A lot of the unsteady 3D ft>w measurements using three-sensor hot-wire probes were presented in earlier papers [Krysinski et al. 1999 – 2002].
Based on earlier tests one could observe that there were no significant differences after the first stator and the first rotor while indexing the airfoils. It was clearly visible how the first stator wakes pass through the first rotor and change their circumferential position downstream. The small fbw-blocking effects (according to the vane clocking) observed during earlier tests were neutralised by keeping the inlet/outlet pressure ratio at the same level with an especially prepared control system (Fig. 1, pos. 13). Significant changes were observed inside the ft>w passing the second stage, especially after the second vane. New test results showed again visible differences due to the clocking effect when compared to the situation when two stators were at the design position (x/T = 0.0), especially it is showed for highly loaded machine (Fig. 7).
Figure 7. Measured relative torque and efficiency versus clocking position and rotational speed
Periodic and random components of unsteady pressure above the first rotor for rotational speed n = 42 Hz are presented in Fig. 8. The presence of the position of the preceding stator is clearly visible for the periodic component. The minimum value of the periodic component is related to the situation when the stator wake (secondary flow structures) flows inside the testing zone (nearby transducer position) and the maximum value is obtained when the inside vane channel ft>w is passing by. Due to the low level of the measured pressure and the low frequency resolution of the pressure transducer the tests above the second rotor were not performed. In this case the clocking effect phenomena are hardly to measure using standard instrumentation.
Fig. 9 shows a comparison of the relative random (er /E) and periodic (ep/E) components of thermoanemometric signals measured on the suction sides of the first stator and the second stator vanes with a help of glue-on hot-film sensors. The results are similar for both vanes. The rapid grow of the signal is
0 Figure 8 RMS of periodic and random components of the unsteady pressure above rotor
clearly visible due to the laminar-turbulent transition zone. The beginning of this phenomenon on the surface of the second stator vane starts earlier and is characterised by higher RMS values. The end of the zone is almost at the same place and its position is related to the inlet conditions. A detailed ft>w measurement data comparison is beyond the scope of this paper and will be discussed in another paper.
Fig. 10 shows the results of the glue-on hot-film signals analysis from two stators compared to the variation of the torque of the turbine for the same clocking positions. The position of the sensor was at the leading edge of the vane and in the middle of the ft>w channel height. Additionally acoustic measurements with the microphone connected pneumatically to the pressure tap nearby the hot-film sensor were performed. The results are shown in Fig. 11. Small variations of the measured values are visible but they are not clearly correlated to the overall performance changes. This due to the fact that the most important performance changes are present nearby the hub and the casing. In this case more detailed tests along the flow channel height are necessary.
The next figure (Fig. 12a) shows differences of the thermodynamic turbine efficiency versus height of the ft>w channel position at different rotational
speeds. The differences are visible for all speeds and the shape of the curves is similar showing the visible drop in the near the walls regions, especially nearby the hub. From earlier studies it is known that the turbulence level is very high in these regions [Krysinski et al. 2001]. Fig. 12 b and c show the efficiency changes due to the clocking effect at different fbw channel heights. The variations in the region near the hub are about 1 %. Along the height of the flow channel the variations of the turbine efficiency are phase shifted. This shift makes the overall efficiency variation to be small and not clearly visible. If the shift does not exist (that means across the fbw channel height the efficiency obtains maximum value at the same clocking position) for the nominal rotating speed we will obtain the efficiency benefit about 0.6 %.
Figure 13. a) Stator and rotor leading edge (LE) and trailing edge (TE) compared to the radial direction (RL) b) Results of the numerical calculation downstream the first stator and the first rotor
Two-stage low-pressure turbine at the Institute of Turbomachinery (Technical University of Lodz, Poland), was prepared for experimental investigations of the stator-to-stator clocking effect. Special attention was directed into machine work conditions and strictly constant inlet conditions, especially in – let/outlet pressure ratio. The changes due to the fbw blocking effect were re
duced with the help of special inlet condition control system. Continuation of earlier experimental investigations of the stator-to-stator interaction has been performed in the axial gaps, on the vane profile and outer casing.
The results of precise measurements of the power and torque output differed slightly according to the stator-to-stator clocking position. Only for the lowest rotational speed the effect of the clocking position was very clearly visible on overall performance. That gave the conclusion that it was very hard to find out the infhence of the clocking position measuring and considering only the external characteristics, especially for the case of not highly loaded turbine.
The ft)w parameters downstream the first turbine stage showed similarities for the different clocking positions. The stator vane wake could be clearly observed also after the rotor. With the improved resolution of the measuring system even the thermal wake after the first stator was observed (Krysinski et al. 1999).
The exit fbw of the second stator was strongly inflienced by the clocking position of the first stator. The differences of the fbw parameters became smaller downstream the second stage due to the strong flow mixing phenomena inside the second rotor but the time-averaged values downstream the turbine showed significant differences relative to the first stage and when compared with different clocking positions. The results showed that the presented phenomena are very complicated. The first stator wakes do not pass directly inside the second stator flow channel or directly impinge the noses of the second stator vanes as other authors presented it. The wakes start immediately to rotate inside the first stator-rotor axial gap and next downstream the turbine. As a result they interact strongly with the channel boundary layers not only at hub and casing regions but also on both surfaces (suction and pressure side) of the following stator vanes.
Parallel to presented results the numerical calculations of the ft>w were performed to understand unsteady flow behaviour in multistage machines and to determine the clocking effect more deeply. Fig.13 shows the geometrical position of the leading and trailing edges of the turbine blading as well some numerical results. The numerical models showed the good accordance with the experimental results. They show also the wake variations, especially nearby the hub region where the wake is strongly shifted. The numerical codes need more and more sophisticated data to be improved. The data presented in this paper provide the community with an understanding of the effects that indexing airfoils can have on the overall turbine efficiency giving the vision of a future turbomachinary performance improvement. The new design with less rotor-to – stator blading number ratio is prepared to find out the influence of the clocking effect for other geometries of the machines working at similar conditions.
b = chord length [ m ] m = mass few rate [ kg/s ] n = rotational (shaft) speed [ Hz ] p = pressure [ Pa ]
T = vane pitch [ m ], temperature [ K ] x = coordinate along circumferential direction [ m ] y, h = coordinate along radial direction [ m ] z = coordinate along axial direction [ m ]
a = circumferential (pitchwise) ft>w angle (absolute frame) [ deg ] в = circumferential (pitchwise) ft>w angle (relative frame) [ deg ]
Subscripts and Superscripts
= inlet conditions
= downstream the first stator
= downstream the first rotor
= downstream the second stator
= downstream the second rotor m = design (metal)
t = total (stagnation)
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 Corresponding Author: atassi@nd. edu
K. C. Hall et al. (eds.),
Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 247-259. © 2006 Springer. Printed in the Netherlands.
Work is executed at financial support of International scientific and technical centre (ISTC), the grant number 672.2.
K. C. Hall et al. (eds.),
Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 261-273. © 2006 Springer. Printed in the Netherlands.
(t) = (V1/c) Rn zn (t) + En q n (t).
The generalized aerodynamic forces are then written in the time domain as
^nOfin 4" у -^nlfin 4" ^^2 J^n24n
Combining the reduced coupled system (5) with Eqs. (16) and (17), we obtain a linear system of second-order differential equations of dimension mn + np :