol techniques have the advantage of being
suitable for a wide range of operation conditions. Due to their increased complexity, however,
gas turbine manufacturers are not fond of them as much as passive flow control techniques
such as bowed stators (Fischer et al., 2003), non-axisymmetric profiled endwalls (Dorfner et al.,
2011), vortex generators (Hergt et al., 2013). Another way for passive flow control is application
of leading edge tubercles. This method is inspired by previous works on the morphology of
humpback whale flippers bymarine biologists (Fish and Battle, 1995).

A number of previous experimental andnumerical works have been performed to explore the
effects of leading edge tubercles on the performance of humpback whale flippers and isolated
airfoils. A numerical study for the NACA 634-021 wing with and without tubercles shows that
large streamwise vortices are formed in the regions posterior to the troughs between tubercles
(Fish and Lauder, 2006). Johari et al. (2007) also take theNACA 634-021 airfoil as the baseline
and carry out an experimental investigation comparing the effect of varying thewavelength and
amplitude of sinusoidal tubercles on airfoil performance.Miklosovic et al. (2004) constructed two
idealized scale models of a humpback pectoral flipper with and without leading edge tubercles
and conducted wind-tunnel tests on them at Re = 505000-520000. The results showed that
tubercles delayed the stall angle by approximately 40% while decreasing drag and increasing
lift in the post-stall regime. Pedro and Kobayashi (2008) performed a numerical simulation of
the setup used for the experimental studies (Miklosovic et al., 2004) with the detached eddy
turbulence model. They indicated that the higher aerodynamic performance for the scalloped
flipper results from the presence of streamwise vortices originated by the tubercles (Pedro and
Kobayashi, 2008).

Also, leading edge tubercles have been applied in cascades. An experimental investigation
(Keerthi et al., 2014) was carried out to quantify aerodynamic benefits of sinusoidal tubercles
in a linear compressor cascade with different tubercle configurations at low Reynolds numbers
(Re = 130000). The results indicated that the performance of the cascade had substantially
improved due to the effect of tubercles in terms of delaying the stall angle.

In consideration of the fact that the application of leading edge tubercles is notwidespread in
turbomachinery, the presentwork is committed to clarifying the effects of leading edge tubercles
on the performance of a high-speed linear compressor cascade and elaborating the underlying
loss mechanism of tubercle structures. The overall performance in terms of entropy increase is
evaluated over the operating range of the cascade with different tubercle configurations. Span-
wise and streamwise entropy distributions are utilized to investigate the difference in the loss
development between the cascades with and without leading edge tubercles. Entropy distribu-
tions with flow visualizations on several axial cross-sections are examined in detail to interpret
the loss development procedure.

2. Numerical setup

2.1. Baseline cascade

Ahigh-speed linear compressor cascade is used in this study.Theblade profile of the baseline
cascade ismodified froman airfoil of a high loading stator of a compressor. The airfoil is suitable



Numerical loss analysis in a compressor cascade... 1085

to be used in axial compressors with a subsonic inlet flow over the full blade span. The blade
profile and geometrical definitions are shown in Fig. 1.

Fig. 1. Blade profile and geometrical definitions

The general design parameters of the cascade are listed in Table 1. The cascade is built with
a blade aspect ratio of 0.48 and a design inletMach number of 0.64. This aspect ratio is selected
in order to study the effects of leading edge tubercles in a certain blade span of about 50% chord
length. Furthermore, this value is also related to the number andwavelength of tubercles. Based
on the design inflow angle (β1 =42

◦), numerical simulations are performed in a wide operation
range of incidence angles from−16◦ to 16◦.

Table 1.General design parameters of the cascade

M1 β1 β2 γ ∆β H c l H/c c/t

0.64 42◦ −9◦ 16.9◦ 51◦ 24.5mm 51mm 53.2mm 0.48 2

2.2. Leading edge tubercles

The structure of tubercles is built by using a sinusoidal-like curve as the leading edge. The
characteristic geometry definitions of tubercles are shown in Fig. 2a. What calls for special at-
tention is that the horizontal axisS represents the camber length direction and the longitudinal
axisXmeans the spanwise direction.The amplitudeA andwavelengthW , characteristic dimen-

Fig. 2. (a) Characteristic geometry definitions of tubercles. (b) A sketch of profiles for the crest, middle
and trough cross-sections



1086 T. Zheng et al.

sions of the sinusoidal-like curve are selected to study their effects on the compressor cascade
performance.

In order to have a distinct comparison of the baseline geometry and two modified ones, a
sketch of threebladeprofiles is shown inFig. 2b.Theyhave the same shapedespite thedifference
in the leading edge.

Different computational cascademodels are constructed covering variations in the amplitude
andwavelength (or wave number). Different amplitudes ofA=0.02l, 0.03l and 0.04l (named as
A2, A3 and A4) combined with several wavelengths of W =0.16c, 0.12c and 0.096c (or several
wave numbers ofN =3, 4 and 5) are systematically investigated in this work. These parameter
values are selected according to the suggestions given by studies of pioneering researchers (Johari
et al., 2007; Hansen et al., 2011). Table 2 shows notations of various configurations. According
to the table, nine cascades are named by combiningA2-A4 withN3-N5. Besides, ORI represents
the baseline cascade.

Table 2.Notations of different configurations

Notations A2 A3 A4 N3 N4 N5

Amplitude 0.02l 0.03l 0.04l – – –

Wavelength – – – 0.16c 0.12c 0.096c

Wave Number – – – 3 4 5

2.3. Numerical method

ANSYS-CFX software package has been used to performRANS simulations on the baseline
cascade and on the cascade with different leading edge tubercles. The overall performance of
these cascades was investigated with the S-A turbulence model. As one of the most prominent
turbulence models, the S-A model is widely used in turbomachinery due to its numerical effi-
ciency and robustness. TheReynolds number based on the characteristic chord length and inlet
velocity was about 7.9 ·105.

In the simulations of these cascades, finemultiblock structuredgridswith anH-O-H topology
were constructed. The grid consisted of 3.1 million nodes with 97 pitchwise and 69 spanwise.
Thus, the blade boundary layer was sufficiently resolved, where y+ ≈ 1 was realized.

Fig. 3. Schematic diagram of cascade grids with and without leading edge tubercles;
(a) baseline cascade, (b) cascade with tubercles

Figure 3 showsa schematic diagramof thebaseline cascade and the cascadewith leading edge
tubercles. At the inlet of the domain, boundary conditions consisted of uniform total pressure,
total temperature and flow direction. The turbulence intensity of 5%was selected. At the outlet
boundary, an average static pressure of 101325Pa was imposed. Solid boundaries were applied



Numerical loss analysis in a compressor cascade... 1087

at the blade surfaces with no slip and impermeability conditions. The side boundaries of the
passage were modeled with matching translational periodicity. At the passage endwalls, the
translational periodicity was also used so as to obtain an “infinite blade cascade”.
A linear cascade constructed with the controlled diffusion airfoil (Steinert et al., 1991) was

simulated to validate thenumericalmethodmentioned above.The loading andflowphenomenon
in this cascadewas similar to the investigated cascade in the paper. Figure 4 shows experimental
and numerical results of Mach number characteristics at the design point. The parameter ω is
calculated by following equations

pt =

∑
ṁpt
∑
ṁ

ω=
pt1−pt2
pt1−p1

(2.1)

where pt means the mass flow averaged total pressure in a local plane. The predicted results
reasonably agree with the experimental data. This gives some confidence on the CFD model
used in the following study.

Fig. 4. Comparison ofMach number characteristics of experimental and numerical results

3. Results and discussion

3.1. Overall loss characteristics

For adiabatic flow through a stationary blade row, the total temperature is constant, and so
entropy changes depend only on total pressure. Hence, for stator blades and cascade flows, total
pressure losses can be taken to be synonymous with specific entropy increase (Denton, 1993).
In order to compare the overall loss characteristics of cascadeswith andwithout leading edge

tubercles, the variation of the mass flow averaged specific entropy increase relative to incoming
flow∆s in the outlet plane is described for different wave numbers and amplitudes. The entropy
increase is calculated and normalized with the reference value ∆sref , the entropy value in the
outlet plane at the incidence angle of i=0◦.
In Fig. 5, the normalized entropy increase ∆s/∆sref in the outlet plane is plotted against

incidence angles for all the cascades. It is seen that the normalized entropy increase for the
baseline cascade equals to 1 at the incidence angle of 0◦. Theminimum entropy increase of the
baseline cascade is obtained at the incidence angle of −4◦. All the modified cascades have the
sameminimum loss incidence angle. Figure 5a shows the loss characteristics for cascades with a
wave amplitude of 0.02l and different wave numbers of 3, 4 and 5. For A2N3, A2N4 and A2N5
cascades, it is observed that the loss reduction is achieved in the range from −16◦ to −8◦ and
from 8◦ to 16◦, compared to the baseline. However, in the operation conditions from −8◦ to 4◦

incidence angles, the leading edge tubercles result in no loss reduction. Inhighnegative incidence
angles ranged from −16◦ to −8◦, the loss reduction gets larger as the wave number increases.



1088 T. Zheng et al.

And yet in high positive incidence angles ranged from 8◦ to 16◦, no definite trend in the loss
reduction is observed as the wave number increases. Figure 5b shows the loss characteristics
for A2N5, A3N5 and A4N5 cascades, with a wave number of 5 and different wave amplitudes
of 0.02l, 0.03l and 0.04l. In high negative incidence angles of −16◦ and −12◦, it is shown that
the loss reduction, compared to the baseline, gets larger as the wave amplitude increases. The
same relation between the loss reduction and wave amplitude is observed in the high positive
incidence angles of 12◦ and 16◦. However, A2N5, A3N5 and A4N5 cascades show similar loss
reductions as the wave amplitude increases at the incidence angle of i=8◦.

Fig. 5. Normalized entropy increase variation with incidence angle: (a) different wave numbers,
(b) different wave amplitudes

Fig. 6. Cascade loss characteristics for different wave numbers and amplitudes: (a) i=0◦, (b) i=8◦

In order to further explore the influence of tubercles on losses, Fig. 6 shows the results
of normalized entropy increase predicted at two incidence angles of i = 0◦ and 8◦ for all the
cascades. Compared to the baseline, a rise in the entropy increase is observed for all the tubercle
configurations at i=0◦, just as shown inFig. 6a.A smaller amplitude is shown to result in lower
additional losses. It means that among all these amplitude configurations, theA2 configuration
with an amplitude of 0.02l produces the least negative influence on the cascade performance.



Numerical loss analysis in a compressor cascade... 1089

Also, there exists a positive relation between the loss and wave number, which indicates a
higher loss for a larger wave number, namely a smaller wavelength. ForA2N5, A3N5 andA4N5
configurations, the losses respectively rise by 4.2%, 6.7% and 8.3% compared to the baseline.
Figure 6b shows that all cascades with leading edge tubercles obtain a decrease in the loss at
i=8◦. And the loss reduction gets larger as thewave number increases. The normalized entropy
increase equals to 6.4333 in the baseline configuration. The loss reductions forA2N5, A3N5 and
A4N5 configurations, respectively, equal to 12.4%, 12.3% and 13.3% in contrast to the baseline.
These values are close to each other.

3.2. Spanwise and streamwise entropy distributions

In this Section, spanwise and stremwise distributions of pitchwise-averaged entropy increase
are analyzed to survey the loss development in the baseline andA2N5 cascades.
Spanwise distributions of the normalized entropy increase at axial positions of z/cz =30%,

90% and 150% are shown in Fig. 7. It is noted that the axial positions of z/cz =0%, 100% and
150% represent the leading edge, trailing edge and outlet. Three wave periods are included in
the range from 20% to 80% span for A2N5. It is shown that the normalized entropy increase
has little change along the span for ORI both at i=0◦ and 8◦. ForA2N5, a periodical variation
of the entropy increase along the span is observed at both operating incidence angles.We focus
on one of the periods in the range from 40% to 60% span for further analysis. The locations
of M0, trough, middle and crest sections are shown in Fig. 8. In Fig. 7a, a rise in the loss is
observed in the range from 52% to 58% span forA2N5 compared toORI at the axial position of
z/cz =30%, and themaximum rise of loss locates at the trough section. At z/cz =90%, the loss
reduction is almost not observed over the full span forA2N5. At z/cz =150%, there exists loss
reductionmerely in a small range from 54% to 56% forA2N5, and themaximum loss reduction
also locates at the trough section. In Fig. 7b, it is shown that there exists a reduction in the loss
between 43% and 47% span at z/cz =30% forA2N5, compared to ORI. And themaximum loss
reduction locates at the crest section at i = 8◦. At z/cz = 90%, no loss reduction is achieved
over the whole span forA2N5. However, at z/cz =150%, the loss reduction is achieved over the
whole span. It is seen that the spanwise variance of∆s tends to be smaller along the streamwise
direction forA2N5 and, finally, an approximately uniform distribution of∆s is achieved.

Fig. 7. Spanwise distributions of normalized entropy increase for baseline andA2N5 cascades:
(a) i=0◦, (b) i=8◦

Streamwise distributions of the normalized entropy increase at several spans for the baseline
andA2N5 cascades are presented in Fig. 9. ForA2N5, theM0, trough,middle and crest respec-



1090 T. Zheng et al.

Fig. 8. Locations ofM0, trough, middle and crest sections

Fig. 9. Streamwise distributions of normalized entropy increase for baseline andA2N5 cascades:
(a) i=0◦, (b) i=8◦

tively correspond to 60%, 55%, 50% and 45% spans shown in Fig. 8. For the baseline cascade,
ORI represents themiddle section of 50% span.Actually, the entropy distributions at these four
spans have little difference between one another.

In Fig. 9a,∆s of ORI rises gradually downstream LE at i=0◦, and the value of normalized
entropy increase equals to 1 at the outlet. As for the M0 section, ∆s also shows a gradual rise
downstreamLE, and the growing rate is larger than that of ORI. The loss reduction is observed
fromLE to 60% z/cz compared to ORI. The∆s curve at themiddle section is almost the same
as that at the M0 section. At the trough section, a rapid increase of ∆s from LE is followed
by a decrease till 90% z/cz. The maximum value is reached at 25% z/cz. At the crest section,
∆s shows the similar trend to that at theM0 section despite a slight difference downstreamTE.
From LE to 80% z/cz, the loss reduction is observed compared toORI. Among all four sections
forA2N5, only∆s of the trough section is smaller than that of ORI at the outlet.

InFig. 9b,∆sofORIshowsa rapid risedownstreamLEat i=8◦, andthevalueofnormalized
entropy increase equals to 6.5 at the outlet. At theM0 andmiddle sections, a sharp increase of
∆s is seen from LE to 20% z/cz, followed by a tender decrease till 46% z/cz and a subsequent
sustained growth till the outlet. As for the trough section, the trend of ∆s downstream LE is
similar to that at theM0 andmiddle sections. A local peak value of the entropy increase lies in
the 36% z/cz. At the crest section, an upward trend of∆s is observed betweenLEand50% z/cz.



Numerical loss analysis in a compressor cascade... 1091

Differently, the loss reduction is achieved from LE to 42% z/cz at the crest compared to ORI.
It is worth nothing that the normalized entropy increases at the M0, trough, middle and crest
sections come to the same value of 5.6 at the outlet, which is smaller than that for the baseline.
The streamwise entropy results are in good consistence with the spanwise distributions of∆s.

From the above analysis of spanwise and streamwise entropy distributions, it is concluded
that the loss reduction at the outlet is merely obtained at the trough section for A2N5 in
contrast to ORI at i = 0◦, while the loss reduction is achieved over the whole span at i = 8◦.
The introduction of leading edge tubercles turns the uniform spanwise distribution of ∆s into
a nonuniform one and leads to local high loss regions in the fore part of the blade. Also, it is
indicated that there exists a spanwise fluidmigration downstream LE forA2N5, which narrows
the gap of∆samong theM0, trough,middle and crest sections andaccounts for the loss decrease
from25% to 90% z/cz behind the trough. It is inferred that entropy variations are inducedby an
altered flowfield by leading edge tubercles.The following Section combines the loss development
process with flow visualizations, making further efforts to interpret the loss mechanisms.

3.3. Discussion of loss mechanism

ThisSection gives a discussionof the loss development process along the streamwise direction
aswell as flowvisualizations,making further efforts to interpret the lossmechanismswithA2N5.

Fig. 10. Distributions of the normalized entropy increase on different axial cross-sections:
(a) ORI, i=0◦, (b) A2N5, i=0

◦, (c) ORI, i=8◦, (d)A2N5, i=8
◦

InFig. 10, distributions of the normalized entropy increase at i=0◦ and 8◦ on different axial
cross-sections are shown. The ORI configuration, representing the baseline cascade, shows an
almost uniform loss distribution along the blade span in Fig. 10a and 10c. High loss regions are
mainly distributed near the blade suction side at i= 8◦, see Fig. 10c. From Fig. 10b and 10d,
it is observed that the introduction of the leading edge tubercles results in the redistribution
of the entropy increase along the span. In the A2N5 cascade, high losses accumulate in several



1092 T. Zheng et al.

rounded areas near the blade suction side at 10% z/cz rather than long narrow strips in the
baseline. It is found that high loss regions are in the downstream location of the wave troughs.
And the number of high loss regions is equal to the wave number. Without doubt, high loss
regions at i= 0◦ are much smaller than those at i= 8◦. Figure 10d also shows an evidence of
the spanwise fluidmigration near the blade suction side, which results in the uniform spanwise
distribution of∆s downstreamTE.

Figure 11 shows an isosurface of zero streamwise velocity at i=8◦, which is indicative of the
size of the separated region. The baseline case is also presented for comparison. It is apparent
from the figure that the size of the recirculation region for A2N5 is dramatically reduced, and
that separation is delayed relative to thebaseline. It can alsobe seen fromthefigure that theflow
separation is delayed behind crests to a greater extent thanbehind the troughs.The reduced size
of the separation region explains the improved aerodynamic performance. However, separation
bubbles are still observed behind the troughs,which correspondwith the high loss regions shown
in Fig. 10d.

Fig. 11. Isosurface of zero streamwise velocity at i=8◦: (a) ORI, (b)A2N5

Slices of streamwise vorticity plotted in Fig. 12 provide insight into the locality where the
normalized entropy increase is greater than 1 at i=0◦ and 8◦ and indicate the development of
counter-rotating vortices along the streamwise direction.

Fig. 12. Slices of streamwise vorticity forA2N5: (a) i=0
◦, (b) i=8◦



Numerical loss analysis in a compressor cascade... 1093

In Fig. 12a, pairs of counter-rotating streamwise vortices are induced by leading edge tu-
bercles and located behind the troughs. The vorticity generally expands in area and declines in
strength along the streamlines. And the vortical structure is still visible at 100% z/cz. As a kind
of secondary flow, the induced vortices may raise the entropy increase and account for a relati-
vely high loss between LE and TE at the trough section shown in Fig. 9a. It is apparent from
Fig. 12b that two different pairs of counter-rotating streamwise vortices are produced behind
the wave trough. The wall vortices are adjacent to the primary vortices and have an opposite
sense of rotation. Thewall vortices gradually disappear along the streamlines and there are only
primary vortices visible downstream 15% z/cz. The strength of primary vortices declines along
the streamlines and there are almost no vortical structures visible downstream 70% z/cz. It
indicates that streamwise vortices feed into the separated flow region and sufficiently interact
with flow separation by transfer of themomentum. The interaction significantly delays the flow
separation near the blade suction side shown in Fig. 11. It should be noted that there is no
flow separation at i=0◦ and this explains the visible vortical structure at 100% z/cz. The wall
vortices with primary vortices may be related to the loss increase upstream TE at the trough
section and the sharp rise of ∆s at the M0 and middle sections between LE and 20% z/cz in
comparison to the baseline. Another observation that the counter-rotating primary vortices in a
pair go away from each other along the streamlines indicates the spanwisemovement of vortices,
which transports momentum in the spanwise direction.
Figure 13 showsdistributionsof thepressurecoefficient on the suction surface and3Dstream-

lines at i=0◦ and i=8◦. The pressure coefficient is defined as

Cp =
p−p1
pt1−p1

(3.1)

where pt1 and p1 mean the reference total pressure and static pressure in the inlet plane. It
is observed in Fig. 13 that the incoming flow is deflected by tubercle geometry such that the
bulk of the flow is redirected behind the trough. The deflection results in the spanwise pressure
gradient, which transports away the low-momentum fluid near the wall from the crests towards
troughs. This pressure gradient also accounts for the production of counter-rotating streamwise
vortices.

Fig. 13. Distributions of the pressure coefficient on the suction surface and 3D streamlines forA2N5:
(a) i=0◦, (b) i=8◦

Fromthe above analysis, loss development procedures along the streamwise direction forORI
andA2N5 cascades are clarified. Loss generations forORI at i=0

◦ are primarily ascribed to the
viscousboundary-layernear theblade suction side.At amorecritical condition of i=8◦, theflow
separation and consequent recirculation flowoccupies themajor part of the high loss. ForA2N5,
the deflection flow resulted from the tubercle geometry leads to the spanwise pressure gradient
which transports away the low-momentum fluid near the wall from crests towards the troughs.



1094 T. Zheng et al.

The loss increase at the trough section and loss reduction at the crest section are ascribed to
the low-momentumfluidmigration in the fore part of the blade. The resulted from the spanwise
pressure gradient, two different pairs of counter-rotating streamwise vortices, wall vortices and
primary vortices locate behind the troughs and extend to the M0 and middle sections in the
spanwise direction at i=8◦. The interaction between these vortices and the flow separation by
the momentum transfer leads to separation delay and consequent loss reduction at the outlet.

4. Conclusions

Taking the lead from humpback whale flippers, leading edge tubercles are applied in a high
speed compressor cascade. This paper clarifies the influence of tubercles on loss distributions
and elaborate the underlying loss mechanism. Several conclusions are drawn as follows:

• For all configurations of leading edge tubercles investigated in thiswork, the loss reduction
is achieved both at high negative and high positive incidence angles, while a rise in the
loss is obtained near the design point. A smaller wave number or a smaller wave amplitude
results in lower additional losses at i = 0◦, while a larger wave number brings about
a greater loss reduction. There is no linear relation between the amplitude and loss at
i=8◦.

• Loss generations for ORI at i = 0◦ are primarily ascribed to the viscous boundary-layer
near the blade suction side. At a more critical condition of i = 8◦, the flow separation
occupies the major part of the high loss. For A2N5, the introduction of leading edge
tubercles turns the uniform spanwise loss distribution into a nonuniform one and leads to
local high loss regions behind the troughs in the fore part of the blade, both at i = 0◦

and 8◦. The flow separation is delayed behind the crests to a greater extent than behind
the troughs, and the loss reduction is achieved over the whole span in the outlet plane at
i=8◦.

• The loss mechanism of tubercle structures by which the size of the flow separation region
is reduced has been explored. The tubercle geometry results in the deflection flow and
the consequent spanwise pressure gradient. This pressure gradient transports away the
low-momentum fluid near the wall from crests towards troughs and also accounts for the
formation of counter-rotating streamwise vortices, including wall vortices and primary
vortices. The interaction between these vortices and flow separation by the momentum
transfer leads to separation delay and consequent loss reduction.

Acknowledgements

This work has been supported by the National Natural Science Foundation of China (No. 51406115),

the “2011Aero-Engine collaborative Innovation Plan”.

References

1. Denton J.D., 1993, Loss mechanisms in turbomachines, Journal of Turbomachinery, 115, 4,
621-656

2. Dorfner C., Hergt A., Nicke E., Moenig R., 2011, Advanced nonaxisymmetric endwall
contouring for axial compressors by generating an aerodynamic separator-part i: principal cascade
design and compressor application, Journal of Turbomachinery, 133, 2, 021026

3. Fischer A., Riess W., Seume J.R., 2003, Performance of strongly bowed stators in a 4-stage
high speed compressor,ASME Proceedings,GT2003-38392, 429-435



Numerical loss analysis in a compressor cascade... 1095

4. Fish F.E., Battle J.M., 1995, Hydrodynamic design of the humpback whale flipper, Journal of
Morphology, 225, 1, 51-60

5. FishF.E., LauderG.V., 2006,Passiveand active flowcontrol by swimmingfishes andmammals,
Annual Review of Fluid Mechanics, 38, 193-224

6. HansenK.L.,KelsoR.M., DallyB.B., 2011,Performance variations of leading-edge tubercles
for distinct airfoil profiles,AIAA Journal, 49, 1, 185-194

7. HergtA.,MeyerR.,EngelK., 2013,Effectsofvortexgeneratorapplicationontheperformance
of a compressor cascade, Journal of Turbomachinery, 135, 2, 021026

8. Johari H., HenochC., Custodio D., Levshin A., 2007, Effects of leading-edge protuberances
on airfoil performance,AIAA Journal, 45, 11, 2634-2642

9. Keerthi M. C., Kushari A., De A., Kumar A., 2014, Experimental investigation of effects of
leading-edge tubercles on compressor cascade performance,ASME Proceedings, GT2014-26242

10. LordW.K.,MacmartinD.G.,TillmanT.G., 2000,Flow control opportunities in gas turbine
engines,Proceedings of AIAA,AIAA 2000-2234

11. MiklosovicD.S.,MurrayM.M., Howle L.E., Fish F.E., 2004, Leading-edge tubercles delay
stall on humpback whale (Megaptera novaeangliae) flippers,Physics of Fluids, 16, 5, L39-L42

12. Pedro H.T.C., Kobayashi M.H., 2008, Numerical study of stall delay on humpback whale
flippers,Proceedings of AIAA,AIAA 2008-0584

13. Steinert W., Eisenberg B., Starken H., 1991, Design and testing of a controlled diffusion
airfoil cascade for industrial axial flow compressor application, Journal of Turbomachinery, 113,
4, 583-590

Manuscript received January 24, 2018; accepted for print March 12, 2018