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Proceedings of ASME/IGTI Aeroengine Congress & Exhibition Turbo-Expo 2002

June, 3-7, 2002, Amsterdam

GT-2002-30441

LOW SPEED STUDIES OF SWEEP AND DIHEDRAL EFFECTS ON COMPRESSOR CASCADES

Bhaskar Roy

P A Laxmiprasanna

Vishal Borikar

Amit Batra

Aerospace Engineering Department, IIT Bombay, Mumbai - 400 076, India e-mail: aeroyia@aero.iitb.ac.in

ABSTRACT The use of three dimensional blade designs incorporating

end bend, sweep and dihedral to reduce secondary flow related losses, improve efficiency and stable operating range has gained ground in the recent years. In the present study a straight cascade, a swept cascade, and a dihedral cascade have been considered. Effects of sweep and dihedral along the span are studied at 0o and +20o stagger. The study shows that both the sweep and the dihedral have lower end-wall losses compared to the straight cascade. However, lower losses are accompanied with lower diffusion factors. At mid-span also the lowering of losses is achieved along with some lowering of diffusion factor. While the dihedral seems to contribute for stable operation more near the end-wall, the swept blade contributes more near the mid-span. The swept blade is able to sustain the flow at higher angles of attack. While the end-wall loss benefits are welcome with lower loading, at mid-span lower loading obtained may need to be corrected by increasing the design angle of incidence.

NOMENCLATURE Cp Coefficient of Static Pressure

= (plocal –p1)/(½ ρ1V12).

DF Diffusion Factor, (Vmax - V2 )/ Vmax

p Static pressure P Total Pressure P Pitch-wise Integrated Pressure

P Pitch-wise and Span-wise Integrated Pressure q Dynamic head , ½.ρ.v1

2

V Velocity α, AOA Angle of Attack

ρ Density θ Stagger Angle ω Loss Coefficient, (P2 –P1 )/q1 ω Pitchwise Integrated Loss Coefficient,

( P -P1)/q1

ω Pitchwise and Spanwise Integrated Loss

Coefficient, ( P - P1)/q1 Y Pitch-wise distance

SUBSCRIPTS 1 inlet 2 outlet max maximum

INTRODUCTION Recent research in axial compressor has focused, to a large

extent, on understanding the loading characteristics and loss mechanism in the 3-D blade designs incorporating dihedral, sweep and end bends to achieve improvements in efficiency and/ or stable operating ranges.

The stable condition at off-design operations depends on boundary layer separation and the behavior and turning characteristics of the blade sections. In order to improve performance, stage loading must rise and the boundary layers on the blades, especially near the end-walls must be controlled. Whether higher loading can be achieved along with higher surge margin or that one may be achieved at the expense of the other has been the focus of attention for quite some time.

The incorporation of end-bends involves a certain degree of local aerofoil lean. During the last few years the deliberate use of local aerofoil lean in compressor has generated

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interesting performance results. The early end-bend concepts were based on two-dimensional approach although aimed at three-dimensional flow problem. The problem of lean can be described by sweep and dihedral, both the terms being borrowed from aircraft wing aerodynamics. The implication of sweep and dihedral are two-fold in axial compressor application – the end-wall related 3-D flow benefits and the 2-D sectional flow effects.

This study is aimed at improving the understanding of the fundamental mechanism of effects of curvilinear stacking lines on the blade sectional characteristics (chord-wise blade loading) and sectional loss characteristics, using swept and dihedral blades in linear compressor cascade arrangements. Both the span averaged and the section-wise loss characteristics are studied at zero stagger, and at 20o stagger with varying inflow angles. No attempt is made to study the secondary flow, which admittedly is an important function of these new shapes.

LITERATURE SURVEY Low Speed Cascade Studies

Compressor cascade blades, installed in a low speed wind tunnel constitutes a low speed compressor cascade testing facility, at Mach numbers corresponding to incompressible flows. Compressor cascade studies, experimental or numerical, form the basis of aerodynamic design of turbo-machine blades. It is desired that the flow over the cascade blades be two-dimensional but after entry into the cascade the flow acquires three dimensionality due to the presence of boundary layers on the end-walls of the tunnel and on the blade surfaces. Definition of Sweep and Dihedral

Blades are said to have sweep when flow direction is not perpendicular to the span wise direction and dihedral when the blade surface is not perpendicular to the end-wall [Smith and Yeh, 1963]. In practical cases such as the entrance region of the axial compressors and nozzle of the steam turbines, there is often a large slope given to the axial flow track. Thus sweep may be present even when the blade itself is radial. Sasaki et al [Sasaki and Breugelmans, 1998] have given a definition of sweep and dihedral. According to them lean/dihedral is introduced by moving the center of gravity of the end-wall section of a blade in a direction normal to the chord line as shown in fig.1. Lean is ‘positive’ if the suction surface makes an obtuse angle with the end-wall and ‘negative’ if it makes acute angle with the end-wall. Sweep is introduced by moving the center of gravity of the end-wall section of a blade along the chord line. Sweep is said to be ‘positive’ or ‘forward’ when the end-wall section is upstream of the adjacent inboard section and ‘negative’ or ‘backward’ if the end-wall section is downstream of the adjacent inboard section (fig. 1,3). Effects of Dihedral and Sweep

Dihedral and sweep have been known for their ability to improve the radial distribution of velocity and minimize separation and losses by imparting some radial acceleration to the flow in a prescribed fashion [Smith and Yeh, 1963]. The benefit appears to be that by use of positive sweep the boundary layers are transported away from the unstable end-wall region,

which improves the stall margin; the negative sweep having the opposite effect. Positive dihedral provides a means of reducing the magnitude of the peak suction pressure over a limited range of span near the end-wall and of locally reducing the blade force per unit span while maintaining flow deflection. It thus reduces corner separations near fixed blade ends in a stator and tip leakage flows at clearance end of a rotor. In general, staggering of swept blades would introduce dihedral and staggering of dihedral blades would introduce sweep [Sasaki and Breugelmans, 1998]. Previous Work

Bruegelmans et al. [Bruegelmans, Charles, and Demuth, 1984] have reported the dihedral effects on a rectilinear compressor cascade. The blades used were NACA 65-12A10-10 with a chord of 100 mm, solidity and aspect ratio of unity, a stagger angle of 28.9° and a nominal air inlet angle of 45°, corresponding to an incidence angle of –1.1° when dihedral is zero. The effect of dihedral is investigated from 0° to 35° dihedral angle. A small amount of dihedral (15°) produces a sufficient span-wise pressure gradient to suppress almost completely the development of a large loss zone in the large corner.

Lyes et. al., [Lyes and Ginder, 1999] have described two design /testing activities that have been carried out on a 4-stage low speed research compressor at Cranfield University. It was observed that the low speed environment was representative and that the modeling was adequate. Low speed blading aims to have similar aerodynamics to ‘equivalent’ high-speed (but still predominantly subsonic) blading by designing for similar blade surface velocity distribution and hence similar boundary layer behavior. In the second phase, 3-D redesign in the areas of high loading and high incidence, flow separation and high loss was done. These areas were off-loaded by restacking the blades using lean and sweep, and also by incorporating extra camber near the leading edges. Most of the study involved using of a symmetrical ‘bowed’ (dihedral) stacking line formed by a parabola. For the rotor, a combination of lean and sweep was found best, giving predicted losses reduction of about 10%. For the stator, the optimum case corresponded closely to tangential displacement of stacking axis (positive lean and sweep), but the loss reductions were smaller. The low speed design shows an efficiency improvement of 1.5% over the datum case near the design flow coefficient; larger improvements in efficiency are apparent at lower flows, and these contribute to considerable strengthening of the pressure characteristics that is evident towards the stall. Stable operating range is increased significantly.

Sasaki et al. [Sasaki and Breugelmans, 1998] studied a controlled diffusion airfoil blade by using different stacking lines i.e., one straight blade, four swept forward, one backward swept and four positive dihedral blades. The blade configurations were symmetrical about the mid-span and consisted of a straight middle portion and swept or leaned portions towards the end-wall. The experimentation consisted of collecting data at 15 different axial planes, with traverses at 13 span-wise locations, most of them near the end-walls, at

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each axial plane. The total pressure loss coefficients are pitch-wise averaged and given as ω . In order to evaluate the actual generation of loss along the passage, averaging over both pitch-wise and spanwise directions is done to define an overall net

loss coefficient at each axial plane. This is given as ω . (See nomenclature). The results of the parametric study showed that the forward swept blades generate less loss and backward swept blades generate more loss at lower inlet angles. These definitions have been used in the present investigation also for the data analysis. Use of sweep and dihedral in compressors

Wadia et al, in pursuit of reducing the overall length of F118-GE-100 engine, have used non-axisymmetric stator configuration ahead of the fan frame struts. They used swept and leaned OGV (outlet guide vane) frame splitter system. The primary benefit of the tangential lean in the OGV hub trailing edge is lowering the OGV hub exit Mach number, thus reducing the duct velocity diffusion ratio. Sweeping aft of the airfoil was done to move the trailing edge meridional projection at mid-span further aft relative to the OGV hub trailing edge. This helps prolong the benefit due to lean (lowering the inlet mach no.) further downstream from the OGV hub trailing edge and thereby providing better control of the core hub duct diffusion. Due to the lean imparted to the more then one OGV crosses the leading edge of the strut [Wadia, et. al., 1999].

In many cases the use of sweep and dihedral may be caused by annulus contraction or flare or simply the need to install blading in a region of changing radius. One such example is the inner fan second stator of CF6 engine where it was necessary to induce the flow from high fan radius into the inboard location of the gas generator inlet [Weingold et al, 1995]. The solution adopted was to use stators having suitable sweep and dihedral to impart radially inward body force into the flow. The existing blading was swept forward one with respect to the incoming flow; the result was that separated boundary layer tended to drift towards the hub region impairing the ability of the blading to sustain high loading. Benefits of Sweep and Dihedral

From the survey of previous research [Sasaki and Breugelmans, 1998] the benefits of sweep and dihedral may be listed as: 1. Positive dihedral and positive sweep are effective in controlling the local pressure gradient within the passage. 2. While sweep is mainly used to control the chord-wise loading distribution and to some degree span-wise loading, dihedral is often used to influence the span-wise pressure field. 3. The regions of sharp transition between the leaned end-wall portion (positive sweep or positive dihedral) and the conventionally stacked portion of the blade can be avoided as they are similar to the configurations of the negative sweep or

dihedral, which produce increased aerodynamic loading and loss. 4. Using the sweep and dihedral profiles in combination avoids the kink section (transition from swept end to the radial blade portion), where increased loading and loss were observed.

As pointed out by Cumpsty [Sasaki and Breugelmans, 1998] only a full 3-D N-S solver and an inverse design methodology can address the problems of 3-D blade design. This has been attempted and reported in some detail by Gummer et al [Gummer, Wenger, and Kau, 2001] for CDA blades for redesigning a stator.

Breugelmans et al [Breugelmans, Charles and Demuth, 1984] conducted tests on circular stacking line of dihedral. They have suggested an optimum positive dihedral angle of 15o

to 25o for the best loss improvement performance. Sasaki et al. [Sasaki and Breugelmans, 1998] have reported that for 15o positive dihedral gives best results for loss improvement and 30o positive sweep gives the best results. Lyes et al [Lyes and Ginder, 1999] have used parabolic variation of stacking lines in their parametric study

In the present work, parabolic stacking lines have been used to impart forward sweep of 30o and to impart positive dihedral of 15o. Low speed cascade studies have been done at 0o stagger and later at 20o stagger. The present study, thus, starts from pure sweep and pure dihedral, and then adds the effects of angle of attack and stagger angle to understand, in a step-by-step manner, the change in sectional characteristics. The studies were later extended to +20o stagger to introduce diffusive (compressor) passage effects. The angle of attack was varied from –10o to +20 in the 0o stagger cascade and then from 0o to 35° in the 20° stagger cascade.

As the sweep/dihedral is distributed across the span in parabolic curvilinear planes, the sectional characteristics are studied at five span-wise sections from the end-wall to the mid-span section. As the end-wall flows are not the focus of attention, closely packed sectional study near the end-walls is not attempted. As the sweep/dihedral is distributed across the span in

Table 1: Cascade Configuration Chord length 100 mm

(200 mm) α, AOA -10° to 25°,

(0°, 20°) Number of blades 10 (5) Stagger angles 0o, 20 ° Leading edge radius

1.2% chord Solidity 1.75

Trailing Edge radius

0.6% chord Aspect ratio 1.5 (1.75)

Max thickness 10% chord Airfoil camber 30o The numbers in parenthesis refer to larger cascades used for

boundary layer studies.

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parabolic curvilinear planes, the sectional characteristics arestudied at five span-wise sections from the end-wall to themid-span section. As the end-wall vortex flows are not thefocus of attention, closely packed sectional study near theend-walls is not attempted. CASCADE DESIGN AND FABRICATION Cascade Design The three cascades - straight, 30o forward swept, and 15o

positive dihedral (of identical size - chord=100mm;span=150mm) were prepared for comparative studies betweenthe three blade shapes and the effect of stacking line. Largebladed cascades were made for boundary layer studies. Sincethe blades were to have curvature for their stacking line, thedefinition of sweep and dihedral angle used are slightlydifferent from that given in the literature [Sasaki andBreugelmans, 1998]. These definitions are as illustrated in theFig. 1. Sweep angle is the angle made by the line joining theend point and mid-point of the stacking line with the normalto the end-wall, whereas in literature since the stacking line isstraight, it is the angle between stacking line and the normalto the end-wall. Dihedral angle is also defined in a similarmanner. In the case of forward swept blades the end-wallsections meets the incoming flow earlier than the mid-spansection. In forward swept blade, the aerofoil sections movealong the chord line while in dihedral the aerofoil sectionsmove normal to chord line (fig. 1,3). To generate the profile of the cascade, a code was developedbased on the definitions of sweep and dihedral given inpreceding paragraph. The code generates 3-D wire-mesheddrawings of the blades in *.dxf format which is compatiblewith AutoCAD. The program is capable of giving positivesweep/dihedral profiles of circular or parabolic curvature. Thechoice of circular or parabolic curvature can be madeindependently for sweep and dihedral. The drawings shown inFig. 3 were generated using this code. The airfoil used for theblades is the C4-series airfoil with circular arc camber (fig. 2).The camber was chosen to be 30o with maximum thickness as10% of chord. The leading edge radius is 1.2% of chord andthe trailing edge radius is 0.6% chord. The chord of the threesmall blades, were 100 mm and the span lengths, were 150mm where as the large blade had 200 mm chord and 350 mmspan, airfoil data remaining the same. The solidity of bothsmall and large bladed cascades were maintained constant at1.75. LOW SPEED CASCADE WIND TUNNEL The low speed cascade wind tunnel at the Department of

Aerospace Engineering, Indian Institute of Technology,Bombay, permits testing of cascade at low speed with amaximum attainable velocity of 60 m/s. The working velocityhowever is limited to about 20 to 30 m/s due to noiseproblems. The diffuser with large divergent angle of 46° hasfour splitter plates to ensure even distribution of airflow intothe settling chamber. The settling chamber has a honeycombof 250 mm length followed by four stainless steel meshscreens to reduce the free stream turbulence. The contraction

Fig. 2: C4 Circular Arc Airfoil

Fig. 1: Definition of sweep and dihedral.

Fig.3: Three Dimensional isometric views of Straight, Swept and Dihedral blades

a. Straight b. Forward Sweep

c. Positive dihedral

Fig. 4: Cascade Details and Measurement Locations

(a) 0° Stagger (b) 20° Stagger

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section has contraction ratio of 12:1 that feeds a jet of uniform velocity profile into the test section. The tunnel sidewall boundary layers are bled out with the help of slits just ahead of the cascade section. The test section has the facility of variable incidence angle (or angle of attack), which can be obtained by rotating the circular disk, on which the cascade is mounted. The tunnel has been calibrated for flow non-uniformity, which is found to be 1% for velocity profile and 0.8% for pressure profile at the cascade inlet. All the probes used were calibrated, in a separate low speed calibration tunnel, at same velocities for directional sensitivity. The shielded total pressure probe showed insensitivity of ±35° yaw angle. The inlet and outlet parameters measured during experiments include inlet velocity and inlet and exit total pressures (pitch-wise averaged) and static pressure distribution on both the surfaces. The instrument used includes digital micro-manometer with an accuracy of 1%. The measured turbulence level of the cascade inlet is 0.87% and that of the cascade outlet is 12.37%. The details of the measurement locations are given in fig. 4 and the schematic of the test facility is given in fig. 5. Traversing Mechanism and instrumentation A 1-D traverse mechanism was used for downstream total pressure measurement was also designed and fabricated. It has maximum traverse of 150 mm along the screw length, keeping in view the need to be able to traverse two blade passages. The probes used are standard pitot static probe (at upstream sections), shielded total pressure probe for loss measurement at the downstream section, and flat nosed boundary layer probe (1 mm thick at L.E.) for boundary layer studies. The

measurements are taken with digital micro-manometer. Overall accuracy of the various parameters, measured and computed, was within 2.5% error band; the results have a 97.5% confidence level. Boundary layer estimation is within ± 10%. Blade Fabrication For each set of cascade of airfoils, blades were fabricated from epoxy resins. The two innermost blades were equipped with static pressure taps. The airfoil thickness requires the instrumentation of two separate airfoils rather than just one. Both the pressure and suction surface tapped airfoils were arranged in cascade to record the flow within a common passage. RESULTS AND DISCUSSION Comparative cascade study at 0o stagger blade setting The Cp distributions for the three blades at the five span-wise sections with the blades set at 0o stagger angle and 0o AOA are given in figs 6(a, b, c). Fig. 7 gives the Cp distribution along the 5 span-wise sections (Section 1 to 5) for straight, swept and dihedral blades for 0o stagger and α=00. For straight blade in fig. 7(e) it can be seen that peak suction pressure at section 5 is higher and it decreases to minimum at end-wall section 1 in Fig. 7(a); consequently (at α=00) the chord-wise pressure gradient (acceleration and deceleration) is higher at the mid-span (section 5) than near the end-wall (section 1). In comparison with the straight blade, in the swept blade (fig. 6 & 7), at the front portion of the blade (at 5% to 65% chord), there is a larger chord-wise pressure gradient near the end-wall than that of the straight blade. This zone of pressure gradient is gradually reduced at sections near the mid-span. At the aft portion the chord-wise pressure gradient is reduced (flattened) to a great extent at end-wall sections, but the mid-span sections show significant loading of the aft portion of blades. The dihedral blade, as seen in fig. 6 & 7, shows lower chord-wise gradient near the end-wall and an increase in the chord-wise pressure gradient at the mid-span.

It can be seen from the figures 6 & 7, that at all the span wise sections there is a reduction in the chord-wise pressure gradient as compared to the straight blades. Swept blades show a reduction in chord-wise pressure gradient (i.e. less overall acceleration and deceleration) at all the sections. Fig. 8 gives the diffusion factor variation for all the 3 blade shapes at α=0°. Dihedral is seen to produce higher diffusion factor than the swept blade at the end-wall. However towards the mid-span the swept cascade provides better diffusion factor than the dihedral. The straight blade holds the diffusion factor, highest amongst the 3 shapes, till the mid-span; the high diffusion is also seen in the Cp plots (fig.6 & 7). The effect of sweep is seen over the entire span, while the effect of dihedral in lowering the blade loading is seen only at the end-wall.

The diffusion factor characteristics at 20o AOA (fig. 9) provide some more indication of the nature of variation of blade loading at high angle of attack. At α=+200 all the blades, as expected, produced higher diffusion factor at all the sections. The dihedral shape is effective in off-loading at only the

Fig. 5: Low speed cascade wind tunnel

(c) Small test section

(a) Wind tunnel

(b) Large test section

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0 10 20 30 40 50 60 70 80 90 100% Chord

-1.50

-1.00

-0.50

0.00

Coe

fficient of P

ressure (C

p)

(a) Section 1

0 10 20 30 40 50 60 70 80 90 100% Chord

-1.50

-1.00

-0.50

0.00

Coe

fficien

t of P

ressur

e (C

p)

(b) Section 2

0 10 20 30 40 50 60 70 80 90 100% Chord

-1.50

-1.00

-0.50

0.00

Coe

fficien

t of P

ressur

e (C

p)

(c)Section 3

0 10 20 30 40 50 60 70 80 90 100% Chord

-2.00

-1.50

-1.00

-0.50

0.00

Coe

fficient of P

ressure (C

p)

(e)Section 5

Straight Blade (Suction Surface)Straight Blade (Presssure Surface) Swept Blade (Suction Surface)Swept Blade (Presssure Surface) Dihedral Blade (Suction Surface)Dihedral Blade (Presssure Surface)

Fig. 7: Chord-wise Cp distribution at all sections for 0o stagger and 0o AOA.

0 10 20 30 40 50 60 70 80 90 100% Chord

-1.50

-1.00

-0.50

0.00

Coe

fficient of P

ressure (C

p)

(d)Section4

0 10 20 30 40 50 60 70 80 90 100% Chord

-2.00

-1.50

-1.00

-0.50

0.00C

oeff

icie

nt o

f Pre

ssur

e (C

p)

a) Straight blade, 0° AOA

0 10 20 30 40 50 60 70 80 90 100% Chord

-2.00

-1.50

-1.00

-0.50

0.00

Coe

ffic

ient

of P

ress

ure

(Cp)

b) Swept blade, 0° AOA

0 10 20 30 40 50 60 70 80 90 100% Chord

-2.00

-1.50

-1.00

-0.50

0.00

0.50

Coe

ficie

nt o

f Pre

ssur

e (C

p)

c) Dihedral blade, 0° AOA

Section 1(Suction Surface)

Section 1 (Pressure Surface)

Section 2 (Suction Surface)

Section 2 (Pressure Surface)

Section 3 (Suction Surface)

Section 3 (Pressure Surface)

Section 4 (Suction Surface)

Section 4 (Pressure Surface)

Section 5 (Suction Surface)

Section 5 (Pressure Surface)

Symbols used in Fig. 6

Fig. 6 Chord-wise CP distribution at 0° AOA for different blade shapes

near end-wall sections and maintains same loading throughout the span. The straight blade gives highest diffusion factor at all the span wise positions with an increment of about 100% over the 0o AOA setting. The swept blade produces sharp decrease in diffusion factor near the end-wall compared to the straight blade. However, by mid-span its diffusion factor rises close to that of the swept blade. The swept blade shows almost 400% and the dihedral blade shows 250% increase across the span. The lowering of blade loading with introduction of sweep and dihedral needs to be studied in conjunction with lowering of loss, as the two of them together decide the blade efficiency.

Table 2: Percentage reduction in losses over straight

blades at various angles of attack: 00 stagger Blades α=-10o α=0o α=10o α=20o Dihedral 16.54 18.35 11.75 4.77 Swept 29.2 38.68 43.44 9.7

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Fig. 10 gives the total (span averaged after pitch-wise

averaging) loss coefficient variation at the four angles of attack. All the blades show that their respective minimum loss at α=00, with the swept blade having the lowest loss across all the angles of attack. The percentage reduction in the total loss coefficient at the four angles of attack for both the dihedral and the swept blades is shown in table 2. It can be seen that the greatest improvement is with swept blades is at 10o.

The total losses occurring at a positive/negative angle of attack is a combination of sweep or dihedral effects and of the airfoil sections. At non-zero angles of attack aerodynamic losses are higher than at 00 angle of attack for all the three blade shapes. At α=200, there is a sharp increase in losses for swept

blades. This is due to the high losses at the end-wall. Cp distribution along the span (fig. 6 & 7) for swept blade at this particular angle of attack indicates a larger chord-wise pressure gradient at the end-wall to which the high losses can be attributed.

Fig. 11 gives the pitch-wise averaged loss characteristics, at various sections from end-wall to mid section. It is observed that span-wise loss variation changes with angle of attack. As AOA is increased from 0o to high positive angles the loss at the end-wall increases and loss at the mid-span remains almost same for all the three shapes. However the end-wall losses are lowest for the swept blades, which also show continuous variation from end-wall to mid-span. CASCADE STUDIES AT 20° STAGGER Cp Characteristics: The end-wall studies have been done in some detail by earlier researchers [Sasaki and Breugelman, 1998; Peng et al, 1991; Weingold et al, 1995; Smith and Yeh, 1985; Gummer, Wenger & Kau, 2001]. Most of this earlier work focused on the end-wall effects. The present study however is focused on determining the effect of shape on the sectional characteristics. The mid-span Cp curve shows higher acceleration as the angle of attack is increased. The acceleration is pronounced from the leading edge to 20% chord axial location that can be observed by steep slopes (Fig 12 a to d). However at higher angles of attack (α=35°) straight and dihedral blades are totally stalled, showing flat Cp curve (Fig. 12 d). Results observed for

Fig. 8: Diffusion factor, DF at θ=0o and 0o AOA.

Fig. 9: Diffusion factor, DF at θ=0° and 20o AOA.

a) AOA=0o

b) AOA=20o

Fig. 11 Span-wise loss coefficients, ω AOA for θ=0o

-20 -10 0 10 20 30Angle of Attack

0.0000.0050.0100.0150.0200.0250.0300.0350.0400.045

Tot

al L

oss F

acto

r

Straight Blade Dihedral Blade Swept Blade

Fig. 10: Loss factor, ω variation with angle of attack for straight, swept and dihedral blades.

Straight Blade

Swept Blade

Dihedral Blade

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swept blades show off-loading compared to the straight blade at all angles of attack especially at 35° (Fig. 12 a to d). The swept blade shows marked off-loading on suction surface in Cp characteristics especially from leading edge (LE) to approximately 40% of chord (Fig 12 a to 12 c). This shows reduction in magnitude of acceleration at the front portion of the blade as compared to the other blade shapes, which means

less probability of early flow separation over swept blade. The comparison between the Cp plots of the three cascades at various angles of attack (Fig. 12 a to d) show moderate levels of acceleration followed by sustained diffusion was achieved by swept blades. This indicated reduction in gradient of acceleration with respect to the other two blades. Dihedral cascade has steeper Cp characteristics than straight blades at

0.00 0.20 0.40 0.60 0.80 1.00X

-3.00

-2.00

-1.00

0.00

1.00Cp

(c) 25° AOA

% chord

0.00 0.20 0.40 0.60 0.80 1.00X

-3.00

-2.00

-1.00

0.00

1.00

Cp

(b) 15° AOA

% chord

0.00 0.20 0.40 0.60 0.80 1.00X

-3.00

-2.00

-1.00

0.00

1.00

Cp

(a) 0° AOA

% chord

0.00 0.20 0.40 0.60 0.80 1.00% chord

-2.00

-1.00

0.00

1.00

Cp

(d) Near Stall AOA

Fig. 13: Cp Distribution for Section 1 (End-wall) for 20° Stagger for Various AOA

Straight Blade (Suction Surface)Straight Blade (Presure Surface)Swept Blade (Suction Surface)Swept Blade (Presure Surface)Dihedral Blade (Suction Surface)Dihedral Blade (Presure Surface)

Fig. 12: Cp distribution at section 5 (mid-span) for θ=20o at various AOA.

0.00 0.20 0.40 0.60 0.80 1.00% chord

-2.00

-1.50

-1.00

-0.50

0.00

0.50

Cp

(b) 15o AOA

0.00 0.20 0.40 0.60 0.80 1.00

% chord

-3.00

-2.00

-1.00

0.00

Cp

(c) 25o AOA

0.00 0.20 0.40 0.60 0.80 1.00

% chord

-2.00

-1.50

-1.00

-0.50

0.00

0.50

Cp

(d) 35o AOA

0.00 0.20 0.40 0.60 0.80 1.00

% chord

-2.00

-1.60

-1.20

-0.80

-0.40

0.00

Cp

(a) 0o AOA

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lower angles of attack, whereas the acceleration gradient over straight cascade at high angle of attack is higher. The comparison between 0° stagger and 20° stagger Cp plots show increase in maximum Cp for all the configurations, however most pronounced off loading with increased stagger appear to be for the swept blade. At α=35°, all the three blades show separation characteristics. The swept blade has a small attached flow zone over first 25% chord, showing some initial acceleration and steep deceleration, at which point the flow separated on the suction surface.

Fig. 13 shows the Cp characteristics at section 1 (near end-wall) from 0° to 25° AOA and at near-stall AOA for the individual blades. As expected, the maximum Cp increases with α and progressively shifts towards the leading edge.

Amongst the three blade shapes, the swept blade shows more controlled deceleration (after the initial acceleration) even at high angles of attack. With increasing AOA, the acceleration around the leading edge increases. At 30o and higher AOA, high initial acceleration causes the straight blade to experience stall. The dihedral blade shows sharp diffusion at 25o and 30o AOA. Because of the gentler diffusion character of the swept blade, it delays stall to about 35o AOA. However, it stands to reason that swept blade yields lower diffusion factor as found in Fig. 14.

Comparison between mid-span (fig. 12) and near end-wall (fig. 13) Cp characteristics show that at mid-span, acceleration and deceleration are more pronounced than near end-wall. The straight and dihedral blades show sharper initial acceleration and stronger diffusion characteristics at mid-span. The swept blade, on the other had, shows a more muted acceleration- deceleration characteristic. Thus the swept blade is expected to give lower loss characteristic as found in fig. 15. TOTAL PRESSURE LOSS CHARACTERISTICS AT 20° STAGGER

The total pressure loss characteristics at 20° stagger for all the cascades (fig.15), as expected, shows increase in loss compared to those at 0° stagger (fig. 10). The total pressure loss surveys (fig. 16) show lower losses for the swept blades at angles of attack from 0° to 25°. However after that the losses rises sharply. On the other hand, the losses for straight and dihedral blades start rising (sharply for straight blades but gradually for dihedral blades) at around 15° angle of attack. Highest losses were observed in the case of straight blades. The averaged loss coefficient (fig. 15) summarizes the loss survey, and indicates better prospect for the swept blade.

0 deg. AOA15 deg. AOA 25 deg. AOA35 deg. AOA

-4.00 0.00 4.000.00

0.05

0.10

0.15

0.20

0.25Loss Coefficient

Y

(a) Straight

-4.00 0.00 4.000.00

0.05

0.10

0.15

0.20

0.25Loss Coefficient

Y

(b) Swept

-4.00 0.00 4.000.00

0.05

0.10

0.15

0.20

0.25Loss Coefficient

Y

(c) Dihedral

Fig. 16: Loss Coefficient, ω at Section 5, θ=20°

-10.00 0.00 10.00 20.00 30.00 40.00AOA

0.00

0.20

0.40

0.60

Diff

usio

n Fa

ctor

( g gg )

Straight Blade at 0 StaggerSwept Blade at 0 StaggerDihedral Blade at 0 StaggerStraight Blade at 20 StaggerSwept Blade at 20 StaggerDihedral Blade at 20 Stagger

Fig. 14: Comparison of diffusion factor, DF at θ = 0o and θ=20o at the mid-span.

0.00 10.00 20.00 30.00Angle of Attack

0.00

0.04

0.08

0.12

0.16

Ave

rage

Tot

al P

ress

ure

Loss

Straight

Swept

Dihedral

Fig. 15: Total loss factor, ω at θ=20o

10

0.20 0.40 0.60 0.80 1.00 1.20Loss Coefficient

0.00

4.00

8.00

12.00

16.00

Dist

ance

from

the

surfa

ce at 94 % chord

at 67.5 % chord

(a) Section 1

0.00 0.20 0.40 0.60 0.80 1.00Loss Coefficient

0.00

4.00

8.00

12.00

16.00

20.00

Dist

ance

from

the

surfa

ce

at 94 % Chord

at 51.5 % Chord

(b) Section 5

Fig. 18: Loss, ω Profiles for Swept Cascade, θ=0°, 0° AOA

Fig. 17: Loss, ω profile at 67.5% and 94% chord for dihedral cascade at θ= 0o and 0o

AOA.

(a) Section 1 (end-wall)

(b) Section 5 (mid-span)

0.00 0.40 0.80 1.20 1.60 2.00Loss Coefficient

0.00

4.00

8.00

12.00

16.00

20.00

Dist

ance

from

the

Surfa

ce (i

n m

m) Swept Blade (94 % Chord)

Swept Blade (67.5 % Chord)Dihedral Blade (94 % Chord)Dihedral Blade (67.5 % Chord)

Fig. 19: Loss, ω profiles, section 5 (mid-span) at 20o stagger, 20o AOA.

(1) 0° Stagger Angle ( 0° AOA) Sections Dihedral Blade Swept Blade %Chord 67.5 94 - 94.0

1

2.5 5.0 6.0 (67.5%c)

14.0

5

2.5 7.0 9.0 (51.5%c)

14.0

(2) 20° Stagger Angle (20° AOA) %Chord 67.5 94 67.5 94.0

5

4.0 12.0 7.0 14.0

Table 3: Boundary layer thicknesses at low AOA

The swept blade is effective in maintaining low average losses forlarge range of angle of attack (up to +25°) than the other twoblades.

The advantages of the swept blade can also be seen fromblade diffusion factor limit (at which complete separation occurs)is higher (α=35°) compared to the other two blades, but the lossesare already rising sharply. The dihedral blade can also achievehigher diffusion compared to the straight blades especially atlower AOA (0° - 15°). Between 15° and 25°, the straight anddihedral blade offers higher diffusion than the swept blade, butwith a loss penalty (Fig. 17). The drastic rise fall in the diffusionfactor of the straight and dihedral blade (Fig. 18) is accompanied

by sharp rise in losses (Fig.17) indicating approach of stall. CONCLUSIONS FOR 20° STAGGER The Cp characteristics of swept blades are devoid of any high CPgradient thus avoiding the tendency of separation. The sweptblades allow smooth mild acceleration and deceleration, whichcan be seen from the CP characteristics up to high angles of attack(25°). The diffusion factor characteristics of the dihedral bladesare nearly similar to the straight blades. Similar characteristics ofswept blades have been reported through experimental andanalytical results [Koller et al, 1998].

11

Table 4: Boundary layer profiles obtained at near-stall AOAs at 20o stagger.

(1) Straight Blade (thickness in mm)

Section End-wall (Section 1)

Mid-span (Section 5)

%chord position

52.5 % c

72.5 % c

96.0 % c

52.5 % c

72.5 % c

96.0 % c

α = 30° 3 6 8 3 6 12

α = 31° 4 8 14 3 6 14

(2) Swept Blade (thickness in mm)

Section End-wall (Section 1)

Mid-span (Section 5)

%chord position

52.5 % c

72.5 % c

96.0 % c

52.5 % c

72.5 % c

96.0 % c

α = 30° 6 8 10 6 8 16

α = 32° 6 9 12 4 12 14

α = 34° 8 10 12 8 12 16

(3) Dihedral Blade (thickness in mm)

Section End-wall (Section 1)

Mid-span (Section 5)

%chord position

52.5 % c

72.5 % c

96.0 % c

52.5 % c

72.5 % c

96.0 % c

α = 29° 6 10 12 3 5 14

α = 30° 8 12 16 4 6 16

α = 33° - 12 - - 6 -

α = 34° - 12 - - 7 -

(b) Straight Blade Endwall at 31° AOA

0.00 0.40 0.80 1.20 1.60 2.00Loss Coefficient

0.00

4.00

8.00

12.00

16.00

20.00

Dista

nce Fr

om the

Sur

face

(m

m)

0.00 0.40 0.80 1.20 1.60 2.00Loss Coefficient

0.00

4.00

8.00

12.00

16.00

20.00

Dista

nce Fr

om the

Sur

face

(m

m)

(d) Swept Blade Endwall at 34° AOA

0.00 0.40 0.80 1.20 1.60 2.00Loss Coefficient

0.00

4.00

8.00

12.00

16.00

20.00

Dista

nce Fr

om the

Sur

face

(m

m)

(c) Swept Blade Midspan at 34° AOA

0.00 0.40 0.80 1.20 1.60 2.00Loss Coefficient

0.00

4.00

8.00

12.00

16.00

20.00

Dista

nce Fr

om the

Sur

face

(m

m)

(e) Dihedral Blade Midspan at 30° AOA

0.00 0.40 0.80 1.20 1.60 2.00Loss Coefficient

0.00

4.00

8.00

12.00

16.00

20.00

Dista

nce

From

the

Sur

face

(m

m)

(f) Dihedral Blade Endwall at 30° AOA

(a) Straight Blade Midspan at 31° AOA

0.00 0.40 0.80 1.20 1.60 2.00Loss Coefficient

0.00

4.00

8.00

12.00

16.00

20.00

Dista

nce from

the

sur

face

(m

m)

End-Wall Section at 52.5 % chordEnd-Wall Section at 72.5 % chordEnd-Wall Section at 96.0 % chord

Fig. 20. Boundary Layer Profile at Near Stall Angles for Straight, Swept and Dihedral Blades

The swept blades are more efficient in terms ofavoidance of separation as compared to straight anddihedral blades. The effectiveness of the dihedral blade inlowering blade loading is observed to be less than that ofthe swept blades. The swept blades can be used over highrange of angle of attack as compared to the other twoprofiles. BOUNDARY LAYER STUDY

Using the similar procedure detailed earlier, cascades oflarge shapes (chord=200 mm; span=350 mm) were usedfor boundary layer studies. A larger test section was usedto study their respective boundary layer characteristics.The objective here was to study the boundary layer profileson the suction surface of the dihedral and the swept bladesat different chord-wise positions. The results are plotted inthe form of loss coefficient, ω variation with pitch-wisedistance from the suction surface of the blade. Theboundary layer is read from the distance at which the lossdoes not change any more. The accuracy of measurementis estimated to be ±1 mm.

Thicker boundary layer can be seen at all of the span-wise sections for the swept blades at 94% chord (Fig. 18);at 94% chord, boundary layer thickness observed is sameat the end-wall as at mid-span. Even at the mid-chordpositions (Table. 3) the swept blade shows greaterboundary layer development than the dihedral blades. Thethicker wakes of swept blades at 20O stagger has beenrecorded in Fig. 16 b. It is also seen that losses in the wakeare more for the swept blade. However, the lower passage

12

losses in the swept blades bring down the overall pitchwise averaged losses (Fig.15) to lower than those of the dihedral blades at α > 25°.

The boundary layer thickness increases with stagger and angle of attack (Fig. 17, 18 &19) at the mid-span section. The dihedral blades show greater effect of stagger (and AOA) than the swept blades in which the boundary layer thicknesses are of the same order as at zero stagger-zero-AOA (Table 3).

BOUNDARY LAYER STUDY AT HIGH AOA (AT 20O STAGGER)

The table 4 summarizes the overall boundary layer thicknesses as read off from the boundary layer profiles recorded in Fig. 20. The straight blade shows the thinnest boundary layer, both at the end-wall as well as the mid-span at 30o AOA (approx. 12o angle of incidence). The swept blade shows much lower chord-wise boundary layer growth at end-wall compared to the dihedral blades. At mid-span, the boundary later on both the blade shapes shows similar thickness near the trailing edge. At 30o AOA, it is also observed that the swept blade produces thinner boundary layer near end-wall than at the mid section; for dihedral blade, boundary layer growth at mid-span is half of that near end wall up to 72.5% chord. Boundary layer growth on dihedral blade at mid-span over the last 25% chord is significantly stronger than the swept blade.

The swept blade shows sustained attached flow till 35o AOA. The straight and dihedral blades stall at 31o and 34o AOA respectively. Above 30o AOA boundary layer measurement over the dihedral blade could not be done owing to difficulty in probe traversing. CONCLUSIONS

1. Both the swept and the dihedral shapes have some beneficial and some adverse effects. Both the shape effects show significant change in sectional characteristics at various span-wise locations. This change in airfoil character may be attributed to span-wise flow induced by the respective shapes.

2. The effect of positive parabolic sweep in comparison with the straight blade is three fold. Firstly, the chord-wise pressure gradient (diffusion) on the suction surface is reduced all over the span. Hence, even as the swept blades show thicker boundary layers than the dihedral blades overall losses are lower. Secondly, the span-wise pressure gradient is stronger at the front portion of the swept blade near the end-wall, whose intensity decreases gradually towards the mid-span. Thirdly, The maximum velocity on the suction surface rises and shifts towards leading edge at mid-span. This results in longer diffusion and thicker boundary layer at mid-span than at the endwall.

3. The effect of positive parabolic dihedral is also three fold. Firstly the chord-wise pressure gradient is reduced in comparison with the straight blade but to a lesser extent than that of the swept blades. Secondly the span-wise pressure gradient near the mid-span region is reduced. Thirdly the chord-wise pressure gradient near the mid-span is increased, which

increase losses. As a result even with somewhat thinner boundary layer profiles compared to the swept blades, the dihedral blades end up with higher losses.

4. Both the swept and the dihedral blades have shown loss reduction compared to the straight blade. Dihedral blades have lesser ability to reduce losses than the swept blades.

5. Even though swept and dihedral blades show thicker boundary layer than the straight blades, their losses are lower. While sweep has a general sobering effect on the boundary layer and losses, it tends to shift the boundary layer growth towards the mid-span; while dihedral delays the boundary layer growth and shifts it towards the chord-wise rear positions.

6. The higher stall angle for the swept blade is obtained by avoiding separation at higher angles of attack but with a penalty of sectional blade loading at all the angles of attack. If this is true, the blades with sweep would be required to be designed with higher local angle of incidence at the sections away from the end-wall to recover some the sectional blade loading, while the end-wall sectional incidences may be left as it is to enjoy the benefits of sweep and dihedral shapes.

REFERENCES Breugelmans, F. A. H., Carles, Y., and Demuth, M.,

1984, “Influence of Dihedral on the Secondary Flow in a Two Dimensional Compressor Cascade,” Transactions of ASME Journal of Engineering for Gas Turbine and Power, Vol. 106, pp. 574-584.

Gostelow, J.P., 1984, “Cascade Aerodynamics,” Pergamon Press, Oxford, England.

Gummer, V., Wenger, U., and Kau, H. P., 2001, “Using Sweep and Dihedral to Control Three-Dimensional Flow in Transonic Stators of Axial Flow Compressor,” ASME Journal of Turbomachinery, Vol. 123, pp. 40-48.

Johnsen, I. A., and Bullock, R. O., 1965, “Aerodynamical Design of Axial Flow Compressor,” NASA SP-36.

Koller, U., Monig, R., Kusters, B., and Schreiber, H. A., 1998, “Development of Advanced Compressor Aerofoils For Heavy-Duty Gas Turbines Part I: Design and Optimization, “ ASME Journal of Turbomachinery, Vol. 122, pp. 397-405.

Koller, U., Monig, R., Kusters., B., and Schreiber, H. A., 1998, “Development of Advanced Compressor Aerofoils for Heavy-Duty Gas Turbines Part II: Experimental and Theoretical Analysis,” ASME Journal of Turbomachinery, Vol. 122, pp. 406-415.

Langstone, L. S., Nice, M. L., and Hooper, 1977, “Three Dimensional Flow Within a Turbine Cascade Passage,” Transaction of ASME Journal of Engineering and Power, Vol. 99, p. 21.

Lyes, P. A., and Ginder, R. B., 1999, “Low-Speed Compressor Test of Swept and Bowed Blade Designs", Proceedings of the 14th International Symposium on Air Breathing Engines, Florence, Italy.

Peng, Z., Wu, G., Yan, M., and Ren, L., 1991, “An Experimental Investigation of Technologies of End-wall Flow Control in a Compressor Plane Cascade,” AIAA paper no. 91-2005.

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Sasaki, T. and Breugelmans F., 1998, “Comparison of Sweep And Dihedral Effects On Compressor Cascade Performance,” Transactions of ASME Journal of Turbomachinary, Vol. 120, pp. 454-463.

Smith, L. H. Jr., and Yeh, H., 1963, “Sweep and Dihedral Effects in Axial Flow Turbomachinery,” Transaction of ASME journal of Basic Engineering, p. 401.

Ucer, A. S., Stow, P. and Hirsch, C., 1985, “Thermodynamics and Fluid Mechanics of Turbomachinery,” Volume II, NATO ASI Series, Martinus Nijhoff Publishers.

Wadia, A. R., Szuchs, P. N., and Gundy-Burlet, K. L., 1999, “Design and Testing of Swept and Leaned Outlet Guide Vanes to Reduce Stator-Strut-Splitter Aerodynamic Flow Interactions,” Transactions of ASME Journal of Turbomachinery, Vol. 121, pp. 416-427.

Wallis Allan R., 1983, “Axial Flow Fans & Ducts,” Wiley-Interscience Publication, John Wiley & Sons Inc.

Weingold, H. D., Neubert, R. J., Behike, R. F., and Potter, G. E., 1995, “Reduction of Compressor Stator End-wall Losses Through the Use of Bowed Stators,” ASME Paper Number 95-GT-380.