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Jun 29, 2017 - ABSTRACT: The present study has adopted the multi-environment probability density function (MEPDF) approach to simulate the turbulent ...
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Multi-environment Probability Density Function Modeling for Turbulent CH4 Flames under Moderate or Intense Low-Oxygen Dilution Combustion Conditions with Recirculated Flue Gases Sangtae Jeon and Yongmo Kim* Department of Mechanical Engineering, Hanyang University, Haengdang-Dong, Seongdong-Ku, Seoul, 133-791, Korea S Supporting Information *

ABSTRACT: The present study has adopted the multi-environment probability density function (MEPDF) approach to simulate the turbulent CH4 flames under flameless combustion conditions with recirculated flue gases. The MEPDF approach is based on an Eulerian PDF formulation with computational efficiency. Micromixing can be represented via the IEM (interaction by exchange with the mean) model, and the chemistry is based on the GRI 2.11 mechanism including the NOx chemistry. Special emphasis is given to the effects of the micromixing model constants on the structure and characteristics of recirculated moderate or intense low-oxygen dilution (MILD) combustion processes. In terms of the temperature and species mole fraction, the multienvironment PDF model with a micromixing constant of 0.5 yields reasonably good agreement with experimental data. In terms of the integrated NO production rate for the MILD combustion condition, the N2O path yields the highest level, followed by the prompt, reburn, NO2, thermal, and NNH mechanisms in that order. Moreover, detailed discussions are made for the flame stabilization and autoignition processes in terms of recirculation rate, distribution of Damköhler number, scalar dissipation rate, and H2CO mass fraction.

1. INTRODUCTION Recently, moderate or intense low-oxygen dilution (MILD) combustion has attracted much attention as a new combustion technology that has desirable features including high thermal efficiency and low NOx emission characteristics. In a MILD combustion situation, fuel, oxidizer, and combustion products are diluted and preheated through proper mixing and the resulting vitiated mixtures with the quite oxygen level are autoignited and react with higher temperature than the autoignition temperature and lower oxygen level compared to conventional combustion technology. Consequently, unlike conventional flames, combustion occurs at a relatively low temperature with the increased temperature uniformity. This MILD combustion field is characterized by the nonvisible flame, temperature uniformity, lower NOx emission, smooth radiation flux, inherent flame stabilization, and lower combustion noises.1,2 The MILD combustion processes generally yield relatively low reaction rates due to moderate temperature and low oxygen level. Thus, the finite-rate chemistry effects are more important for MILD combustion than for conventional nonpremixed combustion. In contrast, crucial mixing processes also exist for the flue gases and fuel or air, as well as the diluted fuel and the diluted oxidizer streams. It is important to realistically represent the turbulence−chemistry interaction under MILD combustion conditions with the intensely turbulent mixing. Particularly for modeling the autoignition process, nonequilibrium chemistry and turbulent mixing are equally important. Although the concepts and experiments of MILD combustion have been extensively investigated, physical modeling for the flameless combustion regime has been relatively less explored.3 In this regard, systematic studies are © 2017 American Chemical Society

needed to evaluate the prediction ability of the turbulent combustion models under flameless combustion conditions. In previous works, the turbulence−chemistry interaction under MILD combustion conditions was modeled mostly via the eddy dissipation concept (EDC). Christo and Dally4,5 numerically investigated the turbulent CH4/H2 flame of the jetin-hot-coflow (JHC) burner6 using the EDC, steady flamelet, and transported probability density function (PDF) models. In these flameless flames with three different oxygen levels, the EDC approach yielded better conformity with measurements than the steady flamelet model. The transported PDF approach also showed predictive capability comparable to the EDC model. There have been several simulation studies on JHC turbulent flames6 in MILD combustion conditions. Frassoldati et al.7 conducted one of these numerical studies, which used the EDC model to investigate the effect of the inlet turbulent boundary condition, applying a detailed NOx postprocessor for the same burner. De and Dongre8 performed a numerical investigation for JHC turbulent flames6 using the Lagrangian PDF model, multi-environment PDF approach, and EDC model. They reported that the PDF transport-based turbulent combustion model yielded better prediction capability compared to other turbulent combustion models. More recently, Tu et al.9 numerically investigated the structure of the JHC turbulent CH4/H2 flame under MILD combustion using the Reynolds averaged Navier−Stokes (RANS) based EDC model together with the detailed chemical mechanism GRI 2.11. Their numerical results obtained by the EDC approach agreed well with the experimental data.6 Received: April 14, 2017 Revised: June 24, 2017 Published: June 29, 2017 8685

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the precise flame structure and NO formation characteristics according to various O2 concentrations of hot-coflow jet. However, the MEPDF approach has not been studied for the MILD combustion processes with recirculated flue gas.20 In this aspect, the MEPDF approach has been applied to numerically investigate the essential features of the MILD combustion processes with the recirculated combustion. In the transported PDF combustion models, the micromixing constant often needs to be tuned according to the combustion situation as well as physical models representing chemistry, turbulence, and micromixing.36 In the present study, to find the optimal micromixing model constant for the flameless recirculated flame, a parametric study was conducted on three micromixing model constants (2.0, 0.5, and 0.15). Special emphasis is given to the effects of the micromixing model constants on the characteristics of the recirculated MILD combustion processes. Furthermore, detailed discussions are made for the flame stabilization and autoignition processes in terms of recirculation rate, distribution of Damköhler number, scalar dissipation rate, and H2CO mass fraction. Finally, in order to evaluate the ability of the present MEPDF approach for the precise structure of the flameless recirculated flames, numerical results obtained by using three micromixing constants (2.0, 0.5, and 0.15) are compared with measurements in terms of the mean temperature and species mole fractions.20

In JHC burners,6 hot combustion products were supplied through the feeding line into the combustion chamber. However, in the practical MILD combustors, the flameless combustion condition could be created by using the internally recirculated flue gases. Several experimental and numerical studies10−16 were carried out for flameless combustion using internal flue gas recirculation. However, only a limited set of experimental data was provided for validation of the turbulent combustion models. Recently, measurements17 and numerical analysis18 have been conducted for the MILD combustors which both inlet and outlet are located at the top of the burner. The numerical investigation18 for this MILD combustor was conducted by using the realizable k−ε turbulence model and two different combustion models including the EDC approach and the joint composition PDF transport model. Graça et al.18 reported that the RANS-based turbulent combustion models had the limitations to correctly predict the flow and flame structure near the inlet. On the other hand, using state-of-theart turbulence and combustion models with various reaction mechanisms, Rebola et al.19 numerically simulated the combustion processes of the MILD furnace20 with flue gas recirculation. Their numerical results indicated that the EDC model together with the standard k−ε turbulence model and detailed chemistry yielded reasonably good agreement with the measurements. The EDC model has been widely adopted for the numerical simulation of turbulent flame, mainly due to the easy incorporation of the detailed chemistry. Moreover, the EDC modeling for various MILD combustion systems performs reasonably well compared to other combustion models. However, the EDC model has the limitations to correctly simulate the jet flame stabilization process.21−23 In previous numerical studies for the JHC configuration,6 due to overestimation of the mean reaction rate, the EDC model results in overestimated peak temperatures and an underestimated lift-off height in the MILD combustion regime.4,7,24 Among the state-of-the-art turbulence−chemistry interaction models, the transported PDF method based on the Monte Carlo particle method has proved to be one of the most reliable approaches for accurate modeling of turbulent reacting flows under complex combustion conditions.25−27 However, to simulate the turbulent flames especially for the large-scale real combustor, the computational burden is excessively required in the stochastic Lagrangian PDF (SLPDF) approach.28 There are two alternatives approaches for solving the transported PDF equations based on an Eulerian frame. These models are the multi-environment PDF (MEPDF) approach29 and the stochastic Eulerian PDF (SEPDF) method.30,31 In MEPDF modeling,29 the joint composition PDF transport equations approximated the combination of weights and weighted abscissas on composition and physical space. The MEPDF approach is based on the form of a traditional Eulerian scheme while also retaining the desired characteristics of a particlebased method and better computational efficiency, compared with the SLPDF approach and SEPDF model.32 Recently, the multi-environment PDF approach based on RANS and large eddy simulation (LES) has successfully predicted turbulent flames with hot vitiated coflow under MILD combustion conditions.23,33−35 According to our previous work,23 the multi-environment PDF transport model with a micromixing model constant of 2.0 has the ability to realistically predict the fundamental features of turbulent nonpremixed CH4/H2 jet flames under hot-coflow MILD combustion without the recirculated flue gas in terms of

2. MATHEMATICAL MODEL Fox29 proposed the MEPDF method and used this approach to calculate the equivalent moments instead of the detailed PDF of particles. The generalized transported equation for joint composition, fϕ(ψ;x,t), with the IEM (interaction by exchange with the mean) mixing model can be written as ⟨ρ⟩ =

∂fϕ ∂t

+ ⟨ρ⟩Ui

∂fϕ ∂xi

+

∂ (⟨ρ⟩Sα(ψ )fϕ ) ∂ψα

⎞ ⎤ ∂ ⎛ Γt ∂fϕ ⎞ ∂ ⎡⎛ 1 ε ̃ ⎟⎟ + ⎜⎜ ⎢⎜⎝ Cϕ ̃ (ψα − ⟨ϕα⟩)⎟⎠fϕ ⎥ ⎦ ∂xi ⎝ σt ∂xi ⎠ ∂ψα ⎣ 2 k

(1)

where ψ is the sample space of composition vector ϕ and Cϕ is the mixing model constant. Γt, σt, ε̃, and k̃ represent the turbulent viscosity, turbulent Schmidt number, turbulent dissipation rate, and turbulent kinetic energy, respectively. The joint composition PDF of the Ns dimensions (number of species +1) is a summation of the multi-dimensional Dirac delta function in composition space, which can be represented by Ne

fϕ (ψ ; x , t ) =

Ns

∑ pn

∏ δ(ψi − ⟨ϕi⟩n )

n=1

i=1

(2)

where Ne is the number of environments and Ns is the number of the composition vector ϕ. Using this relation of joint composition PDF, the transported composition PDF equation can be written in the following set of transport equations for weights, pn, and weighted abscissas, ⟨s⟩αn = pn⟨ϕα⟩n: ∂pn ∂t

+ ⟨Ui⟩

∂pn ∂xi

−

∂ ⎛ ∂pn ⎞ ⎜Γt ⎟ = an ∂xi ⎝ ∂xi ⎠

∂⟨s⟩αn ∂⟨s⟩αn ∂ ⎛ ∂⟨s⟩αn ⎞ + ⟨Ui⟩ − ⎜Γt ⎟ = bαn ∂t ∂xi ∂xi ⎝ ∂xi ⎠ 8686

(3a)

(3b)

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three micromixing constant were calculated by the following formulation.45 me recirculation rate ≡ K v = mf + mo (7)

In the case of using the IEM mixing model, the source term of weights, an, is set to zero, and the source terms of weighted abscissas, bαn, for two environment systems can be expressed by 1 bα1 = ⟨ϕα⟩1 − ⟨ϕα⟩2 +

1 ε Cϕ p (ϕ ̃ − ⟨ϕα⟩1) + p1 Sα(⟨ϕ⟩1) 2 k 1 α

−1 bα 2 = ⟨ϕα⟩1 − ⟨ϕα⟩2 +

⎛ ∂⟨ϕα⟩n ⎞2 ∑ pn Γt⎜ ⎟ ⎝ ∂xi ⎠ n=1 2

Here, me is the mass flow rate of recirculated exhaust gas, mf is the mass flow rate of fuel jet, and mo is the mass flow rate of preheated air. Additionally, in order to analyze the NO emissions for flameless combustion, the present study classified the NO formation and oxidation with thermal, N2O, NO2, prompt, NNH, and reburn mechanisms.46,47 The thermal NO (Zeldovich) mechanism involves the following reactions:

(4a)

⎛ ∂⟨ϕα⟩n ⎞2 ∑ pn Γt⎜ ⎟ ⎝ ∂xi ⎠ n=1 2

1 ε Cϕ p (ϕ ̃ − ⟨ϕα⟩2 ) + p2 Sα(⟨ϕ⟩2 ) 2 k 2 α

(4b)

N + NO ⇔ N2 + O

The first term of eqs 4a and 4b is the correction term, which makes it possible to move away from the mean value in the composition space, and the second term of eqs 4a and 4b is the micromixing term, which keeps the abscissa at the mean value; these two terms directly affect the variance of composition vectors. The correction term of eqs 4a and 4b in the multienvironment PDF formulation possibly causes numerical problems such as singularity.37 To avoid this numerical singularity, the present approach has employed our previous approach23 which combines the three singularity treatments.38−40 The present multi-environment PDF model has been implemented in our in-house code.23,41 In order to investigate the interaction between turbulence mixing and chemical kinetics according to the combustion model and micromixing constants, the Damköhler number was calculated. The Damköhler number, Da, represents the ratio of flow time scale to chemical time scale: Da ≡

τ characteristic flow time = flow characteristic chemical time τchem

N + O2 ⇔ NO + O N + OH ⇔ NO + H

The N2O mechanism consists of the following three reactions: N2O + O ⇔ 2NO NH + NO ⇔ N2O + H

The NO2 mechanism consists of the following four reactions: HO2 + NO ⇔ NO2 + OH NO + O + M ⇔ NO2 + M NO2 + O ⇔ NO + O2

(10)

NO2 + H ⇔ NO + OH

The NNH mechanism contains only one reaction formula as follows:

(5)

NNH + O ⇔ NH + NO

(11)

The reburn mechanism consists of the following chemical path: CHi + NO ⇔ products

(6a)

(12)

Finally, the GRI 2.11 mechanism contains 11 elementary reactions of the reburn mechanism. The prompt NO mechanism is considered in this study, but the reactions are so numerous that we do not mention them here. The difference in mechanism of the NO formation will be discussed according to a combustion model, such as multienvironment PDF in the flameless combustion environment, through the aforementioned classified NO reaction mechanisms.

with chemical reaction rate constant ≡ cr max1 < i < 279 Arrhenius rate of reaction no. i = ρ

(9)

NCO + NO ⇔ N2O + CO

In the present study, the Damköhler number is defined as follows:42 ⎛ υc 2 ⎞1/2 turbulence Damkohler number ≡ Da T ≡ ⎜ r ⎟ ̈ ⎝ ε ⎠

(8)

(6b)

where ρ is the local mixture density, ε is the local dissipation rate of turbulent kinetic energy, υ is the kinematic viscosity, and cr is a local parameter that is defined as the maximum of the chemical reaction rate constant among 279 elementary reactions of GRI 2.11.43 More detailed research related to the turbulent Damköhler number was carried out by Isaac et al.44 The method used in this study was not as accurate as the calculation of the turbulent Damköhler number obtained by Isaac et al.,44 but this method in this study showed similar results in terms of an efficient computational cost. Wünning et al.45 noted that the recirculation rate plays an important role in establishing a MILD combustion condition inside the combustion chamber. In this study, to evaluate the degree of mixing between the preheated oxidizer and the recirculated combustion products, the recirculation rates for

3. NUMERICAL RESULTS AND DISCUSSION The present multi-environment PDF approach has been applied to numerically analyze the MILD combustion processes encountered in the combustion furnace.20 Figure 1 shows a geometric configuration and schematic dimension of the MILD combustor with the internal flue gas recirculation. The combustion chamber is a cylinder with a diameter of 150 mm and a length of 300 mm. The burner consists of a central fuel jet with an inner diameter of 4 mm, and preheated air is supplied through a conventional double concentric configuration with an inner diameter of 15 mm. In this furnace, the 8687

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probability density function approach. The IEM model48 is adopted to represent micromixing. In the present study, computations are made for three micromixing model constants, including 2.0, 0.5, and 0.15. The inflow boundary values of weights are imposed by 1.0/0.0 at the central methane fuel jet and 0.0/1.0 at the preheated air, respectively. Previous studies49,50 reported that there was no significant difference between the numerical solutions obtained using GRI Mech 2.11 and GRI Mech 3.0.51 Moreover, according to the recent study52 for the MILD combustion, numerical results obtained by GRI Mech 2.1143 agreed reasonably well with experimental data. Thus, the present study has employed GRI Mech 2.11. The radiative heat transfer is modeled by the discrete ordinates approach,53 and the absorption coefficient of the gaseous medium is evaluated by the weight sum of the gray gas model. The NOx formation process is directly evaluated by the multienvironment PDF procedure rather than the postprocessing approach. To check for grid convergence, the present study used two mesh arrangements including a base grid (80 × 150) and a finer grid (100 × 250). For this flameless recirculated flame with the much broader temperature uniformity, as displayed in Figure S1 in the Supporting Information, there were marginally small differences in the predicted temperature fields for the two numerical mesh arrangements. Thus, all computations were based on the base grid. Figure 2 shows the predicted flow and flame patterns in terms of streamlines, mean temperature, and O2 mole fraction. Figure 1. Geometric configuration of the flameless combustor.

burned gas is exhausted through the bottom end using a convergent nozzle with a length of 50 mm and an angle of 35°. More detailed burner configurations and various experimental conditions were described in detail in experimental literature.20 The flue gas flows upstream along the recirculation flow due to the combustor configuration. The recirculated flue gas is entrained and the air jet is diluted with the flue gas before it is burned due to the high momentum of the air jet. This process results in the ignition of the mixture at a lower O 2 concentration. The injection velocity of the methane fuel jet is 24.4 m/s, and the temperature of the fuel is 20 °C. The velocity of the preheated air is 102.1 m/s, and the inflow air temperature is 500 °C. At the inflow boundary, the radial velocity is assumed to be zero and the axial velocity is imposed by the uniform distribution. According to the measurements20 of wall temperature, a uniform temperature was imposed at the wall boundary (900 °C). In dealing with the MILD combustion processes with recirculated flue gas, Rebola et al.19 reported that the state-ofthe-art RANS-based turbulence models yielded comparable results for this nonswirling recirculating flame, and the standard k−ε model showed the best conformity with measurements.20 Thus, in the present study, the turbulence is represented by the standard k−ε model. In terms of inlet turbulence intensity, the previous study19 reported that two different boundary conditions (5%, 10%) marginally influenced numerical results. Moreover, our recent computations indicate that the maximum difference in the predicted temperature field is roughly within 3% for two inflow intensities. Thus, for convenience of presentation, the discussions are made only for numerical results of 10% inlet turbulence intensity. The turbulence− chemistry interaction is modeled using the multi-environment

Figure 2. Predicted contours of the mean O2 mole fraction (left side) and temperature (right side) and predicted flow patterns (solid lines).

As displayed in Figure 2, the predicted streamlines clearly indicate that the high momentum of the preheated air jet due to high injection velocity in the sudden expansion geometry drives the large recirculation zone formed up to the near exit of the combustion chamber. In this flow reversal region, the hot combustion products generated in the downstream are recirculated and the injected air is diluted with these recirculated combustion products through the intense exchange of mass, momentum, and energy. Consequently, this process creates the MILD combustion condition by forming lowoxygen hot vitiated mixtures. In this MILD combustor, the hot walls play a certain role to maintain the relatively broad 8688

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Figure 3. Centerline profiles of the mixture fraction variance and scalar dissipation rate.

Figure 4. Predicted contours of the scalar dissipation rate (log scale) in the MILD combustion furnace.

uniformity of temperature field in the recirculation zone. Along the inner lean-side edge, autoignition takes place through the mixing process between the fuel mixture and the low-oxygen hot vitiated products, and then the subsequent MILD combustion processes occur. According to Wünning et al.,45 the MILD combustion processes were characterized by the recirculation rate, which is defined as the ratio of the mass flow rate of the recirculated exhaust gas to the mass flow rate of reactants. In this MEPDF approach, the calculated results indicate that the recirculation rate is increased by decreasing the micromixing constant. The recirculation rates for the three micromixing constants (0.15, 0.5, and 2.0) are 2.01, 1.94, and 1.82, respectively. Since the computed recirculation rates are higher than 1.9, especially for the relatively low micromixing constants (0.15, 0.5), these turbulent flow fields are accompanied by intense turbulent mixing between the recirculated combustion products and the preheated air before chemical reaction occurs. Through the corresponding strong entrainment process, the air jet is considerably diluted with the recirculated combustion products, and then combustion takes place at the mixture condition with a substantially low oxygen concentration. This is the essential

condition for establishing MILD combustion with the flameless oxidation process. Basically, the value of the mixing constant affects the level of scalar fluctuations, which are represented in terms of the mixture fraction variance and scalar dissipation rate. The distribution of the mixture fraction variance directly corresponds to the variation of the scalar dissipation rate (SDR). Figures 3 and 4 show the predicted centerline profiles of the SDR and mixture fraction variance as well as SDR contours for three different micromixing constants. These numerical results clearly indicate that the lower micromixing constant leads to the much longer penetration of vitiated mixture and the much higher scalar fluctuations in the inner central region. It can be also seen that the decreased micromixing constant leads to the elevation in the peak level of the mixture fraction variance and SDR. Thus, the micromixing constant substantially affects the SDR, which plays an important role in complex turbulent flame. In the MILD combustion situations, the SDR accounts for interaction between the nonequilibrium chemistry and turbulence. In the vicinity of the inlet, the gradient of the mixture fraction is drastically elevated and the intense turbulence is generated due to high velocity of preheated air. Consequently, the SDR abruptly increases to reach a peak level. 8689

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Figure 5. Predicted contours of the mean temperature and heat release rate in the MILD combustion furnace.

Figure 6. Predicted contours of the mean H2CO and OH mass fractions in the MILD combustion furnace.

indicate that, by decreasing the micromixing constant, the temperature level and the temperature gradient are decreased because of the increased recirculation rate. It is also found that the low-temperature central zone is expanded with a decrease of the micromixing constant because the autoignition time and the subsequent combustion process are progressively delayed due to much weaker mixing in the composition space. In contrast, the temperature in the hot flame zone increases with an increase of the micromixing constant. In terms of the heat release rate, the peak values for the three micromixing constants are placed at the downstream shear layer between the cold fuel mixture and the recirculated hot vitiated products. It is identified that the higher micromixing constant yields a much larger peak level and a relatively upstream distribution of the heat release rate. The largest mixing constant (2.0) yields the maximum heat release rate, which is 4 times larger than that of the intermediate mixing constant (0.5). Figure 6 presents the predicted contours of the H2CO and OH mass fractions in the MILD combustion furnace. Since formaldehyde (H2CO) is an important intermediate radical produced at the low-temperature region of hydrocarbon-fueled combustion, the region with an H2CO distribution could be roughly regarded as the location in proximity to the ignition

Shortly from the near-inflow region, the SDR gradually decreases to a low value in the downstream region. For SDR higher than a certain level, since the diffusion losses of radical species and heat in the reaction zone become much larger than radical formation and heat release induced by combustion, it is impossible to stabilize the flame. As the SDR gradually decreases, the residence time in a combustor becomes longer and a chemical reaction possibly occurs. At the lower SDR with the progressively small diffusion losses, radical species and heat generated by chemical reactions are gradually accumulated and the vitiated mixtures are eventually ignited. Thus, the flame in the MILD combustion condition is stabilized through the autoignition process along the inner lean-side edge where the SDR is lower than the certain level. Figures 5 and 6 show the overall distribution of the mean temperature, heat release rate, and H2CO and OH mass fractions for three micromixing constants (0.15, 0.5, and 2.0). As displayed in Figure 5, the present MEPDF approach with two of the micromixing constants (0.15, 0.5) predicts the broad hot zone with a relatively low temperature and temperature gradient. This trend is caused mainly by the strong entrainment of the combustion products as well as partly by heat exchange with the hot wall in the recirculation zone. Numerical results 8690

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Figure 7. Centerline profiles of mean temperature, heat release rate, and H2CO and OH mass fractions.

Figure 8. Predicted contours of the turbulence Damköhler number in the MILD combustion furnace.

sites.50,54 In the MILD combustion furnace, the peak H2CO level is mainly distributed at the inner lean side of the relatively downstream shear layer between the cold fuel mixture and the

recirculated vitiated products. In terms of the H2CO mass fraction, it is also found that a smaller micromixing constant generates a much lower peak level and a much broader 8691

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Energy & Fuels distribution. These results imply that the smallest micromixing constant (0.15) possibly generates the broadest ignition site. As illustrated in Figures 3 and 4, these trends are directly tied to the much longer penetration of vitiated mixture and the much higher scalar dissipation rate predicted by the smaller micromixing constant. Recently, Zhou et al.55 experimentally identified that MILD combustion mode generated the reaction zone with the more uniform distribution of OH radical. The present numerical results also reveal that the OH mass fraction starts to increase after the appearance of formaldehyde, which is mainly distributed in the outer hot zone of the reactant jet flow in the recirculation zone and the downstream region. In terms of the OH mass fraction, a lower micromixing constant produces a much lower peak level at the downstream nearcentral region and a much broader and uniform distribution in the recirculation zone. Figure 7 shows the centerline profiles of the mean temperature, heat release rate, and H2CO and OH mass fractions. In terms of temperature, heat release rate, and species mass fraction, a larger micromixing constant yields a much higher peak level as well as a more upstream creation of the peak level zone. It is also identified that the location of the peak heat release rate is close to the region with the rapid temperature rise and the peak OH level. In contrast, the peak H2CO level is placed at a more upstream region than the peak OH level. In terms of H2CO mass fraction, the smallest micromixing model constant results in a much lower peak level and a much broader distribution of H2CO mass fraction, representing a much wider centerline ignition site. In terms of the centerline profile of the mean temperature, the present approach considerably underestimates the temperature level at the upstream region, compared with measurements.19 These discrepancies are basically attributed to the shortcomings to correctly predict the turbulent mixing near the nozzle due to the limitation of the RANS-based turbulence model. Figure 8 shows the predicted contours of the turbulent Damköhler number for the three micromixing model constants. In terms of the turbulent Damköhler number, a smaller micromixing constant creates a much higher level and a much broader zone in the MILD combustion furnace. Since the recirculating rate is increased by decreasing the micromixing constant, the corresponding mixing time (residence time) is much longer for a smaller micromixing constant. In contrast, a smaller micromixing constant generally has a relatively long chemical time. However, the chemical times for three micromixing constants are slightly different at the hot flue gas recirculating zone and the far downstream region with the relatively high temperature while the residence time is much longer for the smaller micromixing constant. Thus, the highest Damköhler number for the smallest micromixing constant (0.15) is formed at the recirculating zone and the downstream region. Figure 9 shows the predicted and measured radial profiles for the mean temperature at five axial locations (x = 30, 90, 150, 210, and 270 mm) in the MILD combustion furnace.20 As displayed in Figure 9, the present MEPDF approach with the three micromixing constants considerably underestimates the temperature level at the central zones in the relatively upstream locations (x = 30, 90, and 150 mm). Similar deviations were predicted in the previous work19 using the standard k−ε turbulence model together with the EDC combustion model. These discrepancies could be mainly due to the weakness of the RANS-based turbulence model to predict the nonisotropic

Figure 9. Radial profiles of the predicted and measured mean temperatures at five axial locations.

turbulent highly entrained recirculating flow, especially at the upstream regions. However, at the flame field excluding the central region, the present MEPDF approach reproduces the measured temperature distribution reasonably well. In contrast, at further downstream locations (210, 270 mm), favorable agreement with measurements is obtained for the micromixing constant of 0.5, while substantial deviations exist for the micromixing constants of 0.15 and 2.0. The smallest micromixing constant (0.15) remarkably underestimates the temperature in the whole radial flame field, while the highest micromixing constant (2.0) greatly overestimates the temperature level due to excessive mixing in the composition space. Even if certain discrepancies at the upstream central zones exist, numerical results indicate that the multi-environment PDF model with the micromixing constant of 0.5 shows better conformity with the measured temperature profiles. 8692

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Energy & Fuels Figures 10 and 11 present the predicted and measured radial profiles of the mean O2 and CO2 mole fractions at five axial

Figure 11. Radial profiles of the predicted and measured mean CO2 mole fractions at five axial locations. Figure 10. Radial profiles of the predicted and measured mean O2 mole fractions at five axial locations.

downstream locations (210, 270 mm), favorable agreement with measurements is obtained for the micromixing constant of 0.5, while considerable deviations exist for the micromixing constants of 0.15 and 2.0. At the whole radial flame field of the further downstream location (x = 270 mm), the smallest micromixing constant (0.15) leads to overprediction of the O2 mole fraction and underestimation of the CO2 mole fraction. In contrast, the largest micromixing constant (2.0) shows an underestimated O2 mole fraction and an overestimated CO2 mole fraction. These numerical results indicate that the micromixing constant of 0.5 shows the best agreement with experimental data among the three micromixing constants. The MEPDF approach with the micromixing constant of 0.5 also yields numerical results comparable to those of the previous EDC model19 even if slight differences exist.

locations. At the central zones in the relatively upstream locations (x = 30, 90, and 150 mm), the present MEPDF approaches lead to overprediction of the O2 mole fraction and underestimation of the CO2 mole fraction. These tendencies are directly related to the underestimation of the mean temperature in the upstream locations. However, at the flame field excluding the central region, the present MEPDF approach with two of the micromixing constants (0.5, 2.0) yields comparable results with measurements.20 In contrast, the lowest micromixing constant (0.15) results in overestimation of the O2 mole fraction and underestimation of the CO2 mole fraction even at the outer radial flame field. At further 8693

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(0.15, 0.5), the EDC model of Rebola et al.19 unrealistically overestimated the peak CO level at all axial locations. Figure 13 shows the predicted and measured radial profiles of the mean NO mole fraction at five axial locations. At all axial

Figure 12 displays the predicted and measured radial profiles of the mean CO mole fraction at five axial locations. Unlike the

Figure 12. Radial profiles of the predicted and measured mean CO mole fractions at five axial locations. Figure 13. Radial profiles of the predicted and measured mean NO mole fractions at five axial locations.

profiles of temperature and major species mole fractions, much larger deviations exist between predictions and measurements. At two upstream locations (x = 30, 90 mm), the MEPDF approach with two of the micromixing constants (0.5, 2.0) reproduces the measured near-zero CO level reasonably well. At the other downstream locations (x = 150, 210, and 270 mm), the MEPDF approach with the three micromixing constants overestimates the peak CO levels, but they are still comparable to measurements. However, it is necessary to note that the predicted and measured peak CO mass fractions are at quite low levels within 0.5%. In contrast, compared to the MEPDF approach with two of the micromixing constants

stations except the near exit (x = 270 mm), the MEPDF approach with the micromixing constant (0.5) yields reasonably good overall agreement with the measured NO distribution. The NO level is considerably underestimated for the micromixing constant (0.15), and it is greatly overestimated for the micromixing constant (2.0). At the near exit (x = 270 mm), the MEPDF approach with two micromixing constants (0.5, 2.0) overestimates the NO levels at the whole radial field. However, it is necessary to note that the predicted and measured peak NO mole fractions are at quite low levels 8694

DOI: 10.1021/acs.energyfuels.7b01060 Energy Fuels 2017, 31, 8685−8697

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recirculation rates for the relatively low micromixing constants (0.15, 0.5) are higher than 1.9. Due to the strong entrainment process and flue gas recirculation, the high-speed air jet is considerably diluted with the recirculated combustion products, and then the combustion takes place at the mixture condition with a substantially low oxygen concentration. 2. In terms of the H2CO mass fraction, the smaller micromixing constant generates the lower peak level, wider distribution, and broader ignition site. These trends are directly tied to the much longer penetration of vitiated mixture and the much higher scalar dissipation rate predicted by the smaller micromixing constant. The lower micromixing constant produces a much lower OH peak level at the downstream near-central region and a much broader OH distribution in the recirculation zone. 3. Even if certain discrepancies at the upstream central zones exist, the multi-environment PDF model with the micromixing constant of 0.5 yields reasonably good conformity with the measured temperature profiles. In terms of the mean CO mole fraction, at all axial locations, overall agreement with the measurements is obtained for the micromixing constant of 0.5. However, the previous EDC approach unrealistically overestimates the peak CO level at all axial locations. 4. At all axial stations except the near exit, the MEPDF approach with the micromixing constant of 0.5 yields reasonably good overall agreement with the measured NO distribution. However, at all axial locations, the previous EDC model remarkably overestimates the radially distributed NO level compared to the MEPDF approach with the micromixing constants of 0.15 and 0.5. In terms of the integrated NO production rate in the MILD combustion condition, the N2O path yields the highest level, followed by the prompt, reburn, NO2, thermal, and NNH mechanisms.

(below 3.0 ppm) within the limit of experimental uncertainty. On the other hand, at all axial locations, the EDC model of Rebola et al.19 remarkably overestimates the radially distributed NO level compared to the MEPDF approach with the micromixing constants of 0.15 and 0.5. Figure 14 shows the

Figure 14. Integrated NO formation rate in the MILD combustion furnace.

integrated NO production rate via various NOx formation routes predicted by the MEPDF approach with the micromixing model constant of 0.5. This integrated NO production rate via various NO paths is evaluated by summing the product of each elementary reaction rate in the whole computational cell volume. In the combustion processes of hydrocarbon fuels, NOx is mainly formed or reduced by six chemical paths, including the thermal, prompt, N2O, NO2, NNH, and reburn routes. In terms of the integrated NO production rate, the N2O path yields the highest level, followed by the prompt, reburn, NO2, thermal, and NNH mechanisms in that order. Thus, the N2O mechanism plays the most important role in the NOx formation for these MILD combustion processes. The prompt route has a relatively high contribution in the total NO production rate. This trend is somewhat different from the previous results,19 which predicted a negligibly small contribution of the prompt NOx. These differences could be mainly caused by the different solution procedures for NOx emission. Previous studies19 adopted the post-treatment procedure to analyze the NOx formation characteristics. However, this post-treatment procedure is unable to accurately predict the NO level because all NO paths, except the thermal route, are strongly coupled with the detailed chemistry in the flame field. In contrast, in the present study, the NO formation characteristics are directly analyzed by the MEPDF approach together with the detailed chemistry. As would be expected, the NO production rate via the thermal mechanism is quite low. In the MILD combustion furnace, the peak temperature maintains a relatively low level which does not exceed 1450 K. Thus, the thermal NOx contribution is marginally small for the total NOx production rate.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.7b01060. Radial profiles of predicted and measured mean temperatures for two different numerical grids (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +82-2-2220-0428. Fax: +82-2-2297-0339. E-mail: [email protected]. ORCID

Yongmo Kim: 0000-0003-1292-1504 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This project is supported by the R&D Center for Reduction of Non-CO2 Greenhouse Gases (2013001690013) funded by the Korea Ministry of Environment (MOE) as a Global Top Environment R&D Program.

4. CONCLUSIONS The present study has employed the multi-environment probability density function approach to simulate turbulent CH4 flames under flameless combustion conditions with recirculated flue gases. Based on the numerical results, the following conclusions can be drawn: 1. By decreasing the micromixing constant, the recirculation rate and the temperature uniformity increase and the lowtemperature central zone is expanded. The computed

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