High-speed rotor wake features and inherent flow unsteadiness

Rotor blade wake unsteadiness resulting in ensemble average data not being representative of the flow field of particular interest is investigated, accomplished through experiments in an axial high-speed axial fan stage comprised of an IGV row and a rotor. Rotor exit flow field data are acquired at a number of rotational speeds. Velocity and total pressure data are stored as instantaneous data and analyzed to determine characteristics of the ensembleaveraged wakes and to quantify the revolution-to-revolution wake variations. Existing correlations are compared to the wake velocity deficit and the semiwake width data. The inherent flow field unsteadiness is also investigated, with a variation of the wake preservation method implemented. Results show that the subsequent wake is less representative of the actual wake than the ensemble averaged wake because of wake motion affecting the subsequent wake. Standard deviations of the velocity data show that increased unsteadiness at the maximum operational speeds causes the wake characteristics to be smeared out with conventional data ensemble averaging. R U u w W w_r a P 5 Nomenclature sectional drag coefficient rotor blade spacing mean absolute velocity vector absolute velocity vector perturbation velocity vector mean IGV-relative velocity vector wake streamwise centerline velocity defect free stream streamwise velocity absolute flow angle relative flow angle semiwake width + Engineer, P&W East Hartford, Member * McAllister Distinguished Professor, Associate Fellow AIAA Copyright © 1998 by Johnston and Fleeter. Published by AIAA, Inc. with permission. Introduction Flows in axial compressors are inherently unsteady, a result of flow phenomena including wake cutting, rotating potential fields, inlet distortions, shock boundary layer interactions, and local flow instabilities. As a result, ensemble averaged measurements which utilize a trigger synchronized to the rotor shaft position are only representative of the flow field if the revolution-to-revolution variations in velocity deficit, wake width, and wake centerline position are small. The effect of rotor wake unsteadiness was modeled and compared with data in a study of rotor-stator interaction noise [1]. The model characterized the effect of wake amplitude and position modulations. Utilizing the data and the model, it was determined that the randomness of amplitude and arrival of the rotor wakes generated the stator broadband noise. Alday et al. [2] analyzed time resolved aspirating probe data and determined that the flow was extremely random in nature. They developed an averaging technique which preserved the wake characteristics and evaluated the wake aperiodicity or position modulation and nonuniformity. Position modulation was characterized by the standard deviation of the instantaneous wake period between two adjacent minimums. Nonuniformity was determined by calculating the RMS of the wake preservation averaged wake and taking the arithmetic average. Results showed that aperiodicity and nonuniformity increased dramatically beyond 80% span. 1 American Institute of Aeronautics and Astronautics Although axial flow turbines are impacted by the unsteadiness in the flow field, most designs are performed using three dimensional steady flow codes with the unsteadiness accounted for with empirical correlations. Unfortunately, although useful in design, these correlations are not representative of the flow physics, with a more thorough understanding of unsteady flow interactions needed to increase turbine design and off-design performance [3]. This can be accomplished through the analysis of time resolved data. This paper addresses the effect of unsteady flow generated by blade row interactions on ensemble averaging data, with rotor wake unsteadiness resulting in ensemble average data not being representative of the flow field of particular interest. Experiments are performed in an axial high-speed axial fan stage comprised of an IGV row and a rotor. Rotor exit flow field data are acquired at a number of rotational speeds, with the rotor relative Mach number varying from fully subsonic to supersonic past 40% span. Pressure sensitive paint measurements indicate that shocks exist on the rotor blade suction surface at the two highest rotor speeds. Velocity and total pressure data are acquired and stored to disk as instantaneous data. These time resolved data are then analyzed to determine characteristics of the ensemble-averaged wakes and to quantify the revolution-to-revolution variations in the rotor wakes. Also, a variation of the wake preservation method is implemented to provide another measure of wake unsteadiness. Axial Fan Facility The Purdue Research Axial Fan facility features a 30.48 cm (12 in.) diameter, 2/3 hub-tip ratio design compressor rotor. Eighteen inlet guide vanes introduce swirl into the 19 bladed axial flow rotor, Figure 1. The drive system consists of a 400 horsepower AC motor driving a magnetic clutch with a variable speed output which drives a gearbox. The IGV's and rotor blades have NACA 65 series profiles on circular arc meanlines. The adjustable IGV's have a nominal 10% thickness with a chord varying from 35.5 mm (1.40 in.) at the hub to 53.3 mm (2.10 in.) at the tip to yield a solidity of one. IGV twist distribution produces a free vortex whirl into the rotor. Rotor blade sections have a 10% to 6% hub-to-tip thickness taper, with a chord of 50.8 mm (2.00 in.). The axial IGV-to-rotor spacing to chord ratio is 60 % (Z/CR = 0.6), with a 10° IGV stagger angle. The IGV row is indexed circumferentially, thereby enabling the IGV wake measurements to be made without circumferential probe traverses upstream and downstream of the rotor. Axial distance downstream of the IGV trailing edge at midspan is denoted as %, with the axial distance upstream of the rotor leading edge is denoted by £u. Data Acquisition & Instrumentation Time-mean data are determined by taking the average of measurements of 100 rotor revolutions sampled at approximately 2,000 samples per revolution for each data channel. At each axial location, the time varying or unsteady velocity and total pressure are also measured. The time variant signals are digitized over ten blade passages using approximately 2,000 samples per burst and over 100 individual revolutions, triggered by a once-per-rev pulse from a photo-optic sensor. The instantaneous voltage measurements from the hot-wire and total pressure probes are stored to disk for postprocessing. Midspan time-variant velocity and total pressure data are acquired downstream of the rotor with hot-film anemometers and unsteady total pressure probes. An Endevco piezoresistive pressure transducer with a sensitivity of 59.85 mV/psi and a frequency response of 70 KHz is installed in a stainless steel probe body. The crossed hot-film has a measurement area of 50.8 um x 1.0 mm, with absolute velocity magnitude and flow angle errors estimated to be less than 2% and 0.5 , respectively. All probes are set to minimize flow angle deviations from the probe axis. Wake Velocity & Semiwake Width Correlations The time averaged IGV wakes are characterized by the semiwake width 8 and the wake centerline velocity defect Wdc. Numerous empirical correlations have been made for these quantities, several of which have been selected for data correlation. All equations have been rewritten using the notation of Majjigi and Gliebe [4]. Majjigi-Gliebe Correlation The Majjigi and Gliebe correlation equations are