Compressor rotor blade performance in steady state operation

17 OKI 1973 VLIEGT'--^4:;""^' ^ - f T

Cranfield Institute of Technology

Compressor Rotor Blade Performance in

Steady State Operation

By

CRANFIELD INSTITUTE OF TECHNOLOGY SCHOOL OF MECHANICAL ENGINEERING

COMPRESSOR ROTOR BLADE PERFORMANCE IN STEADY STATE OPERATION

R. E. PEACOCK M.Sc. J. OVERLI

Recent developments in pressiire sensing and trajisfer techniques have made possible the detailed investigation of the aerodynamic behaviour of rotor blades. Tests on a

lightly loaded single stage compressor using this instrianent-ation have yielded pressure distributions at rotor blade hub, mid-height and tip sections and give new evidence on rotor behaviour. It is concluded that the combined effect of centrifugal force and annulus vail boundary layer skewing improve the performance of the rotor, suggesting that

efficiency of compressors would be improved if designed for reactions rather more than ^0%. The presence of a tip shroud has an adverse effect on rotor performance in the region of the tip section.

The experimental resvilts presented in this paper form part of a Ph.D. dissertation.

Summary

Nomenclature

1.0 Introduction

Page Numbers

2.0 Compressor and Instrumentation 2.1 The Test Compressor

2.2 Instriomentation

3.0 The Experimental Programme

U.O Discussion

k.l Blade Mid-Height Observations

k.2 Blade Hub Observations

k.3 Blade Tip Observations with a Shroud

h.k Blade Tip Observations without a Shroud

h

5

6

7

8

₁₀

₁₁

pressure coefficient shape factor

incidence

pressure gradient parameter local static pressure

static pressure at entry plane radius of measuring section

Reynolds Niomber based on blade chord

Reynolds Number based on momentum thickness blade pitch

blade maximum thickness

tiurbulence l e v e l

blade speed

local velocity

free stream velocity

air relative inlet velocity to blade streamwise direction

air absolute inlet angle to rotor blade momentum thickness

1.0 INTRODUCTION

Cascade results have traditionally played a major part in the aerodynamics of axial compressor design, correlations of deflection,

deviation and stall limit forming the basis of blading design methods. In this respect, the work of Howell (Ref.l), Carter (Ref.2) and the NACA

(Ref.3) are well known.

Although there is probably a close similarity between the aero-dynamics of a cascade and that of a row of stator blades, rotor aeroaero-dynamics is complicated by phenomena which cannot be simulated in a cascade. These include centrifugal force effects upon the flow, the highly skewed nature of the annulus wall boundary layer at the rotor hub and the complex situation present at the tip with both a tip gap and relative movement between the rotor blade and annulus wall in the presence of boundary layers.

As a resiilt of the centrifugal force, a radial migration of the rotor blade boundary layers towards the rotor tip may be anticipated. Results of Lieblein (Ref.4) in measuring the wake momentum thickness down-stream of rotor blades have indicated this trend with a thickening of the shed wake towards the tip for uniform load over the blade height. In such conditions the rotor boundary layers would no longer be two-dimensional in nature and, over much of the blade height, woixld be likely to be thinner than in the two-dimensional case, fluid being transported from other parts of the blade surface towards the tip section. The highly three-dimensional nature of the flow at hub and tip, due to boundary layer skewing, the tip gap and the relative movement of the blade tip and annulus outer wall create situations that are even less clearly londerstood.

There is little evidence of the effect of these mechanisms upon compressor performance. It has, however, been observed in one instance that a compressor design of 60% reaction tended to operate at a slightly higher efficiency than one of 50^ reaction, suggesting that a higher pressure rise cotild be sustained by the rotor boundary layers than by the

In the absence of more quantitative evidence of rotor boundary layer behaviour, the measured performance and limits of equivalent

cascades have served as a basis for compressor design. Rotor evidence has been difficult to obtain, since the problems of bovmdary layer measurement in a representative rotating system are great. Recent developments in instrumentation techniques at Cranfield have, however, made possible the acquisition of such evidence by the accurate measurement of pressures on the rotor blade surfaces.

It is the purpose of this report to present results from a series of tests on a single stage compressor in which rotor pressiire distributions were obtained over a wide variety of operating conditions. From these results it is possible to indicate the powerful effect of centrifugal force and the other factors contribution towards the detailed aerodynamic

behaviour of the rotor blades.

2.0 CO^gRESSOR AND INSTRUMENTATION

2.1 The Test Compressor

The compressor used for the experiments was a lightly loaded single-stage xmit designated the C13^ compressor. Of constant annulus cross-section, the compressor with a tip diameter of 20.0" and a channel height of 5'00" was fitted with free vortex,«Q ~ 0 design blades. The stage was, in this build, preceded by a row of uncambered zero stagger inlet

guide vanes, Ck blade sections being used throughout. A variable speed 5 H.P. electric motor drove the compressor at speeds up to a maximum of 1500 rev/min, mass flow being controlled by a throttle-valve situated at the tail-pipe exit.

A diagram of the compressor layout is shown in fig.l.

2.2 Instrumentation

The rig was fitted as standard with instrumentation necessary to evaluate the overall performance characteristics, mass flows and pressures being measured by rakes of probes disposed orthogonally in the anniilus.

In addition to the standard instrumentation, instrumentation to determine pressure distributions around the rotor blades at the mid-height section, the hub section and the tip section, was also fitted to various rotor blades. Static pressure tappings were located at the designated sections, one tapped surface per blade and ten tappings per surface. The blades, paired by the sections at which the tappings occurred, were fitted to opposite sides of the rotor disc for balancing reasons. For simplicity of data acquisition, measurements were taken at one section only in any particular test.

2.3 Accuracy of Instrumentation

For experiments of the type described in this paper centrifugal

force was a possible source of inaccuracy. An evaluation, both by calculation and calibration allowed for a suitable correction to be made to the observed readings. The correction was, for most tests, negligibly small.

3.0 THE EXPERIMENTAL PROGRAMME

Experiments were carried out at three compressor rotational speeds, 1500 rev/min (the design speed), 1250 rev/min and 1000 rev/min. Mass flow was varied in the usual manner by a control valve at the tailpipe exit and this had the effect of varying the incidence of the blades. Variations of Reynolds Number were consequent both upon speed change and mass flow change.

Measurements at the compressor inlet and outlet yielded the overall-performance characteristic map (fig.2). Detailed measurements on the rotor blade surfaces were made on each compressor characteristic over a wide range of mass flow representing a range of incidence from i - 0 to i - lit.5 close to the siirge line. The rotor sections under investigation were close to the hub (r = 5.l8"), the blade mid-height (r = 7.35") and the blade tip

(r = 9.86"). Tip section behaviour was investigated both in a normal con-figviration and with a tip shroud fitted.

Turbiilence measurements were made over the whole range of the

characteristic. Plotted against the mass flow coefficient V /U (fig.3) they a

all fell on a single line, turbiilence levels varying from 0.8^ at high mass flow to 2.k% close to the surge line. These data are super-imposed upon the overall characteristic in fig.2.

it.o DISCUSSION

At all rotor sections, for each rotational speed and incidence under consideration, the blade pressure distribution was plotted in terms of the non-dimensional pressure coefficient:

c =Zlii

and the non-dimensional chordwise position x/c. Examples of the results are plotted in figs, k-6 (blade mid-height section) figs. 10-12 (blade hub-section), figs. 15-17 (blade tip section with a tip shroud fitted) and figs. 19-21 (blade tip section with normal geometry).

An integration of the pressure distribution at each test point, non-dimensionalised in dividing by the inlet relative dynamic head, led to a plot of the rotor blade normal force coefficient against incidence for each section under test. Figs. 7» 13, I8 and 22 show the resiilts for the

different blade sections and also include the results from distributions omitted for the sake of clarity from the figures previously mentioned.

There is little directly comparable cascade data. Some of the cascade tests carried out by Rhoden (Ref.5) were, however, with a cascade of closely similar geometry to that of the blade mid-height section (see Table l) and, where incidences and Reynolds Numbers were close to those of the compressor tests, the results from cascade and compressor are compared

in fig.8.

As an universal means of comparison though, pressure distributions calcvilated using Martensen's theory (Ref.6) were superimposed upon typical experimental results in fig.9 (blade mid-height section) fig.l^t (blade hub section) and fig.23 (blade tip section). Martensen's method, being inviscid, does not account for boimdary layer behaviour. In an unstalled condition an error is likely because boundary layer growth is not accounted for: in stalled flow, the effect of the separation cannot be assessed. In order

to take some accoiont of the convex surface boundary layer, methods due to Thwaites (Ref.7), Head (Ref.8) and a correlation of Seyb (Ref.9) were used to predict the transition and separation points of the section surface two-dimensional boundary layer at various operating conditions, using the Martensen predicted pressure distribution.

U.l Blade Mid-Height Observations

Initial measurements were made at the rotor blade mid-height section and typical pressure distributions are presented in fig. i+,5 and 6 at rotational speeds of 1500 rev/min, 1250 rev/min and 1000 rev/min.

At low incidence the distribution measured at each rotational speed was as anticipated. Increasing the incidence had the effect of producing a sharper suction peak and increased suction surface diffusion in the normal manner. The bo\mdary layer method predicted that a stall

would be initiated at an incidence of about 5 for two-dimensional conditions (see fig. 9b) but the experimental resiilts gave no evidence of a stall. With further increases of incidence the stall free condition continued, although the boundary layer method predicted a forward movement of a turb\ilent

separation point. At high values of incidence, in the range 12.7 to lk.6

with the compressor operating close to the s\irge line, the pressure distri-butions still gave no evidence of stall. In support of this, the level of normal force coefficient rose continuously with incidence until the surge line was reached, (fig.7).

A comparison between compressor results obtained at incidence and Reynolds Number levels similar to results of Rhoden's (Ref.5) is made in

fig.8. With an incidence of -1.0° and Reynolds Number of .878 x 10 (fig.8a) Rhoden's result clearly showed the presence of a laminar separation bubble

followed by a flow re-attachment and normal pressure recovery. The equivalent compressor result, at -0.2° incidence and Reynolds Number of O.883 x 10 also showed a separation bubble at about the same chordal position. For the case of it.O incidence the compressor result was interpolated: at this incidence and also at 9.0 incidence there was a good agreement between the compressor and cascade result. It may be noted that at every incidence, the rate of pressure recovery over the rotor convex surface was greater over most of the chordal length than for the cascade, indicating a thinner boundary layer for the rotor.

Fig.8 shows a comparison of the Martensen prediction with the distribution experimentally obtained for typical values of incidence. As with all sections, a reasonable agreement was obtained in the absence of stall.

It is evident that, at high incidence values, the experimental results differed from those expected on the basis of two-dimensional theory. The presence of significant three-dimensional flows in the rotor must

therefore be admitted whose effect was to inhibit the separation of the suction surface bovmdary layer. This was due to the presence of a centri-fugal force field which caused a radial migration of the low energy

boundary-layer fluid, resulting in a thinner boundary-layer than for the two-dimensional case. Lieblien's observations (Ref.U) support this in showing a thickening of the wake momentum thickness towards the tip.

k.2 Blade Hub Observations

In the blade hub region of a cascade, where the convex surface intersects the sidewall, data (Ref.lO) show the presence of an area of stalled flow in the corner. The structure of this stall is described in Ref.lO. Its existence is known to be due to secondary distributed flows in the cascade channel and a resultant migration of the sidewall boundary layer into the corner. Similar observations have also been made in rows of stators, both in compressors and turbines (e.g. Ref.ll). The

investi-gation at the rotor hub was especially concerned with examining this phenomenon in rotating machinery.

Experimental pressure distribution data from the compressor rotor hub section are plotted in figs. 10, 11 and 12 at the three speeds.

As with the resxilts at the blade mid-height section there was no evidence of stalled flow, the pressure recovery on the convex surface con-tinuing to the blade trailing-edge. The maximxim incidence recorded was at 15.1 with a rotational speed of 1000 rev/min. In the same manner as at the blade mid-height section the normal force coefficient continued to rise up to the surge line.

Referring to fig. ik, it is again noted that the Martensen result gave a reasonable approximation to the real situation, irrespective of incidence.

In the hub region of a compressor rotor, there is, in addition to the centrifugal force, a skewing of the annulus wall boundary layer as it advances into the rotor blade channel. The po-verful effect of the centrifugal force has already been noted in the blade mid-height observations and it may be prestuned to have had some effect in the hub region. The skewing of the annulus wall boundary layer in this region of a compressor relative to the

rotor blade, is in the opposite direction to that which arises from

secondary flow considerations. Instead of an accumulation of the annulus wall boundary layer in the convex surface corner as observed in cascades

(Ref.lO) the skewing due to rotor rotation would have the effect of moving the boundary layer towards the corner formed by the concave surface and the ann\ilus wall. In this region the pressure in the chordwise direction is usually substantially constant beyond about 30^ chord where such an accumulation would occur, so the tendency for separation would be minimal.

The elimination of the corner stall phenomenon in the rotor may there-fore be attributed either to the centrifugal force effect or the skewing of the annulus wall bo-undary layer or some combination of the two phenomena. It is impossible to separate the two effects conveniently at the hub section, but their relative importance may be judged from further experimental evidence from the tip section.

it.3 Blade Tip Observations with a Shroud

In an attempt to evaluate the relative importance of centrifugal force and botmdary layer skewing in suppressing the corner stall, a shroud was fitted at the rotor tip section. This created a convex surface/annulus wall corner similar geometrically to that at the hub. In this case, however, whereas the boundary layer skewing was in the same sense as at the hub, the centrifugal force was in the opposite sense, convecting boundary layer fluid into the corner.

The resulting pressure distributions at the three test speeds are plotted in figs.15, l6 and 17 and indicate significantly different aero-dynamic behaviour in the corner. At about 6 incidence a separation was precipitated and at all incidence values greater than this, stalled conditions were noted to exist, the stallpoint moving forward as the

incidence increased. With incidence greater than 10.3 the stall was initiated at about 33^ chord, well forward to the theoretically predicted point (see fig.22).

It is also interesting to note that the point of initiation of the corner stall was ahead of that encountered in a cascade of similar geometry, that of Table 1, at similar levels of Reynolds Number (Ref.12). In the case of the tip shrouded rotor, then, the corner separation was more severe than in cascade at high incidence, but at low incidence it was suppressed.

As a consequence of the stall the section normal force

co-efficient decreased rapidly with increasing incidence. This is shown in

fig.18.

From this evidence and that of the hub data, it may be concluded

that, whereas the skewed boundary layer probably had some effect on

suppression of the corner stall, the over-riding effect was that due to

the centrifugal force. This force, at the tip section of the shrouded rotor

caused a convection of low energy boundary layer fluid into the corner which

increased the tendency for corner separation to occur at high incidence.

k.h Blade Tip Observations without a Shroud

Compressor rotors are, in almost all cases, unshrouded and with a

tip gap. To complete the investigation in the tip region of this compressor,

therefore, tests were also conducted with this geometry.

The pressure distribution data are plotted in figs. 19, 20 and 21.

It was only at the maxim\im incidence for each speed that the flattening of

the convex surface pressure distribution which characterizes a stalled

condition, was recorded. The plot of normal force co-efficient for the

xznshrouded tip section against incidence indicates that there was a stall

inception at about 11 incidence, above which the normal force deteriorated.

Based upon the predicted separation of the boundary layer (see fig,22) the

section did not stall until a higher incidence than for a two-dimensional

flow, fig. 22b indicating a predicted separation at 6.5 incidence.

A comparison of the tip section performance with and without shroud

yields some significant points.

Over the unstalled incidence range for the shrouded blade, the

unshrouded tip section operated with a normal force coefficient between 2it^

and 35^ higher than that of the shrouded tip section. At higher values of

incidence the difference was much greater so that over the whole of the

operating range on the overall characteristic map the unshrouded tip section

performed better.

In spite of the radial migration of the blade surface boundary

layer towards the tip, stall was delayed on the unshrouded tip until an

incidence higher than that anticipated in the two-dimensional case.

It may therefore be concluded that, not only can an unshrouded compressor rotor blade behave better than a shrouded one, but that the tip gap can effect on improvement in performance over two-dimensional predictions. This comment must, however, be related to the size of the tip gap, in this case .031" or 0.6^ annulus height, for it may be antici-pated that very large tip gaps can have a deleterious effect.

5.0 CONCLUSIONS

The results of experiments carried out on the rotor blades of the C13i+ compressor have indicated the powerful effect of centrifugal force on the aerodynamic behaviour of the blade over its height.

At the mid-height section the radial migration of the low energy fluid resulted in a thinner boimdary layer which, on the convex surface, was resistant to separation. As a result no stall was detected up to the surge point. At the root section the centrifugal force convected the low energy corner flow away from the corner and, with the complimentary effect of the skewed annulus wall boimdary layer, suppressed the corner stall phenomenon. At the tip section, the effect of a shroud was to contain the low energy boundary layer in the convex surface/shroud corner and this

magnified the corner separation problem at high incidence. At low incidence the skewed boundary layer suppressed the corner stall. The effect of the tip gap in the unshrouded case was to enhance the tip performance and a corner stall was registered only at high incidence, an improvement over the cascade flow situation.

It may be concluded that,

1) the effects of centrifugal force and boiindary layer skewing aid the performance of a rotor blade and,

2) as a result, compressor designs for reactions in excess of 50^ should yield an efficiency improvement,

3) the presence of a tip shroud compromises the tip performance but that a tip gap can, in certain circximstances, effect an improvement.

6.0 ACKNOWLEDGEMENTS

This research forms part of a compressor research programme supported by the Science Research Council of Great Britain.

The C13i<- compressor was supplied by the National Gas Turbine Establishment, Pyestock, Great Britain.

REFERENCES HOWELL, A. R. CARTER, A. D. S. HERRIG, L. J. EMERGY, J. C. ERWIN. J. R.

'Fluid Dynamics of Axial Compressors' Proceedings of the Institution of Mechanical Engineers. 19i^5 Vol. 153.

'The Axial Compressor'

Gas Turbine Principles and Practice G. Newnes Ltd., London. 1955

'Systematic Two-Dimensional Cascade Tests of NACA 65-Series Compressor Blades at Low Speeds•

NACA RM L51G31 (l95l). LIEBLEIN, S. SCHWENK, F. C. BRODERICK, R. L. RHODEN, H. G. MARTENSEN, E. THWAITES, B. HEAD, M. R. SEYB, N. J.

'Diffusion Factor for Estimating Losses and Limiting Blade Loadings in Axial-Flow-Compressor Blade Elements'

NACA RM E5 3D01

'Effects of Reynolds Number on the Flow of Air through a Cascade of Compressor Blades'

ARC R & M 2919 1956.

Die Berechnung der Druckverteilung an dicken Gitter Profilen mit Hilfe von Fredholmschen Integralflechvingen. Arch.Rat.Mech. Anal. Part 2. No.3 p.235.

'Approximate Calculation of Laminar Boundary Layer'

Aeronautical Quarterly. Vol.1 November, 19^+9 •

'Entrainment in the Turbulent Boundary Layer'

ARC R & M 3152 i960.

'The Role of Boundary Layers in Axial Flow Turbomachines and the Prediction of their Effects'

10. PEACOCK, R. E.

11. ROHLIK, H. E. et al.

12. PEACOCK, R. E.

13. THOMPSON, B. G. J.

Ik. LUDWIG, H.

TILLMANN, W.

'Boundary Layer Suction to Eliminate

Corner Separation in Cascades of

Aerofoils'

ARC R & M 3663. 1971

'Secondary Flows and Boundary-Layer

Accumulations in Turbine Nozzles'

NACA 1168.

Unpublished work at University of

Cambridge.

'The Calculation of Shape-Factor

Development in Incompressible

Turbulent Boundary Layers with

Transpiration'

AGARDograph No. 97.

1965-'Investigations of the Wall Shearing

Stresses in Turbulent Boiondary

The boundary layer calculations have been carried out using the velocity distribution around the blade calculated by the Martensen method.

(Ref.6).

For the laminar boundary layer the calculation method chosen was suggested by Thwaites (Ref.7). The relevant equations

are:-g2 ^ OA|_V ^5 ^ V * 0

ƒ

^^^

. i ! dv

m

For the turbvilent boundary layer Head's method (Ref.8) was used. This involved an integration of the momentum integral equation.

do Cf , , 0 dv

•^

= 4 - (H + 2) - ai

and the entrainment equation

f = vF(H,)

Where Q = Vffli Hi = GH

Thompson's empirical equations (Ref.13) for F and H and Ludwig and Tillmann's skin friction equation (Ref.ll+) were used.

Calculations of the laminar separation point were based on the assumption that laminar separation occurred when m > 0.082. Transition from a laminar to a tvirbulent state was accepted to be a function of momentiam thickness 0, Reynolds number Rg, pressure gradient parameter m and turbulence level Tu, so a correlation of experimental results presented by Seyb

(Ref.9) was used for this.

Turbulent separation was considered to take place when the calculated skin friction value approached zero.

e

S

s/c

t/c

30°

-36°

1.0

.10

29.6°

-30.9°

0.898

.12

1.004

1.002

FIG. 2 OVERALL CHARACTERISTIC MAP OF SINGLE STAGE COMPRESSOR

LU - J 00 cc r> I -LU O < I

-z

FIG. 4 ROTOR BLADE MID-HEIGHT SECTION PRESSURE DISTRIBUTIONS N= 1500 REV/MIN.

-1.0

.883 x 10^

.849 x 10^

775 x 1 0 ^

735 x 10^

FIG. 6 ROTOR BLADE MID-HEIGHT SECTION PRESSURE DISTRIBUTIONS N = 1000 REV/MIN

0/

a

5°

FIG. 7 VARIATION OF ROTOR BLADE MID-HEIGHT SECTION NORMAL FORCE COEFFICIENT WITH INCIDENCE

- 1.0 COMPRESSOR - O - i =-0.?, Re = 0 . 8 8 3 x 1 0 ^ CASCADE i =-1.0°, Re = 0 . 8 7 8 x 1 0 ^ COMPRESSOR i = 4.0°, Re = 0.830 x 10^ CASCADE i = 4.0°, Re = 0.897 x 10^ 1.0 ^/c i = 8.9°, Re = 0.973 x 10^ i = 9.0°, Re = 0.910 X 10^

FIG. 8 COMPARISON BETWEEN ROTOR MID-HEIGHT RESULTS AND RESULTS FROM A SIMILAR CASCADE

Cp -0,5 - 1 . 0 L 1.0 Vc i ^ Q . < ^ ^ ' Cp 1.0 ^Ic Cp MARTENSEN PREDICTION ^/ ji FIG.9 COMPARISON BETWEEN ROTOR MID-HEIGHT SECTION

B i = 4.5°, Re = 1.038 X 10^

A i = 8.5°, Re = 0.959x10^

0 i = 14.3°, Re = 0.885 X 10^

FIG. 10 ROTOR BLADE HUB SECTION PRESSURE DISTRIBUTIONS N= 1500 REV/MIN

944X 10^

8 5 8 X 1 0 ^

7 9 3 X 1 0 ^

7 3 3 X 1 0 ^

FIG. 11 ROTOR BLADE HUB SECTION PRESSURE DISTRIBUTIONS N = 1250 REV/MIN

1.0 _ 1.0 ^/c 0 i = 0.9°, Re = 0.747 x 10-Q i = 5.4°, Re = 0.680 x 10^ A i = 9.1°, Re = 0.633 x 10^ <i> i =15.1°, Re = 0.583 x

10-FIG. 12. ROTOR BLADE HUB SECTION PRESSURE DISTRIBUTIONS N = 1000 REV/MIN

C H 0.65 0.55

O,

5°

A

• A.

O

A N ^ I250 REV/Mlh4

• N ^ 1000 REV/l^«N

W

Cp O -0.5 _ - 1 . 0 1.0 Cp O - 1 . 0 1.0 Cp

o

FIG. 14 COMPARISON BETWEEN ROTOR HUB SECTION RESULTS AT N = 1500 REV/MIN&THEORY

Ej i = 2.0°, Re = 1.518 x 10^ A i = 6.5° Re = 1.454 x 10^ O i = 8.6°, Re = 1.422 x 10^ 7 i = 10.3°, Re = 1.412 x 10^

FIG. 15 ROTOR BLADE SHROUDED TIP SECTION PRESSURE DISTRIBUTIONS N = 1500 REV/MIN

Q i = 4.5°, Re = 1.234 X A i = 7.2°, Re = 1.204 X

10-0 1 =11.5°, Re = 1.166 X 110-0^

FIG. 16 ROTOR BLADE SHROUDED TIP SECTION PRESSURE DISTRIBUTIONS N = 1250 REV/MIN

1.0

FIG. 17 ROTOR BLADE SHROUDED TIP SECTION PRESSURE DISTRIBUTIONS N = 1000 REV/MIN

CN 0.45 0 N = 1500 REV/MIM

A N = t250

EI N «1000

FIG. 18 VARIATION OF ROTOR BLADE SHROUDED TIP SECTION NORMAL FORCE COEFFICIENT WITH INCIDENCE

1 . 0 -CD A

0

FIG. 19 ROTOR BLADE UNSHROUDED TIP SECTION PRESSURE DISTRIBUTIONS N = 1500 REV/MIN

= 0.982 X 10^

= 0.938 X 10^

= 0.906 X lo'^

FIG. 21 ROTOR BLADE UNSHROUDED TIP SECTION PRESSURE DISTRIBUTIONS N = 1000 REV/MIN

0.65 _ 0.55 0 N = 1500 REV/MIN A N = 1250 REV/MIN • N = 1000 REV/MIN

5°

FIG. 22 VARIATION OF ROTOR BLADE UNSHROUDED TIP SECTION NORMAL FORCE COEFFICIENT WITH INCIDENCE

1.0 Vc i = 10.4° 1.0 ^/c 1.0 - O — UNSHROUDED TIP — « _ SHROUDED TIP MARTENSEN PREDICTION FIG. 23 THE EFFECT OF THE ROTOR SHROUD ON TIP SECTION