investigation of the shear flow effect on secondary …investigation of the shear flow effect on...
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Investigation of the Shear Flow Effect on Secondary Flow and
Losses in a Low Speed Axial Flow Compressor Cascade
Mahesh K. Varpe and A. M. Pradeep
Department of Aerospace Engineering
Indian Institute of Technology, Bombay
Mumbai, India 400 076
Email: [email protected].
ABSTRACT
This paper explores the effect of a prescribed intense shear flow
on the flow structures in an axial flow compressor cascade. An
approximate shear flow is generated in the test section of an open
circuit cascade wind tunnel by using a planar grid of parallel rods
with varying solidity. To study only the effect of shear, a
compressor cascade based on NACA65 series with a relatively low
camber was chosen. The cascade was analysed experimentally as
well as computationally (using ANSYS Fluent). The computational
results of the cascade were compared with the available measured
data. The results agreed well with the experimental data. Detailed
analysis of the numerical results was then carried out to explore the
complex flow features caused by the shear flow in a cascade. With
uniform flow, the secondary flow was found to be negligible from
experiments as well as from the computations. Therefore, in an
attempt to amplify secondary flow, a shear flow generator was
placed upstream of the cascade. Experiments showed quite
contrasting results with shear flow, as compared to the uniform flow,
in terms of the wake loss. Numerical analysis revealed the
formation of vortices in the wake of the cascade due to secondary
flows caused by the incoming shear flow and other interesting flow
features.
Keywords: Shear flow, Low-camber, Secondary flow, Endwall loss,
Deviation.
NOMENCLATURE
a Mean-line designation, fraction of the chord from
leading edge over which loading is uniform at the
ideal angle of attack
Cp Static pressure coefficient, = (P2 - P1) / (1/2*ρ*U2)
Cp0 Total pressure loss coefficient, = (P01 - P02)/(1/2*ρ*U2)
H Blade span, m
h semi-blade span/ height of shear generator, m, =H/2
i Incidence angle, degrees
K0 Grid resistance
P.S Pressure surface of the blade
P1, P2 Upstream and downstream static pressure respectively,
Pa
P01, P02 Upstream and downstream stagnation pressure
respectively, Pa
Re Reynolds number based on chord length
S Pitch of blade, m
s Pitch/spacing between rods, m
S.S Suction surface of the blade
SWG Standard wire gauge
Turb. intensity = 2 2 2( ' ' ' ) / 3 /u v w U
U Mean inlet velocity, m/s
u, v, w Velocity components, m/s
u’, v’, w’ Fluctuating components of the velocity, m/s
x, y, z Cartesian coordinates
λ Velocity gradient, 1/s, =∂U/∂z
λ h/U Shear parameter
ωe End wall loss
σ Solidity of rods
INTRODUCTION
The secondary flow in a blade row is defined as any flow, which
is not in the direction of the reference (primary or stream wise) flow.
Hawthorne (1951) proposed that secondary flows are generated due
to the turning of the vorticity vector generated as a result of the
boundary layer approaching a row of blades. The strength of the
secondary flows is a function of the blade turning angle and the
incoming vorticity (Squire and Winter, 1951). In an actual
compressor, the spanwise gradient in velocity may be caused by
endwall boundary layers or by the presence of an upstream blade
row. Since the early work of Hawthorne (1951), extensive
publications are available on details of secondary flows. In a
modern day compressor with higher blade loading on low aspect
ratio blades, the effects of secondary flows are significant. This
obviously leads to a major loss in the performance and hence an
attempt to further enhance the efficiency encourages studying the
behaviour of flow in a cascade under shear flow at the inlet.
Various devices like rods, screens, perforated plates, honeycomb
etc. were used in the past, by researchers to generate an
approximate homogeneous, turbulent and nearly uniform shear
flow to study the turbulent structures that would help in developing
flow models. Most of the earlier methods to generate shear profile
were rather crude. Owen and Zienkiewicz (1957) developed a
mathematical approach to produce a desired velocity profile using a
grid of rods. The rate of shear and velocity profile suffers no
appreciable decay downstream of the grid from x/h = 1.2 ~ 4.2,
excluding the boundary layer region. The turbulence intensities are
maintained uniform by the constant mean shear downstream. The
shear flow generated did not accompany any large-scale secondary
flow. Based on Owen’s design, Livesey (1964) used a shear
parameter as high as 0.8 and obtained a symmetrically high shear
flow, which deviated from uniformity. In the near wall region,
reduced velocity can be obtained by changing the local solidity
International Journal of Gas Turbine, Propulsion and Power Systems October 2014, Volume 6, Number 2
Copyright © 2014 Gas Turbine Society of Japan
Manuscript Received on August 6, 2013 Review Completed on April 21, 2014
17
between the rods. Any profile decay, in the far downstream, was
attributed to the encroaching boundary layers and a change in the
sign of the shear flow at symmetry. The selection of suitable
resistance grading ensures a constant total pressure downstream of
the grid that eventually leads to a constant vorticity. Some
modification to the theoretical resistance grading of the rods is
necessary to achieve a non-decaying velocity profile(Livesey,
1964).
Lloyd (1966) compared the shear flow profile from the grid of
rods and flat plates and found that the former generated a less
accurate profile. The theory to generate shear profile with flat plate
fails for plates with a turbulence generator, in which case, a trial and
error method has to be adopted. Flat plates with turbulence
generators provide flexibility of varying turbulence and velocity
independently. With variation of velocity and turbulence intensities
with height, it is difficult to achieve a proper exchange of
momentum between the neighboring layers. The non-uniform flow
through the wire gauzes, in different configurations, has been
mathematically analysed by Elder (1959) and Davis (1962). Any
deviation of the measured velocity profile from the computed
profile, using Elder’s method, is attributed to higher order terms in
linearisation (1973). Tavoularis and Karnik (1989) demonstrated
shear flow with fair uniformity along the span, using strips of
selected wire gauzes based on an empirical approach. The
generated shear flow has a self-preserving structure with
unidirectional mean velocity downstream of the screens, Hergt
(2005). Higher shear rates with low turbulence intensities can be
generated by using the multiple screens in parallel (1959). Similar
shear profile is possible by honeycombs using the method
developed by Kotansky (1966).
The inflow disturbance (steady or unsteady) is one of the vital
parameter which affects the aerodynamic performance of an axial
flow compressor. Huges and Walker (2001) studied the transition
phenomena due to the variation of inflow disturbance periodicity in
an axial compressor. The inlet disturbance was produced by inlet
guide vane clocking. The study indicates that the length of the
unstable laminar flow regions and the transitional flow extends up
to 20% chord each. A similar investigation was carried out by
Hilgenfeld and Pfitzner (2004) with cylindrical bars moving
parallel to compressor cascade. The periodic variation of inlet
velocity caused a variation of 2 degrees in the incidence angle. This
induced the periodic variation of the blade loading. Large velocity
fluctuations inside the boundary layer reduced the time-mean
momentum thickness significantly compared to the steady ones.
This was attributed as a potential cause for loss reduction effects.
Brandt et. al. (2002) demonstrated by the numerical study that
thicker inflow boundary layer shifts the roll-up point of the tip
leakage vortex upstream towards the leading edge. The thicker
boundary layer at the inlet adversely affects the stall mass flow
similar to higher tip clearance. Choi et.al (2008) found the adverse
effects of inlet boundary layer thickness on the rotating stall in an
axial flow compressor. The study reveals that the size of the hub
corner stall is proportional to the inlet boundary layer thickness at
higher blade loading. It is also a major contributor to the first
disturbance which triggers the rotating stall. The performance
drops sharply in the presence of thicker boundary layers at higher
flow coefficient. Zaki et. al. (2010) has well documented the
mechanism of boundary layer breakdown to turbulence on the
blade surface under the influence of turbulence intensity as a source
of inlet disturbance. The numerical investigation by Varpe and
Pradeep (2013) show that the shear flows reduces the tip leakage
losses considerably in terms of kinetic energy associated with it. It
also limits the majority of the blade loading towards the blade
midspan irrespective of the tip clearance. The inlet shear flow
induces substantial endwall effects for the tip leakage to influence
which deleteriously affects the total pressure loss in the wake. Lee
et. al. (2014) investigated, through numerical study, the effects of
idealized local shear flows on the two dimensional airfoil and
proposed a lift correction model. The study indicates that the high
shear rate in a flow causes substantial changes in the lift coefficient
and is proportionate to the reference velocity at the inlet.
The secondary flows interact with the corner vortices and the
wall boundary layers leading to complicated loss sources. It also
influences the outlet angle of the flow (Hawthorne, 1956), which
may produce off- design conditions for the downstream row of
blades. Secondary flows are influenced by the inlet vorticity and the
camber angle of the blade. In an actual multistage axial flow
compressor, the spanwise gradient in velocity may be caused by the
growing endwall boundary layers or by the presence of an upstream
blade row. Therefore, with the aim to study only the effect of shear
flow on an axial flow compressor cascade, the camber angle chosen
was relatively low. The secondary flow in this cascade
configuration can be amplified by a simulated shear flow at the inlet
of the cascade. Since the camber of a typical turbine blade is quite
high compared to the blade of an axial flow compressor, the
secondary flows are stronger. Hence, most of the literature related
to the secondary flow is on turbine cascades. The inflow
disturbance, as found in published literature, was preferably in
pitchwise direction only. Therefore, this paper explores the flow
physics of a low-speed axial flow compressor cascade in the
presence of a shear flow (spanwise variation).
SHEAR FLOW GENERATOR-DESIGN For the selected geometry of compressor blades for the
cascade, the camber angle was relatively low. Therefore, secondary
flow can be studied only by inducing it with an inlet vorticity. A
method of generating maximum shear with negligible decay
downstream has to be adopted. Amongst the various available
alternatives of designing a shear flow generator, it is important to
evaluate each, for suitability to a particular application. It is
difficult to find screens with varying porosity as desired for shear
flow generation. Specific shaped screen with constant porosity or
multiple screens with different gauges are cumbersome and
difficult to work with. Other options like honey comb and
perforated plates would render heavy drag that may subsequently
lead to considerable loss. This would also correspond to effective
resistance to flow and could cause rapid rates of decay of the
Fig. 1 Arrangement of rods in a planar grid with coordinate system
2 1 1 11 (1)02 1 2
1 0 0
1 2, - / , 1.1/ 1 , /0 1 2 02
yhKU K a h
where K P P U a K U y
velocity profile. Therefore, rods become an obvious
choice as they offer simplicity. Design details provided by
Owen and Zienkiewicz (1957) are limited only to weak
shear flows. Non-uniformity of the grid-generated
turbulent field limits the maximum solidity to about 0.4 ~
0.5 and the maximum shear parameter (λ h/U) to 0.45.
The restriction on the maximum solidity limits the
attainable maximum mean shear and, consequently, the
usefulness of a grid-produced flow of more intensely
JGPP Vol.6, No. 2
18
sheared flow.
To have stronger secondary flows in a cascade, the
near wall velocities should be as small as possible. With
higher mean velocity and large height of the test section,
one has to use aggressive values of shear parameter with workable size of the rods. Initially, using
the Eqn. (1), attempts were made to design a wire grid of SWG 9
(3.175 mm) and 20 (0.914 mm). An initial tension (pull) was
required to maintain the wires parallel to each other. However, this
was not successful as these wires were susceptible to yielding under
initial tension. Therefore, rods of 5 mm diameter were chosen.
After initial trial and error attempts, shear parameter as large as 1.2
and a grid resistance (K0) around 7 across the grid was achieved.
The distribution of the solidity up to the mid-span was then adjusted
to have a nearly uniform shear flow with lower velocity near the
endwall as shown in Fig. 2. The applied distribution of rods to the
experiments aided in achieving a strong shear flow unlike the
earlier published work that was limited to weak shear flow due to
non-uniformity of the grid generated turbulent field.
Fig 2 Grid solidity distribution, based on the analysis of Owen and
Zienkiewicz (1957)
EXPERIMENTAL SET-UP The experimental investigations were carried out in a low
speed, open circuit, cascade wind tunnel, shown in Fig. 3. A 55 kW
centrifugal blower to provide uniform flow at the inlet of test
section powers the facility. The test section is a rectangular duct of
cross section 690 mm x 150 mm to accommodate eight NACA65
(10)08 blades. The cascade arrangement along with the grid of rods
in the test section is shown in Fig. 4. The cascade parameters are
summarized in Table 1. The cascade was operated at a Reynolds
number of 2.1x105, based on the blade chord. A minor variation in
the inlet mean velocity of the approximate 0.5% was found at mid
span along the pitch-wise direction.
Fig. 3 Schematic diagram of open circuit cascade wind tunnel
TABLE 1. Specification of the cascade.
Chord length (C) 115 mm
Stagger ( ) 300
Solidity (C/s) 1.51
Aspect ratio (H/C) 1.3
Blade inlet angle ('β1
) 460
Blade outlet angle ('β2
) 7.50
Reynolds number 2.1x105
Fig. 4 Plan-view of the wind tunnel test section with shear
generator upstream of a cascade.
INSTRUMENTATION To acquire detailed information of the static pressure
distribution, a large number of pressure ports were provided on the
blade surface. Sixteen pressure taps of 2 mm diameter running
along the span, were embedded on the two blades forming the
central flow passage. On each surface of interest, 12 rows of ports
were internally connected to the pressure taps. The first row of
ports was 6 mm away from endwall, while the others were spaced 5
mm apart and the last row was located at the mid-span. The markers
in the Cp contour plots, discussed later in section 5.2.1, indicate
these measuring locations. This arrangement had a total of 192 taps
on the pressure surface and the suction surface. The static pressures
of each row, by masking remaining rows, were picked up by a 16
channel pressure transducer (from M/s Scanivalve Corp, USA).
The raw data was acquired and processed using the DSALINK©
software provided along with scanivalve. The total pressure
distribution and velocity vectors in the wake was measured using a
7 hole conical probe (from M/s Aeroprobe Inc, USA) placed at 24%
of the chord length behind the trailing edge of the cascade blades.
The diameter of the probe head was 3.2mm. At the inlet, located
one chord ahead of the leading edge of the cascade, the 7-hole
probe picked up velocity and static pressure. The estimated
uncertainty of the pressure measurements on the blade surface was
about 1% in static pressure coefficient values.
The endwall loss is obtained by subtracting the total pressure
loss at a location from that at the mid span. The pitch averaged
outlet flow angle at the midspan is taken as the reference outlet flow
angle for determining the secondary flow vectors. The secondary
flow vectors are non- dimensionalised with the inlet mean velocity.
COMPUTATIONAL STUDY To get a better insight of the effect of the inlet shear flow
(generated by the array of rods) on the cascade, a detailed
numerical analysis using ANSYS Fluent© was carried out. The
experimentally measured velocity profile was prescribed at the inlet
of the domain.
JGPP Vol.6, No. 2
19
Fig. 5 Plan-view of the multi-block structured mesh with the ‘O’
grid around the airfoil
x/C
Cp
0 0.2 0.4 0.6 0.8 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
ExperimentCFD
(a) z/H= 50 %, mid-span
x/C
Cp
0 0.2 0.4 0.6 0.8 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
ExperimentCFD
(b) z/H=4%, near endwall
Fig. 6 Cp on blade surface with experiment and CFD at i = 00
A multi-block structured mesh with ‘O’ grid attached to the
airfoil was generated using the grid generator, GAMBIT© and is
shown in the Fig. 5. A grid insensitivity analysis was carried out to
234
56 6
7 78
9
x/C
y/S
0 0.2 0.4 0.6 0.8 100.20.40.60.8
11.21.41.6
P.S
S.S
a) Experiment
34
56 67
77
8
8
9
9
x/C
y/S
0 0.2 0.4 0.6 0.8 100.20.40.60.8
11.21.41.6 b) CFD
P.S
S.S
LevelCp0:
1-0.43
2-0.34
3-0.25
4-0.17
5-0.08
60.01
70.10
80.18
90.27
100.36Cp
Fig. 7 Contours of Cp on endwall between the experiment and CFD
at i = 00
study the effect of different grid sizes on the cascade performance.
Based on this study, a mesh size of about 2.4 million was finalized.
This mesh was refined near the wall to capture the viscous effects
adequately. The y+ corresponding to this case was about 2.0. The
steady-state flow solution was achieved using κ-ω SST turbulence
model. To yield better accuracy by reducing numerical diffusion, a
third order MUSCL discretization was employed. SIMPLEX
method is used for pressure velocity coupling. For convergence of
the scaled residuals to 10-6 for all the equations, approximately
4000 iterations were required.
VALIDATION OF THE CFD WITH EXPERIMENTAL DATA
Comparisons of CFD and experiment with uniform flow at the
inlet, in terms of static pressure coefficients on the blade surface
and the endwall were carried out. The static pressure coefficients of
the blade surface at the mid-span and close to the endwall are as
shown in Fig. 6. At the mid-span, the CFD results agree closely
with the pressure distribution from the experiments. It obviously
indicates that numerical modeling with the prescribed boundary
conditions is reliable. Near the endwall, CFD model’s prediction of
the pressure distribution on the blade surface is poor. This may be
due to CFD model’s limitation to account for three-dimensional
separations induced by secondary flow and boundary layers of the
blade and the endwall. The other possible explanation for this
discrepancy could be the fabrication errors that might have altered
the flow conditions close to blade surface in the experiments.
The close agreement of Cp on the endwall between CFD and
experiment is shown in Fig. 7. As the ports on the endwall were
away from blade surface, influence of corner vortex is partly
captured.
RESULTS AND DISCUSSION
Shear Profile Generation The solidity distribution obtained from the shear flow theory,
generated a nearly stable velocity profile, but with considerable
velocity near the walls. To achieve maximum shear from the
available flow energy at the inlet, the velocity near the wall should
be as minimum as possible. Therefore, the spaces between the rods
were adjusted by reducing the gap between the endwall and the first
rod, and then fitting a smooth second order trend line. The resulting
velocity profiles generated downstream of the shear generator at
different axial locations, for i=±60, are shown in Fig. 8. The
measurement locations are with respect to the coordinates system
shown in Fig. 1. The velocity components u, v and w are along the
‘x’, ‘y’, and ‘z’ directions respectively. To check any variations in
the velocity profile along ‘y’ direction, the measurement was done
at y/s=±0.277 so that nearly a two-dimensional flow is generated in
an ‘x-z’ plane. As the flow proceeds downstream of the shear
generator, the peak axial velocity is reduced by the shear stress
produced from the resistance grading of the shear generator. The
turbulence produced by the small-scale shear between the
consecutive jets and wakes of the rods, increases the interaction
between the near wall flow region and the free stream flow. This
increases the mean velocity in the region near the endwall, as can be
seen in Fig. 8a. The overall effect is the reduction of the shear rate
in the downstream regions. Grid generated turbulence decays
downstream under the influence of the shear stresses. Thus, the
velocity field has a nature of self-preserving development of a
turbulent flow. The rate of profile decay is a function of the rod size.
Smaller the size of the rods, the more stable is the velocity profile.
However, fabrication of such a shear generator is very difficult.
There is, therefore, a compromise has to be made between the grid
size and the profile stability.
Among the lateral components, ‘z’ velocity variation along the
span of the grid is higher as seen in Fig. 8(c). This is because the
fluid under shear, on account of its reduced velocity in the
x-direction, readily acquires a motion in the z-direction in response
to the pressure gradient than the faster-moving fluid in the main
stream. Once a lateral flow is well established in the boundary
JGPP Vol.6, No. 2
20
layers, a compensating flow must appear in the main stream in
order to preserve continuity, which would occur under stable flow
z/Z
u/U
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6 x/h = 2.67x/h = 4.67, y/s = +0.277x/h = 4.67, y/s = - 0.277x/h = 7.88
( h)/U = 1.219
(a)
z/Z
v/U
0 0.2 0.4 0.6 0.8 1-0.1
-0.05
0
0.05
0.1 x/h = 2.67x/h = 4.67, y/s = +0.277x/h = 4.67, y/s = - 0.277x/h = 7.88
(b)
z/Z
w/U
0 0.2 0.4 0.6 0.8 1-0.05
0
0.05
0.1
0.15
0.2
0.25x/h = 2.67x/h = 4.67, y/s = +0.277x/h = 4.67, y/s = - 0.277x/h = 7.88
(c)
Fig. 8 Span-wise variation of velocity components for ±60,
downstream of the plane of rods
conditions. In general, the velocity profile decays very slowly in the
interested region (with respect to the cascade test section)
downstream of the grid. Figure 8 shows that the magnitude of the
shear parameter (λh/U=1.219) obtained through experimentation is
close to the designed value. This indicates that a stable and strong
shear flows can be generated using a planar grid of rods.
Effect of Shear Flow on the Cascade Cascade performance parameters like blade loading, wake loss
etc. are greatly influenced by the incidence angle, as the apparent
camber or the flow turning angle changes with incidence.
Consequently, the flow physics gets affected. It was therefore
decided to evaluate the overall performance of the cascade, in the
incidence angle range of ± 60.
Static Pressure Distribution On Blade Surface The span-wise distribution and the contours of surface static
pressure on the blade at different incidences are shown in Fig. 9.
The left column shows the Cp distribution on the pressure surface
and right column shows on the suction surface. The shear-imposed
flow with boundary layer interaction renders minor variation of Cp
on the pressure surface at small incidences. However, on the
suction surface, the zones of low-pressure regions from the leading
edge to the trailing edge can be observed. With shear flow, the
dynamic pressure varies along the span. Since drag is a function of
the square of velocity, the span wise fluid layers towards the
midspan will experience relatively larger flow resistance from the
blade surface compared to those away from the midspan. Therefore,
any reduction in the dynamic pressure would correspond to a
proportional rise in the static pressure for the available total
pressure. This does not happen with uniform flow as the velocity is
almost constant along the span and the span wise static pressure
remains nearly invariant. In addition, the secondary flow that
prevails near the wall region carries fluid layers partly away from
the pressure surface towards the suction surface, (which is
discussed in the subsequent section), contributes to the drop in
static pressure on the pressure surface. Further, the total pressure is
one of the factors that influence the blade loading. It increases away
from the endwall in a shear flow. Therefore, the Cp on the blade
surface is higher for the locations away from the endwall. Since the
flow is sensitive to the curvature of the surface, the static pressure
rises on the concave surface. On the other hand, the static pressure
reduces on the suction surface. In the NACA65 (10)08 blade with
a=1, the pressure surface is relatively flat and in the operating range
of incidence, adverse pressure gradient on the suction surface
becomes severe. Near the pressure surface, the flow moves slowly
downstream from the stagnation point and then it is carried by the
accelerating flow from the leading edge of the suction surface and
the passage and later decelerates due to diffusion. As a result, the
pressure surface shows higher Cp towards the leading edge and
trailing edge of the blade. Near the leading edge, on the suction
surface, the contours are relatively denser than the rest of the
surface indicating rapid acceleration and subsequent gradual
deceleration of the flow. On the contrary, static pressure decreases,
rapidly and then gradually rises owing to diffusion in the later part
of the flow passage. Local dynamic pressure is influenced by the
curvature of the blade surface negotiated by the fluid stream and the
drag, which in turn gets affected by the incidence. As the incidence
increases, the static pressure, which is proportional to the local
dynamic pressure, rises on the pressure surface and reduces on the
suction rises along the span. The slope of the Cp contours depends
on the incidence and the shear rate of the flow at inlet. From the Fig.
9, it is observed that the slope of the contours on the suction surface
increases with the increase in the incidence, and increases on
pressure surface. This effect may be due to the local resultant
dynamic pressure influenced by the factors mentioned earlier.
7
x/C
z/H
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5L.E P.S T.E
6
67
x/C
z/H
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5L.E S.S T.E
i= - 60
8
8
x/C
z/H
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5L.E P.S T.E
4
5 6
6
7
7
x/C
z/H
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5L.E S.S T.E
i= 00
8
8
8
8
9
x/C
z/H
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5L.E P.S T.E
2
345
6
6
7
7
x/C
z/H
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5L.E S.S T.E
i= 60
x/C
z/H
0 0.2 0.4 0.6 0.8 100.10.20.30.40.5
LevelCp:
1-1.9
2-1.6
3-1.3
4-1.0
5-0.7
6-0.3
7-0.0
80.3
90.6
100.9
Fig. 9 Distributions of the static pressure coefficient on the blade
JGPP Vol.6, No. 2
21
surface for inlet shear flow, at different incidence angle
Surface Static Pressure - Endwall The pressure coefficients on the end wall at different
incidences are shown in Fig. 10. The region of flow acceleration
and deceleration shrinks and shift towards the leading edge with
increase in the incidence. This is also indicated by the Cp contours
on the suction surface. With increased incidences, the pitch wise
pressure gradient rises and encourages secondary flow near the
endwall. This leads to the separation point shifting towards the
leading edge. Static pressure ratio between the outlet and the inlet
on the suction surface side rises considerably compared to the
pressure surface side. This indicates that the pressure surface being
nearly flat, has relatively less contribution towards the rise in static
pressure.
The magnitude of the secondary flow depends on the balance
between the forces due to the pitch wise pressure gradient and the
inertia of the flow. As the incidence increases, the flow has to
negotiate a longer path owing to the apparent increase in the turning
angle by utilizing its energy. Therefore, the pitch wise pressure
gradient rises adequately relative to the inertia of the flow that leads
to stronger secondary flows. With increase in the incidence, in the
corner region formed by the endwall and the blade suction surface,
the static pressure contours retreat. This indicates the influence of
corner stall formed by the interaction of secondary flows and the
boundary layers of the blade and the endwall. The corner vortex
thus formed, siphons out the energy from the passage flow and
dissipates it. Therefore, the secondary flow not only forms a flow
blockage, but also contributes to loss mechanisms.
5 5
6 6
6
7
x/C
y/S
0 0.2 0.4 0.6 0.8 100.20.40.60.8
11.21.41.6
T.EL.E
S.S
P.S
5
6 6 6
77 7
7
8
x/C
y/S
0 0.2 0.4 0.6 0.8 100.20.40.60.8
11.21.41.6
T.EL.E
S.S
P.S
i= - 60 i = 00
34
56 6
7 78
8 8
99
x/C
y/S
0 0.2 0.4 0.6 0.8 100.20.40.60.8
11.21.41.6
T.EL.E
S.S
P.S
6 8
x/C
y/S
0 0.2 0.4 0.6 0.8 100.20.40.60.811.21.41.6LevelCp:
1-0.3
2-0.2
3-0.1
4-0.1
50.0
60.1
70.2
80.2
90.3
100.4
S.S
i= 60
Fig. 10 Contours of Cp on the endwall with shear flow at the inlet
4
4
5 5
56
6
6
67
7
7
78
8
8
89
9
9
910
10
1010
y/S
z/H
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5P.S S.S
4 45 5
5
6
6
6
6
7
7
7
7
7
8
8
8
8
8
9
9
9
910
10
10
y/S
z/H
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5P.S S.S
3
44
5
5
5
5
6
6
6
6
7
7
7
78
8
8
8
9
9
9
910 10
y/S
z/H
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5P.S S.S
i= - 60 i = -30 i = 00
2 23
3
4
4
4
5
5
5
5
66
6
7
7
7
7
7
8
8
8
8
89
9 9
9
y/S
z/H
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5P.S S.S
4
45 5
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
y/S
z/H
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5P.S S.S
8
L e v e l
w :
1-0 .6
2-0 .4
3-0 .3
4-0 .1
50 .0
60 .2
70 .3
80 .5
90 .6
1 00 .8
P .S
C :p 0 i = 30 i = 60
Fig. 11 Contours of total pressure loss coefficient at 24% chord downstream from trailing edge at different incidence angle
JGPP Vol.6, No. 2
22
z/H
0 0.4 0.80
0.1
0.2
0.3
0.4
0.5 Uf i = 0Sf i =- 6Sf i =- 3Sf i = 0Sf i = 3Sf i = 6
Midspan
Endwall
i
e
(a)
D e v ia tio n fro m m id s p a n flo w
z/H
-1 5 -1 2 -9 -6 -3 0 3 6 9
0 .1
0 .2
0 .3
0 .4
0 .5
U f, i= 0S f, i= -6S f, i= -3S f, i= 0S f, i= 3S f, i= 6
P SS S
i
(b )
Fig. 12 Mass averaged: - a) endwall loss and b) deviation from the
midspan flow, along the span
Total Pressure Loss, Endwall Loss And Flow Deviation wrt
Reference Outlet Flow Angle In The Wake
The contours of the exit total pressure loss coefficient
superimposed by the secondary vectors in the wake of the blades
for different incidences are shown in Fig. 11. With shear flow at
the inlet, it is expected that a rise in total pressure loss would occur
with increase in the incidence as in the case of uniform flow. In
contrast, the contours of the total pressure loss indicate decrease in
the loss with increase in incidence, where as secondary flow
increases, but less intensely. This behavior can be attributed to the
significant turbulence generated by the planar grid of rods that
promotes intense mixing between the layers. Consequently, the
peak loss is alleviated and redistribution of loss occurs. With
increase in the incidence, the passage vortex becomes stronger and
The span-wise variation of the endwall loss and the flow
deviation from the midspan flow is shown in Fig. 12. With a shear
flow at the inlet, it is expected that a rise in endwall loss would
i (deg.)-6 -3 0 3 60
0.1
0.2
0.3
SF
UF
Cp
0
(a)
i (deg.)
Cp
-6 -3 0 3 60
0.1
0.2
0.3
0.4
SF
UF
(b)
i (deg.)
(de
g.)
-6 -3 0 3 620
25
30
35
SF
UF
(c)
2
i (deg.)
SK
E%
-6 -3 0 3 60
0.5
1
1.5
2
2.5
3
SF
UF
(d)
Fig. 13 Overall effects in the wake, with reference to incidence,
UF- uniform flow, SF-shear flow
occur in proportion to the incidence angle as in the case of uniform
flow. In contrast, the endwall loss contours show an opposite trend,
where as secondary flow is enhanced. This behavior can be
attributed to the significant turbulence generated by the flow as it
travels through the blade passage. The net intensity of turbulence
can be considered as the resultant of the grid generated turbulence
and the turbulence generated by the instability of shear stress
between the layers of shear flow while negotiating the flow path.
The secondary flow is influenced by the blade loading and
becomes stronger at higher incidence angle. Therefore, later
component of turbulence is relatively more intense for higher
incidences. The flow path to be negotiated by the shear flow
increases with the incidence angle. The low energy fluid in the
near wall region can negotiate the curvature of the path more
easily as compared to the flow away from the wall due to inertia.
However while doing so it also spends energy resulting in a
relatively slow moving chunk of fluid i.e. stalling zone. This in
combination with secondary flow induces the instability of the
shear stress between the fluid layers that manifest into second
intensity of resultant turbulence promotes mixing. As the flow
proceeds downstream the mixing process energizes the fluid in the
region close to the wall. Therefore the endwall loss reduces with
the increase in incidence angle. Since the endwall effects are
stronger in a shear flow conditions, the endwall loss is
considerable compared to uniform flow.
The strength of secondary flow is indicated by the
overturning cause in the near wall regions as shown in the Fig. 12b.
It appears that the influence of secondary flow is in 20% of the
span and becomes more intense with increase in incidence. This is
obvious as the blade loading, which influences the secondary flow,
increases with the rise in the incidence angle. Since the flow is
three dimensionally complex, under the influence of shear flow,
turbulence and secondary flow, for which the deviation trend
seems random in nature near midspan and appears to be nearly
sinusoidal along the span.
Overall Effect In The Wake The effect of intense shear flow on the blade and in the wake
were detailed in previous sections it is interesting to know, in
comparison with uniform flow, the gross effects in terms of
secondary kinetic energy, coefficient of total pressure loss,
coefficient of static pressure and exit flow angle with respect to
incidence angle.
As seen from the Fig. 13(a), with the increase in the incidence
of uniform flow, the rise in total pressure loss is small compared to
inlet shear flow. This occurs due to the tendency to the flow
separation from the suction surface owning to the increase in
apparent turning angle. It is expected to have the same behavior of
Cp0 with the intense shear flow but it is observed that the trend of
Cp0 is opposite to that with the uniform flow accompanied with
large magnitudes. This attributes to the turbulence produced by the
shear flow generator and the shear effect that promotes rapid
mixing. Higher turbulence delays the flow separation on the
suction surface by initiating early transition
of the wall boundary layers. Further the flow profile decays
gradually downstream that increase the momentum in the near
wall regions. The stall region formed near the trailing edge of the
suction surface is energized and therefore the resulting effect is the
reduction of loss with increase in incidence angle.
The coefficient of static pressure, as seen in Fig.13 (b), improves
with the incidence angle, irrespective of the inflow conditions.
This occurs owning to the increased blade loading with the flow
incidence. Since losses with the shear flow are higher in
comparison to uniform flow, therefore the corresponding pressure
rise is lower.
Similarly, the exit flow angle and secondary kinetic energy,
refer Fig.13 (c)-(d), exhibit the trend of Cp. However, the exit flow
angle is a function of incidence angle and deviation angle. The
enhanced secondary flows due to shear effect lowers the
magnitude of exit flow angle and increases the secondary kinetic
energy with inlet shear flow.
Wake -Secondary Flow Structure The critical point theory is a technique used to analyze the
flow structure near the wall surfaces to know the flow separation,
attachment and other 3D flow features. In this paper, this
technique is applied to the streamlines on a plane far away from
the wall surfaces to understand the complex flow structure using
streamlines only. The combined influence of shear effect,
JGPP Vol.6, No. 2
23
turbulence intensity and incidence angle makes the secondary
flow structure complicated. Therefore, it is interesting to
understand the secondary flow structure using critical point
analysis.
Figure 14 shows the variation of the secondary flow
structure with respect to incidence angle. At incidence angle of -60,
the saddle point ‘C1’ appears at 40% of pitch close to the endwall
and it connects the separation node ‘N1’ through a separating line
‘S1’. The node ‘N1’ is close to ‘C1’ and away from the midspan
region. This indicates that the flow in the wake is three
dimensional with a stable ‘N1’node. The separation lines prevent
the streamlines of the respective side from intersecting. This also
conveys that the vortex core is closer to the endwall region. At
incidence of 0o, the point ‘C1’ slightly moves leftwards and ‘N1’
toward the midspan. This attributes to the tendency of the
secondary flow to under-turn the flow at higher incidence and
lifting up of loss core away from the endwall region. An additional
separation node ‘N2’ appears. In critical point theory, since two
similar nodes cannot connect each other and therefore an
additional point ‘C2’ connects them through a separation lines
‘S2’ and ‘S3’ respectively. Further, at incidence at +6o, only the
node ‘N1’ and point ‘C1’ exits. Now the node ‘N1’ has slightly
moved towards the right side where as ‘C1’ continues to shift
y/S
z/H
0 0.2 0.4 0.6 0.8
0.1
0.2
0.3
0.4
P.S S.S
S1
C1
N1
(a)
y/Sz/H
0 0.2 0.4 0.6 0.8
0.1
0.2
0.3
0.4
P.S S.S
S1
N1
C1
N2
S3
S2
C2
(b)
y/S
z/H
0 0.2 0.4 0.6 0.8
0.1
0.2
0.3
0.4
P.S S.S
S1
N1
C1
(c)
i = - 60 i = 00 i = 60
Fig.14 Experimentally determined stream lines of secondary flow in the wake, normal to the exit flow angle, with SF at i = -6,0 and 6 degrees
a) With uniform flow
b) With shear flow
z/H = 0.04 and 0.5 z/H = 0.1 and 0.3 z/H = 0.1 , 0.3 and 0.5
Wake view Pitchwise view
C p 0 : 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0Tu rb . in te n s ity % :
Fig.15 Path lines superimposed with turbulence intensity, as predicted by CFD, in the wake and in the pitch wise view at different span wise
location
JGPP Vol.6, No. 2
24
leftward and towards the endwall. The combined effect of higher
intensity of turbulence and downstream decay of shear flow
alleviates the net loss and the flow appears to be less complicated
compared to 0o incidence. Hence, additional critical points ‘N2’
and ‘C2’ disappear.
Passage Flow Behavior The conventional instrumentation makes it difficult to probe
into the passage of the blades and the intrusive methods would
affect the flow. Therefore, CFD was used to explore the flow
structure along the passage. Comparison of the streamlines at
different positions along the span, with uniform flow and shear
flow are shown in Fig. 15. The static pressure in the region near
the wall is proportional to the local dynamic pressure evolved
under the influence of the inlet shear rate, curvature of the blade
surface and the drag. In the case of shear flow, the fluid layers near
the endwall are dominated by the pitch wise pressure gradient and
are deflected towards the suction surface. Secondary flow
encounters the boundary layers of the blade surface and suffers
further deceleration. Consequently, the rise in static pressure is
relatively higher compared to the flow away from the endwall,
which has higher inertia and is less influenced by the pitch wise
pressure gradient. As a result, the near wall flow, marked as ‘AB’,
climbs up on the suction surface. Further it pickups up the energy
from neighboring flow by the exchange of momentum and
undergoes a twist of 90o as indicated by ‘A1B1’ in Fig. 15. On the
pressure surface, with higher energy of the flow and a minor
variation of static pressure along the span, the fluid layers away
from the endwall would respond rapidly than those closer to the
endwall. Therefore, near the pressure surface, as the flow closer to
the endwall moves away from the pressure surface, the flow from
relatively higher span moves toward the endwall region to
maintain continuity. Streamlines in the pitch wise view on to the
suction surface and pressure surface clearly indicates the
magnitude of movement towards and away from the endwall.
In spite of the low camber of the blade, shear flow at the inlet
results in a complex three-dimensional flow in the passage.
Therefore, in the secondary flow definition, one has to choose the
primary or reference flow direction and carefully resolve velocity
vectors to obtain the secondary vectors. For an airfoil, a minimum
inlet velocity results in the lowest loss due to separation on the
suction surface of the blade. With shear flow, the total pressure and
velocity varies along the span. The separation point moves
towards the trailing edge with the position away from endwall. In
the region near the endwall, the flow is dominated by the pitch
wise pressure gradient. Along the span and away from the endwall,
the dynamic head counters the pressure gradient and promotes
delay in separation on suction surface, thereby reducing the
corresponding losses.
CONCLUSIONS In this paper, the effect of a prescribed shear flow on the flow
structures in an axial flow compressor cascade. A NACA65 series
blade with a relatively low camber was used for the compressor
cascade. The shear flow was generated in the test section of. Both
numerical and experimental approaches were used to understand
the flow physics through the compressor cascade under inflow
shear. The computational results of the cascade were compared
with the available measured data. The following conclusions can
be drawn from this study:
Profile decay downstream of the shear flow generator
can be controlled by choosing low resistance wire
gauges or rods provided the wires remain parallel to
each other without yielding.
Fluid layers near the endwall are turned through 900 by
the flow passage under the influence of shear flow at the
inlet.
Majority of the blade loading occurs towards the
midspan region due to the presence of relatively higher
energy fluid.
The grid generated turbulence reduces the endwall loss
with the increase in incidence angle.
The trend of static pressure coefficient, yaw angle and
the secondary kinetic energy in the wake with respect to
the incidence angle is similar to uniform flow case but
with an offset.
Secondary flows were successfully induced in a low
cambered compressor cascade using shear flow at the
inlet. This would aid in designing and evaluating
different control mechanisms to alleviate secondary
flows and the associated losses in a low speed
applications.
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