Multiscalar imaging in partially premixed jet flames with argon dilution

doi:10.1016/j.combustflame.2005.08.027

Combustion and Flame

Volume 143, Issue 4, December 2005, Pages 507-523

https://doi.org/10.1016/j.combustflame.2005.08.027 Get rights and content

Abstract

Simultaneous imaging of depolarized and polarized Rayleigh scattering combined with OH-LIF and two-photon CO-LIF provides two-dimensional measurements of mixture fraction, temperature, scalar dissipation rate, and the forward reaction rate of the reaction $CO + OH = {CO}_{2} + H$ in turbulent partially premixed flames. The concept of the three-scalar technique for determining the mixture fraction using CO-LIF with depolarized and polarized Rayleigh signals was previously demonstrated in a partially premixed CH₄/air jet flame [J.H. Frank, S.A. Kaiser, M.B. Long, Proc. Combust. Inst. 29 (2002) 2687–2694]. In the experiments presented here, we consider a similar jet flame with a fuel-stream mixture that is better suited for the diagnostic technique. The contrast between the depolarized and the polarized Rayleigh signals in the fuel and air streams is improved by partially premixing with an argon/oxygen mixture that has the same oxygen content as air. The substitution of argon, which has a zero depolarization ratio, for the nitrogen in air decreases the depolarized Rayleigh signal in the fuel stream and thereby increases the contrast between the depolarized and the polarized Rayleigh signals. We present a collection of instantaneous 2-D measurements and examine conditional means of temperature, scalar dissipation, and reaction rates for two downstream locations. The emphasis is on the determination of the scalar dissipation rate from the mixture-fraction images. The axial and radial contributions to scalar dissipation are measured. The effects of noise on the scalar dissipation measurements are determined in a laminar flame, and a method for subtracting the noise contribution to the scalar dissipation rates is demonstrated.

Introduction

Mixture fraction $(ξ)$ , scalar dissipation $(χ)$ , and reaction rate are fundamental quantities in the study of turbulent combustion but are particularly challenging to measure. Multidimensional measurements of these quantities are needed to improve our understanding of flow–flame interactions in turbulent nonpremixed and partially premixed combustion. The determination of mixture fraction requires simultaneous measurements of all major species and temperature. For multidimensional measurements, it is not feasible to measure all of these quantities, so mixture fraction must be determined from a reduced set of measurements. Over the past 23 years, the diagnostic capabilities for measuring mixture fraction in turbulent nonpremixed flames have evolved from single-point Raman/Rayleigh [1], [2], [3], UV-Raman [4], [5], and Raman/Rayleigh/LIF ([6], [7], [8], [9] and references therein) measurements to 1-D [10], [11], [12], [13], [14], [15], [16] and 2-D [17], [18], [19], [20], [21], [22], [23] techniques. The single-point measurements have provided insights into turbulent nonpremixed flames, and well-documented data sets are currently used for the development of turbulent combustion models via the TNF Workshop [24].

Scalar dissipation, which is defined as $χ = 2 D (\nabla ξ \cdot \nabla ξ)$ , where D is the mass diffusivity, requires multidimensional measurements to determine the gradient of mixture fraction. One-dimensional measurements of mixture fraction provide only a single component of the mixture-fraction gradient [10], [16]. To improve on this limitation, the projection of the mixture-fraction gradient onto the flame normal can be determined using simultaneous flame-orientation measurements [11], [12]. However, this approach does not provide a direct measurement of the full scalar dissipation rate, and the determination of the flame orientation over a wide range of mixture fractions is challenging. Two-dimensional mixture-fraction imaging affords wide-field measurements of two components of the scalar dissipation and can provide intuitive physical insight into the flame structure. Each image of mixture fraction or scalar dissipation contains on the order of 10⁴–10⁵ point measurements.

Schemes for determining mixture fraction in two dimensions involve the measurement of two or three judiciously selected scalars. Ideally, the measured quantities provide good sensitivity to variations in mixture fraction and have high signal-to-noise ratios. A two-scalar method, which is based on fuel mass fraction $(Y_{fuel})$ and sensible enthalpy $(h = c_{p} T)$ , can be derived by simplifying the chemistry to a one-step reaction between fuel and oxidizer and assuming unity Lewis number [25], [26]. In this formulation, the conserved scalar is $β = Y_{fuel} + c_{p} T / q$ , and the mixture fraction is given by $ξ_{2 scalar} = \frac{β - β_{2}}{β_{1} - β_{2}} = \frac{Y_{fuel} + (c_{p} T - c_{p, 2} T_{2}) / q}{Y_{fuel, 1} + (c_{p, 1} T_{1} - c_{p, 2} T_{2}) / q},$ where q is the lower heat of combustion per unit mass of fuel, and subscripts 1 and 2 designate the fuel and oxidizer streams, respectively. This formulation has been used for mixture-fraction imaging in both H₂/air [21] and CH₄/air jet flames [17], [18], [21]. An iterative procedure is used to determine fuel mass fraction and temperature from measurements of fuel concentration and Rayleigh scattering. In this procedure, laminar flame calculations are used to tabulate the temperature and mixture-fraction-dependent auxiliary variables, which include $c_{p}$ , the effective Rayleigh cross section, $σ_{Ray}$ , and the mixture molecular weight, $W_{mix}$ . Within the iteration, a “reactedness” can be computed from the local Rayleigh temperature, and the values of $c_{p}$ , $σ_{Ray}$ , and $W_{mix}$ are linearly interpolated between their values in a laminar flame and in a nonreacting flow [19]. Thus nonequilibrium behavior is taken into account in an approximate fashion for these variables. However, the two-scalar approach has further limitations that stem from the assumption of one-step chemistry. This issue is most prominent in fuel-rich regions where rich-side chemistry converts the parent fuel into intermediate species, which are not accounted for in a one-step reaction. In flames with a significant likelihood of local extinction, one single reaction step is a particularly poor approximation.

These inherent errors in the two-scalar approach can be reduced by measuring an intermediate species and constructing a conserved scalar from three measured quantities. Carbon monoxide is a key intermediate species that can be measured by two-photon LIF. A conserved scalar can be constructed from sensible enthalpy, fuel and CO mass fractions by considering the two-step chemical mechanism for methane oxidation, ${CH}_{4} + \frac{3}{2} O_{2} = CO + 2 H_{2} O + Q_{1},$ $CO + \frac{1}{2} O_{2} = {CO}_{2} + Q_{2},$ where $Q_{1}$ and $Q_{2}$ are the heat released per mole of consumed CH₄ and CO, respectively. The expression for a new conserved scalar is derived from the Shvab–Zel'dovich formalism of coupling functions [27]. The simplified unsteady species conservation equation is $L (Y_{i}) = w_{i}$ , where the operator L is given by $L \equiv ρ \frac{\partial}{\partial t} + ρ v \cdot \nabla - \nabla \cdot (ρ D \nabla)$ , and $w_{i}$ is the rate of production of species i by chemical reaction. By definition, a conserved scalar has no chemical source term, and therefore $L (β) = 0$ . The two-step mechanism in Eqs. (2), (3) can be rewritten on a mass basis as ${CH}_{4} + 3 O_{2} = \frac{7}{4} CO + \frac{9}{4} H_{2} O + q_{1},$ $CO + \frac{4}{7} O_{2} = \frac{11}{7} {CO}_{2} + q_{2},$ where $q_{1}$ and $q_{2}$ are the heat released per unit mass of consumed CH₄ and CO, respectively. To derive a conserved scalar, we set $β = Y_{fuel} + a Y_{CO} + b c_{p} T$ , apply $L (β) = 0$ using Eqs. (4), (5), and solve for the coefficients a and b. From Eqs. (4), (5), $L (β) = w_{1} (- 1 + 7 / 4 a + b q_{1}) + w_{2} (- a + b q_{2}) = 0,$ where $w_{1}$ and $w_{2}$ are the rates for the first (4) and second (5) reaction steps, respectively. If the two terms in parentheses are set equal to zero, then the coefficients a and b are independent of the reaction rates for the two reaction steps. The resulting coefficients are $a = q_{2} / q$ and $b = 1 / q$ , and the conserved scalar is $β = Y_{fuel} + q_{2} / q Y_{CO} + c_{p} T / q$ . The three-scalar mixture fraction is given by $ξ_{3 scalar} = \frac{β - β_{2}}{β_{1} - β_{2}} = \frac{Y_{fuel} + q_{2} / q Y_{CO} + (c_{p} T - c_{p, 2} T_{2}) / q}{Y_{fuel, 1} + (c_{p, 1} T_{1} - c_{p, 2} T_{2}) / q},$ where $q_{2} / q = 0.20$ according to the heat-release rates for the two-step mechanism. The mixture fraction, temperature, fuel, and CO mass fractions are determined by an iterative routine that uses the Rayleigh and the CO-LIF signals. Conversion of the CO-LIF signal to CO mass fraction requires an estimate of the variations in Boltzmann fraction and quenching rates. The variations in Boltzmann fraction are determined from the temperature measurements, and the quenching rates are estimated from laminar flame calculations. In the present experiments, we found that using $q_{2} / q = 0.27$ in the iterative algorithm for determining mixture fraction produced results that were most consistent with detailed point measurements of turbulent jet flames [6], [24]. In the remainder of this paper, we will refer to the measured mixture fraction simply as ξ with the subscript “3 scalar” implied.

The fuel concentration is central to the reduced formulations of mixture fraction and has previously been measured by LIF of fuel tracers [17], Raman scattering from the fuel [17], [18], [19], [22], and difference Rayleigh scattering [23], [28]. Difference Rayleigh scattering provides the most promising method for imaging the fuel concentration since fuel Raman signals are comparatively weak, and LIF from fuel tracers is plagued by pyrolysis of the tracer [17]. In difference Rayleigh scattering, the polarized and depolarized components of Rayleigh scattering from a polarized laser beam are simultaneously recorded on separate detectors. Rayleigh scattering from isotropic molecules, such as CH₄, contains no measurable depolarized component. In contrast, Rayleigh scattering from anisotropic molecules, such as N₂, O₂, CO₂, H₂O, H₂, and CO, contains both depolarized and polarized components. The methane concentration can be related to the difference between the polarized and depolarized Rayleigh signals when these signals are normalized to their respective values in air. To ensure that the difference signal is not multivalued with respect to the methane concentration, a linear, or nonlinear, combination of the polarized and depolarized signals can be used instead of the simple difference [23], [28].

Fuel mixtures that have no depolarized component provide optimal contrast between the difference Rayleigh signal in the fuel mixture and the air coflow. The use of anisotropic diluent gases, such as nitrogen and oxygen, in the fuel mixture decreases the dynamic range of the difference Rayleigh signal. Partial premixing of methane with air, however, produces more robust flames and significantly reduces broadband fluorescence interference from polycyclic aromatic hydrocarbons. For partially premixed flames, the dynamic range of the difference Rayleigh signal can be significantly improved by replacing the nitrogen in air with a noble gas, which has zero depolarization ratio. In the present study, we consider a fuel mixture that is similar to the Sandia piloted methane/air jet flames A–F in the Turbulent Nonpremixed Flame Workshop (TNF) [6], [24] but has argon instead of nitrogen as the inert part of the diluent. The new fuel mixture has the same methane/diluent ratio (1/3 by volume) as the original series of jet flames, but the dilution air is replaced by a mixture of argon and oxygen with the same oxygen content as air. Flames with this new fuel mixture are designated “4Ar” flames to reflect the argon/oxygen ratio (3.76/1 by volume). Piloted jet flames with this fuel composition were previously used for combined Rayleigh/CH₄-Raman/N₂-Raman imaging by Fielding et al. [22]. The argon-diluted flames have a stoichiometric mixture fraction, $ξ_{st}$ , of 0.41, and the air-diluted flames have $ξ_{st} = 0.35$ . To match the air-dilution value of $ξ_{st}$ with an argon–oxygen mixture would require an argon/oxygen ratio of 13/1. However, highly turbulent flames with this diluent could not be stabilized on the piloted jet burner.

The increase in air–fuel contrast that is provided by argon dilution is demonstrated in Fig. 1 using calculated Rayleigh signals. The Rayleigh signals in Figs. 1a and 1b were computed from counterflow–flame calculations with air-diluted and argon/oxygen-diluted fuel mixtures, respectively [29], [30]. The mixture fraction in these plots was determined from a linear combination of the hydrogen and carbon mass fractions [6]. The oxidizer stream contained room-temperature air, and the global strain rate was 200 s⁻¹. The depolarization ratios for computing the depolarized Rayleigh signals are from Fielding et al. [28]. Fig. 1 includes plots of the CO and OH concentrations that are normalized with respect to their peak values. A previous study demonstrated that difference Rayleigh scattering can provide a measurement of fuel concentration in an air-diluted methane jet flame, and the result was used for determining the mixture fraction via a three-scalar approach [23]. In the present analysis, emphasis was placed on optimizing the signal-to-noise ratio of 2-D mixture-fraction measurements in flames with a relatively low probability of local extinction. Consequently, the fuel concentration was derived from the polarized Rayleigh signal, which had the largest signal-to-noise ratio of all the measured scalars. A surrogate signal, $S_{fuel}^{'}$ , for the fuel concentration was constructed by subtracting an offset from the polarized Rayleigh signal and normalizing with respect to the signal in the fuel stream $(S_{fuel}^{'} = (S_{Pol} - S_{Polmin}) / (S_{Pol, fuel} - S_{Polmin})$ , where $S_{Polmin}$ is the minimum polarized Rayleigh signal). Fig. 2 shows a laminar flame calculation of the methane concentration and the predicted fuel surrogate signal normalized to their respective values in the fuel stream. This calculation has a global strain rate of 200 s⁻¹. The variations in $S_{Polmin}$ for strain rates between 100 and 600 s⁻¹ are within the noise of the measured Rayleigh signal. On the rich side of $ξ_{st}$ , the curves for $S_{fuel}^{'}$ and the normalized methane concentration show excellent overlap. The polarized Rayleigh signal, however, is multivalued with respect to mixture fraction, and an additional measurement is needed to eliminate the ambiguity between the rich and the lean regions of the flame. A linear or nonlinear combination of the polarized and depolarized Rayleigh signals can be used to identify the rich and lean regions. This identification is significantly enhanced by the increased contrast between the depolarized and the polarized Rayleigh signals that is afforded by the presence of argon in the diluent. We used the linear combination $S_{mask} = S_{Pol} - 2 S_{Dep} + 0.077$ to determine a mask signal, $S_{mask}$ , which was negative for lean conditions and positive for rich conditions. This particular linear combination did not scale with the fuel concentration but instead was chosen to provide a larger slope near stoichiometric conditions to improve the sensitivity of the mask. A binary mask was created by thresholding $S_{mask}$ at 0, and $S_{fuel}^{'}$ was multiplied by the mask to eliminate the ambiguity. The increased contrast provided greater certainty about the local presence or absence of fuel. Alternative schemes for exploiting this increased contrast to determine fuel concentration and mixture fraction in flames with arbitrary degrees of local extinction are under development. These approaches involve a more integrated use of all the measured scalars but may result in larger noise contributions to the measured scalar dissipation rates. In the present analysis, the surrogate for fuel concentration becomes less accurate in regions of localized extinction.

The experimental methods are described below followed by a presentation of results using the three-scalar technique for determining mixture fraction in argon/oxygen-diluted laminar and turbulent jet flames. Mixture-fraction images are used to determine the axial and radial components of the scalar dissipation rate in a turbulent partially premixed methane jet flame. Images of mixture fraction, scalar dissipation, temperature, and the forward reaction rate for the reaction $CO + OH = {CO}_{2} + H$ are presented. The reaction rate is determined from the OH-LIF and two-photon CO-LIF signals, whose excitation–detection scheme is chosen such that the pixel-by-pixel product is proportional to the forward rate of the reaction $CO + OH = {CO}_{2} + H$ over the relevant range of mixture fractions [23], [31]. We estimate the noise contribution to scalar dissipation measurements in a laminar flame and use these results to provide a first-order noise correction for scalar dissipation measurements in a turbulent flame. Conditional means of reaction rate and temperature are presented as a function of scalar dissipation rate.

Section snippets

Laser and detector arrangement

The experiments were performed in the Advanced Imaging Laboratory at Sandia National Laboratories. Single-shot images of polarized and depolarized Rayleigh scattering, two-photon CO-LIF, and single-photon OH-LIF were simultaneously collected. The experimental facility was similar to that used by Frank et al. [23] and Fielding et al. [28], and is shown schematically in Fig. 3. The beams from five lasers at three wavelengths were combined and focused into a sheet by a fused-silica cylindrical

Imaging results from turbulent flames

We first consider a comparison of measurements in the air-diluted and argon/oxygen-diluted turbulent flames. Fig. 4 shows an example of simultaneous single-shot measurements of polarized and depolarized Rayleigh scattering as well as CO-LIF and OH-LIF signals in Flame D. The imaged region is centered 15 diameters downstream of the nozzle exit and spans 4 diameters in the radial direction. The images in the figure have not been smoothed, and the LIF signals have not been corrected for variations

Conclusions

Multiscalar imaging of depolarized and polarized Rayleigh scattering combined with OH-LIF and two-photon CO-LIF provided simultaneous measurements of temperature, mixture fraction, scalar dissipation rate, and the forward reaction rate of the reaction $CO + OH = {CO}_{2} + H$ . The technique was demonstrated in a partially premixed turbulent jet flame with a CH₄/O₂/Ar fuel-stream mixture. The flame considered here (Flame D4Ar) had the same fuel/diluent ratio ( $1 / 3$ by vol) and jet velocity as the air-diluted

Acknowledgements

This research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94-AL85000. The authors thank R. Sigurdsson for assistance during the experiments. The work on imaging of mixture fraction in turbulent flames has gone on in

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