Two-component planar Doppler velocimetry in the compressible turbulent boundary layer

Transcription

1 Experiments in Fluids 24 (1998) Springer-Verlag 1998 Two-component planar Doppler velocimetry in the compressible turbulent boundary layer S. A. Arnette, M. Samimy, G. S. Elliott 323 Abstract Non-intrusive Planar Doppler Velocimetry (PDV) has been extended to two-component measurements in a Mach 3, flat plate turbulent boundary layer and the distorted boundary layers downstream of 7 and 14 expansions. PDV results were compared to redundant Laser Doppler Velocimetry (LDV) measurements. Mean velocity results obtained with the two techniques agree to within 5%. PDV measurements were obtained within 0.4 mm of the surface while LDV could be employed only to within approximately 2.0 mm, highlighting a near-wall resolution advantage for PDV. Effects including those associated with separate filtered and reference cameras led to PDV uncertainties of the same order as the encountered moderate turbulence intensities, precluding an investigation of instantaneous turbulence fields. Despite these difficulties, the current multi-component measurements in distorted, compressible boundary layers highlight the potential of PDV and represent progress in its ongoing evolution. Sources of error and improvements required for quantitative turbulence measurements are discussed. Further advances can be expected from ongoing development efforts. 1 Introduction Experimental difficulties in compressible turbulent shear flows stem from a lack of spatial and temporal resolution. The difficulty in fully resolving the near-wall of compressible turbulent boundary layers is highlighted by this study, where the mean velocity for a Mach 3 boundary layer at n/δk0.04 is Received: 14 February 1997/Accepted: 26 August 1997 S. A. Arnette1, M. Samimy, G. S. Elliott2 Department of Mechanical Engineering The Ohio State University Columbus, OH 43210, USA Current address: 1 Dept. of Mechanical and Aerospace Engineering, University of Dayson, Dayson, OH , USA 2 Dept. of Mechanical and Aerospace Engineering, Rutgers Univerity, Piscataway, NJ , USA Correspondence to: M. Samimy Support for this work from the Air Force Office of Scientific Research (Contracts AFOSR and F ) is gratefully acknowledged. Thanks are also expressed to David Milam for his help conducting experiments and processing data. 60% of the freestream velocity. As discussed by Spina and Smits (1987), fully resolving temporal variations requires a frequency response of at least 10v/u2, which translates to approximately 25 MHz for the current study. Since these requirements are beyond the capabilities of established diagnostics, there is a need for improved measurement techniques. The potential value of a planar, instantaneous, non-intrusive velocimetry technique has spurred significant effort regarding the use of molecular iodine filters to measure the Doppler shift contained in scattered light. Miles et al. (1991) with Filtered Rayleigh Scattering (FRS) and Komine et al. (1991) with Doppler Global Velocimetry were the first to use iodine filters for flow diagnostics. In addition to flow visualizations, Miles et al. (1992) showed that average kinematic and thermodynamic properties can be measured with FRS by scanning the laser frequency and collecting filtered images. Two filter-based techniques capable of planar velocity measurements from particle scattering have emerged, Doppler Global Velocimetry (Komine et al. 1991; Meyers 1992) and Planar Doppler Velocimetry (PDV) (originally referred to as Filtered Planar Velocimetry by Elliott et al. 1994). Developed and employed to obtain one-component measurements in a supersonic free jet and compressible mixing layer by Elliott et al. (1993, 1994), PDV has been extended to the measurement of two velocity components in supersonic boundary layers. A fully-developed, Mach 3, turbulent boundary layer (Re ) and the effects of expansion regions on the boundary layer have been investigated with various nonintrusive diagnostics in the current investigation (Arnette et al. 1994, 1995, 1996; Samimy et al. 1994; Arnette 1995). For expansions like the 7 and 14 centered expansions considered here (Fig. 1), the boundary layer encounters normal and streamwise pressure gradients, streamline curvature, and dilatation, giving rise to a highly distorted boundary layer. Planar diagnostics such as PDV will be important to improving our understanding of such complex flows. 2 Experimental procedure 2.1 Flow facility and boundary layer models All experiments were performed at the Aeronautical and Astronautical Research Laboratory at The Ohio State University, and descriptions of the facility have been given previously (Arnette et al. 1995). The stagnation pressure was 0.82 MPa

2 324 Fig. 1. Schematic of the two centered expansion models (Δθ 7 and 14 ). The (x, y) origin is on the surface at the expansion corner. The n coordinate is zero at the surface and normal to the local surface (8.2 atm) 1% and the stagnation temperature was nominally 280 K. The boundary layer develops on a flat plate from the stagnation chamber to the test section (the Mach 3 convergingdiverging nozzle is opposite the flat plate in the top of the tunnel). The expansion models are fixed to the flat plate in the test section. The incoming Mach 3 flow occupies the top half of the test section, mm wide by 76.2 mm high. After the expansions, the model surfaces diverge away from the expansion corner towards the bottom of the test section, which has a total cross section of mm wide by mm high. The coordinate system is presented in Fig. 1. The streamwise coordinate, s, is measured along the model surfaces and s 0 occurs at the expansion corner. The normal coordinate (n) is zero at the surface and projects outward normal to the local surface. Windows in the top and side walls provide optical access. Schlieren images and static pressure distributions at the model surfaces have been presented elsewhere (Dawson et al. 1994; Arnette 1995). Laser Doppler Velocimetry (LDV) measurements give streamwise and normal turbulence intensities of less than 1.5% and 1.0% (respectively) in the Mach 3 freestream, of which a significant portion is a reflection of LDV uncertainties. The freestream velocity is approximately 600 m/s. At the expansion corners, the boundary layer thickness (δ 99 %) is 9.1 mm (denoted δ 0 below), the momentum thickness is estimated to be 0.6 mm, and the momentum thickness Reynolds number is approximately (Arnette et al. 1996). 2.2 Laser Doppler velocimetry LDV was employed to obtain measurements of streamwise and normal velocities in the interrogated boundary layers. A TSI Model LDV system was used in conjunction with the blue (488 nm) and green (514.5 nm) beams of a Model 2020 Spectra Physics 5 W Argon-ion laser. The beam pairs propagated through the test section in the spanwise direction at an orientation of 45 with the normal and streamwise directions. Measurements were acquired in the spanwise center of the test section. This coupled with the beam convergence permitted measurements only to within 2 mm of the surface. Forward scattering was collected at an angle of 10 with the beam axis to reduce stray laser light detection. Calculated ellipsoid measurement volume dimensions were 0.33 mm in the spanwise direction and 0.13 mm in diameter at the e 2 intensity level. Photomultiplier tube outputs were filtered and processed with a Model IFA-750 digital burst correlator. For each point, 8192 measurements were collected. The system was located on a table with closed-loop control to accurately position the probe volume. The flow was seeded with silicone oil particles from a TSI Model 9306 six-jet atomizer quoted to be less than 1 μm in diameter. To avoid boundary layer perturbation, the particleladen air stream was injected through the back wall of the stagnation chamber through an array of spanwise-aligned ports 10 mm above the flat plate on which the boundary layer formed. The main concern with respect to LDV measurement accuracy is the response of the seed particles to the expansions. Comparisons of the LDV results to an inviscid (rotational method of characteristics) simulation of the mean flow indicate particle lag is a problem only in the vicinity of the expansion very near the surface (Arnette et al. 1996). Consistent with past work (Samimy et al. 1986), the mean velocity uncertainty is estimated to be less than 1% and turbulence intensities have an estimated uncertainty of about 2% where particle lag is not a concern. Since these levels are lower than those for PDV, direct comparisons of PDV and LDV results were used to examine the PDV measurement accuracy. 2.3 Two-component particle Doppler velocimetry Introduction The employed Spectra Physics Model GCR-4 frequencydoubled Nd:YAG laser (532 nm) has a pulse rate of 10 Hz and is capable of approximately 700 mj/pulse. Its 10 ns pulse duration results in essentially instantaneous measurements. The laser is injection-seeded to obtain a narrow linewidth (approximately 50 MHz) and its center frequency can be controlled. A course adjustment allows for tuning through more than 100 GHz and fine adjustments are possible through a range of about 40 GHz. Narrow linewidth and control over center frequency are central to PDV and FRS. The use of FRS to interrogate flow fields was originally proposed by Miles et al. (1991) and has been discussed elsewhere (Miles et al. 1992; Elliott et al. 1992, 1993). An optical cell containing diatomic iodine vapor is placed in front of the collecting lens. Iodine possesses electronic transitions that absorb the frequency-doubled Nd : YAG radiation, and the cumulative absorption of the iodine forms a notch or band-reject filter in the transmission versus frequency domain. For appropriate arrangements, light scattered by the flow (or suspended particles) possesses a positive Doppler shift. The center frequency of the Nd : YAG laser can be tuned so the iodine filter absorbs unwanted background reflections while passing Doppler shifted scattering to the camera. When the collected scattering is the Rayleigh scattering from the molecules of the flow, it is difficult to absorb unshifted background reflections without also absorbing a large portion of the molecular scattering. This is because achieving Doppler shifts larger than the half-width of the Rayleigh scattering profile is difficult, at least for the case where collecting camera(s) are oriented nominally perpendicular to the illuminating laser sheet (Elliott et al. 1992). For the case of scattering from particles insensitive to thermal molecular

3 motions, the scattering linewidth is simply that of the laser. As a result, background elimination with no signal attenuation is easier. For this reason, small water condensation particles which form during the expansion to Mach 3 were utilized in FRS visualizations (Samimy et al. 1994; Arnette et al. 1995). The condensate comes from the small amount of water vapor in the supply air after passing through desiccant dryers and the particle dimension is on the order of 50 nm. Water vapor in the boundary layer is superheated, so there is no condensation within the boundary layer. This provides a means to visually differentiate the boundary layer and freestream. Although there is no a priori reason to expect the edge of the condensate to coincide with the boundary layer edge, thicknesses from ensemble-averaged visualizations coincide with those from LDV (Arnette 1995). The desire for more quantitative information about the flow than is available from FRS visualizations is the motivation for PDV development Principle of operation for planar Doppler velocimetry Light scattered by a moving particle or molecule contains a Doppler shift given by Fig. 2. Filter profiles employed for the PDV measurements 325 Δ f 1 V (o i) (1) λ where Δ f is the Doppler shift, λ is the illuminating wavelength, V is the scatterer s velocity vector, i is the unit vector specifying the propagation direction of illuminating sheet, and o is the unit vector specifying the propagation direction of the collected scattering. Using this relationship, the velocity of a scattering particle can be found if the Doppler shift present in collected scattering can be determined. This is the principle of operation for PDV. Diatomic iodine vapor in a transparent cell is again used as an optical filter. The cells were 9 cm in diameter and 22 cm long, identical to those employed by Elliott et al. (1994). In FRS visualizations, the filter eliminates unshifted background reflections. Accordingly, a Doppler or thermal broadened absorption profile in which absorption lines exhibit a rapid transition from near-zero to maximum transmission is required. In PDV, the filter is used to measure the Doppler shift. To do this, the filter attenuates scattering an amount solely dependent on the frequency of the scattering and a profile possessing a more gradual transition from peak absorption to peak transmission is employed. As originally proposed by Elliott et al. (1993, 1994), Lorentz broadening via the addition of nitrogen gas to the cell was used to generate the required absorption profile. The system used to measure the absorption profiles is identical to the system described by Elliott (1993) and Elliott et al. (1993, 1994). Further discussion is presented by Arnette (1995). The portion of the Lorentz broadened profile used for the PDV measurements appears in Fig. 2. The employed absorption line is located at cm 1. Two filters were required for the two-component measurements. The cell conditions were P N2 20 torr, T I C, and T C where P N2 is the partial nitrogen pressure added to filter, T is the temperature of Fig. 3. Schematic of pressure broadened absorption profile used in Planar Doppler Velocimetry the filter, and T I2 is the temperature of the filter sidearm housing iodine crystals. The small deviation between the profiles used for cameras 1 and 2 does not adversely affect the PDV measurements since the measured profiles are used to determine the Doppler shift incident on each camera. Redundant profiles obtained during the course of the investigation (and over the course of several years) were very repeatable, as expected. Partial absorption of particle scattering by a Lorentz broadened filter in PDV is illustrated in Fig. 3. Different scattering particle velocities give rise to different Doppler shift magnitudes for a given configuration, resulting in different filter transmission ratios. If the transmission ratio can be determined, the scattering frequency can be obtained from the absorption profile (Fig. 2). The Doppler shift is realized as the difference between the scattering frequency and the laser frequency, which is combined with the optical configuration to solve Eq. (1) for the flow velocity Flow seeding issues Despite the relatively low temperatures of supersonic flows, the Rayleigh scattering from the molecules which comprise the

4 326 flow is several GHz in linewidth (Elliott et al. 1992), wider than the iodine absorption wells used for scattering suppression. As a result, determining Doppler shift magnitudes by deconvoluting the Rayleigh scattering from the absorption profile is difficult. The line shape of the Rayleigh scattering is needed to determine the scattering center frequency as a function of measured filter transmission. Unfortunately, the shape of the Rayleigh scattering is a function of thermodynamic properties (Elliott et al. 1992) and instantaneous planar measurements of enough properties to specify the local thermodynamic state are not currently possible. This may be remedied as progress has been made in measuring instantaneous thermodynamic properties at a point with an anamorphic Filtered Rayleigh Scattering technique (Elliott and Samimy 1996). For these reasons, the flow was seeded with scattering particles. If the particles are insensitive to thermal motions of the molecules, the Doppler shifted scattering from the particles can be confined to one side of a Lorentz broadened absorption profile. In Fig. 3, the Doppler shifted scattering is confined between the local minimum and adjacent local maximum transmission for the range of expected velocities. Determining the centre frequency is then straightforward. Images of the flow are acquired one through a molecular filter and one without a filter. Dividing the filtered image by the non-filtered image yields the transmission ratio at each point in the flow. The scattering center frequency (Doppler shift) can then be obtained from the measured filter profile. In order to obtain a scattered signal within the boundary layer, the flow was seeded with acetone. Small liquid droplets generated with a Spraying Systems Model LNND22 atomizing nozzle were injected into the stagnation chamber. The acetone evaporates upon injection and then condenses to form small particles during expansion to supersonic speeds. Although particle size measurements were not attempted, signal levels comparable to those encountered in FRS visualizations utilizing only trace water condensation and observed sensitivity to laser polarization direction suggest a particle dimension on the order of 50 nm PDV implementation for boundary layer measurements Digital images were collected with thermoelectrically cooled Princeton Instruments 14-bit ICCD cameras with sensitivities of 10 to 100 counts/photon. The laser provides an output at each pulse for camera synchronization. An image is not acquired until the previous image is stored in memory, resulting in a framing rate of about 1 Hz for full array images. Parts of the array can be disabled or the array binned to form superpixels consisting of agglomerated groups of adjacent pixels to improve this rate if spatial resolution is not a primary concern. The limited framing rate results in consecutive instantaneous images being totally uncorrelated. For elastic scattering techniques, the boundary layer is more optically challenging than compressible mixing layers or free jet flows because of the surface adjacent to the flow. The typical approach would be to bring the laser sheet into the boundary in the downward normal direction, as was done in previous PLIF and FRS experiments. In PLIF experiments where ultraviolet light at 266 nm was used for illumination and visible light near 500 nm was collected, lens inefficiency in the ultraviolet was sufficient to remove surface reflections. In FRS visualizations, the iodine filter sharply attenuated surface reflections but could not achieve total elimination. As a result, the near-wall region was masked. Since the boundary layer was void of condensation (and thus scattering), this was acceptable. A similar approach for the PDV measurement was not acceptable since velocity measurements very near the surface were desired and surface reflections can be a source of significant PDV error. If the laser is tuned to near-zero transmission and background reflections are present, they are imaged by the unfiltered camera but not the filtered camera, causing the ensuing transmission ratio and Doppler shift to be artificially low. For relatively weak background reflections, the corrective action of Elliott et al. (1993, 1994) can be employed in which a Doppler broadened filter is placed in front of the reference camera to eliminate background reflections while passing Doppler shifted scattering. Since in a boundary layer the velocity and Doppler shift go to zero at the wall, this approach would not be suitable for some finite region adjacent to the surface. For these reasons, efforts were taken to avoid the creation of surface reflections. This was done by illuminating the flow with a collimated laser sheet which propagated up the tunnel axis just above the surface. In order to form the upstreampropagating sheet, a prism was placed in the flow. A 12.7 mm wide section of a right angle prism with 50.8 mm faces was epoxied into a rectangular aluminium fixture which could be mounted at the downstream end of the models. The exposed front and top prism faces were protected from impact by replaceable 3.0 mm thick quartz windows held in place by retaining clamps. The fixture proved sufficient, as the quartz windows cracked only once during the experiments. The redirection of the laser sheet up the tunnel axis is illustrated schematically in Fig. 4. The Nd : YAG beam was formed into a sheet with a cylindrical lens and a spherical lens was placed such that its focal point coincided with that of the cylindrical lens, insuring the sheet was collimated. The spherical lens was located such that the sheet waist occurred at the measurement location, giving a sheet thickness of only a fraction of a millimeter. The system was effective in illuminating the flow without incurring surface reflections. Forkey (1996) and Forkey et al. (1996) noticed a center frequency variation of approximately 100 MHz across the beam of their Nd : YAG laser, which can translate to significant PDV Fig. 4. Redirection of the collimated laser sheet with a prism assembly mounted in the flow for the Planar Doppler Velocimetry measurements

5 measurement errors. Similar variations have been observed by Clancy and Samimy (1997) who propose using only a small central portion of the beam to reduce the variation. Motivated primarily by the desire to minimize the intensity variation across the laser sheet, and unaware of the spatial frequency variation in the laser beam, this was the approach adopted in the current work. Focal lengths of the cylindrical and spherical lenses (25 mm and 1000 mm respectively) used to form a collimated sheet resulted in only a small central portion of the expanding sheet being collimated and passed to the tunnel (about 12% of the sheet width). Had this not been the case, the agreement between the LDV and PDV results presented below would have undoubtedly been degraded. The system was configured to measure instantaneous streamwise (U) and spanwise (W ) velocities as illustrated in Fig. 5. There was one filtered camera on each side of the tunnel and one ulfiltered camera, at all the same normal elevation as the laser sheet. As a result,the o and i unit vectors in Eq. (1) had no components in the normal direction (neglecting the small normal component of o associated with focussing through the camera lens). The resulting Doppler shifts observed by camera 1(z 0 side of the tunnel) and camera 2 are given by Δ f 1 1 λ (Ue x Ve y W e z ) [(1 cos θ 1 ) e x sin θ 1 e z ] and 1 λ [U (1 cos θ 1 ) W sin θ 1 ] Δ f 2 1 λ (Ue x Ve y W e z ) [(1 cos θ 2 ) e x sin θ 2 e z ] 1 λ [U (1 cos θ 2 ) W sin θ 2 ] (2) Fig. 5. Top view of the optical arrangement for the two-component Planar Doppler Velocimetry measurements where subscripts 1 and 2 refer to cameras 1 and 2. After obtaining the Doppler shifts observed by cameras 1 and 2, deriving U and W at each point is a matter of solving two equations with two unknowns. For the employed configuration, θ 1 +θ Accordingly, Camera 1 observed a Doppler shift essentially proportional to (U W ) and Camera 2 s shift was proportional to (U W). The actual camera angles were determined by measuring the distances from the center of the laser sheet to the center of the camera lens and to the axis parallel to the flow passing through the same point on the lens. The resulting angles are accurate to within Imagining W 0 and θ 90 in Eq. (2), one can derive that this uncertainty translates to a velocity uncertainty of about 0.5%. Before filtered images could be normalized by reference images to obtain transmission ratios, several processing steps were required. First, the images of the various cameras were aligned pixel-for-pixel. This insures the coupled filtered and unfiltered measurements used to determine velocity magnitude are from the same spatial location in the flow. The alignment was accomplished by acquiring images of a two-dimensional grid. Since cameras were on both sides of the tunnel, a grid was printed on a transparency and mounted in a frame, and images were acquired with the grid in the plane of the laser sheet. At grid reference points, it was a simple matter to count the number of pixels the reference points in cameras 2 and R needed to be shifted to align with camera 1. At most pixels, no reference point was present and appropriate vertical and horizontal pixel shifts were calculated based on the shifts for the four surrounding grid points. Elliott et al. (1994) used a two-dimensional linear interpolation. In the present study, this method was compared with a weighting method. Consider pixel A surrounded by reference points 1, 2, 3, and 4 for which the shifts required for inter-camera alignment are given by ξ 1, ξ 2, ξ 3, and ξ 4 respectively. The shift at pixel A was calculated as Π d ξ 1 ξ 1 Π d 2 ξ 2 Π d 3 ξ 3 Π d 4 ξ 4 Π d 1 Π d 2 Π d 3 Π d 4 where Π i 1..4 d i and d i is the distance between point A and reference point i. To calculate the horizontal (vertical) shifts at pixel A, the horizontal (vertical) shifts at the reference points are substituted for the ξ i s in Eq. (3). The resulting mapping was used to align the images of the three cameras. Alignments performed with the weighted and linear interpolation methods displayed no noticeable differences, so the weighted method was employed. The work of Clancy and Samimy (1997) indicates the use of sub-pixel resolution can improve the alignment. To obtain the correct transmission ratio from the normalization, the filtered and unfiltered cameras must have the same response characteristics. Specifically, if in the absence of any filter the cameras yield the same count read-out at common spatial locations, the normalization isolates the effect of the filter. Unfortunately, this is not generally true. In addition to differences from varied gain and aperture settings, the optical configuration can give rise to differences since the angle from a scattering particle is different for each camera. The (3) 327

6 328 polarization direction of the light sheet was normal to the plane defined by the three cameras so that, if the scattering were within the Rayleigh regime, all cameras would see the same amount of scattering. However, the condensed particle scattering more likely fell somewhere between the Rayleigh and Mie regimes, which would cause the scattered intensity to vary at least mildly with observation angle. To account for these effects, flow images were collected with the molecular filters removed. This was done just after the PDV data were acquired so that everything was the same except for the removal of the filters. These calibration images allowed the count readout that would have been registered by filtered cameras 1 and 2 to be determined from the pixel readout of the reference camera at the same spatial location. Dividing reading at each filtered pixel by the reading that would have been recorded without the filter in place gave the local transmission ratio. The employed Princeton Instruments cameras are linear devices (quoted nonlinearity of less than 2%). Accordingly, the number of counts recorded by cameras 1, 2, and R (with the molecular filters removed) can be expressed as I m I b I m (α I ) b (4) I m (β I ) b 0 where I, I, and I are the number of counts recorded by 1 2 cameras 1, 2, and R at pixels corresponding to the same spatial location (respectively), the m are the constants of proportionality between incident intensity and recorded counts, the i b are the readings for zero incident intensity, and I is the i 0 intensity incident on a pixel in camera 1. The incident intensity for cameras 2 and R has been multiplied by the constants α and β to include the possibility that angular variations in scattered intensity arise. Isolating I in Eqs. (5) and combining gives 0 I 1 M 1 I B 1, I 2 M 2 I B 2 (5) where M 1 m 1 /βm and B 1 b 1 m 1 b /βm, etc. Thus, even though the particle scattering was probably not Rayleigh scattering, a linear relationship exists between the readout of cameras 1 and 2 (with the filters removed) and the number of counts recorded by camera R at common spatial location. For each set of PDV data, 300 images were acquired with the iodine filters removed. After alignment, a linear regression was used to find M 1, M 2, B 1, and B 2. Instead of using a least squares regression to minimize (I 1 I )2 [or [(I 2 I )2], a weighted least squares regression was used to minimize [(I 1 I )/I ]2 (or [(I 2 I )/I ]2). If the deviation between the unfiltered camera 1 and camera R is spread over the entire 14-bit dynamic range (0 to 16383), the deviation as a percent of the nominal value will be smaller at the high end of the dynamic range with this method. Minimizing normalized residuals achieves the best inter-camera relation over the entire dynamic range. M 1, M 2, B 1, and B 2 were computed for each pixel in the respective array. However, the values did not vary significantly over the array and, for the sake of computational expediency, single M and B values were employed. In the mean, excellent agreement between the unfiltered images of the three cameras was achieved. The average deviation at individual pixels as a fraction of the reference camera read-out was approximately 0.1%, which was very encouraging for the ensuing mean velocity calculations. Instantaneously, the agreement was not as good. The sandard deviation of the normalized inter-camera deviations was about 5% at all pixels, which translates directly into an uncertainty in the instantaneous velocity measurements. The significant deviations are undoubtedly an indication that the scattering is most correctly classified as Mie scattering and that the scattering particles were not spherical. By disqualifying pixels where one camera recorded a much larger signal than the others (order of magnitude difference), it was insured that the instantaneous deviations were not a result of the spurious occurrences of large particles which might scatter much more light to camera than the others. An improvement to the PDV system employed to take care of instantaneous inter-camera deviations is possible. Meyers (1992) suggested placing a beam splitter in front of the molecular filter to split off an image identical to that passed through the filter. For the sake of speeding up data acquisition and minimizing the amount of collected data, the PDV data of this study were acquired with the camera array binned to 192 pixels 288 pixels (though the full array is capable of 384 pixels 576 pixels). One could split off an image before the molecular filter and direct it to half of the array while collecting the filtered with the other half of the array, which was the approach adopted by McKenzie (1995), Smith et al. (1996), and Clancy and Samimy (1997) in other PDV systems. This enables each camera to acquire its own reference image without any notable loss in spatial resolution, eliminating the problems associated with the inter-camera intensity alignment. For each set of PDV data, 750 images were acquired with the molecular filters in place before the 300 unfiltered calibration images were acquired. After M 1, M 2, B 1, and B 2 had been acquired, the procedure for obtaining instantaneous velocities was as follows. The reading at each pixel in an instantaneous reference image was used in conjunction with M 1 and B 1 (M 2 and B 2 ) to obtain the reading camera 1 (camera 2) would have recorded at the same spatial location with the filter removed, referred to as I 0,1 (I 0,2 ). The read-out in the filtered image of camera 1 (camera 2) at that pixel was then normalized by I 0,1 (I 0,2 ) to obtain the transmission ratio. The transmission ratios were then compared to the appropriate filter profile and combined with the laser frequency setting to obtain the Doppler shift incident on camera 1 (camera 2). The laser frequency (zero velocity frequency) was measured before and after the data collection using the filter profile measurement set-up. The Doppler shift magnitudes and relevant configuration angles were then substituted into Eqs. (2) and (3) to obtain instantaneous streamwise and spanwise velocities. 3 Results and discussion 3.1 Flat plate boundary layer The mean of 750 instantaneous streamwise velocity images of the flat plate boundary layer is given in Fig. 6. Brightness

7 Fig. 6. Average streamwise velocity image of the flat plate boundary layer obtained with Planar Doppler Velocimetry (δ mm) Fig. 7. Mean velocity profiles obtained with PDV and LDV in the flat plate boundary layer is proportional to streamwise velocity magnitude. Profiles extracted from the mean velocity image are plotted in Fig. 7 along with the mean profiles from LDV. In Fig. 7, the normal coordinate has been normalized with the local boundary layer thickness from LDV measurements. The agreement between PDV and LDV is encouraging. Assuming LDV gives an accurate representation of the true profile, dashed curves have been added at 8% to give an indication of PDV accuracy. The PDV profile falls within the 8% boundaries, suggesting the 8.6% uncertainty (a twostandard deviation level) computed by Elliott et al. (1994) is conservative for mean velocity results. In addition to the cited concerns with angular scattering uniformity, analysis indicates laser frequency variations are the primary source of uncertainty (Elliott et al. 1994). This part of the uncertainty could conceivably be minimized by measuring the laser frequency at each acquisition using a beam sample and reference iodine filter (Clancy et al. 1998). Improvement in near-wall resolution for PDV relative to LDV is also evident in Fig. 7. Measurements were obtained with a resolution of about 0.35 mm/pixel and seemingly good results were obtained at the first pixel above the surface. This was not a limiting resolution. A fairly large field of view was desired and all measurements were acquired with 2 2 pixel binning. If a local temperature of 1.85T is assumed (value measured by Smits (1990) in a Mach 2.8 turbulent boundary layer), the velocity of 0.6U 0 (approximately 360 m/s) gives a Mach number of 1.3 at n/δ , highlighting the need for good near-wall resolution. Since the average spanwise velocity was essentially zero everywhere in the measurement plane (magnitudes of less than 3% of the freestream velocity everywhere in the image), the average spanwise velocity image is not presented. This result confirmed the tunnel flow to be highly two-dimensional, which was a point of interest in the study. Given the decision to measure two velocity components (which required three cameras), it would have been most desirable to measure streamwise and normal velocities. The employed configuration was insensitive to velocities in the normal direction. Unfortunately, there was no easily achieved configuration for streamwise and normal velocity measurements. The obvious solution is to measure all components, which is possible with three cameras if split-imaging is employed (Clancy et al. 1998). Discontinuities appearing as lines parallel to the surface are present in the average velocity image of Fig. 6. Recall that the prism that directs the laser sheet up the tunnel axis is within the supersonic flow. In instantaneous images, the shock waves and recirculation zone in front of the prism give rise to small intensity discontinuities in the illuminating sheet. These are due to the large density variations (index of refraction variations). When the laser sheet encounters index of refraction variations, the net result is a sheet with regions of increased and decreased intensity relative to the sheet entering the tunnel. Similar results were obtained by Fourguette et al. (1995) in passing a sheet through a jet with index of refraction significantly different than the ambient fluid. Since these effects are present in the images of all cameras, the velocity measurements should not be adversely affected so long as sufficient illuminating intensity is present at all locations. Although the discontinuities are fairly gradual in the instantaneous images, thinner striation-like discontinuities with a width of only a fraction of a millimeter (single pixel) are present in the instantaneous images. Given the small spatial scale of the discontinuities, the alignment algorithm may not be exactly aligning the striations in the images. Qualitative observation of aligned images shows the striations exhibit a spatial jitter of 1 pixel. Given these significant changes in incident intensity at small spatial scales (due to index of refraction gradients), small alignment inaccuracies can lead to significant measurement uncertainties. Because of the unsteady nature of the recirculation zone and associated shock wave jitter, the striations change position from image to image. The small amplitude discontinuities are largely absent from Fig. 6, undoubtedly due to averaging. The instantaneous results probably indicate the need for better image alignment (i.e. sub-pixelization). The more gradual horizontal discontinuities evident in Fig. 6 are suggestive of a connection to mean sheet discontinuities associated with the mean shock, recirculation zone, etc. However, similar discontinuities are not present in the mean 329

8 330 velocity images downstream of the expansions (presented below), which is puzzling. It is possible that the small angular misalignment (7 or 14 ) between the sheet propagation direction and camera array for the expansions resulted in better image alignment, minimizing the effect of sheet distortion. All data were acquired with 2 by 2 pixel binning. As discussed by McKenzie (1997), it is likely that the streakiness could have been helped by larger pixel bins (i.e. 3 3). Redundant profiles of standard deviations for streamwise velocity fluctuations obtained with LDV and PDV were examined. PDV uncertainties were the same order as the moderate turbulence intensities encountered in the LDV measurements (σ /U %). Given the approximate 5% agreement for mean velocity results obtained with LDV and PDV, this is not surprising. This precluded a quantitative investigation of turbulence fields. Results are presented elsewhere (Arnette et al. 1995). For all cases except the flat plate, turbulence levels derived with PDV are higher than the corresponding level obtained with LDV as expected. The cited angular variations of the scattered intensity (which could be remedied through split-imaging) and aero-optical sheet distortion undoubtedly contribute to the deviations, and the results also suggest the possibility of non-negligible surface reflections (some are expected given the sheet distortion). A complete accounting for the deviations is not currently possible. The turbulence results highlight the need for improvement beyond the current implementation of PDV, but are not indicative of a fundamental limitation for the technique. For example, good agreement between PDV (with split-imaging) and LDV turbulence results has been obtained by Clancy et al. (1998) in a supersonic jet. Fig. 8. Average streamwise velocity images obtained with Planar Doppler Velocimetry at two streamwise locations downstream of the 7 expansion 3.2 Boundary layer downstream of the 7 centered expansion The mean streamwise velocity images obtained downstream of the 7 centered expansion are presented in Fig. 8. As with the flat plate boundary layer, the mean spanwise velocity was no more than 3% of the Mach 3 freestream velocity everywhere in the measurement plane, confirming the post-expansion flow to also be two-dimensional. LDV and PDV profiles obtained at s/δ and 2.8 are presented in Fig. 9. At s/δ 0 1.5, the agreement between the two is quite good, with maximum deviations of less than 5% of the freestream velocity. At s/δ there is a region which displays deviations of approximately 5% of the mean velocity. Though significant, these deviations are well within the previously estimated uncertainty of 8.6%. Profiles obtained at s/δ and 19.2 also display good agreement. More complete LDV and PDV results, both mean velocity and turbulence profiles, are presented by Arnette (1995), as is a discussion of the expansion s effect on the mean velocity in the near-wall region as inferred from PDV measurements. 3.3 Boundary layer downstream of the 14 centered expansion The average streamwise velocity image obtained downstream of the 14 centered expansion is presented in Fig. 10. The average spanwise velocity was everywhere less than 3% of the freestream velocity, again indicating the tunnel flow was highly two-dimensional. The low velocity region in the bottom right of the image is due to the prism assembly blockage. Due to the shorter length of the 14 expansion model, the face of the prism assembly was only about 19δ 0 downstream of the corner, leaving a smaller distance downstream of the corner where the boundary layer was unaffected by the prism (relative to the other models). Profiles obtained at s/δ and 2.8 from the PDV and LDV measurements are presented in Fig. 11. Although there is good agreement away from the surface, significant deviations are present for n/δ at s/δ and n/δ at s/δ If the problem was primarily associated with the LDV particle lag, LDV measurements less than PDV measurements would be expected. Since this is not the case, the discrepancies may be due to surface reflections. Although it was intended to pass the collimated laser sheet along the model surface, it is possible that it was either not perfectly collimated and/or directed slightly into the surface for the 14 experiments, giving rise to artificially low velocity measurements. Given the aero-optical distortion of the laser sheet, some reflections are expected. However, the normal extent of the deviations seems larger than would be expected if only surface reflections are to blame. It is unlikely that the prism interference affects the flow at s/δ and 2.8, which would lead to larger LDV velocities relative to PDV.

9 331 Fig. 9. Mean velocity profiles obtained with LDV and PDV downstream of the 7 centered expansion at s/δ 0 1.5, 8.4, 14.0, and 19.2 Fig. 10. Average streamwise velocity image obtained with Planar Doppler Velocimetry downstream of the 14 expansion 4 Conclusion The Planar Doppler Velocimetry (PDV) technique was extended to the measurement of streamwise and spanwise velocities in a Mach 3, fully-developed turbulent boundary layer and the boundary layers downstream of 7 and 14 expansions. PDV offered a large improvement in near-wall resolution relative to LDV. While LDV measurements were possible only to within about 2 mm of the boundary, PDV measurement were acquired to within 0.4 mm (which is not a limiting value). Unfortunately, current PDV measurement uncertainties are the same order as the moderate turbulence levels in the boundary layers, precluding quantitative investigations of instantaneous turbulence fields. Despite the uncertainties, mean streamwise velocities obtained with PDV and LDV agreed to within 5% (with some exceptions for the 14 expansion) and mean spanwise velocities measured with PDV were within 3% of the expected value. These levels are consistent with the 8.6% two-standard deviation uncertainty

10 332 Fig. 11. Mean velocity profiles obtained with LDV and PDV downstream of the 14 centered expansion at s/δ and 2.8 estimate derived previously. Laser frequency fluctuations and cited effects associated with the combination of separate filtered and reference cameras (as opposed to image splitting) and the nature of the collected scattering are thought to be the major sources of uncertainty. The ability to acquire planar, simultaneous, instantaneous measurements of multiple velocity components with spatial resolution on the order of 100 μm was demonstrated. Methods of improving measurement accuracy beyond that achieved here are also discussed. All indications are PDV will be a valuable quantitative tool for investigations of compressible turbulence as ongoing development leads to further gains in measurement accuracy. References Arnette SA; Samimy M; Elliott GS (1994) The effect of expansion on large scale structure evolution in a compressible turbulent boundary layer. AIAA Arnette SA; Samimy M; Elliott GS (1995) Structure of supersonic turbulent boundary layer after expansion regions. AIAA J 33: Arnette SA (1995) The effects of expansion regions on supersonic turbulent boundary layers. Ph.D. Dissertation, Dept of Mechanical Engineering, The Ohio State University Arnette SA; Samimy M; Elliott GS (1996) The effects of expansions on the turbulence structure of a compressible boundary layer. AIAA , submitted to J Fluid Mech Arnette SA (1995) The effects of expansion regions on supersonic turbulent boundary layers. Ph.D. Dissertation, Dept of Mechanical Engineering, the Ohio State University Clancy PS; Samimy M (1997) Multiple-component velocimetry in high speed flows using Planar Doppler Velocimetry. AIAA , AIAA J 35: Clancy PS; Samimy M; Erskine WR (1998) Planar Doppler Velocimetry: Three-Component Velocimetry in Supersonic Jets. AIAA Dawson JD; Samimy M; Arnette SA (1994) The effects of expansion on a supersonic boundary layer: surface pressure measurements. AIAA J 32: Elliott GS; Samimy M; Arnette SA (1992) Filtered Rayleigh scattering based measurements in compressible mixing layers. AIAA Elliott GS; Samimy M; Arnette SA (1993) Molecular filter-based diagnostics in high speed flows. AIAA Elliott GS; Samimy M; Arnette SA (1994) A molecular filter based velocimetry technique for high speed flows. Exp Fluids 18: Elliott GS; Samimy M (1996) Rayleigh scattering technique for simultaneous measurements of velocity and thermodynamic properties. AIAA J 34: Forkey JN (1996) Development and demonstration of filtered Rayleigh scattering a Laser Based Flow Diagnostic for Planar Meaurement of Velocity, Temperature, and Pressure. Final Report for NASA Graduate Student Researcher, Fellowship Grant NGT Forkey JN; Finkelstein ND; Lempert WR; Miles RB (1996) Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements. AIAA J 34: Fourguette DC; Dimotakis PE; Ching WK (1995) Index-of-refraction imaging and aero-optics effects in a fully-developed axisymmetric turbulent jet. AIAA Komine H; Brosnan SJ; Litton AB; Stappaerts EA (1991) Real-time Doppler global velocimetry. AIAA McKenzie RL (1995) Measurement capabilities of planar doppler velocimetry using pulsed lasers. AIAA McKenzie RL (1997) Planar Doppler velocimetry performance in low-speed flows. AIAA Meyers JF (1992) Doppler global velocimetry: The next generation? AIAA Miles RB; Lempert WR; Forkey J (1991) Instantaneous velocity fields and background suppression by filtered Rayleigh scattering. AIAA Miles RB; Forkey J; Lempert WR (1992) Filtered Rayleigh scattering measurements in supersonic/hypersonic facilities. AIAA Samimy M; Arnette SA; Elliott GS (1994) Streamwise structures in a high Reynolds number supersonic boundary layer. Phys Fluids 6: Samimy M; Petrie HL; Addy AL (1986) A study of compressible, turbulent, reattaching free shear layers. AIAA J 24: Smith MW; Northam GB; Drummond JP (1996) Application of absorption filter-planar doppler velocimetry to sonic and supersonic jets. AIAA J 34: Smits AJ (1990) New developments in understanding supersonic turbulent boundary layers. 12th Symp on turbulence, Rolla, Missouri Spina EF; Smits AJ (1987) Organized structures in a compressible, turbulent boundary layer. J Fluid Mech 182: