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Effect of free stream turbulence on NOx and soot formation in turbulent diffusion CH4-air flames
International Communications in Heat and Mass Transfer 37 (2010) 611–617
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International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Effect of free stream turbulence on NOx and soot formation in turbulent diffusion CH4-air flames☆ Khalid M. Saqr a,⁎, Hossam S. Aly b, Mohsin M. Sies a, Mazlan A. Wahid a a b
High-Speed Reacting Flow Laboratory, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai - Johor Bahru, Malaysia Department of Aeronautical Engineering, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai — Johor Bahru, Malaysia
a r t i c l e
i n f o
Available online 15 March 2010 Keywords: Turbulence Turbulent diffusion flames Pollutant formation Eddy dissipation model Mixing controlled reactions Co-flowing methane flame
a b s t r a c t A two-dimensional axisymmetric RANS numerical model was solved to investigate the effect of increasing the turbulence intensity of the air stream on the NOx and soot formation in turbulent methane diffusion flames. The turbulence–combustion interaction in the flame field was modelled in a k − ε/EDM framework, while the NO and soot concentrations were predicted through implementing the extended Zildovich mechanism and two transport equations model, respectively. The predicted spatial temperature gradients showed acceptable agreement with published experimental measurements. It was found that the increase of free stream turbulence intensity of the air supply results in a significant reduction in the NO formation of the flame. Such phenomenon is discussed by depicting the spatial distribution of the NO concentration in the flame. An observable reduction of the soot formation was also found to be associated with the increase of inlet turbulence intensity of air stream. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Recently, the effect of free stream turbulence on the structure of CH4air flames was reported by the authors [1]. The turbulence intensity of air stream supplied to the flame region was found to affect the shape and size of the reaction zone significantly, inducing flame extinguish at elevated values. The numerical simulation of the turbulent reaction zone revealed some information on the prominent dependency of the flame surface on the free stream turbulence compared to its dependence on the reaction induced turbulence. In the present study, the effect of turbulence intensity, introduced to the flame through the oxidizer stream, on the nitrogen oxides and soot particulate formation is investigated. The NO formation rate and flame thickness were predicted and examined firstly in 1981 by Hahn and Wendt for laminar flat opposed non-premixed methane jet flames. They have predicted the NO formation rate as a function of the flame stretching [2]. A decade later, with the large leap in computational power and technology, there have been intensive efforts to accurately predict the NOx and soot formation rates in non-premixed flames. Such efforts were also motivated by the growing environmental concerns about the ozone depletion and acid rain. Räkke et al. have presented simplified explicit expressions for local, instantaneous NO production rates [3]. Such expressions involved rate constants of only fourteen elementary steps in a two-reaction-zone description of the laminar flame. Chen and Chang have modelled NO formation in a turbulent, non-premixed jet flame using the joint scalar ☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail addresses: [email protected], [email protected] (K.M. Saqr). 0735-1933/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2010.02.008
probability density function (PDF) approach and the traditional flamelet model in 1996. They have evidently demonstrated that the radiative heat loss becomes increasingly important for NO predictions in the far field, and it can lower the predicted values by a factor of 3 leading to a better agreement with the experimental data [4]. The same approach was used by Yamashita et al. to present a new computational method that is able to predict the emission index of turbulent non-premixed flames [5]. Another new model was developed by Kok et al. in 1999 to predict turbulent non-adiabatic premixed gaseous combustion under gas turbine conditions [6]. Their model showed good agreement when compared with measured results of NOx and CO emissions. The mechanism of NOx formation in turbulent flames was investigated by Yamashita in 2000 [7]. By conducting a direct numerical simulation for a 2D fuel jet diffusion flame, Yamashita was able to verify that the formation of NOx in the turbulent flow field has the same mechanism as that in the unsteady laminar diffusion flame even for the case of extinction. Kim et al. used the Eulerian particle flamelet modelling (EPFM) to predict 2D and 3D recirculating flames [8]. They found that the EPFM correctly predicted conditional and unconditional mean scalar structures, and allowed a detailed analysis of NOx formation mechanisms including thermal NO path, prompt and fuel NO formation, and reburn by hydrocarbon radicals, unlike the steady flamelet model. Numerous researches have investigated the NOx formation in different combustion regimes in the consequent few years [9–17]. The most intensive work, recently, on the numerical simulation of NOx prediction in gaseous flames was published by Lopez-Parra and Turan [18–20]. They have used several numerical approaches to model the formation of thermal NOx, prompt NOx and their reburn rates of various diffusion flames. The present study aims to describe the effect of free stream turbulence of air in a co-flowing methane-air diffusion flame on the NOx
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Nomenclature Latin symbols Br Brinkman number (dimensionless) Specific heat at constant pressure for species k(kj kg− 1 Cpk k− 1) Constant, 1.44 Cε1 Cμ Constant, 0.09 Cε1 Constant, 1.92 De Effective diffusion coefficient (m2.s− 1) Dt Turbulent dilatation dissipation term E Stored energy per unit mass (kj kg− 1) fkj Volume force acting on species k in direction j (N) hk Sensible enthalpy of species k (kj kg− 1) ∘ hk Enthalpy of formation for species k(kj kg− 1) k Turbulence kinetic energy (TKE) (m2 s− 2) ke Effective conductivity (W m− 1 k− 1) Mk Molecular weight of species k(mol) Pk Turbulence production (kg m− 1 s− 3) p Pressure (Pa) R Universal gas constant (dimensionless) Rsoot rate of soot generation (kg.m− 3.s− 1) r Location on the radial (Y) direction (mm) r/R Dimensionless radial location SNO NO source term due to thermal NO formation T Temperature (k) V Overall velocity vector (m s− 1) Yk Mass fraction of species k (dimensionless) Greek symbols ε dissipation rate of turbulence kinetic energy (m2.s− 3) γ Isentropic expansion factor (dimensionless) σε Turbulent Prandtl number for ε, 1.3 (dimensionless) ω∘ k Reaction rate of species k(s− 1) μ Dynamic viscosity (kg m− 1 s− 1) τ Stress tensor as defined in [16] σk Turbulent Prandtl number for k, 1.0 (dimensionless) ρ Macroscopic density (kg m− 3) ψk Diffusion velocity of species k(m s− 1) μt Turbulent (eddy) viscosity ∂ ∂ ∇ Differential operator, i ∂x + j ∂y δ Kronecker tensorial symbol Abbreviations FST Free stream turbulence EDM Eddy dissipation model EPFM Eulerian particle flamelet modelling PDF Probability density function
and soot formation. The NOx and soot prediction models used in the present study have been thoroughly validated previously for the same type of flames [10,19,20]. A recent research examined the effect of fuel inlet flow perturbations on the NOx formation in methane-air diffusion flames [10]. Using a numerical methodology based on the k − ε and EDM turbulence and reaction models, respectively [10], it was evidently shown that a significant reduction in the NO and soot emissions can be achieved by such perturbations. However, to the best of our knowledge, there are no available data on the effect of air turbulence intensity on the NOx and soot formation in CH4-air diffusion flames.
sentation of the shear layer between the latter streams is the backbone for modelling the turbulence–reaction interaction in turbulent diffusion flames. In the present work, the turbulent interface between the fuel and air streams is predicted via the k − ε model [21,22]. The modelling of the chemical reaction in the diffusion flame, herein, is undertaken by solving additional transport equations for species conservation. The oxidation of methane in the present study is represented by a single-step reaction model. The definition of the reaction time scale is based on the work of Magnussen and Hjertager which represents the reaction time scale as a function of the large-eddy time scale [23]. The eddy dissipation model (EDM) quantifies the large-eddy time scale to be proportional to the ratio between the local turbulent kinetic energy and its dissipation rate. The modelling of thermal formation of NOx adopted the extended Zildovich mechanism, by which NO is formed by two-reaction expressions. The soot formation was predicted using the soot formation model proposed and validated by Brookes and Moss for turbulent diffusion flames. Their model is based on two transport equations for the normalized radical nuclei concentration and the soot mass fraction [24]. The intensity of the free stream turbulence is defined, in this study, as the ratio between the root mean square velocity fluctuations and the mean flow velocity. This quantity is the main variable in the present analysis. The formation of NOx and soot is monitored with different values of free stream turbulence intensity, which is varied as a boundary condition for the inlet air stream. 3. Flame configuration The flame configuration investigated herein is axisymmetric, coflowing turbulent methane diffusion jet flame. Methane is injected through a 4 mm diameter jet nozzle, concentric within a 1 m long annular burner. The flame configuration is illustrated in Fig. 1. The TKE of inlet air was varied from 20% to 80%, and it was set as a boundary condition in the four cases of analysis. The mass flow rate of methane and air was fixed at 1.72 × 10− 4 kg/s and 118 × 10− 4 kg/s for all cases, respectively. 4. Mathematical formulation The governing equations of the flow field are the reacting conservation equations in the XY Cartesian coordinates. The following assumptions are made to simplify the mathematical treatment of the problem: The reacting flow is assumed to be steady-state. The effect of gravity (i.e. buoyancy) is neglected. Radiation heat transfer is neglected. Combustion is assumed to be adiabatic (no heat transfer to surroundings). 5. Thermal energy created by viscous shear is neglected (Br bb 1.) 1. 2. 3. 4.
The governing equations, after simplification, are given below in their differential forms.
2. Modelling strategy In diffusion flames, the reaction zone is formed on the interface between the fuel and oxidizer streams. Therefore, the accurate repre-
Fig. 1. Flame configuration. Dimensions in mm.
K.M. Saqr et al. / International Communications in Heat and Mass Transfer 37 (2010) 611–617
613
μ ε ε2 ∇⋅ðρVεÞ = ∇⋅ μ + t ∇ε + Cε1 Pk −Cε2 ρ k σε k
4.1. Conservation of mass and species Total mass conservation:
ð12Þ
where
∇⋅ðρV Þ = 0
ð1Þ
2
μt = ρCμ
Mass conservation for species k ∘
∇⋅ðρðV + ψk ÞYk Þ = ωk
ð2Þ
∘
where ψk and ω k are the mass diffusion velocity and the reaction rate for species k, respectively. The diffusive term in the equation is subjected to
k εk and Dt = 2ρ γRT ε
ð13Þ
Turbulence intensity is expressed as V′ I= = Vavr
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3k u2 + v2
ð14Þ
4.5. Combustion modelling
N
∑ Yk ψk = 0
ð3Þ
k=1
and the reaction rate is governed by N
∘
∑ ωk = 0
ð4Þ
k=1
The present study adopts the eddy dissipation model in order to calculate the effect of turbulent chemical reaction rate. This model takes the minimum of the following rates as the local average reaction rate in equation [27]: ∘
ω
Fuel
4.2. Conservation of momentum for a reacting flow
= ρAYFuel
∘
ω
X direction: ∇⋅ðρuV Þ = −
Oxygen
N ∂τyx ∂p ∂τxx + + ρ ∑ Yk fkx + ∂x ∂y ∂x k=1
ð5Þ
Y direction: ∇⋅ðρvV Þ = −
∘
ω
Pr oducts
= ρA
=ρ
ε k
ð15Þ
YOxygen ε λ k
ð16Þ
A⋅B ε Y 1 + λ Pr oduct k
ð17Þ
4.6. NOx prediction model
∂τxy ∂τyy ∂p + + ρ ∑ Yk fky + ∂x ∂y ∂y k=1 N
ð6Þ
The extended Zildovich mechanism [29] describes the thermal formation of NOx in the following revisable reactions:
4.3. Conservation of energy
O þ N2 ↔N þ NO
ð18Þ
The following version of the energy equation was derived based on [25], [26] and [27]:
N þ O2 ↔O þ NO
ð19Þ
N þ OH↔H þ NO
ð20Þ
! ∘ N h ∘ ∇⋅ðV ðρE + pÞÞ = ∇⋅ ke ∇T− ∑ hk ψk + τ⋅V + ∑ k ωk ð7Þ k=1 k = 1 Mk N
where
The temporal rate constants for these reactions are given in [30]. These constants are in Table 1. Such constants are used to predict the NO mass fraction as a function of the oxygen, nitrogen and hydrogen concentrations. The transport equation for NO is:
2
E = h−
p V + ρ 2
N
T2
k=1
T1
h = ∑ Yk ∫ Cpk dT 2 1 T ∇⋅V + ∇⋅V τ = μ 2S− δ∇⋅V and S = 3 2
ð8Þ
∂ ðρYNO Þ + ∇⋅ðρVYNO Þ = ∇⋅ðρDe ∇YNO Þ + SNO ∂t
ð9Þ
4.7. Brookes and Moss soot prediction model
ð10Þ
4.4. Turbulence modelling The k − ε turbulence model presented by Launder and Spalding [21,22] is used to model the turbulent kinetic energy and its dissipation rate. Since the flow is treated according to the ideal gas flow, only the effect of thermal compressibility is considered to influence the dissipation of turbulent kinetic energy [28]. The turbulent kinetic energy is obtained from the following equation: μ ∇⋅ðρVkÞ = ∇⋅ μ + t ∇k + Pk −ρε−Dt σk
ð11Þ
ð21Þ
To the present moment, there is a considerable dispute over the mechanism of soot formation in turbulent diffusion flames. However, the sequence of soot particulate formation was generally classified into three phases; nucleation, surface growth and agglomeration [31]. In the fuel rich zones of the flame, the fuel exhibits pyrolysis, which
Table 1 Rate constants for the extended Zildovich reaction mechanism for NO formation. O + N2 → N + NO N + NO → O + N2 N + O2 → O + NO O + NO → N + O2 N + OH → H + NO H + NO → N + OH
R1 = 1.8 × 108e− 38,370/T R′1 = 3.7 × 107e− 425/T R2 = 1.8 × 104Te− 4680/T R′2 = 3.81 × 103Te− 20,820/T R3 = 7.1 × 107e− 450/T R′3 = 1.7 × 108e− 24,560/T
614
K.M. Saqr et al. / International Communications in Heat and Mass Transfer 37 (2010) 611–617
Fig. 2. Axisymmetric schematic of the cell size gradient.
results in the formation of soot particulates. Once these particulates are formed, they tend to absorb an important portion of the combustion heat, and transfer such heat by means of radiation to the surroundings. Thus, it is vital to couple the soot prediction model to the chemical reaction modelling mechanism, as well as to the heat transfer model [10]. The model used in the present study was presented in 1996 and it is based on two transport equations; one for the radical nuclei concentration and the other for the soot mass
fraction [32]. The model was built specifically for methane flames, such as the case in hand. The governing transport equations are: ∂ μt dMC ð22Þ ðρYSoot Þ + ∇⋅ðρVYSoot Þ = ∇⋅ ∇YSoot + σSoot dt ∂t ∂ ⁎ μt dNd ⁎ ⁎ ∇YNuc + ρYNuc + ∇⋅ ρVYNuc = ∇⋅ σNuc dt ∂t
‖ ‖
ð23Þ
Fig. 3. (a) Axial temperature, (b) radial temperature at 150 mm axial distance, (c) radial temperature at 200 mm axial distance and (d) radial temperature at 300 mm axial distance.
K.M. Saqr et al. / International Communications in Heat and Mass Transfer 37 (2010) 611–617
discretization of Eqs. (1)–(2), and (5)–(7) [33]. A momentumweighted averaging method was implemented in order to interpolate the cell-centre velocity values to the face values [34]. This technique aims to prevent the instability in the pressure calculations.
5. Numerical scheme The computational domain was spatially discretized to 20 × 103 variable density quadrilateral grid cells as in Fig. 2. The direction of cell size growth tends to locate the smallest cells in the region where the fuel interfaces with the air, hence, provides further accuracy for the solution of the flow field in the reaction zone. The reacting flow field variables in each cell were assumed to have an average value at the cell centre. This first order upwind scheme was used in order to calculate the pressure, velocity, and temperature through the
Fig. 4. Axial NO concentration at different radial distances (a)
615
6. Model validation In order to validate the numerical model, the predicted axial and radial temperature gradients are compared to flame temperature measurements reported by [24]. Fig. 3a–d shows the comparison
r R
= 0:0, (b)
r R
= 0:1, (c)
r R
= 0:3, (d)
r R
= 0:6 and (e)
r R
= 0:9.
616
K.M. Saqr et al. / International Communications in Heat and Mass Transfer 37 (2010) 611–617
between the two sets of results. The predicted axial temperature gradient shows satisfactory agreement with the measurements in terms of both trend and values. The radial temperature gradients, in the present flame, represent the breadth of the reaction zone of the flame. The predicted radial gradients of temperature imply a broader reaction zone, when compared to their corresponding measurements. As shown in Fig. 3b, the predicted and measured locations of maximum temperature are 25.2 and 16.1 mm, respectively. While the predicted and measured values of maximum temperature are 1897.19 and 1770.42 K, respectively. Such over-prediction is also detected when examining Fig. 3c and d. The authors estimate that the adiabatic flame assumption used in the predictions is the major reason behind such over predictions in the reaction zone size and maximum temperature. No heat transfer with the surroundings was permitted to take place in the numerical simulation. While in contrast, the flame experimental setup reported in [24] allowed heat transfer from the flame to the surroundings to occur. In addition, the predicted axial temperature gradient plotted in Fig. 3a is in good qualitative agreement with the predictions and measurements reported in [35]. 7. Results and discussion 7.1. Effect on NO formation The axial NO concentration at different radial distances is reported, as shown in Fig. 4a–d. It is clear that the increase in free stream turbulence (FST) intensity resulted in a significant reduction in both mean and local NO concentrations. When the FST intensity was increased from 20% to 40%, a noticeable reduction in the local NO concentration is observed in the flame, as in Fig. 4a–d. The magnitude of such reduction is less in the case where the FST increased from 40% to 60%. The maximum NO concentration, at the flame axis of symmetry, decreased from 194.74 ppm to 138.68 ppm when the FST increased from 20% to 40%, respectively. The location of the maximum NO concentration also retracted 0.12 m in the latter case. At different radial locations, the local concentration of NO exhibited a similar reduction in terms of magnitude and location of the maximum value. On the other hand, the increase in FST from 20% to 40% has yielded less reduction in the NO concentration. The reduction of NO concentration in proportion to the increase in turbulence intensity in the diffusion flame is, conceptually, in agreement with the results published in [10,18]. However, the spatial details of such reduction are different from the latter researches due to the alternation in the fuel type and other flame characteristics. 7.2. Effect on soot formation The increase in the free stream turbulence of air was found to reduce the rate of soot in the considered flame. In Fig. 5, the axial gradients of soot rate are plotted at two different radial distances. At the flame axis, the maximum rate of soot decreases from 0.066 kg.m–3.s–1 to 0.056 kg.m–3.s–1 when the free stream turbulence was increased from 20% to 60%, respectively. While at a higher location, as in Fig. 5b, the rate of soot decreased from 0.053 kg.m–3.s–1 to 0.044 kg.m–3.s–1 when the free stream turbulence was increased from 20% to 60%, respectively. The reduction in the soot formation, also, agrees with the results presented in [10], when fuel stream excitation was presented to a similar type of flame. The reduction in the soot rate due to the increase of air free stream turbulence intensity can be justified by one physical explanation. Such explanation is that the added turbulence intensity resulted in an enlargement in the mixing layer in the rich region of the flame, which in sequence increased the amount of oxidizer entrainment in such region.
Fig. 5. Axial gradients of soot rate at (a)
r R
= 0:0 and (b)
r R
= 0:1.
8. Conclusion A numerical analysis of the effect of free stream turbulence on the NOx and soot formation in the turbulent diffusion flame of CH4-air flame was presented. The mathematical treatment of the flame adopted the eddy dissipation model and the k − ε turbulence model to represent the interaction of turbulence and reaction in the flame. The numerical model was validated by comparing the temperature predictions with published measurements of local axial and radial flame temperatures. The investigation of the steady-state spatial distributions of NO and soot concentrations has revealed that the increase of turbulence intensity in the oxidizer (i.e. air) stream reduces the formation rate of both pollutants. This reduction was qualitatively and quantitatively reported by depicting the local concentration of NO and soot particulates in different regions of the flame. Acknowledgement Partial financial support was provided by the Malaysian Ministry of Higher Education (MOHE) through the FRGS project number 78358. References [1] K.M. Saqr, M.M. Sies, M. Abdulwahid, Numerical investigation of the turbulence– combustion interaction in non-premixed CH4-air flames, International Journal of Applied Mathematics and Mechanics 5 (8) (2009) 69–79.
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Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Effect of free stream turbulence on NOx and soot formation in turbulent diffusion CH4-air flames☆ Khalid M. Saqr a,⁎, Hossam S. Aly b, Mohsin M. Sies a, Mazlan A. Wahid a a b
High-Speed Reacting Flow Laboratory, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai - Johor Bahru, Malaysia Department of Aeronautical Engineering, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai — Johor Bahru, Malaysia
a r t i c l e
i n f o
Available online 15 March 2010 Keywords: Turbulence Turbulent diffusion flames Pollutant formation Eddy dissipation model Mixing controlled reactions Co-flowing methane flame
a b s t r a c t A two-dimensional axisymmetric RANS numerical model was solved to investigate the effect of increasing the turbulence intensity of the air stream on the NOx and soot formation in turbulent methane diffusion flames. The turbulence–combustion interaction in the flame field was modelled in a k − ε/EDM framework, while the NO and soot concentrations were predicted through implementing the extended Zildovich mechanism and two transport equations model, respectively. The predicted spatial temperature gradients showed acceptable agreement with published experimental measurements. It was found that the increase of free stream turbulence intensity of the air supply results in a significant reduction in the NO formation of the flame. Such phenomenon is discussed by depicting the spatial distribution of the NO concentration in the flame. An observable reduction of the soot formation was also found to be associated with the increase of inlet turbulence intensity of air stream. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Recently, the effect of free stream turbulence on the structure of CH4air flames was reported by the authors [1]. The turbulence intensity of air stream supplied to the flame region was found to affect the shape and size of the reaction zone significantly, inducing flame extinguish at elevated values. The numerical simulation of the turbulent reaction zone revealed some information on the prominent dependency of the flame surface on the free stream turbulence compared to its dependence on the reaction induced turbulence. In the present study, the effect of turbulence intensity, introduced to the flame through the oxidizer stream, on the nitrogen oxides and soot particulate formation is investigated. The NO formation rate and flame thickness were predicted and examined firstly in 1981 by Hahn and Wendt for laminar flat opposed non-premixed methane jet flames. They have predicted the NO formation rate as a function of the flame stretching [2]. A decade later, with the large leap in computational power and technology, there have been intensive efforts to accurately predict the NOx and soot formation rates in non-premixed flames. Such efforts were also motivated by the growing environmental concerns about the ozone depletion and acid rain. Räkke et al. have presented simplified explicit expressions for local, instantaneous NO production rates [3]. Such expressions involved rate constants of only fourteen elementary steps in a two-reaction-zone description of the laminar flame. Chen and Chang have modelled NO formation in a turbulent, non-premixed jet flame using the joint scalar ☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail addresses: [email protected], [email protected] (K.M. Saqr). 0735-1933/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2010.02.008
probability density function (PDF) approach and the traditional flamelet model in 1996. They have evidently demonstrated that the radiative heat loss becomes increasingly important for NO predictions in the far field, and it can lower the predicted values by a factor of 3 leading to a better agreement with the experimental data [4]. The same approach was used by Yamashita et al. to present a new computational method that is able to predict the emission index of turbulent non-premixed flames [5]. Another new model was developed by Kok et al. in 1999 to predict turbulent non-adiabatic premixed gaseous combustion under gas turbine conditions [6]. Their model showed good agreement when compared with measured results of NOx and CO emissions. The mechanism of NOx formation in turbulent flames was investigated by Yamashita in 2000 [7]. By conducting a direct numerical simulation for a 2D fuel jet diffusion flame, Yamashita was able to verify that the formation of NOx in the turbulent flow field has the same mechanism as that in the unsteady laminar diffusion flame even for the case of extinction. Kim et al. used the Eulerian particle flamelet modelling (EPFM) to predict 2D and 3D recirculating flames [8]. They found that the EPFM correctly predicted conditional and unconditional mean scalar structures, and allowed a detailed analysis of NOx formation mechanisms including thermal NO path, prompt and fuel NO formation, and reburn by hydrocarbon radicals, unlike the steady flamelet model. Numerous researches have investigated the NOx formation in different combustion regimes in the consequent few years [9–17]. The most intensive work, recently, on the numerical simulation of NOx prediction in gaseous flames was published by Lopez-Parra and Turan [18–20]. They have used several numerical approaches to model the formation of thermal NOx, prompt NOx and their reburn rates of various diffusion flames. The present study aims to describe the effect of free stream turbulence of air in a co-flowing methane-air diffusion flame on the NOx
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Nomenclature Latin symbols Br Brinkman number (dimensionless) Specific heat at constant pressure for species k(kj kg− 1 Cpk k− 1) Constant, 1.44 Cε1 Cμ Constant, 0.09 Cε1 Constant, 1.92 De Effective diffusion coefficient (m2.s− 1) Dt Turbulent dilatation dissipation term E Stored energy per unit mass (kj kg− 1) fkj Volume force acting on species k in direction j (N) hk Sensible enthalpy of species k (kj kg− 1) ∘ hk Enthalpy of formation for species k(kj kg− 1) k Turbulence kinetic energy (TKE) (m2 s− 2) ke Effective conductivity (W m− 1 k− 1) Mk Molecular weight of species k(mol) Pk Turbulence production (kg m− 1 s− 3) p Pressure (Pa) R Universal gas constant (dimensionless) Rsoot rate of soot generation (kg.m− 3.s− 1) r Location on the radial (Y) direction (mm) r/R Dimensionless radial location SNO NO source term due to thermal NO formation T Temperature (k) V Overall velocity vector (m s− 1) Yk Mass fraction of species k (dimensionless) Greek symbols ε dissipation rate of turbulence kinetic energy (m2.s− 3) γ Isentropic expansion factor (dimensionless) σε Turbulent Prandtl number for ε, 1.3 (dimensionless) ω∘ k Reaction rate of species k(s− 1) μ Dynamic viscosity (kg m− 1 s− 1) τ Stress tensor as defined in [16] σk Turbulent Prandtl number for k, 1.0 (dimensionless) ρ Macroscopic density (kg m− 3) ψk Diffusion velocity of species k(m s− 1) μt Turbulent (eddy) viscosity ∂ ∂ ∇ Differential operator, i ∂x + j ∂y δ Kronecker tensorial symbol Abbreviations FST Free stream turbulence EDM Eddy dissipation model EPFM Eulerian particle flamelet modelling PDF Probability density function
and soot formation. The NOx and soot prediction models used in the present study have been thoroughly validated previously for the same type of flames [10,19,20]. A recent research examined the effect of fuel inlet flow perturbations on the NOx formation in methane-air diffusion flames [10]. Using a numerical methodology based on the k − ε and EDM turbulence and reaction models, respectively [10], it was evidently shown that a significant reduction in the NO and soot emissions can be achieved by such perturbations. However, to the best of our knowledge, there are no available data on the effect of air turbulence intensity on the NOx and soot formation in CH4-air diffusion flames.
sentation of the shear layer between the latter streams is the backbone for modelling the turbulence–reaction interaction in turbulent diffusion flames. In the present work, the turbulent interface between the fuel and air streams is predicted via the k − ε model [21,22]. The modelling of the chemical reaction in the diffusion flame, herein, is undertaken by solving additional transport equations for species conservation. The oxidation of methane in the present study is represented by a single-step reaction model. The definition of the reaction time scale is based on the work of Magnussen and Hjertager which represents the reaction time scale as a function of the large-eddy time scale [23]. The eddy dissipation model (EDM) quantifies the large-eddy time scale to be proportional to the ratio between the local turbulent kinetic energy and its dissipation rate. The modelling of thermal formation of NOx adopted the extended Zildovich mechanism, by which NO is formed by two-reaction expressions. The soot formation was predicted using the soot formation model proposed and validated by Brookes and Moss for turbulent diffusion flames. Their model is based on two transport equations for the normalized radical nuclei concentration and the soot mass fraction [24]. The intensity of the free stream turbulence is defined, in this study, as the ratio between the root mean square velocity fluctuations and the mean flow velocity. This quantity is the main variable in the present analysis. The formation of NOx and soot is monitored with different values of free stream turbulence intensity, which is varied as a boundary condition for the inlet air stream. 3. Flame configuration The flame configuration investigated herein is axisymmetric, coflowing turbulent methane diffusion jet flame. Methane is injected through a 4 mm diameter jet nozzle, concentric within a 1 m long annular burner. The flame configuration is illustrated in Fig. 1. The TKE of inlet air was varied from 20% to 80%, and it was set as a boundary condition in the four cases of analysis. The mass flow rate of methane and air was fixed at 1.72 × 10− 4 kg/s and 118 × 10− 4 kg/s for all cases, respectively. 4. Mathematical formulation The governing equations of the flow field are the reacting conservation equations in the XY Cartesian coordinates. The following assumptions are made to simplify the mathematical treatment of the problem: The reacting flow is assumed to be steady-state. The effect of gravity (i.e. buoyancy) is neglected. Radiation heat transfer is neglected. Combustion is assumed to be adiabatic (no heat transfer to surroundings). 5. Thermal energy created by viscous shear is neglected (Br bb 1.) 1. 2. 3. 4.
The governing equations, after simplification, are given below in their differential forms.
2. Modelling strategy In diffusion flames, the reaction zone is formed on the interface between the fuel and oxidizer streams. Therefore, the accurate repre-
Fig. 1. Flame configuration. Dimensions in mm.
K.M. Saqr et al. / International Communications in Heat and Mass Transfer 37 (2010) 611–617
613
μ ε ε2 ∇⋅ðρVεÞ = ∇⋅ μ + t ∇ε + Cε1 Pk −Cε2 ρ k σε k
4.1. Conservation of mass and species Total mass conservation:
ð12Þ
where
∇⋅ðρV Þ = 0
ð1Þ
2
μt = ρCμ
Mass conservation for species k ∘
∇⋅ðρðV + ψk ÞYk Þ = ωk
ð2Þ
∘
where ψk and ω k are the mass diffusion velocity and the reaction rate for species k, respectively. The diffusive term in the equation is subjected to
k εk and Dt = 2ρ γRT ε
ð13Þ
Turbulence intensity is expressed as V′ I= = Vavr
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3k u2 + v2
ð14Þ
4.5. Combustion modelling
N
∑ Yk ψk = 0
ð3Þ
k=1
and the reaction rate is governed by N
∘
∑ ωk = 0
ð4Þ
k=1
The present study adopts the eddy dissipation model in order to calculate the effect of turbulent chemical reaction rate. This model takes the minimum of the following rates as the local average reaction rate in equation [27]: ∘
ω
Fuel
4.2. Conservation of momentum for a reacting flow
= ρAYFuel
∘
ω
X direction: ∇⋅ðρuV Þ = −
Oxygen
N ∂τyx ∂p ∂τxx + + ρ ∑ Yk fkx + ∂x ∂y ∂x k=1
ð5Þ
Y direction: ∇⋅ðρvV Þ = −
∘
ω
Pr oducts
= ρA
=ρ
ε k
ð15Þ
YOxygen ε λ k
ð16Þ
A⋅B ε Y 1 + λ Pr oduct k
ð17Þ
4.6. NOx prediction model
∂τxy ∂τyy ∂p + + ρ ∑ Yk fky + ∂x ∂y ∂y k=1 N
ð6Þ
The extended Zildovich mechanism [29] describes the thermal formation of NOx in the following revisable reactions:
4.3. Conservation of energy
O þ N2 ↔N þ NO
ð18Þ
The following version of the energy equation was derived based on [25], [26] and [27]:
N þ O2 ↔O þ NO
ð19Þ
N þ OH↔H þ NO
ð20Þ
! ∘ N h ∘ ∇⋅ðV ðρE + pÞÞ = ∇⋅ ke ∇T− ∑ hk ψk + τ⋅V + ∑ k ωk ð7Þ k=1 k = 1 Mk N
where
The temporal rate constants for these reactions are given in [30]. These constants are in Table 1. Such constants are used to predict the NO mass fraction as a function of the oxygen, nitrogen and hydrogen concentrations. The transport equation for NO is:
2
E = h−
p V + ρ 2
N
T2
k=1
T1
h = ∑ Yk ∫ Cpk dT 2 1 T ∇⋅V + ∇⋅V τ = μ 2S− δ∇⋅V and S = 3 2
ð8Þ
∂ ðρYNO Þ + ∇⋅ðρVYNO Þ = ∇⋅ðρDe ∇YNO Þ + SNO ∂t
ð9Þ
4.7. Brookes and Moss soot prediction model
ð10Þ
4.4. Turbulence modelling The k − ε turbulence model presented by Launder and Spalding [21,22] is used to model the turbulent kinetic energy and its dissipation rate. Since the flow is treated according to the ideal gas flow, only the effect of thermal compressibility is considered to influence the dissipation of turbulent kinetic energy [28]. The turbulent kinetic energy is obtained from the following equation: μ ∇⋅ðρVkÞ = ∇⋅ μ + t ∇k + Pk −ρε−Dt σk
ð11Þ
ð21Þ
To the present moment, there is a considerable dispute over the mechanism of soot formation in turbulent diffusion flames. However, the sequence of soot particulate formation was generally classified into three phases; nucleation, surface growth and agglomeration [31]. In the fuel rich zones of the flame, the fuel exhibits pyrolysis, which
Table 1 Rate constants for the extended Zildovich reaction mechanism for NO formation. O + N2 → N + NO N + NO → O + N2 N + O2 → O + NO O + NO → N + O2 N + OH → H + NO H + NO → N + OH
R1 = 1.8 × 108e− 38,370/T R′1 = 3.7 × 107e− 425/T R2 = 1.8 × 104Te− 4680/T R′2 = 3.81 × 103Te− 20,820/T R3 = 7.1 × 107e− 450/T R′3 = 1.7 × 108e− 24,560/T
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Fig. 2. Axisymmetric schematic of the cell size gradient.
results in the formation of soot particulates. Once these particulates are formed, they tend to absorb an important portion of the combustion heat, and transfer such heat by means of radiation to the surroundings. Thus, it is vital to couple the soot prediction model to the chemical reaction modelling mechanism, as well as to the heat transfer model [10]. The model used in the present study was presented in 1996 and it is based on two transport equations; one for the radical nuclei concentration and the other for the soot mass
fraction [32]. The model was built specifically for methane flames, such as the case in hand. The governing transport equations are: ∂ μt dMC ð22Þ ðρYSoot Þ + ∇⋅ðρVYSoot Þ = ∇⋅ ∇YSoot + σSoot dt ∂t ∂ ⁎ μt dNd ⁎ ⁎ ∇YNuc + ρYNuc + ∇⋅ ρVYNuc = ∇⋅ σNuc dt ∂t
‖ ‖
ð23Þ
Fig. 3. (a) Axial temperature, (b) radial temperature at 150 mm axial distance, (c) radial temperature at 200 mm axial distance and (d) radial temperature at 300 mm axial distance.
K.M. Saqr et al. / International Communications in Heat and Mass Transfer 37 (2010) 611–617
discretization of Eqs. (1)–(2), and (5)–(7) [33]. A momentumweighted averaging method was implemented in order to interpolate the cell-centre velocity values to the face values [34]. This technique aims to prevent the instability in the pressure calculations.
5. Numerical scheme The computational domain was spatially discretized to 20 × 103 variable density quadrilateral grid cells as in Fig. 2. The direction of cell size growth tends to locate the smallest cells in the region where the fuel interfaces with the air, hence, provides further accuracy for the solution of the flow field in the reaction zone. The reacting flow field variables in each cell were assumed to have an average value at the cell centre. This first order upwind scheme was used in order to calculate the pressure, velocity, and temperature through the
Fig. 4. Axial NO concentration at different radial distances (a)
615
6. Model validation In order to validate the numerical model, the predicted axial and radial temperature gradients are compared to flame temperature measurements reported by [24]. Fig. 3a–d shows the comparison
r R
= 0:0, (b)
r R
= 0:1, (c)
r R
= 0:3, (d)
r R
= 0:6 and (e)
r R
= 0:9.
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between the two sets of results. The predicted axial temperature gradient shows satisfactory agreement with the measurements in terms of both trend and values. The radial temperature gradients, in the present flame, represent the breadth of the reaction zone of the flame. The predicted radial gradients of temperature imply a broader reaction zone, when compared to their corresponding measurements. As shown in Fig. 3b, the predicted and measured locations of maximum temperature are 25.2 and 16.1 mm, respectively. While the predicted and measured values of maximum temperature are 1897.19 and 1770.42 K, respectively. Such over-prediction is also detected when examining Fig. 3c and d. The authors estimate that the adiabatic flame assumption used in the predictions is the major reason behind such over predictions in the reaction zone size and maximum temperature. No heat transfer with the surroundings was permitted to take place in the numerical simulation. While in contrast, the flame experimental setup reported in [24] allowed heat transfer from the flame to the surroundings to occur. In addition, the predicted axial temperature gradient plotted in Fig. 3a is in good qualitative agreement with the predictions and measurements reported in [35]. 7. Results and discussion 7.1. Effect on NO formation The axial NO concentration at different radial distances is reported, as shown in Fig. 4a–d. It is clear that the increase in free stream turbulence (FST) intensity resulted in a significant reduction in both mean and local NO concentrations. When the FST intensity was increased from 20% to 40%, a noticeable reduction in the local NO concentration is observed in the flame, as in Fig. 4a–d. The magnitude of such reduction is less in the case where the FST increased from 40% to 60%. The maximum NO concentration, at the flame axis of symmetry, decreased from 194.74 ppm to 138.68 ppm when the FST increased from 20% to 40%, respectively. The location of the maximum NO concentration also retracted 0.12 m in the latter case. At different radial locations, the local concentration of NO exhibited a similar reduction in terms of magnitude and location of the maximum value. On the other hand, the increase in FST from 20% to 40% has yielded less reduction in the NO concentration. The reduction of NO concentration in proportion to the increase in turbulence intensity in the diffusion flame is, conceptually, in agreement with the results published in [10,18]. However, the spatial details of such reduction are different from the latter researches due to the alternation in the fuel type and other flame characteristics. 7.2. Effect on soot formation The increase in the free stream turbulence of air was found to reduce the rate of soot in the considered flame. In Fig. 5, the axial gradients of soot rate are plotted at two different radial distances. At the flame axis, the maximum rate of soot decreases from 0.066 kg.m–3.s–1 to 0.056 kg.m–3.s–1 when the free stream turbulence was increased from 20% to 60%, respectively. While at a higher location, as in Fig. 5b, the rate of soot decreased from 0.053 kg.m–3.s–1 to 0.044 kg.m–3.s–1 when the free stream turbulence was increased from 20% to 60%, respectively. The reduction in the soot formation, also, agrees with the results presented in [10], when fuel stream excitation was presented to a similar type of flame. The reduction in the soot rate due to the increase of air free stream turbulence intensity can be justified by one physical explanation. Such explanation is that the added turbulence intensity resulted in an enlargement in the mixing layer in the rich region of the flame, which in sequence increased the amount of oxidizer entrainment in such region.
Fig. 5. Axial gradients of soot rate at (a)
r R
= 0:0 and (b)
r R
= 0:1.
8. Conclusion A numerical analysis of the effect of free stream turbulence on the NOx and soot formation in the turbulent diffusion flame of CH4-air flame was presented. The mathematical treatment of the flame adopted the eddy dissipation model and the k − ε turbulence model to represent the interaction of turbulence and reaction in the flame. The numerical model was validated by comparing the temperature predictions with published measurements of local axial and radial flame temperatures. The investigation of the steady-state spatial distributions of NO and soot concentrations has revealed that the increase of turbulence intensity in the oxidizer (i.e. air) stream reduces the formation rate of both pollutants. This reduction was qualitatively and quantitatively reported by depicting the local concentration of NO and soot particulates in different regions of the flame. Acknowledgement Partial financial support was provided by the Malaysian Ministry of Higher Education (MOHE) through the FRGS project number 78358. References [1] K.M. Saqr, M.M. Sies, M. Abdulwahid, Numerical investigation of the turbulence– combustion interaction in non-premixed CH4-air flames, International Journal of Applied Mathematics and Mechanics 5 (8) (2009) 69–79.
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