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Numerical Investigation of an OxyfuelNon-Premixed CombustionUsing a Hybrid Eulerian Stochastic Field/Flamelet Progress Variable Approach: Effects of H_{2}/CO_{2} Enrichment and Reynolds Number

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## Abstract

**:**

_{2}addition effect on the flame behaviour is demonstrated while studying a non-premixed oxy-flame configuration. This consists of an oxy-methane flame characterized by a high CO

_{2}amount in the oxidizer and a significant content of H

_{2}in the fuel stream, making it challenging for combustion modelling. Comparisons of numerical results with experimental data show that the complete model reproduces the major properties of the flame cases investigated and allows achieving the best agreement for the temperature and different species mass fractions once compared to the classical presumed PDF approach.

## 1. Introduction

_{2}emissions in the world [1].

_{2}and water vapor, from which, CO

_{2}can be easily separated enabling its capture, storage or recycling. It is characterized by a faster chemical reaction, higher adiabatic flame temperature and faster burning velocity, when compared to air combustion. Thereby, controlling and optimizing such processes is very important.

_{2}dilution effect on the flame behaviour of a non-premixed oxy-methane jet flame asexperimentally studied in reference [28]. It is characterized by a high CO

_{2}amount in the oxidizer and a significant content of H

_{2}in the fuel stream. In this environment, the flame becomes more prone to extinction, so that extra stabilization mechanisms for example by enriching the fuel stream with H

_{2}, appear mandatory. This results in a complex flow and mixing structure behaviour making it challenging for combustion modelling. Three aspects are especially investigated in the present paper, namely the impact of the addition of H

_{2}by comparing its enrichment in flames A1 and A3, the effect of high level dilution of CO

_{2}in oxidizer stream for all cases and the influence of the Reynolds number by comparing cases A1 and B3 from [28]. In fact, based on the experimental study by Sevault et al., and different studies reporting the carbon capture and storage technique, using O

_{2}/CO

_{2}mixtures instead of air for fuel combustion ideally produces water in exhaust gases, which can be easily separated by condensation and pure CO

_{2}that can be captured and stored. Following previous studies in references [29,30], it has been reported “that the molar percentage of oxygen in the oxidant should be around 30% to reach air flame stability.” Thereby in the experimental study on which the numerical work is based, for the oxidizer mixture, the oxygen percentage is set to 3% and consequently 68% of CO

_{2}is diluted.

## 2. Modelling Approach

#### 2.1. Reynolds Averaged Transport Equations

#### 2.2. Chemistry Modelling Using Flamelet/Progress Variable FPV Approach

_{2}% enrichment, the maximum value of heat release locally reaches 7.10

^{9}J/m

^{3}s. It is reduced to 5.10

^{9}J/m

^{3}s once the H

_{2}% enrichment is decreased to 37% in Flame A3 as shown in Figure 1b.

#### 2.3. Modelling of Turbulence-Chemistry Interaction

#### 2.3.1. Joint Probability Density Function and Eulerian Stochastic Field Method

#### 2.3.2. Presumed Probability Density Function Approach

#### 2.4. Numerical Set Ups

#### 2.4.1. Presumed PDF/FPV

#### 2.4.2. Eulerian Stochastic Field/FPV

## 3. Experimental Configurations and Case Setups

_{2}/CO

_{2}dilution in the oxidizer stream, of H

_{2}% enrichment in the fuel nozzle and of Reynolds numbers.

#### 3.1. Validation case: Sandia Flame D

_{fuel}= 0.0072 m and the bulk velocity equal to 49.6 m/s. The pilot jet is composed of lean (phi = 0.77) mixture of C

_{2}H

_{2}, H

_{2}, air, CO

_{2}and N

_{2}with the same nominal enthalpy and equilibrium composition as methane/air at this equivalence ratio. The experimental configuration is represented in Figure 2 where also a 2D computational domain with 32,000 control volumes used is shown. Thereby, the symmetry property of the configuration is exploited in order to save computational costs. The reader is referred to [27] for more details about the experimental set up. Table 1 summarizes the operating conditions in accordance with experiments.

^{−6}to ensure CFL-number below one. The convergence of the iterative procedure is assumed if all normalized residuals are smaller than 10

^{−6}. The calculations are achieved on 16 to 64 processors depending on the number of stochastic fields used (1 to 128SFi).

#### 3.2. Oxy-Fuel Jet Flame Series

_{2}content in the fuel jet helps the flame to remain attached to the nozzle. The fuel jet has its tip 40 mm above the coflow so that the mixed flows are considered fully developed once they reach the tip of the nozzle. Regarding the inlet compositions of the Oxyfuel flame, Table 2 summarizes the different compositions of the fuel for flames A1, A3 and B3 under investigation in the present paper. For the oxidizer stream, a molar percentage of 32% of O

_{2}and 68% of CO

_{2}-diluted are used rather than N

_{2}. As shown in Figure 3 the two jets are surrounded by a third co-flow which is considered as wind tunnel from where fresh air is flowing in order to accompany the flow of interest and prevent early mixing with ambient air. The third flow is for purely experimental reasons as clearly described in reference [28]. According to [28,50], using the O

_{2}/CO

_{2}mixtures instead of air for fuel combustion, the flame temperature can be reduced and NOx emissions are expected to be much lower than in air-diluted conditions. In particular, the composition of the fuel and oxidizer streams generates density fields very different to those found in methane-air flames.

^{−6}. Also in these cases, the convergence of the iterative procedure is assumed if all normalized residuals are smaller than 10

^{−6}.The number of CPU’s applied to carry out the simulations varies from 16 to 64 depending on the number of SFi employed (varying between 1 and 128SFi).

## 4. Results and Discussion

#### 4.1. Validation Case: Sandia Flame D

#### 4.2. Application to a Turbulent OxyfuelJet Flame

#### 4.2.1. Oxyflame B3 and Combustion Modelling Comparison

_{2}/CO

_{2}dilution and ofH

_{2}% content as well as the impact of the Reynolds number on the flow field and the flame properties using the novel hybrid ESF/FPV approach.

_{2}mass fraction in (b) are smooth and continuous. In Figure 6, the mean mixture fraction distribution and the mean axial velocity profile are displayed. From the contour plots, the flame seems to be attached to the nozzle of the burner by reason of important amount of diluted H

_{2}in the fuel mixture as it is mentioned in the experimental paper [28]. But unfortunately clear experimental qualitative images from the experiments are not available to be compared with the modelled contour-plots in Figure 5 and Figure 6.

_{2}and H

_{2}from the ESF/FPV calculation using different stochastic fields numbers, with experimental data is reported at 3 different axial positions (z/d = 3, z/d = 5 and z/d = 10). For the H

_{2}species, an acceptable agreement is clearly observed between the data at different positions for all SFi numbers. However, for the mean O

_{2}mass fraction prediction, the ESF/FPV calculations using high numbers of SFi are matching the experimental data, whilst there is an under-prediction of O

_{2}mass fraction with 1SFi results at z/d = 5 and z/d = 10. The deviation of the 1SFi results with respect to measurements is also visible in Figure 8 for the prediction of mean mass fraction of CO and H

_{2}O going from z/d = 3 to z/d = 10 for both species. These results are expected since using 1SFi means applying simple laminar FPV chemistry without any sub-grid model which is the similar behaviour of a perfectly stirred reactor. Increasing the number of SFi to 16 SFi leads to an under-prediction of both CO and H

_{2}O mass fraction at z/d = 10 while the cases using 48 and 128 SFi seem to be in very good agreement with experimental data further from the nozzle. This means that, the use of very high number of stochastic fields in the order of 128 is reproducing closely similar results to the case with 48 stochastic fields. This makes clear that the 48 SFi emerge as acomprise number between better prediction and computational costs. To note is that 128 SFi necessitate 64 CPUs while the 48 SFi only requires 32 CPUs.

_{2}O mass fraction once compared to experimental data. While the hybrid ESF/FPV reproduce closely the reference experimental data of the species, the assumed β-PDF approach suffers from some limitations due to intrinsic assumptions made, like the consideration of statistical independence between single PDF, along with the modelling applied to the source term during its calculation. This prediction failure of the presumed PDF method is also confirmed by the evolution of the mean temperature profile as function of the mixture fraction at z/d = 3 close to the fuel nozzle in Figure 9. In reference [28], the stoichiometric mixture fraction is reported as 0.056 with maximum adiabatic temperature around 1750 K. The hybrid ESF/FPV calculations reproduce a value of 1700 K for both simulations with 48 and 128 SFi. In contrast, the ß-PDF results clearly under-estimate the temperature evolution with a maximum value of 1300K.

#### 4.2.2. H_{2}% Enrichment in Fuel Side

_{2}% enrichment in the fuel side, with 55% and 37%, respectively. As reported in reference [28], the extinction level increases from flame A1 to A3 and its effect is reported together with the reduction of the mean temperature values around the stoichiometric mixture fraction as reproduced numerically at the axial positions z/d = 3 and z/d = 5 in Figure 10.

_{2}% enrichment is observed close to the nozzle from A1 to A3, this temperature difference disappears at positions far from the nozzle at z/d = 10 where the numerical prediction of the temperature profile of both flames leads to similar results. Unfortunately, experimental results of temperature at further positions, z/d$\ge $10, are not available as can be seen in Figure 10. Not only is the temperature’s peak value changing while reducing the H

_{2}% enrichment in the fuel for flame A3 at z/d = 3 but also the shifting of the maximum adiabatic temperature from stoichiometry toward rich side is visible. Further, Figure 11 presents the radial profiles of mean mass fraction of both CO and H

_{2}O.

_{4}/H

_{2}ratio, both CO and H

_{2}O productions are higher than in flame A3 at different axial positions in accordance with experimental findings. This is of interest despite that the Lewis number effect has not been included at the present stage of the FPV combustion model assuming Le = 1.

#### 4.2.3. CO_{2} Dilution in Oxidizer Side

_{2}amount diluted within the oxidizer is constant in flames A and B series and is about 68% which is quite a high level. This results in the high level of production of CO and H

_{2}O as it can be seen in Figure 11. For flame cases A1 and B3 which include both the same H

_{2}% enrichment in fuel side and same CO

_{2}dilution, the CO mass fraction locally reaches at z/d = 5 an amount of 0.14 and increases at z/d = 10 to reach 0.16 which is not a regular value for cases with air-diluted flames. This confirms previous finding by Masri et al in reference [51] who presumed that the CO

_{2}diluted in oxidizer is not inert and CO high level formation is the result of the reaction of CO

_{2}with H to form CO species. Therefore, the CO production level in flames A1 and B3 is manifestly higher than in A3 at all positions. Only the results with the hybrid ESF/FPV could reproduce this trend except for H

_{2}. Furthermore, the temperature is slightly reduced once compared to the air/methane flame.

#### 4.2.4. Reynolds Number Effect

_{4}/H

_{2}ratio in the fuel side but are characterized by different Reynolds numbers. From Figure 10, one can observe that the maximum adiabatic temperature location toward the mixture fraction space remains nearly the same for both flames at 3 and 10 diameters above the nozzle. However in Figure 11, there is a clear augmentation in the production of mean mass fraction of both CO and H

_{2}O species at the axial position z/d = 3 for flame A1 with lower Re-number. The difference of CO and H

_{2}O formation is reduced far from the nozzle. It turns out that the mixing state near the nozzle with lower jet Reynolds number likely leads to higher CO formation level. It turns out, that only the hybrid ESF/FPV is able to reproduce satisfactorily this trend.

## 5. Conclusions

_{2}diluted level in the oxidizer and different CH

_{4}/H

_{2}ratios, have been carried out using a novel hybrid Eulerian Stochastic Field (ESF)/Flamelet Progress Variable (FPV) combustion model within the RANS modelling framework. After a successful validation of the combustion model in the piloted CH4/Air jet flame, the combustion behaviour of an oxyfuel jet configuration featuring the flame series A1, A3 and B3 has been studied. These flames exhibit different CH

_{4}/H

_{2}and O

_{2}/CO

_{2}ratios in the fuel and oxidizer streams, respectively and are characterized by different Reynolds numbers. This study allowed for tracing the impact of these properties on the temperature profiles and the CO and H

_{2}O formation. The obtained results were compared to available experimental data and to achievements accomplished by using a presumed β-PDF combustion model. Following important conclusions can be drawn down:

- A good prediction of different experimental and flow field variables, is reported by using the novel ESF/FPV approach.
- Related to the convergence of the stochastic field number (SFi), it turned out that starting the calculations with 48 SFi emerged as the compromise between accurate prediction and computational costs.
- Comparing the two different PDF-based combustion models, it turned out that the hybrid ESF/FPV clearly showed superiority in better predicting the temperature, H
_{2}O mass fraction and specially CO mass fraction, unlike the presumed β-PDF model which under-estimates the maximum adiabatic temperature and over-predicts the CO formation level at different positions above the nozzle downstream. - With lower H
_{2}% enrichment in fuel side, fixed CO_{2}/O_{2}ratio and constant Reynolds number, the maximum adiabatic temperature value decreases in a significant manner near the fuel nozzle and its location in the mixture fraction space is shifted toward the reach side of the fuel. - With lower Reynolds number, constant CO
_{2}/O_{2}and CH_{4}/H_{2}ratios, the CO formation is considerably intensified near the nozzle.

_{2}differential diffusion effect which may affect the prediction of other minor species. The results reported in the present paper may suffer from the limitations of the RANS turbulence model used. The task of coupling the hybrid ESF/FPV approach with Large Eddy Simulation technique for more accurate prediction of the turbulence, along with the turbulence-chemistry interaction, is left for future research work.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${\mathrm{C}}_{f}$ | Model constant for mixture fraction variance |

${\mathrm{C}}_{\mathsf{\epsilon}1}$ | Model constant in dissipation rate equation |

${\mathrm{C}}_{\mathsf{\epsilon}2}$ | Model constant in dissipation rate equation |

${\mathrm{C}}_{\mathsf{\mu}}$ | Model constant |

${\mathrm{C}}_{\Phi}$ | Micro-mixing model coefficient |

$\mathrm{dW}$ | Wiener term |

f | Mixture fraction |

$\mathrm{F}$ | Joint probability density function |

${\mathrm{G}}_{\mathrm{k}}$ | Production of turbulence kinetic energy |

$\mathrm{K}$ | Turbulent kinetic energy |

$\mathrm{N}$ | Number of stochastic field |

${\mathrm{N}}_{\mathsf{\alpha}}$ | Number of the chemical table controlling variables |

$\mathrm{p}$ | Pressure |

$\mathrm{P}$ | Probability density function |

$\mathrm{Re}$ | Reynolds number |

${\mathrm{S}}_{\mathrm{ij}}$ | Strain rate tensor |

$\mathrm{t}$ | Time |

$\mathrm{T}$ | Temperature |

${\mathrm{U}}_{\mathrm{i}}$ | Velocity component in i^{th} direction |

$\mathrm{W}$ | Molar mass |

${\mathrm{x}}_{\mathrm{i}}$ | Positions coordinate in i^{th} direction |

$\mathrm{Y}$ | Mass fraction |

${\Delta}_{\mathrm{t}}$ | Time increment |

${\mathsf{\delta}}_{\mathrm{ij}}$ | Kronecker-symbol |

$\mathsf{\rho}$ | Density |

$\mathsf{\mu}$ | Dynamic molecular viscosity |

${\mathsf{\mu}}_{\mathrm{t}}$ | Dynamic turbulent viscosity |

$\mathsf{\sigma}$ | Schmidt number |

${\mathsf{\sigma}}_{\mathrm{t}}$ | Turbulent Schmidt number |

${\mathsf{\sigma}}_{\mathrm{k}}$ | Model constant |

${\mathsf{\sigma}}_{\mathsf{\epsilon}}$ | Model constant |

$\mathsf{\epsilon}$ | Dissipation rate of turbulent kinetic energy |

$\dot{\mathsf{\omega}}$ | Chemical source term |

$\Phi $ | General species variable |

$\mathsf{\delta}$ | Dirac delta function |

$\mathsf{\psi}$ | Composition space of species |

$\mathsf{\alpha}$ | Referring to table controlling variable |

${\mathsf{\xi}}_{\mathsf{\alpha}}^{\mathrm{n}}$ | n^{th} stochastic field of the variable $\mathsf{\alpha}$ |

$\tilde{(.)}$ | Favre weighted quantity |

$\overline{(.)}$ | Mean quantity |

T-PDF | Transported probability density function |

ESF | Eulerian Stochastic Field |

PV | Progress Variable |

FPV | Flamelet Progress Variable |

P-PDF | Presumed probability density function |

SDE | Stochastic differential equations |

RANS | Reynolds averaged Navier–Stokes |

CCS | Carbon Capture and Storage |

FGM | Flamelet Generated Manifold |

CMC | Conditional Moment Closure |

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**Figure 1.**Production rate of heat release in the mixture fraction space coloured with source term of the PV. (

**a**) distribution of heat release in Flames A1, B3 tables, (

**b**) distribution of heat release in Flame A3 table.

**Figure 2.**Sandia Flame-D configuration, (

**a**) Description of the piloted CH4/Air jet FlameD (

**b**) A 2D numerical block structured Grid.

**Figure 3.**Oxyfuel configuration (

**a**) Description of the Oxyfuel configuration according to the experimental set up in reference [28]. (

**b**) Inlets part from the 2D numerical block structured grid.

**Figure 4.**Comparison between experimental data for Flame-D [16] and RANS numerical results for different numbers of SFi at different axial positions; d = 1, d = 15 and d = 30, (

**a**) mean mixture fraction, (

**b**) rms of mixture fraction, (

**c**) mean temperature and (

**d**) mean velocity.

**Figure 5.**Contour plots from ESF/FPV simulation for Oxyfuelflame B3: (

**a**)Temperature distribution, (

**b**) meanCO

_{2}mass fraction.

**Figure 6.**Contour plots from ESF/FPV simulation for Oxyfuel flame B3: (

**a**) mean velocity, (

**b**) mixture fraction.

**Figure 7.**Mean O

_{2}(

**a**) and H

_{2}(

**b**) mass fraction from ESF/FPV simulation for different SFi at different axial positions in comparison with Raman/Rayleigh data of B3 from [28].

**Figure 8.**Mean CO (

**a**) and H

_{2}O (

**b**) mass fraction from ESF/FPV simulation for different SFi at different axial positions in comparison with Raman/Rayleigh data of B3 from [28].

**Figure 9.**Mean Temperature from ESF/FPV simulation for different SFi at axial position z/d = 3 in comparison with Raman/Rayleigh data of B3 from [28].

**Figure 10.**Mean temperature profile in mixture fraction space (

**a**) and H

_{2}mass fraction (

**b**) results from ESF/FPV simulation with 48 SFi at different axial positions for flame cases A1, A3 and B3 in comparison with β-PDF results and Raman/Rayleigh data from [28].

**Figure 11.**Mean CO (

**a**) and H

_{2}O (

**b**) mass fraction from ESF/FPV simulation with 48 SFi at different axial positions for flame cases A1, A3 and B3 in comparison with β-PDF results and Raman/Rayleigh data from [28].

Parameter | Fuel | Pilot | Co-Flow | Units |
---|---|---|---|---|

Mixture fraction | 0.156 | 0.043 | 0 | --- |

Progress variable | 0 | 7 | 0 | --- |

T | 294 | 1880 | 291 | K |

Velocity | 49.6 | 11.4 | 0.9 | m/s |

ν | 1.513 × 10^{−5} | m^{2}/s | ||

Reynolds Number | 22,000 | --- |

Flame | %H_{2} in Fuel | Re_{fuel} | Vel. Fuel [m/s] | Vel. Oxy [m/s] | PV_{Oxy} | ν [m ^{2}/s] |
---|---|---|---|---|---|---|

A1 | 55 | 15,000 | 84.4 | 0.775 | 0 | 3.271 × 10^{−5} |

A3 | 37 | 15,000 | 75.8 | 0.739 | 0 | 3.271 × 10^{−5} |

B3 | 55 | 18,000 | 117.8 | 0.933 | 0 | 3.271 × 10^{−5} |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mahmoud, R.; Jangi, M.; Fiorina, B.; Pfitzner, M.; Sadiki, A.
Numerical Investigation of an OxyfuelNon-Premixed CombustionUsing a Hybrid Eulerian Stochastic Field/Flamelet Progress Variable Approach: Effects of H_{2}/CO_{2} Enrichment and Reynolds Number. *Energies* **2018**, *11*, 3158.
https://doi.org/10.3390/en11113158

**AMA Style**

Mahmoud R, Jangi M, Fiorina B, Pfitzner M, Sadiki A.
Numerical Investigation of an OxyfuelNon-Premixed CombustionUsing a Hybrid Eulerian Stochastic Field/Flamelet Progress Variable Approach: Effects of H_{2}/CO_{2} Enrichment and Reynolds Number. *Energies*. 2018; 11(11):3158.
https://doi.org/10.3390/en11113158

**Chicago/Turabian Style**

Mahmoud, Rihab, Mehdi Jangi, Benoit Fiorina, Michael Pfitzner, and Amsini Sadiki.
2018. "Numerical Investigation of an OxyfuelNon-Premixed CombustionUsing a Hybrid Eulerian Stochastic Field/Flamelet Progress Variable Approach: Effects of H_{2}/CO_{2} Enrichment and Reynolds Number" *Energies* 11, no. 11: 3158.
https://doi.org/10.3390/en11113158