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Abstract
Toluene laser-induced fluorescence (LIF) has been applied to image the mixing deficit on the molecular level in the transonic wake of two different blunt-body injectors in a compressible accelerated nozzle flow. A single-color excitation and two-color detection scheme is employed to measure the signal red-shift caused by the quenching effect of molecular oxygen on the fluorescence of toluene, which reduces and red-shifts the LIF signal if both substances interact on a molecular level. To this end, toluene is injected alternatingly with O2-contaning and O2-free carrier gas into the air main flow. Differences of both signals mark regions where mixing on molecular level is incomplete. A zone of molecular mixing deficit extending several millimeters in stream-wise direction is identified. The effect of local variations in temperature on the sensitivity of this technique is discussed using photo-physical data measured in a stationary low-temperature cell.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Efficient and fast mixing on the molecular level is essential to enable supersonic combustion and reactions in shock-wave flow reactors [1]. Practical realizations often feature central injectors that add a low-momentum feed of one reactant into a high-momentum sub- or supersonic flow containing the other [1, 2]. The fundamental understanding of mixing processes in such wake flows has been subject to fundamental research for several decades [3].
Planar laser-induced fluorescence (LIF) of organic tracers [4] has proven particularly useful for visualizing instantaneous species distributions in high-speed gas flows due to its high time resolution. The spatial resolution of the optical detectors and the light-sheet thickness, however, restrict direct measurements to macroscopic structures. These are typically orders of magnitude larger than the length scales relevant for the molecular interaction of reactants. Several approaches to measure the level of molecular mixing have been proposed. They are based on the photo-physical sensitivity of the laser-excited species on collisions with constituents of the admixed gas, e.g., by fluorescence quenching: Clemens et al. [5] introduced an approach that exploits the quenching of nitric oxide (NO) fluorescence by O2. They identified the level of molecular mixing in the shear layer of a coaxial jet of N2 in air by alternatingly adding NO to each flow. King et al. [6] proposed a two-tracer approach. They marked the air flow with acetone, a ketone tracer insensitive to quenching by O2, and the second O2-free flow with NO. This method requires tracers with spectrally-separable fluorescence and, in this case, excitation at two separate wavelengths. Koban et al. [7] simplified this approach by substituting the O2-sensitive NO with toluene, and acetone with 3-pentanone. The LIF signal intensity of aromatics like toluene strongly depends on the O2 partial pressure [8] and is spectrally well-separated from that of 3-pentanone, while both can be excited with the same UV laser. Further simplification was introduced by Mohri et al. [9] who used toluene as single tracer and exploited the O2-induced red-shift [10] of the LIF signal to detect micro-mixing indirectly by measuring the local O2 distribution. The red shift was quantified by using two cameras equipped with filters for two separate portions of the fluorescence spectrum.
Knowledge about the status of molecular mixing is also relevant from a diagnostics point of view. The determination of flow composition and temperature using O2-sensitive tracers depends on the local (molecularly mixed) O2 partial pressure [11, 12]. A quantitative analysis of LIF signals in areas of incomplete mixing requires accurate measurement of the level of molecular mixing (and ultimately, additional photo-physical data for the dependence of the LIF signal as a combined effect of mixing state and temperature).
This work demonstrates the application of single-color excitation, two-color detection toluene LIF, similar to Ref [9], to a transonic accelerated nozzle flow [13] to qualitatively identify zones of deficient molecular mixing in the wake of two different central injectors.
2. Theory
The LIF signal emitted by organic tracers after electronic excitation by a laser pulse depends on the incident laser intensity Ilaser, the detection efficiency η, the tracer number density ntracer, the absorption cross-section σ(λ,T), and the integrated fluorescence quantum yield ϕ(λ,T,pO2) (Eq. (1). The absorption cross-section depends on the excitation wavelength λ and the temperature T, and the quantum yield additionally depends on the O2 partial pressure pO2.
O2-induced quenching has been studied for various aromatics like toluene [10], anisole [14], and naphthalene [15]. Besides reducing ϕ by decreasing the fluorescence lifetime, O2 also causes a red-shift of the LIF emission for certain excitation wavelengths [10] similarly to the effect caused by increasing temperature [16]. This red-shift can be sensed by measuring the ratio R of the short- and long-wavelength section of the fluorescence spectrum using two detectors equipped with either a “red” or a “blue” filter (Eq. (2)). The ratio is independent of the incident laser intensity, the local tracer concentration, and the absorption cross-section.Because quenching requires molecular collisions between O2 and the tracer, R depends on the mixing state of tracer and quencher on the molecular level. Figure 1 shows normalized toluene-LIF spectra for various pO2 at room temperature [10] and the derived signal ratio R for the filter pair used in this work.
Fig. 1 (a) Toluene-LIF spectra at room temperature in N2 for a series of O2 partial pressures after excitation with 248 nm [10] and transmission curves of filters used in the present experiments. (b) Intensity ratios R (black symbols and line) and sensitivity (red line) of the two-color method.
In areas where molecular mixing has not happened, R is independent of pO2 because collisions with O2 do not occur. These areas can be identified by comparing two measurements where toluene is used either with air or with N2 as carrier gas injected into a toluene-free air flow. R, however, also depends on temperature. Therefore, Rair (measured with air as carrier gas, i.e. mixing with the air main flow does not change the local pO2) is divided by RN2 (obtained from measurements with N2 as carrier gas). The resulting quotient ξ = Rair/RN2 then only represents the O2-induced red-shift and, thus, marks the areas where molecular mixing is incomplete. When calculating the ratio, the detection system efficiency such as the angle-dependent filter transmission cancels. Also, the effect of T cancels, as long as it can be considered identical for both measurements, Rair and RN2.
To help understand the meaning of ξ, toluene-LIF spectra were measured between 264 and 295 K (cf. Fig. 4) for pO2 between 0 and 210 mbar in a stationary cell after excitation with 248-nm laser light generated from an EXPLA PL 2413 picosecond laser in combination with an EXPLA PL 401 parametric generator. A Horiba iHR320 Spectrometer was used to capture the toluene fluorescence [17]. The measured spectral data was used to calculate the quotient ξ for the filter pair used. The results are shown in Fig. 2, where unity indicates full molecular mixing and a value of 3 absence of mixing. The figure also shows the error in ξ caused by varying the temperature by 30 K within the relevant (low-temperature) range of our experiment, which is below ~7%. A more complete analysis of the low-temperature photophysics of toluene is underway. In the context of this paper, where the aim is to qualitatively locate areas with deficient molecular mixing, this detailed analysis is not required.
Fig. 2 Oxygen-dependence of ξ for the used filter pair calculated from LIF spectra obtained in a temperature-controlled static cell at atmospheric total pressure for different temperatures T within the range relevant for this paper.
3. Experiment
The experiments were performed at the supersonic test facility in Stuttgart. 517 g/s pressurized air was provided at a total temperature of 380 K to a modular transonic flow channel with a rectangular cross-section and a constant width of 40 mm (see Ref [18]. for details). The channel comprises a convergent-divergent nozzle (26.3 mm throat height) designed for an exit Mach number of 1.7. Optical access is provided laterally through fused silica windows and orthogonally through so-called laser slot windows whose inside polished surfaces follow the shape of the nozzle. Figure 3(a) shows the dimensions of the nozzle and the positions of the central injectors. The wake flows of two injectors that extend over the whole channel width as shown in Fig. 3(b) were analyzed: A ‘subsonic’ (Inj A) and a ‘supersonic’ (Inj B) injector providing injection either prior or after the nozzle throat, respectively. Both injectors deliver the tracer through four 2.5-mm diameter holes spaced by 4.8 mm. In case of injector B, the nozzle throat is narrowed by the height of the injector trailing edge and, thus, the exit Mach number increases to 2.0. A constant main mass flow is ensured by setting the total pressure at the flow channel entry to 2.5 bar for injector A and 3.0 bar for injector B. The wake forming downstream of the injectors is dominated by periodic flow structures. These have been investigated in the wake of bluff bodies [19, 20] in the past. The size, the extent, and the frequency of these structures mainly depend on the free-stream Mach number (sub- or supersonic flow, compressibility effects) [21]. The detailed wake flow physics is not the topic of this paper; however, its periodic character is important to better understand the results.
Fig. 3 (a) Cross-section of the nozzle module and (b) dimensions of the two injector types Inj A and Inj B. Both injectors extend in z-direction to the full channel width of 40 mm.
Figure 4 shows free-stream Mach numbers and resulting temperatures downstream of the injectors calculated from the nozzle shape assuming isentropic flow conditions. In the case of injector A, the main flow Mach number increases from 0.26 to 1.71 throughout the nozzle and the mean temperature drops from 375 to 240 K, which is confirmed by measurements with laser-induced thermal acoustics in the nozzle without injector under the same main flow conditions [18]. For injector B, no experimental data are available yet. The isentropic flow equations, however, indicate that the main flow Mach number and temperature at the point of injection are approximately 1.42 and 270 K. While the flow is accelerated to Ma ≈2.0 to the nozzle exit, the temperature drops to ~213 K.
Fig. 4 Adiabatic temperature distribution calculated from 1D adiabatic relations with respect to changes of the cross-section in stream-wise direction.
An evaporator system (Brooks DLI) provides the injector flow of 0.30 g/s toluene either in 0.45 g/s air or N2 corresponding to 0.14 wt.% of the main flow. The injector flow is heated to 380 K matching the main flow total temperature. Even though these conditions may lead to supersaturation assuming a worst-case scenario where the injector flow remains unmixed while being in thermal equilibrium with the main flow, unwanted condensation could be excluded. This was evidenced by monitoring the signal ratio of the red and blue channel at different positions throughout the flow channel while varying only the toluene concentration to the evaporator’s maximum. Subpixel-sized droplets should induce a signal red-shift, since excimers forming in liquid toluene are known to fluoresce at 320 nm [22]. The absence of such a signal indicates that the local concentration is low enough or that the residence time is insufficient for nucleation.
The optical setup is sketched in Fig. 5(a). A rectangular beam provided by a 248-nm KrF excimer laser (8 Hz, 20 ns pulses) is formed by a f = 500 mm cylindrical lens to a 0.3 mm thin and 24 mm wide light sheet that is directed through the laser windows in the measurement section by a mirror below the channel as shown in Figs. 5(b) and 5(c). The light sheet is positioned in the center of the channel illuminating the flow between the second and third injector hole (cf. Fig. 3). In the case of injector A, the laser light passes an additional cylindrical lens (f = −40 mm) to expand the light sheet over the complete observable area behind the central injector (Fig. 5(b)). The laser fluence is attenuated to ~70 mJ/cm2 before entering the channel to ensure linear signal response. An energy monitor records pulse-to-pulse energy fluctuations. A dichroic beam splitter (Semrock Brightline FF 310) divides the LIF signal into a blue and a red channel. The blue channel is further equipped with a bandpass filter (Semrock Brightline BP 280) while an additional long-pass filter is used on the red channel to suppress scattered laser light (cf. Fig. 1(a)). Two ICCD cameras (LaVision imager intense, IRO) capture the signal. All optical equipment is mounted on a three-axis translatable optical table.
Fig. 5 (a) Optical setup and light sheet positions within the nozzle with (b) injector A and (c) injector B.
4. Results
Two-color ratioing methods require image mapping after geometric adjustment of the cameras. Since the channel shifted during the experiments due to thermal expansion, additional spatial calibration was needed: A transparent backlit target was placed on the camera-facing observation window and the optical table was moved away from the flow channel by the distance of the target to the light sheet position. The LaVision DaVis software was used to generate a mapping function with a residual error of ~0.8 pixels. To account for the deflections caused by the window, the correlation between 200 pairs of LIF images was calculated and maximized iteratively after applying the mapping function.
To assess the degree of molecular mixing the ratio R of the red and the blue channel, representing the signal red-shift, is calculated according to Eq. (3) for each laser pulse. The signals of both channels S are corrected for pulse-to-pulse intensity variations and for background signal by subtracting averaged (200 pulse) background images ⟨BG⟩.
For comparison of the case of homogeneous O2 concentration to the O2-free case, averaged ratios ⟨Rair⟩ and ⟨RN2⟩ are calculated from 1000 single ratios each. The results are plotted in Figs. 6(a)-6(d). In all cases, only regions where both channels provided sufficient signal (i.e. > 20 counts/pixel) are considered. Figures 6(e) and 6(f) show the standard deviation of R related to its average value to indicate the temporal fluctuation, where the upper half of each figure refers to Rair and the lower half to RN2. A measure for concentration fluctuations is provided by the relative standard deviation of the signal intensity. This is shown in Figs. 6(g) and 6(h) for the red channel (less sensitive to signal red-shift as the blue channel) for injection with homogeneous O2 concentration. The area of strong fluctuations in the wake of injector A results from the periodic character typical for subsonic wakes that involve large coherent flow structures. In the case of injector B, the length and time scales of those structures are smaller and, thus, the fluctuations are less.Fig. 6 Signal red-shift in the wake of injectors A and B after using alternatingly (a)-(b) air (homogeneous O2 concentration) and (c)-(d) N2 as carrier gas of the tracer flow, respectively. The surrounding flow is air in both cases, the grey boxes indicate the injector trailing edge position. (e)-(f) show the standard deviation of R and (g)-(h) show the standard deviation of S, each divided by the respective average value. Regions without sufficient signal (less than 20 counts/pixel in either LIF signal channel) were masked in all images S prior to the ratioing operations.
The quotient ⟨ξ⟩ of both averaged ratios as defined in Eq. (4) is shown in Fig. 7. This represents a measure of the degree of incomplete molecular mixing indicated by values above 1.
Fig. 7 Averaged quotient ξ as a measure for the O2-induced red-shift and, thus, incomplete molecular mixing for (a) injector A and (b) injector B.
To determine the extent of this zone in stream-wise direction, as relevant for technical processes requiring molecular mixed reactants at a certain point after injection [1], centerline (y = 0 mm) profiles of R and ξ are extracted as shown in Fig. 8. For both injectors, the red-shift near the trailing edge is considerably stronger if O2 is present in the injected flow (blue lines) compared to the case with N2 (red lines) as carrier gas. This zone extends to about 7 mm past the trailing edge of injector A and 16 mm past injector B. Further downstream of that zone, the signal ratio is nearly independent of the injector flow composition while still decreasing. This reduction can be attributed to the blue-shift of the LIF signal due to gas-dynamic cooling (cf. Fig. 4).
Fig. 8 Profiles (extracted from Figs. 6(a)-6(d) and Fig. 7) of the O2-induced fluorescence red-shift represented by the quotient ξ (bottom) calculated from the averaged signal ratios R of both channels (top) for (a) injector A and (b) injector B along the centerline (y = 0 mm). The grey bands represent the standard deviation of ten 100-shot averages.
In the wake of both injector types, ξ increases before it drops again further downstream. This can be traced back to the light sheet position that is aligned in between the two center injection holes (cf. Figs. 3(b), 5(b), and 5(c) for details). In the very vicinity of the trailing edge the leftmost portion of the image only represents the recirculated mixture, while 3D-flow effects further downstream entrain unmixed injector flow into the image plane. In addition, in the case of injector B, two droplets (approx. 2 mm in diameter) form on each side-window inner surface about 2 mm behind the injector trailing edge. Both are visible in Figs. 6(b), 6(d), and 7(b) and cause a sudden drop followed by an increase of the signal around x = 12 mm in Fig. 8(b). The droplets can be observed at various conditions by naked eye even without tracer flow. Thus, we suspect residual water in the main flow to condensate due to rapidly changing conditions in the recirculation zone at the trailing edge of injector B.
5. Conclusions and Outlook
A single-color excitation and dual-band detection tracer LIF technique has successfully been applied to monitor the mixing deficit on molecular level in a transonic nozzle flow. The wakes of two central injectors feeding a low-momentum jet into an accelerating air flow were analyzed showing that the extend of the zone with apparent incomplete mixing depends on the point of injection: In the case of the injection into a supersonic (Ma = 1.42) main flow, it extends with approximately 16 mm more than twice the distance in stream-wise direction compared to the injection in a subsonic flow (Ma = 0.26) with 7 mm. The results presented here are of qualitative nature. For quantification, detailed photo-physical data for the complete range of conditions in the flow channel are required, which are subject to ongoing work in our lab. Further, complementary measurement techniques are required to measure and to correct for temperature and pressure effects accordingly.
Funding
The authors gratefully acknowledge funding by the German Research Foundation DFG (SCHU 1369/21-1 and WE 2549/31-1).
Acknowledgments
The authors thank Thomas Baranowski for his assistance in measuring additional fluorescence spectra during the review process.
References and links
1. A. Grzona, A. Weiß, H. Olivier, T. Gawehn, A. Gülhan, N. Al-Hasan, G. H. Schnerr, A. Abdali, M. Luong, H. Wiggers, C. Schulz, J. Chun, B. Weigand, T. Winnemöller, W. Schröder, T. Rakel, K. Schaber, V. Goertz, H. Nirschl, A. Maisels, W. Leibold, and M. Dannehl, “Gas-phase synthesis of non-agglomerated nanoparticles by fast gasdynamic heating and cooling,” (Springer Berlin Heidelberg, 2009), pp. 857–862.
2. A. Wohler, K. Mohri, C. Schulz, and B. Weigand, “Flow structures in subsonic-to-supersonic mixing processes using different injector geometries,” in 4th European Conference for Aerospace Sciences (EUCASS, 2011).
3. P. E. Dimotakis, “Turbulent Mixing,” Annu. Rev. Fluid Mech. 37(1), 329–356 (2005). [CrossRef]
4. C. Schulz and V. Sick, “Tracer-LIF diagnostics: Quantitative measurement of fuel concentration, temperature and air/fuel ratio in practical combustion systems,” Pror. Energy Combust. Sci. 31(1), 75–121 (2005). [CrossRef]
5. N. T. Clemens and P. H. Paul, “Scalar measurements in compressible axisymmetric mixing layers,” Phys. Fluids 7(5), 1071–1081 (1995). [CrossRef]
6. G. F. King, J. C. Dutton, and R. P. Lucht, “Instantaneous, quantitative measurements of molecular mixing in the axisymmetric jet near field,” Phys. Fluids 11(2), 403–416 (1999). [CrossRef]
7. W. Koban, J. Schorr, and C. Schulz, “Oxygen-distribution imaging with a novel two-tracer laser-induced fluorescence technique,” Appl. Phys. B-Lasers O 74(1), 111–114 (2002). [CrossRef]
8. W. Koban and C. Schulz, “Toluene laser-induced fluorescence (LIF) under engine-telated pressures, temperatures and oxygen mole fractions,” SAE Technical Paper (2005).
9. K. Mohri, M. Luong, G. Vanhove, T. Dreier, and C. Schulz, “Imaging of the oxygen distribution in an isothermal turbulent free jet using two-color toluene LIF imaging,” Appl. Phys. B-Lasers O 103(3), 707–715 (2011). [CrossRef]
10. W. Koban, J. D. Koch, R. K. Hanson, and C. Schulz, “Oxygen quenching of toluene fluorescence at elevated temperatures,” Appl. Phys. B-Lasers O 80(6), 777–784 (2005). [CrossRef]
11. W. Koban, J. D. Koch, R. K. Hanson, and C. Schulz, “Toluene LIF at elevated temperatures: implications for fuel-air ratio measurements,” Appl. Phys. B-Lasers O 80(2), 147–150 (2005). [CrossRef]
12. M. Gamba, V. A. Miller, M. G. Mungal, and R. K. Hanson, “Temperature and number density measurement in non-uniform supersonic flowfields undergoing mixing using toluene PLIF thermometry,” Appl. Phys. B-Lasers O 120(2), 285–304 (2015). [CrossRef]
13. A. Wohler, B. Weigand, K. Mohri, and C. Schulz, “Mixing processes in a compressible accelerated nozzle flow with blunt-body wakes,” AIAA J. 52(3), 559–568 (2014). [CrossRef]
14. S. Faust, T. Dreier, and C. Schulz, “Photo-physical properties of anisole: temperature, pressure, and bath gas composition dependence of fluorescence spectra and lifetimes,” Appl. Phys. B 112(2), 203–213 (2013). [CrossRef]
15. S. Faust, G. Tea, T. Dreier, and C. Schulz, “Temperature, pressure, and bath gas composition dependence of fluorescence spectra and fluorescence lifetimes of toluene and naphthalene,” Appl. Phys. B-Lasers O 110(1), 81–93 (2013). [CrossRef]
16. M. Luong, W. Koban, and C. Schulz, “Novel strategies for imaging temperature distribution using Toluene LIF,” J. Phys. Conf. Ser. 45, 133–139 (2006). [CrossRef]
17. T. Benzler, S. Faust, T. Dreier, and C. Schulz, “Low-pressure effective fluorescence lifetimes and photophysical rate constants of one- and two-ring aromatics,” Appl. Phys. B 121(4), 549–558 (2015). [CrossRef]
18. J. Richter, J. Mayer, and B. Weigand, “Accuracy of non-resonant laser-induced thermal acoustics (LITA) in a convergent-divergent nozzle flow,” Appl. Phys. B-Lasers O, in press (2018).
19. I. Wygnanski, F. Champagne, and B. Marasli, “On the Large-Scale Structures in Two-Dimensional, Small-Deficit, Turbulent Wakes,” J. Fluid Mech. 168(-1), 31–71 (1986). [CrossRef]
20. M. Matsumoto, “Vortex shedding of bluff bodies: A review,” J. Fluids Structures 13(7-8), 791–811 (1999). [CrossRef]
21. F. Motallebi and J. F. Norbury, “The effect of base bleed on vortex shedding and base pressure in compressible flow,” J. Fluid Mech. 110(-1), 273–292 (2006). [CrossRef]
22. J. B. Birks, C. L. Braga, and M. D. Lumb, “‘Excimer’ Fluorescence. VI. Benzene, Toluene, p-Xylene and Mesitylene,” Proc. Royal Soc. London Series A 283(1392), 83–99 (1965). [CrossRef]
