# Annular compressor cascade with tip clearance

## Overview of Tests

Experimental data from the annular compressor cascade is available for four experiments. These correspond to tip-clearance sizes of 2% and 4% chord and with a rotating (N=6540rpm) or still (N=0) hub. Since all test cases correspond to the same mass flow rate, the main problem definition parameters (PDPs) are the tip-clearance size and the rotating hub speed. The test cases are summarized in Table EXP-A.

CASE GNDP PDPs MPs
Re ${\displaystyle {(10^{6})}}$ m (kg/s) t/C (%) N (rpm) Raw Data DOAPs
EXP-1 1.1 13.2 2 6540 ${\displaystyle V_{axial},V_{per},V_{rad},{a},Pt,Ps,M}$ Circumferential mass average ${\displaystyle V_{axial},V_{per},V_{rad},{a},Pt,Ps,M}$, PLC
EXP-2 1.1 13.2 2 0 ${\displaystyle V_{axial},V_{per},V_{rad},{a},Pt,Ps,M}$ Circumferential mass average ${\displaystyle V_{axial},V_{per},V_{rad},{a},Pt,Ps,M}$, PLC
EXP-3 1.1 13.2 4 6540 ${\displaystyle V_{axial},V_{per},V_{rad},{a},Pt,Ps,M}$ Circumferential mass average ${\displaystyle V_{axial},V_{per},V_{rad},{a},Pt,Ps,M}$, PLC
EXP-4 1.1 13.2 4 0 ${\displaystyle V_{axial},V_{per},V_{rad},{a},Pt,Ps,M}$ Circumferential mass average ${\displaystyle V_{axial},V_{per},V_{rad},{a},Pt,Ps,M}$, PLC

Table EXP-A: Summary of all test cases. Since we are dealing with a three-dimensional test case, and in order to reduce the amount of the experimental data, the competency of the calculations is judged on the basis of the circumferential mass average span-wise distributions of the flow quantities at measuring stations. Since the peripheral uniformity of the flow has been experimentally confirmed, the same distributions of the flow quantities at inlet and outlet stations provide the boundary conditions for the CFD calculations. The averaging of the flow quantities has been carried out using a simple averaging technique, with the mass flow rate being the weighting factor. The data corresponding to the mass average distributions is summarized in Table EXP-B.

CASE DOAP 1 DOAP 2 DOAP 3
Span (%) Ps (Pa), Pt P(a), ${\displaystyle V_{axial}/V_{ref},V_{per}/V_{ref},V_{rad}/V_{ref},{a}{(^{0})},M}$, PLC at station 2 Span (%) Ps (Pa), Pt P(a), ${\displaystyle V_{axial}/V_{ref},V_{per}/V_{ref},V_{rad}/V_{ref},{a}{(^{0})},M}$, PLC at station 8 Span (%) Ps (Pa), Pt P(a), ${\displaystyle V_{axial}/V_{ref},V_{per}/V_{ref},V_{rad}/V_{ref},{a}{(^{0})},M}$, PLC at station 9
EXP-1 exp11.dat exp12.dat exp13.dat
EXP-2 exp21.dat exp22.dat exp23.dat
EXP-3 exp31.dat exp33.dat
EXP-4 exp41.dat exp43.dat

Table EXP-B: Summary of all assessment parameters and available data files.

Description of experiment

Many studies have been performed to investigate the effects of the tip-clearance flows on the performance of axial compressors and to study the structure of the flow-field, however there has been a lack of detailed measurements on high-speed machines. The experimental work conducted at NTUA/LTT addresses this need by producing original data for an annular compressor cascade for two different tip-clearance sizes. In addition, and in order to study the effects that the relative end-wall/blade motion introduces to the flow, measurements have been carried out for both a rotating (N=6540rpm) and a still hub for both tip-clearance configurations.

To provide as a complete a set of flow field data as possible, two types of measured data have been acquired:

+ Measurements aiming at defining the operating point of the cascade and monitoring the operation of the facility. They have been carried out using long-nose 5-hole probes at measuring stations 2 and 9 (see Figure 5 for the definition of the measuring stations), which are regarded as the inlet and the outlet to the cascade, respectively. Measurements at the cascade inlet have been performed in order to obtain the actual flow conditions at the inlet to the test cascade, after the flow has developed within the annulus following the bent duct. Additionally, by examining the distributions of the measured quantities, the circumferential uniformity of the flow is assessed. In order to cover the whole blade-to-blade region, measurements have been performed by rotating the casing of the blade with respect to the probe that remained fixed at both stations.

Figure 5: Definition of the measuring stations for the NTUA annular compressor cascade.

+ Detailed measurements of the flow field at different axial locations on the blade passage, which provide the complete description of the three-dimensional flow field in the annular cascade. These measurements have been performed at five stations (4, 6, 8, 8a and 8b) using two long-nose 5-hole probes and at another five stations (3, 4, 5, 6 and 7) using a three-dimensional Laser Doppler Velocimetry (LDV) system. Two transparent glass windows enabled the optical access to the blade passage.

With respect to the pneumatic measurements, the probes were manufactured especially for this application according to the requirements posed by the geometry of the annulus and aiming at a minimal flow disturbances production. Their stem was inserted at the corresponding axial location, so that the nose head was located at the measuring plane. The probe nose was fixed on the stem at an angle greater than 90o in order to have the possibility of approaching the hub. On the other hand, this allowed coverage of a small part of the span-wise traverse, and to compensate for it a second probe was used. The second probe featured a smaller nose angle that was used to measure the flow field up to 50% of the span, since all phenomena of interest occur in this area. In order to verify the periodicity of the flow a circumferential extent of about 1.5 passages was covered at the measuring stations that were located downstream of the blade. At each axial plane 13-15 peripheral transverses of 17-24 peripheral locations were conducted, giving rise to a total of about 250 measuring locations at each station.

The data reduction was adapted to the particular requirements of the present geometry. The flow field quantities were derived from the pressure readings and the probe’s calibration data. In this way the total and static pressure values were obtained, while the velocity vector referred to the coordinate system attached to the head of the probe. Thus a transformation was employed to derive the orientation of the vectors in a cylindrical coordinate system.

The three-dimensional LDV system used in the measurements comprises two independent systems, a one component and a two-component system, which employ independent laser sources, fibre optics and small diameter optical probes for the transmission and the collection of the scattered light from the three measuring volumes. Its layout is presented in Figure 6. The two-dimensional probe transmits two orthogonal beam-pairs and measures the axial and peripheral velocity components, while the one-dimensional component that transmits a third pair of laser beams is placed at an angle of 25o with respect to the two-dimensional component and therefore measures a component inclined with respect to the plane of the components measured by the two-dimensional component, allowing thus the measurement of the third component of the velocity vector. The flow was seeded with a TSI six-jet atomizer, using a solution of paraffin oil and benzene as a seeding medium. It is introduced at the inlet of the bellmouth, at a location of the stream-wise position on this plane, which corresponds to the test passage. The span-wise traversing is accomplished by means of a remotely controlled carriage, while the circumferential traversing is performed by means of rotating the cascade with respect to the fixed laser carriage.

Figure 6: Layout of the 3-D Laser Doppler Velocimetry system.

Acquisition of the data (frequencies) obtained by the laser is conducted via an IEEE data acquisition board. The processing of the data is achieved by a PC using custom-made LDV software. The acquisition of the analogue signals (DC voltage), obtained from the pressure transducers connected to the 5-hole probes, is conducted via a 16-channel AD data acquisition board (ADDVTECH PCL-818). The acquisition board, having a maximum total sampling frequency of 1MHz, variable input voltage range (maximum range ±10 V) and a 12-bit Analogue-to-Digital converter with a sensitivity of 4.88mV, feeds the data to a PC utilising in-house software for on-line processing.

Apart from the pneumatic measurement readings, several other quantities of interest are monitored at different locations of the facility during operation, namely:

+ The rotational speed of both the compressor driving the cascade and the hub.

+ The vibration levels of the compressor bearings, in order to ensure safe operation.

+ The total and static pressure at the scroll inlet.

Boundary Data

At the inlet boundary (Station 2) the flow is considered circumferentially uniform, as confirmed by the experiments. As such, all flow quantities included in the data files for this station can be used as boundary conditions. Although flow is turbulent, detailed measurements of turbulence quantities have not been performed and only estimates of these quantities can be reported (for a example a realistic value for turbulent intensity at inlet is 2%). With such estimates, the impact of the inlet turbulent quantities on the DOAPs is expected to be low. The outflow boundary (Station 9) is located far downstream and an adequate mixing of the flow has occurred. As such, the corresponding data files provide enough information on the boundary conditions. The hub and the casing are walls that are considered to be smooth. This is the case for the blade surfaces too, the pressure and suction sides, as well as the blade tip. Finally the remaining boundaries are periodic and must be treated as such.

Measurement Errors

The inaccuracy of angle measurements for the alignment of the LDV/probe assembly yields a systematic error of the order of ±0.3o to the measured flow angles. For the LDV measurements, the statistical errors for the measured quantities were ±2% for the normal and shear stresses, ±1% and ±2.6% for the directly and indirectly, respectively, measured velocity components. For the 5-hole probes, the expected errors of the measured quantities were ±0.5o and ±1.3o for the yaw and the pitch angles, respectively, and ±1% for the total velocity and the static and total pressure. These figures are valid for all experimental cases.

It has already been mentioned that the flow in the cascade has been measured twice. In Figure 7 the circumferential mass average span-wise distributions of the flow quantities are plotted at Station 2 (inlet to the cascade). Qualitatively, these distributions are similar, despite the small differences, of the order of 2%, that appear. The differences appearing in these plots provide a realistic estimation of the overall accuracy of the experimental set of data. Nevertheless, the first set of measurements subjects to a larger degree of uncertainty, since an inspection of the test facility before the second measurements revealed large deposits of dust accumulated on the walls (particularly in the inlet section) as a result of construction work conducted at the laboratory at that time.

Figure 7: Span-wise distributions of the circumferential mass average flow quantities at Station 2 for EXP-1. Red lines: First experimental set, green lines: second experimental set.

## References

+ Doukelis, A., Mathioudakis, K., Founti, M. and Papailiou, K. (1997), “3-D LDA Measurements in a Annular Cascade for Studying Tip Clearance Effects,” 90th on the Propulsion and Energetics Panel on Advanced non Intrusive Instrumentation for Propulsion Engines, Brussels Belgium, published by AGARD.

+ Doukelis, A., Mathioudakis, K., and Papailiou, K., (1998a), “The Effect of Tip Clearance Gap Size and Wall Rotation on the Performance of a High-Speed Annular Compressor Cascade,” ASME Paper 98-GT-38, Presented at the International Gas Turbine & Aeroengine Congress & Exhibition, Stockholm, Sweden, June 2-5, 1998.

+ Doukelis, A., Mathioudakis, K., and Papailiou, K., (1998b), “Investigation of the 3-D Flow Structure in a High-Speed Annular Compressor Cascade for Tip Clearance Effects,” ASME Paper 98-GT-39, Presented at the International Gas Turbine & Aeroengine Congress & Exhibition, Stockholm, Sweden, June 2-5, 1998.

+ Doukelis, A., Mathioudakis, K., and Papailiou, K., (1999), “Effect of Wall Rotation on the Performance of a High-Speed Compressor Cascade with Tip Clearence,” ISABE Paper 99-7267, Presented at XIV ISABE, September 5-12, 1999, Florence, Italy.

+ Mathioudakis, K., Papailiou, K., Neris, N., Bonhommet, C., Albrand, G., Wegner, U., (1997), “An Annular Cascade Facility for Studying Tip Clearance Effects in High Speed Flows,” Proceedings of XIII ISABE, September 7-12, 1997, Chattanooga, Tennessee, U.S.A., Edited by F. S. Billig, Published by AIAA, Vol. 1, pp. 831-839.

+ Pouagare, M. and Delaney, R. A. (1986), “Study of Three-Dimensional Viscous Flows in an Axial Compressor Cascade Included Tip Leakage Effects Using a SIMPLE-Based Algorithm,” ASME Journal of Turbomachinery, Vol. 108, pp. 51-58.

## Test Case EXP-1

Measured Data

This test case corresponds to a tip-clearance size t/C=2%, a hub rotational speed N=6540rpm and a mass flow rate m=13.2kg/s. Circumferential mass average span-wise distributions of flow quantities (axial component of velocity, Vaxial, peripheral component of velocity, Vper, radial component of velocity, Vrad, flow angle, a, Mach number, M, total pressure, Pt, and static pressure, Ps) derived from the corresponding measurements at three stations are provided. PLC distributions are derived using Equation (1). Velocity components are non-dimensional with respect to the peripheral velocity at hub.

exp11.dat (ASCII file; headers: Station 2, t/C=2%, N=6540rpm, m=13.2Kg/s, columns: span, Ps, Pt, Vaxial/Vref, Vper/Vref, Vrad/Vref, a, M, PLC)

exp12.dat (ASCII file; headers: Station 8, t/C=2%, N=6540rpm, m=13.2Kg/s, columns: span, Ps, Pt, Vaxial/Vref, Vper/Vref, Vrad/Vref, a, M, PLC)

exp13.dat (ASCII file; headers: Station 9, t/C=2%, N=6540rpm, m=13.2Kg/s, columns: span, Ps, Pt, Vaxial/Vref, Vper/Vref, Vrad/Vref, a, M, PLC)

## Test Case EXP-2

Measured Data

This test case corresponds to a tip-clearance size t/C=2%, a still hub (N=0rpm) and a mass flow rate m=13.2kg/s. Circumferential mass average span-wise distributions of flow quantities (axial component of velocity, Vaxial, peripheral component of velocity, Vper, radial component of velocity, Vrad, flow angle, a, Mach number, M, total pressure, Pt, and static pressure, Ps) derived from the corresponding measurements at three stations are provided. PLC distributions are derived using Equation (1). Velocity components are non-dimensional with respect to the peripheral velocity at hub.

exp21.dat (ASCII file; headers: Station 2, t/C=2%, N=0rpm, m=13.2Kg/s, columns: span, Ps, Pt, Vaxial/Vref, Vper/Vref, Vrad/Vref, a, M, PLC)

exp22.dat (ASCII file; headers: Station 8, t/C=2%, N=0rpm, m=13.2Kg/s, columns: span, Ps, Pt, Vaxial/Vref, Vper/Vref, Vrad/Vref, a, M, PLC)

exp23.dat (ASCII file; headers: Station 9, t/C=2%, N=0rpm, m=13.2Kg/s, columns: span, Ps, Pt, Vaxial/Vref, Vper/Vref, Vrad/Vref, a, M, PLC)

## Test Case EXP-3

Measured Data

This test case corresponds to a tip-clearance size t/C=4%, a hub rotational speed N=6540rpm and a mass flow rate m=13.2kg/s. Circumferential mass average span-wise distributions of flow quantities (axial component of velocity, Vaxial, peripheral component of velocity, Vper, radial component of velocity, Vrad, flow angle, a, Mach number, M, total pressure, Pt, and static pressure, Ps) derived from the corresponding measurements at three stations are provided. PLC distributions are derived using Equation (1). Velocity components are non-dimensional with respect to the peripheral velocity at hub.

exp31.dat (ASCII file; headers: Station 2, t/C=4%, N=6540rpm, m=13.2Kg/s, columns: span, Ps, Pt, Vaxial/Vref, Vper/Vref, Vrad/Vref, a, M, PLC)

exp33.dat (ASCII file; headers: Station 9, t/C=4%, N=6540rpm, m=13.2Kg/s, columns: span, Ps, Pt, Vaxial/Vref, Vper/Vref, Vrad/Vref, a, M, PLC)

## Test Case EXP-4

Measured Data

This test case corresponds to a tip-clearance size t/C=4%, a still hub (N=0rpm) and a mass flow rate m=13.2kg/s. Circumferential mass average span-wise distributions of flow quantities (axial component of velocity, Vaxial, peripheral component of velocity, Vper, radial component of velocity, Vrad, flow angle, a, Mach number, M, total pressure, Pt, and static pressure, Ps) derived from the corresponding measurements at three stations are provided. PLC distributions are derived using Equation (1). Velocity components are non-dimensional with respect to the peripheral velocity at hub.

exp41.dat (ASCII file; headers: Station 2, t/C=4%, N=0rpm, m=13.2Kg/s, columns: span, Ps, Pt, Vaxial/Vref, Vper/Vref, Vrad/Vref, a, M, PLC)

exp43.dat (ASCII file; headers: Station 9, t/C=4%, N=0rpm, m=13.2Kg/s, columns: span, Ps, Pt, Vaxial/Vref, Vper/Vref, Vrad/Vref, a, M, PLC)