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Study of single-stage axial flow compressor performance deterioration
Wear, 119 (1987)
51
51 - 61
STUDY OF SINGLE-STAGE AXIAL FLOW COMPRESSOR PERFORMANCE DETERIORATION W. TABAKOFF Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, OH 45221 (U.S.A.) (Received July 29,1986;revised
February 18,1987;
accepted March 17,1987)
Summary Compressors operating in a polluted atmosphere with solid particles are subjected to performance deterioration. This paper presents an investigation carried out on a single-stage axial flow compressor to study the effect of erosion on performance deterioration.
1. Introduction The experimental and theoretical study presented by Tabakoff and Balan [l] establishes the nature of the cascade performance decrease due to erosion. The material removal, the changes in the profile, the surface roughness and the overall pressure distribution can be predicted reasonably well. At the present time, there is no experimental data available in the literature on particulate flow related to performance deterioration. For this reason, it was decided to conduct experiments on a single-stage axial flow compressor. The development of the test facility and the experimental program is described below.
2. Experimental set-up 2.1. Drive unit A schematic diagram of the experimental set-up is shown in Fig. 1. The basic prime mover in this case is a three-phase a.c. motor producing 75 kW of power. This motor runs at a constant speed of 3500 rev mm-‘. The motor is connected to the test equipment by means of an electrical clutch, which is controlled by an electronic feedback control system. The clutch output shaft speed can be controlled from zero to the full speed of 3500 rev min-‘. The torque of the output shaft is independent of the output speed. The feedback control system enables the output shaft to rotate at any desired speed under all load conditions. The clutch is also equipped with 0043-1646/87/$3.50
@ Elsevier Sequoia/Printed
in The Netherlands
52 EXHAUST
t
PARTICLE
TO SEPARATOR
INLET 4--
f
I
/
\
I
\
II
II
Fig. 1. Schematic diagram of the experimental set-up: A, a.c. motor; B, clutch-brake unit; C, gear box; D, torque transducer; E, test compressor; F, particle injector.
an eddy current brake, which enables the test equipment to be brought to rest immediately if needed. The brake is employed automatically whenever the clutch is disengaged. The breaking torque has two preset values. One for gradual reduction in speed under normal conditions and the other for emergency conditions. Both the clutch and the brakes are water cooled. The output shaft of the clutch-brake unit is connected to the test compressor through a gear box. The ratio of the speed increase is 1:3.46. This gear box enables the test compressor to be run at any speed up to 12 100 rev min-’ under any load condition. 2.2. Test compressor The test compressor is a single-stage axial compressor without any inlet guide vanes. The same NACA 65(10)-10 airfoils which were used in the twodimensional cascade tests were chosen for the compressor [l]. The aspect ratio of 0.75 and the pitch-to-chord ratio of 0.5 were maintained for the compressor. It was decided to limit the rotor tip relative Mach number to 0.5 and the whirl at the exit of the stator to within 15” from the axial direction. This resulted in a compressor with the following design specifications: speed, 9000 rev min-‘; tip diameter, 300 mm; pressure ratio, 1 .l; mass flow, 3.67 kg SK’; hub-to-tip ratio, 0.75. 2.3. Particle feeding mechanism The particle feeder is similar to that described in the twodimensional erosion tunnel [l]. However, the particles are injected at four locations around the periphery in the air intake. The four nozzles which inject the particles into the air intake are controlled individually to provide a uniform distribution of the particles through the compressor. 2.4. Instrumentation The main power input to the compressor is measured by a rotary transformer-type torque transducer located between the gear box and the test
53
compressor. This torque transducer is also provided with a magnetic speed pick-up. The compressor is instrumented with total pressure and total temperature rakes. These are located at two chords upstream of the rotor inlet, two chords downstream of the stator exit and at the exit manifold. The wall static pressures are measured at the same planes where the total pressure and temperature rakes are located. In addition, there are also provisions for traversing combination probes to measure the total pressure, total temperature and flow exit. All the pressures are recorded using the scanivalve pressure transducer digital recorder system. For better control, there is also a provision to use a multitube manometer bank. The mass flow through the compressor is measured by the calibrated air intake.
3. Test procedure First the performance of the compressor stage with smooth blading was measured under different mass flow conditions and at a constant speed of 5000 rev mm’. The mass flow through the compressor was adjusted by a throttle valve in the exhaust line. The inlet flow was assumed axisymmetric and the flow quantities, such as the inlet total pressure, total temperature and static pressure, were measured at 16 radial positions one chord upstream of the rotor-blade row. The non-uniform flow at the stage exit was scanned one chord behind the stator at seven radial locations. At each radial location, the flow properties were measured over two blade pitches in steps of 0.75”. The Reynolds number based on the inlet velocity and chord length was between 1.25 X lo5 and 2.85 X lo5 depending on the mass flow. The inlet Mach number was limited to approximately 0.17 under the maximum mass flow conditions. The next step was to erode the compressor blades. The blades were eroded in steps by using 5 kg of sand per step. The duration of the sand ingested at each step was 121 s. The compressor was operated at the maximum efficiency point during the period of sand ingestion. The rotational speed of the unit remained constant during the period of sand ingestion. However, it was noted that the power required to drive the unit went up by 12.5% during the period of sand ingestion as indicated by the torque cell. The performance measurements were repeated after each step of sand ingestion, but without particulate flow. The results presented in this paper are only for the initial conditions with uneroded blades and for the final conditions with maximum eroded blades. In both cases, the flow was without solid particles. 4. Analysis of the results On the basis of the measurements, the mass averaging of the flow properties in the pitch direction yielded the mean flow properties such as exit total pressure Tte at each radius for the various mass flow conditions.
54
Mass averaging of these quantities for the given mass flow in the radial direction yielded the overall stage exit total pressure Iite and exit total temperature Tt;,,. However, the temperature measurements were not accurate enough to estimate the overall adiabatic efficiency of the stage. Hence, the actual power input Aht for the working fluid was computed by subtracting the bearing and seal losses from the total power input to the stage. The bearing and seal losses were estimated by spinning the rotor without the blades at the test speed. The total isentropic enthalpy rise Ah,, was computed as
(1) where y is the ratio of specific heats, R is the gas constant, Ftl,,is the mean inlet total temperature and Pti is the mean inlet total pressure. The total adiabatic efficiency qtad of the stage was estimated as Ah,, (2) %,d = Ah, In addition, assuming that the fluid is incompressible, the mean stage loading $ was calculated as $=
Fte -Fti
(3) But2 where p is the mean gas density and ut is the blade tip speed. Also, the local blade loading $ along the blade height was calculated as $=
Pte -
pti
(4)
Put2
where P,, and Pti are the pitch averaged local values at a particular radius. The results were then reduced to the reference state values using similarity laws. The reference state was standard conditions at the inlet: Tti = 288.15 K and Pti = 1.013 bar
(5)
The effects of the presence of solid particles on the turbomachinery performance may be found in refs. 2 and 3. 4.1. Erosion damage The compressor stage was subjected to a total of 25 kg of sand ingestion over a period of 605 s. The size of the sand particles was 165 pm. The compressor blades were inspected by using fiber optic techniques after each erosion run of 5 kg of sand ingestion through the stage. The erosion damage of the rotor was at the blade tip sections, along the leading edges
55
and on the pressure side of the blades. Finally, the compressor stage was disassembled and the damage to the rotor and stator was recorded. The rotor leading edge was severely eroded along the blade span. (1) There was an erosion step fo~ation on both the suction and the pressure surfaces of the blades, near the blade leading edges. In addition, the blade leading edges were flattened and rougher. (2) The pressure surfaces of the blades were eroded moderately and the erosion was associated with a significant increase in the pressure-side roughness. This roughness was measured and it was fotmd to fluctuate between 20 and 70 ,um. (3) The trailing edge of the blades was eroded severely on the pressure side and the trailing edge became very thin. (4) The blade suction surfaces remained unaltered for most of the blades, except for the step formation at the leading edge and increased surface roughness on a small region around the center of the blade chord. (5) The decrease in blade chord was about 1.2%. (6) At the tip, the rotor blades were completely damaged. The changes in the tip clearance were very high, over 300 pm. A view of the erosion damage of the rotor blades is shown in Fig. 2. The pressure side was eroded severely near the tip and along a small portion near the leading edges. There was moderate erosion on most parts of the pressure side except on a small region starting from the hub at about 50% chord and extending to about 20% of the span near the trailing edge. The suction side was eroded along the leading edge and along the small portion of area about l/2 chord wide, starting from the tip region and extending to about 3/4 span (see Fig. 2). The stator blades were also eroded along the leading edges and on the pressure sides. The pressure surface was eroded more towards the tip. There was no pronounced erosion on the suction side. 4.2, PerfOrnWTWed&?riOMtiOn Figure 3 shows the changes in the stage loading as a function of the mass flow. It can be observed from this figure that there is a decrease in the stage loading of 2.4% at a mass flow of 1.36 kg s-l, 3.32% at a mass flow of 1.732 kg s-i and 4.27% at a mass flow of 2 kg s-i. The total adiabatic efficiency of the stage is given in Fig. 4 as a function of the mass flow. It can be seen that a maximum efficiency of only 82% is obtained at the mass flow of 1.732 kg s-l. The rotor blade design is strictly two dimensional. Subsequently, there is a considerable variation in the incidence angle along the blade span owing to the low hub-to-tip ratio of 0.75. In addition, the blades were originally manufactured for the purpose of twodimensional cascades and hence were of large chord (50.8 mm). This resulted in a blade aspect ratio of only 0.75 even though the hub-to-tip ratio is fairly low. The overall effects of such a large chord, untwisted blades and a low hub-to-tip ratio are the cause of the low efficiency. The efficiency of the eroded stage after injection of 25 kg of sand through the machine dropped by about 1.86% at a mass flow of 1.36 kg s-l, 2.16% at a mass flow of 1.732 kg s-’
(4
(b)
(cl Fig. 2. Erosion damage of (a) the compressor stage rotor blade pressure surface, (b) the compressor stage rotor blade suction surface and (c) the compressor stage stator blade pressure surface.
and by about 2.89% at a mass flow of 2 kg s-l. The decrease in efficiency is probably due to increased losses at the blade leading edges particularly in the tip region. It is also possible that the tip leakage has increased considerably owing to the severe erosion of the blade tips as well as of the casing. The experimental data obtained for the local blade loading $ are plotted us. the blade height in a radial direction for the mass flow of 1.732 kg s-l as shown in Fig. 5. An inspection of this figure shows that the performance is affected severely near the tip region. It can be seen from Fig. 5 that the change in the blade loading is not significant for most parts of the blade up to a radius ratio of 0.9. The blade loading at the tip section decreases sharply by about 5.5% after erosion with 25 kg of sand as compared with the uneroded stage values. On the basis of this, we can conclude that the loss in efficiency and the power rise across the stage are mainly due to the deterioration of the leading edges together with the change in the airfoil shape, particularly near the tip region. In the present case, the change in the thickness distribution owing to the material removal on the pressure surface and the suction surface of the rotor blades may be less important than the
57
1.50
1.25
MASS
Fig. 3. Effect
0.90
0.85 : E
G
1.75
2.00
2.25
FLOW, m, kg/set
of erosion on stage loading:
0, uneroded;
*, eroded
(25 kg).
r t
0.80
z; c; L:
1.25
1.50
MASS Fig. 4. Effect
1.75
2.00
2.25
FLOW, m, kgisec
of erosion on adiabatic
efficiency:
0, uneroded;
A, eroded
(25 kg of sand).
58 0.45 r
0.251 0.75
I
I
I
0.80
0.85
0.90
RADIAL
POSITION,
I 0.95
I 1.00
r/rt
Fig. 5. Effect of erosion on blade loading as a function of radial position: 0, uneroded; 0, eroded (15 kg); A, eroded (25 kg).
leading edge deterioration, owing to the relatively large physical dimensions of the blades used. In addition, the trailing edge was very thin near the tip owing to the material removed during erosion. The trailing edge was fairly unaltered near the hub region. It is possible for the trailing edge to vanish under high degrees of erosion which may lead to considerable changes in the exit flow angle as well as in additional losses. It should also be noted that for small blades, operating at high Reynolds’ numbers, the increase in surface roughness may also play an important role. 4.3. Compressor stage particle trajectories The erosion of the rotor and stator blades can be predicted by analyzing the trajectories of the particles through the compressor stage. An analysis of the particle trajectories was carried out using a threedimensional particle trajectories program which was developed as part of this research. The analysis indicates the various locations of particle impacts and the possible erosion regions. The purpose of the present analysis was only to identify the erosion regions and compare them with the experimental data. The particle trajectories were computed for an assumed uniform inlet particle distribution. The trajectories were computed by introducing the particles at various equispaced radial and tangential locations. 5. Analysis The equations governing the particle motion in the turbomachinery flow fields are written in a rotating frame of reference using cylindrical
59
coordinates. The three components of the equations of motion in a frame rotating about the engine axis with angular velocity o are given by
d28 _-E=&-
(7)
” dr2
_ -d2ZP - -F, dr2
where rP, 0, and zP define the particle location in cylindrical polar coordinates, V,, V, and V, represent the relative gas velocities in the radial, circumferential and axial directions respectively, o is the blade angular velocity and r is the time. The centrifugal force and Coriolis acceleration are represented by the last terms on the right-hand side of eqns. (6) and (7). The first term on the right-hand side of eqns. (6) - (8) represents the force of interaction between the two phases, per unit mass of particles. It is dependent on the relative velocity between the particles and the gas flow, as well as on the particle size and shape. Under the particulate flow conditions in turbo-machines, the effect of the forces due to gravity and interparticle interactions is negligible compared with those due to the aerodynamic and centrifugal forces. In addition, the force of interaction between the two phases is dominated by the drag due to the difference in velocity between the solid particles and the flow field. The force of interaction per unit mass of solid particles is therefore given by
F=i ..c& #-
fgy+
(vo-!$)‘, (vi-$-)‘/“2’“-vp’ (9)
where p and ps are the gas and solid particle densities, d is the particle diameter, 7 and VP are the gas and particle velocities relative to the blade and Co is the drag coefficient. The drag coefficient is dependent on the Reynolds number, which is based on the relative velocity between the particle and the gas. Empirical relations, as shown in ref. 4, are used to fit the drag curve over a wide range of Reynolds’ numbers. The particle trajectory calculations consist of the numerical integration of eqns. (6) - (9) in the flow field, up to the point of the blade, hub or tip impact. The impact location can be determined from the particle trajectory calculations and the local geometry of the impacted surface. The magnitude and direction of the impact velocity relative to the surface, for a large number of particles, constitu~ the essential data needed for the evaluation of the erosion of the various turbomachinery components. Figure 6 shows the trajectories of the 165 pm particles through the rotor blade channel in the Z-0 plane. It can be seen that there is a consid-
60
Fig. 6. Particle trajectories through the rotor blade passage. ROTOR
STATOR
Fig. 7. Particle trajectories through the compressor stage in meridional plane.
erable amount of impacts on the entire rotor blade pressure surface. In addition, some of the particles rebound off the leading edge and impact on the suction surface of the rotor blade. There are also a few particles which impact on the leading edge region and rebound away from the blades. These particles reenter the blade rows at some other locations which are not shown in this figure. Figure 7 shows the trajectories of 100 particles in the r-2 plane. From this azimuthal view it can be seen that there is a considerable impact on the tip casing. The particles, which were introduced at 10
61
radial locations, diffuse so much that they occupy the entire span after rebounding. In addition, the trajectories indicate that the particles do not impact the hub region of the stator blades at all. Comparing the trajectories of the particles through the compressor stage with the experimental observation as shown in Fig. 2, it can be seen that there is very good agreement. The trajectory analysis indicates erosion on the entire rotor blade pressure surface and on a region near the midchord position on the suction surface. There is no significant erosion on the stator blade suction surface. The stator blade pressure surface is not eroded near the hub region. 6. Conclusions From the compressor rig experiments, it was found that erosion damage can lead to a significant reduction in the engine efficiency as well as in performance. The decrease in performance is mainly due to changes in the blade leading and trailing edges, tip leakages, surface roughness and pressure distribution. The data obtained from the trajectory calculations are in very good agreement with the experimental findings. Acknowledgment This research was sponsored by the U.S. Army Research Office under contract number DAAG2982-K-0029. References 1 W. Tabakoff and C. Balan, Effect of sand erosion on the performance deterioration, 6th Znt. Symp. on Air Breathing Engines, Paris, June 6 - 7, 1933, American Institute of Aeronautics and Astronautics, New York, 1983, pp. 458 - 467. 2 W. Tabakoff, Turbomachinery performance deterioration exposed to solid particles environment, J. Fluids Eng., 106 (1984) 125 - 134. 3 W. Tabakoff, W. Hosny and A. Hamed, Effect of solid particles on turbine performance, J. Eng. Power, 98 (1976) 47 - 62. 4 F. Hussein and W. Tabakoff, Dynamic behavior of solid particles suspended by polluted flow in turbine stage,J. Aircr., 10 (1973) 434 - 440.
51
51 - 61
STUDY OF SINGLE-STAGE AXIAL FLOW COMPRESSOR PERFORMANCE DETERIORATION W. TABAKOFF Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, OH 45221 (U.S.A.) (Received July 29,1986;revised
February 18,1987;
accepted March 17,1987)
Summary Compressors operating in a polluted atmosphere with solid particles are subjected to performance deterioration. This paper presents an investigation carried out on a single-stage axial flow compressor to study the effect of erosion on performance deterioration.
1. Introduction The experimental and theoretical study presented by Tabakoff and Balan [l] establishes the nature of the cascade performance decrease due to erosion. The material removal, the changes in the profile, the surface roughness and the overall pressure distribution can be predicted reasonably well. At the present time, there is no experimental data available in the literature on particulate flow related to performance deterioration. For this reason, it was decided to conduct experiments on a single-stage axial flow compressor. The development of the test facility and the experimental program is described below.
2. Experimental set-up 2.1. Drive unit A schematic diagram of the experimental set-up is shown in Fig. 1. The basic prime mover in this case is a three-phase a.c. motor producing 75 kW of power. This motor runs at a constant speed of 3500 rev mm-‘. The motor is connected to the test equipment by means of an electrical clutch, which is controlled by an electronic feedback control system. The clutch output shaft speed can be controlled from zero to the full speed of 3500 rev min-‘. The torque of the output shaft is independent of the output speed. The feedback control system enables the output shaft to rotate at any desired speed under all load conditions. The clutch is also equipped with 0043-1646/87/$3.50
@ Elsevier Sequoia/Printed
in The Netherlands
52 EXHAUST
t
PARTICLE
TO SEPARATOR
INLET 4--
f
I
/
\
I
\
II
II
Fig. 1. Schematic diagram of the experimental set-up: A, a.c. motor; B, clutch-brake unit; C, gear box; D, torque transducer; E, test compressor; F, particle injector.
an eddy current brake, which enables the test equipment to be brought to rest immediately if needed. The brake is employed automatically whenever the clutch is disengaged. The breaking torque has two preset values. One for gradual reduction in speed under normal conditions and the other for emergency conditions. Both the clutch and the brakes are water cooled. The output shaft of the clutch-brake unit is connected to the test compressor through a gear box. The ratio of the speed increase is 1:3.46. This gear box enables the test compressor to be run at any speed up to 12 100 rev min-’ under any load condition. 2.2. Test compressor The test compressor is a single-stage axial compressor without any inlet guide vanes. The same NACA 65(10)-10 airfoils which were used in the twodimensional cascade tests were chosen for the compressor [l]. The aspect ratio of 0.75 and the pitch-to-chord ratio of 0.5 were maintained for the compressor. It was decided to limit the rotor tip relative Mach number to 0.5 and the whirl at the exit of the stator to within 15” from the axial direction. This resulted in a compressor with the following design specifications: speed, 9000 rev min-‘; tip diameter, 300 mm; pressure ratio, 1 .l; mass flow, 3.67 kg SK’; hub-to-tip ratio, 0.75. 2.3. Particle feeding mechanism The particle feeder is similar to that described in the twodimensional erosion tunnel [l]. However, the particles are injected at four locations around the periphery in the air intake. The four nozzles which inject the particles into the air intake are controlled individually to provide a uniform distribution of the particles through the compressor. 2.4. Instrumentation The main power input to the compressor is measured by a rotary transformer-type torque transducer located between the gear box and the test
53
compressor. This torque transducer is also provided with a magnetic speed pick-up. The compressor is instrumented with total pressure and total temperature rakes. These are located at two chords upstream of the rotor inlet, two chords downstream of the stator exit and at the exit manifold. The wall static pressures are measured at the same planes where the total pressure and temperature rakes are located. In addition, there are also provisions for traversing combination probes to measure the total pressure, total temperature and flow exit. All the pressures are recorded using the scanivalve pressure transducer digital recorder system. For better control, there is also a provision to use a multitube manometer bank. The mass flow through the compressor is measured by the calibrated air intake.
3. Test procedure First the performance of the compressor stage with smooth blading was measured under different mass flow conditions and at a constant speed of 5000 rev mm’. The mass flow through the compressor was adjusted by a throttle valve in the exhaust line. The inlet flow was assumed axisymmetric and the flow quantities, such as the inlet total pressure, total temperature and static pressure, were measured at 16 radial positions one chord upstream of the rotor-blade row. The non-uniform flow at the stage exit was scanned one chord behind the stator at seven radial locations. At each radial location, the flow properties were measured over two blade pitches in steps of 0.75”. The Reynolds number based on the inlet velocity and chord length was between 1.25 X lo5 and 2.85 X lo5 depending on the mass flow. The inlet Mach number was limited to approximately 0.17 under the maximum mass flow conditions. The next step was to erode the compressor blades. The blades were eroded in steps by using 5 kg of sand per step. The duration of the sand ingested at each step was 121 s. The compressor was operated at the maximum efficiency point during the period of sand ingestion. The rotational speed of the unit remained constant during the period of sand ingestion. However, it was noted that the power required to drive the unit went up by 12.5% during the period of sand ingestion as indicated by the torque cell. The performance measurements were repeated after each step of sand ingestion, but without particulate flow. The results presented in this paper are only for the initial conditions with uneroded blades and for the final conditions with maximum eroded blades. In both cases, the flow was without solid particles. 4. Analysis of the results On the basis of the measurements, the mass averaging of the flow properties in the pitch direction yielded the mean flow properties such as exit total pressure Tte at each radius for the various mass flow conditions.
54
Mass averaging of these quantities for the given mass flow in the radial direction yielded the overall stage exit total pressure Iite and exit total temperature Tt;,,. However, the temperature measurements were not accurate enough to estimate the overall adiabatic efficiency of the stage. Hence, the actual power input Aht for the working fluid was computed by subtracting the bearing and seal losses from the total power input to the stage. The bearing and seal losses were estimated by spinning the rotor without the blades at the test speed. The total isentropic enthalpy rise Ah,, was computed as
(1) where y is the ratio of specific heats, R is the gas constant, Ftl,,is the mean inlet total temperature and Pti is the mean inlet total pressure. The total adiabatic efficiency qtad of the stage was estimated as Ah,, (2) %,d = Ah, In addition, assuming that the fluid is incompressible, the mean stage loading $ was calculated as $=
Fte -Fti
(3) But2 where p is the mean gas density and ut is the blade tip speed. Also, the local blade loading $ along the blade height was calculated as $=
Pte -
pti
(4)
Put2
where P,, and Pti are the pitch averaged local values at a particular radius. The results were then reduced to the reference state values using similarity laws. The reference state was standard conditions at the inlet: Tti = 288.15 K and Pti = 1.013 bar
(5)
The effects of the presence of solid particles on the turbomachinery performance may be found in refs. 2 and 3. 4.1. Erosion damage The compressor stage was subjected to a total of 25 kg of sand ingestion over a period of 605 s. The size of the sand particles was 165 pm. The compressor blades were inspected by using fiber optic techniques after each erosion run of 5 kg of sand ingestion through the stage. The erosion damage of the rotor was at the blade tip sections, along the leading edges
55
and on the pressure side of the blades. Finally, the compressor stage was disassembled and the damage to the rotor and stator was recorded. The rotor leading edge was severely eroded along the blade span. (1) There was an erosion step fo~ation on both the suction and the pressure surfaces of the blades, near the blade leading edges. In addition, the blade leading edges were flattened and rougher. (2) The pressure surfaces of the blades were eroded moderately and the erosion was associated with a significant increase in the pressure-side roughness. This roughness was measured and it was fotmd to fluctuate between 20 and 70 ,um. (3) The trailing edge of the blades was eroded severely on the pressure side and the trailing edge became very thin. (4) The blade suction surfaces remained unaltered for most of the blades, except for the step formation at the leading edge and increased surface roughness on a small region around the center of the blade chord. (5) The decrease in blade chord was about 1.2%. (6) At the tip, the rotor blades were completely damaged. The changes in the tip clearance were very high, over 300 pm. A view of the erosion damage of the rotor blades is shown in Fig. 2. The pressure side was eroded severely near the tip and along a small portion near the leading edges. There was moderate erosion on most parts of the pressure side except on a small region starting from the hub at about 50% chord and extending to about 20% of the span near the trailing edge. The suction side was eroded along the leading edge and along the small portion of area about l/2 chord wide, starting from the tip region and extending to about 3/4 span (see Fig. 2). The stator blades were also eroded along the leading edges and on the pressure sides. The pressure surface was eroded more towards the tip. There was no pronounced erosion on the suction side. 4.2, PerfOrnWTWed&?riOMtiOn Figure 3 shows the changes in the stage loading as a function of the mass flow. It can be observed from this figure that there is a decrease in the stage loading of 2.4% at a mass flow of 1.36 kg s-l, 3.32% at a mass flow of 1.732 kg s-i and 4.27% at a mass flow of 2 kg s-i. The total adiabatic efficiency of the stage is given in Fig. 4 as a function of the mass flow. It can be seen that a maximum efficiency of only 82% is obtained at the mass flow of 1.732 kg s-l. The rotor blade design is strictly two dimensional. Subsequently, there is a considerable variation in the incidence angle along the blade span owing to the low hub-to-tip ratio of 0.75. In addition, the blades were originally manufactured for the purpose of twodimensional cascades and hence were of large chord (50.8 mm). This resulted in a blade aspect ratio of only 0.75 even though the hub-to-tip ratio is fairly low. The overall effects of such a large chord, untwisted blades and a low hub-to-tip ratio are the cause of the low efficiency. The efficiency of the eroded stage after injection of 25 kg of sand through the machine dropped by about 1.86% at a mass flow of 1.36 kg s-l, 2.16% at a mass flow of 1.732 kg s-’
(4
(b)
(cl Fig. 2. Erosion damage of (a) the compressor stage rotor blade pressure surface, (b) the compressor stage rotor blade suction surface and (c) the compressor stage stator blade pressure surface.
and by about 2.89% at a mass flow of 2 kg s-l. The decrease in efficiency is probably due to increased losses at the blade leading edges particularly in the tip region. It is also possible that the tip leakage has increased considerably owing to the severe erosion of the blade tips as well as of the casing. The experimental data obtained for the local blade loading $ are plotted us. the blade height in a radial direction for the mass flow of 1.732 kg s-l as shown in Fig. 5. An inspection of this figure shows that the performance is affected severely near the tip region. It can be seen from Fig. 5 that the change in the blade loading is not significant for most parts of the blade up to a radius ratio of 0.9. The blade loading at the tip section decreases sharply by about 5.5% after erosion with 25 kg of sand as compared with the uneroded stage values. On the basis of this, we can conclude that the loss in efficiency and the power rise across the stage are mainly due to the deterioration of the leading edges together with the change in the airfoil shape, particularly near the tip region. In the present case, the change in the thickness distribution owing to the material removal on the pressure surface and the suction surface of the rotor blades may be less important than the
57
1.50
1.25
MASS
Fig. 3. Effect
0.90
0.85 : E
G
1.75
2.00
2.25
FLOW, m, kg/set
of erosion on stage loading:
0, uneroded;
*, eroded
(25 kg).
r t
0.80
z; c; L:
1.25
1.50
MASS Fig. 4. Effect
1.75
2.00
2.25
FLOW, m, kgisec
of erosion on adiabatic
efficiency:
0, uneroded;
A, eroded
(25 kg of sand).
58 0.45 r
0.251 0.75
I
I
I
0.80
0.85
0.90
RADIAL
POSITION,
I 0.95
I 1.00
r/rt
Fig. 5. Effect of erosion on blade loading as a function of radial position: 0, uneroded; 0, eroded (15 kg); A, eroded (25 kg).
leading edge deterioration, owing to the relatively large physical dimensions of the blades used. In addition, the trailing edge was very thin near the tip owing to the material removed during erosion. The trailing edge was fairly unaltered near the hub region. It is possible for the trailing edge to vanish under high degrees of erosion which may lead to considerable changes in the exit flow angle as well as in additional losses. It should also be noted that for small blades, operating at high Reynolds’ numbers, the increase in surface roughness may also play an important role. 4.3. Compressor stage particle trajectories The erosion of the rotor and stator blades can be predicted by analyzing the trajectories of the particles through the compressor stage. An analysis of the particle trajectories was carried out using a threedimensional particle trajectories program which was developed as part of this research. The analysis indicates the various locations of particle impacts and the possible erosion regions. The purpose of the present analysis was only to identify the erosion regions and compare them with the experimental data. The particle trajectories were computed for an assumed uniform inlet particle distribution. The trajectories were computed by introducing the particles at various equispaced radial and tangential locations. 5. Analysis The equations governing the particle motion in the turbomachinery flow fields are written in a rotating frame of reference using cylindrical
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coordinates. The three components of the equations of motion in a frame rotating about the engine axis with angular velocity o are given by
d28 _-E=&-
(7)
” dr2
_ -d2ZP - -F, dr2
where rP, 0, and zP define the particle location in cylindrical polar coordinates, V,, V, and V, represent the relative gas velocities in the radial, circumferential and axial directions respectively, o is the blade angular velocity and r is the time. The centrifugal force and Coriolis acceleration are represented by the last terms on the right-hand side of eqns. (6) and (7). The first term on the right-hand side of eqns. (6) - (8) represents the force of interaction between the two phases, per unit mass of particles. It is dependent on the relative velocity between the particles and the gas flow, as well as on the particle size and shape. Under the particulate flow conditions in turbo-machines, the effect of the forces due to gravity and interparticle interactions is negligible compared with those due to the aerodynamic and centrifugal forces. In addition, the force of interaction between the two phases is dominated by the drag due to the difference in velocity between the solid particles and the flow field. The force of interaction per unit mass of solid particles is therefore given by
F=i ..c& #-
fgy+
(vo-!$)‘, (vi-$-)‘/“2’“-vp’ (9)
where p and ps are the gas and solid particle densities, d is the particle diameter, 7 and VP are the gas and particle velocities relative to the blade and Co is the drag coefficient. The drag coefficient is dependent on the Reynolds number, which is based on the relative velocity between the particle and the gas. Empirical relations, as shown in ref. 4, are used to fit the drag curve over a wide range of Reynolds’ numbers. The particle trajectory calculations consist of the numerical integration of eqns. (6) - (9) in the flow field, up to the point of the blade, hub or tip impact. The impact location can be determined from the particle trajectory calculations and the local geometry of the impacted surface. The magnitude and direction of the impact velocity relative to the surface, for a large number of particles, constitu~ the essential data needed for the evaluation of the erosion of the various turbomachinery components. Figure 6 shows the trajectories of the 165 pm particles through the rotor blade channel in the Z-0 plane. It can be seen that there is a consid-
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Fig. 6. Particle trajectories through the rotor blade passage. ROTOR
STATOR
Fig. 7. Particle trajectories through the compressor stage in meridional plane.
erable amount of impacts on the entire rotor blade pressure surface. In addition, some of the particles rebound off the leading edge and impact on the suction surface of the rotor blade. There are also a few particles which impact on the leading edge region and rebound away from the blades. These particles reenter the blade rows at some other locations which are not shown in this figure. Figure 7 shows the trajectories of 100 particles in the r-2 plane. From this azimuthal view it can be seen that there is a considerable impact on the tip casing. The particles, which were introduced at 10
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radial locations, diffuse so much that they occupy the entire span after rebounding. In addition, the trajectories indicate that the particles do not impact the hub region of the stator blades at all. Comparing the trajectories of the particles through the compressor stage with the experimental observation as shown in Fig. 2, it can be seen that there is very good agreement. The trajectory analysis indicates erosion on the entire rotor blade pressure surface and on a region near the midchord position on the suction surface. There is no significant erosion on the stator blade suction surface. The stator blade pressure surface is not eroded near the hub region. 6. Conclusions From the compressor rig experiments, it was found that erosion damage can lead to a significant reduction in the engine efficiency as well as in performance. The decrease in performance is mainly due to changes in the blade leading and trailing edges, tip leakages, surface roughness and pressure distribution. The data obtained from the trajectory calculations are in very good agreement with the experimental findings. Acknowledgment This research was sponsored by the U.S. Army Research Office under contract number DAAG2982-K-0029. References 1 W. Tabakoff and C. Balan, Effect of sand erosion on the performance deterioration, 6th Znt. Symp. on Air Breathing Engines, Paris, June 6 - 7, 1933, American Institute of Aeronautics and Astronautics, New York, 1983, pp. 458 - 467. 2 W. Tabakoff, Turbomachinery performance deterioration exposed to solid particles environment, J. Fluids Eng., 106 (1984) 125 - 134. 3 W. Tabakoff, W. Hosny and A. Hamed, Effect of solid particles on turbine performance, J. Eng. Power, 98 (1976) 47 - 62. 4 F. Hussein and W. Tabakoff, Dynamic behavior of solid particles suspended by polluted flow in turbine stage,J. Aircr., 10 (1973) 434 - 440.