ROTOR WAKE BEHAVIOR IN A TRANSONIC COMPRESSORSTAGE AND ITS EFFECT ON THE LOADING AND

PERFORMANCE OF THE STATOR

Mohammad Durali

GT&PDL Report No. 149 April 1980

ROTOR WAKE BEHAVIOR IN A TRANSONIC COMPRESSORSTAGE AND ITS EFFECT ON THE LOADING AND

PERFORMANCE OF THE STATOR

Mohammad Durali

GT&PDL Report No. 149 April 1980

This research, carried out in the Gas Turbine and Plasma DynamicsLaboratory, MIT, was supported by the NASA Lewis Research Centerunder Grant No. NGL-22-009-383.

2

ABSTRACT

The structure and behavior of wakes from a transonic compressorrotor and their effects on the loading and performance of the downstreamstator have been studied experimentally.

The rotor is 2 feet in diameter with a tip Mach number of 1.23 anda measured pressure ratio of 1.66. Time and space resolved measurementshave been completed of the rotor and stator outlet flows, as well as ofthe pressure distribution on the surface of the stator blades. The datais analyzed and the rotor-stator viscous interaction is studied bothqualitatively and quantitatively.

It is found that the wakes from this rotor have large flow angle andflow Mach number variations from the mean flow, significant pressurefluctuations and a large degree of variation from blade to blade and fromhub to tip. There is a significant total pressure defect and practicallyno static pressure variation associated with the stator wakes. Wakesfrom the rotor exist nearly undiminished in the exit flow of the statorand decay in the annular duct behind the stator.

The pressure at all the points along the chord over each of the statorblades' surfaces, fluctuates nearly in phase in response to the rotor wakes,that is the unsteady chordwise pressure distribution is determined by thechanges in angle of incidence to the blade and not by the local velocityfluctuations within the passage. There are large unsteady forces on thestator blade, induced by the rotor wakes, as high as 25% of the steadyforces.

The stator force due to the rotor wakes lags the incidence of thewake on the leading edge by approximately 1800 for most radii.

3

TABLE OF CONTENTS

Page

Symbols

Figures

Introduction

Apparatus and Instrumentation

Data Analysis

Results

Conclusions

References

Appendices

A. Calculation of Efficiency

B. Mass Flow Calculation

1.

2.

3.

4.

5.

6.

4

6

8

12

23

29

41

44

124

126

4

LIST OF SYMBOLS

A area

a speed of sound

c blade chord length

cp specific heat

k compressible reduced frequency

M Mach number

P, p pressure

P. pressure at ith diaphragm on the probe

Ps static pressure

PS. ith transducer on stator blade pressure surface

Pt total pressure

R gas constant

R radius

SS. ith transducer on stator blade suction surface

T temperature

T time normalized by blade passing period

t time

U rotor rotational velocity

V flow velocity

mass flow rate

x distance along the chord

at blade angle

flow angle

5

e

y

Y

a

TI

Subscri pts

t

t

r

0

x

tangential flow angle

stagger angle

ratio of specific heat

blade solidity

radial flow angle

turning angle

efficiency

frequency, rad/sec

reduced frequency Q = cw/2V

density

tip

stagnation conditions

in relative coordinates

in tangential direction

in axial direction

6

LIST OF FIGURES

Number Title Page

2-1 View of the M.I.T. Blowdown CompressorFacility

2-2 Typical Pressure Signal in the BlowdownTunnel During the Experiment

2-3 Sectional View of the Test Section

2-4 Blade Position vs. Time

2-5 Miniature Pressure Transducer Assembly

2-6 Instrumented Traversing Blade

2-7 The Configuration of the Bridge Elementson the Transducer's Diaphragm

2-8 Output Signal from Diaphragms Locatedat Different Chordwise Locations

2-9 The 5-Way Probe

2-10 Electrical Layout for Probe's Transducers

2-11 Data Storage Layout

3-1 Comparison between Raw Data and the DataDigitally Bandpass Filtered

3-2 Frequency Spectrum of Raw and FilteredData

4-1 Average Flow Quantities vs. Radius behindthe Rotor

4-2 Average Flow Quantities vs. Radius behindthe Rotor

4-3 to Flow Angles, Pressure Ratio and Mach4-9 Numbers behind the Rotor vs. Time for

3 Radius Ratios

7

Number Title Page

4-10 to Flow Angles, Pressure Ratios and Mach4-33 Numbers behind the Stator vs. Time for

3 Radius Ratios at 3 Axial Positions

4-34 to Pressure Fluctuations and their Power4-39 Spectrum for Both Pressure and Suction

Surfaces at 20, 35, 50, 65, and 80% ofthe Chord, for 3 Radius Ratios

4-40 to Stator's Chordwise Distribution of4-42 Unsteady Pressure vs. Time

4-43 to Stator's Chordwise Distribution of4-45 Unsteady Lift Coefficient vs. Time

4-46 to Unsteady Loads on Stator Blade for4-48 3 Radius Ratios

4-49 Stator's Chordwise Distribution ofSteady State Pressure and LiftCoefficient

4-50 Steady State Tangential and AxialForces on Stator Blade vs. Radius

8

CHAPTER 1

INTRODUCTION

In recent years transonic compressors and fans have received much

attention from aircraft engine designers. This is due to the improvements

made in thrust-to-weight ratio of the aircraft engine by using high

pressure ratio transonic compressor stages. Typical stages of this kind

have a rotor that operates with moderate supersonic relative velocities

near the tip and high subsonic velocities near the hub. The high over-

all pressure ratio of such stages requires the outflow from the rotor to

have large swirl and high subsonic velocities.

The swirl put into the air by the rotor has to be removed

by stator blades before flow enters the next stage. A significant frac-

tion of overall static pressure rise across the stage comes from the

removal of this swirl by the stator. Flow through the stator is very

unsteady as a result of the rotor wakes being transported through the

stator passages.

The rotor wakes subject the stator to large changes in incidence

angle and as they are transported through the blade row they subject the

suction surfaces to unfavorable pressure gradients and impinge on the

pressure surface of the stator blades. These effects result in large

unsteady forces on the blades and potentially to increased viscous losses.

Time averaged pressure measurements carried out between the blade

rows using stagnation pressure probes, hold the stators responsible for

one-third of the overall stage losses. But a time averaging measurement

9

of this kind does not yield information about the mechanism by which the

losses due to unsteadiness in the stator occur. The aeroelastic response

of the stator to excitation by rotor wakes, and fan noise generated as a

result of rotor wakes interacting with stators are other important

phenomena which deserve extensive detailed studies if optimum designs are

to be achieved.

Current design practice assumes flow at a mean angle and Mach number

and uses experimental results from two dimensional cascades tested in

steady state flow, to calculate the required blade solidity and geometry.

Although this method has given acceptable results, it clearly does not

form a basis for an optimum design to minimize the losses due to unsteady

flow.

The complex flow field associated with the interaction between the

blades in a compressor has limited theoretical studies to two dimensional,

inviscid flow through cascades of simple geometries. The well known

formulations of Kemp and Sears [1,2] for aerodynamic interference between

moving blade rows have been extended by Horlock [4] to include chordwise

gusts.

Experimental measurements of pressure on isolated airfoils in

unsteady flow have supplied a great deal of information about the unsteady

flow over airfoils for example [13,15], but comparable data for cascades

is scarce. Blade measurements of unsteady pressure have been done at mid-

span on stator blades of low speed high hub-to-tip radius ratio test com-

pressors [5,6,7], but these results leave open many questions concerning

10

the effects of compressibility and hub-to-tip variation in highly loaded

transonic stages. The rotor wakes in a highly loaded transonic compressor

may be very different from those modeled by two dimensional theories or

found in low speed stages, having large radial flows, significant pressure

fluctuations and a high degree of variation from blade to blade and from

hub to tip [8].

There is therefore a need for documentation of the rotor wakes

structure and interaction with the stator in a typical transonic stage,

to provide a basis for development of more accurate models for the rotor-

stator interaction in transonic compressor stages. The objective of this

research was to construct a data base that will contribute to meeting this

need.

The M.I.T. Transonic Compressor is typical in the sense of having

a normal tip Mach number of 1.2, pressure ratio of 1.6 and conventional

blade shapes. It is not a highly developed design, hence it has somewhat

higher losses than the best contemporary stages with these design parameters.

But this is not considered a serious disadvantage for the present purposes

of advancing the phenomenological understanding of the rotor-stator inter-

action.

For this study one stator blade was instrumented with high frequency

miniature pressure transducers to allow time resolved measurements on

both the suction and pressure surfaces. The instrumented blade was made

to traverse radially across the annulus to obtain the distributions of

static pressure on the blade as a function of time at all radii. The

steady and unsteady loads on the stator blades can then be calculated

11

by integration of the pressure over the blade surfaces.

In order to relate the response of the stator blades to the wakes

from the rotor, time resolved radial and circumferential surveys of the

flow fields behind the rotor and behind the stator were also carried out.

Such data gives information about the structure and the frequency content

of the rotor wakes before and after interaction with the stator. It is

obtained by using the M.I.T. miniature pressure probe (also known as the

5-way probe), [10], to survey the flow field behind the rotor and behind

the stator. Radial surveys with the probe behind the rotor furnish

measurements by which the flow angles, total and static pressure and flow

Mach numbers can be calculated (as a function of time and radial and

circumferential positions).

A similar time resolved map of flow properties behind the stator

was obtained by replacing the traversing blade with another blade similar

to the rest of the stator blades, and allowing the stator to slowly

rotate during the probe traverse. Since the rotor blade passing rate is

much higher than the stator blade passing rate, the result is a time resolved

measurement of events connected with rotor blade passing, while the radial

and circumferential surveys are essentially quasi steady.

Some attempt was made to correlate the stator measurements with

the stator inflow and outflow, but this task remains in need of much more

work. It is hoped that the documentation of the flow will be sufficiently

complete to allow others to carry on with this effort0

12

CHAPTER 2

APPARATUS and INSTRUMENTATION

The experiments were performed in the M.I.T. Blowdown Compressor

Facility. The blowdown facility is described in detail in reference

[9]; for future reference it is briefly described here, along with the

experimental apparatus unique to the present study.

2.1 The Blowdown Facility

It consists of a compressor test section which is initially

separated from a supply tank by an aluminum diaphragm. The test section

is followed by a dump tank into which the compressor discharges. The

facility is capable of accommodating transonic stages having a tip

diameter up to 23.25 inches (Fig. 2-1).

To prepare for a test the system is evacuated. The supply tank

is then filled with a mixture of 82% Argon and 18% Freon-12. This mix-

ture has a ratio of specific heat equal to 1.4, but the speed of sound

in this mixture is about 75% of that in air, hence the desired Mach

numbers can be achieved at lower shaft speeds and lower stress levels.

The supply tank is filled to 495 mm Hg. when the M.I.T. compressor stage

is to be tested.

The rotor is then brought to speed in vacuum. The test starts by

rupture of the diaphragm which allows the gas in the supply tank to flow

through the test section. A throttle plate downstream of the test section

controls the mass flow through the stage.

13

During the test time the rotor is driven by its own inertia, hence

slowing down as it works on the fluid0 The supply tank total pressure

and temperature also decrease as a result of expansion of the gas into

the dump tank. By correct matching of the rotor inertia and supply tank

pressure the Mach number and rotor inlet velocity triangle can be kept

constant.

The forward flow duration time is only about 0.2 seconds after which

the gas sloshes back and forth until it comes to rest (Fig. 2-2). The

first 70 milliseconds of this time period is essential to establish the

flow through the test section. The next 40 milliseconds is the quasi-

steady period during which the useful data is to be taken. After this

period the throttle orifice behind the stage unchokes and the stage

rapidly stalls as a result of the increased pressure ratio across the

test section. Measurements are made through several instrumentation

ports along the length of the test section0

2.2 The M.I.T. Compressor Stage

This compressor stage originally designed by Kerrebrock [9] has a

transonic rotor with a tip tangential Mach number of 1.2. The stage has

a design pressure ratio of 1.6.

The rotor has 23 blades, an inlet hub to tip diameter ratio of 0.5

and an outlet hub/tip diameter ratio of 0.64 with a tip diameter of

23.25 inches. The relative Mach number at the tip is 1.3 and the inlet

axial Mach number is 0.5. The design parameters for the rotor are listed

in Table 2-1. The rotor is followed by a stator 3/4" axially spaced.

14

Muj~ MWr2

Ri/Pt 0.5 0.6 0.7 0.8 0.9 1.0

R 2/Rt 0.64 0.71 0.78 0.85 0.93 1.0

Mt 0.60 0.72 0.84 0.96 1.08 1.2

M 0.78 0.88 0.98 1.07 1.29 1.30

50.2 55.2 59.2 62.5 65.2 67.4

a2 23.8 35.7 44.2 50.6 55.6 59.5

Cr 2.00 1.67 1.43 1.25 1.11 1.00

Dr 0.50 0.49 0.45 0.43 0.40 0.38

ic 11.5 10.4 9.9 7.7 4.5 1.3

c 22.0 14.7 9.0 7.5 6.7 8.1

al 38.7 44.8 49.3 55.0 61,2 66.1

a2 16.7 30.1 40.3 47.5 54.1 58.0

y 28.9 38.1 45.0 51.1 56.3 61.7

t/c 0.10 0.086 0.072 0.058 0.044 0.030

M) 0.68 0.65 0.62 0.60 0.58 0.57

Table 2-1. The Rotor Blade Design Parameters

15

The stator has 48 blades and an outlet hub/tip diameter ratio of

0.68. The stator blades initially designed by Kerrebrock [9 ] could not

be used in this experiment, since they had radially varying stagger, while

the traversing blade is required to have a constant shape from tip to hub

and uniform twist so that the stagger angle and cross section can be held

constant at each radius during the traverse.

These two requirements led to a design for the stator that does not*

completely remove the swirl put into the flow by the rotor . The blades

have a total twist of 11.5 degrees from hub to tip (a chord length of

1.9" and a maximum thickness to chord ratio of 0.07). The design para-

meters for the stator are listed in Table 2-2.

To enable a survey of the flow field behind the stator in the cir-

cumferential direction as well as in the radial direction the stator

assembly is supported on bearings and is allowed to rotate during the

test time. The motion of the stator, at rest before the test, is caused

by the torque acting on the stator due to swirl in the flow. The moment

of inertia of the stator assembly is chosen large enough to avoid the

stator's spinning too fast. The maximum angular velocity of the stator is

2% of the rotor angular velocity. During the traversing blade experiments

the stator assembly is locked in position to prevent rotation (Fig. 2-lb),

one of the 48 blades being replaced by the traversing blade.

2.3 Traversing Blade Assembly

The traversing blade has the same sectional geometry as the rest of

the blades, but is three times longer. At the hub and the tip teflon

guides keep the blade at a constant setting angle during the traverse. At

*

The optimum design in this case would be to have the mean flow from thestator in the axial direction.

16

R/Rt 0.68 0.74 0.8 0.86 0.93 1.00

Cs 1.57 1.41 1.28 1.18 1.08 1.00

D 0.55 0.53 0.52 0.52 0.48 0.47

47.5 44.6 42.0 39.4 37.0 35.0

1 7.23 6.73 6.66 6.28 6.14 5.96

6.54 6.76 6.86 7.07 7.37 7.62

O 40.27 37.87 35.34 33.12 30.96 29.04

a2 2.77 0.37 -2.16 -4.38 -6.64 -8.56

2 9.31 7.13 4.7 2.69 0.73 -0.84

37.5 37.5 37.5 37.5 37.5 37.5

y 21.52 19.12 16.54 14.37 12.11 10.29

Design Parameters for StatorTable 2-2.

17

the ends of the traverse the instrumented location of the blade goes into

cavities beneath the teflon guides, providing reference pressures at each

boundary at the annulus (Fig. 2-3).

The traversing blade is moved by a pneumatic driver which is

designed to move the blade with a nearly constant traverse speed and quick

acceleration and deceleration at the two ends. The total traverse time

is controlled and can be as short as 25 milliseconds including the start

and stop. A typical trace of the blade position versus time is shown in

Figure 2-4.

The traversing blade is instrumented at one spanwise position and

five chordwise locations on each of the suction and pressure surfaces,

the locations on the suction and pressure surfaces being displaced about

0.25" spanwise from each other. The transducers used here are Entran

miniature silicon semiconductor transducers installed on Invar rings for

stress isolation (Fig. 2-5a). The straingauge transducer itself is a

silicon circular diaphragm 0.056" in diameter and 0.001" thick, with a

Wheatstone bridge on the back. The transducers have a natural frequency

of 150 KHz. and can withstand pressure differences up to 50 psi.

To stress isolate the transducers, they were assembled on Invar

rings of 0.125" diameter and 0.025" thick. Each transducers has five

leads, four essential to complete the bridge and one for thermal compensa-

tion. The complete transducer assemblies were then flush mounted on the

blade surface, being isolated from the blade with soft epoxy (Fig. 2-5b).

All the transducers have a vacuum line connected to their back for

pressure reference.

18

2.3.1 Orientation of Transducers and Stress Isolation

Although considerable effort was put into stress isolation

of the transducers, the attempt was not wholly successful. Low fre-

quency vibration of the blade due to mechanical shocks from large

acceleration and deceleration at the two ends of traverse, as well as

the D-C loading due to torsion of the blade during the traverse introduce

low frequency noise with large amplitude to the pressure signal measured

by the transducers.

Careful examination of the signals from all the transducers during

a test shows the following characteristics. For the first harmonic of

the blade bending vibration (at 250 Hz) which dominates the low frequency

disturbance, the phase and the amplitude of the vibrations are sensed

differently by different transducers. For transducers which are at the

same chordwise location but placed on opposite surface of the blade

there is always a phase difference of 180' between the noise signals.

But the transducers located on the same side of the blade sense the noise

with no phase difference although with different amplitudes. The difference

in phase and amplitude of the noise seen by different transducers could not

be explained by an argument based on their geometrical location on the

blade.

Figure 2-7 shows the shape and the configuration of the bridge

elements on the diaphragms. It can be seen that if the diaphragms are

strained in x-x direction the resistance of the bridge elements will not

be affected. On the other hand the maximum change in the resistance of

19

the bridge elements will happen when the diaphragms are strained in the

y-y direction.

Based on this argument the sensitivity of the transducers to stress

in the blade depends on the relative orientation of the x and y axes with

the direction of principle strain. For bending mode vibrations of the

blade the signals from three different transducers are compared in Fig.

2-8.

This problem could have been avoided by carefully installing the

transducers such that x-x axis lies along the blade span. But this

problem was identified during the experiment.

Here the problem was dealt with by two means:

1) Since the bending vibration signal was nearly

a pure frequency it was removed by a narrow

band digital filter.

2) The strain loadings that affect the measure-

ments were determined by covering the trans-

ducers to isolate them from pressure variations,

then repeating the blowdown tests. The signal

so obtained could then be subtracted from the

original pressure signal to remove the noise.

2.2.5 Thermal Compensation of Transducers

Since the strain-gauge elements have very little thermal

capacity and large temperature coefficients of resistivity, they are

very sensitive to temperature changes. This is a problem faced by all

users of such high frequency transducers to some degree. For the in-

strumented blade all the transducers were thermally compensated using

resistive compensation circuits.

20

The resistive compensation does not eliminate the temperature

sensitivity completely, but as the transducers on the blade are surround-

ed by large amounts of metal and are located far enough apart (relative

to their size) to prevent heating by the excitation power, the resistive

compensation seemed adequate.

2.4 The 5-Way Probe

The time dependent radial and circumferential distribution of Mach

numbers and flow angles as well as total and static pressure were

determined using a spherical probe [10].

The probe consists of a nearly spherical head on which transducers

of the type described in 2.3 are mounted (Fig. 2-9). One transducer in

the center is surrounded by four others so located that the surface of

each is at a 45* angle from the next one. The heat transfer characteris-

tics of the sphere in high Mach number flows make the thermal drift

problem more severe for the probe than for the stator blade. In this

case the resistive compensation did not suffice. To overcome the thermal

drift problem the current through a branch of the bridge was recorded too.

This signal is a measure of thermal drift because the current through

the bridge does not change due to pressure changes. By correct scaling

this signal can be subtracted from the pressure signal to correct for

thermal drift (Fig. 2-10).

The probe is traversed across the annulus using a pneumatic driver.

The total traverse time can be as little as 25 milliseconds. The traverse

ports are numbered 1 through 7 in Fig. 2-1b.

21

2.5 Other Time Dependent Measurements

The flow quantities in the facility which have a time constant of

variation on the order of one millisecond are referred to as low speed

quantities. Such quantities are wall static pressure at different

locations of the test section and the supply and the dump tank stagna-

tion pressures. These pressures are measured using pressure transducers

which have a lower natural frequency and are more stable.

The high frequency pressure at the casing, such as gapwise

pressure distribution or the pressure at the leading edge of the rotor,

are measured using high frequency pressure transducers of a similar type

to the one described in Section 2.3. The rotor angular position was also

monitored electronically and recorded during the test time.

2.6 Data Storage Layout

The signal from the blade or probe transducers and also the low

frequency data were first amplified. The amplified signal was then

recorded two ways:

a) digital storage, using an analog to digital converter (A/D)

having six high speed channels, each capable of sampling data

at a rate of 100,000 points per second. The digitized data was

then transmitted to a computer and stored on the disc.

b) analog temporary storage, in which a 14-channel high

speed FM tape recorder was used. The tape recorder can record

data with a tape speed up to 120 inches per second. The tape

recorder was used because the A/D did not have the capacity to

accept all of the data during the test time. After the test the

22

tape recorder was played back at 120 inches per second to

the analog to digital convertor. This way the rest of the

data channels were digitized and sent to the computer to be

stored on the disc. All the data was backed up onto digital

magnetic tape for permanent storage (Fig. 2-11).

23

CHAPTER 3

DATA ANALYSIS

As mentioned before the data taken during each test was stored on

computer disc and digital magnetic tapes. The unique opportunity pre-

sented by the Gas Turbine Laboratory computer facility for data acquisi-

tion and reduction made it possible to analyze the data in a very

accurate and efficient manner.

To be able to study rotor wake related phenomena in the compressor,

the data sampling frequency had to be much higher than the rotor blade

passing frequency. During the test time the analog signals from high

frequency transducers are sampled at a rate of 100 KHz. by the analog

to digital convertor. For each test over 150,000 data points were

recorded.

The analysis of the data can be divided into two parts, probe data

analysis and the analysis of the data from the traversing blade. In

the following the steps involved. in the analysis of each set of data are

described in some detail0

3.1 Probe Data Analysis

The results of the calibration of a 5-way probe model in a two-inch

diameter free jet were used to reduce the probe data. The model probe

was geometrically similar to the actual probe and was twice as large.

Pressure taps were located on the model probe at the same locations as

the high frequency transducers on the probe.

24

For several values of flow Mach number and different values of

$ and e angles (see Fig. 2-9) the pressures at the five points on the

probe were recorded. The following nondimensional parameters were then

retrieved from the calibration measurements and plotted versus 1 and e:

P. - P1P IP-1 + s- 1 f( qeqM) i =293 (3.1)

F45 P4- p 5 g( ,M) (3.2)45+ 4-5-P1+ = gGP 1)

P2 3 3F23 = (P3 P) + (P = h(,6,M) (3.3)

p - pC = ".I _- = j($,O,M) (3.4)

P -P

CP1 t 5 S(34

H = (P3- + (PP = k ($,M) (3.5)

Pt = Ps( + y-1 M2 )Y/Yl (3.6)

The functions on the right hand-side of Eq. (3.1) to (3.5) are

the calibration functions which depend on pitchwise and radial angles

and Mach number. Having these calibration functions, the above set of

25

equations could be solved for each data point to calculate total and

static pressures and flow angles. A computer program was written that

numerically solves the above set of equations for each data point.

Note that according to Eqs. (3.1) to (3.5) five known pressures,

PI to P5 , are used to find four unknown parameters (total and static

pressures and flow angles). This says that there is a redundancy in the

analysis. Ideally these equations should form a consistent system of

equations that enables us to use the redundant piece of information to

check the calculations. But actually the information from transducer

P5 (transducer next to the stem of the probe) was not used in this

analysis, for it results in unrealistically high negative radial flow

angles. This is partly due to the geometrical differences between the

stems of the actual and the calibrated probes. Also the thermal drift

characteristic of transducer P 5 is different from the other four, hence

the compensation scheme used for other transducers is inadequate for P5

To overcome this difficulty a local pressure coefficient for transducer

P4 was used instead of F45 (Eq. .(3.2)), defined as follows:

P4 - PC = t _ =

Using CP4 requires a higher number of iteration steps, because

the solution requires an initial prediction for three of the parameters

used in the equations (Pt' s, M).

26

The calculated flow parameters for measurements between rotor and

stator and behind the stator at different axial and radial positions are

shown in Figs. 4-1 to 4-33.

3.2 Traversing Blade Data Analysis

It was pointed out in Chapter 2 that the transducers mounted on the

blade were strain sensitive and that the data from the blade was disturbed

by low frequency noise and some D-C offset. The output signals from the

transducers on the blade are the result of the following effects:

i) actual static pressure at the point,

ii) strain due to twist of the blade during the

traverse and aerodynamic loadings on the blade;

iii) strain due to large radial forces during accelera-

tion and deceleration at the two ends of the traverse;

and finally

iv) strains due to mechanical vibration.

From all these only the first, the static pressure, is of interest here

and all the others are assumed to be disturbances to be separated from

the signal. The traversing blade data was used to study phenomena

related to rotor blade wakes and also to determine the steady state

loadings on the stator blades. The separation of the disturbances from

the desired pressure signal was done in different ways for the steady

and unsteady pressures.

3.2.1 High Frequency Studies

For the study of the high frequency part of the pressure

signals the data was filtered using a digital filter. Fortunately the

27

vibratory noise in the data had a frequency (250 Hz.) much lower than

blade passing frequency (3500 Hz). Therefore use of a digital filter

with sharp enough band pass (50 Hz max.) guarantees that the information

contained in the frequency range of interest is well preserved. This

digital filter played a very important role in the analysis of the blade

data, therefore it deserves a few words. The computer program of this

filter was written on the basis of the logic presented in [11]. The

related subprograms presented in Ref. [11] were modified to give the

program the capability of filtering frequencies as low as .00025 of the

sampling frequency. The filter could have up to 2000 terms. The result

of band-pass filtering (edges at 50 and 1000 Hz.) performed on a typical

signal from one of the transducers on the blade is shown in Fig. 3-1.

Filtering at this frequency range does not introduce a loss of power

in lower or higher dominant frequencies. The results of spectral analysis

of the signal before and after filtering are shown in Fig. 3-2.

For high frequency studies the data was high pass filtered at

2000 Hz. and then run through a chain of programs to calculate: frequency

content of the unsteady pressure distribution on the stator blade, axial

and tangential forces and pitching moment on the blade due to wakes, and

frequency content of the forces acting on the blade. The results of the

above calculations are shown in Fig. 4-34 through Fig. 4-48.

3.2.2 Steady State Studies

The steady part of the pressure measurement can not be

separated from the noisy signal by filtering only. To achieve a separa-

tion the transducers on the blade were covered with small aluminum caps

28

to completely isolate them from pressure inputs. The instrumented blade

was then put back into the facility and the same traversing blade tests

were repeated. These tests clearly yields the measurement of loading

and vibratory stress signals.

The D-C pressure distribution was then found as follows: the

loading signal was subtracted from the original signal and the result

was then low pass filtered at 100 Hz. Figure 4-49 shows the chordwise

pressure distributions on the stator blades at three radii. The radial

distribution of steady state axial and tangential forces on the stator

blade are shown in Fig. 4-50.

29

CHAPTER 4

RESULTS

4.1 Rotor Overall Performance

The overall performance of the rotor is calculated from both the

probe measurements and wall static measurements. The calculations show

that the rotor has an average total pressure ratio of 1.66, changing

from 1.71 at the tip to 1.6 at the hub (Fig. 4-lb), and an average

total-to-total isentropic efficiency of 0.80 (see Appendix A), changing

from 0.58 at the tip to 0.90 at the hub (Fig. 4-ld). In calculating the

time-resolved efficiency Euler's equation was used to find total tempera-

ture ratio across the rotor. These calculated efficiencies may not be

directly comparable to values determined by conventional steady state

methods of stagnation temperature and pressure measurement. They should

be comparable for the portion of the flow which has not undergone exten-

sive viscous interaction, but not necessarily for the wakes. This point

requires further examination. A corrected mass flow rate of 115 ibm/sec

was also measured (mass flow is corrected to standard sea level conditions).

The mass flow through the stage has been calculated by four different

methods. These methods (see Appendix B) and the corresponding calculated

values are as follows:

i) from the measured rate of pressure drop in the

supply tank (114.5 lbm/sec);

ii) from the measured static pressure downstream of

the stage before the choke plate (116 lbm/sec);

30

iii) from the rotor inlet Mach number which is com-

puted from the static pressure upstream of the

rotor (109.7 lbm/sec); and,

iv) from the integration of the flow quantities

measured by the probe along the radius (104.5 lbm/sec).

The results of the first two methods agree within 2%. The mass flow

calculated by method iii is 5% lower than the first two methods. Com-

parison of the results of pressure measurement on the casing using a

high frequency transducer with those from a low frequency transducer

which was originally used to measure static pressure upstream of the

rotor, showed that the latter measures a pressure higher than the actual

temporal mean wall static pressure. Although the low frequency trans-

ducer was located two rotor chords upstream of the rotor, it appears

that it was influenced by the upstream shocks from the rotor. The

measurement by the low frequency transducer located 1 rotor chord up-

stream of the rotor was 20% higher than the weighted average of the

pressure measured by a high frequency transducer at the same location.

Although the mechanism leading to this error has not been determined

this indicates that low frequency response pressure transducers with

conventional pressure tappings may give unreliable results upstream of

transonic rotors where strong shocks exist.

Method iv gives a mass flow much lower than the other three methods.

This is partly due to excluding the boundary layer regions at the hub

and the tip in integration and in part due to the error in the D-C

level of the flow quantities measured by the probe.

31

4.2 Stage Overall Performance

The stage has an average total pressure ratio of 1.57 and an

average efficiency of 70% (radially averaging the circumferentially

averaged flow behind the stator). A stage pressure ratio of 1.6 and an

efficiency of 73% result from radially averaging the time averaged total

pressure measured downstream of the stator at the middle of the stator

passage. These stage efficiencies are calculated by assuming constant

total temperature across the stator and finding the stage total tempera-

ture rise from Euler's equation. Consequently the results are very

sensitive to the level of the measured total pressures behind the stator.

Clearly the overall performance of the stage should not be judged on the ba-

sis of these values. However the changes in these efficiencies across the

wakes in every axial position can be used to estimate the losses. This

suggests an average 2.5% decrement in total pressure and 3% decrement in

efficiency due to stator wakes. Most of these losses come from the stator

hub region. The causes of these losses are discussed later.

The torque acting on the rotor and stator should balance with

the changes in the fluid's angular momentum. The torque acting on the

rotor calculated from the rate at which the rotor slows down as it works

on the fluid during the test time is 850 lbf-ft (normalized to atmospheric

conditions in the supply tank) and from the change in the angular momen-

tum across the rotor the torque is calculated to be 1116 lbf-ft. The

large difference between the two numbers is due to insufficient resolution

in the measurement of the rotor speed which results in an incorrect cal-

culation of rotor deceleration. The dynamic coupling between the rotor

32

and the drive motor, and the flexibility of the interconnecting shaft and

couplings plus the oscillations in the supply tank pressure make the

rotor speed oscillate with a frequency higher than the shaft rotational

frequency. These oscillations cause up to 25% changes in rotor decelera-

tion, which cannot be detected if the rotor speed is measured with a one

pulse-per-revolution tachometer, as was done here.

The stator torque was calculated by three different methods and

the results agree within the experimental accuracy. Dynamic calculation

using stator acceleration gives 750 lbf.ft (normalized for atmospheric

conditions in the supply tank), the fluid angular momentum balance gives

800 lbf-ft and integration of the pressure over the blade surface using

the traversing blade data gives 850 lbf.ft torque for the stator. This

agreement provides an important consistency check on the stator pressure

data.

4.3 Flow Field Behind the Rotor

The analyzed probe data behind the rotor are shown in Figs. 4-3 to

4-9, in which the rotor outlet flow angles and Mach numbers as well as

total and static pressure ratio, local efficiency and rotor outlet relative

Mach number are plotted versus blade passing periods for three different

radius ratios. In each of Figs. 4-3 to 4-9 the ensemble average over 3

blade passages is presented at the right.

The data presented in Figs. 4-3 to 4-9 show that there is a large

tangential and radial flow angle variation associated with the wakes,

sometimes up to 250 or more. The radial flow angle is large and positive

near the suction side, drops down across the passage and reaches a negative

33

value on the pressure side. This says that there is a radial shear in

the wake, shedding streamwise vorticity downstream. There are signi-

ficant total and static pressure fluctuations in the wakes and the flow

Mach number changes as much as 30% across the wake (Figs. 4-6, 4-7). The

local efficiency is near 100% in the "inviscid" flow between the wakes

near the hub and drops down in wakes (Fig. 4-8). Near the tip the

efficiency is low also in the flow between wakes, apparently due to shock

pressure losses.

The significance of the ensemble averages is that the most periodic

part of the signal will be emphasized, since the blade-to-blade variations

are suppressed. Comparison of the ensemble averages to the true time

dependent signals shows there are large blade-to-blade variations,

particularly in the pressure ratios.

Comparison between the data from different radii shows that near

the hub there is a much larger velocity defect in the wakes, a higher

pitchwise flow angle variation and a larger axial Mach number defect, than

at other radii. The axial Mach number in the wake reduces to 50% of its

mean value near the hub.

Close to the tip, there is a large degree of variation between the

wakes from different blades and the wakes are not nearly as strong as

they are at other radii.

Figure 4-9 compares the rotor outlet relative Mach number for

three different radii. It shows that the relative flow Mach number is

nearly constant across the passage and drops down in the wakes.

34

The results presented in Figs. 4-3 to 4-9 show that the outlet flow

from the rotor is very unsteady, highly three dimensional and the wakes

from the rotor are very different from the two dimensional models adopted

in theoretical studies.

4.4 Flow Behind the Stator

The results of probe data analysis behind the stator are shown in

Fig. 4-10 through Fig. 4-30, for different axial and radial positions.

Figures 4-10 to 4-18 correspond to measurements at a plane which is only

0.1 rotor chord downstream of the stator. In each figure the data from

the circumferential survey of the probe over the outlet of a full stator

passage plus the wakes of the two bounding blades are shown. The data

in the mid-passage shows the time history of the rotor wakes as they are

convected through the stator passage and the two stator wakes on the

sides of the figures show the stator wake structure under the influence

of rotor wakes (consult Fig. 4-10 on the top).

For some of the flow quantities such as radial and tangential flow

angles and Mach number the data reduction program is incorrect when the

probe is aligned with the stator trailing edge, due to insufficient

spatial resolution of the probe in this region. The "spikes" in these

regions should therefore be ignored.

The following results can be observed in reference to Figs. 4-10 to

4-18. The stator wakes are deeper and stronger at the tip than they are

at the hub. This is mainly due to the large mean angle of incidence at

the inlet to the stator near the tip region. According to the tangential

angle plots the flow is turned more by the suction side than by the pressure

35

side, and there is a large total pressure drop in the stator wakes, whereas

static pressure is nearly constant in the stator wakes.

One interesting point is that the rotor wakes still exist nearly

undiminished in the flow downstream of the stator. In fact the radial

and tangential flow angles in the stator "inviscid" flow change as much

as 200 due to the rotor wakes (Figs. 4-10, 4-13, 4-16), and there are

significant total and static pressure fluctuations in the flow downstream

of the stator as a result of the rotor wakes. Comparison of the results

for different radii shows that unsteadiness related to the rotor wakes

appears more regularly in the tip region, while close to the hub some of

the wakes seem to have been filled up.

Similar sets of data from measurement at one and two rotor chord

lengths behind the stator are shown in Figs. 4-19 to 4-27 and 4-28 to 4-30.

The rise in Mach number levels and the static pressure drop in the set of

data presented in Figs. 4-28 to 4-30 are due to the fact that the corres-

ponding measurement port is close to the throttle orifice and the flow

acceleration towards the orifice opening shows in the data. Nevertheless

the unsteady part of the data at mid-span (the data shown in Figs. 4-28

to 4-30) can be used for comparison.

Comparison between these three sets of data for the three axial

positions behind the stator and the data taken between rotor and stator

gives the following results: the rotor wakes appear nearly undiminished

in the exit of the stator relative to the rotor exit whereas they are

seen to decay at a more rapid rate in the annular duct behind the stator

36

(see Figs. 4-31 and 4-32). The stator wakes decay very rapidly so that

at a distance of one rotor chord behind the stator they have virtually

ceased to exist.

4.5 Traversing Blade Results

Figures 4-34 to 4-39 show the unsteady pressures measured on the

stator blade at different radii. On each figure the curves are from top

to bottom the measurements at 20, 35, 50, 65 and 80 percent of the chord

for both the suction and the pressure surfaces of the stator blade. In

part "b" of each figure the power spectra of the pressure signals are

plotted. These figures show that the pressure on the surface of the

stator blade changes periodically with a dominant frequency equal to

rotor blade passing frequency,

The probe data shown in Figs. 4-3 to 4-9 at different radii are so

chosen in time as to correspond to the flow properties at the leading

edge of the stator for the periods at which the unsteady traversing

blade data are analyzed at corresponding radial positions. (Note these

two sets of data come from two different tests.)

An immediate result of the comparison among the pressure traces

(Figs. 4-34 to 4-39) is that they are very nearly in phase, but this

phase relationship does not support the simple convective models of wake

behavior in stator in which on blade pressure fluctuations are associa-

ted with the local wake induced velocity fluctuations. In reference to

Figs. 4-3 to 4-9 (which show the flow properties at the stator leading

edge), it can be seen that as the angle of incidence to the blade is

changed due to the rotor wakes, the pressure at all the points on the

37

blade changes almost immediately, These observations lead to the

conclusion that the chord-wise pressure distribution on the stator

blades is determined by the change in circulation around the blade

as a result of the change in angle of incidence, the local velocity

fluctuations within the stator passage having a lower order effect

on the unsteady chordwise pressure distribution.

These results are in qualitative agreement with previous work on

isolated airfoils and cascades. Based on Sears' calculation [1,2] for

incompressible flow over an isolated airfoil, the pressure at all

points over the chord changes in phase in response to the gust. More-

over the experimental observations of Commerford and Carta [13] showed

that for an isolated airfoil in a compressible flow there is no phase

difference between the pressure fluctuations on the pressure surface,

and that there is a scattering in the phase for the suction surface.

A large scattering in the phase angle of the pressure fluctuations

over the chord can also be observed in the experimental results of

Fleeter, Jay and Bennet [7]. However the phase angles for most points

over the chord seem to be nearly equal for their 100% corrected speed

operation data, a point which seems to have been ignored by the authors.

Furthermore the time marching calculations of Mitchell [16] also

showed that the unsteady pressure distribution over a blade in a cascade

does not depend on the local fluctuations within the passage, which

agrees with what we have found.

The unsteady data from the traversing blade can be presented in

forms that are more descriptive as far as the loadings on the stator are

38

concerned. Figure 4-40 to Fig. 4-42 show the instantaneous pressure

distribution over the chord of the blade for 30 time intervals during

one rotor blade passing period, for three different radius ratios. In

part "d" of each of these figures the absolute radial and tangential

flow angles and total Mach number of the flow at the leading edge of the

blade are plotted for one blade passing period. The values of the angles

and Mach number are also written on the top of each pressure distribu-

tion plot. The distribution of the unsteady lift coefficient (normalized

pressure difference across the blade) over the chord is shown in

similar fashion in Figs. 4-43 to 4-35. Finally the unsteady tangential

and axial forces and pitching moment acting on the stator blades are

plotted versus rotor blade passing periods for three different radius

ratios in Figs. 4-46 to 4-48. Next to each loading plot its spectral

density is also plotted. Comparison of the plots in Figs. 4-40 to 4-45

gives an animated picture of what happens to the pressure distribution

around the stator blade as the wakes go by. For all the radii the

introduction of the wake to the leading edge of the stator is associated

with a large negative tangential force on the blade which is mostly

acting on the middle and rear part of the blade.

Comparison between the data presented in Figs. 4-3 to 4-9 with

the unsteady force plots (Figs. 4-46 to 4-48) shows that the wave form

of the tangential force very much follows the shape of the incoming

gust, and the dominant frequencies in both cases are the rotor blade

passing frequency and its harmonics. As mentioned earlier a positive

incidence as a result of wake passage seems to result in a negative

39

tangential force on the stator blade. To find the exact phase relation-

ship between the corresponding frequency components of the force and the

gust they were both decomposed into their Fourier components at blade

passing frequency and its harmonics. It turns out that the phase between

the components of force and the components of the gust referred to the

stator leading edge is a constant at each radius and equal to 90' for

the hub region and about 1809 for other radii.

Arnoldi [12] showed that the phase angle between the gust and the

induced lift calculated from Sears' function becomes a constant (equal to

450) for reduced frequencies higher than 2, if the gust is to be referred

to the leading edge instead of the mid chord of the airfoil.

The reduced frequency based on rotor blade passing frequency "p"

is equal to 3.58. Although the compressible reduced frequency parameter

K = QM/(l-M2)1/2 for the fundamental harmonic is about 3 which is well

above the incompressible limit, it seems that our results are in quali-

tative agreement with the result for isolated airfoils in incompressible

flow. Actually the effect of inter blade phase angle becomes less as the

reduced frequency goes above 2 [12], which says for high reduced fre-

quencies the blades in a cascade will behave like isolated airfoils.

Reduced frequency 0 is defined as 0 = where c is the stator chord

length, w is the rotor blade passing frequency in radians and. v is

the mean stator inlet flow velocity.

40

The radial variation of the measured phase angle between the force

and the gust (90' for the hub region and 1800 for other radii) is most

likely due to the variation in the mean angle of incidence to the stator

blade. It was shown by Commerford and Carta [13] that as the mean angle

of incidence to an isolated airfoil is increased the phase between the

gust and the induced lift differs more from the value predicted by the

Sears' function.

In Fig. 4-50 the steady state tangential and axial force variation

with radius are shown. Figure 4-49 shows the steady pressure distribu-

tion and lift coefficient versus chord length for different radii. Com-

paring Fig. 4-46 to 4-48 with Fig. 4-50 shows that the amplitude of the

unsteady tangential force on the blade is as high as 25% of its steady

state value, and for axial force this figure is 15%.

The frequency content of the unsteady load on the stator blade is

of great importance to the designer. According to Figs. 4-46 to 4-48

the axial and tangential forces on the blade oscillate with rotor blade

passing frequency near the hub and at rotor blade passing frequency and

its second harmonic at other radii. However the pitching moment oscillates

at rotor blade passing frequency and its fourth harmonic near the tip and

at blade passing frequency and its second harmonic at other radii.

41

CHAPTER 5

CONCLUSIONS

1. A time and space resolved survey of the flow downstream of a

transonic rotor shows that the rotor wakes have:

i) large pitchwise flow angle variations, up

to 250,

ii) large radial outflows with a radial angle

up to 30',

iii) significant total and static pressure

gradients,

iv) significant Mach number variation, and

v) large degree of variation from tip to

hub and from blade to blade.

Therefore they have a highly three dimensional structure and are very

different from two dimensional models.

2. Ensemble averaging of blade-to-blade measurements suppresses

the blade-to-blade variation, especially for the pressure measurements,

and may lead to a distorted view of the rotor stator interaction.

3. Time and space resolved measurements of flow behind a row of

stator blades downstream of the transonic compressor rotor show that:

i) under the influence of the rotor outflow, the

wakes from the stator are deeper and stronger

near the tip than they are near the hub;

ii) there is a significant total pressure defect

and practically no static pressure variation

associated with stator wakes;

42

iii) the wakes from the rotor exist nearly un

diminished in the exit flow from the statorbut the decay in the annular duct behind the

stator;

iv) unsteadiness related to rotor wakes appears

more frequently in the tip region.

4. Analysis of time resolved measurements of the stator blade

surface pressure from tip to hub lead to the following conclusions:

i) the pressure distribution over the stator blade

is nearly periodic with a frequency equal to

rotor blade's passing frequency;

ii) the pressure fluctuations are nearly in phase

at all points along the chord, the chordwise

unsteady pressure distributions being deter-

mined by the changes in the angle of incidence

and not by the local velocity fluctuations

within the stator passage.

iii) there are large rotor wake induced, unsteady

forces on the stator blades, as high as 25%

of the steady forces for the configuration in-

vestigated.

iv) the unsteady axial and tangential forces on

the stator blades fluctuate with rotor blade

passing frequency in the tip region, and with

rotor blade passing frequency and its second

harmonic at other radii;

v) there seems to be a scattering in phase and

magnitude of the forces on the blade relative

to those of the rotor wakes, that cannot bepredicted by existing two-dimensional models.

43

5. The data presented here form a basis for development of models

for rotor stator interaction which more accurately represent the actual

wake structure in transonic compressor stages.

44

REFERENCES

[1] N.H. Kemp and W.R. Sears, "Aerodynamic Interference BetweenMoving Blade Rows", J. of Aeronautical Sc., Vol. 20, No. 9,Sept. 1953.

[2] N.H. Kemp and W.R. Sears, "The Unsteady Forces Due to ViscousWakes in Turbomachines", J. of Aeronautical Sc., Jul. 1955,pp. 478.

[3] J.L. Kerrebrock and A.A. Mikoljczak, "Intra Stator Transport ofRotor Wakes and Its Effect on Compressor Performance",J. of Eng. for Power, No. 70-GT-39, 1970.

[4] J.H. Horlock, "Fluctuating Lift Forces on Airfoils MovingThrough Transverse and Chordwise Gusts", J. of Basic Eng.,Vol. 90, 1968, p. 494/500.

[5] H.E. Gallus, "Results of Measurement of the Unsteady Flow inAxial Subsonic and Supersonic Compressor Stages", AGARD-CP-177.

[6] H.E. Gallus, W. Kummel, J.F. Lambertz and T. Wallmann, "Measure-ment of the Rotor-Stator-Interaction in a Subsonic AxialFlow Compressor Stage", R.F.M., Symposium in Aeroelasticityin Turbomachines, Oct. 1976, p. 169.

[7] S. Fleeter, R.L. Jay and W.A. Bennet, "Rotor Generated UnsteadyAerodynamic Response of a Compressor Stator", J. of Eng.for Power, 78-GT-112, 1978.

[8] W.T. Thompkins, Jr., "An Experimental and Computational Studyof the Flow in a Transonic Compressor Rotor", M.I.T. G.T.L.Report No. 129, 1976.

[9] J.L. Kerrebrock, "The M.I.T. Blowdown Compressor Facility", M.I.T.GTL Report No. 108, 1970.

[10] W.A. Figeiredo, "Spherical Pressure Probe for RetrievingFreestream Pressure and Directional Data", GTL Report No.137, Aug. 1977.

[11] J.F. Kaiser and W.A. Reed, "Data Smoothing Using Low-Pass DigitalFilters", Rev. Sci. Instrum., Vol. 48, No. 11, Nov. 1977.

[12] R.A. Arnoldi, "Unsteady Airfoil Response", NASA SP-207, pp. 247-256.

45

[13] G.L. Commerford and F.O. Carta, "Unsteady Aerodynamic Responseof a Two-dimensional Airfoil at High Reduced Frequency",AIAA Journal, Vol. 12, No. 1, Jan. 1974, pp. 43-48.

[14] J.J. Adamczyk and R.S. Brand, "Scattering of Sound by an Airfoilof Finite Span in a Compressible Stream", J. of Sound andVibration, Vol. 25, 1972, pp. 139-156.

[15] D.W. Holmes, "Experimental Pressure Distribution on Airfoilsin Transverse and Streamwise Gusts" Cambridge UniversityPublication CUED/A-Turbo/TR 21(19705.

[16] N.A. Mitchell, "Non-Axisymmetric Flow through Axial Turbomachines",Ph.D. Thesis, St. John's College, Cambridge University,England, 1979.

[17] R. Mani, "Compressibility Effects in the Kemp-Sears Problem",NASA SP-304, Part II, 1974, pp. 513-533.

[18] S. Fleeter, "Fluctuating Lift and Moment Coefficient forCascaded Airfoils in a Nonuniform Compressible Flow",AIAA J. of Aircraft, Vol. 10, No. 2, Feb. 1973.

46

BoundaryLayer

Manifold for Boundary Layer BleedBleed

Dump Tank

Supply TankSeto

Diaphrogm

Scale: - = I foot

FIG. 2-la View of the M.I.T. BlowdownCompressor Facility

MEASUREA4ENT PORTS

I I SUPPORT I

STRUTstator choke

rotor plate

SSTA TORINGi

SPIN R

CENTER BODY

PTAR BEARING

ROTOR SHAFT

FIG. 2-lb Sectional View of the Test Section(Stator Free to Move)

0 0 P2 PROBE00

0rw

0

0

L:u

0

0D

0.4

00 1.

3 .00 80.00 160.00 240.00

FIG. 2-2 Typical Pressure Signal in theBlowdown Tunnel During theExperiment

320.00T IME (MS)

00

O~)

0

c'J

o

L. 0 0 90.50 91.00 91.50 92.00T I ME (MS)

400.00 480.00 560.00

= ]C0

I:

-~PNUMA TICDRIVER

T RAV ERSWNG

~I BLADE

-o.-TR ANSDUCERS

-- stator chokerotor plate

FIG. 2-3 Sectional View of the Test Sectionwith Traversing Blade Installed

C)

0D

CEO

C)

0.00 70.00 90.00T I ME (MS)

FIG. 2-4 Blade Position v.s. Time Duringthe Traverse

110.00 130.00

49

DIA PH RA GMSLAT RING

RINGDIAPHRAGM

EPOXY

FIG. 2-5 Miniature Pressure TransducerAssembly; a. Sectional ViewbComp] eted Unit

INVAR

W/RE VACUU TUBE BLA E 8XY I

50

S2 SS3 ss4 SS5

S ps4 PS5PS/I\ 3

PS

b

Instrumented Traversing Blade;a. Blade Cross-section at Instru-mented radii; b. Suction Surface

(transducers covered)

FIG. 2-6

0

CD

CONNECTINGWIRES SOLDER

y Rs R

RPLA TES

R3~~ _R

Y

0

C5

Cu_

0

Vu

'115.00

VIBRATIONSWAKE S(DA TAj

SS3

PS5

S5WINAAMF

1'20.00 125.00 1'30.00T I ME (MS)

FIG. 2-7 The Configuration of the Bridge Ele-ments on the Transducer's diaphragm

FIG. 2-8 Output Signal from DiaphragmsLocated at Different ChordwiseLocations on the Blade

U,

135.00 1'40.00

52

\450 +

I /__________ r

U

.20

-4---

/

FIG. 2-9 The 5-Way Probe

i -I

53

TRANSDUCER

~~A PRESSURESIGNAL

Jill~50K[A

5 v

1.5 V

FIG. 2-10 Electrical Layout for Probe'sTransducers

A/D

C OMPRESSOR

FM TAPE RECORDER

DISC STORAGE

COMPUTER

VERSATEC PLOTTERDIGITAL MAG.

TA PE

FIG. 2-11 Data Storage Setup

TEAIPPRATURESIGNAL

--- --j

54

0

5-i

SIGNAL DUE TO BLADE VIBRATION

WAKES (DATA)

0

1-0

(D

1 10.00

0

851

ac 6

LU 0

Lj0

1-6

110.00

FIG. 3-1

115.00

115.00

120.00T IME (M

125.00S)

120.00 125.00T IME (MS)

130.00

130.00

135.00

135.00

Comparison between Raw Data and theData Digitally BandDass Filtered

c;

00

0~D.

POWER SPECTRUM DENSITY OF RAW DATA

20.00 U0. 00FREQUENCY

C00

C-1

C*\

xn

ROTOR BLADEPASSING FREQ.

0

CD-

A60.00 80.00

(HZ) )(1021'00.00 1'20.00

C30''0.O0 K A

20.00 LIo.ooFREQUENCY

0.oo s0.oo(HZ) x102

FIG. 3-2 Frequency Spectrum of Raw andFiltered Data

00

=0-

a-

0:CCc

POWER SPECTRUM DENSITY OF FILTERED DRTA

U,L,

0~0'

U.. ; 100.00 30.00F

A

56

RADIAL VARIATION OFTIME AVERAGED DATA

C BETR RNGLE(TANGENTIAL)A PHI ANGLE (RADIAL)+ RELATIVE FLOW RNGLE

0.92 0.84Rf/RT

0.76

Average Flow Angles vs. RadiusBehind the Rotor

RADIAL VARIATION OFTIME AVERAGED DATA

0.92 0.84R/RT

0.68

O TOTAL PRESS RATIOA STATIC PRESS RATIO

0.76 0.68

Average Pressure Ratios vs. Radiusbehind the Rotor

co.-Jo

zD-Cj

0r

-1.0

1.00

FIG. 4-la

0.60

(f)D

(0Um

-1~ .00

FIG. 4-lb

0.60

57

RADIAL VARIATION OFTIME AVERAGED DATA

CDA

TOTAL MACH #AXIAL MACH #

-t itlNGENIL MMC

X RADIAL MACH #* RELATIVE MACH"-

z

r.

0.76 0.68

Average Flow Mach Numbers vs.Radius behind the Rotor

RADIAL VARIATION OFTIME AVERAGED DATA

0.92 0.84f/RT

0 EFFICIENCY

0.76 0.68

Average Efficiency vs. Radiusbehind the Rotor

0.84R/RT

0.92

FIG. 4-2a

CU

0.60

ElL)zU

IL

LU

0

03.00

FIG. 4-2b

0.60

H aa

1 .00

58

R/RT-0. 72

0 BETA ANGI E

2.00 4.00 6.00 8.00ROTOR BLADE PASSING PERIODS

c-0

0~

LUI-

0

10.00

R/RT-0.82

( BET ANGLE

2.00 4.00 6.00 8.00ROTOR BLADE PASSING PERIODS

10.00

R/RT-0.92

0 BETA ANGLE

2.00 4.00 61.00 8.00ROTOR BLADE PASSING PERIODS

10.00

LU-JO(n

X:o

1-00-61-

L-jC.D

c0-J

LUo

CD

-

ROTE

U;_

L

.4

U,

I.-

0

Lrbo

ROTI

00OR

R/RT-0. 723 PASSAGE AVERAGED

0 BE1A ANULE

2.00 4.00BLADE PASSING

R/RTo0.823 PASSAGE AVERAGED

( BETA ANGLE

6.00PERIODS

2.00 4.00 6.00BLADE PASSING PERIODS

R/Rr-0.923 PASSAGE AVERAGED

0 BETA ANGLE

00OR

2.00 4.00 6.00BLADE PASSING PERIODS

FIG. 4-3 Tangential (Pitchwise) Flow Anglebehind the Rotor vs. Time forDifferent Radius Ratios

0ROTOR

0C3

o

0C3

-J

zoa:o

0-

0-JOLo

U-)

~09of.'b.i)0

C0

U-(0

LUO

10

(b. o

)M. jlv

59

0.R/RT-.72

) PHI ANGLE

LLJ 0...Jo008cZ(U

:

-Jo4Li..

C0C)

-J

LLc

c

-JoU.

ib. 00

001

0.00ROTOR

R/RT-0. 723 PASSAGE AVERAGED

C) PHI flNt

2.00 4.00 6.00BLADE PASSING PERIODS

R/RT-0.82

PHI ANGLE

2.00 4'.00 6.00 8.00ROTOR BLADE PASSING PERIODS

10.0c

0

LJJ-JO

:

-Jo0U-.

MC)

ROT'

0.R/RT-0. 92

C PHI ANGLE

ZcuaE

-JoU..0

C:

-Jo-Z,

0

:

C30

0

M

C3'0

0LC

0aj:)U0

6-4

C~:

C

10.0c

R/RT-0.823 PASSAGE AVERAGED

0 PHI ANGLE

.00OR

2.00 4.00BLADE PASSING

6.00PERIODS

R/RT-0.923 PASSAGE AVERAGED

) PHI ANGLE

'0.00 2.00 4'.00 6'.00ROTOR BLADE PASSING PERIODS

FIG. 4-4 Radial Flow Angle behind theRotor vs. Time for DifferentRadius Ratios

2,.00 4.00 6.00 8.00ROTOR BLADE PASSING PERIODS

0.00

.00

2'.00 4'.00 6.00 -8 .00ROTOR BLADE PASSING PERIODS

0.00'

60

09.cuR/RT0.72

( C TOTAL PRESS RATIOA STATIC PRLI RAT IO

0

cc,

U,L

I-W.

a:c

LC

ct I8.00PERIODS

3.00

R/R7r.723 PASSAGE AVERAGED

(!) TftIIL I'lt TAT 10A STATIC NW5RATIO

3.00ROTOR

2.00 4.00 6.00BLADE PASSING PERIODS

R/RT-0.82

D TOTAL PRESS RATIO

A STATIC PRESS RATIO

2.00 4.00 6.00 8.00ROTOR BLADE PASSING PERIODS

R/RT-0.92

O TOTAL PRESS RATIOASTATIC PRESS RATIO

2.00 4.00 6.00 8.00ROTOR BLADE PASSING PERIODS

ib.oo

01C019

CC.

0

o2cc-(n

00

Lc'

ROTh

0C)

0.

cro0o

10.00

R/RT-0.823 PASSAGE AVERAGED

( TOTAL PRESS RATIOA STATIC PRESS RATIO

00jR

2.00 4.00BLADE PASSING

6.00PERIODS

R/RT-0.923 PASSAGE AVERAGED

C TOTAL PRESS RATIOASTATIC PRESS RATIO

ROTOR2.00 4.00 6.00

BLADE PASSING PERIODS

FIG. 4-5 Pressure Ratios behind the Rotorvs. Time for Different RadiusRatios

2.00 4.00 6.00ROTOR BLADE PASSING

I.0

C3

q:

LUN

L O

o0o

0

I.-

U

U,ciia00

'b. o

'

61

00D

R/RTwO. 72

0

zL) 3,

cc0 -

(30;

2'. 00 4.00 6'.00 8'. 00ROTOR BLADE PASSING PERIODS

R/RT-0.82

D TOTAL MACHA AXIAL MACH -

2.00 4.00 6. 00 8.00ROTOR BLADE PASSING PERIODS

'.oo W.ooROTOR

CDODJ

80

z

CC 0X: 0

10. 00 ROooROTOR

R/RTeO. 723 PASSAGE AVERAGED

(D WftOI MOCHaAXIAL MlCH a

2-..00 W00BLADE PASSING

R/RT-0.823 PASSAGE AVERAGED

0 TOTAL MACH *A AXIAL MACH *

2.00 4.00BLADE PASSING

2.00 4'.00 6'. 00ROTOR BLADE PASSING

8.00PERIODS

Ib. 00

0CD* R/RT-0.928- 3 PASSAGE AVERAGED

ROTOR BLADE PASSING PERIODS

FIG. 4-6 Total and Axial Mach Numbersbehind the Rotor vs. Time forDifferent Radius Ratios

.00

z0'3

cc

Q

0

Mc)1z

29j

6.00PERIODS

006.00

PERIODS

0

C)

z

CE:

0:;

Q'

D. 00

R/R7-0.92

TOTAL MACH aAXIAL MACH a

'1

62

R/RT-0. 72

0 TANGFNTIAL MACHRADIRL MACH

2R .00 BL. 0 6.00 8 .00ROTOR BLADE PASSING PERIODS

.;4

z

=i0

cr,;-:

0

0

z

.0

R/RT-0. 723 PASSAGE AVERAGED

( 1hMN.Nr L MIhH aA AV i L MNCH

2'. 00 4 .00BLADE PASSING

6.00PERIODS

0R/RT-0.82

TANGENTIAL MACHRA31AL MA

0

U'

0

00

zo

X:

2.00 4. 00 6.00 8'.00ROTOR BLADE PASSING PERIODS

10. 00

R/RT-0.823 PASSAGE AVERAGED

D TANGENTIAL MACHA RAC1AL MACH a

pNJr~hJ~~

0.00ROTOR

0D

6-1R/RT-0.92

O TANGENTIAL MACHRADIAL MACH

2'.00 4'.00 6.00 8'.00ROTOR BLADE PASSING PERIODS

1'0.00

0

X:

2o.00 4.00 6.00BLADE PASSING PERIODS

R/RT-0. 923 PASSAGE AVERAGED

(D TANGENTIAL MACHA RACIAL MACH a

10.00 2.00ROTOR BLADE PASS

4.00 6.00ING PERIODS

FIG. 4-7 Tangential and Radial Mach Numbersbehind the Rotor vs. Time forDifferent Radius Ratios

'I 0 1 0 010.00 ROTOR0.00

0.

ci

0

Q

z

U Qa:~

10'.00

03

z=L)2:

0E-

0.00

1

63

R/RTE C.E72

0 EFFICIENCY

2'.6o O.00 6. 00ROTOR BLADE PASSING

8'.00PERIODS

i'b.oo

R/RT-0.82

) FICIENCY

2'.00 4'.00 6.00 8'.00ROTOR BLADE PASSING PERIODS

10.00

R/RT-0.92

( EFFICIENCY

3.-0

Li..

-An

H/RT-0. 723 PASSAGE AVERAGED

0 EPH-CILNCT

0

U- 0

-.

L.00

ROT

0

0O

zoLU

La.. 4

-0

(-3

'b'. oROTOR

-0

>- 0

Zc-LuP" (Ui.

LL. t

2.00 'L.0D0 6.00ROTOR BLADE PASSING

8E.00PERIODS

ib.oo

2'.00 4.00 6 '.00BLADE PASSING PERIODS

R/RT-0.823 PASSAGE AVERAGED

0 EFFICIENCY

2.00 L'.0o 6.00BLADE PASSING PERIODS

R/RTsO.923 PASSAGE AVERAGED

( EFFICIENCY

-j

Ca-,~

Do.0 21.00 '.00 61.00ROTOR BLADE PASSING PERIODS

FIG. 4-8 Local Efficiency behind the Rotorvs. Time for Different RadiusRatios

.00OR

cb'.oo

3.03

(-

-LJ

C-o

-j=a:

.00

0.0

Luo

-LJ6-4

-)

'b'.o

64

R/RT-0. 72

0 RELAlIVL MACHI

2'.00 1'.00 6.00 8Y.00ROTOR BLADE PASSING PERIODS

10.00

R/RToO.82

n A LATIVE MACH

2.00 4.00 6.00ROTOR BLADE PASSING

8.00PERIODS

R/RT-0.92

0 RELATIVE ACH

2.00 4.00 6'.00 8.00ROTOR BLRDE PASSING PERIODS

1'0.00

0;

0#

0

(-jW:2: C

0b

ROT'

R/RT-0. 723 PASSAGE AVERAGED

0 RLLATIV MCLHv

0

>0

-

a:m

2:

>0

CC

-j

ROT'

0

Lirl

-JLiir0E

R/RT-0.823 PASSAGE AVERAGED

0 A LATIVE MACH

.00OR

2.00 4.00BLADE PASSING

A/AT-0.923 PASSAGE AVERAGED

0 RELATIVE MACH

10.00 .00 2.00 4.00 6.00ROTOR BLADE PASSING PERIODS

Relative Flow Mach Number behindthe Rotor vs. Time for DifferentRadius Ratios

00OR

00cbi.

aI:

>0Q

2.00 4.00 6.00BLAOE PASSING PERIODS

.00 6.00PERIODS

0

0

#04

a:

cc

-jLUra= to

V. Do

FIG. 4-9

' '

65

0.1 ROTOR CHORD BEHIND THE ISTATOR

R/RT=O. 75ROTOR WAKES

BETA A

STATOR PASSAGE FLOW

LU

zo

0

-j

U.

(n)o

XIr

0

10.00BLADE PR

15.00SSING PER

OR WAKE

20.00IODS

25.00

R/RT=0.750.1 ROTOR CHORD BEHIND THE :TA1't

0 PHI ANGLE

ibo10.00BLADE PR

15.0cSSING

20.00PERIODS

Flow Angles behind the Stator,R/RT = 0.75

'I

.00 5.00ROTOR

U 0

cr_

Lmc3

LL 0

-Pa:

0:c:a:.

0.00 5.00ROTOR

FIG. 4-10

25.00

how-

66

R/RT.0. 750.1 ROTOR CHOW!D BEHIND THE STAT(DR

0 TOTRL PRESS RRTIO

C)

I--J0..:-

-cb10.00

BLADE PASS

R/RT=0. 75

15.00I NG PE

20.00RIODS

Of. 1 ROTOR Ci :RD ECHLND TI-E iTATYR

0 STRTIC PRESS RRTIO

5.00ROTOR

10b.BLADE

00PASS

15.00ING PER

FIG. 4-11 Pressure Ratios behind the StatorR/RT = 0.75

C3

(0

5.00ROTOR

.00 25.00

0D0)

:)uJi

Ur

CEG

20. 00IODS

25.008

67

C/3 T 70.1 ROTOR CHORD EIEHIND THE T2TCR

U0-oCE

CC 0

0 U:)

0.00 5.00 10.00 15.00 20.00 25.00ROTOR BLADE PASSING PERIODS

.. /.1 2OTOR CHORD DELHIND THE STATOR

#

C-

z:)

1-q

a:)

0.00 5.00 10.00 15.00 20.00 25.00ROTOR BLADE PASSING PERIODS

FIG. 4-12 Flow Mach Numbers behind theStator, R/RT = 0.75

68

R/RT -0.820.1 ROTOR CHORD BEHIND THE STATCR

VNN4

20.00PERIODS

R/RT=0.82

5.00ROTON

0.1 ROTOR CHORD BEHIND THE STATOR

( PHI RNGLE

10.BLRDE

00PAS

15.00SING

20.00PERIODS

Flow Angles behind the Stator,R/RT = 0.82

co1

0U-Jo

zcc

-JO

zuLJL:)zo)

cr)1'0.00

ii5.00

ROTOR10.

BLRDE00PRSS

15.0ING

25.00

00

0cn,

..Jo

z-(3:

-J.

CD Ma:ccoc)

1'0 .00

FIG. 4-13

25.00

BETR ANGLE

69

R/RT=0.82 Z.1 ROTOR CHORD B :HIND THE ST.ATOR

RATIO

15.00SSING PER

R/RT=0.820.1 ROTOR CHORD BEHIND THE SLoiTUR

C STATIC PRESS RATIO

5.00ROTOR

1B0.BLADE

00PASS ING

I20.00PERIODS

25.00

Pressure Ratios behind the Stator,R/RT = 0.82

Cu-

LL cICC cu0 .C _

.M

C) 0

5.00ROTOR

10.BLADE

00PA

20.001ODS

25.00

00

Cuc

U-

6-4

.00

FIG. 4-14

I

Q) TOTAL PRESS

70

Cr Lr)

o0

CEo

M-)a:-

00PASS

R/RT=0.82 0.1 ROTOR CHORD BEHINDTH

MT

M,,AD.

15.00 20.00 2EING PERIODS

R/RT=0.820.1 ROTOR CHORD BEHIND THE STATOR

MTA N.

10.BLADE

00PASS

15.00ING P

20.00ERIODS

125.00

FIG. 4-15 Flow Mach Numbers behind theStator, R/RT = 0.82

.00'0 5.00ROTOR

10.BLADE

.00

0.0-- I

-)

U

zCC

1-04a:)

5.00ROTOR

IY4 1)

.00

71

R/RT=.92

MM

CD

C .i

-J

Li.(n m

e-D

1'0 10.BLADE

0.1 ROTOR CHRCD D:HRND THE STATi:

00PASS

15.00ING PE

R/RT=.92

5.00ROTOR

0.1 ROTOR CHORD B2IHIND THE 3TATOR

( PHI RNGLE

10.BLADE

00PASS

15.00ING

In

I '1

I I

20.00PERIODS

k25.00

Flow Angles behind the Stator,R/RT = 0.92

5.00ROTOR

DBET NGLEI

-J

00

(j~ J

20.00RIODS

25.CO

CF)

LUC)-Jo)CD 0CD-

-is.

LL. C

-Ja:_

xcr

1'0 .00

FIG. 4-16

.

72

R/RT=.920 1 ROTOR CHORD BEHIND THE STATOR

M~0

Cu-

I0

aJO

-.

5.00ROTOR

10.BLADE

00PASS

15.00ING P

20.00ERIODS

25.00

R/RT=.920.1 ROTOR CHORD BEIiIND THE STATOR

( STRTIC PRESS RRTIO

5.00ROTOR

10.BLADE

00PASS

15.00ING PE

20.00RIODS

25.00

FIG. 4-17 Pressure Ratios behind the Stator,R/RT = 0.92

0 TOTRL PRESS RRTIO

00

a:b

0:0

C-

C0

aco

Ci

cLc'

- I

a:00a

73

R/RT=.92 0.1 ROTOR CHORD BE-IND THE STATOR

MT

1 115.00 20.00ING PERIODS

R/RT=.92

5.00ROTOR

10.BLADE

00PASS

0.1 RO'OP CE(ORD BEHI1ND TE FT7e

15.00ING PER

Flow Mach Numbers behind theStator, R/RT = 0.92

C30D

U

-r

U0

-rLfj

CC

Ou")

10.00 5.00ROTOR

10.BLADE

00

-41

00PASS

125 .00

-r

EU

C-

za ,066

-j

Cc0

N.

0.00

FIG. 4-18

20.00I DS

25.00

74

R/RT.0. 75

0M

LU

-IJ

I.j~0

10

10.BLADE

1.0 ROTOR CHORD BEHIND THE 'TTR

00PAS

15.00SING PER

R/RT=0.75 1.0 ROTOR CHORD BEHI-ND THE STATC2

(D PHI RNGLE

5.00ROTOR

10.BLADE

00PASS

15.00ING

20.00PERIODS

25.00

FIG. 4-19 Tangential and Radial Flow Angles10 Rotor Chord Downstream of theStator, R/RT = 0.75

5.00ROTOR

.00 20.00IODS

25 .00

10

Lc

X M

0

crPEO

co C

S0.00

Me

75

R/RT-0.75 1.Z ROTOR CHORD BEHIND THE STATCR

0D TOTRL PRESS. RRTIO

-4I-0C

(

Co

-

C)-O

Cj5 10.BLADE

00PASS

1 I

15.00 20.00ING PERIODS

R/RT=0.75 1.0 ROTOR CHORD BEHIND THE STATOR

(D STRTIC PRESS RATIO

5.00ROTOR

10.BLADE

00PASS

15.00ING

20.00PERIODS

25.00

FIG. 4-20 Total and Static Pressure Ratios1.0 Rotor Chord Downstream of theStator, R/R = 0.75

00"I-,

5.00ROTOR

.00 25.00

C

0-

U

CCCO

cU

t~o

oS/

I --

.00

76

1.0 ROTOR CHORD D ,1IND THE STATOR

STOTRL MRCHA~ RROIRL MRCH #s

00PA

1'5.00 20.00SSING PERIODS

25.00

R/RT=O. 751.Z ROTOR CHO .D BflHIND THE STA .1C1

0 AXIRL MRCH #A TwNGENTIRL MRCH #

00PASS

1 5.00ING

20.00PERIODS

25.00

Flow Mach Numbers 1.0 Rotor ChordDownstream of the Stator,R/RT = 0.75

C3R/RT-O. 75

0)O

cU0

0

CC

F- 0

F-.

0.00 5.00ROTOR

1'0.BLADE

00

C)

~Lf0

z

Ccr

0.00

FIG. 4-21

5.00ROTOR

10.BLADE

77

R/RToO.851.0 ROTOR CHOPI) 3ZHIND THE :T"'"

LuJ

cro

-j

ug

C)

)0c

co)'0 15.00

ING PE20.00

RIODS25.00

R/RT-0.851.0 C'O cH B3HRND T'HE STATUR

(D PHI ANGLE

10.00BLADE PASS

15.00ING

20.00PERIODS

Tangential and Radial Flow Angles1.0 Rotor Chord Downstream of theStator, R/RT = 0.85

0;0.

10.00BLADE PASS

.00 5.00ROTOR

00

cr,

-Jo

L-

cco)

10 .00 5.00ROTOR

FIG. 4-22

25 .00

00

i

78

R/RT=0.851.0 ROTOR CHORD BEHIND THE STATOR

9( TOTAL PRESS. RATIO

00PRSS

15.00I NG PE

20.00RIODS

25.00

R/RT-0.851 .0 ROTOR CHO 1D BEHIND THE 5TATCOR

( STATIC PRESS RATIO

00PRSS

15.00ING PE

20.00RIODS

25.00

FIG. 4-23- Total and Static Pressure Ratios1.0 Rotor Chord Downstream of theStator, R/R = 0.85

00

0.

I-

Cr O

CC 'U0_-_2

bs

-aDF-

UO-Co

_Co

U

C:0

5.00ROTOR

10.BLRDE

00 5.00ROTOR

ib.BLRDE

.

79

._ R/RT-0.851.0 ROTOR CHORD BEHIND THE 3TATCR

STOTRL MRCH #A MROIRL MRCH #

I ____________

5.00ROTOR

10.00BLADE PASS

15.00ING

20.00PERIODS

25.00

R/RT-0. 851.0 ROTOR CHORD BEHIND THE STATG2

D NXIRL MRCHATRNGENTIRL MRCH

5.00ROTOR

FIG. 4-24

10.BLADE

00PASS

15.00ING PER

20.00IODS

25.00

Flow Mach Numbers 1.0 Rotor ChordDownstream of the Stator,R/RT = 0.85

.00

$t

9

0

-J

C3,M-)

0.

0

C0

0

CC):o

CJX:

0.00

80

R/RT=0.95 1., ROTOR CHdrD DH iD TWE S'ATOR

KfiAInAWRs\

5.00ROTOR

10.BLADE

00PASS

15.00ING P

20.00ERIODS

25.00

R/RT=0.951.Z ROTOR CHORD BEHIND THE STATOR

(D PHI RNGLE

5.00ROTOR

10.00BLADE PASS

i i

15.00 20.00ING PERIODS

2 co

Tangential and Radial Flow Angles1.0 Rotor Chord Downstream of theStator, R/RT = 0.95

Li

C;(0

1,

L-

LL 0

r)

1'.00

0

UJ

-JC

LL-0

cr

10 .00

FIG. 4-25

81

R/RT=0.95

10.BLRDE

1.0 ROTOR CHORD BEHIND THE 5TATOR

(D TOTRL PRESS. RRTIO.

00PRSS

15.00ING PER

20I00I ODS

25.00

R/RT=0.951.0 ROTOR CHOPRD BEHII1D THE STLV u1.

(D STRTIC PRESS RRTIO

5.00ROTOR

10.00BLRDE PRS

15.00SING

20.00PERIODS

FIG. 4-26 Total and Static Pressure Ratios1.0 Rotor Chord Downstream of theStator, R/R = 0.95

)CU(

CD

I-0

CrLLJO-J3rC~j

00 5.00ROTOR

I

cb

0.

F-*CC0ac'J

~CD

(0

)a

cbo00 25.00

82

R/RT0.951.3 ROTOR CHORD BEHIND THES sATOR

UC

C0

0

-

c:1cDc:

ED U"

5.00ROTOR

10.BLADE

00PASS

R/RT=0.95

15.00ING PER

20.00IODS

(D AXIAL MACH #A TRNGENTIRL MACH e

25.00

1.0 ROTOR CHORD 3HIND THE sT&422

10.BLADE

00PA

15.00 20.00SSING PERIODS

Flow Mach Numbers 1.0 Rotor ChordDownstream of the Stator,R/RT = 0.95

TOTRLMACH

.000

U

Ln

za:I-oD'

0:

CC

640

a:.rCC .

I I0.,00 5.00

ROTORFIG. 4-27

25.00

83

R/RmO 52 .0 ROTOR CHIORD BEIND THEjj ST-VYC.

0Z ET A NGLE am

10.BLADE

00PASS

LuJ

Zo

-

U-0

Lu 9

Loo

X~~0

15.00ING PER

20.00IODS

25.00

R/RT=0. 852 /. rOTOR CHORD B"IiIND THE ATr

() PHI ANGLE

10.BLADE

00PASS

15.00ING P

20.00ERIODS

25.00

FIG. 4-28 Tangential & Radial Flow Angles2.0 Rotor Chords Downstream of theStator, R/RT = 0.85

00

0

0o~1

00 I

5.00ROTOR

S0.00

03

Cl,

-Jo

aj:)

cD

U-J

a:.1'0.00 5.00

ROTOR

I I

84

R/RT-0.852.0 ROTOR CHORD B2111D THE SAMTOR

D TOTAL PRESS RATIO

5.00ROTOR

10.BLRDE

00PRSS

15.00 20.00ING PERIODS

R/RT=0.85

10.00BLADE PA

2.0 ROTOR CHORD EAIJIND THE STATOR

0 STATIC PRESS RATIO

15.00SSING

20.00PERIODS

25.00

FIG. 4-29 Total & Static Pressure Ratios 2.0Rotor Chords Downstream of theStator, R/RT = 0.85

C30

CZ51

0

CJOLi-Jo0-0u

cbO

25.00

000

F-cmoCC =0cc =

Co

Co

F-CO

(Cb

)

.00 5.00ROTOR

85

R/RT=0.852.0 ROTOR CHORD BEHIND THE S TATCR

0 TOTRL MRCH #

"E A RRIRL MRCH #

zo

(:X: C3f

0)

:)

0.00 5.00 10.00 15.00 20.00 25.00ROTOR BLADE PASSING PERIODS

R/RT0.852.0 ROTOR CHORD BEHIND THE SI

CD RXIRL MRCH#

A TRNGENTIRL MRCH #

C)

10

0.00 5.00 10.00 15.00 20.00 25.00ROTOR BLADE PASSING PERIODS

FIG. 4-30 Flow Mach Numbers 2.0 Rotor ChordsDownstream of the Stator,R/RT =0.85

86

BETWEEN ROTOR AND STATOR

Z.1 ROTOR CHORD BEHIND THE STATOR

Ln

1.0 ROTOR CHORD BEHIND THE STATOR

2.0 ROTOR CHORD BT7HIND THE STAIOR

0.00 5.00 10.00 15.00 20.00 25.00ROTOR BLRIE PASSING PERIODS

FIG. 4-31 Comparison Between Total Mach No.as Measured at Different AxialLocations in the Stage, R/RT = 0.85

87

BETWEEN ROTOR AND STATOR

0.1 ROTOR CHORD BEHIND THE STATOR

1.0 ROTOR CHORD BEHIND THE STATOR

2.0 ROTOR CHORD B1HIND THE STATCR

.00 5.00 10.00 15.00ROTOR BLRDE PRSSING PER

FIG. 4-32 Comparison Between Axial Mach No.as Measured at Different Axial

20.00IODS

25.00

Locations in the Stage, R/RT = 0.85

LO

C

C3

0

88

(D RRDIRL MRCH #A RADIRL MRCH #

0.1 ROTOR CHORD BEHIND THE 6TATOR

1.0 ROTOR CHORD B7HIND THE STA7CR

2.0 ROTOR CHORD BEHIND THE STATOR

00 5.00 10.00 15.00ROTOR BLRDE PRSSING PERI

FIG. 4-33 Comparison Between Radial Mach No.as Measured at Different AxialLocations in the Stage, R/RT = 0.85

220.00ODS

5.00

L()M

II

CE

a:

0.

N f"

89

ct

0 i.00 2. 00 4l.0 0 6 .00 .8.00 10.00oROTOR BLADE PASSING PERIODS

FIG. 4-34a Pressure Fluctuations over theStator Blade, Pressure Side,R '/Rt = 0.72

(from top'to bottom at 20%, 35%, 50%,65% and 80% of chord)

90

00

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT PSIR/RT - 0.72

09

CC0

090

I-

-jo

x0

0A A

.00 1'0.00FREQUENCY

2b.00(KHZ)

POWER SPECTRUM DENSITY OFUN0TEAD1 PRES. AT PSYR/RT - 0.72*

%1.00 ib.ooFREQUENCY

2b.00(KHZ)

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT PS2R/RT - 0.72

00 10.00FREQUENCY

('V POWER SPECTRUM DENS1TY OFUNSTEADY PRES. AT PS5H/RI 0.72

0L(0-

0UJ en.

I- O

- .0o 100 2.o RQEC (KZ

2'0.00(KHZ)

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT PS3R/RT - 0.72

FIG. 4-34b Frequency Spectrum of PressureFluctuations over Stator Blade,Pressure Side, R/Rt = 0.72

.A I

000

0

0

C93

0Vn0rC

0

0

LLCV

Ij-

*09CC0

.oo 0.ooFREQUENCY

20.00(KHZ)

Ik

91

0.00 2.00 '1.00 6.00 8.00 10.00ROTOR BLADE PASSING PERIODS

FIG. 4-35a Pressure Fluctuations over theStator Blade, Suction Side,R/Rt = 0.72

(from top to bottom at 20%, 35%, 50%,65% and 80% of chord)

92

POE SPECTRUM DENSI11 OFUNSTEADY PRES. AT S51

A/I* 0.72

C%0-..

a-c3

30

-0-

0

0:)0

00

LiJ

0

2:

bo oF

00

0(~1~

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT SS2R/RT = 0.72

II.00 10.00FREQUENCY

POWER SPECTRUM DENTITY OFUNSIERDY PRES. AT SS4R/RT - 0.72

ib. 00REQUENCY

20.00(KHZ)

POI1ER SPECTRUM DENSITT OFUNSTEADY PRES. AT SS5R/RT = 0.72

X0-

U.J

0

90.00 10.00 20.00FREQUENCY (KHZ)20.00

(KHZ)

POWER SPECTHUM OENSITY OFUNSTEADT PRES. RT SS3R/RT = 0.72

9.00 1'0.00FREQUENCT FIG. 4-35b Frequency Spectrum of Pressure

Fluctuations over Stator Blade,Suction Side, R/Rt = 0.72

C

Iii

j0

0-

X:

0r

CD.

0

U

1-0

~0j r

20.00(KHZ)

I

93

0 i.00 2 1.00 '4.00 6 .00 6.00 10.00oROTOR BLADE PASSING PERIODS

FIG. 4-36a Pressure Fluctuations over theStator Blade, Pressure Side,R/Rt = 0.82

(from top to bottom at 20%, 35%1, 50%,65%/ and 80% of chord) /

94

00

(01

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT PSIR/RT - 0.82

b. oo 10.00FREQUENCY

POWE.R SPECTRUM DENSITY OFUNSTEADY PRES. AT PS4R/RT - 0.82

CDO

0

0

cb oo 10.00 20.00FREQUENCY (KHZ)20.00

(KHZ)

00

0~(0

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT PS2R/RT = 0.82

C)0

Vc

00 0.00FREQUENCY

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT PS5R/RT - 0.82

-oX-aE:

FREQU20.00(K HZ)

10.00 20.00ENCY (KHZ)

POWER SPECTfiUM DENsIT( OFUNSTEADT PRES. AT P53R/RT = 0.62

FIG. 4-36b

.00 10.00FREQUENCT

Frequency Spectrum of PressureFluctuations over Stator Blade,Pressure Side, R/Rt = 0.82

0

X 0.

LUI

:30'-9

6-0

_j :

&0

CD

'-9

UjN

:0

0

Cb

0-(0

LUC):30

1-9a:10

20.00(KHZ)

95

0 i.00 2. 00 14. 00 6 1.00 8.00 '10.00ROTOR BLADE PASSING PERIODS

FIG. 4-37a Pressure Fluctuations over theStator Blade, Suction Side,R/Rt = Q.82

(from top to bottom at 20%. 35%, 50%,65% and 80% of Chord)

96

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT SS1R/RT - 0.82

00

0

010.ICI

LLI~D .4

I-

-Jo

0-

20.00(KHZ)

POWER SPECTRUM DENSITY OF

UNSTEADY PRES. FT SSR/RT - 0.82

boo 10.oo 20.00FREQUENCY (KHZ)

0.0Y

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT SS2R/RT = 0.82

CbC)F0 RE.U NFREQUENCY

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT SS4R/RT - 0.82

L(0-

09X0.

CJOD

C9 ti-

9j.oo 10.00 20.00FREQUENCY (KHZ)

20.00(KHZ)

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT SS3R/R = 0.82

FIG. 4-37b Frequency Spectrum of PressureFluctuations over Stator Blade,Suction Side, R/Rt = 0.82

00

0

0io

0rc

%'.oo 10.00FREQUENCY

0~

Cr CD.

Q

CD

7w C3-

I- c

C0 .1. -1 1'b. oo ib.oo

FREOUENCY20.00

(KHZ)9

97

0.00 2.00 4.,0 0 6 9.00 8 .00 10.00

ROTOR BLRDE PASSING PERIODS

FIG. 4-38a Pressure Fluctuations over theStator Blade, Pressure Side,R/Rt = 0.92

(from top to bottom at 20%0, 35%, 50%965% and 80% of chord)

98

090to1 POWER SPECIRUM VENS11TY OF

UNSTEADY PRES. AT PSIR/RT - 0.92

C

1-90-0

0-X:

010 -

9b.o00 10.00 20.00FREQUENCY (KHZ)

(0 POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT PS4R/RT * 0.92

0c-9

9.00 10.00 20.00FREQUENCY (KHZ)

0

0POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT PS2R/RT - 0.92

X 0..

'-9C0-

0-

a:

00 ib.ooFREQUENCY

2K.00(KHZ)

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT PS5R/RT = 0.92

E.U00 10.00F RE QUE NCY'

20.00(KHZ)

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT PS3R/RT = 0.92

.oo 10.00FREQUENCY

FIG. 4-38b Frequency Spectrum of PressureFluctuations over Stator Blade,Pressure Side, R/Rt = 0.92

C)

0c).0

-4e

X:0c

09

Ct

S-

LU

0

:

(KHZ)

I A '

99

0'.00 2.00 4. 00 6.00 8.00 ib. ooROTOR BLRDE PASSING PERIODS

FIG. 4-39a Pressure Fluctuations over theStator Blade, Suction Side,R/Rt = 0.92

(from top to bottom at 20%, 35%, 50%,65% and 80% of chord)

100

POWER SPEC79UM DENSITI OFUNSTEADY PRES. AT SSIR/RT - 0.92

0"

- -=30

1-9.0"00

O.

b.

0

d.0

oo o.-

xo_

a:

-0-

0

D-~0

-9"

a-00

0

0

=0Uj0

=)o

LaJc

0-

a:

POWER SPECTRUM DENSITY OFUNSTEADY ElEs. AT SS4A/RI - 0.92

9b.oo 10.00FREQUENCY20.00

(KHZ)

030o

POWER SPECTRUM DENSITY OFUNSTEADY PRES. AT SS2R/RT = 0.92

00 10.00FREQUENCY

20.00(KHZ)

POWER SPECTRUM DENSITY OFUNSTEADY PRES. FT SS5R/RT - 0.92

-.

-0 -0-

:

T.oo 10.00FREQUENCY20.00

(KHZ)

20.00(KHZ)

POWER SPECTRUM DENSITT OFUNSTEADY PRES. AT SS3R/RT - 0.92

FIG. 4-39b Frequency Soectrum of PressureFluctuations over Stator Blade,Suction Side, R/Rt = 0.92

00 i.ooFREQUENCY

.09 1o.oo

FREQUENCY2'.noH

(KHZ)

--A- - i - - -

101

&= 40. 1

I-

$=-2.6 M=0.621

1.0

0x

S.S.P. S.

X/C

T=0. 033

&=39.7 0 =-2.8 M=0.610

x/cT=0. 067

0=39.5 1) =-2.8 M=0.599

1.0

*1 ~~ --* -~ -- */cT=0. 100

*=40.0 0 =-2.0 M=0.590

.1.0T=O. 133

40.3 I=-1.6 M=0.586

.0

T=I.167

40.1 $=-1.1 M=0.588

1.0

T=0. 200

e=39.7 0=-C.9 M=0.594

1.0

X/C

T=0. 233

e=39.1 0=-0.6 M=0.610

T=0. 267

1.0+/

-&=39.6 (0=2.3 M=0.610

/ 1.0-- r /

T=0. 300

&=42.5 0=7.8 Ml=0.578

T=0. 333

&=48.2 0 =9.3 =0 50l2

T=0.367

I =50.2 =8. 7 M=0.682

x/C

T=0. 400

e=PITCHWISE FLOW RNGLE AT STRTOR L.E.4=RRDIRL FLOW RNGLE AT STATOR L.E.M=TOTRL MACH # AT STRTOR L.E.T=TIME / ROTOR BLRDE PASSING PERIOD

TEST MIT 240 R/RT=0.72FIG. 4-40a Stator's Chordwise Distribution

of Unsteady Pressure vs. Time

SCALE: =0.20 ATM

I F - i

%.j --------- lc=r-ll-----t&-k --------- 6

102

&=56.1 $ =8.5 M=0.671

w~z~ -~

0x

1.0

S.S.P.S.

%J tv-

T=0. 433

e60. 5 01 = 6.9 M=0.6'43

~ 1.0

x/ c

T=0. 467

e =45.2 O =2.4 M=0.638

T=0. 633

-&= 44.8 $=2.6 M=0.639

(p~ Pi 1.0

/IC

T=0. 667

e=59.2 0 =7.7 M=0.635

x-1.0

T=0.500

55. 7 0=6.5 M =0.660

1.0

T=0.533

50. 3 =6.1 M=0.674

T=0. 567

I e= 44.6 01=3.1 M=0.642

1. 0

T=0. 700

=43. 3 l=2.1 M=0.646

T=0. 733

&=42.7 l=1.8 M=0.645

1.0

x/c

T=0. 767

&=47.7 l =3.6 M=0.685

T=O. 600

-&PITCHWISE FLOW RNGLE RT STRTOR L.E.$=RROIRL FLOW RNGLE RT STATOR L.E.M=TOTAL MRCH * RT STATOR L.E.T=TIME / ROTOR BLRDE PASSING PERIOD

TEST MIT 240 R/RT=O.72

&= 42.3 $ =1.9 M=0.647

p

SCALE:

1. 0x/C

T=0. 800

=0.20 ATM

FIG. 4-40b Stator's Chordwise Distributionof Unsteady Pressure vs. Time

(9 m tm

I

-= 41.9 =1.1 M=0.646

p ~-' -.

7'

(D

x.0

c/C

S.S.P.S.

T=0. 833

&=41.7 0 =0.7 M=0.639

1.0X/C

T=0. 867

42.2 0 =0.4 M=0.629

a- x/CT=0. 900

1.0

=42. 7 $=0.1 M=0.629

T=0. 933

Se=41.9 (0 =-0. 6 M =0. 633

- p ~ 1.0

T-0. 967

e=40.7 0 =-2.0 M=0.630

1.0X/C

T=1 .000

FIG. 4-40c Stator's Chordwise Distributionof Unsteady Pressure vs. Time

TEST MIT 240 R/RT=0.72

00

0-

UJ c-o

-

-- Jc

ao

..5C a

0-J -

In-CC

m

C)

00

(...CD

LUC-

LO..Z Ln-

c- Ln

co-0...

x~=1

U~

0

T.

FIG. 4-40d

00 0.25TIME/BL.

SCALE: =0.20 ATM

Flow Angles and Mach No. atStator Leading Edge, R/Rt = 0.72

0.50PFSS

0.75ING PER.

1.00

103

0 0 ~Q~zr~

a)

LO

C)

(0.-

In

C3

104

e=41.3 O =-4.2 M=0.647 0

x

S.S.P.S.

T=0.033

e =40.6 ( =-5.9 M=0.651

.0

/CX

T=0.06

e=42.0 0 =-3.2 M=0.658

x/C

T=0.233

&=42 7 0 =-0.3 M=0 .677

1.0X/C

T=0. 267

e=40.4 4)=-6.1 M=0.648

1.0

X/C

T=0.10

I = 41.0 ( =-5.6 M=0.642

1.0

X/C

T=0. 133

e=43 $=3.0 M=0.689

1.0X/C

T=0.300

4 2 2.I M=0.622

,1--x

V X/C

T=0.333

&=41.3 0 =-5.8 M=0.642

~ 1.0X

.../C

T=0. 167

1.0x/C

T=0.200

e=56 ) =-1.6 M=n.55:1

1.0

x/C

T=0.367

-=59 4 0=-3.2 M =0.539

1.0x/C

T=0. 400

GePITCHWISE FLOW ANGLE RT STRTOR L.E.(D=RROIRL FLOW ANGLE RT STATOR L.E.M=TOTRL MACH # RT STRTOR L.E.T=TIME / ROTOR BLADE PRSSING PERIOD

TEST MIT 240 R/RT=0.82 SCALE: =0.10 ATM

FIG. 4-41a Stator's Chordwise Distributionof Unsteady Pressure vs. Time

1 1 -3c"

I

' - -

-- 46

-&= 41.3 (P = -4. 7 M =0. 651

105

=57.2 =i.5 M=0.551

~1.

K

0

X/C

P.S.

T=0.433

*=52.5 0 =6.3 M=0.601

1.0

X/c

T=0.46

=43.6 0 =0.4 M=0.632

__.0

X/C

T=0.633

-=43.0 =0.6 M=0.649

T=0.667

e=48.8 $=2.4 M=0.622

.7

T=0.500

-&=46.8 (=2.8 M=0.621

1.0

-.9 X/C

T=0.533

-=42.1 0 =0.2 M=0.6 4 3

X/C

T=0.700

e=42.9 0=0.8 M=0.6 40

1.0

x/c

T=0.733

44. 8 $=1.2 M=0.638

1.0

X/C

T=0.567

7 =-0.1 M=0. 634

1.0

X/C

T=0.600

e-=41.8 1 =-0.3 M=0.647

1.0

X/C

T=0.767

&=41.8 =-1.5 M=0.647

X) .0.0

,,, T = 08 0 X/C

&=PITCHWISE FLOW RNGLE RT SIRTOR L.E.4=RROIRL FLOW RNGLE RT STRTO L.E.M=TOTRL MRCH # RT STRTOR L.E.T=TIME / ROTOR BLADE PRSSING PERIOO

TEST MIT 240 R/RT=0.82

FIG. 4-41b Stator's Chordwise Distributionof Unsteady Pressure vs. Time

SCALE: =0.10 ATM

0

X/C

X/C

106

-& = 41.6 (D =-1.6 M=0.651

1.0

/C

a P.S.

T=O.833

e G=41.6 ' =-3.8 M=0.632

--e 1.0

x x/ C

T=0. 933

-= 40.8 ' =-3.5 M=0.647

~Z2Z T=. 867

1.0x/c

&= 41.6 ' =-4. 1 M=0.629

1.0

x/C

T=0. 967

&=41.0 'P =-3.5 M=0.640

-e: 1.0X/C

T=O.900

-& =41.5 ( =-4. 1 M=0.629

1.0

X / C

T=1 .000

FIG. 4-41c Stator's Chordwise Distributionof Unsteady Pressure vs. Time

TEST MIT

(~1

C-

X:

Jco

_oo

- C

ED

.M

C

LUOI CD

z

la- .

C.

aE

02

o

Ci

240

0

C DA

LU

-o0C.

V)

C)

Ecn

0CD

0.00

R/RT=0.82

FIG. 4-41d

0.25TIME/BL

SCALE: =0.10 ATM

Flow Angles and Mach No. atStator Leading Edge, R/Rt = 0.82

0.50PFSSING

0.75PER.

1.00

.1

I

107

43.7 t=-3.1 M=0.667

T=0. 033

43.2 $=-3.0 M=0.666

I x/c

0x

S.S.P.S.

T=0.067

42.9 $=-3.6 M=0.666

1.T=0. 100

- =42.6 (D=-2.6 M=0.669

x/C

T=0. 233

t &=42.7 $=-1.9 M=0.670

1.0

xC

T=0.267

=42.9 1.1 M=0.678

x3.0

T=0. 300

42. B =-3. 1 M =0.667

I.0

T=0.133

42.6 0 =-3.3 M=0.665

I x /c

T=0. 167

G=43.1 l=0.8 M =0.687

1.0

T=0.333

=44. 4 '=6.1 M=0.687

T=0. 367

42.6 0 =-3.2 M=0.667

=~3.2M

T=0.200

I 417. 3 '~)10. 7 M =0.6541.0+/

T=0. 400

e-=PITCHWISE FLOW RNGLE RT STTOR L.E.4=RROIRL FLOW RNGLE RT STRTOR L.E.M=TOTRL MRCH # RT STRTOR L.E.T=TIME / ROTOR BLRDE PRSSING PERIOD

TEST MIT 240FIG. 4-42a

R/RT=O.92

Stator's Chordwise Distributionof Unsteady Pressure vs. Time

SCRLE: =0.10 ATM

1..

108

=49.L4 =13.7 M=0.633

1.0X/c

T=0. 433

=49.5 1=8.6 M=0.626

I l? Im . 111 I.0

(/c

&= 48.1 0 =5.4 M=0.650

ye )4-= M .0

0x

S.S.P. S.

-=L45.5 0 =-1.2 M=0.698

X/C

T=0. 633

&=45. 4 l=-1.2 M=0.690

T=0.667

=45.4 $=-2.0 M=0.671

=0.

T='0.700

t&=415.1 (D =-1.7 M=0.663

xfC

T= 0 .5 0

e=47.8 $=3. M=0.680

1.0

x/ccr- ',1=

-.0

x/C

-& =46.14 $=1.9 M=0.706

1.0

x/c

T

-= 45.1 4) =0.2 M=0.694

x/C

T= .60

*1-

- =44.9 -1-. 4 M= 0.655

.0

x/c

T=0. 767

=414. 3 l=-1. 0 M =0. 662

~ 1.0x/c

T=0. 600

-&=PITCHWISE FLOW ANGLE AT STRTOR L.E.O=RRDIRL FLOW ANGLE RT STATOR L.E.M=TOTRL MACH # AT STATOR L.E.T=TIME / ROTOR BLROE PASSING PERIO

TEST MIT 2

FIG. 4-42b40 R/RT=0. 92 SCALE: =0.10 ATM

Stator's Chordwise Distributionof Unsteady Pressure vs. Time

T=O. 467

2""" T = O7 3 3

109

e= 45.0 l =-0.8 M=0.664 0

x1.0

X/C

s.s.P.S.

T=0. 833

= 44. 6 l =-1.4 M=0.667

T=0. 867

e=44.3 l =-2.3 M=0.668

X/C

T=0. 933

4- 14. 1 -. 5 M=0 6

~=~5226x / cT=0. 967

&=44. 4 $=-2. 1 M=0.666

1- ~<1. 0X/C

T=0. 900

=43. 4 l =-2.9 M=0.667

X/C

T=1 .000

FIG. 4-42c Stator's Chordwise Distributionof Unsteady Pressure vs. Time

TEST MIT 240

..Cd

C-D

L)

I-

0

.I =

EDC0

C)

W c0

LO00

Z:

-jCoE

cc5

C)c I

00

c\J-U-)

ALUJ

-o-0CL.=o-

(~T

LLJU-4O

F-

0-

C)C)

20.00

R/RT=0.92

FIG. 4-42d

0.25TIME/BL.

SCALE: =0.10 ATM

Flow Angles and MachStator Leading Edge,

iNo, atR/Rt = 9.92

I I0.50 0.75

PFSSING PER.1.00

I Lh. , o

110

& =40.1 $=-2.6 M=0.621

:1.0X/C

T=0. 033

*& 39.7 ( =-2.8 M=0.610

1.0X/C

T=0.067

e=39.7 l=-0.9 M=0.594

1.0X/C

T=O. 2

&=39.1 0=-0.6 M=0.610

1.0

X/C

T=0. 7

I =39.5 $=-2.8 M=0.599

1.0I X/C

T=0. 100

= 40.0 l)=-2.0 M=0.590

1.0X/C

T=0. 133

e=39.6 '=2.3 M=0.610

1.0

X/CT= 0.

I =42.5 =7.8 M=0.578

1.0X/C

T=O. 3

*=40.3 q =-1.6 M=0.586

1.0X/C

T=0. 167

&=40.1 $=-1.1 M=0.588

1.0X/C

T=0. 200

I =48.2 l=9.3 M =0.602

1.0

X/C

T=0. 367

e=50.2 0 =8.7 M=0. 682

1.0

X/C

T=0. 400

1*ePITCHWISE FLOW RNGLE RT STTOR L.E.(=RRDIRL FLOW RNGLE AT STRTOR L.E.M=TOTRL MRCH # AT STRTOR L.E.T=TIME / ROTOR BLADE PASSING PERIO

TEST MIT 240 R/RT=0.72FIG. 4-43a Stator's Chordwise Distributio

Unsteady Life Coefficient vs.

"LIFT COEFFICIENT"

SCRLE: =0.50

n of ..Time

ill

e=56.1 =8.5 M=0.671

1.0*1

T=0. 433

e&=60.5 1 =6.9 M=0.643

1.0

X/C

T=0. 467

*=45.2 0 =2. 4 M=0.638

1.0

7 x/c

T=0. 633

e=44.8 0 =2.6 M=0.639

3.0

- X/C

T=0. 667

&=59. 2 7.7 M=0.635

1.0I X/C-

T=0. 500

&=55.7 =6.5 M=0.660

1.0

X/C

T=0. 533

&=44.6 $ =3.1 M=0.6 42

1.0X/C

T=0.700

I &= 43.3 0 =2.1 M=0.646

1.0X/C

T=0.733

e = 50.3 C =6.1 M =0.674

1.0

X/C

T=0.567

&=47.7 ( =3.6 M=0.685

K.0X/C

T=0.600

e=42.7 =1.8 M=0.645

1.0

X/C

T=0.767

S =42. 3 1.9 M =0.647

3.0

x/C

T=0.800

e=PITCHWISE FLOW RNGLE RT STRTOR L.E.O=RROIRL FLOW RNGLE RT STRTOR L.E.M=TOTRL MRCH # RT STRTOR L.E.T=TIME / ROTOR BLRDE PRSSING PERIOD

TEST MIT 240FIG. 4-43b

R/RT=0. 72Stator's Chordwise DistributioUnsteady Lift Coefficient vs.T

"LIFT COEFFICIENT"

SCALE: =0.50

n ofime

112

&=41.9 0 = 1.1 M=0.646

X/C

T=0.833

&=41.7 4) =0.7 M = 0.639

X/C

T=0. 867

e-=42.7 =0.1 M=0.629

X/C

T=0. 933

=41.9 =-0.6 M=0.633

X/C

T=0.967

&=42.2 $ =0.4 M=0.629

1.0

X/c

T=0. 900

e-=40.7 1 =-2. 0 M=0.630

1.0

X/1

T=1.000

FIG. 4-43c Stator's Chordwise Distribution ofUnsteady Lift Coefficient vs. Time

TEST MIT 240 R/RT=0.72 SCALE:

FIG. 4-43d

0.25TIME/BL.

Flow Angles and Mach No.at Stator Leading Edge,R/Rt = 0.72

0.50PRSSI

0.75NG PER.

=0.50

Cn#. ito

C-ED

.C30

H-

rs0n

LLJ0

:z

a: CC3Eo

-o.

a:cc

CD0 o

f.

C)C)

CO-0

1C)

LO

0

r~

CD

Co

m4

OX. 00 1.00-

.

113

e=41.3 $ =-4.2 M=0.647

1.0

X/C

T=0.033

G=40.6 '=-5.9 M=0.651K. i.0

T=0. 067

I&= 40. 4 (=-6.1 M=0.648

1.0

k/CT=0.100

=42.0 I =-3.2 M=0.658

1.0

X/C

T=0.233

=42.7 =-0.3 M=0.677

1.0

X/C

T=0.267

&=43.9 =3.0 M=0.689

1.0X/C

T=[.i300

-= 41.0 I1 =-5.6 M=0.642

I. I1.0

X/C

T=0. 133

/x/C

T=0.333

=41.3 ( =-5.8 M=0.642

1.0X/C

T=0.167

- = 41.3 1$ =-4.7 M = 0.651

1.0

X/C

T=0. 200

e 56.3 (0 = - 1.6 M =0. 551

1.0X/C

T=0.367

e=59. 4 $ =-3.2 M=0.539

1.0

X/C

T=O. 4

e=PITCHWISE FLOW RNGLE RT STRTOR L.E.(1=RRDIRL FLOW RNGLE RT STRTOR L.E. "LIFT COEFFICIENT"M=TOTRL MHCH # RT STRTOR L.E.T=TIME / ROTOR BLRDE PRSSING PERIOD-

TEST MIT 240 R/RT=0.82 SCALE: =0.40

FIG. 4-44a Stator's Chordwise Distribution of IUnsteady Lift Coefficient vs. Time

=48. 6 $ 2. 1 M =0.622_

A - 1.( 0

114

G=57.2 $=1.5 M=0.551

1.0

x/c

T=0. 4

e=52.5 $=6.3 M=0.601

1.0

x/c

T=0. 467

e=43.6 1 =0.4 M=0.632

1.0X/c

T=O. 633

6,1.1x/C

T=0.667

&=42.1

T=(

=48.8 0 =2.4 M=0.622

1.0

X/c

T=0.500

I =46.8 ( =2.8 M=0.621

1.0

x/c:

T=0.533

=0.2 M=0.6143

1.0

X/c

).700

T =42.9 $ =0.8 M=0.640

1.0x/c

T=0.733

I =44.8 ( = 1.2 M=0.638

1.0

x/c

T=0.567

e=143.7 1 =-0. 1 M=0.634

1.0

T=0.600

I =41.8 =-0.3 M= n. 4-

1.0

x/C

T=0. 767

4 = 1. 8 =-1.5 M= 0.647

1.0

---- x/c

T=0.800

e=PITCHWISE FLOW RNGLE RT STRTOR L.E.O=RRDIRL FLOW RNGLE RT STRTOR L.E.M=TOTRL MRCH # RT STRTOR L.E.T=TIME / ROTOR BLRDE PRSSING PERIOD

TEST MIT 240 R/RT=0.82FIG. 4-44b Stator's Chordwise Distributio

Unsteady Lift Coefficient vs.

"LIFT COEFFICIENT"

SCRLE: =O.40

n ofTime

115

) =-1.6 M=0.651

1.0X/C

T=0. 833

&=40.8 P =-3.5 M=0.647

X/C

T=0. 867

=411.0 $=-3.5 M=0.640

X/C

T=0. 900

FIG. 4-44c Stator's Chordwise Distribution ofUnsteady Lift Coefficient vs. Time

TEST MIT 240

CD

Co

LUJ

C O

LUJ

C)

F-

ZEco..

H-

CL.

R/RT=0. 82

FIG. 4-44d

0.25T IM E /BKL

e =41.6 l =-3.8 M=0.632

1.0

X/C

T=0.933

G=41.6 0 =-4. 1 M=0.629

1.0

X/C

T=0. 967

=41.5 (P =-4. 1 M=0.629

/C

C =1.000

CRLE: =.4

Flow Angles and MachStator Leading Edge,

0.50PASSING

S

No. atR/Rt =

0.75PER.

0.82

1'.00

& =41.6

C

C)

-Jo

aj:)-Jo

CE

C)

C\j

C

Co

a: L

-

ED

C

&,

0.00

116

e=43.7 $ =-3.1 M=0. 667

_.0

X/c

T=0. 033

&=43.2 $=-3.0 M=0.666

1.0

X/C

T=0. 067

=42.6 $=-2.6 M=0.669

1.0X/C

T=0.233

e&=42.7 =-1.9 M=0.670

1.0

X/C

T=0.267

=42. 9 ( =-3.6 M =0.666

1.0X/c

T=0. 100

I =42.8 )=-3.1 M=0.667

C1.0IX/C

T=0. 133

=42. 6 =-3. 3 M =0. 665

.- 1.0X/C

T=0. 167

j =43.1 c=0.8 M=0.6F,7

1.0

X/C

T=0.333

=0. 687

1.0X/C

T=0.367

-=42.6 l=-3.2 M =0.667

1.0

X/C

T=0.200

'&=PITCHWISE FLOW RNGLE RT STRTOR L.E.(P=RRDIRL FLOW RNGLE RT STRTOR L.E.M=TOTRL MRCH 4 RT STRTOR L.E.T=TIME / ROTOR BLROE PRSSING PERIOD

&=47.3 l=10.7 M=0.654

1.0X/C

T=0. 400

"LIFT COEFFICIENT"

TEST MIT 240 R/RT=O.92 S CRLE:FIG. 4 -45a Stator's Chordwise Distribution of

Unsteady Lift Coefficient vs. Time

3.0x/IC

T=0.300

=0. 40

-& = 42. 9 0 = - I. 1 M =0. 678

-& = 44. 4 0 = 6. 1

117

e =49. 4 ( =13.7 M=0.633

IA 1.0X/C

T=0. 433

G=49.5 4) =8.6 M=0.626

1.0

- X/C

T=0. 467

e=145.5 0 =-1.2 M=0.698

I >.0

X/C

T=0. 633

S -= 45. 4 0 =-1.2 M=0.690

p/ 1.0I~ -/C

T=0.667

*=48.1 =5. 4 M=0.650

.1 1.0X/C

T=O.5

O&= 47.8 0 =3.0 M=0.680

1.0X/C

T=0. 3

=45.14 1=-2.0 M=0.671

1.0X/C:

T=0.700

M=0.663

1.0X/C

T=0. 733

=46.4 =1.9 M=0.706

1 1.0X/C

T=0. 7

=45.1 l=0.2 M=0.694

1.0x/C

T=0.

44.9 =-1.. 4

N11

T=0.800

&=PITCHWISE FLOW RNGLE RT STRTOR L.E.(D=RRIRL FLOW RNGLE RT STRTOR L.E.M=TOTRL MRCH # RT STRTOR L.E.T=TIME / ROTOR BLRDE PASSING PERIOD

TEST MIT 240 R/RT=0.92FIG. 4-45b Stator's Chordwise Distributio

Unsteady Lift Coefficient vs.

"LIFT COEFFICIENT"

SCALE: =o.40

n ofTime

M =0. 655

1.0

T=0.767

& =44.3 0 =-1.0 M=0.662

1.0x/C

X/C

-&= 45. 1 0 =-1.7

118

I 45. =-0.8 M=0.664

1.0

X/C

T=O.833

e-44.6 0=-1.4 M=0.667

1.0X/C

T=0. 867

44. 4 =-2.1 M=0.666

1.0

T=0.900

-=44.3 ' =-2.3 M=0.668

.. 1.0X/C

T=O. 933

44. 1 $=-2.5 M=0.665

X/C

T=0. 967

e=43.4 0 =-2.9 M=0.667

X/C

T=1 .000

FIG. 4-45c Stator's Chordwise Distribution ofUnsteady Lift Coefficient vs. Time

TEST MIT 240 R/RT=O.92 SCALE: =0.40

FIG. 4-45d Flow Angles and Mach No. atStator Leading Edge, R/Rt = 0.92

0.25TIME/BL.

0.50PRSS

1.000.75ING PER.

0

Co

I C-- J

CDoz

-JCEo-C

cC C

CC

C

*K

._J=r

-

(D

C

0co

CJ

LD.z c.

Co0

It.

0o0C:

0.001 -1

119

UNSTEAOD LORO ON STATOR BLADER/RT =0.72

2'.OO 4'.OO 6'.0 8'.00ROTOR BLADE PASSING PEIODS

UNSTEROT LORD ON STATOR BLADER/RT =0.72

I'b. oo

_j

CC

wAc

CC*

91

C3

S-j

C-X:

2'.00 ti.00 6o.00 8.00ROTOR BLADE PASSING PEIODS

UNSTEADY LOAD ON STATOR BLAOE

R/RT =0.72

0.oo

aa0t~1.

'a0

0.0

POWER SPECTRUM DENS17T

OF AXIAL FORCER/RT - 0-72

S 29o

.3

FREQUENCY (KHZ.)

ao

ar0i

C3

_cu

4IINJAAW

2'.00 4'. 00 6'.00 . 8'.00ROTOR BLADE PASSING PEIODS

a'b.oo

POWER SPECTRUM DENSITY

OF PITCHING MOMENTR/RT - 0.72

4.ho 20.00 40.00FREQUENCY (KHZ.)

FIG. 4-46 Unsteady Loads on Stator Blade,R/RT = 0.72

a

POWER SPECTRUM OENS1TI

OF TANGENIIAL FORCE

1KR 0..7

=)o

V0.

Ca

'b! 0 2.oo 400 b. ooFREQUENCY (KHZ.)

C .00

0

a

=C.

LL0

crc

sr

1 0

a3V

.00

z

*U.3

L-J

O.00

*AW;A

i-

UNSTEADY LOAD ON STATOR BLADER/RT =0.82

2'.00 '.00 6.B00 8'00ROTOR BLADE PASSING PEIOOS

0

POWdER SPECTRUM DENSITYOF TANGENTIAL FORCE

C:o A/AT *0.82

LUJ0

ccrn

CD

9:,.oo 20.00 '10.00FREQUENCY (KHZ.)

UNSTEADY LOAD ON STATOR BLADE

R/RT =0.82

60

ZO.wn

ff~V4I rPV;2.00 '.00 6.o 8.00

ROTOP BLADE PASSING PEIODSIb.oo

UNSTEAOT LOAD ON STATOR BLADER/RT =0.

/o 1\A2'.00 4'.00 6. 00 8.00

ROTOR BLADE PASSING PEIODS

FIG. 4-47 Unsteady Loads onR/RT = 0.82

i'.oo

POWER SPECTRUM DENSITYoF AXIAL FORCE

R/RT a 0.82

Lio3=aI

0-X:cc

00 20.0 Do 10.00O

FREQUENCY (KHZ.)

POWER SPEC1RUM DENS17T

Or PITCHING MOMENTA/RT * 0.82

10

-9e

cc

b .oo 20.0o '10.0oFREQUENCY (KHZ.)

Stator Blade,

120

00

"a

zn

JO

0occ

.LL.(3ZJ

CC

F-"AyO.O

0It

10.00

Lu

C)

-

cr

0.00

-

Li

CDC

z

un0

0.00

UNSTEADY LOAD ON STATOR BLADE

R/RT -0.92

yVqw

UNSTEADY LOAD ON STATOR BLADER/RT =0.92

2.00 t'.00 6.00 8.00ROTOR BLADE PASSING PEIODS

UNSTEADY LOAD ON STATOR BLADE

R/RT =0.92

i'.oo

ib.o o

.00 2.00 L'.o 6.00 8.00ROTOR BLADE PASSING PEIODS

C

0

0

OF. Do NON2b. ORCE o0 A/AT * 0.92Z.

POWER SPEC7RUM OENSTOF AXIAL FORCE

C:j0 R/R7 0.92

a)

Lu

I-Ia

j:r

93oo 20.00 '40.00

FREQUENCY (KHZ.)

2.00 4.00 6.00 8.00ROTOR BLFIDE PASSING PEIDS

Unsteady Loads onR/RT = 0.92

10.00

090CU

POWER SPECTRUM DENSITYOF PITCHING MOMENT

A:C: /RT -0.92

L

cI:

FREQUENCY (1KHZ. )

Stator Blade,

121

0

zou0

00

cc:

0

In

-J

UL

cc

a:c

0:.

0.00

0C00)

IO.

2: A ~ft

0.00

FIG. 4-48

PRE S-.U'

.75

,75 -a-

4- - -

A-

A

AI.

II

0

I,

A

X/C

Stator's Chordwise Distribution ofSteady State Pressure and LiftCoefficient

UC IVN

I--

-4---- '47

I.)

'J-J)A -,

0 .9'

C'.

0.0 I.

FIG. 4-49

T '1 C,

IJ

Q

-1

A YIAI

FIG. 4-50 Steady State Tangential and AxialForces on Stator Blade vs. Radius

_-z

I. -9 / ~/i t

() 'YT, ' Cl

t-

124

APPENDIX A

CALCULATION OF EFFICIENCY

The total-to-total adiabatic efficiency for a compressor rotor

is

t2tl - 1(Tt2/Ttl) -

(Al)

where subscripts 1 and 2 denote upstream and downstream of the rotor.

The calculation of efficiency requires both total pressure and total

temperature to be measured. It is not possible to measure total

temperature in the Blowdown Facility, instead the Eulers equation is

used to calculate total temperature rise across the rotor.

A(r w V )Tt2 -Ttl cp

orr u V02

Tt2/Ttl - 1 = cp Tt2

The right hand side of A2 can be written as:

R w V02 Tt2cp Tt2 tl

R w V 0

cp T 2(1 + 2 M)2 ~22

yR (R w Ve2 )

cp(yRT 2 ) ( + y.7 M2)

(A2)

Tt2

tl

Tt2

ti

(A3)

125

but speed of sound a = VyRT and

Rw=--R W RURt = Rt t

where Ut is the rotor tip speed. From Eqs. (A2) and (A3) we get

Tt2

1 - 1)M~t M0 2 (R/Rt)

(1 + I--, M,2 2

Therefore

=(Pt2tl - 1

(y-1) Mt M02 R/Rt

(1 + M2 (Y-1) tMe2 R/Rt

126

APPENDIX B

MASS FLOW CALCULATION

The mass flow through the rotor can be calculated four different

ways. These four methods are as follows:

i) The rate of change of pressure in the supply tank is related

to the mass flow as

. vT10 )dplw=2 T dt

(1+6) a,, 1 d

where v is the supply tank volume, 6 is percent of flow through the

boundary layer bled, a10 and T10 are the temperature and speed of

sound in the supply tank in the beginning of the test and p1 and T,

are supply tank pressure and temperature.

ii) Calculation of rotor inlet Mach number M2 from pressure

measurement upstream of the rotor leads to

-P 2A 2 2 ( 10 Ll ) Y la) y-1 T P2 2

where 1 and 2 denote supply tank and rotor upstream conditions,

respectively.

iii) Calculation of mass flow through the choked throttle orifice

using the measured value of p3 , pressure upstream of the orifice gives

w YP 3A [(2)(1 +Y+!

is the orifice area and M 3 is determined by the area ratio

iv) Radial integration of flow quantities measured by the 5-way

probe leads to

Rt

w = J 27R p Vx dr

But

p vP

J V = '-M px

- RT x ~-

TtT = Tt2

2 (1_y- - M2)2

_ t2/P tir (Tt2/Tti- 1

(B4)

(B5)

(B6)

(B7)

Combining Eqs.

T 2

(B6) and (B7) we get

2t 1

1 + Y- M 22

127

M2

Awhere*

A /A 3

- 1)/r

y+1

02(Y-1)

*

128

The mass flow can then be computed from the measured Mach numbers

and pressure ratios

w = 2TrR2 7Rt vR

t

h

R_ )Mp d( R )Rt V7- Rt

0