Hypersonic FLEET velocimetry and uncertainty characterization in a tripped boundary layer

Femtosecond laser electronic excitation tagging (FLEET) velocimetry is applied in a hypersonic boundary layer behind an array of turbulence-inducing trips. One-dimensional mean velocity and root-mean-square (RMS) of velocity fluctuation profiles are extracted from FLEET emissions oriented across a 2.75∘ wedge and through a boundary layer above a flat plate in two test campaigns spanning 21 tunnel runs. The experiment was performed in the Texas A&M University Actively Controlled Expansion tunnel that operated near Mach 6.0 with a Reynolds number near 6 × 106 m−1 and a working fluid of air at a density near 2.5 × 10−2 kg m−3. Detailed analysis of random and systematic errors was performed using synthetic curves for error in the mean velocity due to emission decay and the error in the RMS velocity fluctuation due to random error. The boundary layer behind an array of turbulence-inducing trips is documented to show the breakdown of coherent structures. FLEET velocimetry is compared to the tunnel Data Acquisition System, Vibrationally Excited Nitric Oxide Monitoring results, and Reynolds-Averaged Navier–Stokes computational fluid dynamics to verify results.


Introduction
The transition to turbulence in hypersonic boundary layers plays a large role in the heating, entropy production, and generation of drag for hypersonic vehicles [1,2].One of the primary design tools available for predicting hypersonic boundary layers is computational fluid dynamics (CFD).Appropriate use of CFD design tools can reduce the time and the cost associated with the development of hypersonic vehicles by reducing manufacturing and testing costs of the vehicles and optimizing design strategy.In order to improve confidence in the CFD simulation accuracy, and thus confidence in hypersonic vehicle design, rigorous validation of CFD tools using highquality experimental data sets is required [3].As documented by Oberkampf and Smith, datasets used for CFD validation must have a high completeness level and well-quantified experimental uncertainty.For hypersonic flows, a dataset with high completeness will have high temporal and spatial resolution without significantly disturbing the flow.Experimental setup and test conditions must be carefully documented to ensure that data is reproducible.Sources of random and systematic errors must be quantified to bound validation efforts.Simple test articles often called canonical models are useful for understanding the flow phenomenon in boundary layers involving certain types of processes or interactions as discussed by Gaitonde [4].
In this paper, femtosecond laser electronic excitation tagging (FLEET) is chosen to perform one-dimensional velocimetry in a tripped hypersonic boundary layer with the goal of understanding the considerations and limitations of FLEET as a validation quality diagnostic method for CFD.The technique of FLEET has matured quickly since its inception a decade ago on bench top experiments reported by Michael et al and has quickly become a popular diagnostic technique for hypersonic flows [5].FLEET can be classified as a molecular tagging velocimetry (MTV) technique and offers nonintrusive, seedless velocimetry in pure nitrogen or air flows in a variety of configurations.FLEET is performed by imaging the longlived fluorescence of nitrogen molecules tagged by a focused femtosecond laser beam at various time delays to record gas displacement.The fluorescence of nitrogen molecules is the result of dissociation and ionization of nitrogen molecules into multiple excited states which recombine, emit photons, and return to the ground state in a rate-limited process [6][7][8].FLEET was first used in orthogonal detection configurations, but many alternative beam orientations have been used and are discussed hereafter.FLEET has been applied in the bore sight configuration where a short focal length lens is used to create an emissive spot to identify two-dimensional velocity [9].Multiple femtosecond beams have been used to generate crossing focused beams to track two-dimensional velocity and local vorticity [2].FLEET has also been applied using selective masking to produce a more continuous onedimensional velocity field [10].A single femtosecond beam was split into a grid pattern and imaged in a bore sight configuration to track two-dimensional velocity and vorticity [11].FLEET has also been applied in the wall-normal imaging orientation with the femtosecond beam terminating on the surface of the model or in a beam port in the model [12,13].Work by Limbach showed heating of the gas caused by traditional FLEET diagnostics [7,14], motivating the development of Selective two-photon absorptive resonance femtosecond laser electronic excitation tagging (STARFLEET).STARFLEET reduces the thermal energy deposited in the flow field while simultaneously increasing the signal and emission lifetime [15][16][17].FLEET has been successfully applied in the AEDC Hypervelocity Wind Tunnel and Sandia's Hypersonic Wind Tunnel which both use a working fluid of pure nitrogen [15,18].Experiments in the AFRL Mach-6 Ludwieg tube has further shown that FLEET diagnostics can produce reliable estimates of mean velocity in a hypersonic tunnel with a working fluid of air [19].
With sufficient signal, single-shot FLEET has been used to measure flow fluctuations.Burns measured the distribution of instantaneous velocities in the freestream of the NASA Langley 0.3 meter Transonic Cryogenic Tunnel [20].Dogariu and Hill have separately conducted campaigns wherein singleshot FLEET has been used to find velocity fluctuation above the surface of test articles in hypersonic tunnels [13,18].In each of these tests the measured instantaneous velocity distribution was used to calculate the one-dimensional velocity fluctuation.Measurement of accurate velocity fluctuation requires low single-shot error, as the distribution of instantaneous velocity can be significantly impacted by imprecise measurements.
FLEET also has several challenges associated with its application to hypersonic flow diagnostics.FLEET emission in air is substantially weaker and has a shorter lifetime than FLEET emission in nitrogen because of high quenching rates caused by oxygen [21].The intensity of FLEET emission decays bi-exponentially over time which will cause systematic under-prediction of the mean velocity if the exposure duration is substantial relative to the emission decay time scale [18,22].Measurement precision is the distribution of velocity caused by random measurement errors and has been investigated by Peters [8,21] who measured the distribution of singleshot FLEET velocity in a benchtop experiment.Precision was found to be dependent on the camera system, signal-to-noise ratio (SNR), and emission decay which all contribute to errors in a centroid fitting routine for images [8,22].Lower signal from FLEET in a working fluid of air, and a long integration time, resulted in larger random errors [5,16].Additionally, a short delay between successive camera exposures, required by short signal lifetime, amplified the impact of random errors [18].In test where precision is on the order of the RMS velocity fluctuation, FLEET measurements of velocity fluctuations are expected to be inaccurate.
The primary objective of this paper is the characterization of boundary layer transition to turbulence due to discrete roughness elements as a precursor to future studies [23,24] of shock-boundary layer interactions in the Actively Controlled Expansion (ACE) hypersonic wind tunnel at Texas A&M University.For this purpose, the authors have applied the FLEET MTV technique to measure velocity profiles behind the tripping array over 21 wind tunnel entries.The secondary objective of the paper is to quantify and correct for random and systematic errors due to low measurement precision and rapid emission decay respectively, which are substantial during operation of the ACE tunnel with air.Notably, this work also reports the first FLEET measurements ever obtained in the ACE tunnel at Texas A&M University.

Experimental methods
To investigate the mean and RMS velocity fluctuation profiles, two sets of experiments were conducted at the Texas A&M National Aerothermochemistry and Hypersonics Laboratory in collaboration with the Aerospace Laboratory for Lasers, ElectroMagnetics and Optics.The test facility, femtosecond laser, experimental methods, data collection system, and image processing program are discussed below.

ACE tunnel
All experiments were conducted in the ACE tunnel at the Texas A&M University NAL.This facility is a pressure-vacuum blow-down hypersonic wind tunnel with an operating fluid of dry air.A schematic of the ACE tunnel is shown in figure 1.Details on ACE design, calibration, and freestream turbulence are provided in [25][26][27][28].The test section cross-sectional area of ACE was 22.9 cm × 35.6 cm.The windows used for this experiment were 2.54 cm thick uncoated fused silica.The run conditions for the tunnel used in the two test campaigns are shown in table 1.The static pressure present in the freestream of the tunnel was 3.3 Torr, while freestream density was calculated to be 0.025 kg m −3 .

Test articles in the ACE tunnel
The first of the two test articles tested in ACE was a 2.75 • halfangle wedge article.Flat plate models in ACE have resulted in pressure differentials that cause streamlines to wrap over the sides of the test article, while the wedge test article produces a boundary layer with a more uniform pressure gradient [29].This test article has a length of 0.508 m and a width of 0.216 m.Extensive previous testing with the wedge test article has been conducted using oil flow, schlieren imaging, IR thermography, high-frequency pressure transducers, kulite sensors, pitot traverses, Optical Emission Spectroscopy, Planar Laser-Induced Flourescence themography and velocimetry [30], and Vibrationally Excited Nitric Oxide Measurements (VENOM) [29,31].Figure 2(a) shows the wedge model mounted in a cutaway of the test section of the ACE tunnel.FLEET measurement locations are reported relative to the trailing edge of the center of the tripping array.The streamwise distance was measured parallel to the model surface in the flow direction, while height was measured normal to the model surface.The wedge test article was fit with a row of tripping elements behind the leading edge to transition the boundary layer to turbulence.The tripping array is sometimes referred to as a set of 'pizza-box' trips [32].Shrestha and Candler used direct numerical simulation to investigate similar tripping elements which provide context to the results observed in this experiment [33][34][35].The tripping array used with the wedge test article was composed of 23 elements each with a square footprint with a diagonal length of 3.42 mm and inter-trip spacing of 3.42 mm.The height of each trip was 2.57 mm and designed to be 1.3 times the height of the incoming laminar boundary layer.
The second of the two models tested in ACE was the base plate of the canonical inlet model discussed by Limbach and coworkers [36].The canonical inlet model was designed with removable side walls and inserts in the plate.The model was run in the ACE tunnel in the configuration shown in figure 2(b), amounting to a flat plate with an array of tripping elements placed near the leading edge of the model.The dimensions of individual tripping elements used for the flat plate test article were identical to the ones used with the wedge test article.An insert with blind holes hereafter called beam ports was placed in the flat plate which was used for femtosecond beam routing.The beam ports in the insert were the only exposed holes on the surface of the model; all other holes were sealed for the run and were not expected to impact the flow.The beam port had a diameter of 1.95 mm and a depth of 8.5 mm.The diameter of the beam port used in this experiment was selected based on work done by Hill wherein a 3.81 mm port was utilized in a similar FLEET tagging experiment and was documented to not disturb the boundary layer [13].The depth of the port was limited by the geometry of the insert within the test article.A through-hole was avoided to prevent flow through the hole caused by the pressure differential across the plate.

Femtosecond laser and beam routing
FLEET measurements were performed using a Spectra-Physics Solstice ACE femtosecond laser system providing 90 fs pulses at a 1 kHz repetition rate.The laser operated at 811 nm with a maximum of 8 mJ pulse energy.Femtosecond laser pulses were routed approximately 6 m from the laser system to the ACE tunnel test section, over which the Gaussian spatial energy distribution was retained.In both test campaigns a single planoconvex lens was used to focus the femtosecond laser into a single beam in the tunnel.
In the spanwise measurement campaign, the femtosecond laser beam was used to perform diagnostics for 20 locations behind the tripping array in and near the boundary layer.The output pulses were limited to 2.5 mJ in the test section for all measurements using a waveplate-polarizer optical attenuator to limit supercontinuum generation in the uncoated fused silica windows.This energy was chosen based on signaloptimization conducted in atmosphere before the campaign.The laser had a diameter of roughly 18 mm at the final lens, and was focused with a 300 mm planoconvex lens.The streamwise locations of the measurements were chosen based on optical accessibility in both the side and top ACE tunnel windows.The height of the spanwise measurements were selected to begin just outside the boundary layer and continue down to as near   the surface of the model as possible.The minimum measurement height during spanwise testing was 1.5 mm above the surface of the model due to the laser beam clipping the sides of the test article.Figure 3 shows the path of the laser beam through the test section.
In the wall-normal measurement campaign, the femtosecond beam was routed to penetrate the boundary layer and to terminate in a beam port 137.5 mm behind the tripping array to permit FLEET measurements as close to the surface of the model as possible, see figure 4. For this experiment, a 200 mm planoconvex lens was utilized to focus femtosecond pulses through a fused silica window to generate FLEET emissions up to 10 mm above the surface of the test article.Beam energy for this experiment was similar to the spanwise measurement campaign with 2.5 mJ expected in the test section.

Data collection
Data collection for both experiments was performed with a Photron Fastcam SA-Z complementary metal oxide semiconductor camera coupled with a LaVision HighSpeed intensified relay optics (IRO) image intensifier.The intensifier unit was equipped with an S25 photocathode which was well-suited to amplify the visible and near-infrared emission coming from FLEET.A ZEISS Milvus 100 mm Macro Lens collected light through a 750 nm lowpass filter with an optical density of 4 that suppressed scattered laser light into the lens.A BNC Model 577 Pulse Generator synchronized the camera-IRO system with the laser pulse.The image intensifier was run in the burst-gating mode to superimpose the initial and displaced FLEET signal onto a single camera image to improve experimental repeatability.
In the spanwise FLEET measurement campaign, the intensifier unit was run in burst mode to superimpose three separate gates to show the displacement of emission.Of the three gates used, only the first two were found to have sufficient SNR to be used for velocimetry.Table 2 shows the gate and delay pairs for the IRO during the run.An intensifier gain of 80% was chosen to amplify FLEET emissions without saturating the camera sensor.Reference images were taken at each diagnostic location to provide spatial calibration and location in a global coordinate system.The image resolution was approximately 25 µm per pixel but varied slightly between runs due to changes in optical alignment.
In the wall-normal FLEET measurement tests the delay between the initial gate and single displaced gate was maximized to increase the displacement between the captured emissions to improve near-wall velocimetry.Table 2 shows the settings of the IRO used for the wall-normal measurements.The camera and intensifier unit were declined 3.25 • to look down onto the plate, which improved the ability of the system to capture near-wall emissions.Image resolution was approximately 50 µm per pixel in this configuration due to the further standoff distance from the test article when capturing data through a window on the side of the ACE tunnel.

Data processing
The images of FLEET emission were processed based on similar MTV and other FLEET data processing techniques.
Each tagged line was fit to an assumed Gaussian line shape to identify the streamwise location of tagged molecules at a given time.Simpler cross-correlation methods were impossible with this data set because emissions were superimposed in the same image.A MATLAB program, described hereafter, fits singleshot images to identify instantaneous velocity distributions that are then used to calculate mean velocity and RMS velocity fluctuation.

Image preprocessing
The reference images were examined to identify the image scale, physical location, and orientation of the image plane relative to the test articles.Next, images were passed through a program described by Limbach that uses a pixel-wise histogram approach to identify and eliminate outliers, especially due to dust particles, in sequential images [7].The mean intensity of each pixel within images, after outlier rejection, was used to represent time-averaged FLEET.
The time-averaged emission images, representing the average from 1000 images evenly obtained from the run duration, were used to determine the bounds used to fit the instantaneous FLEET profiles.The bounds limited the Gaussian centroid locations to four times the standard deviation of intensity for each acceptable image.The time-averaged gate amplitudes were fit with a single-exponential decay equation to identify a representative decay constant for the FLEET emissions using the time-independent emission intensity to account for the unequal IRO gate duration.The SNR of the third gate window was so low that it was excluded in the fit.That is, the fitting used only undisplaced line and first displaced gate interval to identify a single-exponential decay constant τ .While real FLEET emission is expected to be modeled more accurately with a bi-exponential function [16,22], the use of a single-exponential fit has been used previously by Dogariu et al [18].The FWHM of the initial line width was approximately 310 µm, while the FWHM of the displaced line width was approximately 625 µm.
In the spanwise measurement campaign conducted using the wedge test article, light from the FLEET emissions was reflected off the surface of the model and was observed as a background behind the FLEET signal.The reflected light was proportional to the original FLEET emission intensity and decreased with measurement height above the plate.This reflected light was fit with a two-dimensional Gaussian surface, and subtracted from images in a test, to minimize the effects of the this background light on the results.Figure 5 shows single shot and time-averaged FLEET emissions for a single diagnostic location in the wake of a turbulence-inducing trip element.
The wall-normal FLEET images required special considerations to estimate the displacement of FLEET emissions near the wall where the displaced gate overlaps strongly with the initial gate as shown in figure 6. Near the beam ports, significant scattered light interfered with the FLEET signal.To address this, a two-dimensional Gaussian was fit to the reflected light from the beam port.The reflected light from the hole did not saturate the camera, permitting subtraction of their effect from images.The reflected light mask was identified for time-averaged image and applied by subtracting it from each single shot image.Variations in the beam port reflections caused the program to increase fluctuations near the surface.Second, the first gate emission was fit far from the wall and then extrapolated as a line to the surface of the test article.The extrapolated fitted values for the initial emissions and the subtraction of the reflected light from the hole injected additional noise near the surface, resulting in greater random error.

Centroid fitting
The processing program loaded, cropped, and registered single-shot images prior to fitting.Image registration was performed using the MATLAB image processing toolbox because of camera motion during the run.All registration translations were tracked and factored into measurement location uncertainty.The images were fit using a double-Gaussian equation, as shown in equation ( 1), to each streamwise row of data using a nonlinear least squares fitting procedure.Figures 7 and 8 show time-averaged and single-shot rows of data fit using equation (1).Fitting was used to identify the location of the FLEET emissions in the camera image, which were called emission centroids.A double-Gaussian fit was chosen over alternative centroid-finding algorithms such pseudo-Voigt fitting because it provided a good estimate of the centroid while simultaneously limiting the number of free variables.This conclusion was made after a comparison of results fit with both a Gaussian distribution and a pseudo-Voigt fit, in which an insignificant difference was observed in centroid location between the two methods.The amplitude of the emission was represented by a, the location of the emissions in the image was represented by µ, and the width of the emissions was represented by σ.The subscripts correspond to the first (initial) and second (displaced) emissions respectively ( The time between laser tagging and the first gate was less than 100 ns, corresponding to a displacement of fewer than four pixels in the streamwise direction.The small streamwise  displacement, and the primarily streamwise flow direction, permitted fitting the first gate as a line.The excellent SNR, as well as relatively short exposure duration compared to the emission decay time constant, minimized the impact of random and systematic errors in the identification of this centroid.The subscript m in the variables µ 1,m and µ 2,m indicates that the these are 'measured' value that in general contain significant contributions from random and systematic error terms as later explicitly defined in equation (12).The displaced centroid had a reduced SNR and a relatively long gate duration, and was not fit as a line to retain spanwise resolution.The error associated from these facts caused the expected error in µ 2,m to be significantly greater than in µ 1,m .In later data processing only the error in µ 2 is considered, However, the error quantification process presented in this work could be applied to both exposures if the error was of a similar scale.The fitting routine applied the time-averaged fitting bounds to identify the emission centroids with 95% confidence intervals.The centroids were obtained for roughly 6 mm across the span of the test article in the spanwise measurement campaign, and 10 mm in height for the wall-normal campaign, defining the spatial extent of viable data.
In every image, SNR was measured as the integral of the signal from the Gaussian distribution fitted to the displaced gate, divided by the residual of the captured emissions to that same Gaussian distribution [16].The displaced gate was chosen for SNR calculations because of its substantially weaker signal and the increased variability compared to the initial gate.Camera pixel rows were not binned, as recommended by Reese [16,37] if the SNR is less than 4, to retain full camera resolution.Velocimetry uncertainty was documented to provide an alternative avenue for bounding errors.

Velocimetry and filtering
The instantaneous velocity was computed using the known time delay between the midpoint of the two IRO gates (t i ), the identified image scale (s), and the calculated displacement between the two centroids (µ i ) as shown in equation (2).A single displacement was used for velocimetry because only one of the two displaced gate were accurately captured.The random uncertainty in centroid location and systematic uncertainty in image scale were propagated into the raw instantaneous velocity Various metrics were used to filter the instantaneous velocity profiles.A mean signal threshold was applied for each row, isolating the region of emissions with sufficient signal for processing.The coefficient of determination (R 2 ), SNR, and velocity uncertainty were each used to filter data, eliminating 7% of data points.A final filtering metric was applied that eliminated data in which the fitted centroids were near the bounds and eliminated an additional 2% of the data points.The centroid fitting bounds corresponded to a difference 300 m s −1 from the mean velocity.This filtering metric was reviewed a posteriori and showed that only data approximately 4σ from the mean velocity were removed, giving the authors confidence that a negligible amount of viable data was eliminated.
The mean velocity was calculated by passing the curated data into equation (3), where instantaneous velocity measurements (V i,m ) were evaluated for the total number of images (N).Equation ( 4) was used to calculate the RMS velocity fluctuation ( V ′2 ).The one-dimensional velocities calculated in camera space were projected in the streamwise direction using the orientation and known inclination of the test article with respect to the tunnel axis.The mean ( Vm ) and RMS velocity fluctuation (V RMS,m ) velocity were reported as the projection of the velocity in the streamwise direction.These calculations are represented as measured values with the subscript 'm', as calibrations are applied to both the mean velocity and RMS velocity fluctuation The random and systematic errors in the instantaneous velocities were propagated into the mean velocity and RMS velocity fluctuation via standard error propagation as shown in equations ( 5)- (7).The prescript δ is used to denote uncertainty in a measured or derived quantity.Additional uncertainty contributions were included due to uncertainty in the beam pointing angle and flow inclination angle to represent the uncertainty in the projection from camera space to the captured velocity projection.The uncertainty quantified up until this point includes contributions from centroid finding, timing, image scale, beam pointing angle, and flow inclination angle

Synthetic data
While emission decay is already known to impact the mean velocity of FLEET measurements [18,22], the impact of random measurement error on the RMS velocity fluctuation is not as well documented.Several assumptions about the flow field and characteristic of the measurement error were made to quantify the impact of measurement error.Real flow fluctuations were assumed to follow a normal distribution of instantaneous velocities about a central mean velocity as shown in figure 9(a).The measurement error was also represented by a normal probability distribution as shown in figure 9(b), with the width of that distribution dependent on the SNR and camera system.Random error is believed to be approximately normal after analysis of a probability distribution of measured instantaneous FLEET velocities in the freestream of the ACE tunnel, where random error is large relative real flow fluctuations.In these conditions it was observed that the distribution of errors appears nearly Gaussian with a slightly greater kertosis observed by heavy tails.By assuming both the real flow fluctuations and error are normal distributions and uncorrelated, the two distributions can assumed to be added in quadrature.Real or simulated measurements with no physical flow fluctuations result in the measured RMS fluctuating velocity representing exclusively measurement error.Synthetic data was generated to imitate captured FLEET emissions with known mean velocity and no fluctuating velocity to permit direct analysis of the resulting mean and RMS velocity fluctuation errors.This model imitated  8) which represents a Gaussian emission in a two-dimensional camera space at a given time, with amplitude (A) modeled by equation ( 9) and centroid location modeled using the spanwise velocity profile in equation (10).In equation ( 9), τ represents the 1/e decay constant associated with FLEET emission in ACE.An arbitrary streamwise position of the laser within the image is provided by µ 0 .This modeling approach is supported by previous fitting efforts that have shown a double-Gaussian approach to FLEET velocimetry to be accurate [15,16,38].A one-dimensional fluid diffusion model was used to represent the diffusion of the FLEET emission, which was fit at various time delays to identify a line width as a function of time σ(t).A rigid sphere model for pure nitrogen self-diffusion was used as the estimate for emission diffusion.This process increased the width of FLEET emission at longer time delays This displacing ideal Gaussian emission shape is then timeintegrated using equation (11).The times for integration, t 0 and t f are set to match the initial and final time of a single intensifier exposure, with subsequent exposures added in summation.The final intensity profile is shown in figure 10(a), with the streamwise and spanwise directions indicated by variables x and y respectively.The final step in the synthetic data generation process was the addition of noise which was essential to replicate the random measurement error observed when processing the real FLEET images.A synthetic binary map was generated that suppresses a portion of the ideal synthetic emissions, between 25%-75% of pixels depending on the SNR of emissions in that row.The binary mapping feature was used to replicate what is believed to be an artifact in images as the FLEET signal approaches the detection threshold of the intensifier system as observed in figures 5 and 6.Binary mapping was performed using input from experimental FLEET results outside of the boundary layer, namely the spanwise locations furthest from the surface and the upper-region of the wall-normal results.By replicating the noise pattern and SNR in this region, where inherent flow fluctuations are minimal, the final noise binary map was tuned to this data set.The amplitude of emissions was normalized using the binary map to ensure that the timeaveraged emissions were not altered due to the suppression of individual pixels.A Poisson distribution was used on the scaled synthetic data to represent shot noise before the emissions pass through a hypothetical intensifier unit.The data was rescaled and passed through a Gaussian blurring function to replicate the camera system imaging the intensifier unit.Beam focusing was replicated using a spanwise scaling factor on the synthetic data.Figure 10(b) shows a synthetic image with noise generated to match a captured FLEET data set.
Synthetic images similar to figure 10(b) were generated for each FLEET measurement.Each image set was processed using the same program as for the original FLEET images, obtaining synthetic mean and RMS velocity fluctuation.

Application of synthetic data
To develop equations that quantify the impact of error, random and systematic error terms were modeled as factors impacting the displaced centroid location.As previously discussed, the displaced centroid had a lower SNR and longer gate duration than the initial fit centroid, as well as was not fit as a line, all causing this centroid to be the dominant source of both random and systematic error.For this reason the random and systematic error in µ 1 is neglected in future calculations.The measured centroid of the displaced gate was modeled as the summation of the real tagged molecule location (µ i,2 ), systematic error (µ i,2,err (τ )), and random error (µ ′ i,2,err (SNR)) as shown in equation (12).This definition of the centroid was plugged into equation ( 2) to produce equation ( 13), using the Reynolds decomposition to separate mean and fluctuating velocity Equation (13) shows the buildup of the four significant contributors to the measured FLEET velocity: the real mean ( V) and fluctuating (V ′ i ) velocity of the flow field, the systematic error in velocity due to emission decay ( Verr (τ )), and the random error in velocity due to measurement error due to the SNR (V ′ i,err (SNR)).The systematic error is due to emission skewing caused by emission decay (τ ), which has been documented to be significant when the decay time of emissions is on the order of the IRO exposure [18,21].The random error in velocity, sometimes called imprecision, has been shown to vary as a function of the SNR [21,22].It is hypothesized that in the ACE tunnel, Verr (τ ) and V ′ i,err (SNR) are especially substantial due to the long second-gate exposure relative the decay-time of emissions, and because of the low SNR.
The systematic error in the mean velocity was obtained by fitting the displaced gate from the ideal synthetic image, such as in figure 10(a), with a Gaussian distribution and documenting the error in the velocity caused by emission decay.Figure 11 shows the process of identifying µ i,2,err for a single input decay constant.Emission strength was significantly skewed across the IRO gate, resulting in centroids fitted nearer to the initial lasing location because of decaying emission intensity.The error in the centroid prediction is then calculated as Verr (τ ).Equation ( 14) shows how this identified error in the mean velocity can then be used to calibrate the mean velocity from experimental FLEET results.An example of the mean velocity correction is shown in figure 12(b), next to the decay constant in figure 12(a) The difference between the physical midpoint of the displaced gate and the fitted centroid was generally on the order of two pixels, which translated to Verr (τ ) ≃ 25 m s −1 .The large impact of emission decay on measurements, compared to other FLEET measurements, was because the displaced gate had a long exposure time (500 ns) relative to the emission decay time (1/e ≃ 400 ns) of FLEET emissions in the low-pressure air in the ACE tunnel [18].The decay constant was calculated on a per-image basis to be constant throughout the spanwise campaign, while a small variation in the decay time was observed for measurements made through a boundary layer in the wallnormal campaign.A calibration value, or curve (as a function of the decay constant) in the case of the wall-normal measurement, was obtained for the measured mean velocity.
The random error in the measured velocity was obtained by fitting the RMS velocity fluctuation from the synthetic data as a single-exponential function of the SNR (V RMS,err (SNR)) as shown in figure 13(a).In this figure the spanwise resolution of the measurement is exploited to visualize the relationship between measured RMS velocity fluctuation and the SNR.In this plot the V RMS,err represents the precision floor of the measurement.This fit was then subtracted in quadrature from the measured RMS velocity fluctuation as shown in equation (15).Equation (16) shows the relationship between the imprecision measured as RMS velocity fluctuation and single-shot measurement error from equation (13).Figure 13(c) shows the RMS velocity fluctuation before and after calibration, with figure 13(b) showing the SNR over that same span.From figure 13(c) it is clear that the calibration reduced the dependence of the fluctuation on the SNR over the span.The uncertainty in the fit to the measurement imprecision was propagated into the uncertainty in the real RMS velocity fluctuation

Results
This section discusses the velocimetry results obtained from experiments in the ACE tunnel for the spanwise and wall-normal campaigns.Section 4.1 discusses the velocimetry results of the spanwise test campaign before and after the implementation of the calibration curves for mean velocity

Calibration of FLEET results
The FLEET images from 20 unique runs specified in table 3 were processed to calculate the mean velocity and RMS velocity fluctuation and associated 95% confidence intervals for the uncertainties considered in this campaign.The steady-state tunnel run duration for the spanwise tests were approximately 20 s, while the run duration for the wall-normal measurement was approximately 10 s, resulting in 10-20 thousand images processed per run.Diagnostic locations were measured relative to the trailing edge of the tripping array and normal to the surface of the test article.The spanwise distances used for velocity plots were normalized by the trip scale shown in figure 14.The FLEET results are compared to similar measurements before and after calibration to show the need for calibration as well as to show the change in results due to calibration.Table 4 is a summary of the calibration results.
The uncorrected mean velocity was compared against the freestream tunnel velocity.The ACE tunnel has a dataacquisition (DAQ) system that recorded stagnation pressure in the tunnel settling chamber using a pitot probe, freestream pressure using a pressure tap in the nozzle, and stagnation temperature using a thermocouple in the settling chamber [25][26][27].
The assumption of isentropic flow permitted the calculation of the freestream Mach number and velocity behind the shock produced by the leading edge of the wedge model.Uncertainty in the measured ACE DAQ freestream velocity was estimated to be 0.39% by Buen et al [29], however, stagnation chamber pressure varied slightly over the run which caused freestream velocity variation less than 1% of the mean freestream velocity over the course of the steady-state portion of the run.
The FLEET data collected at the 130 and 255 mm downstream locations, and 12 mm normal to the plate, best approximate the freestream velocity above the boundary layer.Previous testing with this model has provided confidence that these measurement locations lie outside the boundary layer [29,31].Tunnel velocity reported by the DAQ was 857 m s −1 was compared to the average of the uncorrected FLEET from the two measurements in the freestream which was predicted to be only 829.5 ± 8.8 m s −1 .The average of uncorrected RMS velocity fluctuation in the freestream was measured with FLEET to be 55.3 ± 4.3 m s −1 .However, the tunnel freestream velocity fluctuations were believed to be more accurately measured using VENOM at around 8.7 m s −1 (1% of the freestream velocity) [31].The error in the FLEET measurements was attributed to the aforementioned systematic errors caused by emission decay and measurement imprecision.The magnitude of these errors motivated the adoption of the calibration curves defined in equations ( 14) and (15).
FLEET emissions were fit to find the τ to vary between 450 ns in the boundary layer and 350 ns in the freestream.The calibration curve for mean velocity was obtained using synthetic data as described in section 3.5, which provided a normalized magnitude of calibration of 2%-4%.The FLEET results for RMS of velocity uncertainty were similarly calibrated using equation (15).The calibration curve V RMS,err (SNR) was generally on the order of 5%-8% of the freestream velocity (40-60 m s −1 ).In some FLEET measurements, increases in measured fluctuations velocity near the edges of the measurement region could not be attributed to imprecision and were not accounted for in the RMS fluctuation correction.It is believed that a minimum SNR (of around 3.5-4 using the definition of SNR provided) is required to calculate RMS velocity fluctuation, which was not achieved for the entire span of a small subset of the data.
The calibrated FLEET data was compared against the ACE DAQ and previous VENOM velocimetry conducted with the same test article to quantify the validity of the mean velocity and RMS velocity fluctuation calibration.Table 4 shows a summary of the same comparison.Figure 15 shows postcalibration freestream FLEET measurements had less than 1% error compared with the ACE DAQ system.This provided confidence in the formulation and application of Verr (τ ).
The FLEET results were then compared against spanwise VENOM results in ACE collected with the same test article and tunnel conditions [31], highlighted in table 4. Freestream velocity fluctuations were measured using VENOM 12 mm above the wedge test article and 380 mm downstream the tripping array to be approximately 1% with a mean velocity estimated to be 825 ± 25 m s −1 .A 1% magnitude of freestream velocity fluctuations was consistent with previous studies in ACE [27].Averaging the two calibrated FLEET measurements that best estimate freestream conditions resulted in a mean velocity of 862.2 ± 12.2 m s −1 and a velocity fluctuation of 1.9 ± 1.5%.A single spanwise FLEET measurement, at location of 53 mm downstream the tripping array and normal height of 3 mm, was compared to a VENOM measurement, at a downstream location of 55 mm at approximately same height.The lower and upper bounds for the mean velocity and RMS velocity fluctuation are provided, as the boundary layer shows substantial non-uniformities due to the trip elements.The calibrated FLEET shows moderate agreement with the VENOM results, with the difference in the lower-bound for mean velocity attributed to insufficient spatial resolution in the VENOM and perhaps slightly different diagnostic heights.At a distance 340 mm downstream of the trips and a normal height near 3 mm above the surface, VENOM measured a mean velocity of 637 m s −1 with velocity fluctuations 10% of the mean velocity [31].FLEET results were linearly interpolated between the 255 and 380 mm locations to match the same location as VENOM, which resulted in a mean velocity of 640.2 ± 9.4 m s −1 and a velocity fluctuation of 9.6 ± 1.7%.This was a close agreement given the spatial interpolation and slight ACE tunnel run condition differences between the measurement sets.These comparisons show that the calibration of FLEET results was moderately successful, improving the accuracy of mean and RMS velocity fluctuation measurements in the freestream and boundary layer.

Quantifying the transition to turbulence in the boundary layer
With the accuracy of results improved through synthetic calibration data, the transition to turbulence in the boundary layer was documented.Figure 16(a), a visual representation of table 3, shows the diagnostic locations at which mean velocity and RMS velocity fluctuation were measured.Figures 16(b) and (c) show the mean and RMS velocity fluctuation respectively for all locations at a normal height of 3 mm above the surface of the wedge test article.
The mean velocity and RMS velocity fluctuation were measured with spanwise uncertainty of approximately 1/2 mm, while streamwise location uncertainty was 1 mm.The mean velocity at 21.5 and 53 mm in figure 16(b) show local minimums behind that were attributed to the flow deceleration in the wake behind the tripping array, while the local minimum between the tripping elements was attributed to counter-rotating vortex pairs generated by the array.Local maximums were observed in the RMS velocity fluctuation in figure 16(c) for the 21.5 and 53 mm data near the sides of each tripping element (±0.2) which was attributed to instabilities in the generation of the vortex pair.The strong spanwise variability observed as far downstream as 53 mm was substantially reduced by the later measurement locations.The increased spanwise consistency in the mean velocity and RMS velocity fluctuation at station 130 mm indicates that the flow was transitioning to turbulence.The downstream stations at 255 mm and 380 mm do not have substantial spanwise variation and were thus considered either highly transitional or fully turbulent flows.
The mean velocity and RMS velocity fluctuation at the 53, 130, and 380 mm downstream measurement locations are shown in figures 17(a)-18(c), wherein the results were visualized using linear interpolation between the measurement locations shown by the dotted lines.Figure 17(a) shows the flow deceleration in the shaded region behind the tripping array that was later washed out by the downstream stations.Figure 18(a) shows two local maximums in the RMS velocity fluctuation at the sides of a turbulence-inducing trip element.These local maximums were believed to be the result of a counter-rotating vortex pair observed behind tripping elements in similar DNS simulations [35].The results became substantially more spanwise-consistent at the downstream locations, indicating transitioning flow after 130 mm downstream of the trips.
In figure 18(a), the local increases in the normalized RMS velocity fluctuation at near ±0.4 normalized spanwise distance is believed to be due to measurement error rather than real fluctuations in the flow field.It was observed that the defocusing of the femtosecond laser filament caused a decrease in the SNR ratio that translated into increased random error.This additional random error resulted in a higher measured RMS velocity fluctuation that could not be easily eliminated using synthetic data.

Wall-normal FLEET velocimetry
The wall-normal FLEET velocity results were calibrated using synthetic data similar to the spanwise campaign.Unlike in the spanwise test campaign, the decay constant was observed to change as a function of height, requiring a variable mean velocity calibration.Wall-normal FLEET mean velocity and RMS velocity fluctuation with 95% confidence intervals (CI) are compared against a RANS CFD simulation in figure 19.
A RANS CFD simulation was generated to compare with the FLEET dataset to set up the framework for future CFD validation efforts.A CFD unstructured, finite-volume flow solver using the Spalart-Alarmas turbulence model was used to generate the simulation.A uniform inflow condition was provided to the test section, which neglected the transition to turbulence provided by the trips.The wall condition at the test article was simulated as adiabatic, which was in line with previous simulations of the ACE tunnel.This simulation serves to provide a fully-developed turbulent boundary layer with which to compare the FLEET measurements of the actual flow field.The generation of the model and the reasoning behind these assumptions are detailed by Pehrson et al [23].
The wall-normal FLEET configuration recorded the minimum mean velocity to be 48 m s −1 at a height of 12 micrometers.Camera and tunnel oscillations during the run caused a vertical uncertainty in the measurement location of 0.1 mm.The wall-normal FLEET configuration resulted in a freestream mean velocity of 870.5 ± 11.4 m s −1 , which was within 1% relative error of both the freestream measured from the CFD simulation and the ACE DAQ.The mean velocity below 7 mm was substantially lower than the mean velocity predicted by the CFD simulation.The lower velocity was found to be consistent throughout the duration of the tunnel run, and thus was not an artifact of tunnel startup or shutdown transients.After testing, a forward-facing step present between the baseplate and the beam-port insert was measured to have a height of 200 µm.This step may have caused a Mach wave that intersected the tagged FLEET molecules.A second theory considered, but ultimately dismissed, was that a counterrotating vortex pair maintained coherence to the measurement location 137.5 mm behind the tripping array where it was captured in the mean velocity profile.Later measurement performed on flat plate models in the ACE tunnel using wallnormal FLEET showed no evidence of a counter-rotating vortex pair at similar downstream locations from the same tripping array [23,24].
The wall-normal FLEET profile of the RMS velocity fluctuation is shown in its entirety in figure 19(red).The measured fluctuation below 0.75 mm above the surface of the test article dramatically increased which was attributed to overlapping emissions from the initial and displaced gates.The fitting algorithm was capable of fitting and suppressing timeaveraged emissions, but introduced additional random error in centroid fitting near the wall.The measured fluctuation above 8 mm was erroneous, as the freestream tunnel fluctuations are on the order of 1% [25,27,31].The increase in measured fluctuation was because the FLEET beam defocused further from the wall, and the emissions decayed faster at freestream conditions, both resulting in a much lower SNR.It was observed that the model for random error lost applicability for SNR below 3.5 because imprecision did not follow the single-exponential model.Between the heights of 0.75 and 8 mm, where the RMS velocity was thought to be reliable, a local maximum was observed in the RMS velocity fluctuation velocity around a height of 1.5 mm.

Summary and conclusions
In conclusion, FLEET velocimetry was conducted for the first documented time in the Texas A&M University ACE tunnel.FLEET was shown to provide accurate results for mean velocity and RMS velocity fluctuation in a complex flow field in a tripped boundary layer in ACE despite the working fluid of air at low density.Tunnel optical access permitted 20 spanwise testing locations.A preliminary wall-normal diagnostic was also performed.Image resolution is sufficient to capture the flow phenomena behind a series of turbulence-inducing trips.Superimposed IRO burst gates were required on a single camera image because the total FLEET signal lifetime (2.5-3.5 µs) was shorter than the minimum inter-frame delay of the imaging system.
Spanwise diagnostics were limited by beam width at the sides of the test article so all spanwise diagnostics were at least 1.5 mm above the plate.The wall-normal diagnostic orientation permitted diagnostics within just 10's of µm above the surface of the test article.The working fluid of air at low pressure in the ACE tunnel resulted in low FLEET signal with a short lifetime.An image intensifier was used to superimpose two gates in each image.In the wall-normal orientation, the superimposed emissions overlapped below 0.75 mm from the surface due to low velocity.These overlapping emissions dramatically increased random error in measurements made in this region that could not be accounted for in error-modeling.Wall-normal diagnostics were complicated by thermal expansion during tunnel preheat and by tunnel vibrations.The random error modeling used to improve the RMS velocity fluctuation velocity appeared successful by comparing results in the freestream and against VENOM boundary layer profiles.
The transition point in the boundary layer behind the set of turbulence-inducing trips was identified.Wake effects dominate up to the 53 mm downstream location, while spanwiseconsistent flow was observed after the 130 mm downstream location.The point at which the flow begins to transition to turbulence behind the tripping array is believed to lie between the 53 mm and 130 mm locations.No significant difference was noted in results taken downstream of the 130 mm location, so no precise determination is given for the downstream point at which the flow is fully turbulent.A strict minimum beam height limits data captured near the model's surface in the spanwise measurement campaign, so only the outer layer of the boundary layer is observed.Wall-normal FLEET is performed 138 mm downstream of the tripping array which shows an anomalous mean velocity profile that is hypothesized to be caused by a shock originating from a 200 µm forward-facing step on the surface of the model.Wall-normal diagnostics provided mean and RMS velocity fluctuation results into the viscous sub-layer, but only the results for mean velocity are believed accurate below 0.75 mm.
Hypersonic FLEET diagnostics will remain relevant in the future for velocimetry in complex unseeded flow fields.The spatial resolution, low uncertainties, and relatively simple implementation of FLEET secures its place as an essential tool for velocimetry.The work presented here serves to prove FLEET as a viable tool to measure mean and RMS velocity fluctuation in hypersonic tunnels with a working fluid of air at low pressure.This work also expands on the wallnormal diagnostic technique to make near-surface measurements without significant light scattering.The random error modeling employed for diagnostics in the ACE tunnel can be applied to other tunnels, especially to improve measurements of RMS velocity fluctuation.In future tests, FLEET calibration could be performed by taking measurement in the freestream of a hypersonic tunnel to quantify measurement uncertainty without the need for synthetic data.The error modeling and measurement uncertainty quantification represent essential steps towards industry-adoption of FLEET velocimetry.

Figure 1 .
Figure 1.Schematic of ACE tunnel flow path.

Figure 2 .
Figure 2. CAD models of test articles with measurement axes.(a) 2.75 • half-angle wedge test article.(b) Flat plate test article.

Figure 6 .
Figure 6.Single-shot (left) and 1000-image time-averaged (right) FLEET emissions for the wall-normal measurement campaign.

Figure 7 .
Figure 7. Single row of spanwise data taken at the center of the span from figure 5. Equation (1) applied to the data to obtain fit.(a) Time-averaged data and (b) single-shot data.

Figure 8 .
Figure 8. Single row of wall-normal data taken 5 mm above the surface in figure 6. Equation (1) applied to the data to obtain fit.(a) Time-averaged data and (b) single-shot data.

Figure 9 .
Figure 9. Physical velocity and random error in measurements.Variable notation adopted from equation (13), although the error in the mean velocity was neglected from this visualization for simplicity.(a) Probability distribution of the physical velocity around a central mean velocity.(b) Probability distribution of the expected non-physical velocity caused by random measurement error.

Figure 10 .
Figure 10.Synthetic images that replicate figure 5. (a) Ideal synthetic image.(b) Single-shot synthetic image with noise applied.

Figure 11 .
Figure 11.Single gaussian fit to find the systematic error in mean velocity.Variable notation taken from equation (12).

Figure 12 .
Figure 12.Calibrating the mean velocity for FLEET measurement taken above the boundary layer in the spanwise orientation.(a) Spanwise-average of the calculated decay constant.(b) The measured and corrected mean velocity.

Figure 13 .
Figure 13.RMS velocity fluctuation calibration for one measurement.Calibration performed as a function of SNR and subsequently visualized across the measurement span.Data taken from a measurement in the upper boundary layer.(a) Comparison of the measured RMS velocity fluctuation with the synthetic RMS velocity fluctuation.Equation (15) used to calibrate RMS velocity fluctuation to account for random error.(b) SNR over the span.(c) Measured and corrected RMS velocity fluctuation over the span.

Figure 16 .
Figure 16.Velocimetry at 5 downstream locations at 3 mm above the test article.(a) All diagnostic locations.(b) Mean velocity.(c) RMS of velocity fluctuations.

Figure 19 .
Figure 19.Perpendicular boundary layer profile 137.5 mm behind the trip array.

Table 1 .
ACE tunnel run conditions.

Table 2 .
Image intensifier settings from each test configuration.Bracketed values represent a sequential list of gates and delays.

Table 4 .
Comparison between FLEET, VENOM, and the ACE DAQ.Spatially interpolated values in the boundary layer indicated with an asterisk.