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Quantitative mixture fraction imaging of a synthetic biogas turbulent jet propagating into a NO-vitiated air co-flow using planar laser-induced fluorescence (PLIF)

  • Ayane JohchiEmail author
  • Jhon Pareja
  • Benjamin Böhm
  • Andreas Dreizler
Research Article

Abstract

 A new approach for quantitative mixture fraction imaging in the turbulent mixing of a fuel jet and a high temperature oxidizer co-flow was developed by means of planar laser-induced fluorescence of nitric oxide (NO-PLIF). Unlike existing strategies, the new approach is based on seeding NO in the oxidizer stream. The method was first evaluated during the laminar mixing of methane in air and \(\hbox {CH}_4/\hbox {CO}_2\) blends (synthetic biogas) in air, at room temperature. Mixture fraction measurements were validated against Rayleigh scattering imaging. Then, the measurements were extended to the turbulent mixing of a cold fuel jet issuing into a NO-seeded, hot air co-flow. By seeding the NO in the air stream, high signal-to-noise ratios were achieved at locations around the stoichiometric mixture fraction. Additionally, a stable in situ calibration region is available at every measurement location, which contributes to reduce the uncertainty. Results showed that the approach is not suitable for CH\(_4\)/air mixtures due to the lack of sensitivity of the fluorescence signal to the mixture fraction. For biogas/air mixtures, the addition of CO\(_2\) increased the response of the fluorescence signal to the mixture fraction, making the measurements feasible. The stoichiometric mixture fraction can be fully resolved for each biogas blend. Two-dimensional instantaneous mixture fraction measurements were feasible with an acceptable uncertainty. The high spatial resolution of the measurement was of the same order of the smallest scale in the concentration field (i.e., Batchelor scale).

Graphical abstract

1 Introduction

Laser imaging diagnostics have widely contributed to understanding complex flame–flow interactions in combustion science through non-intrusive in situ measurements of velocity and scalar fields and other important parameters (Schulz et al. 2007). An extremely useful variable for the study of turbulent mixing and non-premixed combustion is the mixture fraction which, for a two-stream mixing process, is a measure of the mass fraction of one of the streams in the mixture (Peters 2000). The gradient of the mixture fraction allows, for instance, quantifying the rate of molecular mixing in turbulent flows by means of the scalar dissipation rate (Sutton and Driscoll 2006). Because derivatives of the scalar are computed to evaluate the scalar dissipation rate, measurements with high spatial resolution and high signal-to-noise ratio (SNR) are required.

Several laser-based planar measurements of the mixture fraction and the scalar dissipation rate have been performed in turbulent non-reacting and reacting flows. Rayleigh scattering and planar laser-induced fluorescence (PLIF) of a tracer (e.g., acetone) have been used to study the mixing of turbulent free jets at room temperature (Su and Clemens 2003; Patton et al. 2012) and the non-reacting mixing of the fuel and oxidizer in regions upstream of lifted jet flames (Su et al. 2000; Mansour 2003).

In non-premixed flows with heat release (e.g., diffusion flames), scalar measurements are very challenging due to the temperature increase and the production/consumption of intermediate species. In this case, the thermo-chemical state can be determined by multiscalar measurement techniques. Previous approaches include two-dimensional (2D) measurements of mixture fraction, temperature and scalar dissipation rate in partially premixed and non-premixed jet flames using Rayleigh imaging combined with OH-PLIF/CO-PLIF (Frank et al. 2005), krypton PLIF (Hsu et al. 2011), Raman scattering (Kelman et al. 1994; Fielding et al. 1998), and nitric oxide PLIF (NO-PLIF) (Sutton and Driscoll 2006). Multiscalar measurements in flames, based only on Rayleigh scattering, can be performed using a special fuel mixture that yields a constant Rayleigh cross-section of the mixture throughout the reaction zone (Frank and Kaiser 2010).

Turbulent mixing studies of non-premixed flows at high temperature are likewise of relevance. The mixing of a hot jet in a cold atmosphere is interesting for technical applications such as explosion safety, pulsed detonation engines and supersonic combustors (Sadanandan et al. 2011). On the other hand, the mixing of a cold jet propagating into a hot co-flow is of importance in Moderate or Intense Low oxygen Dilution (MILD) combustion and auto-ignition studies (Arndt et al. 2016; Macfarlane et al. 2017). At high temperatures (above 1000 K), the decrease of the Rayleigh scattering signal and the thermal stability of the tracer for PLIF-based methods impose some challenges for scalar measurements. Moreover, the temperature field is necessary to quantify the mixture fraction.

In the literature, measurements of mixture fraction fields, during the pulsed injection of fuel jets auto-igniting in high temperature co-flows, have been reported using Rayleigh imaging (Papageorge et al. 2014; Arndt et al. 2018). A high power laser (>1 J/pulse at 532 nm) was employed to increase the SNR, while non-reacting adiabatic mixing was assumed to quantify the correlation between mixture fraction and temperature during mixing of the two streams. Regarding PLIF methods, mixture fraction measurements in a jet-in-cross-flow configuration at high temperature and pressure were demonstrated using NO-PLIF (Sadanandan et al. 2012). NO was seeded in the jet and numerical calculations and spectroscopic simulations were performed to correlate the NO-PLIF signal and the mixture fraction. NO as a LIF tracer is very attractive for high temperature PLIF measurements because its high thermal stability, well-characterized spectroscopy (Paul 1997) and strong absorption (i.e., high SNR) at wavelengths accessible by available dye lasers (Bessler et al. 2002; Sadanandan et al. 2012).

For studies of the turbulent mixing of reacting flows at high temperature, preceding ignition or auto-ignition events, it is relevant to have reliable measurements of the mixture fraction particularly at low ranges (i.e., regions near the oxidizer stream) (Mastorakos 2009). In this sense, the present study proposes a new methodology for 2D mixture fraction measurements using NO-PLIF in which, unlike previous approaches, the NO tracer is seeded in the oxidizer stream. In this way, high SNRs are achieved at locations of low mixture fraction due to the high concentration of NO. Additionally, a stable calibration region (i.e., signal reference) is available in the same image at every measurement location, which contributes to reduce the uncertainty of the quantitative determination of the mixture fraction. One of the difficulties of the quantitative LIF technique is the non-linear relationship between the fluorescence signal and the mixture fraction, caused by the non-linear dependence of state-dependent quantities (e.g., absorption coefficient and fluorescence quantum yield) on temperature, pressure and species concentration (Schulz and Sick 2005). In this study, the state-dependent quantities were calculated using the spectroscopic simulation program LIFSim (Bessler et al. 2003).

In the first part of the manuscript the approach is described in detail, including an experimental verification of the spectroscopic simulations. Then, an evaluation of the approach using the isothermal laminar mixing of a round jet and an air co-flow is presented. Mixture fraction profiles in the laminar mixing layer were measured using NO-PLIF for the mixing of methane (CH\(_4\)) with air and blends of CH\(_4\)/CO\(_2\) (synthetic biogas) with air. Biogas is an important renewable fuel (Bedoya et al. 2011; Hosseini and Wahid 2013) and the CO\(_2\) addition increases the sensitivity of the fluorescence signal to the mixture fraction. The mixture fraction measurements during laminar mixing are validated against results using Rayleigh scattering. The accuracy, advantages and limitations of the approach are discussed. Finally, the approach is tested during the turbulent mixing of a biogas jet issuing into a high-turbulence, hot air co-flow seeded with NO.

2 Methodology

The present experimental approach for the measurement of the mixture fraction field, during the mixing of fuel and oxidizer streams, is based on NO-PLIF. In this case, the tracer (NO) is seeded in the oxidizer stream and the mixture fraction, \(\xi \), is defined by the mass fraction of NO (\(Y_\text {NO}\)) as follows:
$$\begin{aligned} \xi =\frac{Y_\text {NO}-Y_\text {NO,ox}}{Y_\text {NO,fuel}-Y_\text {NO,ox}}, \end{aligned}$$
(1)
where \(Y_\text {NO,ox}\) and \(Y_\text {NO,fuel}\) are the NO mass fractions in the oxidizer and fuel streams, respectively. Because \(Y_\text {NO,fuel} = 0\), \(\xi =1\) at locations of pure fuel, and \(\xi =0\) at those of pure oxidizer. Equation (1) is based on the assumption that NO is neither consumed, nor generated during the mixing process, therefore it is only valid prior to the onset of reactions which include NO chemistry.

2.1 Test experiments

The NO-LIF-based measurement approach was first evaluated during the isothermal (300 K) mixing of a laminar round jet issuing into a low-speed air co-flow seeded with 7900 ppm of NO. This concentration resulted from the mixing of 79 vol% N\(_2\) (with a content of 1 vol% NO) with 21 vol% O\(_2\) to obtain a vitiated air with a NO content similar to that one of the co-flow for the high temperature mixing (as detailed below).

The jet was generated using a tube with an inner diameter, \(d_\text {lam}\) = 8 mm, and a length of 300 mm to achieve fully developed pipe flow at the exit. The concentric co-flow nozzle had an inner diameter \(D_\text {lam}\) = 52 mm. The nozzles of the jet and the co-flow were tapered to a sharp edge at the exit to minimize recirculation. For the jet, pure methane (CH\(_4\)) and blends of CH\(_4\)/CO\(_2\) (synthetic tbiogas) with 10, 20, 30, 40 and 50 vol% CO\(_2\) were used. For simplicity, the jets will be referred in this manuscript as F00, F10, F20, F30, F40 and F50, based on the respective CO\(_2\) content. The flow rates of the jets, air and NO were adjusted by mass flow controllers (Bronkhorst). For each blend, the bulk exit velocity of the jet was 4m/s, resulting in a Reynolds number (Re) of \(\sim \) 2000. The bulk exit velocity of the co-flow was 0.3 m/s (\(Re\approx \) 800) for all conditions.

Additionally, the approach was tested for the measurement of the mixture fraction during the turbulent mixing of a fuel jet issuing into a high-turbulence, hot air co-flow. This mixing process leads to auto-ignition and a lifted flame is stabilized. The experiments were performed using a microwave plasma heater (MWPH) test rig, described in detail elsewhere (Eitel et al. 2015). Figure 1 shows a schematic cross section of the burner head of the MWPH test rig. For the current configuration, the fuel lance had an inner diameter (\(d_\text {jet}\)) of 6 mm and a length of 550 mm. The blend F20 was used as fuel. At the exit, the fuel temperature (\(T_\text {fuel}\)) was 560 K and the bulk velocity was 115 m/s (\(Re\approx \) 15,000). The air co-flow was accelerated using a contoured nozzle with an inner diameter at the exit (\(D_\text {coflow}\)) of 82 mm. The turbulence level of the co-flow was controlled using two turbulence grids with a hole diameter of 8 mm and a blockage ratio of 35 %. The co-flow was heated using the plasma heater up to \(T_\text {ox}\) = 1323 K (measured at the second turbulence grid). The bulk velocity of the co-flow at the exit was 25 m/s (\(Re\approx \) 10,000). \(T_\text {ox}\) and \(T_\text {fuel}\) where measured using type N thermocouples (class 1) with a diameter of 0.6 mm.

NO was produced as a side effect of the plasma heating of air, which results in a self-seeding of the air co-flow. At the steady-state operation of the MWPH (± 2 K), the NO concentration in the co-flow was 11,000 ppm for the current operating condition. The NO seeding concentration in the present experiments is significantly larger than the one used in previous studies using NO-PLIF (Sutton and Driscoll 2006; Sadanandan et al. 2012). The NO concentration can be reduced, while keeping the co-flow temperature, by reducing the oxygen concentration in the oxidizer that flows through the plasma. To keep the oxidizer composition same as air, oxygen can be added into the flow in the mixing section of the test rig.

The oxidation of NO is a relatively slow process (Skalska et al. 2010). The conversion of NO into NO\(_2\) at the co-flow temperatures was evaluated via homogeneous reactor simulations. For the short residence times of the present experiment (i.e., from the exit of the burner head up to the measurement location) this conversion is negligible and the NO in the co-flow can be considered as inert tracer until auto-ignition reactions begin. Measurements of the mixture fraction were performed upstream of the base of the lifted flame (\(x/d_\text {jet} \approx \) 15).
Fig. 1

Burner head of the MWPH test rig

2.2 Laser diagnostics system

For the NO-PLIF measurements, transitions of the A-X(0,0) band of the NO molecule around 225 and 226 nm were evaluated for the excitation scheme. The transitions were excited using the UV output of a dye laser (Precision Scan, Sirah Lasertechnik), operated with Pyridine 1, and pumped with a 10 Hz frequency-doubled Nd:YAG laser (GCR-4, Quanta Ray, 600 mJ/pulse at 532 nm). For the laminar mixing experiment, the P\(_{2}\) + Q\(_{12}\) (20.5) transitions around 226.46 nm were excited. With this excitation wavelength, at room temperature, the resulting fluorescence signal is sufficiently high while the laser attenuation is less compared to other transitions. The laser beam was expanded with a cylindrical telescope to a laser sheet of 25 mm height and \(\sim \) 0.2 mm thickness at the measurement volume. The pulse energy was adjusted to 0.6 mJ/pulse at the measurement volume to avoid fluorescence saturation. A laser irradiance of \(4 \times 10^6\) W/cm\(^2\)/cm\(^{-1}\) was calculated for a pulse duration of 10 ns and a line width of 0.3 cm−1. This value is below the spectral irradiance limit of \(5 \times 10^6\) W/cm\(^2\)/cm\(^{-1}\) required for linear fluorescence (Namazian et al. 1994). The output wavelength of the dye laser was stabilized (± 0.3 pm) in a closed-loop control using a wavelength meter (WS6-600, High Finesse). The emitted fluorescence signal from the A-X (0,1)–(0,4) bands was collected by a 150 mm UV lens (f/2.5, B. Halle Nachfl.) equipped with a UV filter (UG5, Schott) and imaged onto a CCD camera (Imager E-lite, LaVision) coupled with Intensified Relay Optics (IRO, LaVision). The IRO was gated to 400 ns.

Mixture fraction measurements using planar Rayleigh scattering were separately performed for all conditions of the laminar mixing experiment to validate the developed quantitative NO-PLIF approach. In this case, a frequency-doubled, Q-switched Nd:YAG laser (SpitLight 1000, Innolas), operating at a repetition rate of 5 Hz and with output energies of 460 mJ/pulse was used. The 532 nm, vertically polarized output of the laser was expanded into a laser sheet of 17 mm height and \(\sim \) 0.2 mm thickness at the measurement volume. The Rayleigh scattering signal was collected and imaged onto a CCD camera (Imager Intense, LaVision) using a 85 mm lens (f/1.2, Canon), coupled with a 250 mm achromat (Leica) and a band pass filter (BP525/72, MidOpt). The exposure time of the camera was set to 3 \(\upmu \)s.

For the NO-PLIF measurements at high temperature, the same laser and camera setup of the laminar experiments was adapted to the test rig, as schematically represented in Fig. 2. In this case, the Q\(_{2}\) + R\(_{12}\) (26.5) transitions at 225.58 nm were excited. With this excitation wavelength, at high temperature (> 1000 K), the resulting fluorescence signal is sufficiently high, the laser attenuation is moderate, and the fluorescence signal has a monotonic response to temperature and mixture fraction (see Sect. 2.3.2). Measurements of the mixture fraction field were performed at locations upstream of the lifted auto-igniting flame base. OH\(^*\) chemiluminescence (OH\(^*\)CL) was simultaneously collected to detect the axial position of auto-ignition spots with respect to the measurement plane of the NO-PLIF. The OH\(^*\)CL signal was collected at 10 Hz using a CCD camera (Imager E-lite, LaVision), coupled with an image intensifier (IRO, LaVision), a 100 mm UV lens (CERCO, f/8) and a band pass filter (BP300-325, Laser Components). The IRO gate was set to 10 \(\upmu \)s. With the long exposure time and line-of-sight nature of the CL measurement, it is not appropriate to determine non-reacting regions in the NO-PLIF measurement plane from the OH\(^*\)CL images. They were used only to identify AI kernels or the lifted flame base that already react with significant heat release, which are not the regions-of-interest of this study.
Fig. 2

Experimental setup for NO-PLIF at the MWPH test rig

2.3 Conversion of the fluorescence signal intensity to mixture fraction

In a linear fluorescence process (low laser irradiance) at atmospheric pressure, the NO fluorescence signal intensity from a gas mixture, \(S_\text {N}\), integrated over the laser pulse length, can be written as:
$$\begin{aligned} S_\text {N}=C_\text {opt} N_\text {NO} I_\nu ^0 \sum \limits _i f_\text {B}\varGamma B_{12} \sum \limits _j \frac{A_{j}}{A_{j}+ Q}, \end{aligned}$$
(2)
where \(C_\text {opt}\) is a constant accounting for the signal collection efficiency of the setup, \(N_\text {NO}\) is the number density of NO, \(I_\nu ^0\) is the normalized laser spectral irradiance, \(f_\text {B}\) is the Boltzmann fraction of molecules in the laser coupled ground state, \(\varGamma \) is the spectral overlap fraction which characterizes the interaction between the laser and the absorption line shapes, and \(B_{12}\) is the Einstein coefficient for stimulated absorption. The summation i is taken over all possible transitions excited by the laser. \(A_j\) is the Einstein coefficient for spontaneous emission and Q is the electronic quenching rate. The summation j is over all allowed emission transitions.
From the ideal gas law, the number density of NO can be calculated as:
$$\begin{aligned} N_\text {NO} = \frac{Y_\text {NO} W_\text {mix}}{W_\text {NO}} \frac{P}{ k T}, \end{aligned}$$
(3)
where \(W_\text {NO}\) is the molecular weight of NO, \(W_\text {mix}\) is the molecular weight of the mixture, P is the pressure, k is the Boltzmann constant, and T the temperature. By substituting Eqs. (2) and (3) in Eq. (1), for the fluorescence signal intensity of any fuel/oxidizer mixture (\(S_\text {N}\)) and the fluorescence signal intensity of the oxidizer (\(S_\text {N,ox}\)), the local mixture fraction can be determined as:
$$\begin{aligned} \xi = 1 - \displaystyle \frac{S_\text {N}}{S_\text {N,ox}} \displaystyle \frac{W_\text {ox}}{W_\text {mix}} \displaystyle \frac{T}{T_\text {ox}} \displaystyle \frac{I_{\nu , \text {ox}}^0}{I_\nu ^0} \displaystyle \frac{\bigg [\sum \nolimits _i f_B\varGamma B_{12} \sum \limits _j \frac{A_{j}}{A_{j}+ Q}\bigg ]_\text {ox}}{\bigg [\sum \limits _i f_B\varGamma B_{12} \sum \nolimits _j \frac{A_{j}}{A_{j}+ Q}\bigg ]} \end{aligned}$$
(4)
Quantities with subscript “ox” correspond to the oxidizer stream which are, in the present approach, known reference values (i.e., temperature, composition, NO concentration). \(S_\text {N}\) and \(S_\text {N,ox}\) are the signals measured by the NO-PLIF camera. For the isothermal mixing case, \(T = T_\text {ox}\). For the mixing at high temperature, the temperature of the mixture, T, was calculated for a two-stream mixing problem (i.e., non-reacting fuel and oxidizer mixing) at each \(\xi \) using an enthalpy balance during the mixing of the fuel at \(T_\text {fuel}\) and oxidizer at \(T_\text {ox}\). However, the local temperature can be measured simultaneously by any other technique such as Rayleigh imaging (Papageorge et al. 2014; Arndt et al. 2016). The state-dependent quantities (values between square brackets) were calculated from spectroscopic simulations using the program LIFSim (Bessler et al. 2003). As described in detail in Sect. 2.3.2, the local \(I_\nu ^0\) was calculated, considering the laser attenuation in the co-flow, by the Beer–Lambert law.
For validation of the isothermal mixing measurements using the Rayleigh scattering method, the mixture fraction, \(\xi _\text {Ray}\), can be determined for the mixing of two non-reacting streams (fuel and oxidizer) as:
$$\begin{aligned} \xi _\text {Ray} = \frac{W_\text {fuel}}{W_\text {mix}} \left[ \frac{S_\text {R}}{S_\text {R,air}}-1\right] \left[ \frac{\sigma _\text {fuel}}{\sigma _\text {ox}}-1\right] ^{-1}, \end{aligned}$$
(5)
where \(W_\text {fuel}\) is the molecular weight of the fuel, \(S_R\) is the Rayleigh scattering signal at measurement location, \(S_\text {R,air}\) is the Rayleigh scattering signal of air at 300 K (i.e., reference condition), and \(\sigma _\text {fuel}\) and \(\sigma _\text {ox}\) are the Rayleigh scattering cross-sections of the fuel and oxidizer, respectively. Calibrations for the Rayleigh cross section of each gas were done using the Rayleigh scattering signal from pure flows.

2.3.1 Spectroscopic experiments and simulations

The program LIFSim (Bessler et al. 2003) provides excitation, emission and absorption spectra using a non-transient, three-level LIF model with temperature, pressure, species concentrations and laser characteristics as input parameters. State-dependent phenomena such as collisional line broadening, shifting and fluorescence quenching are taken into account. LIFSim uses a ”harpoon model” to calculate the cross-sections for collisional electronic quenching of NO by other molecules and its temperature dependence (Paul et al. 1993, 1995). However, some disagreement of the quenching of some molecules has been previously reported (Tamura et al. 1998). In this study, empirical fits of recent measurement data were used for calculating the quenching cross-section of CO\(_2\), NO and O\(_2\), (Settersten et al. 2006). Because the dry air used for the co-flow had a residual water content of 500 ppm (dew point < 0 \(^\circ \)C at 12 bar), water vapor (H\(_2\)O) was not considered for calculating the quenching rate of the fluorescence signal. Nevertheless, H\(_2\)O has a high quenching cross-section (\(\sim \) 120 \(\AA ^2\) at 294 K and  45 \(\AA ^2\) at 1249 K (Settersten et al. 2006)), and it should be taking into account when the flows have a high content of water vapor.

For verification purposes, preliminary zero-dimensional (0D) measurements of the NO-LIF signal for different excitation lines and temperatures were conducted and compared with predicted LIF signals from spectroscopic simulations. NO-LIF signals were measured in flowing air at room temperature, seeded with 7900 ppm of NO. The output wavelength of the dye laser was scanned, with a resolution of 1.5 pm through absorption lines of the NO molecule around 226 nm. 20 images were measured at each excitation wavelength. The experimental excitation spectrum was obtained by calculating the mean signal intensity of the 20 images within the first 2 mm region in the direction of the laser propagation to neglect the effect of laser attenuation (i.e., no special image processing is required). Figure 3 compares the simulated (solid line) and the measured (cross markers) NO-LIF excitation spectra between 226.35 and 226.65 nm. Both spectra were normalized by the peak values within the compared wavelength range. A detailed view of the line at 226.46 nm, used for the laminar mixing experiments, is shown in the box. The vertical error bars represent the 95% confidence interval of the measured signal intensity and the horizontal ones show the absolute accuracy of the wavelength meter. Similarly, the excitation spectrum at high temperature (1323 K) was measured around 225.58 nm and compared with the simulations in Fig. 4. The measurements were performed using the MWPH test rig with air with 11,000 ppm of NO. Measurements and simulations of NO-LIF showed good agreement at room and high temperature, particularly at the excitation lines used for the mixture fraction measurements. The slight difference between the spectra could be caused by the signal level at off-resonance excitation wavelengths. Background signal in the measurement spectrum could also appear as a line broadening.
Fig. 3

Measurement and simulation of NO-LIF excitation spectrum at room temperature. A detailed view of the line at 226.46 nm is shown in the box

Fig. 4

Measurement and simulation of NO-LIF excitation spectrum around 225.58 nm at 1323 K

The temperature dependence of the NO-LIF signal was additionally evaluated in the range between 300 and 1473 K. For the experiments, a laminar air flow was heated using an electrical in-line heater (Sandvik). The temperature was measured with a type-K thermocouple, and corrected by radiation losses (Dunn et al. 2007). For the NO-LIF measurements and simulations, the Q\(_{2}\) + R\(_{12}\) (11.5) transitions at 226.54 nm and the Q\(_{1}\) + P\(_{21}\) (18.5) transitions at 225.86 nm were used because of their different state-dependent characteristics. 100 images were recorded at every temperature and used to calculate mean signal intensity. Figure 5 compares the temperature dependence of simulated (solid lines) and measured (markers) NO-LIF signal intensity of the two excitation lines. All intensities are normalized with the maximum signal intensity in the temperature range. Error bars represent the 95% confidence interval of the measured signal intensity. The simulated temperature dependence of both excitation lines matched well to the corresponding measurements.
Fig. 5

Experimental and simulated temperature dependence of the LIF signal for excitation wavelengths at 226.54 and 225.86 nm

2.3.2 Data processing

Before post-processing, a mean background was subtracted from each NO-PLIF raw image. Then, a 5 \(\times \) 5 binning was applied, resulting in a pixel size of 100 \(\times \) 100 \(\upmu \)m\(^2\). The spatial resolution of the collection system (i.e., camera, intensifier, UV lens and filter) was evaluated by measuring the step response function (SRF) using the scanning knife-edge method (Wang and Clemens 2004). With the SRF, the line spread function (LSF) was calculated and the resulting full-width-half-maximum (FWHM) of the LSF was 150 \(\upmu \)m. Because of the high dynamic range of the fluorescence signal, the SNR varied from 46 at co-flow locations to 33 at locations around the stoichiometric mixture fraction (\(\xi _\text {st}\)) and 22 at locations around \(\xi =0.75\).

An example raw image after binning and background subtraction, measured during isothermal mixing, is shown in the bottom part of Fig. 6a. For visualization, the velocity of the jet was increased to generate a turbulent mixing field. A camera fixed coordinate (x,y) was defined with the x-axis aligned with the main direction of the flow and the y-axis aligned with the propagation direction of the incident laser. In the co-flow region, marked by the white dashed box in Fig. 6a, the gas composition is constant (\(\xi (x,y)\) = 0) and is used for calibration (i.e., to calculate \(S_\text {N,ox}\) in Eq. (4)) of each single shot. In this region, the inhomogeneity of the signal intensity along the x-axis corresponds to the laser-sheet intensity profile. The laser sheet was collimated and the decrease of the signal intensity in the y-direction is caused by molecular absorption of the laser energy (laser attenuation).
Fig. 6

a Example raw image (bottom) along with mean profiles of the signal intensity (top, black dash-dotted line) and local laser intensity (top, red solid line). The black and white dashed lines in the bottom image indicate the mixing and co-flow regions, respectively. b Resulting mixture fraction field after image processing

As illustrated in the top part of Fig. 6a, the local normalized laser irradiance, \(I_\nu ^0(x,y)\), was determined in the mixing region (marked by the black dashed box) using the Beer–Lambert law:
$$\begin{aligned} I_\nu ^0 (x,y) =I_\nu ^0 (x,y_0) \text {exp}\left( -\int \limits _{y_0}^y\kappa _\nu \text {d}y\right) , \end{aligned}$$
(6)
where the incident \( I_\nu ^0(x,y_0)\) was defined at each x-location as the signal intensity at \((x,y_0)\). The spectral absorption coefficient, \(\kappa _\nu \), was determined by exponential fitting of the signal intensity profile, depending on the local temperature and gas composition.
Focusing again on Eq. (4), \(W_\text {mix}\) is a function of composition, \(f_B\) is a function of temperature while \( I_\nu ^0\), \(\varGamma \) and Q depend on both temperature and gas composition. Therefore, an iterative algorithm to determine \(\xi (x,y)\), satisfying Eqs. (4) and (6), was implemented. First, the signal in the mixing region, \(S_\text {N}(x,y)\), was normalized by the reference signal intensity, \( S_\text {N,ox}\). Assuming no-laser absorption (i.e., \( I_\nu ^0(x,y) = I_\nu ^0(x,y_0)\)), an initial mixture fraction field, \(\xi (x,y)\), was calculated from Eq. (4) using a preliminary simulated signal \(S_\text {N}(\xi ,T\)) like the one shown in Fig. 7. In this way, the dependence of the absorption spectrum and quenching on the temperature and gas composition are accounted for. When using the adiabatic mixing assumption (i.e., known \(\xi (T)\)), \(S_\text {N}(\xi ,T\)) is represented by the solid black line on the signal map of Fig. 7.
Fig. 7

Simulated LIF signal intensity map as a function of temperature and mixture fraction for excitation at 225.58 nm. The solid line represents the relationship between T and \(\xi \) under adiabatic mixing assumption

Subsequently, the absorption coefficient field, \(\kappa _\nu (x,y)\), was calculated from the initial \(\xi (x,y)\). Because \(\kappa _\nu (x,y)\) is integrated in the direction of laser propagation, it is highly sensitive to shot noise. To minimize the error propagation, an 8 \(\times \) 8 median filter was applied before mathematical integration. Then, \( I_\nu ^0(x,y)\) was calculated from Eq. (6) and was substituted into Eq. (4) to yield a new mixture fraction field \(\xi '(x,y)\). The iteration continues by updating \(\xi \) until the \(|\xi -\xi '| <1 \times 10^{-5}\). In the upper part of Fig. 6a, a dash-dotted line shows a mean signal intensity profile in the y-direction (S\(_N\)). The solid line shows the resulting local laser intensity profile (averaged along the x-direction) in the mixing region (\( I_\nu ^0(x,y) / I_\nu ^0(x,y_0)\)) after the final iteration. A valid converged solution was typically found in 3–5 iterations. The resulting mixture fraction field, after data processing of the raw image from Fig. 6a, is shown in Fig. 6b.

3 Results and discussion

3.1 Laminar mixing layer

Figure 8 shows radial profiles of the mean mixture fraction, measured with NO-PLIF, during isothermal cold laminar mixing of the fuel jet and air co-flow for different CH\(_4\)/CO\(_2\) blends. The profiles were calculated by averaging 500 mixture fraction fields in the region of \(x=1.5d_\text {lam} \pm 1\) mm. For validation, mean \(\xi \) profiles determined from Rayleigh scattering, using Eq. (5), are plotted in Fig. 8 for the F00 and F20 cases. Because differential molecular diffusion of CO\(_2\) and CH\(_4\) in air is negligible at the present experimental conditions, the mixing layers of all cases are expected to show similar profiles in the absence of turbulence. As shown in Fig. 8, all \(\xi \) profiles from NO-PLIF overlapped particularly well, excepted for the case with pure methane (F00). This can be explained by examining the simulated fluorescence signal intensities of Fig. 9, when varying \(\xi \), for different CH\(_4\)/CO\(_2\) blends. For the F00 case, the fluorescence signal sensitivity to \(\xi \) is too low to resolve small mixture fraction changes and the \(\xi \) profile in Fig. 8 is largely shifted towards the jet side. On the contrary, the addition of CO\(_2\) increases the \(S_\text {N}\) sensitivity to \(\xi \) because of the high collisional quenching cross-section of CO\(_2\). This high sensitivity at low \(\xi \) values implies that the signal fluctuations (i.e., noise) will induce less uncertainty on the mixture fraction determination.
Fig. 8

Radial profile of the mean mixture fraction from NO-PLIF for CH\(_4\) and different CH\(_4\)/CO\(_2\) laminar jets in air. Results from Rayleigh scattering are plotted along for the fuel blends F00 and F20

Fig. 9

Simulated NO-LIF signal intensity (normalized) at 300 K for CH\(_4\)/air and different CH\(_4\)/CO\(_2\)–air mixtures

The different sensitivities of \(S_\text {N}\) to \(\xi \) are explained by comparing the quenching rate of NO fluorescence reported in Table 1. The quenching rate was calculated for NO/air/fuel mixtures, and for each fuel blend, at \(\xi _\text {st}\) (\(Q_\text {st}\)) and \(\xi \) =1 (\(Q_{1}\)). As it can be seen, for F10 to F50, Q increased with the increase of \(\xi \) and CO\(_2\) content. Particularly, Q remained almost constant when varying \(\xi \) for the F10 blend, which explains the reduced non-linearity of the corresponding \(S_\text {N}(\xi )\) curve (plus sign markers in Fig. 9). The low sensitivity of \(S_\text {N}(\xi )\) for pure CH\(_4\) (F00) is caused by the decrease of Q for increasing \(\xi \) (i.e., the decrease in number density of NO is almost balanced by the decrease of Q). In this sense, the measurement technique presented in this study is not limited to CH\(_4\)/CO\(_2\) mixtures and it could be extended to mixing problems involving other common hydrocarbon fuels that have a high quenching cross-section of NO fluorescence. This includes fuels such as ethylene (C\(_2\)H\(_4\)), acetylene (C\(_2\)H\(_2\)), ammonia (NH\(_3\)) and carbon monoxide (CO).
Table 1

Quenching rate and stoichiometric mixture fraction of NO/air/fuel mixtures for the fuel blends F00 to F50

Gas

\(\xi _\text {st}\)

\(Q_\text {st}\) (\(10^8\) s−1)

\(Q_{1}\) (\(10^8\) s−1)

F00

0.055

7.3

0

F10

0.064

8.2

9.5

F20

0.071

9.0

18.9

F30

0.079

9.9

28.2

F40

0.085

10.7

37.6

F50

0.090

11.4

47.0

Q was calculated, including the self-quenching of NO, at \(\xi _\text {st}\) (\(Q_\text {st}\)) and \(\xi \) =1 (\(Q_{1}\)). As reference, Q of NO in air is 8 \(\times \) \(10^8\) s−1

The comparison of all \(\xi \) profiles from NO-PLIF in Fig. 8 with those from the Rayleigh scattering measurement, revealed a particularly good agreement up to \(\xi = 0.8\). At higher mixture fractions, \(\xi _\text {F10}\) to \(\xi _\text {F50}\) slightly deviated from \(\xi _\text {Ray,F00}\) and \(\xi _\text {Ray,F20}\). This is likely to be caused by low SNR (lower NO concentration) and halation effect of the image intensifier, which is discussed in detail in Sect. 3.2.

3.2 Measurement uncertainty estimation

The main sources of uncertainty of the approach are the signal intensity fluctuations, the procedure for local signal intensity estimation (laser attenuation), the excitation wavelength measurement, the calculation of the quenching rate and the temperature measurement. Because the uncertainty depends on the signal intensity level (i.e., mixture fraction), it was estimated at the signal level corresponding to \(\xi _\text {st}\) for the F20 fuel blend.

The uncertainty associated with the fluorescence signal intensity, \(\delta S_\text {N}\), was caused by experimental shot noise and was estimated at the co-flow region as 1.8%. The uncertainty of the local signal level for \(\xi _\text {st}\), was 2.3%. Because the local laser intensity was calculated based on the local fluorescence signal intensity and laser absorption, \(\delta S_\text {N}\) propagates in the direction of the incident laser. The effect was evaluated by modifying the measured signals within the 95 % confidence interval (\(S_\text {N} \pm 2\delta S_\text {N}\)) and processing again. The combined uncertainty propagation of the signal fluctuation and laser attenuation was 6.6%. The wavelength of the incident laser was actively controlled by the wavelength meter with an absolute accuracy of \(\pm 0.3\) pm, and the uncertainty of the excitation wavelength, \(\delta \lambda \), was estimated based on the excitation spectrum as 1.0 %. Based on the standard deviation of the quenching cross section fitting model (Settersten et al. 2006), the uncertainty of the quenching rate, \(\delta Q\), was estimated as 1.1 % and 1.6 % for \(\xi \) = 0 and \(\xi _\text {st}\), respectively. The combined uncertainty of the quenching rate for the calculation of \(\xi \) was hence estimated as 1.9 %. Assuming that the uncertainties are independent, the random uncertainty of the measurement was estimated as 6.9% for the isothermal cold measurement. At high temperature, the uncertainty of the temperature measurement using a class 1, type N thermocouple was 0.4% (according to the manufacturer). In this case, \(\delta Q\) was 1.8% and the random uncertainty of the measurement did not vary much and was estimated as 7%.

Additionally to the random uncertainties, the use of an image intensifier, which suffers from halation effects (van Breda 1992; Charogiannis and Beyrau 2013), induces a systematic uncertainty to the measurement. This effect can induce large errors in LIF-based quantitative measurements, particularly at low \(\xi \) values, when the tracer is seeded in the fuel jet (Gordon et al. 2009). For the present approach, the uncertainty due to halation was estimated using the laminar mixing measurements. At the region of \(x/d_\text {lam}\) = 1.5 and pure fuel jet, where the signal level was expected to be zero after background subtraction, the signal intensity showed an offset of \(\sim \) 20 counts. Subtracting the signal offset from the mean raw signal for each condition, a new mixture fraction mean profile, \(\xi _\text {offset}\), was determined and compared with the original \(\xi \). Figure 10 shows the effect of the offset due to halation for each fuel blend, by plotting the absolute difference value of \(\xi - \xi _\text {offset}\) at different mixture fraction values. Because of the normalizing procedure, the offset did not affect the region where \(\xi = 0\), and \(|\xi -\xi _\text {offset}|\) increased with the mixture fraction. The effect was severer with the increase of CO\(_2\) addition due to the differences in the S\(_N(\xi )\) curve for each CH\(_4\)/CO\(_2\) blend (see Fig. 9). In the case of the F20 fuel at \(\xi _\text {st}\), the systematic uncertainty was 3.4%. Therefore, the total uncertainty of the measurement, at the signal level corresponding to \(\xi _\text {st}\) was 10.3%. The systematic uncertainty for \(\xi \approx \) 0.9 can be as high as 6 and 15% for the F10 and F50 jets, respectively. Because the available literature on this issue is very limited, halation effects should be further investigated when using intensifiers in flow and combustion imaging applications.
Fig. 10

Effect of a signal offset in the low-\(\xi \) region for different CH\(_4\)/CO\(_2\) blends. The zoomed-in detail shows the offset values around \(\xi _\text {st}\). Because the images are normalized to the signal level of the co-flow region, the offset had not effect on \(\xi \) = 0

3.3 High temperature turbulent mixing

Figure 11a shows an example of an instantaneous mixture fraction field from the mixing of fuel jet (F20) with a hot air co-flow seeded with NO. The measurement was performed at the axial location \(13.5< x/d_\text {jet} <16.3\). The location \(r/d_\text {jet}\) = 0 corresponds to the jet center line. The main flow direction is from left to right and the laser sheet propagated from bottom to top in the image. In this case, no CL signal was detected in the measurement volume. As can be observed, there was not pure fuel at such an axial location and the maximum mixture fraction in the image was \(\sim \) 0.6. On the contrary, there was a large region of pure co-flow (\(\xi \) = 0) at \(2<r/d_\text {jet}<3\) (not completely shown here) that was used as signal reference for the quantification. This further illustrates the advantage of seeding the NO in the co-flow, which allows measuring \(\xi \) at such downstream locations without requiring a separate setup for signal calibration. The stoichiometric mixture fraction contour (\(\xi _\text {st}\)=0.071) is marked in the image by the white solid line.
Fig. 11

Example instantaneous mixture fraction field (a) from the mixing of a F20 jet with a hot air co-flow seeded with NO along with the corresponding scalar dissipation rate field (b) approximated as \((\nabla \xi )^2\). The main flow direction is from left to right. The laser sheet propagation from bottom to top. \(r/d_\text {jet}\) = 0 corresponds to the jet center line. The \(\xi _\text {st}\) contour is marked by the white contour line in the images

The scalar dissipation rate, \(\chi \), can be calculated by the gradient of the mixture fraction field as follows:
$$\begin{aligned} \chi = D \nabla \xi \cdot \nabla \xi , \end{aligned}$$
(7)
where D is the local mass diffusivity. The instantaneous scalar dissipation field of Fig. 11a was approximated as the squared gradient of the mixture fraction field, \((\nabla \xi )^2\), and is shown in Fig. 11b. The gradient was calculated by a second order central difference scheme. Prior to gradient computation, the mixture fraction field image was filtered with a binomial filter of order 4 to further reduce the noise without inducing a phase shift in the image. The distribution of scalar dissipation structures with different sizes indicate a strong mixing region around \(0<r/d_\text {jet}<1.7\). The dissipation structures exhibited the characteristic thin sheet-like layers (Buch and Dahm 1998; Tsurikov and Clemens 2002; Sutton and Driscoll 2006). The stoichiometric mixture fraction contour (white solid line) appears to be aligned with regions of high scalar dissipation rate.
The finest scale in the concentration field is the Batchelor scale, \(\lambda _B\). The strain-limited mass diffusion scale, \(\lambda _\text {D} \approx \text {6}\lambda _B\) , represents the smallest scale at which the scalar mixing occurs. \(\lambda _\text {D}\) was calculated as (Buch and Dahm 1998):
$$\begin{aligned} \lambda _\text {D} = \varLambda \delta Re_\delta ^{-3/4} \text {Sc}^{-1/2}, \end{aligned}$$
(8)
where \(\varLambda \) = 11.2 is the scaling constant in turbulent round jets (Buch and Dahm 1998), \(\delta \) is the outer length scale, \(Re_\delta = U_\text {c}\delta /\nu _\text {ox}\) is the outer Reynolds number and \(Sc =\nu _\text {fuel}/D_\text {fuel,ox}\) is the Schmidt number. \(Re_\delta \) = 2990 was calculated with the kinematic viscosity of air (\(\nu _\text {ox}\) = 1.94 \(\times \) 10\(^{-4}\) m\(^2\)/s ) at \(T_\text {ox}\). The outer scale center line velocity, \(U_c\) = 29 m/s, and \(\delta \) = 0.02 m, were determined using scaling laws for a turbulent jet in a high velocity co-flow, based on previous Particle Image Velocimetry (PIV) experiments (Eitel et al. 2015). Sc = 0.68 was calculated using the kinematic viscosity of the fuel F20 (\(\nu _\text {fuel}\) = 4.45 \(\times \) 10\(^{-5}\) m\(^2\)/s) and mass diffusivity of CH\(_4\) in air (\(D_\text {fuel,ox}\) = 6.53 \(\times \) 10\(^{-5}\) m\(^2\)/s) at \(T_\text {fuel}\). The resulting \(\lambda _\text {D}\) was 670 \(\upmu \)m (\(\lambda _\text {B} \approx \) 112 \(\upmu \)m). The comparison of \(\lambda _\text {D}\) and \(\lambda _\text {B}\) with the spatial resolution of the imaging system, indicates that the present measurements can resolve scales of the same order of the smallest scale in the concentration field, at the measurement location and for the current operating conditions.

4 Conclusions

A new approach for quantitative mixture fraction imaging in the turbulent mixing of a fuel jet and a high temperature oxidizer co-flow using NO-PLIF was presented. Unlike existing strategies, the NO tracer was seeded in the oxidizer stream. State-dependent spectroscopic parameters were taken from spectroscopic simulations using the program LIFSim. The approach was first evaluated during the laminar mixing of the fuel and oxidizer at room temperature. Methane and different blends of CH\(_4\)/CO\(_2\) (synthetic biogas) were used as fuels while NO-seeded air was used as the oxidizer.

The mixture fraction measurements using NO-PLIF during the laminar mixing were compared against Rayleigh scattering imaging. This comparison revealed that the present approach is not suitable for CH\(_4\)/air mixtures due to the lack of the sensitivity of the fluorescence signal to the mixture fraction. For biogas/air mixtures, the addition of at least 10%vol CO\(_2\) increased the response of the fluorescence signal to the mixture fraction making the measurements feasible.The minimum resolvable difference in mixture fraction depends on the CO\(_2\) content and on the excitation wavelength. For the present approach the stoichiometric mixture fraction was fully resolved for each biogas blend with an acceptable uncertainty.

By seeding the NO in the oxidizer stream, high SNRs were achieved at locations of low mixture fraction (i.e., around the stoichiometric value) due to the high concentration of NO. Additionally, a stable calibration region is available in situ (i.e., in the same image) at every measurement location, which contributes to reduce the uncertainty of the quantitative determination of the mixture fraction.

The measurements were extended to the turbulent mixing of a cold fuel jet issuing into a NO-seeded, hot air co-flow. Two-dimensional instantaneous mixture fraction measurements were feasible with an acceptable uncertainty using a non-reacting adiabatic mixing assumption to determine the temperature dependence of the fluorescence signal. The spatial resolution of the optical setup allowed resolving the smallest scale in the concentration field (i.e., Batchelor scale). Future efforts should include multiscalar laser techniques to measure the instantaneous temperature field.

Notes

Acknowledgements

The authors acknowledge the funding by the Deutsche Forschungsgemeinschaft (DFG) through SFB-Transregio 129. Ayane Johchi for the funding of the Alexander von Humboldt Foundation. Andreas Dreizler is grateful for the support by the Gottfried Wilhelm Leibniz program of DFG.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Reaktive Strömungen und Messtechnik, Technische Universität DarmstadtDarmstadtGermany

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