Combustion diagnostics is a field of long standing interest with many resources continually dedicated to its study. Turbulence has significant effects on combustion processes such as turbulence-chemistry interactions, turbulence-radiation interactions, scalar dissipation, transport, and mixing. Nonintrusive optical diagnostic methods have been used to study combustion and all must consider the effects of turbulence. Laser-based methods are highly effective and widely used due to their high spectral and temporal resolution [1]. Dispersive instruments [2,3] and Fourier-transform spectrometers [4] have been used with optical scanners to tomographically deconvolve temperature and species concentrations. High-speed infrared cameras with various bandpass filters have been used to map spatial variations in radiant intensity and relate these to various measures of turbulence (e.g., integral length and time scales) [5] as well as the spatial distribution of scalar values (e.g., temperature and mole fraction) [6].

An imaging Fourier-transform spectrometer (IFTS) is a hyperspectral imager that combines a Michelson interferometer with a staring infrared focal-plane array (FPA). There are several potential advantages of this instrumentation for combustion diagnostics. High spectral resolution across a wide bandpass enables identification of multiple species. Proper interpretation of the spectrum can permit simultaneous determination of temperature and species concentrations [7]. High spectral resolution is also beneficial to tomographic reconstruction techniques [8]. High-speed broadband infrared imagery is collected during each interferometric scan. This captures turbulence information and enables similar types of analysis already performed using infrared cameras. IFTS provides a useful passive and nonintrusive technique for studying combustion and is particularly useful when (1) both high-speed imagery and spatially resolved spectra are required, (2) characterization of high-pressure systems is required and collisional broadening effects become important, (3) more than one optical port is not available, limiting the types of laser-based methods available for interrogation. The present work presents the first IFTS measurements of a canonical turbulent jet flame. The scope of this work includes a qualitative discussion of the spectral imagery and a quantitative comparison with existing spectral measurements acquired at select locations in a similar flame. The impact of turbulent intensity fluctuations on interferogram formation is also described. Quantitative interpretation of flame spectra is the ultimate goal of this effort. However, it requires scalar-field fluctuation statistics, and this important topic will be considered in future work.

The experiment consisted of the Telops Hyper-Cam IFTS, two calibration blackbodies, and the flame. The flame tube is 480 mm long with an 8 mm exit diameter ($D$), mounted vertically, and moveable via unislide to allow combined imaging of the entire visible flame length without camera tilt. The flame replicates Flame DLR_A from the International Workshop on Measurement and Computation of Turbulent Nonpremixed Flames (TNF Workshop) with a jet exit Reynolds number of 15,200 and exit velocity of $42.2\mathrm{m}/\mathrm{s}$. Mass flow rates were 313, 59, $1105\mathrm{mg}/\mathrm{s}$ for ${\mathrm{CH}}_4$, ${\mathrm{H}}_2$, and ${\mathrm{N}}_2$, respectively. Flow rates were calibrated using a dry turbine meter and controlled by setting the pressure upstream of three choked orifice plates [5].

The TNF Workshop flames are well characterized and designed for collaborative comparisons of measurements and models. A library of local velocities and scalar values (temperature, species mole fractions) measured simultaneously using laser Doppler velocimetry, Raman, Rayleigh, and LIF techniques is available for download [9,10].

The IFTS is based on a traditional Michelson interferometer coupled to a high-speed $320\times 256$ indium antimonide staring FPA via $f/\#=2.5$ imaging optics [7,11]. The spectral range covers 1800–$6667{\mathrm{cm}}^{-1}$, and the spectral resolution can be selected between 0.25 and $150{\mathrm{cm}}^{-1}$. An interferometric “datacube” is a collection of snapshot images taken at equally spaced optical path differences (OPDs), and Fourier-transformation along this dimension produces a spectrum at each pixel.

An external $0.25\times$ telescope expanded the field-of-view and reduced the minimum working distance to the flame. A 45% transmission neutral density filter, used to prevent saturation, limited the short-wavelength response to 2.22 μm ($4500{\mathrm{cm}}^{-1}$). The IFTS was located $(47.5\pm 1.0)\mathrm{cm}$ from the flame. The imaging system has an effective focal length of 19.7 mm at this working distance. The 30 μm pixel pitch of the FPA yields an instantaneous field-of-view (IFOV) of 1.52 mrad which translates to $(0.72\pm 0.02)\mathrm{mm}$ at the flame and is constant across the array. The mean RMS spot size radius is 13.7 μm, and increases from 11.2 to 21.1 μm moving from center to corner of a $128\times 192$ window. Mapping the Rayleigh $\lambda /4$ wavefront error depth-of-focus criterion, $\delta f=\pm 2\lambda {(f/\#)}^2$, to object space produces a conservative estimate of the depth-of-field of $\pm 2\mathrm{cm}$ when computed at 2.5 μm, the shortest wavelength with appreciable energy arriving at the FPA. Throughout much of the flame, the spectral imagery can thus be interpreted as integrated along the line-of-sight (LOS). However, the widest part of the flame is $\sim 15\mathrm{cm}$, indicating some blurring will occur along the LOS. A detailed Zemax [12] optical model of our system indicates that more than 75% of the energy (relative to the diffraction-limited case, 86.4%) comes from the LOS for a pixel viewing the center of the widest ($\pm 7.5\mathrm{cm}$) flame region.

The IFTS was mounted to a gimbal with preset locations for intermittent calibration measurements. A standard two-point calibration using the wide-area blackbodies set to 595°C and 200°C was performed pixel-wise to determine the system response [gain, $G_i(\tilde{\nu })$] and instrument self-emission [offset, $L_i^I(\tilde{\nu })$]. The higher blackbody temperature produced a peak signal at $\sim 90\%$ of the detector’s dynamic range and slightly exceeding that from the brightest part of the flame. At 595°C, the Planckian distribution monotonically decreases with frequency across the detector bandpass. This resulted in a nominal signal-to-noise ratio (SNR) in $G(\tilde{\nu })$, which decreased nearly linearly from 15 to 1 between 3000 and $5000{\mathrm{cm}}^{-1}$. Since the system response is known to vary smoothly and slowly with $\tilde{\nu }$, a spline was fit to each pixel’s gain curve to mitigate the impact of low-gain SNR on the calibrated spectrum.

Two sets of flame measurements were made. The first set was collected with high spectral resolution ($0.25{\mathrm{cm}}^{-1}$) in a small window ($8\times 192$) traversing the flame at 20, 40, and $60D$ above the burner to facilitate identification of various chemical species. Interferometric datacubes consisted of 52,742 images and were collected at a rate of 0.55 Hz, and 512 cubes were averaged to produce a mean, calibrated image of the flame radiance. The second set increased the FPA window height ($128\times 192$) to facilitate measurement of the entire flame and decreased spectral resolution ($16{\mathrm{cm}}^{-1}$) to simplify data reduction. Datacubes consisted of 1186 images and the acquisition rate increased to 4.2 Hz. Seven separate regions of the flame were imaged to produce a composite image of the entire flame. In each set the camera’s integration time was 20 μs, and imaging frame rates exceeded 5 kHz. Ambient temperature, pressure, and humidity were monitored with a Kestrel 4500 Weather Meter with averages of 25°C, 989 hPa, and 44% respectively.

Fourier-transform spectrometry is typically used to study static scenes, so we briefly review interferogram formation so that the impact of stochastic intensity variations from the turbulent flame can be properly understood. The formation of an interferometric datacube is depicted in Panel A of Fig. 1. Light enters the Michelson producing an interference pattern at the FPA which encodes the spectral radiance at each pixel in the image. This interferogram is a function of the OPD, $x$, or time, $t$ (the two being related by the constant mirror sweep speed $v$):

 

Fig. 1. Panel A: schematic illustrating the FPA capturing infrared images at fixed OPDs as the Michelson sweeps, generating an interferometric datacube. Panel B: single interferogram (green, upper curve) and corresponding raw spectrum (red, lower curve) at flame center $20D$ above exit. Panel C: Time-averaged interferogram (green, upper curve) and corresponding mean flame spectrum (red, lower curve).

Download Full Size | PDF

For a turbulent jet the scene radiance is stochastically fluctuating on a timescale much shorter than the interferometer’s acquisition rate. Thus, the “DC” term is now time-dependent and the AC term has no simple interpretation as it is the cosine transformation of a stochastically varying signal. This is illustrated in Panel B of Fig. 1 showing a single interferogram and corresponding raw magnitude spectrum. The fluctuations in integrated intensity dominate the signal and obscure the zero-path difference (ZPD) where all wavelengths constructively interfere. The corresponding spectrum is dominated by the frequencies associated with turbulent radiation fluctuation, although a feature near $2300{\mathrm{cm}}^{-1}$ resembling emission from the asymmetric stretching mode (${\nu }_3$) of ${\mathrm{CO}}_2$ is recognizable. Large intensities below the detector cut-off ($\tilde{\nu }\le 1800{\mathrm{cm}}^{-1}$) are due to turbulent fluctuations.

For an ergodic system, an ensemble of measurements will produce a mean interferogram corresponding to the mean spectral radiance since Eq. (1) is a linear transformation. Panel C presents the same pixel’s mean interferogram from 512 measurements, demonstrating that the turbulent fluctuations are suppressed. The resulting spectrum is now recognizable with rotational fine structure associated with vibrational transitions in ${\mathrm{H}}_2\mathrm{O}$, ${\mathrm{CH}}_4$, $\mathrm{CO}$, and ${\mathrm{CO}}_2$.

Figure 2 presents uncalibrated broadband imagery in Panels A and B, dividing the flame along the axis of symmetry into single-snapshot and time-averaged quantities. Each segment is temporally independent from the others. In Panels A and B the images were acquired at a common OPD near $x=370\mathrm{\mu m}$. Away from ZPD the imagery is similar to what an infrared camera would measure ($I_i(x)\simeq I_i^{\mathrm{DC}}$) since the broadband nature of radiation ensures $|I_i^{\mathrm{AC}}(x)|\ll I_i^{\mathrm{DC}}$. At the burner tip, the distance traveled by the jet during the FPA’s integration time is 0.84 mm, exceeding the IFOV by approximately 12%, a conservative estimate of blurring due to the rapid deceleration of the jet. Moreover, the turbulence integral length scales for this flame between 20 and $60D$ are within 9.1–24 mm [5]. Thus, the turbulent structures exceed the spatial resolution by an order of magnitude. The time between repeated observations at a particular OPD is 240 ms, greatly exceeding the turbulence integral time scales (2.3–5 ms between 20 and $60D$). Repeated observations at each OPD are statistically independent.

 

Fig. 2. Panel A: single broadband images from the lower spectral resolution ($16{\mathrm{cm}}^{-1}$) datasets with $128\times 192$ FPA window. Panel B: corresponding time-averaged broadband images. Panel C: Time-averaged radiance spectrally averaged over a prominent ${\mathrm{CO}}_2$ band. Panel D: Time-averaged radiance spectrally averaged over a prominent ${\mathrm{CH}}_4$ band. (Last spatial region limited due to unislide range.)

Download Full Size | PDF

Also shown in Fig. 2 are calibrated images (via the time-averaged interferometric cubes) resulting from integration over spectral bands corresponding to ${\mathrm{CO}}_2$ (Panel C) and ${\mathrm{CH}}_4$ (Panel D). The imagery provides a qualitative impression of the distribution of these species throughout the flame. For example, ${\mathrm{CO}}_2$ emission is low near the burner tip but increases axially as air is entrained to fuel the combustion reaction. The ${\mathrm{CO}}_2$ band radiance peaks at $55D$, in agreement with previous narrow-band $(4.34\pm 0.10)\mathrm{\mu m}$ measurements of the same flame [5]. Temperature, species concentration and the LOS distance through the flame all affect the band-integrated radiance. For example, the initial increase in ${\mathrm{CH}}_4$ intensity with distance from the tip is due to increasing temperature despite decreasing concentration. Proper interpretation of the spectrum will enable the deconvolution of these interdependencies.

The mean high-resolution spectrum acquired from a diametric path at $20D$ is presented in Panel A of Fig. 3. Emissions from ${\mathrm{CH}}_4$, $\mathrm{CO}$, ${\mathrm{CO}}_2$, and ${\mathrm{H}}_2\mathrm{O}$ are resolved, and major vibrational transitions are annotated using common spectroscopic notation [13]. Individual lines associated with the P-branch of CO are visible between 2000 and $2150{\mathrm{cm}}^{-1}$; lines from the R-branch overlap with the strong ${\mathrm{CO}}_2$ emission band associated with the asymmetric stretching mode. The mean low-resolution spectra from diametric paths at 20, 40, and $60D$ are compared with previous (nonimaged) LOS measurements of flame A by Zheng et al. [2] in Panel B of Fig. 3. A spatial average over a $3\times 3$ window was performed to approximate the 2 mm resolution of Zheng’s data. The solid lines represent the apparent (i.e., at-sensor) radiance. For proper comparison, atmospheric correction was performed (dashed lines) using measured lab conditions and assuming 500 ppm ${\mathrm{CO}}_2$ concentration. Agreement is excellent at 40 and $60D$. However, the ${\mathrm{CO}}_2$ peak near $2300{\mathrm{cm}}^{-1}$ is $\sim 20\%$ below the previously reported value at $20D$. Radiance uncertainties (95% confidence interval) are shown and include the effects of both systematic errors in calibration and noise. Noise is estimated as the root-mean-square value of the imaginary component of the time-averaged spectrum. Turbulent fluctuations are minimized in the time-averaged interferogram, so the error band does not quantify the large variance in flame radiance. At 20 and $60D$, the mean uncertainty between 2200 and $2350{\mathrm{cm}}^{-1}$ is 5% and 4%, respectively. Between 3000 and $4000{\mathrm{cm}}^{-1}$, the uncertainty increases to 20% and 10%, respectively, at 20 and $60D$.

 

Fig. 3. Panel A: diametric, high-resolution ($\delta \tilde{\nu }=0.25{\mathrm{cm}}^{-1}$) apparent flame spectrum at $20D$ with spectroscopic transitions annotated. Panel B: apparent (—) and atmospheric-corrected (⋯) low-resolution diametric flame spectra ($\delta \tilde{\nu }=16{\mathrm{cm}}^{-1}$) at 20, 40, and $60D$ (black, red, blue) compared with previous measurements (○). Radiance uncertainty (95% confidence interval) presented as a translucent band around each apparent spectrum. The ${\mathrm{CO}}_2$ and ${\mathrm{CH}}_4$ bands used in Fig. 2 are identified.

Download Full Size | PDF

This work makes two key contributions. First, it validates the use of IFTS for studying turbulent flames and provides complete time-averaged hyperspectral imagery of flame A. Segments of the flame were imaged with spectral resolution an order-of-magnitude better than previous measurements, and this data could be used to evaluate and improve narrowband radiation models. Second, it demonstrates the potential of IFTS for combustion diagnostics. Mean hyperspectral images contain information about the distribution of both temperature and many major gas species throughout the flame. Additionally, the high-speed broadband imagery comprising each interferometric measurement contains information about the fluctuation statistics. High resolution in all three domains—spectral, spatial, and temporal—is extremely valuable in the study of turbulent combustion and is captured in IFTS measurements. Having demonstrated the validity of time-averaged spectra in this work, our efforts will now turn to leveraging the high-speed imagery contained within IFTS measurements to understand scalar fluctuation statistics, a key step in the quantitative interpretation of turbulent flame hyperspectral imagery.