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Abstract
We present a feasibility demonstration of the instantaneous determination of temperature fields in gaseous flows based on planar laser-induced fluorescence by integrating structured illumination with the two-line thermometry technique using nitric oxide as a tracer. This approach allows the capture of two fluorescence images originating from the simultaneous probe of two rotational states of nitric oxide (X2Π, v” = 0) using one detector and their subsequent deconvolution using spatial frequency analysis. Average experimental temperature measurements in an underexpanded jet demonstrate the viability of this approach, suggesting that the laser spatial modulation frequency and laser orientation with respect to the flow field under study impose the achievable spatial resolution limits.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The study of rapidly evolving fluid flows, particularly those involving complex phenomena such as chemical reactions, gradients, turbulence, and non-equilibrium conditions, requires diagnostic tools capable of providing measurements of velocity and scalar quantities (e.g. species densities, pressures, and temperatures) with high time and space resolution, and thus, a variety of quantitative imaging techniques based on pulsed lasers have been developed to explore such environments. Many of these diagnostic tools rely on planar laser-induced fluorescence (PLIF) of a molecular tracer that is already present in the flow under study or that can be easily seeded. The use of PLIF techniques are advantageous due to (1) the availability of high-energy UV laser sources required to excite a number of tracers, (2) high signal levels resulting from high fluorescence quantum yields, and (3) the ability to provide 2-D measurements. Several PLIF-based techniques employed to perform temperature imaging require a simple one laser/one detector setup. These techniques have been developed using tracers such as acetone [1] and nitric oxide [2], and are based on a direct relationship between fluorescence intensity to temperature. Although this approach can provide an instantaneous determination of temperature, it requires homogeneous seeding as well as knowledge of the tracer’s concentration and flow field pressure distributions. Additionally, careful interpretation of the fluorescence signals and their relationship with temperature demands precise knowledge of the tracer’s photophysical properties, particularly those defining the dependence of fluorescence intensity on temperature, pressure, and gas composition. Other techniques providing instantaneous 2-D temperature determinations are based on the relationship of the tracer’s fluorescence spectral shift with varying temperature and employ one laser and two detectors fitted with optical filters, as in the case of toluene [3,4]. PLIF temperature determinations can also be achieved using dual-excitation schemes that result in a reduced dependence of the measurement accuracy on the knowledge of tracer photophysics. Demonstrations of this approach employ a tracer such as 3-pentanone or acetone that is sequentially excited at two different wavelengths. The resulting fluorescence signals are imaged separately and ratioed to yield temperature [1,5]. The use of diatomic tracers such as OH and NO for dual excitation PLIF thermometry, i.e. the two-line technique, takes advantage of the natural occurrence of these tracers in combustion systems or heated air flows [2,6], and require the excitation of two transitions originating from two different rotational states within the same vibrational level, resulting in a measurement of rotational/translational temperature. A simple determination of the fluorescence intensity ratio at a region of known temperature suffices to calibrate the measurement, assuming a Boltzmann distribution. The use of NO as a tracer for quantitative PLIF applications is advantageous because of its thermal stability, its virtually identical heat capacity ratio to the one of air, and its well-documented spectroscopy. Additionally, NO can be seeded in a wide variety of flow fields, including cold high-speed flows, without worrying about tracer condensation. Given the spectral overlap of the broadband fluorescence from the A2Σ+ state resulting from the excitation of two rotational states, a time separation between the two acquired fluorescence signals is necessary, requiring a two laser/two camera setup, or the use of two lasers with an interline CCD camera to capture two images with a time separation. Although a time delay on the order of 1 microsecond between the two fluorescence events would effectively accomplish an instantaneous temperature determination for slow-moving flow fields, a time separation in supersonic flows would incur spatial averaging along the direction of the flow displacements, resulting in a strictly non-local and non-instantaneous measurement.
In this paper, we present a new configuration to perform instantaneous dual wavelength PLIF thermometry, demonstrated using the NO two-line technique, where the two fluorescence images are captured simultaneously by a single detector. This approach additionally results in a simpler experimental setup than the conventional two-line approach when using two cameras. PLIF imaging techniques are traditionally based on the homogeneous illumination of an area of interest using a laser shaped into a sheet. Simultaneous imaging of two spectrally overlapping fluorescence signals arising from separate excitation sources can be accomplished by embedding a spatial modulation pattern to one of these signals, and their subsequent separation can be performed using a spatial frequency lock-in algorithm. This imaging approach originated in the optical microscopy field to achieve increased spatial resolution and to reduce background interferences of light from out-of-focus regions, and involves the use of a sinusoidally patterned illumination source [7–9]. Reduced background interference is achieved by imposing a periodic illumination pattern to spatially encode the signal of interest located in the in-focus area to differentiate it from the rest of the light reaching the detector. Since the illumination spatial modulation results in alternating regions of high and low signal intensity, multiple images obtained at different modulation phase offsets are required to reconstruct the entire area of interest in order to avoid adverse effects on spatial resolution [9]. The use of this illumination principle to reduce background interferences outside of the optical microscopy field has been primarily applied in the study of sprays via laser scattering. This strategy has demonstrated a significant reduction of interferences produced by multiply scattered photons that affect interpretation of the resulting 2-D elastic scattering signals [10–12]. However, the requirement of three sequentially obtained images to reconstruct the entire area of interest limits the applicability of this technique to static or steady flow fields. Although some work has been performed to extend the applicability of structured illumination to single-shot imaging, these efforts have primarily focused on the elimination of unwanted background in scattering applications [13], and the qualitative determination of the spatial distribution of chemical species [14]. The two-line thermometry imaging approach that we present in this paper is based on the simultaneous excitation of two rotational states by two laser sheets, in which one sheet contains a sinusoidal modulation pattern, followed by the deconvolution of the fluorescence signals using appropriate spatial-frequency analysis. This work also demonstrates quantification of both fluorescence signals as opposed to only extracting one modulated signal from an unwanted background.
2. Instrumentation
2.1 Flow field description
The evaluation of the proposed thermometry technique was performed in a high-speed test facility previously described in detail elsewhere [15,16], in which the converging-diverging nozzle was replaced by a 1 mm diameter sonic nozzle operated continuously by keeping the instruments’ pulsed valves permanently open. The underexpanded jet flow field has been previously used to demonstrate measurements of velocities and temperatures due to its challenging wide range of densities, velocities, and temperatures [17–21], and the overlap of these conditions with those encountered in cold high-speed flows generated via gas expansions. Additionally, the presence of sharp temperature gradients at the barrel and Mach disk shocks in the underexpanded jet presents an opportunity to observe the performance of the suggested thermometry imaging approach in terms of spatial resolution. The gas flow was composed of mixtures of 2% nitric oxide in nitrogen and 5% nitric oxide in nitrogen, and fed into the nozzle at a stagnation pressure of 60 kPa to be expanded through the nozzle into the vacuum chamber kept at 253 Pa using a roots blower pump assembly, producing an underexpanded jet with a pressure ratio (JPR) of 234.
2.2 Laser system
The experimental setup used in these demonstration measurements is shown in Fig. 1
Fig. 1 Experimental setup of the NO PLIF imaging system. The laser sheet sent from above was aligned through an aluminum grid to produce a fluorescence spatial modulation.
The lasers were tuned to probe the R1 + Q21 (1.5) and the R12 + Q2 (9.5) lines in the A2Σ+(v’ = 0) X2Π1/2(v” = 0) band, respectively. The laser sheet probing the low-J state, aligned from above, was additionally sent through an evenly spaced aluminum mesh located 50 mm above the nozzle exit. This aluminum mesh provided a modulation pattern of high and low fluorescence intensity regions in the low-J image that was subsequently employed to separate this fluorescence signal from the one originating from the excitation of the high-J state. The fluorescence signals were simultaneously imaged by a gated Princeton Instruments PI-MAX4 ICCD camera that was fitted with a CERCO 100 mm F/2.8 UV lens and was mounted on the side of the vacuum chamber perpendicular to the laser sheets. A set of extension rings comprised of one 36 mm, two 20 mm, and one 12 mm was used between the camera and the lens to increase magnification. No optical filters were employed. Scatter was avoided by timing the camera gate right after the laser excitation using a BNC 575 digital delay/pulse generator. 200 single-shot images were acquired using camera gates of 100 ns and averaged in each case, resulting in images of a 12 x 12 mm region with a spatial resolution of 85 pixel/mm.
3. Results and discussion
The top and middle panels of Fig. 2
Fig. 2 Average fluorescence images of the underexpanded jet probing J = 1.5 (a) and J = 9.5 (b) separately. Experimental composite image obtained probing both rotational states simultaneously using a modulation on the low-J state excitation (c). Flow direction is from left to right.
Figure 2(c) shows the average PLIF image obtained by simultaneously probing J = 1.5 and J = 9.5, with the modulation grid placed in the path of the laser sheet exciting the low-J state. The deconvolution of the two fluorescence signals from a single image is based on the fact that the amplitude of the modulated signal is related to its absolute intensity, as shown in previous light scattering work [13]. Following this principle, quantitative interpretation of a fluorescence signal resulting from single-photon excitation is possible if such a process occurs in the linear regime. Thus, the amplitude of the modulated fluorescence signal originating from the excitation of the low-J state was extracted and employed to obtain its absolute intensity. Verification of the direct proportionality between the low-J modulated signal amplitude and its absolute intensity was performed experimentally by measuring the fluorescence modulation amplitude obtained with the grid on the laser path as a function of absolute fluorescence intensity obtained without the grid. Figure 3
shows a plot of the normalized values of the measured modulated amplitudes as a function of unmodulated fluorescence intensity, corroborating that the modulation amplitude can be used as a metric of fluorescence intensity in the range of fluorescence intensities resulting from these experiments. Furthermore, it was determined that the use of the aluminum mesh as a modulating tool resulted in a homogeneous reduction of the fluorescence signal at the signal modulation valleys by 18.5 ± 3.1% at all employed laser powers.Pre-processing of all images included background subtraction, as well as correction for lens distortions and inhomogeneities of the laser sheet intensities. The J = 1.5 and J = 9.5 images obtained separately [Figs. 2(a) and 2(b)] were ratioed, and the resulting image, R12, was used to determine a temperature map using the expression:
where the calibration constant C12 was experimentally determined from the average fluorescence ratio at a region outside the jet known to be at room temperature, and had a value of 0.15. The resulting temperature map is shown in Fig. 5(c). This reference temperature map is in good agreement with previous measurements and Computational Fluid Dynamics (CFD) simulations of this flow field under the same JPR conditions [16].The analysis methodology employed to deconvolve the low-J and high-J fluorescence signals from a single image is based on a post-processing lock-in detection algorithm. Lock-in detection is commonly used to detect and extract one-dimensional signals strongly affected by noise. This signal detection methodology employs frequency analysis and requires the signal of interest to contain a modulation at a precisely known frequency. The signal at the frequency and phase of interest is extracted and signals at any other frequencies are rejected. In our experiments, this well-known spatial modulation frequency was imposed horizontally by the aluminum mesh to the J = 1.5 image. Using the measured modulation frequency of 0.33 mm−1 and the fact that, under the experimental conditions, this grid blocked 18.5% of the light, a lock-in detection algorithm was used to extract the low-J signal from the composite experimental image. The post-processing routine used to deconvolve the two fluorescence signals is illustrated in Fig. 4
.To accomplish the separation, two synthetic reference images containing a modulation at the same frequency as the experimental image, phase-shifted by 90 degrees from each other, were generated. Multiplication of the raw image by the phase-shifted reference images followed by low-pass filtering effectively extracts the in-phase and quadrature components of the modulated fluorescence, Xc and Yc, that are in turn used to recover the absolute intensity distribution attributed to the low-J excitation [22,23]. The remaining fluorescence intensity in the raw image is attributed to the unmodulated J = 9.5 fluorescence signal. The results of this deconvolution process are shown in Figs. 5(a) and 5(b)
Fig. 5 Fluorescence images, corresponding to J = 1.5 (a) and J = 9.5 (b), recovered from the experimental composite image shown in Fig. 2(c). Temperature map in Kelvin obtained by using the traditional two-line thermometry approach (c). Temperature map in Kelvin obtained using the PLIF images recovered by the present approach (d).
The recovered J = 1.5 image shows a clear agreement with the PLIF J = 1.5 image for all structural features of the underexpanded jet, including resolution of the barrel and Mach disk shocks. The recovered J = 9.5 image, although showing an overall qualitative agreement with the corresponding PLIF image, shows a higher level of disagreement in the region preceding the Mach disk. While the barrel shock structure is preserved, the intensity gradient at the Mach disk is blurred. We attribute this disagreement to the low signal levels in this region as well as to the orientation of the fluorescence modulation. The resulting temperature map is shown in Fig. 5(d). The temperature calibration constant C12 was 1.4 for the recovered images. This value differs from the calibration constant of 0.15 in the reference two-line temperature determination since two different camera gain levels were used to obtain the two separate PLIF images and the laser powers were adjusted in each case to maximize the use of the dynamic range of the detector. Achieving a sensitive temperature measurement when using the two-line technique requires maximizing the energy difference between the two probed rotational states. High rotational states are not significantly populated at the lowest temperature regions of the flow, i.e. approaching the Mach disk, where the signal-to-noise level for the high-J PLIF image is as low as 5. The highest disagreement in temperature occurs near the Mach disk, as observed in Figs. 5 and 6
Fig. 6 Temperature profile along the underexpanded jet centerline obtained using the suggested approach. The temperature profile resulting from traditional two-line thermometry approach is shown for comparison.
In general, the spatial resolution of the temperature measurement using this approach is mainly limited by the frequency of the modulated fluorescence signal, resulting in the largest errors in regions where strong temperature gradients are encountered. However, we have observed that the degradation of the spatial resolution can be significantly mitigated by adjusting the orientation of the signal modulation with respect to these gradients. The modulation of the fluorescence signal is perpendicular to the Mach disk shock, and parallel to the barrel shock. This resulted in a well-preserved barrel shock structure in the recovered fluorescence images, and in a better agreement of the recovered temperature gradient with that obtained using PLIF two-line thermometry. The orientation of the fluorescence modulation was used to apply the lock-in detection post-processing methodology in the horizontal direction of the image. Since this post-processing involves applying a low-pass filter only in this direction, an apparent high-frequency component noise is still present in the vertical direction of the recovered images and the resulting temperature map. However, this could be filtered out as part of the analysis. The presented images have not been additionally filtered to illustrate that the directionality of this excess noise depends on the alignment of the modulation. A quantitative comparison of the temperature profiles along the centerline of the underexpanded jet recovered using the traditional two-line thermometry technique and the approach suggested in this work is shown in Fig. 6.
4. Outlook
The approach presented in this paper would provide a successful temperature determination in an environment with no significant luminous background interferences. However, modulating both laser sheets would, in principle, allow quantification of the resulting fluorescence signals in the presence of a significant background. As mentioned above, the conventional two-line thermometry configuration, where the fluorescence images are obtained sequentially, leads to spatial averaging along flow displacements, which can be of a concern in a high-speed flow. The magnitude of this averaging would reach the millimeter scale in measurements with time delays of 1 microsecond or less for a flow moving at ∼1000 m/s. Being a steady flow, the underexpanded jet provides the additional advantage of strong temperature gradients in different directions to serve as a test of the resolution limits of this approach. A complete study of the maximum achievable spatial resolution of temperature measurements using this combination of two-line thermometry and structured illumination that accounts for modulation frequency and orientation is underway. This forthcoming study will include single-shot temperature determinations and implementation strategies for the study of high-speed flows.
Funding
St. Olaf Faculty Development Program 2016-2017.
Acknowledgments
We thank Professors Simon North and Rodney Bowersox, as well as the Texas A&M National Aerothermochemistry Laboratory for the access to their facilities.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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