Introduction

The benefits of wavelength-agility for diode-laser sensing in high-pressure, nonuniform-temperature, transient, and otherwise harsh environments have been thoroughly detailed [1–4]. Recently, demonstrations of wavelength-agile sensing in practical combustion systems (such as a coal power plant [5]) have emerged. In the present work, measurements in a pulse detonation engine (PDE), seen as a step toward practical sensing in industrial propulsion systems, are presented.

Previous work [1,3] has established the superior tunability of selected VCSELs over conventional edge-emitting diode lasers. Here, a VCSEL similar to one scanned through 30 cm^-1 at 10 kHz repetition rate [1] is scanned through 10 cm^-1 at 1 MHz repetition rate. The slight decrease in scan range is traded for a great increase in scan repetition rate by switching from standard ramp modulation (using a commercial diode laser current source) to direct, square-wave voltage modulation (using a commercial pulse generator). Although this “aggressive” tuning approach removes laser protection circuitry and therefore may increase the risk of laser failure, it ensures that the laser’s tunability is limited only by its thermal inertia. The high scan repetition rate is needed in this application to provide enhanced sensor time response and immunity to PDE noise.

Atomic cesium, studied extensively in static cells [6–7] and flames [8] using diode laser sensors, was chosen as a tracer species for this work. Native absorbers such as H₂O might be preferable, but VCSELs and advanced wavelength-agile lasers (e.g., c-VCSELs [9], SGDBR lasers [10]) are not yet available at wavelengths necessary to access such species. Furthermore, at the high temperatures (up to ~ 4000 K) produced by PDEs, the absorbance of molecular species becomes prohibitively weak due to three effects: partition function (more rotational and vibrational states populated means less population in any one state), number density (decreases as 1/T), and chemical equilibrium (H₂O dissociates to OH, H, and O). Of atomic absorbers, Cs was chosen for its low natural abundance (eliminating the possibility of unwanted seeding from trace contaminants), simple spectroscopy (a single natural isotope, ¹³³Cs, is present in nature) and its low melting point as described below. However, because of other concerns such as toxicity, a variety of other atomics might be considered for future applications.

PDEs have received significant attention in recent years, owing to their high theoretical specific impulse and few moving parts [11]. Several laser-based PDE studies have been reported, primarily in the areas of PLIF imaging [12] and diode-laser sensing [13]. The high pressures (up to ~ 30 bar), high temperatures (up to ~ 4000 K), and shock waves generated by PDE flows undermine all but the most robust optical diagnostics. The sensor presented here overcomes these challenges through wavelength-agility: the laser wavelength scans so rapidly that all PDE noise sources are effectively frozen while an individual Cs lineshape is recorded [4]. A major aim of the work presented here is to advance PDE development by validating numerical detonation simulations and by enabling PDE monitoring and control. The success of wavelength-agile sensors in this role should motivate their use in other harsh-flow sensing applications.

Experiment

To seed Cs into gas-phase flows, researchers have typically used CsCl aerosols (e.g., saltwater sprayed into a flame [8]) or surface coatings (e.g., saltwater painted onto an intrusive sting [14] or shock tube diaphragm [15]). However, sprays are experimentally messy and can alter flow properties; surface coatings tend to provide nonuniform seeding and can bias measurements toward boundary layer regions [4,16]. To circumvent these issues, we used the novel approach depicted in Fig. 1 to seed Cs rather uniformly – enabling line-of-sight-averaged measurements – into the PDE fill gases. The Stanford PDE facility shown in Fig. 1 consists of a stainless steel tube closed at one end and open to a large dump tank at the other. Along with feedstock C₂H₄ and O₂, Cs is seeded into the tube near the closed end from a tank containing Cs vapor and argon. During an engine fill, when all three supply-line valves are opened, a relatively weak Ar flow (containing trace Cs vapor) is mixed with the C₂H₄/O₂ fill gases. The Cs immediately reacts with feedstock oxygen to form CsO particulate in the mixing tee. Thus the charge that fills the PDE contains a trace of CsO dust. During combustion, the CsO dissociates to yield a significant fraction of atomic Cs that is probed by the sensor [14]. The temperature of the Cs tank (and its mixing tee supply line) can be adjusted to optimize the Cs seeding fraction (in this case ~ 5 ppm was achieved at a temperature of ~ 500 K). Cesium is the easiest alkali metal to seed in this way because it has the lowest melting point (and the highest vapor pressure at any given temperature). Cesium metal is typically supplied in glass ampules which must be broken inside the tank while under Ar purge. The tank, valves, and supply line must be made of inert materials; we found that stainless steel components with teflon seals were acceptable. In liquid-fueled engines, a simpler seeding strategy is available; Cs can be added to the fuel in the tank (e.g., as CsCl salt) to generate a roughly uniform Cs concentration in the charge.

 

Fig. 1. Schematic of the Stanford PDE facility, with VCSEL-absorption sensor applied to measure gas temperature and pressure near the exit. Detector 1 monitors Cs absorption lineshapes and detector 2 monitors thermal emission from Cs.

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Fig. 2. Raw transmission data recorded by detector 1 of Fig. 1, with etalon trace overlaid. The first scan is prior to the detonation wave arrival. The detonation arrives during the second scan, and for this scan only the associated beamsteering noise is on the order of the scan repetition rate, thus preventing an accurate absorption measurement. The third scan provides a high-quality absorption feature exhibiting strong collisional broadening. The fourth scan is approximately 4 ms after the detonation wave arrival, and reveals hyperfine splitting.

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Figure 3. Raw Cs emission signal recorded by detector 2 of Fig. 1. Emission is in the 852 ± 5 nm spectral region and is proportional to the Cs population in the excited 6²P_3/2 state. The interfering emission in this band (on the order of 10% of the Cs emission) has been characterized using unseeded detonations and subtracted to obtain this trace.

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The diagnostic shown in Fig. 1 uses a single, rapidly scanning VCSEL near 852 nm and two detectors. A diffraction grating is used to direct the VCSEL beam (in zeroth order) through the flow and the PDE luminosity (in first order) to a detector on the VCSEL side. It is worth noting that if the grating is appropriately blazed, the efficiencies of the VCSEL beam reflection and the luminosity diffraction can both be greater than 50%; using a 30 degree blaze-angle grating, we achieved ~ 70% throughput for both channels in this case. Thus the system shown in Fig. 1 outperforms the more standard beamsplitter-based system [17].

As a detonation wave passes the measurement station, detector 1 monitors Cs absorption lineshapes; a raw data trace, overlaid with an etalon trace, is shown in Fig. 2. Detector 2 simultaneously monitors Cs emission from the volume probed by the VCSEL beam; a raw data trace is shown in Fig. 3. These data are digitized on a 12-bit scope at 100 megasamples per second. Two different Cs vapor temperatures, an electronic temperature and a kinetic temperature, can be obtained from this sensor; these are expected to be equal because the electronic excitation time constant for typical PDE conditions is < 1 μs [18]. The electronic temperature, T_{Cs, electronic}, is obtained from the ratio of the Cs population in the excited electronic state (6²P_3/2, given by detector 2) to the Cs population in the ground electronic state (6²S_1/2, given by the integrated absorbance areas of the lineshapes recorded by detector 1: n_Cs,6²S1/2[cm^-3] = 3.2×10¹² [cm^-1] × Area[cm^-1]/L[cm]). The kinetic temperature, T_Cs,kinetic, is obtained from the FWHM collisional width in the detector 1 lineshapes, Δν_c, governed by

where γ (= γ_{Cs-detonation products}) is the overall collisional broadening parameter, P is the pressure (typically measured by a wall-mounted transducer), T_o is a reference temperature (300 K in this paper), γ_o is the value of γ at temperature T_o, and n is the temperature broadening exponent. Thus, with measurements of Δν_c and P (and thus of γ), T_{Cs, kinetic} can be obtained from eq. 1, provided γ_o and n are known.

Results and Discussion

Given the data shown in Figs. 2 and 3, the first step in obtaining either temperature is to fit the Fig. 2 data as illustrated in Fig. 4. The data shown in Fig. 4 correspond to the Cs absorption feature obtained immediately after detonation wave passage; the high pressure accounts for the large collisional width and shift relative to the hyperfine structure, provided for reference in Fig. 4.

 

Fig. 4. Cesium absorption feature recorded immediately after detonation wave passage. Although the feature contains six hyperfine-split transitions (splittings given in MHz in the diagram at right), a two-line Voigt fit (assuming fixed spacing and fixed relative heights) is sufficiently accurate for extracting total feature area, collisional linewidths (assumed equal), and feature position.

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Even though the hyperfine structure contains 6 individual transitions, the small upper-state splittings can be neglected for current purposes. Thus, a two-line Voigt profile is fit to the data. An arbitrary two-line Voigt fit would have 8 total free parameters: two each of (area, Δν_c, Doppler width Δν_D, and position ν_o). However, in this case (partly because of Cesium’s high molecular weight and partly because of the high gas pressures existing during much of the detonation experiment), fixing both Δν_D values to 0.03266 cm^-1 (their values at the lowest expected temperature of 2000 K) introduces negligible errors. Also, the ratio of the two areas is fixed at 9/7, the line separation Δν_o is fixed at 9193 MHz = 0.3066 cm^-1, and the two Δν_c are assumed equal. Thus, 5 of the 8 free parameters have been removed; the two-line Voigt fit now returns only three parameters: area, Δν_c, and ν_o. The area is used to obtain T_{Cs, electronic}, Δν_c is used to obtain T_{Cs, kinetic}, and ν_o is not used. Note that ν_o contains pressure-shift information; like Δν_c, such information is pressure- and temperature-dependent, and therefore could be incorporated in future sensors. Histories of area and Δν_c obtained by repeated application of the two-line Voigt fit during a 7 ms detonation experiment (3710 total scans) are shown in Fig. 5.

 

Fig. 5. History of pertinent lineshape parameters obtained by repeated application (3710 total fits) of the two-line Voigt fit shown in Fig. 4. The integrated Cs absorbance area (right-hand axis) provides the ground state (6²S_1/2) Cs population, which is used to calculate T_{Cs, electronic} (shown in Fig. 6). The collisional linewidth of each component line, Δν_c, is used to calculate T_{Cs, kinetic} (also shown in Fig. 6).

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The area can also be used to infer the Cs vapor mole fraction (44 ppb for the scan shown in Fig. 4). In this experiment, the measured Cs vapor mole fraction is always much less than the Cs seeding fraction (5 ppm; see Fig. 1) because the majority of the Cs is present as either CsOH or Cs⁺ (the former at temperatures below ~ 2600 K and the latter at temperatures above ~ 2600 K [14]). The ionization to Cs⁺ at high temperatures is actually convenient for emission measurements because it limits the required dynamic range (if Cs⁺ were not favored at 4000 K, the emission would be some 10000 × the emission at 2000 K, rather than the ~ 50 × seen in Fig. 3).

The measured emission (Fig. 3) is corrected for radiative trapping using the absorption data and then divided by the measured area (Fig. 5); from this ratio, T_{Cs, electronic} is inferred using the Boltzmann distribution. However, because the emission measurement is not absolute, the T_{Cs, electronic} history requires calibration. Conveniently, in this well-controlled detonation experiment, the first T_{Cs, electronic} data point can be fixed to the Chapman-Jouget (C-J) temperature [19]; this can be done with high confidence (±3%) in the Stanford PDE because fueling [20] and detonation initiation [21] have been thoroughly characterized. The resulting electronic temperature history is shown in Fig. 6; we estimate the uncertainty to be ± 5%.

 

Fig. 6. Measured and computed gas temperatures for detonation of stoichiometric C₂H₄/O₂.

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Note that in less-controlled detonation experiments (particularly in practical PDEs) it may not be appropriate to calibrate the T_{Cs, electronic} sensor using the Chapman-Jouget value; in many instances one may wish to measure whether individual detonations reach the Chapman-Jouget temperature. The T_{Cs, kinetic} sensor, discussed below, is suitable for this purpose. Also shown in Fig. 6 is an initial comparison of the temperature measurements to a simulation performed by the Naval Research Laboratory (NRL); although discrepancies are apparent, the trends in the temperature histories generally agree. Such comparisons are part of an ongoing collaboration aimed at advancing PDE development. Details of the simulation are available in the literature [22].

Knowing both T_{Cs, electronic} and pressure (from a wall-mounted transducer; see Fig. 9), the corresponding equilibrium species concentration histories can be computed, as shown in Fig. 7. Note that the predicted equilibrium gas composition changes dramatically during this detonation experiment, and with it the ratio of specific heats, k.

 

Fig. 7. Calculated equilibrium species concentration histories for detonation of stoichiometric C₂H₄/O₂, obtained using the measured T_{Cs, electronic} history shown in Fig. 6 and the measured P_{spectroscopic} history shown in Fig. 9. The ratio of specific heats, k, is indicated at selected compositions.

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To determine T_{Cs, kinetic} from the Δν_c record shown in Fig. 5, we first divide Δν_c by 2 × P to obtain γ (following eq. 1). Next, best-fit values of the parameters n (-2.02) and γ_o(9.48 cm^-1/atm) are found using T_{Cs, electronic} as the temperature standard, as shown in Fig. 8. Although such data are scarce in the literature, these values can be compared with an estimation of n = -1.38 and γ_o = 0.68 cm^-1/atm for N₂-broadened potassium [16]. The large discrepancy in γ_o values is reconciled by a finding that sodium’s D₂ line is broadened much more severely by H₂O than N₂ (γ_Na-H2O,2000K ≈ γ_Na-N2,500K [23]). Note that direct measurement of room-temperature γ_o values for atomic alkalis broadened by species such as H₂O and CO₂ are difficult because of the extreme reactivity of these gases.

Returning to the linear fit in Fig. 8, the curvature of the data at high temperatures indicates that a single γ_o and n are somewhat inappropriate over the full temperature range, presumably because of the changing gas composition shown in Fig. 7. A composition-dependent fit is applied to capture this curvature. The linear fit is applicable over the 2000–3200 K temperature range; the composition-dependent fit is applicable over the full temperature range. Neither fit is intended to provide fundamentally accurate spectroscopic data; rather, the fits are designed to enable Δν_c-based temperature measurements over a limited temperature range and for a specific gas composition (namely, one approximating the equilibrium products of C₂H₄/O₂). Further work is required to extend the kinetic temperature measurement technique presented here to other gas compositions or temperature ranges.

 

Fig. 8. Determination of the best-fit overall Cs collisional broadening parameter, γ_{Cs-detonation products,} and its temperature dependence, using the measured Cs electronic temperature as the standard. A linear fit and a gas composition-dependent fit are shown. The composition-dependent fit is used to determine the gas (kinetic) temperature result shown in Fig. 6 from lineshape and pressure measurements. To demonstrate an alternate approach, the same fit is used to find the gas pressure result shown in Fig. 9 from lineshape and (electronic) temperature measurements.

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Using the composition-dependent fit shown in Fig. 8, the measured γ values plotted in Fig. 8 can be converted to the T_{Cs, kinetic} record shown in Fig. 6. The uncertainty in T_{Cs, kinetic} is estimated at ± 7%. The fit performed in Fig. 8 forces the two temperature records plotted in Fig. 6 to agree (to the extent that the composition-dependent fit matches the Fig. 8 data). Even so, the agreement represents a critical advancement, because now both detector 2 and the diffraction grating can be removed from the Fig. 1 setup and temperature measurements based on absorption only can be performed. Furthermore, the absorption-based (Δν_c-based) measurements are absolute; the single-laser, single-detector sensor can be used without calibration to obtain gas temperature in any Cs-seeded, C₂H₄/O₂ combustor (using an auxiliary pressure measurement).

Alternatively, detector 2 can be retained for calibrated T_{Cs, electronic} measurements and the Δν_c records and composition-dependent fit can be used to obtain gas pressure rather than T_{Cs, kinetic}; this approach has been used to generate Fig. 9. The spectroscopic pressure measurement agrees well with the transducer measurement, until t ≈ 5 ms. After this time, the transducer’s poor low-pressure accuracy, exacerbated by the recent high-pressure transient, is believed to be responsible for the disagreement. Because of unreliable transducer measurements, data after t ≈ 5 ms has been omitted from the Fig. 6 T_{Cs, kinetic} plot and the Fig. 8 fit. Both measured pressures shown in Fig. 9 agree reasonably well in an initial comparison with pressure histories simulated by NRL.

 

Fig. 9. Measured and computed pressures for detonation of stoichiometric C₂H₄/O₂.

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Summary

A wavelength-agile VCSEL has been used to measure gas temperature and pressure in a cesium-seeded PDE. The VCSEL scans through 10 cm^-1 every microsecond to recover Cs absorption lineshapes even in the high pressure PDE gases where the collisional widths reach 4 cm^-1. The rapid acquisition of lineshapes enables immunity to PDE noise sources [4] as well as microsecond time response in the temperature and pressure data. A video summary of the measurements is given in Fig. 10. The left panel shows the Cs absorption data and the 2-line Voigt fit. The upper right panel is T_{Cs, electronic}, and the lower right panel is P_{spectroscopic}. The T_{Cs, electronic} sensor requires calibration; in this controlled case, the Chapman-Jouget temperature was used as the calibration point. The T_{Cs, kinetic} and P_{spectroscopic} sensors rely on lineshape broadening data which was obtained here for a specific mixture (equilibrium products of stoichiometric C₂H₄/O₂) using the T_{Cs, electronic} and transducer pressure data. In future experiments involving other gas compositions, lineshape broadening data could be obtained in shock tubes, flames, or static cells rather than determined in-situ as demonstrated here.

 

Fig. 10. (2.37 MB) Animated summary of the sensor’s results for a single pulse of the PDE. The left panel shows the Cs absorption data (light blue circles) and the 2-line Voigt fit (solid blue fill). A Cs absorption feature is recorded every 2 μs. Each feature produces a T_{Cs, electronic} data point (upper right panel) and P_{spectroscopic} data point (lower right panel). 3710 consecutive scans over the Cs feature are used to obtain the ~ 7ms long temperature and pressure history. Time accelerates during the animation to emphasize the data recorded immediately after detonation passage. (7.64 MB version)

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Because wavelength-agile diode-laser sensing has been successful in this harsh PDE flow, applications in other harsh flows such as gas turbine and piston engines are anticipated. As wavelength-agile lasers become available at wavelengths above 1 μm, native species such as H₂O and fuel vapor can be targeted using similar sensing strategies, thus eliminating the need for seeding. Because of the small footprint and robust nature of wavelength-agile sensors, they are amenable to widespread industrial use.