1. Introduction
Laser-absorption spectroscopy (LAS) is widely used to provide non-invasive measurements of temperature, chemical species, pressure, and velocity. The demand for LAS measurements in high pressure and highly transient combustion and propulsion environments (e.g., detonation engines, rocket motors) continues to propel innovations in LAS diagnostics [1–5] and data-processing techniques [6–8]. Several of these innovations have focused on increasing the usable spectral bandwidth of LAS diagnostics while maintaining or improving temporal resolution.
LAS diagnostics utilizing large spectral bandwidth benefit from the greater diversity of spectral information collected. This helps mitigate some challenges associated with determining the non-absorbing baseline and reduced levels of differential absorption at elevated pressures, as well as improve the dynamic-range of thermometry. Broadband LAS diagnostics must, however, achieve fast temporal resolution in order to characterize highly transient processes such as chemical or internal non-equilibrium and to avoid time-varying, non-absorbing transmission losses such as those from beam steering or particle scattering. To date, broadband LAS diagnostics with fast time resolution can be grouped into two classes: (1) those employing broadly tunable CW light and (2) those employing ultrashort pulses. Regarding the former, vertical cavity surface-emitting lasers (VCSELs) and rapidly tunable external-cavity quantum-cascade lasers (EC-QCLs) have been utilized in the near-IR and mid-IR, respectively, to provide broadband (10s to 100s of cm−1) measurements of atomic and molecular absorbance spectra in combustion environments; however, such light sources are currently available at only a few central wavelengths. As a result, here we will focus on diagnostics employing broadband pulses within various architectures, namely, supercontinuum lasers (SCLs), dual-frequency-comb spectrometers (DFCS), optical-parametric oscillators (OPOs), and optical-parametric amplifiers (OPAs).
Regarding SCLs, Sanders utilized a femtosecond-laser-pumped SCL producing 1000 cm−1 of bandwidth near 1.56 𝜇m to acquire temperature and species measurements at 50 kHz in gases at 10 bar. Similarly, Werblinski et al. used an SCL with 500 cm−1 of bandwidth near 1.4 𝜇m to acquire 10 kHz measurements of temperature, pressure and H2O in a rapid compression machine (RCM) at pressures up to 65 bar. While the large bandwidth and repetition rate of such diagnostics are extremely attractive, SCL-based diagnostics are often limited by pronounced shot-to-shot intensity variations (requiring multi-shot averaging) and complexities associated with accurately modeling various instrument-broadening sources, particularly when dispersing fibers are used. More recently, DFCS has emerged as an effective tool for providing high-fidelity, broadband measurements of absorbance spectra with unprecedented spectral resolution. For example, Draper et al. utilized a DFCS with 160 cm−1 of bandwidth near 1660 nm to acquire 1.4 kHz measurements of temperature and CH4 at up to 30 bar inside of an RCM. However, DFCS also typically requires time-averaging to achieve high signal-to-noise ratio (SNR) and such diagnostics in the mid-IR are still emerging.
Last, the recent advent of high-speed, cryogenically cooled, mid-IR cameras has, in part, enabled the first single-shot, ultrafast (i.e., sub-nanosecond) absorption measurements in the mid-IR, as well as broadband absorption measurements with near-microsecond time resolution at 10s of kHz. Regarding the latter, Loparo et al. employed a mid-IR OPO which produced ultrashort pulses at 100 MHz to provide 476 cm−1 of bandwidth near 3.25 𝜇m. This enabled the authors to acquire measurements of CH4, C2H4 and C2H6 at 21.5 kHz in a shock tube at pressures near 2.5 bar. To date, this technique has demonstrated a measurement time resolution of 37 𝜇s (set by the integration time of the camera).
Here we build on our recent development of ultrafast laser-absorption spectroscopy (ULAS) to provide the first single-shot, ultrafast, mid-IR measurements of temperature and species in high-pressure and multi-phase combustion gases. Further, we demonstrate for the first time that ULAS can provide 1D, single-shot, ultrafast measurements of temperature and species in a flame which represents a significant advancement beyond previously developed broadband LAS diagnostics. These new capabilities were made possible through advancements in the optical setups employed and several notable refinements to the spectral-modeling and -fitting procedures. This manuscript describes these advancements and the key principles of ULAS in detail. Additionally, a supplemental document discusses important practical considerations for spectral interpolation and imaging ultrashort pulses in the mid-IR.
2. Experimental setup
2.1 Optical setup
Figure 1 shows a schematic of the optical setup used for this work. Special attention is given to the new additions and modifications to the basic ULAS optical setup (described by Tancin et al.) which enabled high-pressure and 1D measurements. The ultrafast-laser system (described in previous work) consists of a Ti:sapphire oscillator which produces 55 femtosecond pulses centered near 800 nm at 80 MHz. The pulses were selectively amplified at 5 kHz to a pulse energy of 2 mJ and subsequently converted into the mid-IR using optical parametric amplification (OPA) and non-collinear difference-frequency generation (NDFG) to achieve a center wavelength near 4.9 𝜇m with a pulse energy of ≈ 5 𝜇J.
After wavelength conversion, a MgF2 Rochon-prism polarizer was used to attenuate the pulse energy to ≈ 2 𝜇J. Next, a spatial filter (optics #1, #2, and #3 in Fig. 1) was used to improve beam quality and reduce the 1/𝑒2 beam diameter to ≈ 2 mm. The improved beam quality provided by the spatial filter improved the spectral resolution and SNR of the diagnostic. The latter of which ultimately enabled 1D measurements through eliminating the need for spatial (i.e., intrapulse) averaging. The laser beam was then directed through the test gas within either a heated-gas cell or propellant flame. The transmitted pulses were then focused onto the input slit of a spectrograph (Andor Shamrock 500i) using a CaF2, plano-convex, cylindrical lens with a focal length of 75 mm. The spectrograph employed a reflective diffraction grating to disperse the light onto the InSb FPA of a high-speed, infrared camera (Telops FAST-IR 2K). The IR camera can acquire at nearly 2 kHz at full-frame resolution (320 x 256) and faster when the resolution is reduced. A frame rate of 10 kHz can be reached at 256 x 52 resolution (what was used here) and a maximum of 90 kHz can be achieved at 64 x 4 resolution. In high-pressure propellant tests, images of single-shot spectra were averaged across the spatial dimension of the image to improve the measurement SNR. A high-resolution (300 lines/mm) diffraction grating providing 10 cm−1 of bandwidth (near 5 𝜇m) and 0.3 nm resolution was used for propellant tests at atmospheric pressure. A low resolution (150 lines/mm) grating providing 35 cm−1 of bandwidth and 0.6 nm resolution was used for high-pressure propellant tests. Both gratings were used at all pressures for gas-cell tests.
Corrective optics were required in order to reduce the loss of signal from severe beam steering encountered in high-pressure propellant flames. Figure 2 illustrates that without corrective optics, complete loss of signal can occur from beam steering-induced angular deflections. These additional optics consisted of a lens telescope (optics #4 and #5 in Fig. 1) with focal lengths of 𝑓 = 200 mm and 𝑓 = 25.4 mm and a final lens (optic #6) with a focal length of 250 mm. The focal point of the lens telescope was centered at the propellant flame and acted to partially correct any angular deflections caused by beam steering, minimizing the loss of signal. The final lens aided in boosting signal counts by reducing the beam size incident on the focal plane array (FPA) of the IR camera. The improvements provided by the corrective optics are illustrated by Fig. 2, which shows the average signal counts with and without corrective optics for a variety of pressures.
For 1D, intrapulse measurements, more significant changes were required in order to improve the spatial resolution and measurement field-of-view. First, the recollimation lens used for the spatial filter (optic #3 in Fig. 1) was replaced with a 150 mm focal length lens such that the beam was expanded to over 1 cm in diameter. Next, optic #4 was replaced with a plano-convex, CaF2 cylindrical lens with a 200 mm focal length to focus the laser beam into a vertically oriented sheet on the centerline axis of the propellant flame. The beam was then recollimated using a similar cylindrical lens with a 75 mm focal length (optic #5). Finally, a plano-convex, CaF2 cylindrical lens (optic # 6) with a 200 mm focal length (oriented to focus the beam in the vertical direction) was used to control the field of view of the imaging system.
2.2 Gas-cell experiments
ULAS measurements were acquired in a high-uniformity, heated, static-gas cell (described by Schwarm et al.) to validate the accuracy of the diagnostic at high temperature and pressure, as well as to determine the instrument response function (IRF) via a multi-spectrum fitting routine (MSFR) discussed in detail in Section 4.2. Spectra were measured in a mixture of 2% CO and 1.8% CO2 by mole with a balance of nitrogen at 1000 ± 20 K and pressures of 0.3, 1, 3, 10, 20, and 40 bar. The gas pressure was measured using a UNIK-5000 pressure transducer with a full-scale range of 0 to 70 bar and an accuracy of ± 0.028 bar. Temperature was measured using three type-K thermocouples with a nominal accuracy of 0.75% (at ≥ 600 K) fixed to the outside of the gas cell as in. The gas cell was equipped with 15 cm long, wedged, CaF2 rods which provided an absorbing path length of 9.4 cm at room temperature.
2.3 Laser-ignited propellant flames
Cylindrical propellant strands with a height of 4 to 6 mm and a diameter of 7 mm were tested. The particle size of ammonium perchlorate (AP) was distributed bimodally with mean diameters of 200 𝜇m and 20 𝜇m in a coarse-to-fine ratio of 4:1. In the aluminized propellants, Valimet H-30 aluminum with a mean particle diameter of 31 𝜇m was used. The AP-HTPB propellant consisted of 80% AP by mass, whereas the AP-HTPB-Al propellant was 68% AP, 15% aluminum and 17% binder by mass.
The propellant strands were ignited using a CO2 laser providing an optical intensity of 38 W/cm2 to the surface of the strand. The data acquisition system was triggered 100 ms prior to the CO2 laser turning on to allow for the baseline laser intensity (𝐼0) to be recorded. The CO2 laser was turned on for 200 ms (400 ms at 1 bar) to ignite the strand. Video of each test was recorded with a Nikon D3200 DSLR camera to ensure that ignition and burning of each strand was uniform, and to provide an estimate of the absorbing path-length. The propellant flames reached a quasi-steady state approximately 100 ms after ignition. Figure 3 shows images of the propellant flames acquired using the DSLR camera.
All propellant tests were conducted in a high-pressure combustion chamber (HPCC), described in detail by Tancin et al.. The ULAS beam was aligned through the centerline of the propellant for all tests. Measurements were acquired at a height of 2 mm and 1 cm relative to the initial surface location of the propellant strand for non-aluminized and aluminized propellants, respectively. Prior to each test, the chamber was evacuated using a vacuum roughing pump before being pressurized with an argon bath gas. A time history of pressure was recorded during each test enabling the data-processing routine to use an updated pressure for each subsequent laser shot. The gas pressure increased by ≈ 0.6 bar during each test. For tests at atmospheric pressure, the HPCC vent valve was partially opened immediately prior to ignition, such that no pressure rise occurred during the test.
Proof-of-concept, 1D-resolved, single-shot temperature and CO measurements were acquired in an HMX (i.e., 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane) flame. The HMX was pressed into cylindrical pellets which were 6 mm in diameter and 4 to 5 mm tall. For this test, the CO2 laser was left on for the full duration of the experiment. The HMX experiment was conducted in air.
3. High-fidelity modeling and spectral-fitting of ULAS spectra
This section provides a detailed description of the data-processing and spectroscopic modeling procedures used to infer gas properties from ULAS measurements of transmitted intensity spectra. In essence, a nonlinear least-squares fitting routine is used to fit simulated absorbance spectra to measured absorbance spectra. There are two workflows: (1) processing measured data and (2) simulating absorbance spectra which are described below and illustrated in Fig. 4.
The procedure for processing measured spectra consists of five key steps.