Characterization of CO₂ flow in a hypersonic impulse facility using DLAS

Abstract

This work documents diode laser absorption measurements of CO₂ flow in the free stream of the Longshot hypersonic impulse facility at Mach numbers ranging from 10 to 12. The diode laser sensor was designed to measure absorption of the P12 (30013) $\leftarrow$ (00001) transition near 1.6 $\upmu$m, which yields relatively weak direct absorption levels (3.5 % per meter at peak Longshot free-stream conditions). Despite this weak absorption, measurements yielded valuable flow property information during the first 20 ms of facility runs. Simultaneous measurements of static temperature, pressure, and velocity were acquired in the inviscid core flow region using a laser wavelength scanning frequency of 600 Hz. The free-stream values obtained from DLAS measurements were then compared to Longshot probe-derived values determined from settling chamber and probe measurements. This comparison enabled an assessment of the traditional method of flow characterization in the facility, which indicated negligible influence from possible vibrational freezing of reservoir gases.

1 Introduction

Laser spectroscopic techniques to measure flow conditions in hypervelocity and high-enthalpy ground test facilities have found wide application owing to their ability to provide accurate gas dynamic property values non-intrusively. Spectroscopic techniques used for these environments include laser-induced fluorescence (LIF) (Jiang et al. 2011; Inman et al. 2011; Danehy et al. 2008; O’Byrne et al. 2006), coherent anti-Stokes Raman spectroscopy (CARS) (O’Byrne et al. 2007), and diode laser absorption spectroscopy (DLAS), which have been developed for a wide range of facility and test gas applications (Hanson and Jeffries 2006).

Application of the DLAS technique to hypervelocity flows has been ongoing since the mid-90s (Arroyo et al. 1994; Mohamed et al. 1996; Sagnier et al. 1997). Recent noteworthy applications of DLAS in ground test facilities include impulse and arc-heated facilities. Sensors have been developed to probe both atomic and molecular species in hypervelocity impulse facilities using DLAS strategies [such as H₂O and potassium (Wehe et al. 1998) as well as NO (Parker et al. 2007) and rubidium (Trinks and Beck 1998)]. Recent progress has also been made to characterize hypersonic wind tunnels simulating high-enthalpy CO/CO₂ flows for Martian atmosphere entry testing (Mohamed et al. 2003, 2008) including NO characterization (Mohamed et al. 1996). These efforts highlight DLAS as a significant non-intrusive diagnostic for high-enthalpy flow characterization.

This work reports on the implementation of a DLAS sensor to measure temperature, pressure, and velocity simultaneously in the free-stream hypervelocity flow of the von Kármán Institute’s (VKI) Longshot free-piston wind tunnel operating with CO₂ as the test gas that began in 2007 (Meyers and Fletcher 2007). An overview of the Longshot facility and the CO₂ test conditions is followed by a description of the DLAS instrument used for this investigation. Three different configurations were used to address specific issues of DLAS integration into the Longshot facility, and these are described and their results discussed. Results from these tests led to a final configuration that provided simultaneous temperature, pressure, and velocity measurements. All DLAS data were reduced prior to comparison with estimates of the probe-derived Longshot stream conditions. Finally, summary remarks are made about the suitability of this sensor for Longshot testing with CO₂.

2 Longshot facility

2.1 Facility description

The VKI Longshot Impulse hypervelocity facility is a free-piston hypervelocity wind tunnel (see Fig. 1) used for high Reynolds number and high Mach number investigations of atmospheric hypersonic flight (Backx 1974; Simeonides 1990). A driver section is filled to high pressure and is separated from the driven section by an aluminum shear plate, which supports the piston. The driven section is kept at an intermediate pressure between the driver section and the evacuated nozzle and test section which are isolated by a second diaphragm. Currently, either N₂, CO₂, or admixtures can be used in the driven section (Charbonnier et al. 1997). The piston is released when excess nitrogen is bled from the circumference of the shear plate supporting the piston, and it rapidly compresses the driver gas. A shock ahead of the piston (traveling at $\approx$600 m/s) reflects off the end of the tube just before the reservoir. This shock then travels toward the piston and slows it down. The shock reflects back and forth until the piston begins to travel back up the tube. This would create a back flow if not for a series of check valves that only allow flow into the reservoir. Peak reservoir conditions can briefly reach 4000 bar and 2500 K, and this ruptures the second diaphragm. The reservoir gas is then fed through a convergent–divergent nozzle into the test cabin.

Nozzle choices include a 42-cm-diameter contoured section and conical sections with exit diameters of 36 and 60 cm. Free-stream velocities from 2.0 to 2.5 km/s are reached depending on the piston weight, driver gas condition, and driven gas composition and condition. Thermodynamically, free-stream static conditions are quite cold and at relatively low pressure with initial values around 150 K and several hundred Pa. Typical test duration for this impulse facility is between 20 and 30 ms. Flow Mach numbers range from 11 to 20 with unit Reynolds numbers between $4\times 10^6$ and $8\times 10^6$ m$^{-1}$ depending on nozzle and test gas choices.

Fig. 1

Longshot impulse hypervelocity facility

2.2 Longshot flow properties

The traditional approach used to determine the Longshot free-stream conditions involves parameters measured with transducers installed in the facility: reservoir pressure, $P_0$, total pressure in the test section, $P_{t2}$, and heat flux to a hemisphere ($\phi$2.54 cm) probe in the test section, $q_{w2}$. Using a simple expanding flow model and a Fay-Riddell heat transfer correlation (Fay et al. 1958) for the test gas starting from $P_0$ and a guessed value of $T_0$, the test section values of $P_{t2}$ and $q_{w2}$ are calculated varying $T_0$ until convergence. Uncertainty for Longshot free-stream temperature, free-stream static pressure, and free-stream velocity values determined from the probe measurements has been most recently been reported to be 10.1, 7.2, and 3.2 %, respectively (Grossir 2015). These uncertainty values were for N₂. No uncertainty estimates are available for CO₂.

While the conventional probe and expanding flow approach to determining the free-stream conditions is believed to work well for N₂ flow, it may not suffice for CO₂ flow fields owing to a higher potential for non-ideal gas behavior. Equilibrium calculations suggest that high reservoir pressures preclude CO₂ dissociation (Meyers 2009); however, vibrational freezing in the expanding nozzle flow and potential condensation owing to the large pressure drop as the gas flows through the check valves are possible. These concerns have been acknowledged as potential sources of error in the traditionally deduced free-stream conditions (Grossir 2015; Fletcher 2003; Walpot 2008; Laurent 2003).

An appropriate non-intrusive sensor offers the possibility to directly measure thermodynamic properties and velocity in the free stream and to thereby assess the existing method of determining test conditions. Candidate techniques include CARS, LIF, and DLAS. While the CARS and LIF techniques are arguably better suited for localized measurements, they are cost-prohibitive. A DLAS sensor was chosen for this application to probe carbon dioxide, which has a well-documented and wide ro-vibrational spectrum in the near-infrared range where a number of affordable tunable laser systems are available. However, the integrated line-of-sight nature of DLAS requires careful consideration of non-uniform flow fields, such as those with shear layers. This issue is addressed later in this report.

2.3 CO₂ tests with N₂-contoured nozzle

For this investigation, the Longshot facility was configured for operation with the 42-cm-diameter contoured nozzle, which was designed using the method of characteristics for nitrogen flow (Simeonides 1990). Further motivation for this DLAS sensor development was to obtain independent information about free-stream conditions to assess CO₂ flows in the contoured nozzle. Test conditions for this investigation are presented in Table 1.

Table 1 Test conditions for CO₂ test with contoured nozzle

Fig. 2

DLAS configurations. a Single perpendicular beam, b single-angled beam, c shear layer shield, and d double-beam velocity

3 Experimental details

The relatively short test time and non-steady nature of the hypersonic flow significantly limited diode laser choices. Relatively low free-stream temperatures ($\le$150 K) presented a further constraint as only the ground vibrational level and low rotational quantum number states were expected to have measurable populations at thermal equilibrium. As discussed in Reference Meyers and Fletcher (2011), these considerations led to the choice of a narrow line width ($<$300 kHz) external cavity diode laser (ECDL) with a tuning range of about 1.3 cm$^{-1}$. Although this limited the absorption to a single ro-vibrational transition in the end, the narrow scanning range enabled multiple time-resolved measurements of the continually varying stream conditions.

The selected laser had a tuning range of 1607.96–1608.41 nm (6219.06–6217.32 cm$^{-1}$) to probe the CO₂ P12 (30013) $\leftarrow$ (00001) combination band transition (here we adopt Air Force Geophysics Laboratory notation of $\nu _1\nu _2l_2\nu _3r$). This transition was selected owing to its sensitivity to core and shear layer temperatures and yields a calculated 3.5 % absorption per meter for peak Longshot free-stream conditions (400 Pa and 150 K).

The DLAS sensor was assembled on a 30 cm $\times$ 40 cm portable breadboard to facilitate transportation from bench to facility. This portable system was placed on a vibration isolation system about two meters away from the Longshot test cabin to improve stability. An air-gapped etalon with a FSR of 1.583 GHz (0.0514 cm$^{-1}$) was used as a frequency marker to convert laser scan data into wave numbers. As no reference intensity was acquired, a reference baseline signal, $I_0$, was inferred from the transmission signal I. These two values were used to calculate absorption through the Beer–Lambert relation, −ln$\left( I/I_0\right)$.

The determination of flow properties from the measured absorption evolved directly from the fact that a single ro-vibrational transition was probed. Pressure was derived from spectrally integrated absorption, and temperature was evaluated from the fit of a spectral model of the transition line shape. Analysis began by determining the spectrally integrated absorption of each scan after all errant particle contamination disturbances (if present) were removed. The absorption signal was then normalized by this area value and fit to a Voigt model described by McLean et al. (1994) that was made to be purely temperature and integrated area dependent. This model, as any Voigt model, depends on the collisional and Doppler width contribution. The Doppler width is a function of temperature as:

$$\begin{aligned} \Delta \nu _D=7.162\times 10^{-7}\nu _0\left( \frac{T}{M}\right) ^{\frac{1}{2}} \end{aligned}$$

(1)

where T is temperature, $\nu _0$ is the transition line center, and M is the specie molar mass. For the collisional width, the pressure was replaced by:

$$\begin{aligned} P = \frac{A}{S(T)L} \end{aligned}$$

(2)

where A is the absorption feature integrated area, S(T) is the temperature-dependent line strength, and L is the absorbing path length. With integrated area, path length, and reference values for the collisional width, $\gamma _0$ and collisional exponent, n (found to be 0.705 Predoi-Crossa et al. 2010) known, a purely temperature-dependent collisional width model can be derived:

$$\begin{aligned} \Delta \nu _C = \frac{2A \gamma _0}{S(T) L} \left( \frac{T_0}{T}\right) ^{n} \end{aligned}$$

(3)

Once temperature was extracted from the fit, pressure was subsequently calculated from Eq. 2. Where applicable, the bulk gas velocity, $u_\mathrm{{gas}}$, was obtained from line center peak spacing between Doppler-shifted and rest absorption profiles, $\Delta \nu$, line center of the transition, angle between flow perpendicular and light propagation direction, $\theta$, and the speed of light, c, through the relation:

$$\begin{aligned} \Delta \nu _\mathrm{{shift}} = \nu _0 \frac{u_\mathrm{{gas}}}{c} \sin \left( \theta \right) \end{aligned}$$

(4)

3.1 Data acquisition

Data were acquired by a Labview controlled National Instruments card sampling at 800 kS/s per channel at 16-bit resolution. While the ECDL can be driven to several kHz via the piezo-mechanical drive, a modest 300 Hz (two scans per period yielding 600 scans per second) sine wave was used to drive the laser. The scan frequency was finally determined as a trade-off between acquiring enough data points per scan with DAQ sampling resolution and generating enough scans per test in the 20-ms run duration. Single scan time at 600 Hz yields 1.6 ms scans with less than 10 % of the scan containing the absorption feature. This implies that the data represent a flow integration time of less than 160 $\upmu$s in all test cases. DAQ sampling of 800 kS/s per channel yields a time between data points of 1.250 $\upmu$s which is more than twice the detector rise time of 0.439 $\upmu$s, producing 100+ samples covering the absorption feature.

3.2 Rigid support frame

The Longshot facility generates significant mechanical forces owing to the rapid large pressure rise in the reservoir from the dissipation of kinetic energy when the high-velocity piston is abruptly forced to slow and change directions. A significant effort went into design and fabrication of components to integrate the laser sensor into the evacuated test cabin with robust optical fiber delivery to avoid vibration. An optical support frame was built as a stable addition to the Longshot facility that can be moved axially to fit a variety of installation configurations. The frame consisted of 10 cm $\times$ 10 cm square tubing constructed in a 100 cm $\times$ 100 cm form to surround the entire nozzle. An arrangement was developed to suspend the portable bench to maintain optical alignment of the diode laser with the optical components on the portable breadboard while in operation near the Longshot. A single-mode fiber-optic cable with a steel jacket was connected to the portable breadboard and delivered into the test cabin through a vacuum feed-through and then connected to a rigidly mounted fiber collimator which sent the 4-mm-diameter collimated light across the flow to the opposing detector or mirror (depending on configuration).

3.3 Pitch and catch optics

Light collection and detection optics located in a catch assembly include a 25-mm-diameter lens of 150 mm focal length to focus the 4-mm-diameter beam onto the 5-mm-diameter active region of the fast response photodetector. A large active region was found necessary as the mechanical vibrations affect the optical alignment during Longshot runs. It was assumed that all the transmitted light is being collected by the detector for stable conditions. The detector was terminated into 50 $\varOmega$ to maximize bandwidth. The detector lacked vacuum operation capability necessitating the isolation of the assembly from the pre-run vacuum condition in the test chamber. This assembly was vented to the atmosphere while not affecting the vacuum environment and was rigidly mounted onto the optics frame for effective vibrational stability.

4 Configuration details

The four test configurations used in this investigation are illustrated in Fig. 2.

4.1 Configuration (A)

Configuration (A) is a perpendicular beam arrangement designed to address whether mechanical vibration, particle contamination, and shear layer absorption will preclude evaluation of the stream conditions by the DLAS sensor. The beam path for this test is located about 7 cm downstream of the nozzle exit.

4.2 Configuration (B)

Configuration (B) represents an angled beam arrangement. In this test, the beam passes through the entire free jet as well but at an angle of 19.3$^\circ$ w.r.t. the flow perpendicular (represented by $\theta$). An angled beam path is needed to enable free-stream velocity measurements via Doppler shifting. This test aimed to further assess shear layer, stability, and contamination issues and to evaluate possible profile asymmetry from Doppler-shifted shear layer absorption. This potential asymmetry arises from the fact that thermodynamic properties and local velocity vary (in both magnitude and direction due to radial flow) through the shear layer region, potentially causing asymmetry in the absorption profile. The center point of the beam path is now located about 9 cm downstream of the nozzle exit.

4.3 Configuration (C)

Configuration (C) shows a shear layer shield arrangement. It was known that most particulate matter in the flow resides in the shear layer (Simeonides 1990). This experiment was intended to be a direct comparison with the perpendicular beam experiment (A) to assess both shear layer and particle contamination influence. Schlieren movies, along with pressure rake data, have shown that the core can be conservatively assumed to be $\approx$32 cm, which suggests an annular shear layer thickness of $\approx$5 cm for the 42-cm-diameter free jet (Meyers et al. 2009). At the nozzle exit, the rested gas was at a higher temperature (closer to the nozzle wall temperature at around 300 K) than that of the core flow gas (around 125–150 K). In theory, this higher temperature shear layer region (25 % of the free jet path length) results in a much weaker absorption transition strength (5–10 times weaker) and thus a minimally detectable difference in the free jet core absorption. A pair of shear layer shields was designed to divert the shear layer while leaving relatively thin boundary layers.

Shear layer shield installation is shown in Fig. 3 with the laser beam path superimposed. The square plexiglass channel base measured 211 mm long with a cross section of 44 mm by 250 mm. A flat plate with a glass optical access was bolted on the end of the channel inserted into the flow. The flat plate measures 104 mm by 291 mm with a sharp 15$^{\circ }$ leading edge to ensure an attached shock wave. This plate was made larger than the square channel so as to prevent the leading bow shock from the square channel from spilling over into the flow on the flat plate side of the shield and affecting the absorbing path. The face opposite the flat plate on the other end of the box is open to the test cabin environment, but well outside of the free-jet region. For these tests, the shields were inserted 5 cm into the flow yielding a 32 cm absorbing path within the 42 cm free jet. The two shields were mounted on an adjustable support attached to the model support rig in the test cabin. The frame was set with the absorbing path about 7 cm downstream of the nozzle exit. Schlieren video image frames of the shear layer shield experiment (Fig. 4) show that the combined boundary layer region will be less than 10 % of the total absorption path for the duration of laser scanning.

Fig. 3

Installation of shear layer shield experiment. Absorbing path of sensor is superimposed

Fig. 4

Schlieren video images of shear layer shield experiment

Fig. 5

DLAS raw data for configurations (a) and (c) as illustrated in Fig. 2

4.4 Configuration (D)

Configuration (D) represents an arrangement to simultaneously acquire free-stream temperature, pressure, and velocity. One constraint with this configuration was to use a single beam path without a gas reference cell as a zero velocity marker. The final design used a crossbeam setup of two counter-propagating beam reflections with one beam leg traveling upstream ($\theta$ = 19.3$^{\circ }$), another downstream at the same angle, and a third leg perpendicular to the flow. The crossing point of the beams was set 9 cm downstream of the nozzle exit. A rigid piece of tubing was mounted onto a model support to provide a low-density, room-temperature gas that is nearly transparent to the transition to avoid an unshifted absorption peak, thus providing better resolution of the two Doppler-shifted peaks. The tube ends were set a few centimeters outside of the free jet and far enough away from the angled beams to prevent any shock layer absorption.

5 Results

5.1 Initial data fidelity observations

Raw DLAS transmission data from both the perpendicular beam test and the shear layer shield test are plotted in Fig. 5. Each vertically pointing arrow identifies the CO₂ absorption feature. These plots illustrate that the system functioned well with a decent transmission signal well into the 30-ms test time with the 1.5 % direct absorption level was adequately resolved. The etalon signal shows influence from vibrations at around 25 ms where the signal becomes difficult to interpret. Whatever influence the shear layer and rested gas have on the absorption is unknown at this point. Particle contamination in the flow is evident and causes noticeable noise throughout the entire 30-ms scan record for Configuration (A). Individual scans from the angled beam tests (Configuration (B)) showed no asymmetry that would be attributed to absorption of lower velocity flow in the shear layer, further illustrating shear layer transparency. This symmetry of features that pass through shear layers for angled absorbing paths is illustrated in the crossbeam velocity results presented later (see Fig. 12). It is clear that particle contamination is greatly reduced by the shields in Configuration (C).

A detailed discussion of determining the transfer function from etalon transmission is given in Meyers and Fletcher (2011). Figure 6 represents a typical narrow tuning range etalon trace with five peaks clearly represented. The five peaks are well resolved temporally and result in a low residual third-order polynomial fit, which is imperative for an accurate transfer function. An effective uncertainty in relative wave numbers of about 0.13 % near line center results from the 0.002 msec maximum possible error in temporal determination of peak location.

Fig. 6

Top typical etalon trace with peak locations highlighted. Bottom resulting third-order polynomial fit to extract time to wavenumber transfer function

5.2 Flow variable measurement uncertainty

Figure 7 represents a typical Voigt fit to raw absorption data of a single-beam pass experiment. Reference Meyers and Fletcher (2011) discusses a series of bench experiments in a controlled environment where pressure was adjusted to manipulate the ratio of Doppler to collisional width. These bench experiments showed that data became more reliable (less scatter in reduced temperature and pressure) as Doppler to collisional width ratios increased and approached those of Longshot (a ratio of about 10). Figure 7 also illustrates the Voigt fit temperature sensitivity. Here, the Voigt profile temperature is varied from the measured value by 25 K (derived uncertainty for first 10 ms Meyers and Fletcher 2011) while holding pressure constant. A noticeable difference between the fits can be seen, especially near the peak. The measured temperatures are certainly reliable to within 25 K during the first 10 msec of test time.

Fig. 7

Fit to absorption data of third scan in perpendicular beam experiment. Residuals above (from top to bottom) represent residuals for +25 K adjusted Voigt model, baseline Voigt fit, and $-25$ K adjusted Voigt model

Figures 8, 9, and 10 show Longshot probe-based data compared with DLAS measurements for configuration (A), (B), and (C) tests. Section 2.2 gave details of how Longshot probe-based flow values are derived along with associated uncertainties. Test start is indicated by the initial pressure spike and vertical dashed line (about 6 ms for both tests represented in Fig. 5). For all tests, the transmission signal quality is much cleaner and more stable pretest than after the flow starts. For the first 10 ms of flow, the transmission signal fidelity decreases but remains significantly better than for the next 10 ms.

The theoretical estimation of uncertainties for temperature and pressure is not trivial owing to the propagation of error through complex numerical fitting schemes and baseline interpretation. However, the uncertainty of the line shape fit to the absorption signal can be estimated with an approach that consists of fitting several partial profiles that comprise the absorption scan (so one sub-scan is composed of every nth point for n sub-scans generated from the parent scan). Each of the absorption scans recorded during Longshot tests was analyzed in this way with n = 5. Each sub-scan was fit with a Voigt profile to find temperature and pressure. The resulting spread in temperature and pressure for the five sub-scans provided a best estimate of uncertainty for that measurement. When taking all scans from test start to 10 ms, this uncertainty analysis led to values of $\pm$25 K and $\pm$50 Pa. These values were doubled for all DLAS scans beyond the 10-ms point owing to the deterioration of scan quality.

Fig. 8

DLAS extracted temperature and pressure compared to Longshot reduced values for configuration (A) as illustrated in Fig. 2

Fig. 9

DLAS extracted temperature and pressure compared to Longshot reduced values for configuration (B) as illustrated in Fig. 2

Fig. 10

DLAS extracted temperature and pressure compared to Longshot reduced values for configuration (C) as illustrated in Fig. 2

5.3 Combined flow variable and velocity remarks

Fig. 11

First 30-ms record of raw data for crossbeam experiment. Inset plot illustrates the two-peak occurrence with the center rested beam attenuated and two Doppler-shifted beams. [Longshot test #1622]

With the fidelity of the system determined, Configuration (D) was used to measure temperature, pressure, and velocity simultaneously. Two tests were done to illustrate repeatability (Longshot tests 1622 and 1636). Figure 11 shows the first 30 ms of test data from the 1622 Longshot test case. Though this optical setup has more sensitivity to facility mechanical vibration with the increased number of optics and path length, decent double absorption features can be resolved. The third unshifted beam has been suppressed by the optically transparent conditions of the cross tube. Test run 1636 shows similar signal quality characteristics and so was not shown in this raw data form. Two-peak Voigt model fit quality is seen in Fig. 12, where the fifth scan of test 1622 is represented. Note that rested gas and shear layer gas absorption paths are effectively doubled for this test, but the symmetry of the two Voigt contributions indicates low absorption from these regions, again validating the P12 transition choice as being most sensitive to core flow properties.

Figure 13 shows free-stream temperature, pressure, velocity, Mach number, and enthalpy comparisons between Longshot probe-based and DLAS-measured values for tests 1622 and 1636, respectively. Temperature and pressure were averaged between the two peaks of the Voigt model for each usable scan, which doubles the averaging time for the non-steady flow conditions. Velocity was taken from the difference in the relative line center values of both profiles in each scan with an effective angle of $2 \times 19.3^\circ$. Velocity measurements in this configuration are quite accurate even with baseline fitting concerns for low absorption levels. Velocity uncertainty was estimated to be $\pm$100 m/s ($\pm$5.0 to 6.6 %) (Meyers 2009).

The DLAS free-stream-specific total enthalpy, $h_0$, can be calculated from the velocity and temperature values derived from the DLAS measurements and values of $C_{P}$ that were estimated using the NASA Chemical Equilibrium and Applications code (Gordon and McBride 1994) as:

$$\begin{aligned} \left( h_0\right) _\mathrm{{DLAS}} = \frac{\left( u_{\infty }\right) ^2_\mathrm{{DLAS}}}{2} + C_{P}\left( T_{\infty }\right) _\mathrm{{DLAS}} \end{aligned}$$

(5)

Fig. 12

Crossbeam experiment fit to absorption data utilizing a two-peak Voigt model. Top plot shows raw DLAS data superimposed onto the total fit function. The bottom plot shows the separate contributions to the total fit. [Longshot test #1622]

The Longshot reservoir enthalpy is available from the standard Longshot data reduction routine using perfect gas stagnation temperature, while the probe-based free-stream total enthalpy can be calculated using the free-stream velocity and temperature values from the Longshot data reduction as:

$$\begin{aligned} \left( h_0\right) _\mathrm{{LS}} = \frac{\left( u_{\infty }\right) ^2_\mathrm{{LS}}}{2} + C_{P}\left( T_{\infty }\right) _\mathrm{{LS}} \end{aligned}$$

(6)

Fig. 13

Free-stream temperature, pressure, velocity, Mach number, and enthalpy comparison between Longshot rebuilt and DLAS-measured values for Longshot tests 1622 (left column) and 1636 (right column)

Kinetic energy provides the main contribution to the Longshot specific total enthalpy; thus, the ${u_{\infty }}^2$ contribution is much larger than the $C_PT_{\infty }$ product. As the DLAS-measured velocity is quite accurate, so too is the total enthalpy even with the modestly accurate DLAS-measured temperature. With this in mind, enthalpy uncertainty is estimated to be $\pm$10 % Meyers (2009).

Even with longer beam transit length and the increased number of optical components enhancing the mechanical vibration sensitivity and particulate contamination present in the raw signal, temperature and pressure determinations were straightforward for test case 1622. However, for test case 1636, a greater number of absorption scans were affected by particle contamination and vibration-induced baseline signal noise. It is likely that this resulted in the greater difference between the DLAS values and Longshot probe-based values. Signal noise and particle contamination strongly affected the laser absorption data, and the impact varied from test to test.

6 Discussion

Although the DLAS results presented thus far are encouraging, the question of whether or not freezing of vibrationally excited CO₂ occurs in the expansion process needs to be addressed. Free-stream total enthalpy values for these tests did not reach conditions equivalent to stagnation values at the highest 2500 K values, but were more on the order of 1500 K as determined from the Longshot probe measurements. Considering the high plenum pressure (about 2000 bar) and attendant high collision frequency, it is unlikely that a non-equilibrium vibrational temperature would reach that level. Nevertheless, we consider the following simple analytic expression to evaluate the specific heat at temperature up to 1500 K:

$$\begin{aligned} \frac{C_p(T)}{R}= & {} \frac{7}{2} + \left[ \left( \frac{\theta _{1}/2T}{\mathrm{sinh}(\theta _{1}/2T)}\right) ^2 \right. \nonumber \\&\left. + \cdots \,2\left( \frac{\theta _{2,3}/2T}{\mathrm{sinh}(\theta _{2,3}/2T)}\right) ^2 + \left( \frac{\theta _{4}/2T}{\mathrm{sinh}(\theta _{4}/2T)}\right) ^2 \right] \end{aligned}$$

(7)

where R is the CO₂ specific gas constant, and the characteristic CO₂ vibrational temperatures are $\theta _{1} = 1934$ K, $\theta _{2,3} = 960$ K (degenerate), and $\theta _{4} = 3383$ K. The ideal-gas free-stream equilibrium velocity can be determined from reservoir stagnation enthalpy and free-stream-specific enthalpy as $\left( u _{\infty } \right) _\mathrm{eq}= \sqrt{2 \left( h_0 - h_ \infty \right) }$. Velocity from a vibrationally frozen flow can be determined by removing vibrational energy as $\left( u _{\infty } \right) _\mathrm{vib}= \sqrt{2 \left( h_0 - h_ \infty -h_\mathrm{vib} \right) }$. Here, $h_\mathrm{vib}$ is simply the assumed vibrationally frozen temperature multiplied by the CO₂ specific heat including the temperature-dependent terms in square brackets of Eq.  7. From these relations, a free-stream velocity deficit can then be determined as:

$$\begin{aligned} \Delta u _{\infty }= \left( u _{\infty } \right) _\mathrm{eq} - \left( u _{\infty } \right) _\mathrm{vib} \end{aligned}$$

(8)

Figure 14 shows the drop in free-stream velocity that would occur if vibrationally frozen flow were present for a reservoir temperature of 1500 K and expanding nozzle flow. As it was shown that direct velocity DLAS measurements match quite well with Longshot reduced values with an uncertainty of $\pm$100 m/s, it is unlikely that there is vibrationally frozen energy above 300 K. However, the accuracy of this sensor is not sufficient to completely rule out freezing at a vibrational temperature below 300 K.

Fig. 14

Velocity loss due to locked vibrationally frozen energy

7 Conclusion

The main goal of this work was to assess the fidelity of the probe-based test conditions determined for CO₂ flows in the contoured nozzle that was designed for N₂ and whether or not vibrational non-equilibrium effects could be observed with the use of direct non-intrusive measurements of free-stream flow properties. To do so, a relatively inexpensive DLAS sensor with off-the-shelf optical components operating near 1.6 $\upmu$m was developed and implemented to directly monitor free-stream temperature, pressure, and velocity for CO₂ flows in the Longshot facility.

7.1 Sensor general comments

Working with a sensor near 1.6 $\upmu$m to probe the P12 (30013) $\leftarrow$ (00001) transition limited absorption to 3.5 % per meter at Longshot conditions. However, with careful attention to system stability and contaminant noise, the sensor does provide temporally resolved free-stream conditions of temperature, pressure, and velocity. It was found that the absorbing path length magnitude mandated a rigid-frame supported fiber delivery system to provide decent measurement results over the first 15–20 ms of the $\approx$ 30-ms test duration. It was also found that by choosing the appropriate P12 rotational number, shear layer gas absorption can be avoided, thus allowing the sensor to access the desired core flow properties. It was also shown that particulate contamination resided almost entirely within the shear layer flow. Even so, with careful attention, absorption could be readily identified from, and corrected for, particulate-produced signal interference even if the beam path passed through shear layer.

7.2 Comparison to Longshot data

Despite the uncertainties in the DLAS-measured values, the results clearly demonstrate the effectiveness of this non-intrusive diagnostic for CO₂ flows in Longshot. For the different configurations, the DLAS measurements of static pressure and temperature agreed reasonably well with the results derived from the probe-based measurements and isentropic expansion, inviscid, compressible-flow theory. The more accurate velocity measurements from the DLAS sensor showed the best agreement with the probe-derived values.

7.3 Statement on equilibrium

As mentioned in the introduction, CO₂ real-gas effects are not included in the thermodynamic model used to estimate flow conditions from the probe measurements. The DLAS results strongly suggest that for these test conditions, real-gas effects, such as non-equilibrium vibrational energy freezing through the expansion process, have negligible influence. This was best illustrated with direct velocity DLAS measurements that match quite well with Longshot reduced values signifying that vibrationally frozen energy above 300 K is unlikely. This further implies that for these same conditions, aerothermodynamic data from CO₂ flows in a contoured nozzle designed for nitrogen can be used with confidence.

7.4 Improved sensor suggestion

There are options to improve upon these measurements and to extend the DLAS research in the Longshot facility if a higher fidelity assessment of flow conditions is desired. One such improvement was attempted. The sensor chosen for this study resulted in relatively weak absorption. A longer wavelength tunable diode laser could access stronger transitions that give greater absorption. After the present tests were completed, a diode laser system that operated near 2.7 $\upmu$m was tested in Longshot for CO₂ (Vallon et al. 2010). However, line strengths in this region are nearly three orders of magnitude stronger than those at 1.6 $\upmu$m. Pure CO₂ tests were not possible as absorption saturation occurred for centimeter length paths. Useful absorption was only realized with a dilute CO₂ and non-absorbing N₂ mixture. The present results and this experience suggest that a diode laser operating near 2.0 $\upmu$m would be most useful for future Longshot CO₂ absorption studies.