EFFECT OF A NEW VORTEX GENERATOR ON THE … · BASELINE COMPRESSOR CASCADE In the present work, a...
Transcript of EFFECT OF A NEW VORTEX GENERATOR ON THE … · BASELINE COMPRESSOR CASCADE In the present work, a...
Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition
IMECE2015
November 13-19, 2015, Houston, Texas, USA
IMECE2015-52293
EFFECT OF A NEW VORTEX GENERATOR ON THE PERFORMANCE OF AN
AXIAL COMPRESSOR CASCADE AT DESIGN AND OFF-DESIGN CONDITIONS
Ahmed M. Diaa Assiut University
Assiut, Egypt [email protected]
Mohammed F. El- Dosoky Assiut University
Assiut, Egypt [email protected]
Mahmoud A. Ahmed Assiut University
Assiut, Egypt [email protected]
Omar E. Abdelhafez Assiut University
Assiut, Egypt [email protected]
ABSTRACT Secondary flows are noxious to axial compressor
performance. To overcome and control those secondary flows,
vortex generators are used as a passive control device.
Controlling secondary flows will lead to a further improvements
in the compressor performance. A new design of vortex
generator is considered in this investigation in order to control
secondary flows in axial compressor cascade at design and off-
design conditions. Numerical simulations of a three-
dimensional compressible turbulent flow have been performed
to explore the effect of the vortex generators on the reduction of
secondary flows. Six different incidence angles are used for the
off-design operation investigations. Based on the simulation
results, the pressure, velocity, and streamline are used to follow
up the development of the secondary flows. Thence, total
pressure loss coefficient, static pressure rise coefficient,
difference in flow deflection angle, and diffusion factor are
estimated. Results indicate that vortex generators have a
significant effect on the development of secondary flows at off
design operation as they cause a reduction in total pressure loss,
they also affect the loading behavior of the cascade as they
cause a slight change in the cascade deflection, and a slight
decrease in the diffusion factor which causes unloading of the
blade. Static pressure rise is significantly reduced at negative
incidence angles while a slight reduction occurs at positive
incidence angles. In a word, the new design of the vortex
generator enhances the cascade aerodynamic performance and
enlarges the operating range of the cascade towards the positive
incidence region.
INTRODUCTION Axial compressor gains importance because of its
relevance to gas turbine applications in military and commercial
airplanes and its usage in stationary power generation.
Therefore, early researches have been carried out to enhance its
overall performance. The secondary flows have noxious effects
on the axial flow compressor due to extract energy from the
working fluid and increase the flow instability. Therefore,
controlling secondary flows will extremely improve the
aerodynamic performance of the compressor. The components
of the secondary flow in the axial compressor are the endwall
boundary layer separation, the horseshoe vortex, the corner
vortex, the tip vortex, the endwall crossflow, and the passage
vortex. Since the early 1950s, numerous researches were carried
out [1–9] to investigate secondary flow phenomena. These
investigations played a decisive role in improving the
compressor performance. Recently, many researchers
investigated the impact of the three-dimensional blades and
their endwall boundary layer separation as well as flow
separation in the corners of the blade passages on the
development of the secondary flows [10-12]. In pursuit of
controlling secondary flows, both passive and active methods
have been utilized to reduce or overcome the effects of
secondary flows in axial compressors. Passive control methods
remain the preferable as simple and inexpensive techniques
[13,14]. Different configurations of passive flow control
devices were used and investigated such as slotted blading in
linear cascades [15], vane and plow vortex generators placed on
several positions [16], counter rotating and co-rotating
rectangular, triangular, and parabolic vane type vortex
generators [17–19], cavity as a control of shock wave
interactions with the turbulent boundary layer [20], low profile
vortex generators to reduce the boundary layer thickness [21],
and doublet vortex generators [22]. An extensive review of
boundary-layer flow-separation control by micro vortex
generators (low profile vortex generators) had been compiled as
reported in references [23-24]. Low profile vortex generators
are used to energize the low momentum flow near the wall
surface without energy expenditure during the momentum
transfer from the free-stream flow to the near wall region. Yet,
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this leads to an overwhelmed stronger adverse pressure gradient
and therefore avoids or delays the flow separation. In case of
turbulent flow over a flat plate, experimental results indicated
that the vane and wheeler type of vortex generators can
efficiently reduce the flow separation. Using the vortex
generator height (h/δ) of 0.1 to 0.4 was fairly efficient with
much reduction in the drag effect [25]. Furthermore, vane type
with height (h/δ) of 0.8 achieved the largest pressure recovery
[26]. An experimental comparison between two passive
methods for controlling shock induced separation on a turbulent
flat plate boundary layer was carried out by McCormick [22]. A
doublet wedge type vortex generator with h/δ=0.36 was used
versus passive cavity (porous wall with a shallow Cavity
underneath). It is reported that the low profile vortex generators
were found to be significantly suppressing the shock induced
separation and improve the boundary layer characteristics
downstream the shock whereas the mass-averaged total pressure
loss reduction increased.
Recently, experimental and numerical studies of the
effect of two vortex generator types with different
configurations on the performance of the compressor cascade
were conducted by Hergt et al. [27]. They concluded that using
different types of vortex generators results in significant
reduction in cascade losses and loading, which in turn shifts the
compressor operating range towards higher positive incidence
angle. They also achieved a total pressure loss reduction by 9%
at design operation. Moreover, vortex generators have a
significant effect on the cascade deflection and a remarkable
enhancement of the cascade stall range. However the static
pressure rise due to inserting a vortex generator was nearly
unaffected. Diaa et al [28-29] have investigated the effect of the
curved side vortex generators as a control device with axial
compressor cascade, they reported a reduction of total pressure
loss of 12%.
Based on the literature survey of the research work related to
the current subject, the suggested curved surface design of
vortex generator is inspired from Wheeler's doublet VG [30]
that was used in several applications on flat plates. It was found
that using doublet VG significantly enhances the mixing process
between the low and high momentum streams. In addition, the
total pressure recovery was found to be increased, and the onset
of separation was delayed or eliminated. Further modification
on the curved side VG design is added by including rounded
nose rather than sharp nose. The new design achieved the
highest total pressure recovery of about 20.7%. More details
can be found in the article.
NUMERICAL METHODOLOGY
BASELINE COMPRESSOR CASCADE In the present work, a linear high speed compressor
cascade that was reported by the research group of
Hergt et al. [24] is used. Their compressor cascade was
designed by “MTU Aero Engines” with the profile shown in
fig.1. The design parameters and the operating conditions of the
cascade are summarized in Table 1.
FIGURE 1 COMPRESSOR BLADE PROFILE.
TABLE 1 DESIGN PARAMETERS AND OPERATING
CONDITIONS
Mach number at inlet M1 = 0.66
Inlet flow angle β1=132°
Turning angle Δβ = 38°
Stagger Angle βst =105.2°
Blade chord C = 40 mm
Blade span L = 40 mm
Pitch to chord ratio s/c = 0.55
Endwall boundary layer thickness δ = 4 mm
Computational domain Computational domain and its boundaries are shown in fig.2.
The non-slip boundary condition is applied at the walls
representing the top boundary, the bottom boundary (Endwall),
and the blade surfaces demonstrating the suction and pressure
sides including the leading and trailing edges. Periodic
boundary conditions are applied on the domain sides. The
pressure outlet boundary condition is defined at the outlet plane.
Figure 2 Boundary conditions of the computational domain
(a top view showing inlet, outlet, blade suction and pressure surfaces, and periodic boundaries.
Fully developed flow is adopted at the inlet with an average
Mach number of 0.66, while the inlet flow angle is varied as
will be shown later.
3 Copyright © 2015 by ASME
Numerical solution The investigated numerical cases present the effect of the
vortex generators on the cascade performance at design and off-
design conditions. Therefore, six different sets of vortex
generators are investigated at six different incidence angles (i)
ranging from i=+6⁰ to i= - 6⁰ with step of 2⁰. Commercial
solver ANSYS FLUENT is used as a CFD tool to solve steady
Reynolds-averaged Navier Stokes fully coupled with transition
shear stress transformation (SST) turbulence model. The
transition SST model is used in this simulation because of its
ability to accurately capture the transition and separation flows.
Three-dimensional grid is constructed using structured mesh of
H-O-H topology as shown in fig.3.
FIGURE 3 THREE DIMENSIONAL MULTI-BLOCK MESH
WITH ENLARGED TOP VIEW OF THE MESHING AROUND THE BLADE AND TWO MAGNIFIED VIEWS OF MESHING
AROUND LEADING AND TRAILING EDGES.
In the present study several criteria are used to measure the
grid convergence. The first one is the grid independency tests
which are shown in Figs. 4, and 5.
Solution with grid independency is reached by testing four
different meh sizes ranging from 0.4 to 1.6 million cells. As
shown in fig.4. Solution with grid independency is reached at a
mesh of 0.8 million cells.
Figure 5 shows the grid convergence test using the velocity
contours at the exit plane. This test is carried out by using
different grid size starting with a coarse grid with 0.4 Million
cells up to a fine grid with 1.6 million cells. It is shown that the
values of velocity contours is not subjected to a significant
change beyond the 0.8 Million cells grid, and that is another reason to adopt this grid in the present simulation.
The second criteria is performed based on the value of
residual of different quantities to be less than or equal to 5.0E-
5. The last one is based on calculations of Grid Convergence
Index (GCI) as reported by Roache[31]. The GCI measures the
percentage of the deviation between the computed values and
the asymptotic values. It specifies the error band and how far
the solution is from the asymptotic value. Also, it shows how
much the solution would change with grid refinement. A small
value of GCI indicates that the computation is within the
asymptotic range. Therefore, Three different meshes with
195000, 420000, 826000 are selected to determine GCI. Table
2 shows the GCI values for axial velocity and static pressure.
For the axial velocity, the GCI is found to be 0.53% for the
highest grid size, in addition for the static pressure the CGI
value is 0.51% for the finest grid. Table 2 shows the calculation
of the GCI for different mesh size. As listed in Table 2,
successive grid refinement results in a reduction in GCI.
Therefore, the solution of the finest grid (826,000) cells is grid
independent.
Table 2: grid convergence index for static pressure and axial
velocity
GCI21 GCI32
Φ=static pressure 6.4% 0.51%
Φ=axial velocity 3.78% 0.53%
Figure 4 Mass averaged velocity at exit plane (located 40%
of chord length behind trailing edge) of different mesh size starting from 0.4 to 1.8 million cells.
Figure 5 velocity contour lines (m/s) at exit plane for
different grid sizes (0.4 – 1.6 Million cells).
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Therefore, the present simulation is performed using 0.8
million cells to get results that independent of the grid size and
to reduce the computational time. The minimum cell height
near the walls is adopted to have y+<1, which is considered to
capture and resolve the boundary layer at the blade surfaces and
enwalls.
To conclude, a new design of vortex generator (VG) is
inserted into the flow passage of a compressor blade cascade,
and its effect on the compressor cascade performance is
investigated for both design and off-design conditions. For the
off design conditions incidence angle will be varied from i= - 6⁰ to i= +6⁰ with step 2⁰.
The new VG is shown in fig.6. Two main configurations of
the new VG are investigated. First one is having a sharp edged
nose as shown in five stets A, B, C, D, and E with different
geometrical dimensions. The second configuration is set F
which has a rounded edge nose. Four different ratios of r/δ=
0.25, 0.5, 0.75 and 1.0 are investigated, but the only reported
results in this manuscript is the case with r/δ=0.5; since it
achieves the highest performance relative to the others. The six
different sets with different geometrical dimension ratios are
summarized in Table 3.
FIGURE 6 TWO CONFIGURATIONS OF THE NEW
VORTEX GENERATOR, (A) WITH SHARPED EDGE NOSE AND (B) WITH ROUNDED EDGE NOSE.
Table 3 Summary of vortex generators geometrical ratios
represented in set A, B, C, D, E and F.
Set h/δ w/h e/h r/δ
A
0.4
3
6 __ B 4
C 5
D
6 E 5
F 0.5
VALIDATION In order to validate the current results, a comparison with
Hergt's [27] results is performed. Isentropic Mach number
distribution on the blade profile at midspan is compared with
isentropic Mach number calculated from the experimental work
by Hergt [27] as shown in fig. 7. The Figure shows a good
qualitative and quantitative agreement with Hergt's results.
FIGURE 7 COMPARISON BETWEEN THE MEASURED
ISENTROPIC MACH NUMBER DISTRIBUTION [27] AND THE PRESENT SIMULATION.
Another validation comparison is carried out using the
mass-flow averaged spanwise pressure loss distribution of the
base case as shown in fig. 8. The figure shows a good
qualitative agreement with maximum deviation of 7% near the
bottom end wall.
FIGURE 8 COMPARISON BETWEEN THE TOTAL PRESSURE
LOSS DISTRIBUTION AT A PLANE LOCATED AT 40% OF CHORD LENGTH BEHIND THE TRAILING EDGE [27], AND
THE PRESENT SIMULATION.
RESULTS AND DISCUSSION In this section, the numerical results with vortex generators
at both design and off-design conditions are presented and
discussed.
In particular, The study focuses on the streamlines at blade
suction surface and other performance parameters such as, total
pressure loss coefficient, flow deflection angle, static pressure
5 Copyright © 2015 by ASME
rise coefficient, and diffusion factor which will clarify the effect
of VG on the cascade performance.
Effect of vortex generator on secondary flows In order to determine the separation lines, secondary flow
components such as the footprint of the propagation of the
passage, corner, and horseshoe vortices are considered. The
limiting streamlines on the blade suction surface are used to
trace the changes in the separation lines after using vortex
generator. In Fig.9, streamlines at blade suction surface with
and without vortex generators show the position of both the
separation lines, the attachment lines and the recirculation
volumes .
For base case without vortex generator, the passage vortex
is firstly separated from the endwall and then reattached to the
suction surface at AL1. The separation line SL1 indicates the
separation of the passage vortex from the suction surface
followed with reverse flow over the blade which is originated
near the midspan towards SL1, and then the flow is separated
from the blade surface by the passage vortex as mentioned
before. In addition, separation line SL2 indicates the separation
of the corner vortex along the blade suction surface, while AL2
shows the reattachment of the corner vortex with the blade
surface. For cases, where VGs are used, the vortex structure
inside the flow passage is affected by the two generated counter
rotating vortices.
For case A, SL1, and AL1 are both moved toward the
trailing edge which is an indicator for the deflection of the
passage vortex into the flow direction. This deflection is due to
one of the generated vortices near the suction side, also, SL2
and AL2 disappeared from the streamlines of this case. Reverse
flow on the blade surface is decreased for case A, as shown in
Fig. 8. As w/h increased for design B, no significant changes in
the position and distribution of the streamlines are identifiable.
Further increase in w/h, as in case C, causes a larger
deflection of the passage vortex which is indicted by the
movement of SL1 and AL1 downstream towards the trailing
edge. Reverse flow on the suction side is diminished.
Another increase in w/h for case D yields a disappearance
of SL1 and AL1, furthermore, the reverse flow also
disappeared, these changes due to increasing w/h are attributed
to a more strength generated vortex by inserting the VG.. In
addition, the movement of the separation lines also indicates to
an increase in stretching rate of the vortex control region with
higher w/h values. Streamlines behavior of case E is similar to
that caused by case F; therefore it is not reported here.
In case F with the rounded nose edge, separation and
attachment lines SL1 and AL1 are vanished. In addition, reverse
flow is noted on the blade surface.
On the top half of the blade surface, for base case a
circulation bubble CB is noticed in the upper and lower half
of the blade span. After using VG, a circulation bubble CB1 is
noticed on the upper half of the blade span suction surface. This
circulation bubble is formed by the interaction of the cross
flow driven by the adverse pressure gradient at the top wall
corners and midspan and the streamwise flow.
FIGURE 9 SKIN FRICTION LINES ON THE SUCTION
SURFACE FOR BASE CASE (WITHOUT VG) AND CASE A, B, C, D, AND F AT DESIGN OPERATION ( i=0 [deg.]).
Effect of vortex generator on total pressure loss
coefficient Total pressure loss coefficient (TPLC) is known as a
compressor performance parameter which is used to judge the
loss behavior of the flow. TPLC is calculated from the
following equation:
11
21 ),( ),(
st
tt
pp
zyppzyTPLC
(2)
Figure 10 shows local TPLC contours at exit plane (which
is located 40% of chord length downstream the trailing edge) at
design and off design. From this TPLC contours, it is clear that
at high negative and positive incidence angles (when i=-6 and
+6[deg.]) TPLC is increased when using VG in comparison
with the base cascade. By decreasing incidence angle to i=-4
6 Copyright © 2015 by ASME
and +4[deg.] a slight decrease in TPLC is noted in all cases
with VG compared with the base case. Further reduction in
TPLC is gained by decreasing the incidence angle to i=-2 and
+2[deg.].Therefore using VG will decrease the total pressure
loss over a range of incidence angles between i=-4⁰ to +4⁰. Total pressure loss factor (TPLF) represents the difference
of total pressure loss coefficient (between case with VG and the
base case) normalized by the total pressure loss coefficient of
the base case as stated in equation 3. To calculate the TPLF, the
local value of TPLC(y,z) in equation 2 is integrated in the
spanwise direction and pitch wise directions for base and all
VG cases.
Base
BaseVG
TPLC
TPLCTPLCT
PLF (3)
Figure 10 TPLC contours measured at exit plane (located
at 40% of chord length behind trailing edge) at incidence angles i=-6, +4,-2, +2, +4, and +6 [deg.] for Base, D, E and F
cases.
Figure 11 shows the TPLF for all cases. At design
condition, for cases A to D, where β1=132 deg., it is noticeable
that by increasing w/h the TPLF is reduced which indicates a
reduction in the total pressure loss in comparison with the base
case. This is due to the increase of the stretching rate of the
generated vortices. The TPLF ranges from -5.3% to -12.6 % for
case A and D respectively. For case E a further reduction in
TPLF is attained with value of -18.6 %.The highest reduction is
reached using case F with rounded nose edge, where the TPLF
value is- 20.7%.
Figure 11 Total pressure loss factor with different incidence
angles for set A, B, C, D, E, and F[%]
At off-design condition, it is clear that TPLF increases with
the increase of incidence angle, for negative incidence angle
i=-6 deg. (β1=126 deg.) there is no reduction in total pressure
loss attained in all cases, instead an increase in the total
pressure loss is achieved by using vortex generator relative to
the base case. At negative incidence angles, the two generated
vortices will not have the same strength as at design condition.
The pressure side generated vortex is strong, but the suction
side generated vortex is far too weak. This non-symmetric
strength of the two generated vortices will cause an opposed
effect on losses reduction, since the weaker vortex will not be
able to mix low and high momentum flows properly. By
decreasing the incidence angle to i= - 4 where β1=128 deg., the
non-symmetric strength still exists but with smaller difference
between the generated vortices, and this is the reason why TPLF
is slightly reduced at this operating point. Furthermore at i= -2
β1=130 deg. TPLF is further reduced for all cases, the highest
reduction is reached at case E with value of -12.3 %.
At positive incidence angles the effect is reversed where
the suction side generated vortex is stronger than that of the
pressure side . TPLF is increased for all cases at i=+2 where
β1=134 deg., and the uppermost value of TPLF reduction at this
incidence angle occurs at case E with value of -12.8 %. TPLF is
further increased with i=+4 where β1=136 deg., for all cases. At
i=+6 deg., where β1=138, all cases have an increase in pressure
loss which is noted by the positive vale of TPLF for all cases at
this incidence angle. Therefore, at design conditions, case F
causes the highest reduction in TPLF; nevertheless, at off-
design operation case E yields higher reduction in TPLF than
this caused by case F. Consequently, optimization of the best
case to be used to cover a wider range of operation with the
highest reduction in pressure losses is still needed.
7 Copyright © 2015 by ASME
Effect of vortex generator on flow turning angle Flow turning angle is computed from Equation 4. In order
to track the change in flow deflection by using vortex
generators, the difference of the flow turning angle will be
normalized by flow turning of the base case as shown in
Equation 5.
21 (4)
Base
BaseVG
__
(5)
The normalized difference of flow turning angle is shown
at midspan for base case and all VG cases in Fig. 12. At design
operation, the flow turning angle is either decreased or
increased by using VG where the maximum reduction is of
- 0.25 % with the case C and the maximum increase of 0.38%
with the case D. Consequently, a slight change is noticed in the
flow turning angle for all cases at this point of operation.
At off-design condition, a high negative incidence angle
i= - 6 deg., causes an increase in the flow turning angle with
value of 1.8 % at case A, slight change in this value is noted for
other cases. As negative incidence decreases to i= -4 deg., flow
turning is increased to 1.2% at case B. Further decrease in
incidence angle to i= -2 deg. flow turning is lowered to 0.53 %
at case B. At positive incidence angles, the change in flow
turning angle is lower than that caused by negative incidence.
At i= +2 deg, a slight increase in flow turning angle is
identifiable with intermediate value of 0.32 % at case B. By
increasing the positive incidence to i= +4 deg, further increase
in flow turning is attained with middle value of 0.45% at case
A. Highest positive incidence angle of i=+6 deg results in an
increase flow turning with central value of 0.63% at case A
.Consequently, using VG has no significant effect on the flow
turning angle at design and off-design operation.
Effect of vortex generator on the diffusion factor Blade loading is assessed by the diffusion factor (DF)
which relates to the peak velocity on the suction surface of the
blade to the velocity at the trailing edge. The Diffusion factor
can be defined by Equation 6[33] .
11
2
21
DF (6)
Normalized diffusion factor in Equation 7 is used to
measure the effect of different cases with VG at different
incidence angles on the diffusion factor.
Base
BaseVG
DF
DFDFDF
___
(7)
Figure 12 Normalized difference of flow turning angle at
midspan for case A, B, C, D, E, and F with various incidence angles [%].
The Diffusion factor is used as an indicator of the
probability of stall, since the increase of DF leads to more
possible separation [34]. Figure14 shows variation in DF for all
cases at the entire operating range.
For sets A, B, C, D, and E , diffusion factor decreases over
the whole operating range and it almost remains constant except
for i=+6 , where DF increases. For set F, diffusion factor is
slightly increased for both positive and negative incidence
angles as shown in Fig.13.
The first two terms of the diffusion factor defined by Eq. 6
represent the deceleration of the flow, while the third term
represents the flow turning [35]. For positive incident angles,
the declaration of the outlet flow is increased for almost all sets
which increases the deceleration term in the DF equation. It is
also noted that flow turning term is slightly decreased at this
range of incident angles as shown in Fig.14. The result is a
slight increase in the DF at this range of operation. At negative
incident angles, flow is less decelerated which allows the
deceleration term in the DF equation to decrease. The flow
turning term is also highly increased at this region as shown in
Fig.14, which is also reflected in the increase of the DF in the
negative incident region.
Figure 13 Diffusion factor for case A, B, C, D, and E with
different incidence angles [%]
8 Copyright © 2015 by ASME
Figure 14 Deceleration term , flow turning , and diffusion factor DF with different incidence angles for set F.
Effect of vortex generator on static pressure rise Static pressure rise coefficient is calculated form
Equation 8 and the normalized difference is calculated as shown
in Equation 9.
11
12
st
ss
PP
PPCp
(8)
Base
BaseVG
Cp
CpCpCp
___
(9)
Figure 15 shows the difference in static pressure rise
coefficient for all cases. As noticed, at negative incidence
angles, the static pressure rise is highly decreased while at
positive incidence angles static pressure is slightly decreased.
Similar effect is noticed for set F as shown in Fig.15.
The rise of Cp at β1=134 is probably attributed to the
difference of the axial velocity density ratio (AVDR) between
both β1=134 and the other positive incidence angles of 136,
138. It was found that the value of AVDR at β1 of 134 is less
than that of 136, and 138. Accordingly, the flow contraction
at β1=134 is less than that of 136, and 138. This means that
the flow is more decelerated at 134 than that of 136, and 138.
Consequently the value of Cp at 134 is greater than that of
136, and 138. As reported in reference [4], the AVDR is
defined by Eq. 10 as follows:.
2 2
1 1
x
x
vAVDR
v
Table 4: AVDR values at different inlet angles
Angle Set F Base Change in AVDR
β1=134 1.09291 1.08583 0.6517%
β1=136 1.12137 1.10868 1.1446%
β1=138 1.13321 1.12218 0.9833%
(10)
Figure 15 Static pressure rise coefficient for set A, B, C, D,
E, and F with different incidence angles [%]
CONCLUSIONS Numerical simulations of a three-dimensional compressible
turbulent flow have been performed to explore the effect of the
vortex generators on the reduction of secondary flows. Six
different sets of a new design of vortex generator are used in the
current work as a passive boundary layer control device in an
axial compressor cascade. The investigation is carried out over
a wide operating range of incidence angles at design and off
design conditions. The inlet Mach number is of 0.66 with inlet
angle of β1=132⁰ at design operation. For off-design operation
the flow incidence angle is changed between i= -6 and i=+6
deg. Numerical simulation is performed using commercial
software ANSYS FLUENT. The results show that for all
investigated configurations, a significant reduction of total
pressure loss up to 20.7% by case F is attained in comparison
with the base cascade without vortex generator at the design
point. In addition, this reduction in total pressure loss occurs at
incidence angles of i=±2, ±4 deg with maximum value of
12.8 %, while at i = ±6 deg an increase in total pressure loss is
noted.
For other investigated performance parameters, the flow
turning angle has a slight change for the different operating
range angles. Also, a slight decrease in the diffusion factor is
noticed for the entire operating range when using vortex
generators. Static pressure rise coefficient is rapidly decreased
by increasing the negative incidence, while it remain constant at
positive incidence angles. Therefore, using this vortex generator
reduces the total pressure loss and enlarges the operating range
of compressor cascade towards the positive incidence angle
region without a significant effect on the flow turning angle and
diffusion factor.
9 Copyright © 2015 by ASME
NOMENCLATURE
Symbols AVDR :Axial velocity density ratio
c : Chord length
Cp : Static pressure coefficient
DF : Diffusion factor
e : Vortex generator's length
GCI :Grid Convergence Index
h : Vortex generator's height
i : Incidence angle
L : Span
M : Mach number
P : Pressure (total or static)
r Rounded nose radius
S : Pitch
TPLC : Total pressure loss coefficient
TPLF : Total pressure loss factor
w : Vortex generator's width
β : flow angle
δ : Boundary layer thickness
ν : Relative velocity
ρ :Density
σ : Solidity
Subscripts is : Isentropic
1 : At inlet
2 : At measurement plane
s : Static pressure
t : Total pressure
Base : Base case without vortex generator
VG : Case with vortex generator
θ : Tangent component
x : Axial component
REFERENCES
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Visulaization study of secondary flows in cascades,”
Technical Report No. 1163, NACA.
[2] Dean, R. C., 1954, “Secondary flow in axial
compressors,” (1949).
[3] B. Lakshminarayana, and Horlock, J. H., 1963,
“Reviw : Secondary Flows and Losses in Cascades and
Axial-FLow Turbomachines,” Int. J. Mech. sci, 5, pp.
287–307.
[4] H. Schlichting, and Das, A., 1966, “Recent Research
on Cascade-Flow Problems,” pp. 221–228.
[5] Gessner, B. F. B., 1972, “The origin of secondary flow
in turbulent flow along a corner.”
[6] Wisler, D. C., 1985, “Loss Reduction in Axial-Flow
Compressors Through Low-Speed Model Testing,”
(3).
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