1 Introduction

Turbulent flows are inherently time-varying, multi-dimensional phenomena, creating a dynamic system spanning several magnitudes of length and time scales. The spatial and temporal complexity of such systems is increased even further when coupled to chemical reactions and heat release as in the case of turbulent combustion processes. It is the multi-scale (and highly nonlinear) nature of turbulent flows and flames that gives rise to the great difficulty in developing tractable and robust models to accurately describe and predict their behavior. Therefore, high-fidelity measurements continue to be needed to detail the governing processes in turbulent flows. In addition, increasingly accurate and sensitive measurements can be used to provide new data for assessment and validation of turbulent flow and combustion models.

For the last four decades, laser-based diagnostics have played a key role in elucidating important physical and chemical processes occurring within turbulent non-reacting and reacting flows. While measurements have evolved to span two and three dimensions with very high spatial resolution, they have been limited in temporal resolution; that is, any two consecutive images have been temporally uncorrelated. For gas-phase flow scalar measurements, typical signal levels are sufficiently small such that high-power, pulsed laser sources are required, especially for “single-shot” measurements in turbulent environments. Commercially-available, high-energy systems including solid-state Nd:YAG or molecular gas excimer lasers typically are limited to laser pulse repetition rates of 10–300 Hz, which cannot track the highly transient properties of the gas-phase flows of interest. Recognizing that turbulent flows are characterized by unsteady and stochastic behavior, spatially- and temporally-correlated measurements are highly desired in order to capture the dynamic nature of the flows. This requirement dictates that multi-dimensional scalar fields should be acquired at acquisition rates much faster than the time scales of the turbulent processes of interest (i.e., ≫1 kHz for laboratory-scale flows).

Recently, high-speed imaging in turbulent flow and combustion environments has been made possible by several technological advances in laser and camera technology as reviewed by Böhm et al. [1], Thurow et al. [2], and Sick [3]. The most popular and rapidly growing approach is the use of commercially-available, continuously-operating, diode-pumped, solid-state (DPSS) lasers and CMOS-based camera systems. The predominate uses of DPSS lasers have been high-speed particle imaging velocimetry (PIV) in reacting and non-reacting flows and OH planar laser-induced fluorescence (PLIF) in reacting flows (see Refs. [1] and [2] for a detailed listing of recent studies). Other examples of high-speed imaging using DPSS lasers include tracer LIF measurements to image fuel–air ratios in non-firing engines (e.g., 4–8) and mixture fraction in unsteady, non-reacting jets [9], respectively; laser-induced incandescence (LII) measurements for time-resolved soot distributions in flames [10]; toluene LIF-based thermometry near surfaces [11]; 1D Rayleigh scattering-based thermometry in non-premixed flames [12]; NO distributions in a plasma torch [13]; and high-speed phosphor-based thermometry [14]. Numerous other examples of high-speed imaging using DPSS lasers are found within the previously cited review papers [1–3]. While the aforementioned applications are impressive, they are a subset of commonly used methods at low repetition rates. For example, 0D/1D spontaneous Raman scattering, planar Rayleigh scattering, and PLIF imaging of additional combustion radicals and intermediates (i.e., CH, CH2O, O, H, etc.) have not been performed with DPSS lasers. This largely stems from the fact that the output energy from DPSS lasers is relatively low due to thermal constraints on the solid-state gain medium. For example, a 200-Watt system operating at 10 kHz outputs only 20 mJ/pulse in the fundamental (1,064 nm), which will be systematically reduced with harmonic generation and frequency conversion (i.e., to the UV for PLIF imaging). Such pulse energies are somewhat prohibitive to “weak” scattering processes such as spontaneous Raman scattering and planar Rayleigh scattering and once converted to the UV are too low for many PLIF strategies outlined above.

As noted in the recent review of ultra-high repetition rate laser diagnostics [2], pulse burst laser systems, as first reported by Wu et al. [15] and Wu and Miles [16], allow the generation of a series of sequential high-energy laser pulses at high repetition rates over a limited period. Because of the relatively low duty cycle of these systems, the time-averaged power output is below thermal damage thresholds with energy outputs similar to that of conventional low repetition rate lasers. While the intent of this paper is not to review pulse burst laser technology (see Ref. [2]), it is noted that the use of a previous generation pulse burst laser system [17] permitted kHz-rate spontaneous Raman scattering [18], planar Rayleigh scattering imaging [19, 20], CH PLIF [21], and CH2O PLIF [22] measurements in turbulent flows and flames for the first time. Most relevant to the current study were our previously-reported, high-speed (10 kHz) planar Rayleigh scattering measurements used to deduce temporal sequences of mixture fraction and temperature in turbulent non-reacting jets and turbulent non-premixed flames, respectively.

In this paper, we present high-speed (10–40 kHz) planar Rayleigh scattering diagnostics applied to study turbulent mixing within turbulent non-reacting jets and thermal transport and mixing via temperature imaging within a turbulent non-premixed jet flame. A particular focus of this paper is to highlight the substantial improvements in our high-speed planar Rayleigh scattering imaging capabilities as compared to our previously reported results [19, 20] in terms of increased signal-to-noise ratios (SNR), record lengths, acquisition rates, and spatial resolution. Although frequently utilized at low repetition rates, planar Rayleigh scattering requires high pulse energies that currently are not available from commercial high-repetition-rate laser systems. However, the use of a new high-energy pulse burst laser system (HEPBLS) [23], which produces long-duration bursts of ultra-high-energy output at 532 nm, allows high-speed (multi-kilohertz) planar Rayleigh scattering imaging. The new HEPBLS has the capability of outputting sufficiently higher pulse energies (e.g., ~1 J/pulse at 532 nm at 10 kHz) as compared to our previous studies [19, 20]. In addition, burst durations (and corresponding image record lengths) exceeding 12 ms are demonstrated, with the existing capability of achieving durations >25 ms. The higher laser pulse energies, in conjunction with an improved optical collection system, have allowed the use of an un-intensified CMOS camera in both non-reacting and reacting flows, which greatly improves spatial resolution and SNR as described below and allows measurements at increased repetition rates (up to 40 kHz in the present study).

2 Planar Rayleigh scattering

For low repetition rate studies (e.g., 10 Hz), planar Rayleigh scattering is a widely used imaging technique for multi-dimensional mixing measurements in non-reacting flows (e.g., 24–30) or temperature measurements in non-premixed and premixed flames (e.g., 28–34). Laser Rayleigh scattering is a non-intrusive diagnostic technique that describes the elastic scattering from atoms and molecules whose effective diameter is much less than the wavelength of the incident laser light. The total Rayleigh scattering intensity can be written as

$$I_{\text{RAY}} = AI_{o} n\sigma_{\text{mix}}$$
(1)

where A is a constant describing collection volume and efficiency of the optical setup, I o is the incident laser intensity, n is the number density, and \(\sigma_{\text{mix}}\) is the mixture-averaged differential Rayleigh scattering cross-section defined as \(\sigma_{\text{mix}} = \sum\nolimits_{i = 1}^{N} {X_{i} \sigma_{i} }\). X i and σ i are the mole fraction and differential scattering cross-section of species i, respectively.

2.1 Mixture fraction measurements in non-reacting jets

The mixture fraction (ξ), which represents the state of molecular mixing in a flow, is an important quantity in the general field of turbulence and in particular, in turbulent combustion. The turbulent mixing field can be uniquely characterized by the mixture fraction, ξ, and for laminar flamelet theory (e.g., 35, 36), the turbulent flame structure can be related back to ξ and its derivatives. Thus, ξ is one of the most fundamental and important scalars in non-premixed and partially premixed combustion and has been a focus of experimental fluid dynamics and combustion research for the past 30 years.

For a flow, that is, both isothermal and isobaric, changes in the Rayleigh-scattered intensity, I RAY, are due only to variations in \(\sigma_{\text{mix}}\). For a two-stream mixing process (jet fluid issuing into co-flowing air stream), Eq. (1) can be re-written as

$$I_{\text{RAY}} = AI_{o} n\left[ {X_{J} \sigma_{J} + \left( {1 - X_{J} } \right)\sigma_{A} } \right]$$
(2)

where X J is the mole fraction of the jet fluid at any point in the flow, σ J is the differential cross-section of the jet fluid, and σ A is the differential cross-section of air. Equation (2) can be re-arranged such that the local mole fraction of jet fluid (X J ) is determined from the Rayleigh scattering signal (I RAY) and a measured calibration signal from pure air (I AIR):

$$X_{J} = \frac{{\left( {I_{\text{RAY}} /I_{\text{AIR}} } \right) - 1}}{{(\sigma_{J} /\sigma_{A} ) - 1}}.$$
(3)

Equation (3) has been written such that for all measurements, the incident intensity, I o , is constant; however, the laser pulse energy and intensity distribution change on a pulse-to-pulse basis, and thus, this “correction” represents one of the data reduction steps discussed in Sect. 3.5. After determination of X J , the mixture fraction is determined from

$$\xi = \frac{{Y_{J} }}{{Y_{J,o} }} = \frac{{X_{J} W_{J} }}{{X_{J} W_{J} + (1 - X_{J} )W_{A} }}$$
(4)

where Y J is the mass fraction of the jet fluid at any point in the flow, Y J,o is the mass fraction of the jet fluid originating from the source, W J is the molecular weight of the jet fluid, and W A is the molecular weight of the air. For the general case, Y J,o can be any value between 0 and 1, but for the present work, a single component fluid, which is different than that of the co-flowing air stream, is used, such that Y J,o  = 1. The relatively large difference in differential scattering cross-sections (σ) between air and potential jet fluid sources such as hydrocarbon gases (i.e., propane; \(\sigma_{{{\text{C}}_{ 3} {\text{H}}_{ 8} }}\) ≈ 13σ air) allows for high measurement sensitivity. This coupled with the straightforward deduction of mixture fraction from the measured signal as shown in Eqs. (3) and (4) makes Rayleigh scattering a desirable technique for highly accurate mixing measurements.

2.2 Temperature measurements in turbulent flames

The time-varying temperature field is of particular importance because it plays a key role in the majority of chemical and physical processes occurring within turbulent combustion environments. Finite-rate chemical kinetics are temperature-dependent, and some kinetic processes including soot and NOx formation are strongly dependent on local temperature fluctuations. Local flame temperature can heavily influence heat transfer and is a key quantity in ignition, local flame extinction, and re-ignition processes. Rayleigh scattering thermometry has been used for more than 30 years, starting with 0D and 1D measurements by Pitz et al. [37], Smith [38], and Dibble and Hollenbach [39] and continuing with recent high-resolution planar Rayleigh scattering-based temperature imaging in turbulent non-premixed flames [28–34].

For variable-temperature flows, the ideal gas law (P = nkT, where P is pressure and k is the Boltzmann constant) is substituted into Eq. (1) yielding

$$I_{\text{RAY}} \, = \,AI_{o} \frac{P}{kT}\sigma_{\text{mix}}$$
(5)

For reacting flows, the constant A typically is accounted for by normalizing the Rayleigh signal from the flame by the Rayleigh signal of a known temperature and species concentrations such as room temperature air. For the flames considered in this paper, the fuel mixture is comprised of 22.1 % CH4, 33.2 % H2, and 44.7 % N2, which results in a mixture-averaged scattering cross-section that varies by <3 % throughout the flame [40–42]. This allows the determination of the flame temperature without the simultaneous measurement of local species concentrations. In this manner, the temperature is determined from

$$T = T_{\text{ref}} \frac{{I_{\text{ref}} }}{{I_{\text{RAY}} }}$$
(6)

where I ref is the reference Rayleigh scattering signal from air at room temperature (T ref).

3 Experimental approach

3.1 High-energy pulse burst laser system (HEPBLS)

A schematic of the new HEPBLS at Ohio State is shown in Fig. 1 as reported previously in Ref. [23]. The HEPBLS was designed to produce a unique combination of high repetition rates and high pulse energies over long pulse burst durations (high average power) for quantitative time-resolved imaging of turbulence and combustion dynamics. The HEPBLS is a master oscillator, power amplifier (MOPA) system that amplifies the low-energy output (~10 μJ/pulse) of a continuously running single-frequency laser (PO, which serves as the master pulsed oscillator) in a series of five, custom, long-duration, flashlamp-pumped Nd:YAG amplifier stages with total system gain >4 × 105. The repetition rate of the pulsed oscillator determines the pulse spacing within the burst, while the flashlamp-discharge duration determines the overall length of the burst and the number of amplified pulses. The master oscillator is a narrow linewidth (~2.5 GHz), pulsed Nd:YVO4 laser operating at 1,064 nm with pulse duration of 25–35 ns (depending on repetition rate) and variable repetition rates ranging from 1 to 50 kHz. In the current paper, all results are reported from 10 to 40 kHz.

Fig. 1
figure 1

Schematic of new high-energy pulse burst laser system (HEPBLS). PO = pulsed oscillator; OI = optical isolator; M = mirror; SL = spherical lens; DP = diamond pinhole; PBS = polarizing beam splitter cube; QWP = quarter-waveplate; HWP = half-waveplate; BD = beam dump; PCM = phase conjugate mirror; BS = beamspliter; VSF = vacuum spatial filter; QR = 90° quartz rotator; DC = dichroic beamsplitter. The “dashed line” connects the “endpoints” of a single relay image pathway. The configuration depicts the inclusion of a 2nd-harmonic doubling LBO crystal. Also shown is an image of an instantaneous beam profile at 532 nm for the operating condition outline in this manuscript

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The continuous train of pulses from the PO is first spatially filtered through a near-diffraction-limited diamond pinhole to create a “super Gaussian” beam profile and amplified in a series of two, double-pass, dual-flashlamp-pump amplifier stages (AMP1 and AMP2) with 4-mm- and 6.35-mm-diameter Nd:YAG rods, respectively. At 10 kHz (100 μs pulse spacing), the gain through AMP 2 is >104 with output pulse energies (within a burst) >150 mJ/pulse at 1,064 nm. As shown in Fig. 1 and described in Ref. [23], there are several important system features aimed at controlling birefringence, diffraction, and thermal lensing effects in order to preserve high beam quality. Beyond spatial filtering, the output of each amplifier stage is “imaged” onto the exit plane of the subsequent amplifier through relay optics. Each relay consists of a set of lens pairs that focus the beam through a diamond pinhole, which serves as a low-pass spatial filter, and re-collimates the light at a desired magnification. This process suppresses diffraction ripples and helps to mitigate birefringence effects at each stage. After two stages of amplification, sufficient energy exists such that the 1,064-nm pulse trains are focused into a phase conjugate mirror (PCM). The PCM, which has been described previously in detail [17, 23], is an optical cell filled with a high index of refraction liquid (FC-75) which uses the process of stimulated Brillouin scattering (SBS) as an intensity filter and stops the growth of Amplified Spontaneous Emission (ASE), which grows exponentially with the number of amplification stages and would limit energy gain in later amplifier stages. When the incident beam intensity is above a minimum threshold, it is coherently retro-reflected, while anything below that threshold (e.g., ASE) passes through the cell to a beam dump.

The retro-reflected pulse train then passes through a 50/50 beam splitter to create two parallel legs (“A” and “B”). By dividing the system into two legs, gain saturation in the final amplifier stages is delayed, and the total output energy is increased as compared to an eight-stage system operated in series. In addition, the versatility of the system is increased by having two output legs that can, in principle, operate independently for multi-parameter diagnostics. The third stages, which employ 9.5-mm-diameter Nd:YAG rods, are arranged in a double-pass configuration. Stages 4 and 5, which use 19.5-mm-diameter Nd:YAG rods are operated in a single-pass configuration with a 90-degree quartz rotator placed between them to help reduce thermally-induced birefringence effects caused by the thermal gradients within the rods. The output of the fifth and final amplifier stage is greater than 1 J/pulse for each leg at 1,064 nm for a total output energy that exceeds 2 J/pulse at 10 kHz with an RMS of the pulse-to-pulse fluctuation within the burst of <5 % as described in Fuest et al. [23].

In this work, a single 1,064-nm leg, operating at approximately 70 % of output capacity, is used to generate the 532-nm output used for the Rayleigh scattering measurements. The 1,064-nm output passes through two type-I LBO doubling crystals (12 × 12 × 20 mm3) arranged in series to generate ultra-high 532-nm output at 10–40 kHz. Figure 2 shows two typical pulse energy traces at 10 and 20 kHz, respectively. The reported 10-kHz pulse trace is 10 ms in duration, although we have successfully tested up to 20 ms, with the capability of exceeding 25 ms. The reported 20-kHz pulse trace is 8.5 ms, with the capability of exceeding 25 ms. It is noted that for the pulse traces reported in Fig. 2, the gain settings were operated at lower gain settings than previously reported [23], such that the average pulse energy at 532 was ~450 mJ/pulse at 10 kHz. This pulse energy trace is from the mixture fraction measurements within a non-reacting jet as reported in Sect. 3; higher pulse energies led to signal levels that started to saturate the cameras at the lower axial positions. As reported in Ref. [23], 532-nm pulse energies >600 mJ have been generated at 10 kHz with a single output leg. Similar to the fundamental output, the 532-nm output exhibits low pulse-to-pulse fluctuation within the burst with an RMS value of <7 %. Figure 2 also shows an example 20-kHz pulse trace used for the non-reacting mixture fraction imaging. Average 532-nm pulse energies of >275 mJ are reported with an RMS fluctuation of <9 % within the burst. However, it is noted that at the time of the measurements shown in Fig. 2, the PO exhibited substantial fluctuations at 20 kHz that propagated through the system and resulted in the observed 9 % RMS fluctuation in the final 532-nm output. Since this time, the PO stability has been restored, and its RMS fluctuation level has been decreased by a factor of six. We expect this to have a great impact on the final amplified pulse-to-pulse fluctuation in future testing. Finally, Fig. 2 shows two examples of single-pulse temporal profiles from the 10 and 20 kHz, respectively. The profiles have pulse widths, defined as the full width at half maximum (FWHM), of 23 and 27 ns at 10 and 20 kHz, respectively. The temporally-compressed rising edge is a result of the PCM as reported in [17].

Fig. 2
figure 2

Example 532-nm pulse energy trace at 10 and 20 kHz. Insert shows instantaneous pulses during the burst with pulse widths of 23 and 27 ns at 10 and 20 kHz, respectively. Dashed lines represent the average pulse energy measured during each respective burst

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3.2 Imaging system

A schematic of the imaging system used for these experiments is given in Fig. 3. The 532-nm, vertically-polarized output of the HEPBLS is formed into a 15 × 0.30 mm2 laser sheet by using a single 750-mm focal length, plano-convex cylindrical lens (CL). The laser sheet thickness is reported as the 1/e 2 value and was determined by rotating the CL 90 degrees and imaging Rayleigh scattering from ambient air, which represents the laser sheet profile. The high-speed planar Rayleigh scattering images are collected with a high-speed CMOS camera (Vision Research, Phantom 711). In this study, we report on a new optimized optical collection setup, where the Rayleigh-scattered signal is collected by the combination of a “fast” achromat (f = 210 mm, D = 100 m) and an 85-mm f/1.4 Nikon camera lens. This combination results in a collection f-number of 3.45 and a magnification of 0.4 which yields an imaged area of 50 × 50 μm2/pixel. At 10,000 frames/s, the CMOS camera operates with a resolution of 1,152 × 664 pixels, and at 20,000 frames/s, the CMOS camera operates with a resolution of 768 × 416 pixels. As will be discussed below, a USAF 1951 target is used to investigate the spatial resolution of the system. For a spatial feature (bar pattern) at the pixel projection size (~50 μm), the contrast of the imaging system was >20 %; for a 100-μm-thick bar pattern, the contrast was ~60 %; and for a 250-μm-thick bar pattern (equivalent to the out-of-plane spatial resolution as defined by the laser sheet thickness), the contrast was >90 %. As discussed in Sect. 3.4, the final imaging results are processed with either 2 × 2 or 3 × 3 median filters (to improve signal-to-noise), which does degrade the in-plane spatial resolution of the system. Using 20 % contrast of a bar pattern to define the limiting spatial resolution, 2 × 2 median filtering decreases the spatial resolution of the system to 80 μm/pixel and 3 × 3 median filtering decreases the spatial resolution to 120 μm/pixel.

Fig. 3
figure 3

Experimental setup for high-speed planar Rayleigh scattering measurements. CL = cylindrical lens; ACH = achromat; BD = beam dump. The cameras denoted “Rayleigh” and “SC” are used for the planar Rayleigh scattering and sheet correction measurements, respectively

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A second high-speed CMOS camera (Vision Research, Phantom 711), denoted “SC,” is shown in Fig. 3, which images a uniform region in air to correct for variations in laser sheet intensity. As noted from the figure, the camera is not aligned normal to the laser sheet (due to space limitations), thus only one portion of the field-of-view (FOV) is in focus. This region of the FOV is carefully mapped out and used for the laser sheet intensity corrections.

3.3 New observations on non-uniform CMOS sensor gain

It is well known that CMOS sensors have the potential to have an independent response for each pixel [19, 43–45] because each pixel in a CMOS sensor acts an independent active circuit in which charge is converted directly to voltage and analog-to-digital conversion occurs in parallel for all pixels. While this parallel conversion allows for the high acquisition rates characteristic of CMOS cameras, it can lead to variations between irradiance and pixel count throughout the CMOS sensor, which manifests itself as sensor “non-uniformity.” In our previous work [19], we followed the procedures prescribed by Weber et al. [44] and Hain et al. [45] to investigate the sensor non-uniformity of our CMOS cameras. In this manner, a calibrated, Ulbricht sphere was used as the uniform light source which illuminated the CMOS sensor. Averaged images obtained using the Ulbricht sphere were used as a means of correcting for sensor non-uniformity in which it was found that the degree of non-uniformity was small (<3 %) and it was independent of incident illuminance (see Fig. 3c in Ref. [13]).

In the present work, we initially followed the same procedure and found nearly identical results; that is, each of our two V711 cameras produced nearly uniform gain profiles across the sensor based on the Ulbricht sphere results. Subsequently, we investigated Rayleigh scattering in ambient air (which should appear uniform along a radial profile) and found very non-uniform intensity profiles. The apparent non-uniformity could be the result of many factors including the optical setup (i.e., inclusion of the achromat) or since the collected Rayleigh scattering is at the same wavelength as the incident laser light, unwanted scattered light from optics, surfaces, etc. The achromat/lens combination was removed and replaced with only a single camera lens, and the results were consistent with those obtained using the achromat/lens combination, indicating no degradation in spatial uniformity due to the presence of the achromat. Subsequently, several light baffling approaches were taken, and identical results were achieved each time, which were independent of laser intensity or horizontal camera translation (i.e., moving closer or away from suspected scattering sources). The first CMOS camera (Cam 1) was removed from the setup, and a second CMOS camera (Cam 2) was put in place. A different, but non-uniform, intensity profile was measured using Rayleigh scattering in ambient air. However, it is noted that both CMOS cameras yielded nearly identical, uniform gain profiles when using the Ulbricht sphere. Finally, a CCD camera was placed within the same optical setup as the two CMOS cameras and a uniform Rayleigh scattering intensity profile was measured, which matched that of the results using the Ulbricht sphere, indicating no unwanted scattering was collected with the current collection optics and geometry. Sample intensity profiles for the two CMOS cameras are shown in Fig. 4. The solid black line represents the results obtained when using the Ulbricht sphere with CMOS Cam 1 using a shutter time of 40 μs. The results of Cam 2 with the Ulbricht sphere are very similar. Figure 4 also shows the intensity profiles from Rayleigh scattering in ambient air averaged over 200 images for the two different CMOS cameras (Cam 1 = solid blue line; Cam 2 = solid red line) indicating the significant differences in the sensor gain profile for the two CMOS cameras when exposed to short-duration intensity.

Fig. 4
figure 4

Example intensity profiles from two CMOS cameras demonstrating non-uniform sensor gain for short-duration incident intensity. The intensity profiles from the two “pulsed sources” are taken from planar Rayleigh scattering images in pure air. The intensity profile from the “continuous source” is taken from a uniform Ulbricht sphere [13]. Each result is derived from pixel 332 in the vertical direction from a 250-shot average

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To interpret these results, it must be noted that the Ulbricht sphere operates as a continuous light source with a constant luminance and in order to have sufficient illuminance (lumens/m2) at the CMOS sensor, the camera shutter was opened and signal was integrated for 40 μs. In contrast, the Rayleigh-scattered intensity only occurs during the laser pulse, which is 10–25 ns (depending on laser source) and represents a timescale more than 103 times smaller than that of the collected illuminance from the Ulbricht sphere. In this manner, we conclude that the current CMOS sensors have a pixel-specific temporal dependence in the complete photon → electron → charge transfer → A/D conversion process, where for short timescales (e.g., ns-pulse lasers), there is significant variability between pixels, but for longer timescales (e.g., >microseconds), the variability diminishes which manifests itself as sensor uniformity. This phenomenon is not observed in scientific-grade CCD cameras. From our current results, we do not have a way to determine which part of the process is responsible for this “temporal dependence,” but we report this as a cautionary guideline when calibrating high-speed CMOS sensor arrays for quantitative measurements.

Examples of the impact of the temporally dependent non-uniformity are shown in Fig. 5. The top figure displays the mean radial profile of mixture fraction for a Re = 15,000 turbulent propane jet (discussed in detail in Sect. 3) at an axial position of x/d = 15 (d is the nozzle diameter) acquired with Cam 1, and the bottom figure displays the mean temperature profile from a laminar (Re = 1,500) non-premixed jet flame using Cam 2. As discussed below, both of these quantities are determined with planar Rayleigh scattering. In each figure, the “dashed lines” represent the profile obtained without accounting for the effects of the ns-duration signal (denoted "w/o Corr"), that is, the observed temporally dependent non-uniformity. As shown in top portion of Fig. 5, there is a 12 % over-prediction in the peak mixture fraction profile and a noticeable non-physical radial shift. In addition, the mixture fraction values for radial positions of r/d < −1 become negative, which is non-physical and consistent with the gain profile of Cam 1 from pixels 0 to 256 shown in Fig. 4. The bottom portion of Fig. 5 shows that without accounting for the effects of the temporally dependent non-uniformity of Cam 2, the peaks of the mean temperature profile are over-predicted by 10 %, which exceeds the adiabatic flame temperature. Such peak temperatures are non-physical. In addition, because of the gain profile of Cam 2 (see Fig. 4), the ambient temperatures for radial positions of r/d < −3 are less than the known room temperature value of 300 K and are as low as 235 K. With the proper accounting of the non-uniformity, as outlined in Sect. 3.4, the ambient temperatures for the given temperature profile are deduced to be 300 ± 3 K.

Fig. 5
figure 5

(Top) Mean mixture fraction profiles from a Re = 15,000 non-reacting jet at an axial position of x/d = 15. (Bottom) Mean temperature profiles from a laminar, Re = 1,500 CH4/H2/N2 non-premixed jet flame. Also shown is the adiabatic flame temperature (Tad) for the current fuel/oxidizer combination. In each figure, the "dashed line" represents the results without correcting for non-uniform sensor gain with a ns-timescale calibration, and the "solid line" represents the result with a proper accounting of the non-uniform sensor gain for short-duration laser sources

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It is further reinforced that the discrepancies between the results shown with "dashed" lines (w/o Corr) and those with the "solid" lines (w/Corr) are not the result of simply ignoring sensor non-uniformity, but represent the differences between performing a classic “whitefield” (non-uniform gain) correction using the results from a continuous light source such as an Ulbricht sphere and accounting for the non-uniformity that manifests itself when the incident intensity occurs on short, nanosecond timescales. Such a difference impacts the way that the collected signal must be converted to the quantities of interest as discussed below in Sect. 3.4. To the authors’ knowledge, this is the first study to comment on the apparent temporal dependence of incident intensity in terms of CMOS detector response.

3.4 Image processing and data reduction

For quantitative measurements, proper reduction in the acquired Rayleigh scattering signal is paramount. In this work, similar systematic reduction procedures are followed as outlined in our previous work [19], with some alternative steps as required by non-uniform sensor gain results reported in Sect. 3.3. First, subtraction of background signals (e.g., darkfield image and stray light scattering subtraction) is performed. The typical procedure for accounting for the background is to acquire a series of images with the lens covered and treat this as the “darkfield” image. However, it has been shown that CMOS cameras demonstrate an increasing “gray level” as a function of operating time [44, 45]; that is, the darkfield correction will change from measurement to measurement. To avoid this effect, the background signal was determined by “padding” each camera image sequence with 75 images beyond the number of pulses within a burst. With no laser pulses present, the average of these 75 images (e.g., 7.5 ms of real time at 10 kHz) represents an accurate representation of the darkfield contribution for each individual pulse burst.

The second data reduction step is the correction for sensor non-uniformity, i.e., “whitefield” corrections. As noted in Sect. 3.3, this correction needs to be performed with a light source operating with the same temporal duration as the Rayleigh scattering measurements. This fact prompted the particular formulation of Eq. (3) to deduce the local jet mole fraction, X J , in which the collected Rayleigh scattering signal, I RAY, is directly normalized by the calibration signal from pure air, I AIR. In this manner, the same time-dependent non-uniform sensor gain is present in the reference air measurements as in the turbulent jet mixing measurements, and the “whitefield” correction is implicit within the data reduction procedure. The air calibration image was formulated by taking the mean of ten 100-image pulse bursts acquired while only the co-flowing air stream was operational. This process was repeated for each spatial location.

The third data reduction step involves corrections for pulse-to-pulse laser energy fluctuations and non-uniformity of the laser sheet intensity distribution. These corrections were applied with two different methods depending on the axial location. For axial locations of x/d = 10–20, the laser sheet intensity correction was determined directly from the individual Rayleigh scattering images by measuring the instantaneous intensity magnitude and spanwise spatial distributions in a region of the uniform co-flowing air stream. At axial positions further downstream, the second CMOS camera, denoted “SC” as shown in Fig. 3, was used to image a region of the uniform co-flowing air stream. The first method is preferred in all axial and radial position that contain a consistent region of the uniform, co-flowing air stream as it provides an optimal energy/intensity distribution fluctuation correction. However, for portions of the jet or flame that do not contain a region of the co-flowing air stream (i.e., on “centerline” at conditions in the farfield of the jet or flame), the first correction method cannot be applied and the two-camera approach must be applied.

The final data reduction procedure involves 2 × 2 median filtering for the non-reacting turbulent jets and 3 × 3 median filtering for the turbulent flame results in order to increase the SNR. In both cases, the effective in-plane spatial resolution (80 or 120 μm) is less than the out-of-plane spatial resolution defined by the laser sheet thickness.

3.5 Turbulent jet and flame operating conditions

The co-flowing jet assembly is mounted on two high-precision translation stages that allow for translation in both the axial and radial directions. The same facility is used for both the turbulent jet and flame measurements. For both sets of experiments, the jet fluid or fuel (in the case of the flames) issues from an 7.75-mm-diameter tube into a 30 cm × 30 cm co-flowing air stream operating at 0.3 m/s. The co-flowing air is supplied from a high-pressure facility line and is filtered, which is essential to remove dust particles, as the scattering from such particles would completely mask the Rayleigh scattering signal. For the turbulent non-reacting jet measurements, propane (C3H8) was chosen as the working jet fluid due to its large differential Rayleigh scattering cross-section as compared to air. The propane issues from the tube with velocities ranging from 6.2 to 12.4 m/s, corresponding to Reynolds numbers of 10,000–20,000 based on jet diameter.

The turbulent non-premixed flames considered in this study are simple jet flames issuing into the low-speed co-flowing air stream. The turbulent flames are the well-studied “DLR” flames that serve as benchmark flames within the International Workshop for the Measurement and Computation of Turbulent Non-premixed Flame (TNF Workshop) [43]. The fuel consists of 22.1 %CH4, 33.2 % H2, and 44.7 % N2 and issues from the tube at 43.2 m/s for DLR flame A (Re = 15,200) and 63.2 m/s for DLR flame B (Re = 22,800). The stoichiometric mixture fraction is 0.167, and the differential Rayleigh scattering cross-section is constant throughout the flame to within ±3 % [44, 45], facilitating straightforward temperature measurements using Rayleigh scattering as described in Sect. 2. In addition to the turbulent flames, a laminar, Re = 1,500 non-premixed flame, using the same fuel composition, is studied to assess image quality in terms of single-shot signal-to-noise and spatial resolution.

4 Results and discussion

This section presents recent results using the new HEPBLS to obtain multi-kHz-rate planar Rayleigh scattering images that can be used to deduce temporally correlated image sequences of the mixture fraction field in turbulent non-reacting jets and temperature field in turbulent non-premixed jet flames. The primary focus of this section is to highlight the substantial improvements in records lengths, acquisition rates, SNR, and spatial resolution as compared to our previously reported results [19, 20].

4.1 kHz-rate mixture fraction imaging in turbulent jets

Figure 6 shows an example mixture fraction image sequence from a Re = 15,000 non-reacting jet at an axial position of x/d = 10. The data were acquired at 10 kHz, but only every other image is shown for clarity (5 kHz). The 25 sequential images are only a subset of the full 130 image sequence (13 ms), representing 5 ms of “real time”. Each image has been placed on a quantitative scale (ξ = 0–1) using Eqs. (3) and (4), and the variation in mixture fraction is represented with a false color map to highlight the high scalar gradients and small-scale scalar features present throughout the jet. Using the new HEPBLS, the full 130 image sequence at 10 kHz represents a record length which is 13 times longer than our previously reported 10 kHz mixture fraction imaging results [19]. To analyze the importance of the longer record lengths, an estimation of a convective time scale or flow-through time (FTT) is made. The FTT is estimated as t f  = d/U c , where d is the jet nozzle diameter, which would most likely represent the size of the largest coherent structures (or “eddies”) within the flow and U c is the velocity of the large-scale structures. The convective velocity of the large-scale structures is estimated as the centerline gas velocity which is calculated using mean scaling laws from Tacina and Dahm [46]. In this manner, the FTT is estimated as 1.5 ms for this Reynolds number and axial location combination. Our previous work [19] was limited to 1 ms of “real time” and thus represented less than one FTT; in contrast, the current measurements represent ~9 FTTs at the current operating conditions with the potential for 17 FFTs if the full 25-ms burst duration is used. The longer record lengths are important for gathering statistically converged results.

Fig. 6
figure 6

Twenty-five-frame (of 120), 10-kHz sequence of the mixture fraction field in a turbulent (Re = 15,000) non-reacting propane jet issuing into air. The field-of-view of the images is 16 mm × 40 mm. Images are centered at x/d = 15. Each image covers the domain of 14 ≤ x/d ≤ 16 and −2.3 ≤ r/d ≤ 2.3. Every other image (5 kHz) is shown for clarity

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A prominent feature of the image sequence shown in Fig. 6 is the high SNR which allows the observations of a multitude of dynamic processes. Examples include the advection of large-scale scalar structures on centerline as noted in frames 4–12 and the simultaneous advection and apparent diffusive behavior noted in frames 21–25. To quantify the image quality, “single-shot” SNR values in the co-flowing air stream (ξ = 0) are determined as the mean value of IRAY/IAIR (Eq. 3) divided by the RMS fluctuation of IRAY/IAIR. Using a 10 × 100 pixel region in the co-flowing air stream, the single-shot SNR for an instantaneous image was measured as 65. Since the current flows are highly turbulent, it is difficult to find a uniform region within the fuel core to directly determine the single-shot SNR at ξ = 1. In this manner, the SNR (for an un-intensified camera) can be estimated using a re-formulated version of Eq. (9) from Ref. [47], SNR = S e /(S e  + N 2cam )1/2, where S e is the camera signal in units of electrons and N cam is intrinsic noise of the camera, which includes the contributions from amplifier, thermal, dark-current shot, and quantization noise from the A–D converter. Since the SNR of the Rayleigh scattering measurements was derived in the co-flow (for a known S e ), N cam is determined directly for the current camera configuration. Furthermore, since the Rayleigh scattering signal increases with increasing mixture fraction as shown in Eq. (2), Se at any mixture fraction, ξ, is estimated as S e (ξ) = S e (ξ = 0)*σ(ξ)/σ(ξ = 0), where σ is the mixture-averaged differential Rayleigh scattering cross-section as defined in Sect. 2. For pure jet fluid, S e (ξ = 1) ≈ 13*S e (ξ = 0). Using these relations, the SNR at ξ = 1 is estimated as >200 for the current set of measurements. The SNR of the current measurements is approximately 7 times higher than our previously reported results [13] at similar spatial resolution.

As reported in [19], our previous measurements were limited to 10 kHz because of the inherent pulse energy and subsequent SNR decreases that correspond to increases in pulse repetition rates. However, using the new HEPBLS, which has significantly higher output pulse energies, higher acquisition rates are possible, allowing access to dynamics occurring at faster timescales. Figure 7 shows an example 25-frame (of 175 frames), 20-kHz mixture fraction image sequence from a Re = 20,000 non-reacting jet at an axial position of x/d = 10. Each image corresponds to a FOV of 14 mm × 38 mm. Figure 8 shows an example 10-frame (of 175 frames), 40-kHz mixture fraction image sequence from a Re = 20,000 non-reacting jet at an axial position of x/d = 7. Each image corresponds to a FOV of 13 mm × 30 mm. These results represent one of the key features of measurements using the new HEPBLS; that is, the repetition rates can be systematically increased as test conditions warrant finer temporal resolution (i.e., measurements near the nozzle exit or with increasing Reynolds number). According to Nyquist--Shannon sampling theory, measurements should be acquired at sampling rates that are at least twice as fast as the appropriate characteristic frequency. In this manner, the combination of the high acquisition rates and long-record lengths allows the examination of flow dynamics over a broad range of time scales. As one example, 25-ms burst durations would allow dynamic events occurring at rates as slow as 80 Hz to be captured. For 40-kHz measurements, this would represent a dynamic range (DR) of 250 and temporal resolution sufficient to track fluctuations over time scales as short as 50 μs.

Fig. 7
figure 7

Twenty-five-frame (of 175), 20-kHz sequence of the mixture fraction field in a turbulent (Re = 20,000) non-reacting propane jet issuing into air. The field-of-view of the images is 14 mm × 38 mm. Images are centered at x/d = 10. Each image covers the domain of 9.1 ≤ x/d ≤ 10.9 and −2.45 ≤ r/d ≤ 2.45

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Fig. 8
figure 8

Ten-frame (of 150), 40-kHz sequence of the mixture fraction field in a turbulent (Re = 20,000) non-reacting propane jet issuing into air. The field-of-view of the images is 13 mm × 30 mm. Images are centered at x/d = 7. Each image covers the domain of 6.1 ≤ x/d ≤ 7.9 and −1.95 ≤ r/d ≤ 1.95

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As an example of the different timescales captured using the current measurements, Fig. 9 shows three time traces of the instantaneous mixture fraction at various radial positions within a Re = 15,000 turbulent jet centered at an axial position of x/d = 15. The three traces represent single radial positions of r/d = 0 (black), r/d = 1.33 (red), and r/d = 1.67 (blue), extracted from the 2D image sequences captured at 20 kHz. Figure 9 shows one of the most prominent features of scalar fields in turbulent flows, that is, the formation of “ramp-cliff” structures as discussed in [48–51]. Physically, the ramp-cliff structures indicate that the scalar gradients tend to concentrate in sharp fronts separated by large periods of weaker gradients. The observation of these structures is a clear indication of the imprint of the large-scale intermittency of the flow onto the smaller scales (i.e., small-scale fluctuations appear to be imbedded on top of the larger-scale fluctuations), demonstrating at any spatial position there may be a large range of important time scales. As shown in Fig. 9, the smaller-scale fluctuations tend to damp out as the radial position is increased, and the larger time scales appear to be independent of radial position (2–3 ms). The three example time traces of Fig. 9 show fluctuations occurring at time scales ranging from 50 μs to >3 ms, corresponding to a DR of >60.

Fig. 9
figure 9

Twenty-kHz traces of the time-varying mixture fraction at various radial positions in a Re = 15,000 propane jet issuing into air. The measurements demonstrate the different timescales occurring with the jet. Images are centered at x/d = 15. The spatial locations of the measurement points are shown in the top image

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4.2 kHz-rate temperature imaging in turbulent flames

Previous work within our group [20] demonstrated two-dimensional, 10-kHz temperature measurements in a series of turbulent non-premixed jet flames using planar Rayleigh scattering and pulse burst technology. The previous pulse burst system [17] output was ~200 mJ/pulse at 532 nm, which was sufficient to measure the instantaneous temperature field at 10 kHz with the combination of a high-speed CMOS camera and high-speed image intensifier (IRO). However, it is known that the use of an IRO degrades spatial resolution [41] and limits the achievable SNR. In addition, the previous laser system was limited to burst durations of 1 ms, which resulted in a limited ten-image sequence. As described in Sect. 3, the new HEPBLS provides substantially longer record lengths (up to 25 ms) and higher output energies which significantly enhance our high-speed temperature imaging capabilities as described below.

4.2.1 Improvements in spatial resolution and signal-to-noise

The high output pulse energies of the new HEPBLS system, in combination with an improved optical collection system, allow for sufficient collection of the Rayleigh scattering signal such that a high-speed IRO is not required as in previous studies [20]. In this section, we will describe the benefits in terms of increased spatial resolution and signal-to-noise of using our new optical collection system, which consists of a CMOS camera and “fast” achromat (see Sect. 3.2) as compared to our previous CMOS + IRO system. While the use of an IRO boosts the collected Rayleigh signal, it is well known that the two-stage intensifier degrades the spatial resolution of the measurements due to non-localized gradient blurring [41]. In addition, the use of an IRO can limit the achievable SNR due to photon multiplication and spurious noise contributions. Figure 10 shows two images of a USAF 1951 resolution target as imaged by the combination of a CMOS + IRO and a CMOS camera only. The IRO gain settings and the exposure time are adjusted such that the signal level (“counts”) is nearly identical to the maximum signal level from the previous work [14]. For the “CMOS only” case (i.e., no IRO), the exposure time is adjusted such that the peak-collected signal is matched to the Rayleigh signal levels from the current Rayleigh scattering temperature imaging experiments reported below. Additionally, the FOVs for both images are identical (41 mm × 61 mm before cropping), and the images are displayed with the same dynamic range; that is, the ratio of the average signals corresponding to “white” and “black” (before normalization) in Fig. 10 is the same. From Fig. 10, it is clear (and expected) that the “CMOS only” images display much higher spatial resolution as compared with the CMOS + IRO images. As one example, a section displaying the smallest features of the USAF 1951 target is extracted and magnified by 300 % to highlight the improved spatial resolution. Almost all of the individual lines from the line pairs in the zoomed-in section of the resolution target are indiscernible from the CMOS + IRO image whereas many of those same lines are quite distinct in the CMOS only image. In addition, it is noted that while the actual signal levels are higher in the CMOS + IRO images (3,000 vs. 1,000 counts), the signal-to-noise is higher for the CMOS only case.

Fig. 10
figure 10

Sample images of USAF 1951 resolution target with and without the use of a high-speed image intensifier (IRO)

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To further investigate the two-camera systems’ response as a function of spatial frequency, Fig. 11 shows normalized intensity profiles taken through various bar patterns within the USAF 1951 target that correspond to different bar thicknesses and number of line pairs/mm. Each plot in Fig. 11 displays the normalized intensity versus normalized spatial position, Δx/L, where Δx is the pixel spacing and L is the local bar thickness. The dashed lines represent the ideal intensity distribution of any given bar pattern, the red lines represent the measured profiles from the CMOS only image, and the blue lines represent the measured profiles from the CMOS + IRO image. The line thicknesses, L, over which the signal levels were obtained are L = 446 μm, L = 280 μm, L = 198 μm, and L = 111 μm. For all bar thicknesses, the effect of the IRO is easily observed. Even for the largest bar thickness (L = 446 μm), the CMOS + IRO profile shows reduced contrast (or modulation); that is, the maximum and minimum signals do not reach a value of 1 or 0, respectively. At L = 111 μm, no contrast is observed for the CMOS + IRO, while the contrast for the CMOS is >0.6 (“ideal” contrast = 1).

Fig. 11
figure 11

Normalized intensity profiles at various positions within a USAF 1951 resolution target. Results are shown for the cases of a CMOS camera with and without the use of a high-speed image intensifier (IRO). The bar thicknesses and spatial frequencies are determined from the group number on the USAF 1951 resolution target

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A more rigorous way to show the improved spatial resolution of the current optical configuration is by estimating the contrast (or modulation) of the two imaging systems from the USAF resolution targets. The contrast (C) is defined as

$$C = \frac{{\text{I}_{\hbox{max} } - \text{I}_{\hbox{min} } }}{{\text{I}_{\hbox{max} } + \text{I}_{\hbox{min} } }}$$
(7)

where I max is the maximum intensity throughout the repeating pattern and I min is the minimum intensity throughout the repeating pattern. Figure 12 shows the estimated contrast for both the CMOS and CMOS + IRO image cases. The C value for the CMOS + IRO camera is ~20 % at 3.5 line pairs/mm. The same C value is achieved for the CMOS only camera setup at 9 line pairs/mm. From these results, we can infer that the smallest feature which is identifiable is between 120 and 200 μm for the CMOS + IRO, and is ~60 μm (limited by the pixel projection area of the camera). The higher pulse energies from the HEPBLS in conjunction with the improved optical setup allow for the ability to take advantage of increased spatial resolution that comes with using a CMOS camera only as opposed to using an intensified CMOS as in the previous high-speed temperature imaging studies from our group [20].

Fig. 12
figure 12

Measured imaging contrast (C) of the CMOS and CMOS + IRO camera systems for the current field-of-view

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Figure 13 presents an instantaneous temperature image acquired in the laminar (Re = 1,500) CH4/H2/N2 non-premixed jet flame. The full image height is 14 mm, but only 9 mm are shown for compactness. The image spans approximately 6 tube diameters in the radial direction. Shown beneath the 2D temperature image is a plot of the radial temperature profile extracted from the axial position indicated by the white dashed line. Also shown on the same radial plot is a red dashed line, which indicates the adiabatic flame temperature (T ad) for the current fuel/oxidizer combination. Since the instantaneous image is from a laminar flame with uniform low- and high-temperature regions, estimations of single-shot SNR can be obtained. From the uniform “air” regions (r/d > 2.5), the SNR, which is defined as the mean temperature divided by the RMS fluctuation of the same region, is approximately 90. Similarly, the 9-mm axial profile at r/d ~ 1.3 represents a nearly uniform, high-temperature region. At this location, the SNR is determined as ~35 at T = 1,900 K. These are significant improvements as compared to our earlier work (using an IRO) in which the SNR was estimated at 35 and 11 at ambient and T ~ 1,800 K, respectively [20].

Fig. 13
figure 13

(Top) Instantaneous temperature image in a Re = 1,500, laminar, CH4/H2/N2 non-premixed jet flame. Image is centered at an axial position of x/d = 7 and covers a domain of 6.4 ≤ x/d ≤ 7.6 and −2.5 ≤ r/d ≤ 2.5. (Bottom) The radial temperature profile corresponding to the axial position indicated by the white, dashed line in the top image. Also shown is the adiabatic flame temperature (Tad) for the current fuel/oxidizer combination. The single-shot SNR is measured as 90 in air and 35 at 1,900 K

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Figure 14 shows two sample turbulent flame images from DLR flames A and B, corresponding to Reynolds numbers of 15,200 and 22,800, respectively. The images on the left are from the previous high-speed temperature study using the previous generation of PBLS [17] in conjunction with an intensified CMOS camera [20], and the images on the right are from the current HEPBLS in combination with an un-intensified CMOS camera. The centerline regions from both DLR flame B images are enlarged and shown below the DLR flame B images. The excerpts are converted to grayscale and are displayed with a 30 % increase in contrast to highlight the small-scale structures. The substantial improvements in both spatial resolution and SNR with the new system are apparent from the turbulent flame images shown in Fig. 14. The small-scale structure is essentially lost in the intensified CMOS image on the left whereas a rich set of small-scale structures are clearly identified in the CMOS only images.

Fig. 14
figure 14

(Left) Previously reported turbulent flame images from a 10-kHz image sequence [14]. (Right) Instantaneous turbulent flame images using the new HEPBLS and un-intensified CMOS camera. The single-frame images are extracted from the 10-kHz image sequences shown below in Figs. 15 and 16. The field-of-view of the images is 14 mm × 40 mm. Images are centered at x/d = 10. Each image covers the domain of 9.1 ≤ x/d ≤ 10.9 and −2.6 ≤ r/d ≤ 2.6

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4.2.2 Sample 10-kHz temperature imaging sequences in turbulent flames

In addition to outputting higher pulse energies, the new HEPBLS also provides extended burst durations as compared to the previous generation of pulse burst lasers. Pulse burst durations of greater than 20 ms have been recorded with the HEPBLS, and durations of 10 ms are reported in this paper at repetition rates of 10 kHz. This longer record length allows for more detailed investigations concerning combustion dynamics and also will allow for unique spatio-temporal statistics to be deduced within turbulent flame environments. Figure 15 shows a partial sequence of temporally-correlated temperature images in the turbulent DLR flame A (Re = 15,200) at an axial position of x/d = 10 using a CMOS camera only (no IRO). The dimensions for each image are approximately 40 × 14 mm2, and the temporal spacing between images is 100 μs. The images were obtained with >500 mJ/pulse at 532 nm, which corresponded to 40 % of the total output capability of the HEPBLS. The high-quality image sequence highlights the time-dependent nature of the thermal field within the turbulent non-premixed jet flames, allowing observation of multi-scale dynamics not previously available. The high-temperature regions of the flame are seen to fold, roll, and sometimes separate throughout the course of the image sequence, indicating the strong interaction with the turbulent flow field. However, as expected from the lower-Reynolds-number DLR A flame, the high-temperature regions remain largely attached and aligned with the axial direction for the majority of the image sequence.

Fig. 15
figure 15

Forty-frame (of 100), 10-kHz sequence of the temperature field in a turbulent (Re = 15,200) non-premixed jet flame issuing into air. Fuel mixture is 22.1 % CH4/33.2 % H2/44.7 % N2 and Re = 22,800 (DLR B Flame). The field-of-view of the images is 14 mm × 40 mm. Images are centered at x/d = 10. Each image covers the domain of 9.1 ≤ x/d ≤ 10.9 and −2.6 ≤ r/d ≤ 2.6

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Figure 16 shows a second example of a 10-kHz temperature sequence obtained within the DLR flame B (Re = 22,800). Similar to Fig. 15, only 4 ms of “real time” data are presented, although the full image sequence corresponds to >10 ms. It is well known that DLR B is near extinction [44, 45] and Fig. 16 displays several examples of strong turbulence-chemistry interaction. From this image sequence, features such as the formation of “flame holes” (cold gas pockets surrounded by hot gas, i.e., “lower right” portion of images 7–16) and possible flame re-ignition (images 23–30) are clearly seen, showing the time-varying (dynamic) nature of thermal mixing, the introduction of steep thermal gradients, and the rapid temporal evolution of the flame topology. High-resolution image sequences, such as these, will provide a new understanding of turbulent thermal mixing and flame dynamics over a broad range of length and time scales.

Fig. 16
figure 16

Forty-frame (of 100), 10-kHz sequence of the temperature field in a turbulent (Re = 22,800) non-premixed jet flame issuing into air. Fuel mixture is 22.1 % CH4/33.2 % H2/44.7 % N2 and Re = 22,800 (DLR B Flame). The field-of-view of the images is 14 mm × 40 mm. Images are centered at x/d = 10. Each image covers the domain of 9.1 ≤ x/d ≤ 10.9 and −2.6 ≤ r/d ≤ 2.6

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The long pulse burst duration also allows for the extraction of novel simultaneous spatial and temporal flame statistics, which will be the subject of future work. In this manner, Fig. 17 presents two temporal traces from the full DLR A temperature sequence, of which a portion was shown in Fig. 15. Figure 17 shows the location of two virtual “probes” on a temperature image from DLR flame A. The two “probes” are located at the same axial position (~x/d = 10) but at different radial positions. One “probe is located at r/d = 1.33, and the other is located at r/d = 1.67. The temperature traces illustrate the different time scales present within the flame at the two radial locations. The measurement at r/d = 1.33 fluctuates more vigorously with much higher temperature gradients (dT/dt ~ 106 K/s) than the measurements at r/d = 1.67, which essentially displays large-scale dynamics. Since the high-speed temperature images characterize the temperature field in two spatial dimensions, similar “probes” can be placed anywhere within the 2D plane. From a large number of traces at various key locations with the reacting flow, it is conceivable that novel and important multi-point, multi-time, scalar statistics can be deduced.

Fig. 17
figure 17

Sample 10-kHz temperature traces at two radial positions within DLR flame A (Re = 15,200). The measurements demonstrate the different timescales occurring with the turbulent flame. The spatial locations of the measurement points are shown in the top image, which correspond to x/d = 10 and r/d = 1.33 and 1.67, respectively

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5 Summary and conclusions

In this study, we have described recent advances in our laboratory in the area of quantitative, high-speed planar Rayleigh scattering as applied to turbulent flows with specific applications of time-resolved image sequences of the mixture fraction field in turbulent non-reacting flows and the temperature field in turbulent reacting flows. Significant improvements as compared to our previously published results [19, 20] include increases in record lengths (12 ms vs. 1 ms), increases in acquisition rates (up to 40 kHz), increases in instantaneous SNR (7 and 3.5 times higher in the non-reacting and reacting flows, respectively), and increases in spatial resolution. The vastly superior image quality, defined as improved signal-to-noise and spatial resolution, of the present results is enabled by the combination of a new HEPBLS as described in [23] and an optimized, high-throughput, optical collection system. This is of particular importance in the high-speed temperature imaging studies, which are now acquired using only a high-speed, user-calibrated, CMOS camera and thus is not affected by the additional noise and resolution degradation associated with high-speed IROs. The improved SNR and spatial resolution allow for the observation of small-scale scalar fluctuations (in both space and time) that were not previously possible.

High pulse energies (>500 mJ/pulse at 532 nm and 10 kHz) are produced from the custom HEPBLS over extended record lengths corresponding to tens of FTTs for the current laboratory-scale flows/flames. The long burst duration allows for the observation of turbulent flow and combustion dynamics occurring at many different time scales. In this manner, the 2D measurements are suitable for both visualization of turbulent flow/flame dynamics and multi-point, temporally based statistical analysis, which will be a near-term research focus.

Finally, we will note that the current work presents what are believed to be the first reported observations of an apparent temporal dependence of incident intensity in terms of CMOS detector response. Calibrations of our high-speed CMOS cameras using a well-established continuous light source (Ulbricht sphere) demonstrated a uniform sensor profile, while instantaneous Rayleigh scattering measurements (occurring over 15 ns) in ambient air demonstrated a noticeable non-uniform sensor gain. It appears, based on our results, that for short, nanosecond timescales, there is a significant variability between pixels, but for longer timescales (e.g., >microseconds), the variability diminishes which manifests itself as sensor uniformity. While we have not determined the individual process responsible for the pixel-specific temporal dependence, we report these observations as a cautionary guideline when calibrating high-speed CMOS sensor arrays for quantitative measurements. However, with proper calibration, high-quality, quantitative images such as the high-speed planar Rayleigh scattering measurements presented here are possible.