compressor bu~des at~gi · "~1umbers in parenthesis rerer to references. 1 . viii literature...

CASCADE PERFOR.'1.~NC£ OF DOUBLE CIRCULAR ARC

COMPRESSOR BU~DES . .11 Hl:GH At~GI.ES OF ATTACK

by

Peter T. Tkacik

Thesis submitted to the Graduate Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

APPROVED:

Master of Science

in

Mechanical Engineering

W. F. O'Brien, Jr .. Cha~rman

H. L. Moses S. 3. Thomason

May, 1982

Blacksburg, Virginia

I I ACK~OWLEDGE:vrE:ns

The author expresses sinc2re ~ppreciation to the men-

bers of his advisory co::nnictee: Professors H. L. Xoses, S.

B. Thomason, and W. F. O'Brien, Jr., Chairman. Dr. O'Brien

was especially helpful throughout the investigation.

Thanks are extended to ?rofessor J. B. Jones and the

Mechanical Engineering Department for providing financial

support during the author's graduate study. He is also

grateful for the assistance of the :I.E. Workshop, S.

Reimers, and D. Bruce during the construction of the wind

tunnel. The author is also indebted to Neta Byerly for her

patient and professional typing of the thesis.

Finally, the author is very indebted to his parents for

their constant encouragement and support.

III TABLE CF CONTE:~TS

I. TITLE

II. ACIGWw"'LEDGEMENTS

III. TABLE OF CONTENTS

IV. LIST OF FIGURES

V. LIST OF TABLES

VI. LIST OF STI1BOLS

VII. INTRODUCTION

VIII. LITERATDRE REVIEW

IX. EXPERIMENTAL EQUIPMENT

A. The Wind Tunnel .

B. The Cascade Test Section

C. The Blade Cascade .

D. The Measuring Equipment

X. RESULTS

XI. DISCUSSION

XII. CONCLUSIONS

XIII. RECOMMENDATIONS

XIV. REFERENCES

XV. APPE~DICES

A. Uncertainty Analysis

B. Inlet Velocity Measurements

c. Blade Production

iii

i

ii

iii

v

.viii

ix

1

7 .., /

13

16

17

21

51

. 58

. 59

. 61

. 63

. 64

. 7 3

. 76

XVI. VITA

ABSTRACT

III TABLE OF CONTENTS (continued)

iv

78

Figure

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

LIST OF FIGURES

Title

Tunnel Schematic

Inlet Filtration System

Inflated Tunnel Blower Junction with Pressure Gage . . . . . . . .

Blade Row Angle Guide, Probe Traverse and Stiffening Box

Blade Profile

The Blade Cascade Showing Close-Up of Instrumented Blade Passageway

Mean Deflection Angle

Mean Total Head Loss .

Stagnation Pressure Loss and Deflection Angle for ).l = 0° .......... .



Stagnation Pressure Loss and Deflection Angle for :i~ = 18° .......... .

J..

Stagnation Pressure Loss and Deflection Angle for :ii= 19° ..... .

Stagnation Pressure Loss and Deflection Angle for -,i = 20° . . . . .....

Stagnation Pressure Loss and Deflection Angle for ').i = 21° . . . . . . . . .

Stagnation Pressure Loss and Deplection Angle for :i. i = 22 ° . . . . . . . . .

v

8

9

11

14

18

20

22

23

25

26

? .., _,

23

29

30

31

. . 32

Figure

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

Al

LIST OF FIGURES (continued)

Title

Stagnation Pressure Loss and Deflection Angle for ::~ = 25° . . . . ...

.I.

Stagnation Pressure Loss and Deflection Angle for '.li = 28° ...

Stagnation Pressure Loss and Deflection Angle for :xi = 30 ° . . . . .

Stagnation Pressure Loss and Deflection Angle for '.li = 35° ...

Velocity Distribution for '.li = 0°

Velocity Distribution for '.ll = 8°



Velocity Distribution for :i.i = 19°


Velocity Distribution for :i.i = 21'



Velocity Distribution for ~i = 28°

Velocity Distribution for

Velocity Distribution for

). I = 300 1

). I = 350 1

Flow Visualization Spanwise Across the Blade at :i.: = 14° . . . ....... . ... Flow Visualization Spanwise Across the Blade at ·:li = 28° . .

Cascade Notation

vi

33

34

35

36

38

39

40

41

42

43

44

45

46

47

48

49

53

55

65

LIST OF FIGURES (continued)

Figure Title Page

A2 Nozzle Velocity Variation Above 65 m/s . . . 75

vii

Table

Al

A2

V. LIST OF TABLES

Title

Instrument Readability and Accuracy

Nozzle Velocity Distribution

vi.ii

72

74

i

L

p

s u

u v

v

x

y

:.1 I (ll

I :.12

'(

VI. LIST OF S'T.-'!BOLS

Incidence angle

Blade Height

Chord

Pressure

Pitch

Velocity component in the x-direction

Freestream velocity at the edge of the boundary layer

Velocity component in the y-direction

Freestream velocity

Air inlet velocity

Air outlet velocity 2 Total pressure loss (P01 - P02 /~oV1 )

~ean total pressure loss

Chordwise direction

Direction perpendicular to blade chord line

Air inlet angle

Flow in:et angle, angle of attack, relative to chcrd line

Air outlet angle

Flow outlet angle relative to chord line

Stagger angle

Deflection angle, ~ 1 - ~2

Mean deflection angle

Blade camber

ix

VI. LIST OF SYMBOLS (continued)

Subscripts

o Signifies stagnation state

x

VII INTRODUCTION

Because of the wide-range performance demands in cur-

rent turbomachines, there is a need for more complete infor-

mation on blade flow characteristics. Presently available

information on axial-flow compressor cascade performance

emphasizes design-point data. Recent interest in pre- and

post-stall behavior of axial-flow compressors has disclosed

a need for detailed experimental investigations of cascade

behavior at high angles of attack. This inf~rmation is

useful for improved understanding of the stall phenomenon,

and for input to numerical models of stalling behavior (1) "

To meet this need, the present investigation was con-

ducted with the goals of designing and developing a cascade

wind tunnel especially for high-angle-of-attack investi-

gations, and conducting an initial evaluation of the per-

formance of the tunnel and a representative set cf com-

pressor blade airfoils. Special attention was given to

measurenents evaluating inlet flow uniformity and turbulence

level, as ~vell as departures from tho-dimensional flow over

the blades at high angles of attack. An initial set of data

for a single stagger angle is presented.

_,_ "~1umbers in parenthesis rerer to references.

1

VIII LITERATURE RE'!IEW

Cascade Wind Tunnels

Due to the complexity of the flow through an axial flow

ccmpressor, most research has been based on models which

simplify the study by investigating specific interactions.

A cormnon simplification is to ass'l.lllle two-dimensional flows

through the blade rows. Cascade tests are of this type,

and, while not addressing many of the phenomena in a com-

pressor such as tip clearance leakage, centrifugal effects,

etc., these tests have proved invaluable in the deter-

mination of turning angles and losses for different blade

profiles. Near design-point operation, compressor cascade

flows are nearly two-dimensional, and cascade tests have

served well as a basis for design.

Departures from two-dimensional flows in a cascade ar2

more severe at high angles of attack. Ikui, Inoue, and

Kuromaru ran high-stagger-angle tests in 1970 (2) which

required a large number of high-aspect-ratio blades in the

cascade in order to obtain two-dimensional flows in the

meas~rement region. As with high-stagger-angle tests, high

angle-of-attack tests also encounter problems with two-

dimensionality. Keller at VPI&SU in 1978 (3) noted endwall

effects in a ca3cade of double circular arc blades with an

aspect ~atio of 2.33 as the angle of attack increased. :n

2

3

order tc extend the Keller tests at VPI&SU, a new wind

tunnel was built with modif icaticns similar to those of

Ikui, et al.

The design of the :~nnel (see Fig. 1) described in this

report was based on standard wind tunnel practices. As

described by R. D. Mehta in 1977 (4), a centrifugal blower

is used because of the cost, efficiency, and non-stalling

characteristics when heavily loaded. This blower is con-

nected to the tunnel with a flexible coupling to reduce

vibration transfer as proposed by R. D. Mehta and P. Brad-

shaw in 1970 (5). A tongue on the blower exit was also

modified according to reconnnendations of Mehta and Bradshaw

(5) .

From the blower, the flow enters a diffuser which has

screens to retard separation and the inherent tendency for

the flow to attach to one wall. These are arranged as

described by L. F. East in 1972 (6) and Mehta, et al. (5).

From the diffuser, the flow passes to a settling chamber.

Three screens are placed in series here to further smooth

the velocity profile and reduce boundary layers. These

scr-=ens are placed in accordance with recormnendations by :1.

A. Jackson in 1972 (7), although Mehta and Bradshaw later

recommended ir.creasing the distance between screens (5).

With a large settling chamber, a uniform velocity

prof~le can be obtained with a minimum of head loss. To

4

obtain high velocities in the cascade test section, a six-

teen-to-one area ratio contraction was employed. This

contraction is characterized by an almost circular-arc

contour, matched to a short inverse circular arc at the exit

region. This was done in accordance with recommendations of

M. N. Mikhail (8).

The design of the tunnel provides for honeycomb flow

conditioner within the settling chamber. These honeycomb

sections were not available at the time of the initial tests.

Even without honeycombs in the settling chamber, this com-

bination resulted in a test-section entrance turbulence

level of only 1.5% and a maximum variation in the nozzle

exit velocity profile of only 1.3%. Furthermore, the flow

is filtered to allow hot-wire anemometry tests. Flow

velocities greater than sixty-five meters per second are

provided.

Other Related Topics

In order to understand some other phenomena that arise

in cascade testing, a library investigation was conducted

on three subjects. The first was blade flutter, which was

anticipated as a problem due to the blade's being pinned at

the centerline, which was not the center of aerodynamic

lift. This caused an extreme flutter problem in tests

described by L. Bcnciani, P. L. Ferrara, and A. Timori at

5

Florence, Italy in 1980 (9), and J. Sparks at VPI&SU (10) i~

1981. In the present cascade, rubber dampers and extra

blade supports were installed to reduce the vibration to a

minimal level.

The second phenomenon investigated was endwall stall as

described by J. H. Horlock in 1973 (11). In the present

cascade, this problem arose at the base of the blades at

angles of attack approaching full stall. A gap at the full

span end of the blades as suggested by Dring prevented

endwall stall in the tip region.

Propagating stall was the third problem area of in-

vestigation. Much was learned about its cascade behavior in

a film by G. Sovran at the General :1otors Research Center

(12). Further investigations on propagating stall in double

circular arc blades were done by F. Cheers and L. E.

Macartney in 1959 (13) and simultaneously with the present

investigation by D. Mathioulakis of the ESM department at

VPI&SU in 1982 (14) .

For measurement of local static pressure, the blades

were manufactured with chordwise static pressure taps as

described by U. Keller (3). Downstream total and static

pressures were measured with a pitot-static probe as recom-

mended by D. J. Kettle in 1954 (15). Calculations of the

mean total-head-loss coefficier.t, :, and blade velocity

curves were done as proposed by S. Lieblein in NASA SP-36 in

6

1965 (16). Lastly, the :low tu~ning angle was based on mass

flow and momentum measured in the blade row direction as

defined by G. C. Oates (17).

IX EXPERI:~ENTAL EQL'IPMENT

A. Wind Tunnel

In order to provide the cascade with sufficient mass

flow and the related velocity, a wind-tunnel facility was

developed. This facility was constructed in the Turbo-

machinery Research Laboratory of the Mechanical Engineering

Department, and is shown in Fig. 1.

The tunnel inlet consists of a horizontal cylindrical

frame four-feet long and up to 45 inches in diameter. It is

mounted between the blower inlet and the laboratory wall and

is covered by a chicken wire mesh. The inlet is covered by

blue media filter material and provides a clean air flow to

the blower with no distortion due to the surroundings.

This filtration system is shown in detail in Fig. 2.

The blower is an Aerovent Model 630 BIA and is of the

centrifugal type. It is equipped with a 15-horsepower motor

and is rated at 12,000 CFM at a delivery pressure of eight-

inches of water. It is of steel construction and is bolted

through a wooden 4" x 4" frame into the concrete floor with

expansion bolts. In order to provide a more uniform exit

velocity profile, the exit tongue was modified as suggested

by Bradshaw (5). Power is controlled by an on-off switch

mounted on the laboratory wall and is of the 220 volt, three-

phase type. An emerger.cy power cuc-o~f switch pushbutton

.., I

Blower

Inlet Filter

Motor

Diffuser

,. ~Screens ~ ..

I ' I I I

I I '

Air I Flow•• I I I

I I I

' I '

PLAN VIEW Settling Chamber

t I I I I I I I I I I

I I I

I I I

I I I

, I I

I I I

' I I

ELEVATION 'JIEW

Nozzle

Figure l. Tunnel Schematic

Cascade co

,, " ... .........

9

.OP

Figure 2. Inlet Filtration System

10

is mounted on the cas~ade test section. The blower is also

equipped with an adjustable pulley drive system which allows

for speed variation.

Between the blower and the tunnel, a vibration ab-

sorption and sealing junction was fabricated. This junction

makes use of an inflated 27" x l.\" bicycle innertube infla-

ted to six P. S. I. :-1ounted on the blower case is a moni-

toring pressure gage and a Schraeder valve for refilling the

tube. These are shown in Fig. 3. A straightening screen is

also mounted at this junction.

As with most tunnels of this type, the flow frcm the

blower is slowed in a diffuser. This diffuser nominally

has an eight-degree half angle and expands for a distance of

six feet to an outlet area of sixteen square feet. To

reduce the possibilities of separation in the diffuser,

another screen was placed midway down the length at the

flange located at that point.

The wind tunnel walls were fabricated from three-

quarter inch A-C plywood, as were the flanges. The tunnel

sections are supported by two-inch steel angle legs with

adjustment bolts as feet to keep the tunnel centerline

horizontal as shown in Fig. 1. The exterior of the tunnel

is painted Nhite. During fabrication, the smooth side of

the plywood was assembled facing inwards and initially

prepared with a coat 0f sander sealer and wood putty. Final

Figure 3.

11

Inflated Tunnel Blower Junction with Pressure Gage

12

preparation included several coats of glossy polyurethane.

From the diffuser, the flow passes through a settling

chamber. The 12,000 CFM flow passes through this chamber at

nominally only sixteen feet per second, so that straight-

ening and smoothing can be done without incurring a large

pressure drop. Provision is made for the mounting of a

five-eights inch cell honeycomb for turbulence reduction.

In the series of tests described, the tunnel was operated

without the turbulence reduction honeyco~b, but with flow

straightening screens installed at twelve, sixteen, and

twenty inches downstream of the entrance. The full length

of the settling chamber is twenty-four inches.

Following the settling chamber is the first nozzle

section. In a distance of two feet, this section reduces

the cross section from four feet square to three feet

square. At three feet square, the dimensions became small

enough for the second nozzle section to be fabricated of

formed sheet metal.

The second nozzle section matches the slope of the

first at the flange connection. Furthermore, to optimize

the flow and reduce the chance of boundary-layer separation,

the first section was brought into the shop and the junction

dimensions were mated by hand, which provided a smooth wall

shape. The profile of the second section is essentially a

combination of two arcs matched together with the radius of

13

the second arc being :he starter as proposed by M. ~.

Mikhail(8). At the outlet, flow area is maintained constant

for two inches to insure the ccrrect exit slope of zero

degrees.

In order to reduce the effect of boundary-layer corner

flows, the cross-section down the tunnel is maintained

square and in the second nozzle section the corners were

rounded with body putty.

B. Cascade Test Section

The cascade test section has a one foot square hori-

zontal inlet with up to eighteen test blades which turn the

flow upwards. To provide both variable stagger and in-

cidence angle the blade row is mounted between two rotatable

discs of plexiglas each four feet in diameter and ~ inch

thick. This is shown in Fig. 4.

!he discs are mounted against three-quarter inch thick

wooden backboards. These are five feet square and have four

foot diameter ports as shown to allow viewing of the blades

for possible laser doppler anemometry tests. These back-

boards are then held rigid by a perimeter frame. At the

outer edge of this frame are three-quarter inch panels

connecti~g both backboards and providing overall cascade

strength. L~rgc openings are provided for the exit flow and

at the inle: to allow for access to the adj~stable top

14

Figure 4. Blade Row Angle Guide, Probe Traverse and Stiffening Box

15

and bottom flow panels as well as che inlet itself.

As shown, the cascade is s 1.ipported at each corner by

one and one-half by three inch steel channel legs. These

are fourty-four inches long and each has an adjustment bolt

as a foot. The inlet design allows this adjustment to be

made independently of any tunnel adjustments and helps to

maintain a smooth transition throughout the inlet region.

This smooth transition proved to be one of the more

difficult jobs of design and construction but was finally

executed with the help of a high-speed router. The router

allowed very clean, straight, and perpendicular cuts.

~1ounted on an arm, this router also allowed the blade mount-

ing discs as well as the disc carriers to be machined to an

accurate radius.

The two blade discs provide a smooth inlet transition

and allow the angle of the blade row to be variable. Since

the tolerances are close around the circumference and the

radius is large, the contact friction is also large. In

order to avoid turning the discs independently and thus

possibly breaking the blades, torsional rigidity between the

two discs is required. This rigidity was provided in the

form of a 16" x 11~" x 12" plexiglas box which is fastened

to both discs and is located below the blades and away from

the tes~ section range. On the front disc is a pointer

i6

which references to marks on the cascade body and identifies

the blade row angle. This angle-oeasurement device, as well

as the box for torsional rigidity, can be seen in Fig. 4.

Since the inlet must remain horizontal and still allow

the blade row angle to be variable, the top and bottom walls

of the inlet are moveable. These walls are completely

removable half-inch plexiglas panels with adjustable feet

mounted at four points. These feet are on tall blocks and

push outward, thus bracing the panels in any position be-

tween the two discs. Since this is a compressor cascade the

inlet section operates below atmospheric pressure; there-

fore, all possible leaks must be sealed (here with duct

tape) in order to avoid feeding boundary layers and dis-

turbing the flow.

Xore of these panels were fabricated to be used as

tailboards downstream of the blades. These were judged to

be unnecessary for the present tests and were not used.

C. Blade Cascade

Eighteen blades constitute the blade cascade. With a

solidity of one, this number of blades allows a blade row

angle as high as seventy-five degrees. The blade row angle

is defined as the angle of attack plus the stagger angle.

For corrnnonly-used stagger angles, very high angles of attack

can ~e reached.

17

At these high angles the t~in blades are heavily loaded

and support becomes a problem. Fer this reason, each blade

and its base were cast as a unit. A description of the

blade-forming process is given in the Appendix. Since the

base can only give support at one end, pins are fitted to

the opposite end of the blade. When assembled, these pins

protrude into shallow holes in the near plexiglas disk and

while giving support, still allow the stagger angle to be

changed. An aluminum bolt is epoxied to the blade base and

is bolted to the far disc. A steel rack mounted in that

disc assures accurate alignment.

The blade cross-section employed is shown in Fig. 5.

This blade was chosen because it represents the midspan

profile of the first stage of a compressor on a common

aviation gas turbine.· The engine referred to is the General

Electric T64-CE-6B. All cascade blades are cast without

twist and have a chord length of 2.58". Since endwall

effects are increased at high angles of attack the blades

were developed with the high aspect ratio of 4.65, i.e. the

blade length is 12.00". The stagger angle selected for the

initial tests is 36.s~.

D. Measuring Equipment

The primary flow measurement device in the cascade is a

pitot-static probe model P~A-12, built by United Sensors &

i.8

-co 0

DIA= 0.055"

0.20"

I •

/~ II

p::;

Figure 5. Blade Profile

19

Control Corp., Massachusetts. This probe is mounted o~ a

traverse 2 mm downst=eam of the b:ades and measures the

total and static pressures across the blade wake and between

the blades. The probe was aligned with the help of a rod

mounted telltale which limited the accuracy to one degree

of yaw angle; however, with this system errors associated

with steep velocity gradients were eliminated. Unfortunate-

ly even this system has low accuracy in a fully stalled

blade wake region but this was felt to be insignificant due

to the low relative mass flow. The traverse is readable to

1/5 of a degree in angular measurements and to 1/4 of a

millimeter in rectilinear measurements.

Static taps were cast into the pressure and suction

sides of opposing blades at the center of the cascade.

Twelve taps on each blade were located at midspan. This

positioning was chosen so as to avoid non-two-dimensional

flows and is shown in Fig. 6.

A multitube inclined manometer is used to display the

pressures from the static blade taps as well as the pitot

static probe. It has thirty-one channels, uses red gage oil

(S.G. = 0.826), and is inclined by 60°. Readings can be

ascertained down to 0.20 mm of water.

A Thermo-System Inc. Hotwire Anemometr:r System was used

to determine the freestream turbulence levels at the in~et

of the cascade.

Figure 6.

20

The Blade Cascade Showing Close-Up of Instrumented Blade Passageway

X RESULTS

The circular arc compressor blade cascade described was

tested at a single stagger angle of 36.5°, and the angle of

attack was varied across twelve angles ranging from 0° up to

35°. The chosen angles of attack were biased towards higher

values for purposes of more fully mapping that region.

The measured mean deflection angle versus angle of

attack is shown in Fig. 7. This was calculated from mea-

surements taken downstream across the blade span. The

relationship uses continuity and conservation of momentum in

the blade row direction. The definition is from G. C. Oates

and describes mean turning angle as follows (17):

s f JUVdS

-1 0 = ~l - tan - s 2 OU ds 0

The mean total head loss calculated versus angle of

attack is shown in Fig. 8. This was calculated from

measurements do·..vnstream across the blade span. The mean

total head loss relation used was as defined in NASA special

publication SP-36 as follows (16):

21

22

25 en w w a:: C) w 20 0 ...

C0 w _J C) z ~

z 0 t-(.) 10 w _J u_ L&J 0 z <t 5 IJ.J ~

0 ... ----------------------------------------. -5 0 5 10 15 20 25 30 35

ANGLE OF ATTACK o;', DEGREES

Figure 7. ~ean Deflection Angle

23

1.0

0.8 13

(('} 0.6 (('} 0 _J

0 <t L&.J 0!4 ~

_J

~ 0 .... z 0.2 <t l.IJ ~

oL----=::::;:;:~;::::::~---.---.,.......--....--..., -5 0 5 10 15 20 25 30 35

ANGLE OF ATTACK ~ , DEGREES

Figure 8. ~ean Total Head Loss

24

1 s Pa1 - Pa2 ~ = - f ds

s o ~ o v2 1

Downstream stagnation pressure loss and deflection

angle were found by the use of a pitot-static probe mounted

on a traverse. The resulting data are plotted with respect

to fraction of chord parallel to the cascade blade row.

Again, in order to observe trends, this information is

plotted for all tested angles of attack, and may be found in

Figs. 9 through 20.

The loss curves show the blade wake levels as cal-

culated versus position down the blade row. Except for the

zero-angle-of-attack situation (negative incidence angle)

the suction side of the blade produces the larger wake.

This can be seen by the fact that the plotted wake loss

maxima are nearly vertical down the left side (pressure

side) and slope more gently down the right side (suction

side). This is true even into the highly-stalled blade

range.

For all unstalled angles of attack, part of the flow

downstream of the blades retains the upstream total pressure

value. At twenty-five degrees where the fully stalled

condition originates, none of the measured downstream total

pressure values are as high as the upstream values. As the

35

30 CJ)

~ 25 a: <!>

~ 20 <..U z 0 .... (.) w _J u.. w 0

15

10

5

0

~ 0.8 g w ~ 0.6 CJ) w a: Cl. 0.4 z 0

~ 2 0.2 <!> ~ Cf)

0

Figare 9.

.,_

25

I

--- Ji - - ~ -0 - - ~ - - ~ r-o

1'7

r R

f I I !

j I \ \ )

J - ~I - - -1.0 1.5 2.0

FRACTION OF CHORD PARALLEL TO CASCADE Stagnation Press~re Loss and ueflection A..~gle for :ii = 0°

35

30 (/)

t!:j 25 a:: (!)

~ 20 .. <-0 z 0 1-u w _J Lr-w 0

15

10

5

0

~ 0.8 g w ~ 0.6 ~ 0::: a.. 0.4 2 0 ~ z 0.2 (!)

~ CJ)

0

~~

26

I

,. _fA. ~ "-' ~ "" ~ -

'7

) )

..,

\ ~

ol

I'"'\ ,... ,... r ,... ,... .'°\ ,... ,... ,... \_ I I

1.0 1.5 2.0 FRACTION OF CHORD PARALLEL TO CASCADE

Figure 10. Stagnation Pressure Loss and Deflection Angle for :ti = 8°

35

3 (/)

~ 2 a:: <!)

5

?. 7

~ 2 0 ~'fl p-o-.___ -.. <.0 z 0 .... u w _J LL.. w 0

5

0

5

0

0

~ o. g 8

w ~ 0. (/) w a::

6

a.. 0 .4 z 0

~ z 0. <!)

~ CJ)

2

0

~,,

Figure 11.

~I ~ l----0- v -"' I'f'·

~~ P--

I~

T\ \ R

\ -J ~ ,.. ('\ ,..., I"' "' ~,..., ,..J, '"'

1.0 1.5 2.0 FRACTION OF CHORD PARALLEL TO CASCADE Stagnation Pressure Loss and Deflection Angle for :tl = 14°

35

3 (/)

~ 2 er: (!)

5

~ 2 0 ... <.u z 0 ..... (.) w _J LL. w 0

5

0

5

0

~ 0. g w

0

8

~ 0. 6 (/) UJ

~ o. 4 z 0 ~ z 0. (!)

~ en

2

0

~ ,.. ~

' ~

28

A~ J \ "\,j - ~ -....._ r ~

IS

("I

\ (" l1

I I

I I c \

j \ "" "' "' j ~ ("I

I


Figure 12. Stagnation PYessure Loss and Deflection Angle for :ti = 18°

35

3 (/'J

t±1 2 0: (!) w 0 2 ..

tU z 0 ..... (.) w ...J LL. w 0

5

0

5

0

5

0

~~I. 0

~ 0. g w

8

~ 0. 6 (/'J IJJ 0: Q.. o. z 0

~ z 0. (!)

~ en

4

2

0

~-

I<

Figure 13.

v

29

I I I T

I ~r~

,_..__,~.:r

~ °'\ I -v-- b-' ~

\0 'CU

~

\ I \

~ ~

I ' \ I \ I~ I

I ~ \ (' l ~ - ~ ~

1.0 1.5 2.0 FRACTION OF CHORD PARALLEL TO CASCADE Stagnation Pressure Loss and Deflection Angle for .ti = 19°

35

3 Cf)

~ 2 a: C!> w 0 2 ..

<.U z 0 ..... (.) w ....J LL w 0

5

0

5

0

5

0

0

~ 0 g .8

w ~ 0. Cf) w

6

ff 0 .4 z 0 ~ z 0. C!> ~ CJ)

2

0

30

~~ v· v~ ~ 0 -~ ~ f-o

0 r---._"' J")

~--~ '7

f\ ~

\ \ \,J

\ \

\ \ I ' \ 0 l ~ \

" ' ' " '


Figure 14. Stagnation Pressure Loss and Deflection Angle for :ii = 20°

35

3

.. t<l z Q .... (.) w _J LL w 0

5

0

5

0

5

0

~ 0. g w

0

8

~ 0. 6 ~ b: 0 z 0

.4

~ z 0. <!>

2 ~ CJ)

0

31

(~ ~

/ '"'""- Q..

~~ ~ ,..__

o/. ~

-~ I~

r\ T\

\ \ \ (l

\ \ \

J ' """ ~ J ~~ n ~


Figure 15. Stagnation Pressure Loss and Deflection Angle for ~i = 21°

(/)

35

30

ttJ 25 a: (.!)

~ 20 .. tU z 0 .... u w ....J LL. w 0

15

10

5

0 C\J 0"" a._ > ~ ~ 1.0 o _,C\I a._

~ 0.8 g w ~ 0.6 (/) w ~ z 0 ~ 2 (.!)

~ Cf)

0.4

0.2

0

~

~u

~.,,~

r\ \

J p'n; 1.0

32

I .--.<"\

~ jJ r-

~ " _[] /

147

r. \

\ \ \ \ \

\

\ j ~.~ 1.5 2.0

FRACTION OF CHORD PARALLEL TO CASCADE Figure 16. Stagnation Pressure Loss and Deflection Angle

for =ii = 22°

(/) LL.I LL.I a: (!) LL.I c .. ~ z 0 ~ u LL.I ...J LL LL.I c

35

25

20

15

10

5

0

1.0

~ 0 g .8

LL.I

~ 0 .6 ffl ~ 0 .4 2 0 ~ z 0 (!)

~ (/)

.2

0

Figure 17.

33

,G ' -I \ I ¢ \ "' ('

~ I ~ I ~-

~ J "'-0

- 0 'Q ~

r\ \ \ b

\

\ \

\ \

J \ I '~

7 \ J 1.0 1.5 2.0

FRACTION OF CHORD PARALLEL TO CASCADE Stagnation Pressure Loss and Deflection Angle for :ii = 25°

Cf)

35

30

~ 25 a: (!)

~ 20 .. t0 15 z

0 ..... (.) w _J LL. w 0

10

5

0 C\J 0 ..

9- ~ l.O o _,C\I Cl.

~ 0.8 g w ~ 0.6 (/) Cf) w ~ z 0

0.4

~ 2 0.2 (!)

~ Cf)

0

34

r ' '"" I o'~

R ~ I c

\ ~ '\ l

/ I

'b---0" 'c-~

r ~ ~~ \ ~ Y7

\ \ \

\ J \ ~ \ \

~ / '\J' )


Figure 18. Stagnation Pressure Loss and Deflection Angle for 1i = 28°

.. <.U z 0 ~ (.) lJJ _J ~ lJJ c

3

3

5

5 v 0

5

0

5

0 "' -

.0

~ 0 g .8

LLJ a:: 0 ~

.6 CJ) LU

~ 0 .4 z 0

ti z 0 (!)

~ Cf)

.2

0

Figure 19.

\

35

/°\, / ~

\ I \ v\\ v \

1 ,,

\ I \ ~ \_ Id

?"- ~

I \ ifl \

\ I \ I \ ' (

\

\ \ ( .

\ \ r ) b

\J r'-.J

1.0 1.5 2.0 FRACTION OF CHORD PARALLEL TO CASCADE Stagnation Pressure Loss and Deflection Angle for :ii = 30°

.. tU z Q ~ (.) LLJ ...J LL LLJ 0

35

3

5

0

5

0

5

I

0 ~-

0

~ 0 g .8

LLJ ~ 0. (/) LU

6

~ 0 .4 2 0 ~ z 0. (!)

t! Cf)

2

0

't;". ?Q ~ i.gure - .

I\

36

/"R 1:> .......--0,

v \ 1~/ v- \ 0

p c

\ / \ I \ I \ \ v 'o_

I-'

1'7

\ r ~ \ I \ I

\ 1/ \ ~

1D

\ \ )

\ J v \ J 1.0 1.5 2.0

FRACTION OF CHORD PARALLEL TO CASCADE Stagnation Pressure Less and Deflection Anele for :ii = 35°

37

angle of attack is increased further, the regions of high

loss increase in extent, but nee in level.

From zero degrees up to sixteen degrees angle of at-

tack, the curve reveals a mini~UI!l in losses. The actual

minima appears to be at about eight degrees, which cor-

resonds to zero incidence angle. At eighteen degrees angle

of attack the mean total head loss starts to increase rap-

idly. This region corresponds to the first maxima on the

deflection curve, Fig. 7. Following this region the de-

flection curve falls off, and simultaneously the slope of

the loss curve reduces. In the high-angle-of-attack region,

where the mean deflection curve begins to rise again, the

mean total head loss curve again further reduces in slope.

For purposes of showing trends, the calculated velocity

distribu~ion on the blades is shown for all tested angles of

attack. (See Figs. 21 through 32.) On the ordinate of each

graph is the fraction cf inlet velocity related to pressure

by the relation:

Fraction cf Inlet Velocity = , ~ v2 ~ - 1

In each case, the suction side blade results are the upper

curve and the pressure side blade results are the lower

curve.

A point cf interest is at an angle of attack equal to

38

1.6

1.4 SUCTION SIDE

>-.... CJ 1.2 0 ...J w \ > \ .... \ UJ ...J /

~ 1.0 LL. PRESSURE SIDE 0 z 0 ~ 0.8 u <l a; LL.

0.6 I

04 .... ________________________________ ___

0 0.2 0.4 0.6 0.8 1.0 FRACTION OF CHORD

Figure 21. Velocity Distribution for :..{ = o~

39

1.6

1.4

> SUCTION SIDE f--u 1.2 0 ..J IJJ > f-IJJ ..J ~ 1.0 lJ.. ' ' 0 -z 0 ~ 0.8 u PRESSURE SIDE ~ a::: lJ..

0.6

04 ...... -----..-------~--------------------o 0.2 0.4 0.6 0.8 1.0 FRACTION OF CHORD

Figure 22. Velocity Distribution for ~i = 8°

.:.o

1.6

04LU-----~.------..-------,-------,.------r 0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD


~l

1.6

1.4

>- SUCTION SIDE .... u 1.2 0 _, w > .... w _, ~ 1.0 LL ..... 0 .... ., z 0 .-= 0.8 (.) ~ a::

PRESSURE SIDE LL.

0.6

04w-----------------------------------o 0.2 0.4 0.6 0.8 1.0 FRACTION OF CHORD

Figure 24. Velocity Distribution for :xi = 18 °

42

1.6

1.4

> SUCTION SIDE .... u 1.2 0 ...J LU > .... LU ...J ~ 1.0

' ' LL ,,.. 0 z 0 ~ 0.8 u PRESSURE SIDE ct a:: LL

0.6

0.4 0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD

F'igure 25. Velocity Distribution for ' 19° ::il =

43

1.6

1.4

> .... u 1.2 SUCTION SIDE 0 ...J UJ > .... UJ ...J z 1.0

..... LL. ' /

0 z 0 t:= 0.8 u

PRESSURE SIDE ct a: LL.

0.6

04u...----------........ ------.,..------.------.., 0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD

Figure 26. Velocity Distribution for ~{ = 20°

44

1.6

1.4

> t-u 1.2

SUCTION SIDE 0 ...J UJ > t-UJ ...J ~ 1.0 ..... .....

/ u.. 0 z 0 ~ 0.8 PRESSURE SIDE (.) ex a:: LI..

0.6

0.4 0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD

Figure 27. Velocity Distribution for I

::il = 21°

1.6

1.4

>- SUCTION SIDE I-u 1.2 0 ...J l&J > I-LLJ ...J ... ~ 1.0 ' .,, LL 0 z 0 t= 0.8 PRESSURE SIDE u ct a:: LL

0.6

0.4 0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD

Figure 28. Velocity Distribution for I

:t 1 = 22°

46

1.6

1.4

> ..... -u 1.2 SUCTION SIDE 0 ...J IJ.J > ..... .....

' IJ.J / ...J ~ 1.0 u.. 0 z PRESSURE SIDE 0 ~ 0.8 u <t a:: u..

0.6

0.4 0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD

Figure 29. Velocity Distribution for ' :i = 1 25°

47

1.6

1.4

> ._ u 1.2 0 SUCTION SIDE _J UJ >

' ._ ' UJ \ _J /

~ 1.0 ~ LL. 0 z PRESSURE SIDE 0 j:: 0.8 (.) <t a:: . LL.

0.6

0.4 0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD

Figure 30. Velocity Distribution for ' = 28° :, 1

48

1.6

1.4

>-._ u 1.2 0 SUCTION SIDE ..J UJ > ._ ' ' LLI / ..J 2 1.0 u.. 0 z PRESSURE SIDE 0 t== 0.8 u ct a: u..

0.6

04 ..... __________ ......,. ______ ,...... ____ _,_ ____ --t 0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD


49

1.6

1.4

> ... u 1.2 0 SUCTION SIDE ..J LIJ > ...

' LIJ ' ..J ,, z 1.0 LL. 0 z PRESSURE SIDE 0 ~ 0.8 u <t a: LL.

0.6

OAw....-----------.------..-----....... ----__, 0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD


50

zero degrees. Here the in~idence ~ngle equals minus eight

degrees, and for the first thirty-five per cent of the chord

there is a lower pressure (higher velocity) on the pressure

side than on the sucticn side. This is due to the negative

angle of incidence.

At an angle of attack of eight degrees, (zero-degree

incidence) the suction side of the blade shows higher

velocity values across the entire chord. This behavior is

maintained for all subsequent values of angle of attack.

As can be seen on the figures, the velocity distri-

bution shows the expected characteristics of airfoils for

angles of attack up to twenty-two degrees. At twenty-five

degrees the suction side of the blade curve becomes level

revealing a fully-stalled flow. This fully-stalled curve

shape is maintained to the highest values of the tested

angles of attack.

XI DISCUSSION

It is shown in Fig. 7 that as angle of attack in-

creases, the turning angle cf the flow also climbs. This

process deteriorates as the blades approach the stalled

condition. As this occurs the mean-turning-angle curve

actually becomes negative in slope. This slope is continued

until about twenty-five degrees angle of attack. At this

point the blades are fully stalled and the shape of the

suction side is thought to be inconsequential with respect

to the flow; however, the flow is forced to pass through the

blade passages and is guided primarily by the pressure side.

For this reason, even though the total losses still climb

with increasing incidence angle, the turning angle is forced

again into a rising condition with rising incidence angle.

The extremes of this phenomenon are uncertain due to

reduced flow in each passageway at the higher angles of

attack. Furthermore, the mean total head loss at thirty-

fi7e degrees angle of attack, is already over eighty-five

per cent and therefore cannot possibly maintain such a high

s}.ope :or much longer; much less to the theoretical limit of

ninety degrees. For this reason very little extrapolation

from the measured data may be done. Reducing the s~agger

angle would allow the necessary high angles of attack but

t~at requires more tests and will be addressed in the

reco~errd2tion sectic~ to follow.

51

The two-dicensicnality of :he flow in the blade passage-

way was of interest. This is a complex question to address,

but some observations have been viewed in the test section

which allow some generalizations. Fig. 33 is a view looking

downwards into the blade row at fourteen degrees angle of

attack. The flow is from bottom to top and strings are

mounted across the leading edge of one blade at 0.5", 1.0",

1.5", 5.0", 7.0", 10.5", 11.0", and 11.5" across the span.

It was observed that under these conditions the strings

(telltales) on the pressure side of the blade showed very

little deflection in the spanwise direction, the exception

being at the extremes where the flow apparently moves toward

the edges feeding the boundary layer below. Due to the gap

on the right hand side the telltale has deflected to the

extent of being blown around the edge and down the suction

side. The gaps are 0.12" on average.·

Cn the suction side of the blade, greater deflection of

the strings is observed. Unlike the pressure side, however,

the direction is toward midspan. In general the greatest

deviation angle is at the outer positions, but at one inch

from the blade ends the deviation is only on the order cf

five degrees. For both the suction and the pressure side at

the five and seven inch locations, no measurable deflection

was noted.

Figure 33.

53

Flow Visualization Spanwise Across the Blade at ai = 14°

54

Figure 34 shows a similar view in the fully stalled·

range. In this photo, t:he angle of attack is twenty-eight

degrees, but similar flow patte=ns csn be observed. On the

pressure side the flow direction is in the downstream di-

rection with deviation only being at the extremes. Again,

deflection is away from midspan. Furthermore, on the right

hand side the telltale is again blown around the edge. For

the most part, the midspan flow appears two-dimensional,

being off-axis by only about five degrees on the left side

and at two inches from the right side showing no deflection

at all.

The suction side of the blade has similar flow patterns

with respect to the unstalled condition but the turbulence

in the stall-generated wake makes this phenomenon difficult

to photograph. With these observations, the error due to

departure from two-dimensional flow at the midspan position

may be considered minimal.

Another question arises concerning the smooth drop in

turning angle at angle of attack of 22° and the smooth

return again to a positive slope at 35° angle of attack.

The ~ain reason for the curve shape however has much to do

with a phenomenon known in compressor testing as "rotating

st:all".

In axial flow compressors rotating stall occurs in the

transi~ion region bet~een normal operation and the fully-

SS

t I

I . .,.,.

- ·.• \ ., f J , I

·- ---· · · c4 f ;

,1111---~-~~R=~- : : . .. I

I • • ;

~ I I

Figure 34.

_-""lulW~---- - .... -

- ~ t

Flow Visualization Spanwise Across the Blade at al = 28°

stalled condition.

stalled passageway

56

This phenomenon consists of a single

interacting w~th the flow such that the

fol lowing passageway stalls ar.d i.mloads the first. This

phenomenon may continue, grow, and extend over several blade

passages. In full rotacing stall, a stall cell propagation

speed will be en the order of half of the engine speed and

can be maintained continuously.

In a linear compressor cascade this phenomenon can also

occur and is called "propagating stall". Since the stall

cell propagates along the blade row it may eventually pass

the instrumented passageway and thus alter the reading.

Fortunately, the question of this effect has been addressed

on similar blades (circular arc) and found that natural

propagating stall initially appears at about twenty-two

degrees. In the present tests, the propagation was found to

~ove at around 0.8 times the flow speed but to travel only

two or three passageways before dying out. For this reason,

tests on propagating stall in cascades usually have an

initiatir.g device for stall cell generation.

As the angle of attack is increased towards the fully-

stalled condition, the strength of the stall cells increases

and propagation will continue along the full blade row. Un-

like the compressor case, the stall cell stops due to the

end of the blade row, this being a discontinuity. As found

in the cascade in question and in the referenced tests, the

57

blades are fully stalled at approxirrately twenty-five

degrees angle of attack.

Based on the above, i~ the :ested cascade at twenty-two

degrees angle of attack propagating stall is likely.

However, due to the velocity of the flow, the time of pro-

pagation past the instrumented passageway is less than a

~illisecond. Considering this and the frequency response cf

the multitube manometer, it is evident that the readings are

time averaged and as the angle of attack goes up from 22°,

the percentage of time spent in a stalled condition in-

creases. This explains the gradual drop on the turning-

angle curve which then smoothly begins to increase at an

angle of attack of 25° where the blades initially become

fully stalled.

Finally, in the transition region, observations were

made which showed endwall stall at the base end of the

blades. This phenomenon did not occur at the pinned ends of

t~e blades due to the gap. The effect of this single end-

wall stall is therefore reduced, and causes less effect with

~espect to stream tube contraction and a related lessening

of total pressure losses. As with propagating stall, this

effect is observed only in the transition region between

normal operation and full stall.

XII CONCLCSIONS

The results have s~o·..m good repeatability with earlier

data (3). Variations exist in the values of mean total head

loss. These variations are minimal and correspond to in-

provements in an endwall contraction effect. It is con-

cluded that these modifications did, in fact, improve the

measurements.

Available data in the high-angle-of-attack regions is

rare. From the experimental results obtained it was found

that as the angle of attack is increased the turning angle

of the flow is increased. For double circular arc com-

pressor blades this situation changes at 22° angle of attack

where the turning angle starts to go down. As the angle of

attack is increased above 25° the blades become fully

stalled and the turning angle begins to climb again.

7he mean total head losses are minimal in the unstalled

region with an actual mimimum corresponding to a zero-

degree incidence angle. As the angle of attack increases

the slope of the mean total head less curve increases. This

=ise in slope reaches a maximum at 22° angle of attack but

t~e values of mean total head loss increase up to the the

tested limit of 35° angle of attack.

58

XIII RECO~NDATICNS

The results of the experi~ents demonstrate that much

progress has been made in the conscruction of the dedicated,

high-angle-of-attack, cascade faci~ity. Prior research has

alleviated some of the inherent oroblems related to high

angle of attack flows. Nevertheless, many refinements can

still be made and include:

(i) manufacturing two test blades of metal to reduce

blade flutter,

(ii) Applying boundary layer suction just upstream of

the tested blade row,

(iii)increasing the gap at the base of the blades to

reduce the endwall stall phenomenon,

(iv) installing honeycomb in the settling chamber and

controlling turbulence levels with screens placed

in the nozzle.

Besides these modifications the following tests are

recommended.

(i) An investigation into the effects of natural

propagating stall in the transition region between

normal operation and fully-stalled operation.

(ii) A study at low stagger angles probing into the

ultra-high-angle-of-attack region including the

59

60

tunnel designed limit of 75'.

(iii)An investigation with Laser Doppler Anemometry

equipment so as to avoid probe interactions with

the flow.

(iv) An investigation into downstream struts to find

steady upstream interactions and perforra flow

visualization tests.

(v) A correlation of results of tests using various

blade cross-sections and stagger angles.

XIV REFERENCES

1. Sexton, M. R., and W. F. O'Brien, "A Model for Dynamic Loss Response in Axial-Flow Compressors," ASME Paper, 81-GT-154, 1981.

2. Ikui, T., M. Incue, and N. Kuromaru, "Researchers on the Two-Dimensional Retarded Cascade; Part 3, Cascade Performance at High Inlet Angles," Bulletin of the J.S.M.E., Japan, August, 1970.

3. Keller, U. J., "Performance of a Double Arc Blade at Low Reynolds Number," Masters Thesis at VPI&SU, Virginia, October, 1978.

4. Mehta, R. D., "The Aerodynamic Design of Blower Tunnels with Wide-Angle Diffusers," J. Aerospace Sci., Vol. 18, pp. 59-120, Pergamon Press, Great Britian, 1977.

5. Mehta, R. D., and P. Bradshaw, "Design Rules for Small Low Speed Wind Tunnels." Aeronautical Journal, pp. 443-449, November, 1979.

6. East, L. F., "Spatial Variations of the Boundary Layer in a Large Low-Speed Wind Tunnel," Aeronautical Jour-nal, p. 43, January, 1972.

7. Jackson, N. A., "Theoretical Velocity Distributions Downstream of Non-Uniform Single and ~1ultiple Smoothing Screens," Aeronautical Journal, p. 251, April 1972.

8. Mikhail, M. N., "Optimum Design of Wind Tunnel Con-~ractions," AIAA Journal, Article No. 78-819, Vol. 17, No. 5, :fay 19 79.

9. Bonciani, L., P. L. Ferrara, and A. ':'imori, "Aero-Induced Vibrations in Centrifugal Compressors," Cen-trifugal Compressor Design Department, Nuovo Pignone, Florence, Itanly, ~ASA Conference Publication 2133, Xay 12-14, 1980.

10. Spa!:'ks, J. F., "A Modeling Technique for Subsonic Stall Flutte'!:' in Cascades," Ph. D. Dissertation at VPI&SU, February, 1981.

11. Horlock, J. H. , "Axial Flow Compressors-Fluid ~!echanics and T~ermodynamL::s," Robert E. Krieger Publishing Company, ~~e~.; York, 197 3.

61

62

12. Sovran, G., "Propc.gating Stall in Airfoil Cascade," (Fil~) FM-7, General Motors Research Center.

13. Cheers, F., and L. E. ~!aca:-tney, "Propagating Stall in a Water Cascade Tunnel," Internal Laboratorv {-!emo-randum, National Research Council, Division of ~!echanical Engineering, Ottawa, Canada, 1959.

14. Mathiolakis, D., "Steady and Unsteady Cascade Measure-ments," Masters Th es is in SS~I at VPI&SU, 1982.

15. Kettle, D. J., "The Design of Static and Picot Static Tubes for Subsonic Speeds," Journal of the Royal Aero-nautical Society, p. 835, December, 1954.

16. Lieblein, S., "Experimental Flow in Two-Dimensional Cascades," NASA Special Publication-36, Aerodynamic Design of Axial-Flow Compressors, NASA Scientific and Technical Information Division, Washington, D.C., 1965.

17. Oates, G. C., "Cascade Flows," Chapter 12, The Aero-namics of Aircraft Gas Turbine En ines, AFA?L-

0 io, Jan.

18. Kline, S. J., and F. A. :.rcclintock, "Describing C'n-certainties in Single-Sample Experiments," ~Iech. Eng. , p. 3, January 1953.

19. Dzung, !... S. ED., "Flow Research on Blanding," Elsevier Publishing Company, New York, 1970.

XV APPENDICES

63

A. UNCERTAINTY ANALYTIS

The uncertainty in calculating the mean flow-turning

angle is found with the methods of Kline and McClintock

(18). The angle notation is as defined in Fig. Al. The

uncertainty W- is generated from the relation

W- = E

N

i=l

2 k 2

h w 3N N.

l. • 1 1

where Ni are the various primary measurements that make up

s. The relation for~ produces the averaged turning angle

based on mass-averaged momentum downstream of the blade row

s (17) .::uvds tan -1 0

~ = :.tl - s 2 .::u ds 0

A finite-difference method of integration was used for

data reduction and the relation developed was simplified to

s ' ' ~ Chz ho2) sin (2 :.t2) - ,, - ~

'-

-1 0 s :.tl - tan s

~ Chz - ho2) sin (:; 2) 0

where h is the level on the measurement manometer and ~2 is

the data step size. The above equation may be simplified by

assuming :(. = 14 ° . .l..

Unfortunately the partial derivatives to

64

65

s

I Gl

I

I

Figure Al. Cascade Notation

66

be used in the generation of the uncertainty are still a

problem. For this reason the uncertainty for the two sum-

mations will be found first and used in a simplified rela-

tion for uncertainty in mean turning angle. The uncer-

tainties of the various parameters may be found in Table Al.

Wsumtop = ( { ih;n Whz} 2 + { ;h:z Wh02) 2

( ' )2 (' )2)~ + :~um W.J.2 + ?~1:1m Wc:.1 J ..l 2 J..:. ,_

In order to proceed we need the various partial derivative

values.

-:.sum = ~

sin ,:_i,tot

= --2- 5.23 mm )sum = jfio2

~sum = 22.54 mm ' ' ' ,) ...... (.,

Wsum top = ((5.25 x 0.2) 2 + (5.23 x 0.2) 2

2 19102 rr.m

+ (19102 x 0.017) 2 + (22.54 x 0.25) 2 )~

Wsum top = 324.8 ? mm-

67

The lower sunnnation was done i:-i a similar fashion with

the resultant,

) Wsum bottom= 313.2 l.!ffi~.

For simplification, the uncertainty of the ratio of

these two summations was then calculated.

Wratio =({'ratio Wsum top)2 +(~ratio Wsum bot}2)~ )sum top l~ sUrll bot

The partial derivatives are then needed.

:!ratio ~sum top = 1

sum bot = 4.90 x 10- 5 -2 mm

:!ratio ~sum bot

= -sum top (sum bot) 2

= 4.90 x 10- 5 -2 mm

The uncertainty of the ratio is then

Wratio = ((4.90 x 10- 5 x 324.8) 2 + (4.02 x 10- 6

x 313.2) 2 )~ = 0.016.

We r.ow have enough information to proceed directly to

the final value of turning-angle uncertainty.

= ~ 1 - tan-l (ratio)

W-

68

1

= -1 = -.993 ~ratio 1 + ratio-

W~ = ((1 x 1°) 2 + (-.993 x 0.016) 2 )~ = + 1.0°.

It may be seen that the accuracy is then limited by the yaw-

probe capabilities and further reductions in uncertainty of

mean turning angle would have to come from a higher pre-

cision yaw-angle measurements.

The uncertainty of mean total head loss is also cal-

culated using the methods of Kline and ~cClintock. As

before, the relation of mean total head loss to its primary

measurements is needed. This is found in ~ASA SP-36 (16).

s JU(POl - P02 )ds

1 0 = 2 s _lz.::Vl ::uds 0

This relation was simplified and then integrated using

finite-difference methods in a manner similar to the mean-

turning-angle calculation. The resulting relation is as

follows.

69

s - (h2 1 0

,I = (hl ho1) - s ~ (h') ... 0

All ter:ns have been previously been defined and as with

the mean turning angle, the uncertainty of the two sum-

mations will be calculated first. The development will be

done in the same order as before.

(( 3sum ) 2

w bottom = 3(h2 ho2) W(h - ho2) + sum - 2

(;~~ woj2 r 3sum = ~ I-# A, = 2.093 ;; Cn 2 - ho2) 2(h2 - h ) ,,.2

02

;sum 16.08

Wsum bottom= ((2.093 x 0.4) 2 + (16.08 x 0.25) 2 )~ = 4.1

The upper summation was done in a similar fashion with

the resultant,

w = 431.6 sum top

70

We now have enough information to proceed directly to

the final value of mean-total-head-loss uncertainty.

1 surr, ton ~ = (h1 - n01 ) sum bot

w:::-=((;(h1 '~ n01J W(hl -hail) 2+(;s~:;top wsum top)

+ ( ; 5~ \ot W sum bot ) 2 ) ~

~sum top

1 = sum top = -8.806 x 10- 5 sum bot

= 1 = -1.523 x 10- 5 (h1 - h01 ) sum bot

--1 -:;.,--.-- = -l sum top = -1.981 x 10-4 3sum bot 2 Ch1 - h01 ) sum bot

10 -5 x ? -5 2 w: = ((8.806 x 0.4)~ + (1.523 x 10 x 431.6)

w:- = + 0.0065

Although the uncertainty band associated with this is

greater than the minimum value of :, most measurement vaiues

exhibit fairly good accuracy. ~uch of this is due to the

dimensionless character of : in which factors such as

..., 1 '~

density and temperature are cance:led out and not included

in the analysis. Nevertheless, L. S. Dzung (19) noted a

strong relationship between turbulence level and mean total

head loss. For this reason, we may conclude that the

results are accurate but should not correlate exactly with

similar tests run with different levels of upstream tur-

bulence.

72

TABLE Al. INSTRUXENT READABILITY AND ACCURACY

Multitube Manometer+ 0.2 mm H20

Rectilinear Traverse Scale+ 0.25 mm

Traverse Yaw Scale + 1/5 Degrees

Probe Yaw Capability± 1.0 Degrees

Blade Row Angle± 0.5 Degrees

Stagger Angle± 0.5 Degrees

Tunnel Air Temperature + l.0°F

Relative Humidity ± Si~

Atmospheric Pressure± 0.1 mm Hg

Turbulence Level = 1.6%

Velocity Variation at Inlet = 1.5%

B. INLET VELOCITY ~1EASTJREMENTS

The following are the results of a velocity profile

measurement at the inlet, four inc~es from the nozzle.

Twenty-five measurements were made with a pitot-static

probe. This did not include measurements on or near the

walls but were spaced evenly two-inches apart. Table A2

lists the velocity values as a function of position. Values

of i are at 2", 4", 6", 8", and 10" from the north wall and

values of j correspond to 2", 4", 6", 8", and 10" from the

top of the section. In an exaggerated format, Fig. Al

reveals the variation in velocity across the inlet.

73

74

TABLE A2. NOZZLE VELOCITY DISTRIBCTION (m/s)

~ 1 2 3 4 5

1 65. 65 65.54 65.75 65.75 66.05

2 65.33 65.43 65.33 65.33 65.54

3 65.22 65.22 65.22 65.22 65.43

4 65.86 65.86 65.86 65.86 65.33

5 66.07 65.75 65.22 65.22 65.22

75

i 1 2 3 4 5

j =

1

2

3

4

5

Figure A2. Nozzle Velocity Variation Above 65 m/s

Vertical Height/0.5'' + 65 = Velocity (m/s)

C. BLADE PRODCCTION

The information on the shape of the blade and the

forming processes used was generated by U. Keller. This

included measurements on an actual blade which was cut at

midspan and also experiments on blade forming techniques.

As with U. Keller's experiments, these tests used blades

molded of fiberglas.

In the final form, the blade manufacturing process was

similar to the Keller method. His notes are so extensive

that this subject will be addressed with details concerning

only the differences.

The basic mold is made of aluminum and has three main

parts for generating the pressure side, the suction side,

and the base of the blade. When manufacturing a blade, the

surfaces which are to come in contact with the resin must be

prepared with a mold release. After much testing it was

found that this coating must be verv thin, or large scale

imperfections appear on the blade surfaces.

The next step is the cutting of the fiberglas clot~

such that three sheets are obtained which will lay in the

suction side of the mold. Due to the size of the mold and

to allow for overhang, these sheets were approximately 2~ x

12 inches. Small two by three-quarter inch strips were

placed at the base end such that fiberglas in the final

blade will add to the strength of the blade-to-base

76

77

connection. When the meld is assembled and sealed with

putty, resin is poured into the mold forming the blade and

the base simultaneously. Curing takes about a day.

When cured, the blade was forced out of the mold.

Care must be taken to avoid damaging the blade. The next

step in blade preparation was trimming the blade to twelve

inches in length. This was followed by drilling a 0.095

inch diameter hole, 0.25 inches in depth, into the center of

the trirruned end. A 0.090 inch diameter dowel pin was then

epoxied into this hole. When trimmed, this dowel fitted

into the cascade wall and supported the tip end of the

blade. At the base of the blade an aluminum mount was

attached with epoxy. This mount was then bolted through the

cascade wall and was the support which maintained the blade

angle.

The vita has been removed from the scanned document

CASCADE PERFOR!'-!.ANCE OF DOUBLE CIRCUL\R AH.C

COMPRESSOR BL\DES AT HIGH ANGLES OF ATTACK

by

Peter T. Tkacik

(ABSTRACT)

The design of a cascade wind tunnel for testing of com-

pressor blades at high angle of attack is described. ~eth

ods to insure uniform velocity profiles and control of inlet

turbulence are discussed. The problem of maintaining two-

dimensional flows at high angle of attack was addressed.

A tunnel capable of testing cascades of compressor

blades at angles of attack up to seventy-five degrees was

constructed. Performance of the tunnel was evaluated and

data were acquired for flow over double-circular-arc blades

with angles of attack extending into the fully-stalled

region. Comparisons were made with available data in the

installed flow regime. Results showed that the tunnel had

adequately uniform inlet velocities and low turbulence

levels, and that two-dimensional flow was maintained over

the center two-thirds of the high-aspect ratio ~lades.

compressor bu~des at~gi · "~1umbers in parenthesis rerer to references. 1 . viii literature...

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