Unseeded Velocimetry in Nitrogen for High-Pressure, Cryogenic Wind Tunnels, Part 1: Femtosecond-Laser Tagging

Abstract

Femtosecond laser electronic excitation tagging (FLEET) velocimetry is characterized for the first time at high-pressure, low-temperature conditions. FLEET signal intensity and signal lifetime data are examined for their thermodynamic dependences; temperatures range from 89 K to 275 K while pressures are varied from 85 kPa to 400 kPa. The FLEET signal intensity is found to scale linearly with the flow density. An inverse density dependence is observed in the FLEET signal lifetime data, with little independent sensitivity to the other thermodynamic conditions apparent. FLEET velocimetry is demonstrated in the NASA Langley 0.3-m Transonic Cryogenic Tunnel. Velocity measurements are made over the entire operational envelope: Mach numbers from 0.2 to 0.75, total (stagnation) temperatures from 100 K to 280 K, and total pressures from 100 kPa to 400 kPa. The velocity measurement accuracy is assessed over this domain of conditions. Measurement errors below 1.15 percent are typical, with slightly decreasing accuracy as temperatures are decreased. Assessment of the measurement precision finds a zero-velocity precision of 0.4 m/s. The precision is observed to have a weak temperature dependence as well, likely a result of the shorter lifetimes experienced at higher densities. The velocity dynamic range is found to have a nominal value of 650. Finally the spatial resolution of the measurements is found to be a dominated by the physical size of the FLEET signal and advective motion. The transverse spatial resolution is found to be 1 mm, while the streamwise spatial resolution is dependent on velocity with a minimum of 2 mm and a maximum of 3.3 mm.

1. Introduction

Transonic cryogenic wind tunnels (TCTs), and high-pressure, cryogenic wind tunnels more broadly, are an important class of ground-test facility. Such wind tunnels possess the ability to operate at flight-accurate Reynolds numbers, enabling the simulation of aerodynamic effects for the commercial design process, risk reduction analyses, and experimental research.[1] For example, the National Transonic Facility located at NASA Langley Research Center (or LaRC) was able to provide integrated force and moment measurements for a scaled Boeing 777–200 [2] and regularly hosts researchers testing experimental equipment and diagnostics. Such facilities typically achieve high Reynolds numbers by operating at high pressures and low (near cryogenic) temperatures in pure nitrogen (N₂) environments. Operating in this manner increases the flow density and lowers the dynamic viscosity of the operating gas in comparison to traditional wind tunnels, greatly increasing the operating Reynolds number of the facility.[3] Moreover, the flow temperature can typically be controlled independently from both the pressure and Mach number, meaning that the effects of Mach and Reynolds numbers on relevant aerodynamic coefficients can be studied independently.[4]

While advantageous for their ability to simulate flight-accurate conditions, TCT facilities are challenging environments for experimentation. The large scale and rugged construction necessitated by the extreme operating conditions make them difficult to instrument. Optical access is often limited in such facilities for these same reasons, making the application of modern optical and laser-based flow diagnostics difficult without extensive and costly modification. The high dynamic pressures and cryogenic operating conditions at which these facilities operate also preclude the use of traditional probe-based sensors (e.g. hot-wire anemometers or pitot probes) without the addition of bulky mounting hardware [5] that limit the placement of such devices and make the measurements far more intrusive. TCT facilities are often subject to large-scale vibrations due to their powerful drive systems and are also prone to motion of their test sections due to thermal expansion and contraction. Both of these effects are detrimental to many optical diagnostic techniques that rely upon accurate alignment of optical components or multiple laser beams. The combination of these deleterious effects has limited the scope and quantity of the optical diagnostics that have been applied in TCT facilities to date.

Surface visualization techniques have found varying degrees of success to date in high pressure, cryogenic wind tunnels. Temperature sensitive paint [6,7], Moiré interferometry [8], and photogrammetry [9] have been used successfully for qualitative and quantitative flow and aerodynamic surface measurements, while the pressure sensitive paint technique has only achieved limited qualitative success, [10,11,12] though modern signal-lifetime-based variants have shown more promise. [13] Techniques sensitive to density, such as shadowgraphy, schlieren, and variants [14,15,16] as well as Rayleigh scattering [17,18,19], have shown some utility at qualitative and quantitative off-body measurements. Optical velocimetry techniques, however, have not been able to achieve wide-spread success in TCTs despite a high level of maturity in other classes of standard and large-scale wind tunnel facilities. Particle image velocimetry [20,21,22] and Doppler global velocimetry [4] have found limited application in the European TCT facilities (European Transonic Windtunnel and the DNW-KKK facility). The seeding methods used in these studies, either the introduction of steam-saturated N₂ or oil droplets from a Laskin nozzle, are prohibited in the TCT facilities at NASA LaRC to prevent potential contamination of the flow circuits or erosion of models or tunnel surfaces through abrasion. Applications of optical velocimetry in these facilities have consequently been limited. The only successful optical velocimetry techniques that have been performed at the NASA TCT facilities are laser Doppler velocimetry [23] and laser transit anemometry, [24] both having been performed in the NASA LaRC 0.3-m TCT facility. While these tests proved successful over a limited range of operating conditions, the seeding methods used were inconsistent and unrepeatable.

This series of papers will examine the use of two nitrogen-based, laser-tagging velocimetry techniques for their potential utility at making measurements in high-pressure, cryogenic wind tunnels. In this first part, the femtosecond laser electronic excitation tagging (FLEET) velocimetry technique [25] will be examined in detail. FLEET velocimetry is an optical velocimetry technique in which an ultrafast, high-intensity laser pulse is used to tag molecular nitrogen. By focusing the high-intensity pulse, the gas within the focal region undergoes numerous nonlinear optical effects; specifically important for FLEET are the photo-ionization of nitrogen molecules. Both of these processes are multi-photon in nature, with photo-ionization requiring at least 11 photons (at the typical wavelength of 800 nm). Through both direct photo-dissociation and dissociative electron-ion recombination of nitrogen, a pool of nitrogen atoms is formed within the focal volume. These atoms ultimately recombine into an electronically-excited nitrogen B-state prior to radiative de-excitation. While the lifetime of the fluorescence from the nitrogen B-state is itself short-lived (O(10 ns)), the atomic recombination reaction ultimately leading to the B-state is rate limiting, leading to a persistent emission with lifetimes on the order of 10 μs. This long-lived emission is thought to originate primarily from the first positive system of nitrogen, and is similar in character to the pink afterglow discharge.[26] By tracking the spatial distribution of this long-lived emission through sequential imaging, information about the velocity and displacement of the tagged gas can be ascertained. References 25 and 27 contain more in-depth analyses of the chemical kinetics associated with the FLEET excitation and de-excitation.

FLEET has been evaluated in a number of lab-scale tests to determine both its utility and signal dependences. Work by DeLuca et al. [28] investigated the pressure dependence of FLEET at low (sub-atmospheric to vacuum) pressures and ambient temperatures. In pure nitrogen environments, which exhibited signal intensities nearly 10 times those observed in air, the signal was found to follow a double exponential decay where a fast decrease in signal was found between atmospheric pressure and 66 kPa, while the decrease in signal with pressure approximately followed a slower exponential decay at lower pressures. Work by Edwards et al. [29] sought to use the FLEET signal to measure temperature through spectral fitting of the rotational energy levels. These measurements were subject to a persistent positive bias in the temperature over a temperature range of 300 to 650 K due to the energy deposited by the laser pulse. A correction using this information allowed for more accurate measurements to be made in a heated jet. Measurements by Limbach and Miles [27] utilized Rayleigh scattering and polarimetry to evaluate the gas heating caused by the deposition of energy from femtosecond laser pulses. The temperature rise was found to depend on the amount of energy used in the excitation process but ranged from 280 to 860 K for 320 μJ to 780 μJ of energy, respectively.

Two variants of the FLEET technique have also been tested in lab environments. A high-speed variant of FLEET known as PLEET (picosecond laser electronic excitation and tagging) was reported by Jiang et al. [30]. These tests utilized a high-speed, pulse-burst laser system to generate the plasma and were able to demonstrate velocity measurements at up to 100 kHz. Another variant of the FLEET method, STARFLEET (selective two-photon absorptive resonance FLEET), [31] used a tunable femtosecond-pule laser system to preferentially excite the photo-dissociation pathway of molecular nitrogen. Similar signal levels to the original FLEET were achieved using a small fraction (~1/30^th) of the energy. The temperature rise accompanying the use of STARFLEET was only found to be on the order of 10 K, substantially less than the 100s of K observed with FLEET.

FLEET presents a unique opportunity to fill a technological gap that has left TCT facilities without a reliable velocimetry technique; the FLEET velocimetry technique is well-suited to TCT applications. Firstly, these facilities typically operate on pure N₂, in which FLEET performs optimally. Secondly, FLEET is experimentally simple, requiring a single laser and a single camera system. Thus the technique is resistant to the vibrations, motion of the test section, and limited optical access that would hinder other related molecular-tagging velocimetry (MTV) techniques. Thirdly, FLEET requires no seed gases, such as water vapor [32] or nitric oxide,[33] that could potentially contaminate the flow facilities. Likewise, no oxygen is required to maintain functionality as are required by other unseeded techniques such as APART (air-photolysis and recombination tracking) [34] and RELIEF (Raman excitation and laser-induced electronic fluorescence).[35] Finally, the lifetime of the FLEET signal has been found to be relatively long-lived (10s of μs in duration at ambient conditions [28]), far in excess of some MTV techniques that have lifetimes of 100s of ns or less. Consequently, it could be possible to make velocity measurements with a much broader dynamic range. To date, initial viability tests were performed and reported by the authors. [36] While these initial tests proved successful, the conditions over which they were conducted were limited to elevated temperatures and suffered from poor measurement precision across all conditions.

The current paper reports on significant advancements to the FLEET method to aid in its application to large-scale, high-pressure, and low temperature test facilities such as transonic cryogenic wind tunnels. These tests demonstrate that FLEET velocimetry functions under high-pressure, low-temperature conditions. Data on the thermodynamic dependence of the FLEET signal intensity and signal lifetimes relevant to TCT applications are presented, which have implications to the dynamic range and precision of the velocity measurements. Specifically, the FLEET signal lifetime and intensity are assessed over conditions of 89 K to 275 K and 85 kPa to 400 kPa. Velocity measurements taken in an actual TCT facility across its entire operational envelope are reported. The measurement accuracy is assessed by comparison with a facility data acquisition system (DAS). The measurement precision is also assessed across the entire operational envelope of the facility. Brief analyses of the measurement spatial resolution and velocity dynamic range of the FLEET technique are also conducted. Finally, additional experimental considerations related to the implementation and execution of the FLEET technique within the 0.3-m TCT facility will be discussed, specifically with a focus on recommendations for future experiments. All results are discussed in the context of previous measurements in TCT facilities as well as those observed in other MTV studies.

2. Experimental and Analytical Methods

2.1. Test Facility

All tests were conducted in the NASA Langley 0.3-m Transonic Cryogenic Tunnel (0.3-m TCT), a closed-loop, fan-driven wind tunnel capable of operating at Mach numbers ranging from 0.2 to 0.75. All tests were conducted in nitrogen (N). Additionally, the operational envelope of the tunnel included total (stagnation) pressures spanning from 100 kPa to 400 kPa and total temperatures from 100 K to 280 K when operating with nitrogen. Combinations of these conditions permitted unit Reynolds numbers in the range of 4×10⁶ 1/m to 270×10⁶ 1/m. The test section has cross-section dimensions of 0.33 m × 0.33 m. Optical access to the facility was afforded by two fused silica windows penetrating the plenum and test section. A single circular window (0.2 m diameter) penetrated the outer plenum wall, and a ‘D’-shaped hexagonal window was situated in the wall of the inner test section to allow optical access to the inner test cell. The layout of the test section is depicted in Figure 1.

Figure 1.

Diagram of test section detailing measurement location and coordinate system.

2.2. Laser, Optical, and Data Acquisition Systems

The FLEET measurements utilized a regeneratively-amplified Ti:sapphire laser (Spectra-Physics Solstice) with a center wavelength of 800 nm, bandwidth of 20 nm, and a repetition rate of 1 kHz. Data sets were collected with nominal pulse energies of 1.2 mJ, although about 50 percent of this energy was attenuated through the beam path. The laser system was situated on a platform roughly 3 m above the test section. The beam was directed to the level of the facility with a pair of periscopic mirrors, after which it was directed through the outer plenum window. Within the plenum, the fs-laser beam was routed through an internal periscope, which was situated inside an evacuated pressure vessel (or laser conduit). This modification, similar to a solution proposed in [15], was intended to reduce or eliminate the distortion to the fs-laser beam by the large density fluctuations within the plenum caused by thermal gradients and buoyancy-driven currents.[14,15] Following this periscope, the beam passed through a f = +200-mm spherical lens before entering the test section through the ‘D’-window. The fs laser pulse came to a focus roughly half-way through the test section, 55 mm from the top wall. The measurement location and coordinate system used in these studies can be seen in the detail of Figure 1, while the overall optical and camera setup at the test section is shown in Figure 2.

Figure 2.

Top-view diagram of the laser and camera layout.

The FLEET signal was captured with a high-speed image intensifier (LaVision HS-IRO) lens-coupled to a high-speed CMOS camera (Photron SA-X2, 12-bit pixel depth). Imaging was done through a 135-mm, f/2 objective lens and an optical bandpass filter that transmitted wavelengths between 400 and 775 nm. The magnification at the sensor was approximately 108 μm/px. The FLEET camera system was operated in a triggered burst mode; bursts of 15 images were captured at 200 kHz with 100 such bursts being captured per second. This selection of imaging frequency imposed an inter-frame delay of 5 μs. The first image containing FLEET signal was acquired approximately 70 ns after the laser pulse, while the preceding images were used for background subtraction in post-processing. A total of 11 frames of data were available for each laser pulse. The FLEET camera system was situated perpendicular to the test section and imaged through both the outer plenum window and internal window to view the FLEET signal in a quasi-boresight configuration, where the camera view is nearly parallel to the direction of laser propagation (offset by approximately 30 degrees). Figure 2 details the orientation of the camera system with respect to the test section.

In addition to the camera system, an extensive facility data acquisition system measured the relevant conditions in the tunnel. This system comprised an array of static and total pressure taps and corresponding transducers throughout the facility, as well as thermocouples and strain gauges. All data from this system were read into a network of facility computer systems for processing. Velocities were calculated based on static and total pressure probes, a total temperature probe, and a real-gas equation of state (Beattie-Bridgeman equation). For each FLEET data collection run, a data point from the facility system was collected for use in validation and verification of the velocity measurements in post-processing.

2.3. Analytical Methods

2.3.1. FLEET signal processing.

A sample of the raw FLEET data is shown in Figure 3. The FLEET data take on intensity distributions that are circular to elliptical in shape. The data take this form because of the boresight imaging configuration; a greater degree of elongation corresponds to a larger angle between the laser beam propagation direction and the imaging line of sight. Unlike the FLEET data taken in preliminary tests,[36] which showed a nearly axisymmetric intensity distribution, the FLEET data are much more ragged in appearance and lack radial symmetry.

Figure 3.

Sample FLEET signal and sample of surface fitting quality.

The raw images first underwent a dark-field correction to remove the mean background intensity. The position of the FLEET signal within each image was then precisely located utilizing a custom surface fitting algorithm, the shifted, rotated, generic ellipsoid (SRGE) algorithm.[38] This surface fitting technique fits a generic ellipsoidal function to the data, which allows for polar variations in the intensity distribution not afforded by simple Gaussian or bi-Gaussian fits. [36] The mathematical details of this fitting algorithm can be found in Ref. 38. The output from this processing kernel is a series of coefficients that analytically define the surface.

After running this processing kernel, the coefficients defining the surface are used to map the analytic function onto a fine uniform mesh, typically with a spacing of 0.001 px. This function was then interrogated for four items of information: peak intensity, integrated intensity (sum of all intensity within the image), location of peak intensity, and location of the intensity-weighted centroid. Thus, each image was ultimately reduced to a small number of values for use in later analysis. The two positions extracted from these data are then transformed to physical coordinates through a nonlinear matrix transform computed from dotcard images used in calibration. This overall processing kernel was applied to every image of each burst of data during data reduction.

2.3.2. Velocity evaluation.

Flow velocities were computed for individual image bursts by numerically approximating the trajectory of the FLEET spot to be a linear function of time. Previous efforts used various methods for measuring flow velocities from similar data, including two time-of-flight methods and a polynomial fitting method.[39] While the polynomial fitting method provided an accurate fit to the position data from the present studies, the measured accelerations were found not to be statistically significant in the present data since the data were acquired in the freestream. By assuming a functional form for the displacement to be that of a linear function, the displacement can be expressed as:

$$s_{i,1\to j}(t)=u_{i,j}t+s_0$$ (1)

The s in Equation 1 denotes the displacement of the FLEET signal, the subscript i refers to the directional index (x or y), and the subscript 1 → j indicates that the displacement corresponds to all images from frame 1 to frame j within a given burst of images. To evaluate the velocities, the initial location of the FLEET signal in the image burst being evaluated was subtracted from all remaining data in the burst. The parameters u_i,j, (velocity of interest) and s₀ are then found using a least-squares fitting algorithm, once each for the x- and y-directions. A small fraction of data was rejected prior to computing velocities; notably, FLEET data that exhibited an insufficient fit quality after the processing kernel (R² < 0.7) or insufficient signal-to-noise ratio (SNR < 5) were removed. The number of frames used in the individual velocity calculations depended on the quality of the data under consideration. To ensure unbiased and sufficiently converged velocity statistics, a minimum of 500 valid bursts of data had to possess images up to the number of frames used. For example, consider a data set consisting of 1000 image bursts. If the data were such that all 1000 image bursts had frames from one through 11 valid, then 11 frames would be considered in the individual velocity calculations for that data set. On the other hand, if the set were of lower quality and very few images containing viable data were available in the 11^th frame, then the 10^th frame would be checked for validity. This procedure would then be repeated until at least 500 valid burst containing all frames from 1 through j were found, and that many image frames would be used in the individual velocity calculations. After the fitting procedure, the R² value was calculated for each velocity calculation. For each data set, the mean and standard deviation of the velocities were calculated. Samples with R² values below 0.95 were excluded from these calculations, which represented less than 0.25 percent of all data.

2.3.3. Signal intensity and lifetime evaluation.

The intensity information extracted during the surface-fitting procedure (Section 2.3.1) allowed the construction of time series of FLEET signal intensities. One such trace is depicted in Figure 4, collected with a sampling rate of 400 kHz (twice the experimental sampling rate) for demonstrative purposes. It was found that the optimum function for fitting the decay of this data was a tri-exponential function; both single and bi-exponential functions failed to capture the long-term behavior of the signal decay. The resulting fit is also shown in Figure 4. While the lifetimes extracted in this manner could be analyzed directly, it was found that they were very sensitive to experimental noise. To simplify the analysis, an empirical approach was taken to model the lifetimes. Each signal decay curve was first fit to a tri-exponential function to capture its total decay behavior. From this analytical fit, two different values were extracted: the time it took the signal to fall to 1/e of its initial value (henceforth called τ₁), and the time it took to fall to 1/e² of its original value (τ₂). Graphical representations of these parameters are shown in Figure 4. These two empirical lifetimes were then used in all the analysis that follows. While this approach was originally taken to avoid the complexities of modeling the sheer number of parameters involved in the fitting procedure, it also proved to be more resistant to experimental noise.

Figure 4.

Sample time series of FLEET signal intensity showing tri-exponential fit and empirical lifetimes.

3. Results

3.1. Thermodynamic Dependences of FLEET signal intensity and lifetime

The thermodynamic dependences of the FLEET signal are crucial in understanding how the technique will perform at conditions that have never been interrogated. That is, no currently available information describes how well FLEET velocimetry will perform in either a high-pressure or a low-temperature environment. Thus it was necessary to assess how the FLEET signal responded to differing thermodynamic conditions. To advance the technique and understand its behavior at these conditions, the thermodynamic dependences of both the FLEET signal intensity and lifetime have been characterized at high-pressure, low-temperature conditions.

3.1.1. FLEET signal intensity.

The response of the FLEET signal to reduced pressure in air and molecular nitrogen has been studied in some detail by DeLuca et al.[28] These studies, which were conducted at ambient temperatures, did not exhibit a monotonic trend with respect to the pressure. Rather, the signal was found to follow two distinct behavioral trends, depending on the pressure regime. At the higher end of their pressure domain (approximately 100 kPa), the FLEET signal intensity was found to be proportional to pressure. At intermediate pressures (1–10 kPa), the gas behaved very differently depending on its composition. In air, the signal leveled off and was found to be largely insensitive to pressure. In N₂, the signal began to increase slightly as pressured decreased in this regime. At still lower pressures, the signal rapidly climbed and leveled off in air, while in nitrogen, the FLEET signal slowly decreased as the pressure was reduced. Given the complex kinetics involved in the generation and sustenance of the FLEET signal, attempting to extrapolate these trends to the high-pressure, high-density conditions present in TCT-type facilities is likely to yield erroneous results. Thus, there is merit in studying the response of the FLEET signal intensity in the desired regime.

The initial FLEET signal intensities are plotted as functions of pressure, temperature, and density in Figure 5. These data were collected 70 to 80 ns after the laser pulse had occurred, and approximately 2000 such shots were used in computing the statistics for each point. Figure 5a shows the dependence of the FLEET signal intensity on the pressure. The data were collected at temperatures from 145 K to 275 K and pressures from 85 kPa to 400 kPa. A trend of increasing intensity with increasing pressure is apparent. Notable vertical spread in the data is observed as well. The data points, which have been color-coded by temperature, indicate that the extent of the spread is dependent on this same parameter. Higher temperatures generally lead to lower signal intensities at the same pressures. The same data have been re-plotted as a function of temperature in Figure 5b. While the data points do not themselves indicate any significant trends, interpretation of the data through the pressure color-coding suggest the same general trend observed in Figure 5a. For a given pressure, increasing temperature amounts to decreased signal intensity; higher pressures also yield higher intensities. The direct proportionality to pressure and inverse dependence on temperature suggest that the signal intensity is largely dependent on the density. Figure 5c confirms this assessment, showing the dependence of the signal intensity on the mass-density of the gas. These data indicate that the FLEET signal intensity is linearly dependent on the density throughout this range of conditions.

Figure 5.

Thermodynamic dependence of the FLEET signal intensity. a) Pressure dependence, b) temperature dependence, and c) density dependence.

It must again be stressed that the FLEET data was collected 70 to 80 ns after the laser pulse. Though the linear dependence on density is suggestive of an elastic scattering phenomenon (e.g. Rayleigh scattering), there was no interference from an optical scattering signal in these images since they were captured after the laser pulse had occurred and only the FLEET signal persisted. It is likely that the time and spectral region over which the data were collected had a strong influence over the observed trends. Acquiring the FLEET data at longer delays (1–2 μs as is typical) will likely yield very poorly defined thermodynamic dependences with respect to the signal intensity; sampling the next closest time in these data (5.07 μs) yields no clear trends with respect to any of the thermodynamic conditions. Consequently, caution should be taken when comparing results with data taken even within the first few microseconds after excitation. Furthermore, the spectral filter used in these studies, which passed light between 400 and 775 nm, blocked both the primary laser band and the short-lived ultraviolet emissions (second positive and first negative bands). Consequently, different trends will likely be observed for data that lack the spectral filtering used in these studies, especially when collected at small delays from the initial excitation. As a final note regarding the data acquisition methodology, the images could not be reliably captured closer in time to the laser pulse because of the overall jitter in the laser system.

The linear dependence on density observed in this section was a relationship between the density inferred by the facility DAS and the observed signal intensity. However, this does not necessarily suggest that the signal intensity scales linearly with the density within the excited volume. Due to the energy deposition that occurs during the excitation process, the temperature within the excited volume increases notably as detailed in Section 1. Accompanying this increase in temperature is a decrease in density, which differs from the density measured by the facility DAS. This distinction is important; since the goal of these studies was to document the performance of the velocimetry at specific tunnel conditions, rather than investigating the physics of the FLEET technique itself, no attempt to correct for this disparity was made.

3.1.2. FLEET signal lifetime.

The thermodynamic dependence of the FLEET signal lifetimes is not well understood; there have been no definitive studies about the behavior of the FLEET signal lifetime and only a few cursory studies. The results from DeLuca et al. [28] have minimal information regarding the time-evolution of the FLEET signal at reduced (sub-atmospheric) pressures. In those studies the lifetime of the FLEET signal appeared to follow similar trends to the signal intensity information reported; a rapid decay in signal lifetime was found above 10 kPa, while the behavior became erratic at reduced pressures. Another study by Michael et al.[37] looked at a single case of signal decay (at STP conditions), which indicated a bi-exponential decay over a time history of 10 μs. Thus, there is not extensive information available regarding the behavior of the FLEET signal lifetime with respect to thermodynamic conditions, with no data currently available for the thermodynamic ranges of interest (90 K to 275 K, 85 kPa to 400 kPa).

As discussed in Section 2.3.3, the signal lifetimes were reduced to two empirical lifetimes to simplify the data analysis. The behaviors of these two lifetimes are plotted against pressure, temperature, and density in Figure 6. The pressure dependence of the two lifetimes, shown in Figures 6a and 6d, indicate that the lifetimes both tend to decrease with increasing pressure. Additionally, the temperature coloration indicates that lower temperatures manifest as shorter signal lifetimes. While the trends are qualitative similar for both τ₁ and τ₂, they do differ quantitatively. The ratio between τ₂ and τ₁ varies between roughly 2 and 3.5 throughout the range of conditions examined in these studies, although there is no well-defined dependence on the thermodynamic state of the gas.

Figure 6.

Thermodynamic dependence of FLEET signal lifetimes. a)-c) pressure, temperature, and density dependence of first lifetime (τ₁) and d)-f) pressure, temperature, and density dependence of second lifetime (τ₂).

The temperature dependence of the lifetimes is shown in Figures 6b and 6e. Consistent with the previous presentation of these data, the lifetimes exhibit a direct dependence on temperature; higher temperatures correspond to longer FLEET signal lifetimes. Additionally, an inverse dependence on pressure is observed. These combined pressure and temperature effects again suggest strong density dependence. Figures 6c and 6f confirm an inverse dependence on density. For modeling purposes, the lifetimes can be expressed in terms of the density using the following relation:

$$\frac{\tau }{{\tau }_{ref}}=C_1{\left(\frac{\rho }{{\rho }_{ref}}+C_2\right)}^{C_3}$$ (2)

The values for the various parameters utilized in Equation 2 are shown in Table 1 for both lifetimes. While purely empirical in nature, the fits do provide some physical insight into the behavior of the FLEET signal lifetime. Perhaps the most obvious observation is that the dependence can be expressed exclusively as a function of density. In a preliminary examination of these data, [38] in which the lifetime data were analyzed by analogy with collisional quenching of fluorescence, it was noted that there was a very weak temperature dependence. After refinements made to the data analysis were incorporated to this model, the temperature dependence previously noted were no longer statistically significant; the data were more accurately represented as a power-law dependence on density. It is difficult to assert the physical significance of these results. As noted in the introduction, the local heating of the gas by the focused femtosecond laser pulse changes the local density significantly from the freestream value. If the temperature rise were to be considered constant, these results would suggest that either the rate at which the dissociated nitrogen atoms recombine scales directly with the density or that the density directly affects the overall rate at which molecular nitrogen is dissociated. However, there is no reason to think that the temperature rise is a constant quantity in this context.

Table 1:

Fit coefficients for lifetime density dependence

	τref [μs]	ρref[kg/m3]	C1	C2	C3
τ1	21.6	1.15	2.42	0.395	−1.57
τ2	69.1	1.15	1.30	0.013	−1.27

3.1.3. FLEET signal intensity and lifetime consistency.

A concern that arose during the preliminary tests with FLEET in the 0.3-m TCT facility concerned the variation of both the signal intensity and signal lifetime with the Mach number or velocity at which the facility operated. Specifically, it was observed that at higher Mach numbers, the signal intensity/lifetime were substantially greater than at lower Mach numbers.[36,39] No physical explanation was found for this trend at the time. Since the extent of this behavior was only discovered after testing had concluded, no examination of the cause could be done. The testing done in this campaign sought explain that phenomenon. To examine the trend more closely, targeted tests were carried out that held the thermodynamic conditions constant but varied the Mach number, thereby eliminating any of the thermodynamic dependences discussed in Sections 3.1.1 and 3.1.2. The results of these studies are presented in Figures 7 and 8. Figure 7, which shows the signal intensity as a function of Mach number, indicates no significant variation in the intensity over the range of Mach numbers tested. Specifically, there is at most a 25 percent variation in the intensity over this range, the trend having no particular dependence on the flow Mach number and lying within the uncertainty at each data point. This null trend is found in the data taken at both pressures. Moreover, the signals taken at two different pressures maintain the linear dependence on density observed in the larger data set; a factor-of-two increase in signal is observed for a doubling of density.

Figure 7.

Signal intensity as a function of Mach number for fixed thermodynamic conditions.

Figure 8.

FLEET signal lifetime as a function of Mach number for fixed thermodynamic conditions. a) 138 kPa and b) 276 kPa.

The signal lifetime data shows a similar lack of trend with Mach number; these data are presented in Figure 8. Figure 8a, which shows the 1/e and 1/e² lifetimes at 138 kPa, indicate little to no variation in the first lifetime; the maximum observed variation lying at approximately 20 percent with no dependence on the Mach number. The second lifetime shows a similar degree of variation, though there does appear to be a longer lifetime at the higher end of the Mach number range (though to a significantly lesser extent than what was observed in the preliminary tests). It is unlikely that this is related to the actual Mach number, however, and is likely related to the lifetime being of the same length as the data recording time. Once the signal exceeds this range, it is partially extrapolated based on the rest of the time history, leading to a larger proportion of longer lifetimes in these data sets. Nonetheless, the overall variation is still within 20 percent, and could be considered constant within the uncertainty of each data point. The data acquired at a higher pressure (Figure 8b) shows virtually no variation in lifetime across the Mach number space; the first and second lifetimes show a maximum deviation around 10 percent with no dependence on the Mach number.

While the outcome of these tests may seem obvious, it was important to establish that the results of the previous tests were not related to the thermodynamic state of the gas. Since both the signal intensity and signal lifetimes showed little to no variation with the Mach number when held at a constant temperature and pressure, this can be stated conclusively. Regarding the previous tests, it is likely that the change in lifetime was instead related to the formation of the FLEET signal itself. While it is not possible to know exactly what was amiss in the previous testing campaign, it is likely that a gross misalignment of the optics was responsible. The 0.3-m TCT test section, which floats relative to the optical system, is known to shift large distances (millimeters) with repeated cycling of the Mach number or the pressure. Unaware of this at the time, the laser beam was likely at the edge of an optic or aperture in the optical system at the start of testing, and as the conditions were changed would repeatedly become well or poorly aligned. The result would be a dramatic gain or loss in the exciting laser energy, which has a substantial influence on the signal intensity and lifetime when near the creation threshold (the lower limit of energy required to generate signal). Since the optical system used in the present tests was set up to accommodate such changes in alignment, no such observations were made.

3.2. Velocity Measurement Accuracy

In order to assess the accuracy of the velocity measurements collected in the 0.3-m TCT facility, the velocities measured through FLEET velocimetry were compared to those calculated by the facility data acquisition system. To make the characterization as comprehensive as possible in the limited testing time, the accuracy was assessed in two separate ways. First, high resolution Mach number scans were conducted at multiple pressures and a total temperature near ambient to characterize the measurement accuracy as a function of velocity. Second, the velocity accuracy was assessed over the full operation range of the tunnel thermodynamic conditions but at a limited number of Mach number conditions to assess the performance as the tunnel operating conditions were varied. To define the aggregate accuracy of the measurements presented, two metrics will be used in the results to follow. The first of these is the standard error (ε), which will be defined as:

$$\epsilon =\frac{{\sum }_{i=1}^n\left|v_i-v_{i,DAS}\right|}{{\sum }_{i=1}^n{v}_{i,DAS}}$$ (3)

When presented as a percentage, the standard error represents the average percent error of all velocity measurements included in the calculation. The other metric is the RMS error (ε_RMS):

$${\epsilon }_{RMS}=\frac{\sqrt{\frac{1}{n}{\sum }_{i=1}^n{\left(v_i-v_{i,DAS}\right)}^2}}{\frac{1}{n}{\sum }_{i=1}^n{v}_{i,DAS}}$$ (4)

This metric represents the aggregate error of all velocity measurements included in the calculation.

A comparison of the measured FLEET velocity and the reference (DAS) velocity measurements over a wide range of velocities are shown in Figure 9 at both 138 and 276 kPa. From visual inspection, the FLEET velocity measurements compare favorably with the data system velocities; individual data points are nearly coincident with the dashed line representing perfect agreement. Furthermore, the scatter in the velocity data is quite small, though this will be discussed in a later section on measurement precision. For the data presented in Figure 9, the standard error was found to be 1.05 percent, while the RMS error was 1.15 percent. These numbers are consistent with previous measurements, which found the accuracy of the FLEET measurements to lie between 0.6 and 2.1 percent. [36]

Figure 9.

Accuracy of FLEET velocity measurements: measured velocities vs reference velocities.

For historical context, the previous velocity measurements made by Gartrell et al. in the 0.3-m TCT facility utilizing LDV (discussed in Section 1) found their velocity error to be typically less than 1 percent.[23] In this context, FLEET velocimetry performs roughly as well as this historical benchmark, although over a broader range of conditions and more consistently. To provide further context, FLEET can be compared to other related techniques. Accuracy figures for molecular tagging velocimetry are not widely reported since it is difficult to obtain a consistent and well-characterized reference measurement. Those assessments that are reported in the literature vary broadly. Velocity measurements by Sijtsema et al. utilizing the APART technique found accuracies ranging from 5 to 13 percent depending on the flow being used to characterize. [40] Lempert et al. assessed the velocity accuracy of acetone MTV measurements applied to supersonic microjets and found it to be approximately 3.5 percent. [41] Recent studies by André et al. compared hydroxyl MTV measurements in a low-speed jet to PIV measurements at the same flow conditions and found that the observed mean velocity error was within 2 percent, while the RMS error was between 0.8 and 1.2 percent.[42] The present measurements thus exhibit accuracies equal to or exceeding related techniques found in the literature without the need for seeding the flow with additional gases or utilizing complicated optical setups.

The second comparison described above is presented in Figure 10, which shows velocity data taken over the full operational envelope of the 0.3-m TCT facility for a limited selection of Mach numbers. Data were collected at nominal Mach numbers of 0.2, 0.5, and 0.75, which are differentiated by symbols in Figure 10. Figure 10a presents the aggregate of all data taken during cryogenic operation, similar to Figure 9. The static temperature at which the run was conducted is indicated by the color scale. As with the constant-condition runs, these data indicate a strong qualitative agreement between the reference velocity and those measured by the FLEET technique. Though barely perceptible, there is a slight positive bias throughout these measurements, which is discussed below. Nonetheless, this assessment indicates a significant leap forward in the demonstrated measurement capabilities of FLEET. The initial viability tests done in the 0.3-m TCT facility [36] were able to make velocity measurements at temperatures above 220 K consistently, but not below this temperature. Thus, these tests represent the first successful demonstration of FLEET at cryogenic conditions.

Figure 10.

Accuracy of FLEET velocity measurements as a function of thermodynamic conditions. a) Comparison of measured velocities with reference velocities, colored by temperature (dashed line indicates perfect agreement) and b) velocity measurement error as a function of both pressure and temperature. Symbol shapes indicate nominal set-point Mach number.

To further analyze these results, the percent error of these data points was assessed as a function of the static temperature and pressure, shown in Figure 10b, where the measurement error is indicated by the color scale. Errors ranging from 0.02 percent up to 3.5 percent are observed. High-pressure and low-temperature operating conditions lead to an apparent increase in the measurement error. The overall standard error for this data set was found to be 1.47 percent, while the RMS error was found to be 1.71 percent, a slight decrease in the overall accuracy found during the constant-condition runs. Several contributing factors are likely responsible for the decreasing accuracy at the more extreme conditions. The test section was subject to both contraction and motion during the cool-down process. Though optical alignment was maintained throughout most of the test matrix by adjusting the laser optical path, it is probable that the angle at which the beam propagated through the test section changed by a few degrees through this process, shifting the location of the FLEET spot closer to the camera. This effect is depicted diagrammatically in Figure 11. High-pressure operation has two additional effects that explain why the deviation is more pronounced. First, an additional shift of the test section accompanying high pressures is observed. Second, high-pressure operation tends to shift the position at which the FLEET signal is generated closer to the focusing lens. It is possible that this second effect is density-dependent, rather than a pressure effect, which would partly explain the why the effect is far more pronounced at the high-pressure condition. Nonlinear focusing effects could also be coming into play. While these explanations are likely, additional effects are also possibly influencing the measurements and or the reference. Evaluation of the imaging system after testing indicated that the magnification only varied by 0.12 percent per millimeter through the depth of field. Since the depth of field was approximately 30 mm and the calibration plane was near the center, it is unlikely that a loss of accuracy exceeding 1.5 percent would be observed without notable blur in the images. Although this will be discussed in greater detail with regards to the measurement precision in Section 3.3, it was found that at high-pressure, low-temperature conditions, the tunnel often contained a dense particulate fog, which intermittently caused the loss of FLEET signal. This fog was the result of the liquid nitrogen injection system and tended to persist if the operating conditions neared the liquid-vapour saturation point. This occurrence could cause two effects that would adversely affect the measurement accuracy. First, the intermittent loss of signal means that the samples which were collected might be biased in some way. For example, pockets of higher-velocity, lower-pressure fluid might allow the fog to dissipate sufficiently to regain signal, which would positively bias the collected velocities. Second, the multi-phase nature of the flow might invalidate the underlying models used in calculating the reference velocity. One such assumption would be that an observed change in enthalpy resulted from a change in velocity, rather than a phase change. The result would be a reference velocity being biased, which would make the measurement error seem larger than it was in reality. Despite the loss in accuracy at the high-pressure, low-temperature conditions, the results throughout the test matrix are still comparable to the accuracy of other MTV techniques as discussed above. Furthermore, measurements were made consistently across the entire operational envelope of the facility, indicating a significant improvement over any previous attempt to perform optical velocimetry in one of the NASA Langley TCT facilities.

Figure 11.

Effect of beam rotation on perceived displacements.

3.3. Velocity Measurement Precision

For this analysis, the measurement precision was taken to be the standard deviation of the ensemble of velocities (σ_u) measured at a particular tunnel condition. This definition makes no attempt at differentiating between natural turbulent fluctuations and precision errors in the velocity measurements. The freestream of this facility is not known to have significant velocity fluctuations. The studies by Gartrell et al. using LDV in the 0.3-m TCT facility found fluctuating velocities to be less than 1 percent across all tested conditions, indicating that the observation of significant velocity fluctuations would likely be the result of the imprecision. [23] Assessing the measurement precision followed a similar tactic to that of the measurement accuracy. First, a battery of tests was performed at ambient temperatures and varied pressures (T = 260 K, P = 138 kPa, 276 kPa). To serve as a reference, a zero-velocity (wind-off) condition was evaluated at each of these thermodynamic states. The wind-off precision was found to be 0.41 m/s and 0.43 m/s at the low- and high-pressure conditions, respectively, indicating little sensitivity to the pressure. The precision measured across the full range of velocities were then compared to this wind-off reference; the comparison is shown in Figure 12 with precision presented as a percentage of the measured velocity. At low Mach numbers (M ≤ 0.4) the measurement precision follows the trend of the wind-off reference. Peak deviations are approximately 0.15 percent and typically favor the high-pressure condition. When Mach 0.4 is exceeded, the measurement precision begins to deviate significantly from the wind-off reference; the deviation grows as the Mach number is increased. These results indicate that the freestream velocity fluctuations in the tunnel have begun exceeding the baseline precision of FLEET velocimetry and have become visible above the precision floor. These results are a drastic improvement over the previous measurements, which indicated a wind-off precision of 3.2 m/s, and the lowest observed measurement of the fluctuating velocity was around 2 percent and exhibited no sensitivity to natural turbulent fluctuations.[36] This drastic improvement in precision is largely an artefact of the data quality and enhanced data processing algorithms. As mentioned above, the LDV studies by Gartrell et al. found velocity standard deviations to lie below 1 percent across the test matrix considered in the same facility, though no sensitivity to Mach number was observed in those studies.[23] These measurements also compare quite favorably to the existing literature regarding MTV-type techniques. Bathel et al. utilized NO velocimetry to study various hypersonic flows. [43] Measurement uncertainties of approximately 3 percent were noted in those studies, which corresponded to 30 m/s. The work by André et al. worked to optimize hydroxyl tagging velocimetry for low-velocity flows. Precisions as low as 0.08 m/s were observed, or about 1.2 percent of the measured velocity. Other optical velocimetry techniques such as filtered Rayleigh scattering [44] and laser induced thermal acoustics [45] exhibit precisions ranging from 1 to 4 percent of measured velocities in lab-scale tests. The FLEET measurements herein presented, though captured in a large-scale ground-test facility, perform at or above the level of precision typical of optical velocimetry techniques.

Figure 12.

Velocity measurement precision as a function of Mach number.

The measurement precision was also assessed over a much broader test matrix like the accuracy previously was. The results of these studies are shown in Figure 13, which detail the measurement precision as a function of the temperature and pressure. Note that the color scale has been made logarithmic to enhance the small differences in precision observed over most of the test matrix. One very apparent trend concerns the effect of temperature on the measurement precision; for a given pressure, decreasing the temperature causes a loss of precision in the velocity measurement. This trend is especially apparent in the horizontal traces at 85 kPa, 120 kPa, 175 kPa, and 270 kPa. Each of these traces represents a fixed Mach number, total pressure condition. It is likely that decreasing signal lifetime is responsible for this change in precision. As the signal lifetime is decreased, the SNR of the data in later frames decreases, leading to a loss of precision in the surface fitting algorithm and subsequently the velocity measurement itself. A similar trend is observed at increased pressures. Another contributing factor is likely the Reynolds number of the facility, which increases both with decreasing temperature and higher pressure. The magnitude of the freestream velocity fluctuations is dependent on the Reynolds number at which the facility operates. Thus, part of the larger precision measurement that is observed is likely the result of naturally higher fluctuating velocities within the facility.

Figure 13.

Precision of FLEET velocity measurements as a function of thermodynamic conditions: velocity measurement precision as a function of both pressure and temperature. Symbol shapes indicate nominal set-point Mach number.

A final note regards the data set taken at 89 K, 285 kPa, and to a lesser extent the data set taken at 117 K, 275 kPa. Numerically, the precisions of these data sets were many times the value as the next closest points. This anomalous behavior likely resulted from operating the facility too close to the liquid-vapour saturation point, represented in Figure 13 by the dashed line. In this instance, a dense particulate fog was visible throughout the test section, resulting from either the incomplete evaporation of the injected liquid nitrogen or a secondary condensation resulting from local pockets of gas closer to or above the saturation point within the facility. In the case of the second point mentioned above, a similar fog was present (but to a lesser extent) because the data acquisition took place before the complete evaporation of the injected liquid nitrogen had occurred. In both instances, this optically dense medium inhibited the proper focusing of the fs-laser beam and thus the generation of the FLEET signal. While not representative of standard TCT operation, these results indicate that FLEET is still capable of making measurements even in suboptimal conditions. Finally, it should be noted that throughout the conditions described in this section, the level of velocity precision was comparable or superior to the precision assessments of other methods described above, indicating the robustness of FLEET velocimetry.

3.4. Velocity Dynamic Range

The velocity dynamic range is defined as the ratio of the largest resolvable velocity to that of the smallest resolvable velocity. In the case of these studies, the upper limit on the velocity has not been established. The maximum observed velocity was approximately 260 m/s in these studies. The limitations placed on the upper bound of velocity stem from a number of factors. The size of camera field of view (FOV), the magnification of the optical system, and the inter-frame delay influence what velocities can be resolved. These factors directly affect the displacement observed in the images. The camera system used in these studies was of a high quality (state of the art) and allowed for relatively large FOVs to be imaged at reasonable magnification and high repetition rate, as previously described. With the 5 μs inter-frame delay, the current optical system would theoretically permit velocities in excess of 10 times those encountered in the current study. When making other considerations, such as requiring a certain number of frames to maintain measurement precision or resolving accelerations, this requirement may become more stringent, and thus the maximum velocity resolvable velocity would be reduced. The lower limit on velocity is prescribed primarily by the measurement precision since this dictates the smallest velocity that can be distinguished from the noise floor. In these studies it was found that the zero-velocity precision was approximately 0.4 m/s (see Section 3.3). With the highest resolved velocity, this yields a dynamic range of 650. This represents a baseline value of what was observed in these experiments. This value greatly exceeds that of the preliminary study, which peaked at approximately 80. The highest resolvable velocity is likely much larger than was observed in these tests (as described above). Likewise the lowest resolvable velocity, being limited by the measurement precision, varies with the thermodynamic conditions at which the data were acquired. It is therefore reasonable to see the dynamic range vary from O(10) to O(10⁴) without any changes to the optical system, depending on the operating conditions and measurement requirements.

3.5. Spatial Resolution

Spatial resolution as it relates to a Lagrangian point measurement could take on several different contextual meanings. One possible interpretation that will be developed in this paper is the notion of resolvable length scales. That is, given the Lagrangian nature of the measurement, the spatial resolution could refer to the length scales of motion that could be accurately measured by the technique. Using this definition, three specific effects need to be considered when establishing the spatial resolution for these measurements: spatial averaging, advection, and the effects of data reduction. The first effect is a result of treating the entire FLEET spot as a singular fluid element. Since the FLEET spot has a finite extent (roughly 1 mm in the transverse direction and 2 mm in the streamwise direction, variable from shot to shot) any motion occurring on scales smaller than these lower limits will not be visible to the technique.

The second consideration in this definition of spatial resolution is advection. The primary factors influencing the perceived motion of the FLEET signal are the inter-frame delay of the camera system and the velocity being resolved. For example, a given velocity will yield greater displacements if a longer inter-frame delay is selected for data acquisition. More importantly, it limits how much of the trajectory is visible to the technique. Consider Figure 14, which shows a sample burst of FLEET images overlaid on each other along with the resulting trajectory measured through analysis of these data; only one of every three images is shown. If only the displayed images were considered in the calculation (representing an inter-frame delay of 15 μs), the dark position markers in Figure 14b would be measured. The subtle vertical and horizontal variations that are observed in the gray data points would be omitted from the velocity calculations. Likewise, a lower velocity would result in smaller displacements between frames given the same delay. In this sense, the velocity and delay set the lower limit on the smallest positional variations that can be resolvable. This limit can be expressed as:

$$\mathrm{\Delta }{s}_{min}=u\mathrm{\Delta }t$$ (5)

which assumes a constant velocity. In Equation 5, Δs_min is the minimum spatial resolution due to advection, u is the local velocity, and Δt is the inter-frame time delay. In these studies, the time delay was fixed at 5 μs, which was a hardware limitation necessary for maintaining a certain FOV on the camera system. This setting yields a minimum spatial resolution ranging from 2 μm to 1.3 mm for velocities ranging from the precision-limited to the maximum observed in these studies, respectively. When considered in conjunction with the spatial averaging caused by the finite size of the FLEET spot, the limit on spatial resolution is additive. Thus, the combined resolution in the streamwise direction is from 2 to 3.3 mm when these two effects are considered. It should also be noted that Equation 5 neglects acceleration because none was encountered in these studies. It could be modified with an extended polynomial if the flow velocities in question were accurately represented by such a model.

Figure 14.

Sample FLEET data burst at Mach 0.75. a) raw data showing every third image and b) measured trajectory corresponding to the data in a). Grayed-out points correspond to omitted images.

The final consideration regarding spatial resolution is the effects of data reduction. The first effect that is introduced by data reduction is the precision of the SRGE surface fitting algorithm, which is used to extract position and intensity information from the raw FLEET images. The precision of this solver is approximately 0.1 px at the poorest acceptable R² and signal-to-residual ratios, or approximately 11 μm at the magnification used in these studies. While this is a high-precision process, it still sets a lower limit on what the smallest resolvable motions can be, since anything smaller falls into the noise of this fitting algorithm. If, for example, the spatial averaging was not a consideration, the spatial resolution would never approach the velocity-precision-limited value because the precision of the surface fitting algorithm is much larger. Finally, and perhaps most importantly, is the effect of the velocity evaluation. As described in Section 2.3.2, a linear regression method was applied to the centroid positions to evaluate the velocity. This method reduces all of the data points over the length of the trajectory to a single velocity value. In this sense it is creating an artificial spatial filter along the length of the trajectory. However, this method does not neglect contributions from individual data points. Unlike the ‘precision’ method described in [39], which improved the measurement precision of velocity measurements by skipping the data lying between non-adjacent centroid positions, the linear regression method is directly influenced by the subtle streamwise and transverse motions of the FLEET signal along the recorded trajectory. For this reason, the minimum resolvable length scale was considered to be the smallest displacement a single centroid location could move from the mean position that would cause a change in velocity equal to the zero-velocity measurement precision. The magnitude of this quantity depends on both the number of image frames considered in the calculation and to which frame the perturbation is applied. Figure 15 shows the sensitivity for several different velocity calculations. It is apparent that the more frames that are included in the velocity calculation, the larger the minimum resolvable displacement is. For 10 frames of data, the peak is approximately 330 μm, whereas for 4 frames of data the maximum is only 21 μm. This intuitively makes sense since the broader the filter is, the greater the effect should be on the spatial resolution. This analysis demonstrates that the linear regression velocity evaluation method does have a notable impact on the spatial resolution, but to a significantly lesser extent than a cursory analysis would suggest.

Figure 15.

Minimum resolvable displacement as a function of the location of perturbation and number of frames for linear-regression velocity evaluation.

Aggregating these different analyses, it is apparent that the limiting factors to the spatial resolution are primarily the effects of advection and spatial averaging. For the present studies, the former affects both the transverse and streamwise velocity measurements, while the latter primarily affects the streamwise component. Depending on the circumstances of the measurement, these roles will likely change. Furthermore, in situations where the Lagrangian measurements are used to make an estimation of velocities in an Eulerian frame of reference, the definition of the spatial resolution will have to be reinterpreted, and some of these analyses will no longer be sufficient, though that work lies beyond the scope of this paper.

4. Conclusions

Femtosecond laser electronic excitation tagging velocimetry has been characterized at high pressure, low temperature conditions. Utilizing the burst-imaging method, time-series of intensity information were measured for FLEET over temperatures ranging from 89 K to 275 K and pressures from 85 kPa to 400 kPa. The FLEET signal intensity taken 70 to 80 ns after the laser pulse was analyzed for thermodynamic dependences, and was found to have a linear dependence on the flow density. In a like manner, the lifetime of the FLEET signal was assessed to have a strong inverse dependence on density with little independent sensitivity to the other thermodynamic conditions. These data have greatly extended the range over which information about both the FLEET signal intensity and lifetime dependences are known.

FLEET velocimetry was then demonstrated in the NASA Langley 0.3-m Transonic Cryogenic Tunnel, which operates over the same range of conditions for which the thermodynamic data were collected and numerous Mach numbers ranging from low subsonic to nearly supersonic. The measurement accuracy was assessed by comparing the measurements to those made by the facility data acquisition system. At temperatures near ambient, the standard and RMS errors were found to be 1.05 and 1.15 percent of the measured velocities, respectively, independent of the pressure. At lower temperatures, a weak temperature dependence was found in the accuracy estimation, with typical measurement errors lying between 1 and 2 percent, with the maximum measurement errors found to be near 3.5 percent. The standard and RMS errors over the broad-condition runs were found to be 1.47 and 1.71 percent of the measured velocities. Over this same range of thermodynamic conditions, the velocity measurement precision was characterized. The zero-velocity precision was found to be 0.4 m/s, while measurements made at elevated Mach numbers exhibited slightly higher fluctuating velocities due to an increase in freestream turbulence intensity. A temperature dependence was also observed in the measured velocity precision. This effect was likely a combined result of the decreased signal lifetime and an increase in the actual fluctuating velocity within the facility. Velocity measurements were made over the entire operational envelope of the facility, even when suboptimal conditions were encountered.

Finally, the measurement dynamic range and spatial resolution were assessed. The dynamic range was found to have a nominal range of 650, although it was noted that much higher velocities than were encountered in these tests could be measured with the system without any hardware or setting changes, effectively increasing the dynamic range by nearly an order of magnitude. The spatial resolution was found to be limited primarily by the FLEET spot size and advective motion of the signal. It was estimated that the transverse spatial resolution in these measurements was approximately 1 mm, while the streamwise spatial resolution varied with velocity, having a minimum of about 2 mm and a peak scale of 3.3 mm at the highest velocities encountered.