6 3d Piv Measurements

6.1 Overview

PIV is a whole field measurement technique that provides quantitative two or three dimensional velocity data over a planar region. The flow is seeded with tracer particles, with the two-dimensional plane of interest illuminated by a laser sheet generated by a timed double pulse of a high-power laser. In the digital PIV technique, CCD cameras are synchronized to the laser for recording images of the particles within the light sheet for both laser pulses. The camera images are divided into rectangular interrogation regions and correlation algorithms, which operate on the seed particle image, are used to determine an average two-dimensional displacement vector for each region. Vectors are then determined by dividing each displacement vector by the specified time between pulses. An additional vector-summing algorithm is used to combine pairs of two-dimensional vector maps into three-dimensional vector maps.

Camera alignment, measurement of the optical magnification factor, and generation of a suitable light sheet are the three main difficulties in instrumenting for 2d-PIV. Care must be taken in ensuring that the image acquisition camera is perfectly aligned normal to the plane of light produced by the illumination laser. Failure to attain this alignment will result in many data acquisition difficulties, and reduced data confidence. Without alignment, the experimentalist is sure to encounter increased population of 'bad' vectors across the measurement plane and an increase in measurement uncertainty. Reduced success results from uneven focus across the measurement plane, thus affecting the effective particle image size from point to point within the image, and reducing the primary correlation peak to the noise modulus. Before a camera can be properly aligned a viable light sheet must be generated, guidelines for such work has been presented by Adrian et. al. (1991) among others, and includes the necessity to ensure perfect co-planarity of the two pulsed sheets.

Likely, the most difficult component of the PIV technique is ascertaining a measurement uncertainty. The calibration process used for measuring the magnification factor of the imaging system drives uncertainty. A magnification value for the system can be resolved from knowledge of the distance between imaging components. Distances from the object plane (measurement plane) to the image plane (CCD chip plane) and to the camera lens principle points must be known precisely. However, in practice, geometric calculation of the magnification factor is a much less reliable than image calibration.

To calibrate magnification factor for a PIV system, an object of known dimensions must be placed in the plane of the illumination light sheet. The certainty of aligning the calibration object with the light sheet is in itself a task that is critical for minimizing measurement uncertainty. Imaging of the calibration object allows measurement of the magnification value if the CCD camera pixel pitch is known. The calibration image then provides a ratio of image pixel to pixel width to object space width, which is the practical magnification factor used in resolving object space particle displacements.

6.2 Practical Implementation for Extension of 2D-PIV to 3D-PIV

Quite simply 3d-PIV differs from 2d-PIV in the need for a second camera. These two cameras view the measurement region from equal angle offsets with respect to the normal view. The introduction of a second camera is not so simple in practice. Greater complexity of component alignment exists, as well as a greater complexity in calibration.

Camera to camera alignment is the first challenge for 3D-PIV. The goal in camera alignment is to maximize the camera-to-camera image area overlap. By imaging a crosshair calibration object, perfect alignment of the cameras is possible. Test images of the calibration crosshair should show that the crosshairs align. This alignment ensures a maximum overlap and proper angular orientation of the camera about its focal axis. This alignment requires precision duplicates of all camera mounting hardware. Proper camera mounting allows the line of sight of both cameras to fall in the same plane. This plane must also be normal to the light sheet, and should be defined by one of the coordinate directions of the measurement plane.

Precise mounting of the calibration object is also required. The calibration object is used for defining the measurement volume, the camera-to-camera alignment, individual camera focusing, the setting of the Scheimpflug condition, and may also be used to verify the orientation of the light sheet with respect to the flow field depending on the mounting method. The calibration object should be mounted on a traversing mechanism, which allows a full traverse of the light sheet thickness.

Parallel alignment of the calibration object to the light sheet is the first step to this calibration. This is accomplished either by fixing the light sheet position and then matching the calibration object position, or the reverse. Care must be taken in ensuring that the traversing axis lies in the camera plane, which is perfectly normal to the light sheet. These tasks are complicated by the fact that light sheets diverge, so that alignment with one surface of the light sheet will certainly result in a lack of alignment at the opposite surface. It is advisable to first align the calibration object mounting hardware to a solid reference plane, preferably the same reference that was used in fixing the light probe. Then a check of the alignment directly with the light sheet should be made. Also, minimizing the degree of light sheet divergence over the measurement area is desirable.

Camera focus should be optimized for best results in both the near surface and the far surface of the finite thickness light sheet. Thus, the calibration object should be traversed through the light sheet thickness, and imaged at multiple traverse points, so as to verify a nearly uniform focus through out. This is further motivation for precision in aligning the calibration object parallel to the plane of the light sheet.

For best focusing of each camera, the image plane, object plane and lens plane must intersect at a line. This optimal focus can only be approximated through geometric calculations, since the precise lens plane location may not easily be known. However, a geometric calculation for setting the camera image plane, which is the plane of the CCD optical chip, serves as a useful guide for manually arriving at optimal focus.

The ultimate purpose of the calibration object is to precisely define the measurement volume for 3D-PIV. Upon completing the alignment process for all mounting hardware associated with the cameras, light sheet, and calibration object, the measurement volume calibration images can be acquired. The center, the top surface, and the bottom surface of the light sheet should have previously been located with the calibration block traversing mechanism so that these positions can be found with favorable repeatability. And image pairs of the calibration object should be taken in these three known positions, at least. These images can be used for generating the coefficients in the final post-processing vector summation algorithm.

A proper setup will maximize the number of valid vectors possible for a given magnification factor, by ensuring the maximum number of stereo pairs for the total number of interrogation regions. Also, a minimization of systematic error for vector summation post processing can also be expected, due to a most accurate definition of the measurement volume.

6.3 Experimental Setup

To image the seal flow region, a 0.41 mm thick laser light sheet is introduced through the turbine case using a combination of cylindrical lenses the last of which is imbedded into a probe that is placed in middle of the second vane row. The laser source, which produces a 5mm diameter beam, is placed 30 inches from the probe exit. This minimal distance reduces the degree of beam expansion, and thus allows the thinnest possible light sheet. Between the laser and light probe is first a lens which reduces the beam spreading so that it can pass into the probe opening, and then a lens that sets the thickness of the light sheet.

This sheet is brought from the vane row upstream through the inter-stage space. Due to the typical large turning in these blade rows, a single vane was removal to introduce the light probe, thus introducing a local reduction in solidity. This vane removal was not ultimately necessary, but was considered easiest for this test of the measurement technology. The measurement plane, typical of that shown in Figure 6.1, sets at 99.65% span (0.3mm from the end wall) and covers the area between rotor-1 trailing edge and vane-2 leading edge. The flow is illuminated in an axial-tangential plane, with the measurement thus resolving those components of the flow. The useful measurement plane area dimensions are 17 mm in the axial direction by 17 mm in the tangential direction.

To image this region, the digital cameras view the flow from an oblique angle through a window located over the first rotor row and the downstream inter-stage space. The optical access window was cut precisely to the inner diameter of the turbine case, and the outer diameter of the window was cut from the same centerline, since this was shown to minimize distortions. Attempts to adjust the outer window radius to smaller values, closer to that predicted by the simple lens maker formula, proved to worsen the distortion cause by viewing at oblique angles. The window thickness is approximately 1.25 in. thick. And the attempts at varying the outer radius showed that a value larger than that produced for a co-axial cut would improve the distortion at stronger oblique viewing angles. Because of the imaging angle, astigmatic corrective optics were expected to be needed but were shown to be unnecessary due to the roughly parallel alignment of the measurement plane with the window. Corrective optics was used in an earlier application of 2D-PIV for which the object plane was tilted 45 degrees from the present case.

The two cameras used Rodenstock 120 series flat field lenses, designed at two-times magnification for minimum distortion. A Nikon PB-6 bellows system was used for mounting the lens to the Kodak cameras. And a specially designed flat profile bellows/camera adapter was fabricated to maximize light transmission for the case of a tilted camera with respect to the lens.

The two cameras were positioned using a three axis positioning system. The precision camera positioners were mounted to a Velmex ball screw positioner for translation along the axis of the turbine. An optical rail fastened to this base and oriented normal to the flow direction held 6 Melles Griot nano-positioners Precise overlap of the measurement images was guaranteed by actuation of the linear nano-positioners. Angular orientation of the lens rail/camera mount assembly was controlled by rotary nano-positioners, and object to image focal distance was controlled by a second set of linear nano-positioners. The angular adjustment of the CCD image plane was made by Velmex rotary tables A5990TS mounted atop the nano-positioners. Using a three-axis mill with a spindle mounted dial indicator of accuracy 0.00005 in, the positioner components were precisely mounted on the base optical rail.

For the near 2x magnification of the 18mm square object, the cameras were placed on a rail located approximately 24 in. radially outward from the measurement plane. Camera-to-camera included angle was set to 60 degrees. An interactive control system was designed for camera positioning using the nano-positioner Labview drivers. Based on three measurements: the desired flow passage span measurement location, the desired included camera angle, and the turbine axis to optical rail axis distance, the camera positioners could be activated for shifting the cameras into precisely the correct position. Focus adjustment, aperture adjustment, and Scheimpflug angle adjustments were made manually.

6.4 Calibration

Calibration required that the turbine drum shaft be loosened from the restraining bolt and slid forward. The rotor row just upstream of the measurement plane is so close to the downstream stator row, that the calibration block traversing mechanism could not be set into place, while the rotors where in the operational axial position. Temporary displacement of the rotor forward by 10mm was required.

The calibration target measured 21.5mm x 21.5mm and was constructed from a commercial engraving blank with white surface and black substrate. Endmills of Diameter 0.015, 0.020, and 0.025 inch diameter were used to remove the white layer by a depth of 0.2 mm. The dot spacing was set at 1.625mm. This calibration object was mounted atop a Melles-Griot vertical translation stage with a range of 4mm and drum dial indications of 0.01 mm. Interchangable calibration objects with verticle, horizontal and cross striping were used for checking camera focus and calibrating the magnification factor. All calibration blocks were fabricated on a precision numerical controlled mill.

6.5 Results

After calibration images were successfully acquired, PIV could be attempted. This was first accomplished without spinning up the turbine. A circulation fan placed over the rig exhaust duct was used to produce a small mass flow, sufficient to pull through seed particles. This simple test was necessary to detect problems with light reflections and camera focus. Often with 2D-PIV the experimentalist would like to adjust the focus so as to improve the pixel images, thus placing the histogram of pixel widths within the desired range. However, this process is not directly applicable to 3D-PIV, as any adjustment to focus, would require that the calibration process be repeated using the new camera focal settings. During this investigation, it was found that the calibration procedure itself was very successful in determining the best possible seed image focus.

Preliminary tests of the system with the turbine rotor locked, allowed a smooth test of the system at part speed and full speed. At the nominal design operating conditions, data was acquired in the amount of 115 instantaneous acquisitions. Note that the 115 pairs of data resulted from an actual acquisition of over 250 pairs, which was then sorted according to good/bad particle seeding. Each instantaneous data set was checked for vector magnitudes within 150% of the mean, with the remaining information discarded. Additionally, each vector correlation peak was checked to be at least 1.2 times higher than any secondary peak. The final data set pair was then matched and summed to arrive at 115 instantaneous 3D vector fields. The data was acquired for 32x32pixel areas with 50% overlap and without interrogation area displacement.

The results of this analysis are shown in Figure 6.2 and 6.3, and give an relatively high range of values for the out of plane velocity component. As work is still progressing on the error analysis based on the calibration coefficients produced by the Dantec system, this data is still considered preliminary. The direction of the out of plane component is given by the color legend. Red is radially outward and out of the page, and blue is radially inward and into the page. The directional trends show an upward flow beginning on the pressure side of the blade and a downward flow on the suction side of the blade. This is consistent with the known rotational direction of a tip vortex. However the point of down ward turning is much farther away from the suction side than expected. The single ensemble average out of plane vector set appears to be reasonable from a qualitative approach. Note that the small segment of blue vectors in the top center of the area is a result of a strong reflection on the rotor blade. Also, notice the flow angles in the axial-tangent plane. These vectors are within the expected velocity range, and have angles that show a turning of the flow to align with the camber angle of the vane-2 leading edge

The final three-dimension perspective of the flow in Figure 6.4, shows the rotor trailing edge looking nearly straight on along the metal angle from downstream toward upstream. The displayed vectors are plotted three-dimensionally, and with every second vector dropped from the view for improved clarity.

After these data were acquired, the turbine axis relative location of the set-up was adjusted so that data acquisition could be attempted in the tip gap. This last attempt was the ultimate goal, but it failed due to the difficulty in placing the light sheet far enough from the rotor tip surface so as to prevent reflection noise from the rough finish on the rotor tip surface.

Figure 6.1. Measurement Plane
Figure 6.2 Raw 3D-PIV Image
Figure 6.3

3-D vector map of rotor tip trailing edge flow.

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