A New Particle Image Velocimetry Technique for Turbomachinery Applications

Measuring the unsteady flow patterns in the rotor blade passage of a multistage compressor is a key step toward understanding the loss-inducing mechanisms in these environments. Traditional probe traversing measurement techniques are often used to study compressor performance, but their intrusive design alters the flow. Thus, a nonintrusive method capable of resolving the flow field is desired. To measure the flow inside the rotor blade passage, noninvasive measurement techniques, such as laser Doppler velocimetry (LDV), have been used in the past [1,2]. However, because LDV is a pointwise measurement, it can be a laborious and time-intensive process, and it can be difficult to resolve the spatial characteristics of the flow field.

Since the emergence of PIV, researchers have begun turning to this method to investigate turbomachinery flows. Previous authors have performed PIV measurements in compressor applications [3,4], and other studies have specifically focused on tip leakage flows and measurements in the rotor tip clearance [5–7]. However, in all of these studies, periscopic optical probes were inserted into the flow for light sheet delivery, which renders the measurement invasive and limits the regions of the flow field which can be imaged. The presence of the probe alters the flow, and using a small probe introduces difficulties in achieving precise alignment of the laser beam. Furthermore, seeding can damage the probe or require a shutdown to clean the optics.

These challenges caused by the physical and geometrical constraints imposed by rotating compressor facilities are further amplified when performing stereoscopic or volumetric measurements due to limited viewing angles and reduced overlapping field of view between multiple cameras. Thus, a viable solution is to perform PIV on the embedded stage of a multistage compressor by delivering the laser sheet through the same window used by the cameras to acquire the image. This work demonstrates, for the first time, the capability of performing three-component, three-dimensional PIV in a multistage compressor, without the need for any invasive imaging or light delivery probes inside the compressor.

For the present study, PIV was performed in the second stage rotor passage (rotor 2) of the three-stage axial compressor facility at Purdue University. The compressor models the rear stages of a modern high-pressure compressor with engine-representative Mach numbers and Reynolds numbers. For the rotor 2 conditions presented herein, the relative Mach number is on the order of 0.45 and the relative Reynolds number based on chord is approximately 7.7 × 10⁵. With a design rotational speed of 5000 rpm, the tip speed is approximately 160 m/s. These PIV measurements were collected as part of an extensive tip clearance sensitivity study, and the data presented herein pertain to a nominal tip clearance height of 2.0 mm, representing 4% rotor tip clearance (based on an annulus height of 50.8 mm). Additional information about the facility is available in Ref. [8].

The experimental setup for the PIV measurements is shown in Fig. 1(a). Optical access to the compressor was accomplished by a window extending approximately 20% axial chord upstream and downstream of the rotor blade and more than two blade pitches in the circumferential direction (69 mm × 127 mm field of view). This window was precision machined to match the curvature of the inner diameter for the compressor. A dual-plane LaVision Type 7 target was mounted between rotor blades for calibration purposes. This calibration target has dimensions of 58 mm square by 5.8 mm thick, with 1 mm spacing between the two planes and 5 mm spacing between marker dots on each plane. However, the rotor blades blocked portions of the calibration target, effectively reducing the measurement domain to 40 mm in the axial direction. Reflections from the incident laser light were a primary concern for this technique, so an MgF₂ antireflective coating was applied to the window to minimize reflections at wavelengths larger than 425 nm.

A Quantel Evergreen Nd-YAG laser (532 nm) was used as the illumination source, and four Imperx CCD cameras were used to acquire the image pairs using a frame-straddling approach. An optimized arrangement of these four cameras, combined with the use of a laser sheet with 4 mm nominal thickness, provided the opportunity to utilize stereo or tomographic reconstruction techniques. Measurements were acquired at 20 phase-locked positions across one rotor blade pitch (based on overlap of the 4 mm laser sheet) to reconstruct a full measurement volume across an entire rotor pitch (Fig. 1(b)). At the steep viewing angle required for this application, the image was out of focus from 60% span toward the hub and, as a result, meaningful measurements were only obtained between 65% span and the casing wall. The timing for the laser and the cameras was precisely controlled using a pulse generator with a once-per-revolution transistor-transistor logic (TTL) tachometer signal to phase-lock measurements at different circumferential positions across one blade pitch. Based on the 10.5 Hz laser repetition rate and camera capabilities, one phase-locked position (comprising 1000 image pairs) required approximately 5 min of steady compressor operation.

The antireflective coating on the window prevented incident light reflections from this surface, but reflections from the blade surface and hub initially led to saturation of image pixels. To overcome this challenge, fluorescent dye with sufficiently separated absorption and emission wavelengths (Rhodamine B 610 chloride powder) was introduced with the seeding fluid. In addition, lens filters blocking wavelengths below 540 nm were used to filter laser reflections, ultimately yielding recorded images with very low background noise.

Flow seeding was one of the primary challenges for this experiment. The use of fluorescent dye with traditional fog fluid leads to significant particle deposition on the window, thereby preventing the use of a fogger for particle seeding. Instead, a TSI 9307-06 six-jet Laskin nozzle was used to atomize the fluorescent dye with propylene glycol as the base fluid. For these tests, the particle generation with the Laskin nozzle was very sensitive to the specific seeding fluid mixture concentration. An ideal mixture for these tests included 1.3% by volume of ethanol added to the glycol to reduce the surface tension of the seed fluid and improve atomization. Ultimately, usable micron-sized tracer particles were successfully obtained when introduced through a 12.7 mm tube into the center of the compressor inlet duct at a position 28 axial chords upstream of the IGV leading edge (Fig. 2).

for particle density, $ρp$⁠, particle diameter, $dp$⁠, air viscosity, $μ$⁠, blade chord, $c$⁠, and blade tip velocity, $Vt$⁠. Using Eq. (1), the Stokes number for these particles represents 0.0087, which satisfies the St $≪$ 1 condition for particles to behave as flow tracers for PIV.

For the present analysis, only the top two camera images were used to reconstruct planar three-component velocity fields for each phase-locked measurement location. In-house PIV software “prana” [9] was used for all the calibrations, cross-correlation image processing, and three-component velocity reconstructions. A polynomial mapping function [10] was used to map the world coordinate system (x, y, and z) in the measurement domain to the image coordinate system (X, Y) for each camera.

Due to the very low seeding density, the use of traditional pairwise image cross-correlation to obtain the planar velocity fields yielded high noise levels and many erroneous measurements. Alternatively, to increase the cross-correlation signal, the sum-of-correlation (or ensemble correlation) approach [11,12] was adopted. Image pairs were cross-correlated, and then, the resulting correlation planes were averaged to yield the final estimate. The ensemble correlation delivered high correlation signal-to-noise ratio and robust velocity estimation, reducing the number of outliers from 15% to 4%. The cross-correlation was performed using 128-pixel square windows with 50% Gaussian spatial filter [13] and a final pass grid resolution of 8 pixels. Robust phase cross-correlation [14] was used to correlate the image pairs. The planar fields were validated using velocity threshold and universal outlier detection to remove erroneous vectors. Then, the estimated planar velocity fields from the two cameras were dewarped onto physical coordinate space and combined with the gradients of the mapping to obtain the three velocity components using a least squares fit [10].

The reconstructed fields were median filtered to remove noisy vectors along the blade edges. The three-component vector fields obtained by generalized stereo reconstruction at each circumferential location were analyzed. The recorded stereo image coordinate system was reoriented and scaled to express the data in terms of the coordinate system defined by axial chord, span, and blade pitch. The blade tip velocity was subtracted from the circumferential velocity component to present the measured absolute frame velocity in terms of the relative rotating reference frame velocity (⁠$W$⁠).

This note aims to demonstrate the feasibility of performing noninvasive three-component and three-dimensional measurements inside the embedded stage of a multistage compressor passage. Experiments were carried out at an operating condition near the peak efficiency point at the design speed, and the 20 measurement positions containing the three-component planar velocity fields were combined to reconstruct the volumetric vector field across one blade pitch. The effective domain was then 70–96% span, 15–90% axial chord, and 100% blade pitch. The velocity field was smoothed with a Gaussian kernel of two standard deviations and a window size of 7 × 7 grid points to reduce the noise in the flow field. The volume of data was then sliced at constant spanwise locations for interpretation purposes.

The alternating regions of positive and negative radial velocity in Fig. 3 are indicative of the tip leakage flow and what has been identified as the tip leakage vortex [15]. Although the measurements were collected across one complete blade pitch, the domain was plotted with periodic repetition in the pitchwise direction for more intuitive visualization. To further assess the viability of this PIV technique, the leakage flow trajectory identified in Fig. 3 is qualitatively compared with a separate experimental method for tracking the tip leakage flow in Fig. 4.

In Fig. 4(a), a slice of PIV data near the wall is presented as contours of normalized radial velocity with vectors shown as projections of the three-dimensional relative velocity vector onto the $r−θ$ plane. For comparison, Fig. 4(b) shows the contours of static pressure unsteadiness measured using high-frequency response piezoresistive pressure transducers in a flush-mounted configuration over the rotors, as described by Berdanier and Key [16]. Using this method, the tip leakage flow trajectory can be tracked by the locus of peak unsteadiness points across the passage emanating from near the leading edge of the blade. In Fig. 4(c), the results from both techniques are superimposed with flood contours of radial velocity from PIV and line contours from the static pressure unsteadiness. In this combined figure, the region of high unsteadiness identified in Fig. 4(b) is bounded by the regions of negative and positive radial velocities from the PIV results in Fig. 4(a). Based on this comparison, the trajectory angle of a line bounding the tip leakage flow identified by either technique (in this case, both are nonintrusive measurements) is similar to within 1 deg across the passage.

These results show that the three-dimensional PIV measurements in a multistage compressor are not only possible, but also a viable option, even with one simple optical access window and without the need for inserting an optical probe into the flow field. The development of this technique unlocks previously unknown possibilities for future implementation of optical measurements in turbomachinery applications which traditionally offer poor accessibility.

Several important steps were required for implementation of this technique, including antireflective coating on the window, fluorescent dye particles, and fluorescent lens filters on the cameras. Challenges with seeding density were resolved through the use of an ensemble correlation technique in the image processing steps, although future variations of particle generation strategies and seeding locations are expected to yield improved results.

Slices of normalized radial velocity at fixed spanwise positions highlighted the development of the tip leakage flow across the rotor passage, and a qualitative comparison of PIV measurements near the wall showed exceptional similarity to a more mature tip leakage flow tracking technique. Data collected from the entire four-camera system are under current refinement with the intent to obtain full tomographic PIV velocity fields using this method.

Technical assistance provided by Dr. Natalie Smith is gratefully acknowledged. This material is based upon the work supported by NASA under the ROA-2010 NRA of the Subsonic Fixed Wing project, with Technical Monitor Dr. Mark Celestina, and in part by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1333468. National Science Foundation Instrument Development for Biological Research Grant No. 1152304 provided additional partial support. The authors would also like to thank Rolls-Royce for the permission to publish this work.

$c$ =

chord

$dp$ =

particle diameter

$P$ =

pressure

St =

Stokes number

$Vt$ =

blade tip velocity

$W$ =

relative velocity

$μ$ =

air dynamic viscosity

$ρp$ =

particle density

Subscripts

$o-in,AA$ =

inlet area-averaged total condition

$r$ =

radial

$RMS$ =

root mean square