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Abstract
Two-dimensional, Rayleigh-scattering-based temperature measurements utilizing a turbulent jet flame were performed in this study at 100-kHz frequency. This tenfold increase in measurement speed—compared to the 10-kHz frequency considered previously—facilitated identification and tracking of several highly dynamic flow features. Findings of this study demonstrate that flow-feature dynamics become uncorrelated qualitatively and quantitatively prior to an elapse of 100 μs between successive measurements, thereby necessitating the temperature-measurement frequency to exceed 10 kHz. At the proposed 100-kHz measurement frequency, resolution of the Taylor microscale and integral scales have been demonstrated in both space and time for this flow.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent times, laser-based diagnostic methods have witnessed significant advancement, regarding the measurement of thermodynamic [1], chemical [2], and flow properties [3] in both space and time. Several studies have been performed to investigate the effectiveness of various combinations of measurement techniques [4], such as particle image velocimetry (PIV) combined with planar laser-induced fluorescence (PLIF) [5,6], Rayleigh scattering combined with PLIF [7,8], and PIV combined with Raman scattering [9], to facilitate simultaneous measurement of flow properties (for example, velocity and density or velocity and temperature). Single-beam/single-detector-based approaches are advantageous when performing measurements in a large test facility or combining multiple measurements to facilitate ease of implementation. Moreover, compared to methods requiring complex multiple beams/detectors, utilization of single-beam/detector techniques facilitates implementation of high-speed measurements [10–12] along three spatial dimensions [13] in a more manageable fashion.
Rayleigh scattering has often been used to measure gas density non-intrusively in both space and time [14]. Additionally, the technique has been used to measure values such as temperature, velocity, mixture fraction [15], and thermal dissipation [16]. Moreover, Rayleigh scattering has been used in solar system studies [17]. A laser beam of any wavelength and pulse duration can produce Rayleigh scattering light, thereby simplifying the experimental setup by eliminating the need for complex wavelength-generation systems that comprise an optical parametric oscillator (OPO), dye laser, optical parametric amplifier (OPA), etc. Additionally, generation of a narrow spectral linewidth or accurate wavelength is not necessary since atomic or molecular transitions are not probed [2]. The frequency-doubled output of a nanosecond (ns)-pulsed duration Nd:YAG laser is often used for Rayleigh scattering, for relative ease with regards to capturing important flow properties using highly-linear cameras with high sensitivity to visible light. However, high-speed Rayleigh scattering is difficult to perform, since high per-pulse energies are often necessary to attain sufficiently high signal-to-noise ratios. Moreover, reacting flows are often characterized by lower gas densities compared to that of ambient air, and consequently, the strength of the Rayleigh signal is generally an order of magnitude lower at flame temperatures. Performing Rayleigh-scattering-based measurements in reacting flows, therefore, inherently requires high per-pulse energies. Additionally, Rayleigh-scattering signals are dependent on the Rayleigh cross-section of fluid molecules, which varies significantly from molecule-to-molecule by a factor of three in typical combustion applications [18]. Therefore, performing quantitative Rayleigh-scattering-based measurements in heterogenous reacting mixtures is difficult without the use of specific fuels which possess a near-constant Rayleigh cross-section [19]. Varying Rayleigh cross-section issues do not arise in high-speed flow application involving a homogenous mixture and can be advantageous to resolve high density gradients.
Quasi-continuous diode-pumped solid-state lasers are popular for use in high-speed applications [11]. However, their effectiveness is limited to low-energy applications (2–20 mJ/pulse at 10 kHz), which inhibits their use in Rayleigh-scattering applications. Continuous-wave lasers have previously been employed for Rayleigh scattering [20], but they require relatively long exposure times (30 $\mu $s) to collect sufficient signal. Appropriate freezing of turbulent-flow dynamics in a single image is difficult with such a long exposure. Many high-repetition-rate burst-mode lasers are capable of producing high per-pulse energies at 10-kHz frequency [21–24]. Studies concerning attainment of ultrahigh repetition rates (100 kHz and even 1 MHz [25]) have been reported to facilitate resolution of finer structures and high-speed flow measurements [26].
In regard to simplicity of the experimental setup, Rayleigh scattering is a viable alternative for performing ultrahigh repetition-rate measurements, wherein the major challenge corresponds to realization of sufficiently high per-pulse energies necessary to produce detectable signal levels. Recently, the authors used a burst-mode laser to perform 100-kHz Rayleigh-scattering-based measurements for determination of the mixture-fraction distribution within a non-reacting turbulent jet of propane and helium exiting into ambient air [27]. The ratios of Rayleigh cross-sections for helium and propane to that of air equaled 1:63 and 13:1, respectively. Therefore, owing to lower gas density, the estimated signal ratio of an order of magnitude in reacting flows is less compared to that reported in [27]. This suggests that ultrahigh-repetition-rate Rayleigh-scattering-based measurements can be performed in reacting flows via similar laser energies reported in [27].
This paper reports 100-kHz Rayleigh-scattering-based two-dimensional density measurements (allowing temperature to be inferred) in a turbulent reacting flow as an extension to the non-reacting flow study reported in [27]. Several axial heights were sampled to compare 10-kHz rate Rayleigh-scattering-based measurements with those performed at the 100-kHz repetition rate. Qualitative comparisons were made to demonstrate the capability of the proposed Rayleigh-scattering-based measurement technique. Moreover, quantitative comparisons were made to describe the benefits and drawbacks of employing a 100-kHz repetition rate.
2. Experimental setup
In this study, the frequency-doubled output of a burst-mode laser was used for performing Rayleigh scattering measurements. This laser was capable of producing 532-nm pulses with energy levels of 700 mJ/pulse at 10-kHz repetition rate [28]. Measurements described in this work were performed at 100-kHz frequency with a pulse-energy of approximately 100 mJ/pulse for 10 ms. The 532-nm beam was directed towards a jet burner, as depicted in Fig. 1, and expanded into a 100-mm wide, 100-$\mu $m thin sheet using cylindrical and spherical lens pairs with focal lengths $f$ = −75 mm and $f$ = 400 mm, respectively. However, only the central 40 mm of the laser sheet was utilized owing to the consideration of beam-profile uniformity. Signal was collected using a Photron SA-Z CMOS camera equipped with an unfiltered LaVision IRO intensifier typically using a gain of 60%. A Nikkor (Nikon) 50 mm $\textrm{f}$/1.8 lens was used to collect and project light onto the IRO. The captured image was relayed onto the SA-Z CMOS chip. The projected per-pixel resolution approximately equaled 72 $\mu $m.
Fig. 1. Experimental setup comprising burst-mode laser, high-speed camera, intensifier (IRO), and jet burner.
The jet considered in this study used a diluted fuel mixture, and a coflowing nozzle (referred to as a coflow) that provided a known boundary condition of low-velocity airflow. The jet measured 8 mm in diameter and comprised a mixture of CH4, H2, and N2 measuring 22.1%, 33.2%, 44.7% by volume, respectively, consistent with a DLR-A flame. The DLR- flames are a class of gaseous flames that are provided standardized flow conditions, as defined in [29]. Moreover, the DLR-A flame is in a stable-burning state. The jet provided gas at a nominal velocity of 42 m/s corresponding to a bulk Reynolds number of 15,200. The 0.3-m-diameter coflow provided air flowing at a nominal velocity of 30 cm/s and was filtered to eliminate dust particles. The DLR flame is ideal for performing Rayleigh-scattering-based temperature measurements, since it ensures uniformity of Rayleigh cross-sections to within 2% for the entire flow [19].
3. Results and discussion
3.1 Qualitative comparison
Rayleigh-scattered images centered approximately 32, 48, and 68 mm downstream of the jet-exit plane were captured at a frequency of 100-kHz. Images captured 32 mm downstream of the jet exit are depicted in Fig. 2. The axis origin of all images reported in this paper was located at the center of the jet exit, and captured images were processed using a median filter to reduce noise between neighboring pixels. The mean signal-to-noise ratio (SNR) was approximately 25:1. Equation (1) describes the signal strength where S denotes the strength of Rayleigh-scattering signal; E denotes laser energy; n denotes number density; ${\Omega }$ denotes the solid angle for signal collection; l denotes sample length; $\epsilon $ denotes collection efficiency; ${\sigma _{mix}}$ denotes the Rayleigh cross section of the mixture; ${X_i}$ denotes mole fraction of the ${i^{th}}$ species; and ${\sigma _i}$ denotes the Rayleigh cross-section of the ${i^{th}}$ species.
Fig. 2. Normalized Rayleigh signals centered at 32 mm downstream of jet exit. Image sequence depicts changes in normalized density with time step labeled in each frame. First five images demonstrate 10-$\mu $s temporal resolution while the last image was captured 100 $\mu $s after the first frame, thereby indicating down-sampled image pairs that would be obtained from 10-kHz measurements.
Images depicted in Fig. 2 were sampled at times indicated by the labels above each frame. The images represent a scaled density-field sequence that illustrates a reacting flow surrounded by cold air maintained at approximately 300 K. The reacting and product mixtures produce higher gas temperatures, and hence lower density, compared to ambient air. This results in generation of Rayleigh signal with strength lower compared to that of corresponding signal for ambient air. Near the jet center, there exist regions of relatively cold, high-density fluid convected along the positive Y-direction. These regions subsequently break up because of turbulent mixing and high shear-strain rates induced by the large fluid-density and velocity gradients.
Normalized-density images depicted in Fig. 2 were converted to temperature—as depicted in Fig. 3—by utilizing the linear relationship between number density and temperature per the ideal gas law. The DLR mixture was characterized by an adiabatic flame temperature of 2130 K, which approximately equaled measured temperatures depicted in Fig. 3. Existence of a high strain rate causes greater heat loss within the reaction layer along with reduction in flame temperatures. Thus, unsteady non-uniform strain-rate interactions within the reaction layer result in generation of non-uniform temperature fields. Figure 3 not only illustrates highly non-uniform spatial-temperature distributions but also unsteady temperature fluctuations. The areas identified by the rectangle and circle on the image sequence represent dissipation of a high-temperature structure and possible extinction, respectively. As can be observed, the temperature of the structure (enclosed within the rectangle) seems to gradually reduce with time. Additionally, thin regions of the structure dissipate at a rate exceeding that of thick regions. Moreover, structures with corner-like features also demonstrate fast dissipation. Out-of-plane motion may also contribute to these observations but cannot be determined from these two-dimensional measurements. The DLR-A flame was characterized by a Reynolds number low enough for reactions to occur in a quasi-continuous sheet. The circle in Fig. 3 represents a flow region, wherein a continuous high-temperature region seemingly breaks upon the elapse of 30 $\mu $s, thereby indicating possible flame extinction. Additional measurements, such as OH PLIF, must be performed to determine whether the observed break in the high-temperature structure indeed occurs along the reaction layer. The 10-$\mu $s-interval image sequence illustrates disconnection of the high-temperature structure near the bottom of the circled region. The remaining high-temperature structure below the observed break location seemingly remains stationary while the upper region either recedes or undergoes convection along the downstream direction.
Fig. 3. Rayleigh-scattering images converted to temperature centered at 32 mm downstream of jet exit with time stamps labeled above each frame. Region outlined by the rectangular box emphasizes a dissipating high-temperature structure and the circle outlines a potential extinction event.
Several flow applications can be better understood by resolving density gradients, especially in the presence of shock waves or high temperature gradients. Rayleigh scattering images can be converted to density, by utilizing Eq. (1) and ambient air as a reference to a known density, and the gradient can be calculated, as shown in Fig. 4. The gradient was calculated using a pixel-wise central difference approximation. In Fig. 4, the highest density gradient appears along the outer region of the jet where the hot gas interacts with the cold coflowing air. Near the jet centerline, small bands of relatively high magnitude density gradients are observed and can be temporally tracked which can provide critical information regarding turbulence-chemistry interaction if additional measurements, such as OH PLIF, were performed. This technique may be particularly beneficial in supersonic or hypersonic flows due to the high-repetition rate and spatial resolution which can potentially resolve shock waves or boundary layers.
Fig. 4. Calculated density gradient magnitude from Rayleigh scattering images in Fig. 2 centered at 32 mm downstream of the jet exit with time stamps labeled above each frame.
Two additional datasets, centered at 46 and 68 mm downstream of the jet-exit plane, were captured in this study. Temperature image sequences captured at these heights are depicted in Fig. 5 and Fig. 6, respectively. As can be observed, the jet widens at higher axial heights, and its overall velocity reduces accordingly. The center of the jet appears to be preheated by the surrounding reaction layer and combustion gases, which in turn elevates the gas temperature above its initial value (300 K) to approximately 700 K. Surrounding the central intermediate-temperature core fluid is high-temperature gas of which nearly equals the adiabatic flame temperature. This high-temperature fluid appears to be more continuous compared to that depicted in Fig. 3 owing to lower velocity and reduced strain rates.
Fig. 5. Sequence of temperature images centered 48 mm downstream of jet exit with time stamps labeled above each frame.
Fig. 6. Temperature sequence centered approximately 68 mm downstream of jet exit with time stamps labeled above each frame.
Figures 2–6 depict five images captured at 10-$\mu $s intervals with the sixth image being captured 60 $\mu $s after the fifth image. Nearly all changes occurring in the flow structure during the first 40 $\mu $s can be easily tracked owing to the small interval between successive images. However, several structures observed within the last frame captured at $\tau $ = 100 $\mu $s can be considered uncorrelated to those observed in previous images, especially the first image captured at $\tau $ = 0 $\mu $s. For example, the boxed and circled structures depicted in Fig. 3 are clearly different in frames captured at 0 and 100 μs. This makes it difficult to base temporal statistics on measurements performed at 10-kHz repetition rate (with an image-capture interval of 100 μs). It must be noted here that the non-correlations have been noted by the authors only at specific regions in this flow after elapse of 100 $\mu $s, and that this does not hold true for the entire flow field or different flow applications. Most uncorrelated structures at $\tau $ = 100 $\mu $s occur near the centerline, which on average, is characterized by higher flow velocity compared to that of the surrounding fluid. Consequently, observed timescales in this region are shorter compared to those of regions away from the centerline.
Temperature time series, depicted in Fig. 7, were obtained by sampling the temperature at points located near the jet centerline and one jet radius (0.5 times jet diameter) away along the radial direction for three different cases—68, 48, and 32 mm downstream of the jet exit. The time series were smoothened with a median filter spanning 30 $\mu $s. The solid and dotted lines represent temperature time series sampled at 100 kHz, whereas the black and green symbols represent the same measurements down-sampled to 10 kHz repetition rate. As can be observed in the figure, measurements performed at 100-kHz sampling frequency sufficiently follow nearly all temperature structures without large discontinuities. This would be especially true for cases involving large temperature gradients. Overall, equivalent measurements performed at 10-kHz frequency demonstrate good temporal tracking of flow features. However, several temperature gradients that occur over short time intervals are either completely missed by the 10-kHz measurements (marked by circles in Fig. 7) or are marked by very few (1–2) points to sample the unsteady temperature structure (marked by rectangles in Fig. 7). Effective extraction of physical factors requires accurate resolution of large gradients in both space and time, and this cannot be realized by performing measurements at 10-kHz frequency.
Fig. 7. Temperature time series sampled along jet centerline and one-half jet diameter along radial direction at (a) 68 mm, (b) 48 mm, and (c) 32 mm downstream of jet exit. The solid blue and dashed red lines were sampled at 100 kHz. The symbols show the 100-kHz measurement which were down-sampled to 10-kHz repetition rate. The circled regions of the time-series emphasize high temporal gradients which were not observed in the 10-kHz measurements and boxed regions have one or two points resolving the gradient.
Spatial temperature profiles obtained 37 mm downstream of the jet exit are depicted in Fig. 8 to demonstrate temperature-profile evolution with time. As can be observed in the figure, there clearly exist structures which evolve shot-to-shot between 0 and 40 $\mu $s. This is particularly true of the double-peak structure observed between 0 and 5 mm, indicated by the two arrows. However, the double-peak structure does not exist at 100 $\mu $s, since its evolution to this point could not be sufficiently resolved from a qualitative perspective. Other structures, such as the peak observed near x = −6 mm, demonstrated longer timescales, which in turn, made them easily identifiable throughout the interval between 0 and 100 $\mu $s.
Fig. 8. Spatial profiles of temperature sampled 37 mm downstream of jet exit and demonstrating its structural evolution. Time stamps are labeled above each graph. Arrows represent a trackable structure from 0–40 $\mu $s.
3.2 Quantitative comparison
Correlation and mutual information [30] are quantitative measures of the connection between two independent measurements. Temperature measurements performed in this study tend to lose structural information with time. Therefore, connections to subsequent measurements performed at a later point in time can be established by computing the correlation and mutual information between measurements with a known time delay. It must be noted that whereas correlation is a measure of linear connectedness between measurements, mutual information is a more general measure of connection [30]. Thus, correlation and mutual information are independent parameters, as described in Eqs. (2) and (3), respectively. In these equations, C denotes correlation; $\nu $ and $\mu $ denote two independent measurements; $MI$ denotes mutual information; ${P_i}$ denotes the probability of temperature being in bin i; and ${P_{ij}}$ denotes the probability of temperature being in bin i with the temperature at a prescribed time delay being in bin j. The parentheses in Eq. (2) denote average values, whereas the prime denotes standard deviation. In this study, values of the correlation and mutual information were calculated at each point in space using the original temperature time series and the same time series with a prescribed time delay, respectively. This provides a quantitative description of how the value of temperature at a given time instant bears a connection with itself at later point in time. By definition, the value of autocorrelation equals unity in cases involving zero time delay, and that its value reduces with increase in time delay. Additionally, the value of mutual information was observed to be maximum for cases involving zero time delay followed by subsequent reduction with increase in time delay. Two independent measurements can be considered unconnected if values of the mutual information and/or correlation are low. Values of the autocorrelation and normalized mutual information concerning temperature measurements performed along the jet centerline 30 mm downstream of the jet exit are plotted in Fig. 9. As can be observed, at this location, values of both autocorrelation and mutual information reduce to zero within 60 $\mu $s, thereby indicating temperature values measured at any instant are unconnected to those measured 60 $\mu $s later. Thus, measurements with temporal resolution greater that 60 $\mu $s would demonstrate no connection between sequential samples at this spatial location.
Fig. 9. Autocorrelation and normalized mutual information calculated 30 mm downstream of jet exit near jet centerline. Both calculations show the temperature at this spatial location, on average, become unconnected approximately 60 $\mu $s later in time.
Calculations similar to those described in Fig. 9 were performed at all pixel locations between axial heights of 22.5 mm and 42.5 mm using the dataset obtained closest to the jet exit. From a practical viewpoint, a small value of correlation or mutual information is required to facilitate temporal resolution of flow features between two successive measurements. To this end, a correlation or mutual-information value equal to 25% of their respective maximums was considered as a threshold to ensure sufficient temporal resolution of flow features. The time (${\tau _{25}}$) required for attainment of this threshold was computed at each pixel. Figure 10 depicts the average temperature field superimposed by contours representing ${\tau _{25}}$ equal to 10 (solid line), 50 (hyphenated line), and 100 (hyphenated-dotted line) $\mu $s when considering correlation (Fig. 10(a)) and mutual information (Fig. 10(b)). Geometrical asymmetries within the jet and averaging effects were thought to be the reason behind observed temperature non-uniformities. Averaging effects could be alleviated with additional bursts, since five bursts were used in this work. Spatial locations enclosed by a contour have greater than 25% correlation or mutual information by the timescale of the respective contour timescale. Points located outside the said contour, especially those located near the jet centerline, demonstrated correlation and mutual-information values measuring less than the corresponding thresholds. Consequently, these points could not be adequately resolved in accordance with the contour timescale. It should be noted that the 10 $\mu $s contour enclosed the entire flame region and adequately resolves the high-temperature region. Points located outside the contours and away from the jet centerline reside within regions of quiescent or low-velocity air, and these must, therefore, be resolved using relatively low repetition-rate measurements. However, noise interference tends to dominate captured signals, thereby resulting in small values of correlation and mutual information at later instants of time. Thus, measurements performed closer to the jet centerline cannot be correlated to subsequent measurements performed after elapse of 100 $\mu $s, and this task can only be accomplished using a repetition rate of 100 kHz or higher. The 100-$\mu $s mutual-information contour resides close to the region of flow characterized by high gradients. This indicates that measurements performed with 10-kHz repetition rate encounter great difficulties in temporally resolving flow features near the reaction layer, where the majority of high temperature gradients are located. Regions near the 100-$\mu $s contour demonstrate similarities with those enclosed within the rectangle and circle in Fig. 7, wherein only up to 2 points resolve a given flow structure in time. All points within the red solid contour could only be resolved by performing 100-kHz measurements.
Fig. 10. Average temperature field superimposed with contours representing ${\tau _{25}}$ equal to 10 (red solid), 50 (white dashed), and 100 (cyan dash-dotted) $\mu $s and demonstrating small connection with earlier measurements in terms of (a) correlation and (b) mutual information.
In theory, the correlation or mutual information can be increased by allowing each pixel to cover a larger area. It is easy to realize that between two successive measurements, a given flow structure would move a distance determined by its velocity and time between successive laser pulses. Since the time delay between two snapshots captured at 10-kHz frequency equals ten times that at 100 kHz, the flow structure would move approximately ten times further. Thus, as a first approximation, similar correlation and mutual information can be obtained from 10 kHz as 100 kHz by having ten times worse spatial resolution. This technique is often employed in PIV measurements to ensure particles move a specific number of pixels based on the bulk velocity and time delay between successive pulses. Thus, in an effort to obtain higher temporal correlation and mutual information, small-scale structures get averaged out in space, thereby resulting in even lower values of correlation and mutual information compared to those expected in accordance with the first approximation. To gain insight into how 10 kHz measurement would appear having ten-times worse spatial resolution, one snapshot of the temperature field with 100 kHz repetition rate was binned by 10 in both directions and shown in Fig. 11. The image demonstrates a 10-times larger field of view; however, each pixel now covers a larger area, thereby resulting in low pixel-to-pixel spatial correlation. The temperature profile obtained 37 mm downstream of the jet-exit plane by performing measurements at 10- and 100-kHz repetition rates were compared in this study. As seen in Fig. 11, compared to the 10-kHz repetition rate, temperature profiles obtained via measurements performed at 100-kHz were observed to be much smoother with adequate resolution of flow features. Therefore, 10 kHz measurements are limited by either resolving the temporal or spatial domain, whereas 100 kHz measurements provide an opportunity to resolve both.
Fig. 11. (a) Sample image of temperature measured at 100-kHz (left) and same image binned by factor of 10 along each direction (right) to obtain higher temporal resolution approaching that obtained at 100 kHz; (b) Sampled temperature profile from both images in (a) 37 mm downstream of jet exit and depicted as solid white line in (a).
It must be noted that all comparisons reported thus far in this paper were performed for a flow field characterized by a relatively high velocity flow for subsonic laboratory flames (approximately 42 m/s), and that different velocities may lead to attainment of different results. For example, flow velocities 10 times lower compared to that considered in this study may demonstrate sufficient resolution of flow features at 10-kHz repetition rates. Conversely, high-speed flows, such as those characteristic of hypersonic wind tunnels, may require substantially higher repetition rates for adequate temporal resolution of flow features. Therefore, a repetition rate of 100-kHz need not necessarily be optimum for use in all application, however, it is certainly necessary in applications involving high-speed turbulent subsonic flows.
The scalar turbulence energy spectrum was computed at several locations and plotted in Fig. 12 using approximately 2000 images. Under homogenous and isotropic turbulence, it is predicted that the energy should decay with the Kolmogorov power law dependence having an exponent of −5/3 [31]. Near the jet center there is a region above 10 kHz which demonstrates a −5/3 scaling. All locations seem to indicate a transition region with frequencies below 5 kHz, where the spectrum decays at a different rate. This region is likely where the integral scale transitions to the inertial scale which does not have universal scaling laws. This scaling anomaly is likely present in other works [10,11] where a different scaling than the −5/3 power law was observed without any clear reason. Moreover, an anomalous scaling feature is present in locations occurring further from the jet center, particularly shown at X = 8 mm, where there is no indication of the −5/3 scaling. At this spatial location, the measurement will be influenced by both hot fluid which has reacted and cold fluid from the coflow. The cold air may be turbulent, however, since only temperature is measured there is no way to measure the turbulent flow fluctuations rendered through variations in temperature since the temperature is nearly constant at 300 K. Figure 12 also shows the frequency spectrum begins to flatten near 25 kHz at most spatial locations and is likely the resolution of this 100 kHz measurement after accounting for noise.
Fig. 12. Energy spectrum at several axial heights and radial locations from the jet center. The overlaid blue line represents a slope of −5/3 for reference.
Overall, Rayleigh-scattering-based measurements performed with 100-kHz repetition rate demonstrate adequate resolution of multiple-scale regimes in both space and time. This is because the proposed approach does not require multiple pixels to be binned or averaged, as is the case with PIV measurements. Scaling laws predict Taylor-microscale length and time scales of 200 $\mu $m and 48 $\mu $s at the jet exit, respectively. Use of the 100-kHz repetition rate facilitates realization of a temporal resolution of 10 $\mu $s and current measurements were performed with 72 $\mu $m spatial resolution. Higher spatial resolution is possible by using a high magnification lens since the diffraction limit is approximately 0.5 $\mu $m—i.e., the maximum pixel resolution. Additional parameters may limit the spatial resolution, for example the laser sheet thickness [32] and imaging depth of field. Since the integral scale is approximately an order of magnitude larger compared to the Taylor microscale in both space and time, both regimes can be resolved in the same measurement. Conversely, the Kolmogorov length and time scales were approximately 5.8 $\mu $m and 1.5 $\mu $s, respectively, which are resolvable in space but not in time. Downstream of the jet-exit plane, for instance, in the flow field depicted in Figs. 3–6, both the length and time scales increase, thereby demonstrating the potential to be simultaneously resolved. As laser technology advances, higher repetition rates (e.g. 1 MHz) with high pulse energies (∼100–200 mJ/pulse) may allow direct observations of the entire turbulence spectrum in two-dimensions and even less energy if measured along a line. The non-intrusive nature of Rayleigh scattering along with realization of high spatiotemporal resolution clearly offers a significant advantage when employing the proposed technique in fundamental turbulent-mixing and combustion experiments.
4. Summary
Through use of a burst-mode laser system, this study demonstrates two-dimensional Rayleigh scattering at a 100-kHz repetition rate in a reacting jet flame. As realized via experiments performed in this study, image sequences of temperature measured at 100-kHz repetition rate demonstrated several flow features to be easily tracked in time. However, when sampled down to a repetition rate of 10-kHz, the temperature measurements did not demonstrate adequate resolution in time. Time series of temperature profiles captured at several axial and radial locations were sampled to demonstrate the inability of measurements performed at 10-kHz repetition rate to resolve flow features with high temporal gradients adequately.
Quantitative measures concerning the timescale over which measurements performed at two different time instants could be considered connected were computed, thereby providing the necessary temporal resolution to resolve the unsteady flow field sufficiently. Regions near the jet centerline demonstrated shorter timescales compared to those located further away owing to differences in velocity magnitudes. Overall, measurements performed with 100-kHz repetition rate were observed to adequately resolve the entire sampled flow field of the reacting jet. Regions identified with timescales measuring less than 100 $\mu $s demonstrated that measurements performed with 10-kHz repetition rate were incapable of adequately resolving the entire flow field in space and time.
Funding
Air Force Research Laboratory (FA8650-15-D-2518); National Aeronautics and Space Administration (80NSSC17C0008).
Acknowledgments
Dr. Stephen Grib is currently sponsored by the National Research Council Science and Technologies Fellowship Program at AFRL. Dr. Paul Danehy was supported by the NASA Aeronautics Research Mission Directorate’s Transformational Tools and Technologies (TTT) Project and the NASA Aerosciences Evaluation and Test Capabilities (AETC) Portfolio. This manuscript has been cleared for public release by the Air Force Research Laboratory (No. 88ABW-2019-4188).
Disclosures
The authors declare no conflicts of interest.
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