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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