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Numerical study of the effect of H2O diluents on NOx and CO formation in turbulent premixed methane-air flame
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Numerical study of the effect of H2O diluents on NOx and CO formation in turbulent premixed methane-air flame Mohsen Nasiri Soloklou, Ali Akbar Golneshan* Thermo-fluids department school of mechanical engineering, Shiraz University, Shiraz, Fars, 71348-51154, Iran
highlights kε/EDM framework is used to study turbulence combustion. The energy absorbed by H2O leads to a severe decrease in temperature. Using H2O diluent leads to reduction in the amount of NOx and CO emissions. By increasing the H2O diluent, enclosures with smaller length can be utilized.
article info
abstract
Article history:
The interaction of turbulenceecombustion inside the flame field is studied in a Launder-
Received 19 July 2019
Sharma Low Reynolds Number (LS-LRN) kε/EDM framework, while suitable coefficients
Received in revised form
have been utilized in the code. A finite volume method (FVM) with staggered grids was
1 October 2019
applied to discrete set of governing equations. SIMPLE algorithm is applied with a fine grid
Accepted 3 October 2019
resolution. The convective terms are discretized using Power Law Scheme (PLS). The sys-
Available online 4 March 2020
tem of governing equations is solved simultaneously using numerical or TDMA finite difference methods (Tri-Diagonal Matrix Algorithm). By implementation of the Zeldovich and
Keywords:
Westbrook-Dryer mechanisms, NOx and CO concentrations were obtained, respectively. It
Turbulent flame
is illustrated that the implemented LS-LRN-kε/EDM method with the new coefficients by
H2O diluent
shorter runtimes has very good agreement with previously published experimental mea-
Pollutant reduction
surements. Increasing the H2O diluent at the inlet leads to an increase in the temperature,
Launder-sharma low Reynolds kε/
which increases the NOx and CO near the entrance, but gradually towards the outlet of the
EDM
combustion chamber. The energy absorbed by H2O leads to a severe decrease in temperature and subsequent reduction in the amount of NOx and CO emissions. With increasing H2O diluent, changes in temperature are not very significant, while changes in pollutants CO and especially NOx, are remarkable. With the increase of H2O diluent, the maximum amount of CO emission displaces towards the inlet of the combustion chamber. However, it should be noted that, at a specific value of H2O diluent, the length of the combustion chamber should not be less than critical value, causing the exhaust of the pollutant with large volume to the environment. After the critical point, the increase in the length of the chamber has little effect on reduction of the pollutant exhaust. However, by increasing the H2O diluent, enclosures with smaller length can be utilized. © 2019 Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.
* Corresponding author. E-mail address: [email protected] (A.A. Golneshan). https://doi.org/10.1016/j.ijhydene.2019.10.083 0360-3199/© 2019 Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 5 ( 2 0 2 0 ) 1 0 8 8 2 e1 0 8 9 4
Introduction In recent decades more attention has been payed to the need for cleaner combustion systems satisfying the energy requirements of human being. By premixing the fuel and oxidizer uniformly prior to combustion, premixed combustion systems lead to improved combustion efficiency and fewer formations of NOx. Improvement of the combustion systems is very significant, specially to avoid combustion instabilities [1,2] and reduction of the pollutant emissions [3e5]. Numerous studies have reported the NOx formation in various combustion regimes [6e10]. Hahn and Wendt [11] examined the flame thickness and NO formation rate of non-premixed methane jet flames. The flame thickness and NO formation rate of non-premixed methane jet flames. They stated that NOx formation rate is a function of the flame stretching. Saqr et al. [12] conducted a numerical study of the effect of free stream turbulence on the NOx in the turbulent flame of CH4air. It was shown that the increase of turbulence intensity in the air stream results in the reduction of the formation rate of pollutants. Shaw [13] studied the effect of dilution with water and the simultaneous effect of pressure on combustion parameters and production of nitrogen monoxide in both kinetic and equilibrium states. He argued that in some cases with processes based on equilibrium, calculations are not valid and contradict the results of kinetic states. In addition, it was shown that increasing the water vapor causes a reduction in the production of nitrogen monoxide in the combustion chamber. Greeves et al. [14] carried out an experimental investigation of carbon monoxide and nitrogen monoxide reduction by injection of water into the combustion chamber in three ways of injecting water into the air, injecting water into fuel and injecting water directly into the compartment. They showed that injection of water in fuel have had more effect on reducing the amount of carbon monoxide and nitrogen monoxide compared to injection of water in air or direct water injection into the combustion chamber. Burnham et al. [15] aimed to reduce the emission of pollutants by an experimental investigation of water vapor injection into a gas turbine, containing natural gas. Their results showed that water vapor injection is an effective and practical way to reduce the production of carbon monoxide in the combustion chamber. Two-tube nozzles were used in this experiment. Vapor and fuel were introduced into the combustion zone through the external nozzles and through the inner nozzles, respectively. Feitelberg et al. [16] investigated the effect of excessive vapor and air on the combustion emissions. They reduced the temperature in the combustion chamber by diluting the fuel with additional air. They observed that the amount of nitrogen monoxide contaminants was decreased. Moreover, these experiments carried out by injection of vapor as the diluent. Comparison of the results in the cases of with and without injection of water vapor indicated that vapor injection at high temperatures reduces the NOx production, remarkably. Gokke et al. [17] examined the combustion of natural gas and hydrogen in the conditions of with and without vapor injection in different equivalence ratios in the turbulent pre-mixed flame. They measured the shape and position of the flame experimentally. They showed that the
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addition of water vapor to the fuel has a significant effect on reducing the emissions of nitrogen monoxide in the combustion chamber. The method of vapor injection into a premixed flame is called Cheng Low NOx (CLN) method. This method was first introduced by Cheng [18]. Cheng claimed that the pre-mixing of water vapor with fuel, in addition to reducing the temperature, diminishes the combustion zone of nitrogen oxide formation and consequently, reduces the mass fraction of nitrogen oxide compared to the method of water vapor injection into the non-premixed flame. Zhou et al. [19] investigated the effect of adding water vapor into the combustion chamber on pressure, temperature and local Mach number parameters by the method of equilibrium analysis. They showed that by injecting water vapor, the temperature of every point through the combustion chamber reduces. In their paper, it was shown that an increase in the amount of injected water vapor has a small effect on reducing the temperature of the chamber and under these conditions, the temperature drop occurs with a slight slope. They also showed that decreasing the temperature leads to decreasing the amount of nitrogen monoxide produced in the combustion chamber. Pugh et al. [20] investigated the effect of water vapor injection into a pre-mixed turbulent flame. Their examination was carried out in the range of equivalence ratio from 0.6 to 0.8. They showed that water vapor injection has a significant effect on the fuel consumption and flame velocity. They also showed that the injection of water vapor reduces the temperature of the chamber. Consequently, it reduces NOx production in the combustion chamber. Dai et al. [21] studied combustion characteristics of a methane flame in hot co-flow diluted by H₂O versus the case by N2. It was shown that by changing the diluent from N2 to H₂O, both the temperature and the dimension of the flame reduce remarkably. Our aim in this work is to predict the pollutants of a turbulent flame by utilizing a code written based on eddy dissipation model (EDM) based on the new coefficients. Our code is able to model turbulent and premixed CH4 flame with reasonable runtimes and it shows good agreement with previously reported experimental results in a RANS environment. In this study, the k ε/EDM combustion model (LS-LRN) was used to model the combustion chamber, which has not been reported in other studies. For the first time, we have investigated the details of the temperature distribution and the modifications of both CO and NOx pollutants simultaneously by injecting different amounts of H2O diluent in the dilution range of zero to 0.03. Moreover, by varying the diluent values, the geometrical relationship between the combustion chamber and the distribution of CO and NOx pollutants is depicted. Furthermore, the effect of H₂O dilution on the temperature distribution, axial velocity, NOx and CO concentrations through the combustion chamber has been examined.
Problem statement and mathematical formulation In this work, we have considered the combustion chamber studied by Banhawy et al. [22] with a rectangular cross section. The mixture of air and fuel methane enters a mixing compartment with various equivalence ratios and goes
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through a flow strainer before entering the combustion chamber. The dimensions of the combustion chamber are 0.47 m 0.157 m 0.04 m, with a h ¼ 0.02 m step at the entry of the combustion chamber, causing the expansion of the flow. The Reynolds number of the mixture, based on the step height as characteristic length is 1:35 104 . The mixture of gas and air entering the combustion chamber with temperature of 300 K. The top and bottom walls cool down by water and maintained at a constant temperature of 300 K. Due to much longer channel width compared to its height, the studied flow can be considered as two-dimensional. The following assumptions are considered in this work: 1. The flow is steady-state and two-dimensional. 2. The pressure inside the combustion chamber is considered to be constant. 3. The ideal gas state equation is governed for every species of reactants and products. 4. Thermodynamic properties of species, density and viscosity of fluid are functions of temperature. 5. The effect of buoyancy is neglected. 6. It is assumed that no radiation heat transfer exists. 7. The walls are maintained at a constant temperature of 300 K. 8. Using the Boussinesq.approximation [23] that the momentum transfer caused by turbulent eddies can be modeled with an eddy viscosity. After considering the mentioned simplifications, the governing equations will be as follows: v rUj ¼ 0: v Xj
Continuity
v rUi Uj vP v ¼ þ v Xj v Xi v Xj v Ui Conservation of momentum ðm þ mt Þ v Xj
(1)
(2)
v r Ya Uj v m v Ya ¼ rDam þ t v Xj v Xj sy v Xj þ u_ a
Mass conservation for species i
p ¼ rRT
Conservation of energy X Ya Ma
State equation
v rUj k v m vk ¼ mþ t þ Pk r ε Dt rD v Xj sk v Xj v Xj
(6)
Turbulent dissipation rate
v rUj ε v m vε ε ¼ mþ t þ f 1 Cε1 Pk f 2 Cε2 r ε þ rE vXj k sε vXj vXj
(7)
Relations (6) and (7) contain a set of variables whose values are calculated from the following relationships. 2
mt ¼ r C m f m
k ε
εk Dt ¼ 2r gRT
pffiffiffi!2 2 2 v k v Ui E ¼ 2yyt vXj vXk vXj vUj vUi vUj Pk ¼ mt þ v Xi v Xj v Xi
D ¼ 2y
(8)
D and E are included in the low Reynolds closure models in order to render the models valid to the wall. And mt , Dt and Pk are turbulent viscosity, Compressibility effect and turbulent kinetic energy produced items, respectively.where: 2
Rt ¼
k ; yε
3:4
f 1 ¼ 1:
f 2 ¼ 1 0:3exp R2t ;
2 Rt 1þ 50
f m ¼ exp (9)
In this case, y and yt are Molecular kinematic viscosity and Turbulence kinematic viscosity, respectively. And g is specific heat ratio. And Dt is defined as the turbulent dilatation dissipation term. f m , f 1 and f 2 are vary with the given models, which f m , f 1 and f 2 are the local turbulent model damping functions. The constants used in this model are as follows [24]: Cm ¼ 0:09 Cε1 ¼ 1:44 Cε2 ¼ 1:92 sε ¼ 1:3 sy ¼ 0:7 st ¼ 0:9
(10)
where Cm , Cε1 , Cε2 , sε , sy and st are the same empirical constant found in the Launder-Sharma Low Reynolds model [23]. (3)
Boundary conditions
N v r Uj T v l mt v T 1 X ¼ þ u_ i v Xj Cp st v Xj Cp i¼1 v Xj 0 hf;a
Launder-Sharma Low Reynolds model [24] leads to the turbulent kinetic energy. Fluid compressibility properties alter only in the dissipation of turbulent kinetic energy [25] due to the assumption of ideal gas for the fluid. Turbulent kinetic energy:
(4)
(5)
In this case, i and j are coordinate components along X and Y. And Uj , T, Ya and u_ a , respectively, are the average velocity, average pressure, average temperature, average of mass fraction of the species, and the average of net production rate of the chemical component. Also r: density, Ya mass fraction of chemical species a, Cp : average specific heat capacity at constant pressure, l: thermal conductivity coefficient, R: constant gases for a species, Ma : molecular mass of species a, 0 hf;a : enthalpy Formation of the standard of the a species.
The boundary conditions for the domain in the combustion chamber, surrounded by solid wall are as follows [26]: Inlet ð0 y 0:02 mÞ ðx ¼ 0Þ : Tin ¼ 300: K
YinCH4 ¼
0:055 S þ 1: S S þ 1:
Re ¼ 1:35 104
YinH2 O ¼
Iinlet ¼ 0:16Re0:125
YinCO2 ¼ 0:0
3 0:22 kinlet ¼ ðuinlet Iinlet Þ2 YinO2 ¼ 2 S þ 1: 1:5
εinlet ¼
0:164 kinlet 0:07Dh
YinN2 ¼
0:725 S þ 1:
(11)
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Definition of S for H2O as diluents: S ¼ f0:0; 0:01; 0:02; 0:03g QUOTE Side wall of combustion chamber ð0:02 m y 0:04 mÞ ux ¼ 0;
uy ¼ 0;
T ¼ 300 K;
vYa vx ¼ 0 ; a ¼ 1; 2; …; I
(12)
Outlet of combustion chamber ðx ¼ 0:470 mÞ : uy ¼ 0;
vux vx ¼ 0;
vT vx ¼ 0;
vYa vx ¼ 0 ; a ¼ 1; 2; …; I (13)
Walls ðy ¼ 0:0 mÞ and ðy ¼ 0:04 mÞ ux ¼ 0;
uy ¼ 0;
T ¼ 300 K;
vYa vx ¼ 0 ; i ¼ 1; 2; …; I
(14)
The values of kinlet and εinlet , respectively, are the inlet kinetic energy of turbulence and the inlet kinetic energy dissipation of turbulence. In the above equations Iinlet is the turbulence intensity and the Dh is hydraulic diameter. Re is also the Reynolds number of the input current. And Yin is the value of concentration of species at inlet. All of the units are based on meters and Kelvin.
Combustion modeling The eddy dissipation model is applied for the calculation of the effect of turbulent chemical reaction rate. The minimum of the following rates as the local average reaction rate in equation is taken [27]: Net mean rate of the fuel: u_ F ¼ rAYF
ε k
(15)
by Zeldovich mechanism [29]. and rate constants for these reactions are calculated by Hanson and Salimian [30]. The first reaction shows the Chemical breakdown of the nitrogen molecule. The second reaction has high activation energy and the limiting factor of the reaction rate in the Zeldovich mechanism. The third reaction is important under conditions of rich fuel and close to stoichiometric values. Due to the strength of the triple bond in the nitrogen molecule, high energy is needed to break this bond and this is the main cause of NOx thermal production at high temperatures. Also, if there is enough oxygen in the fuel with high temperatures the combined nitrogen and oxygen demand increases and a pseudo-equilibrium state for free nitrogen production and consumption is obtained. This pseudo-equilibrium assumption in dilute fuels is assumed to be correct. Therefore, the NO formation rate can be calculated as follows.
2
k2 ½NO 1 kk1 1 ½N2 k2 ½O2
d½NO ¼ 2k1 ½O½N2 dt ½NO 1 þ k2 ½Ok1 2 þk3 ½OH
(20)
In this equation, a partial equilibrium method is used to determine the concentration of O and OH radicals and the values of these concentrations are calculated as follows [31,32]. 27123 ½O ¼ 36:34T0:5 ½O2 0:5 exp T
(21)
4595 ½OH ¼ 2:129 103 T0:57 ½O0:5 ½H2 O0:5 exp T
(22)
Net mean rate of the oxidizer: (16)
Net mean rate of the production: u_ Pr ¼ r
A:B ε YPr 1 þ St k
(17)
YF is Mass fraction of fuel, YOx is Oxidizing mass fraction, YPr is mass fraction of combustion products, St is Stoichiometric ratio of oxidizing mass to fuel mass. A is a fixed model with a standard value of 4. In this paper, this numerical constant is equal to 1. And B is fixed at 0.5 [28].
To include NO formation for this type of flame, the thermal mechanisms are employed [36]. The transport equation for NO can be written as follows: (18)
in which, YNO , De , and SNO are mass fraction, effective diffusion, and the source term, respectively. SNO can be calculated by the relation: SNO ¼ MNO
d½NO dt
CO prediction model The two-step model of Westbrook and Dryer is used [34] for simulation of the chemical reaction of methane combustion, CH4 þ 3 2O2 /CO2 þ 2H2 O
(23)
CO þ 1 2O2 /CO2
(24)
=
NOx prediction model
V:ðrVYNO Þ ¼ V:ðrDe VYNO Þ þ SNO
The NOx thermal mechanism has the greatest effect on NOx production at high temperatures. Increased nitrogen monoxide production has a direct relationship with increasing temperature [33]. Therefore, in this study, due to the fact that combustion occurs at atmospheric pressure and high temperatures, a developed Zeldovich mechanism is used to predict NOx produced in the combustion chamber.
(19)
where MNO is the molecular weight of NO and d½NO is calculated dt
=
YOx ε u_ Ox ¼ rA St k
Thermodynamic relations Viscosity, specific heats coefficient and thermal conductivity are evaluated as: k¼
I X a¼1
Ya ka ;
Cp ¼
I X a¼1
Ya Cpa ;
m¼
I X
Ya ma
(25)
a¼1
Furthermore, the viscosity of species, thermal conductivity and effective diffusion coefficient of species vary in terms of temperatures which can be given as [28]:
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ma ¼ ma0
T T0
0:7
;
ka ¼ ka0
T T0
0:7 (26)
where ma0 and ka0 are viscosity and thermal conductivity coefficient of species, calculated at T0 ¼ 298 K and atmospheric pressure. Furthermore, specific heat coefficient of species are predicted by Ref. [35]: Cpa ¼ a1a þ a2a T þ a3a T2 þ a4a T3 þ a5a T4 RT
(27)
Also effective binary diffusion coefficients Dam are written as [35]: Dam ¼ PI
1 Xa
(28)
bsa ðXb =Dab Þ
In which Xa ; Dab are mole fraction and ordinary multicomponent diffusion coefficients. To use the above equation, the mass transfer coefficient of each chemical species must be calculated relative to each other. The dual mass transfer coefficient for the pair of chemical species a and b is obtained from the simplified relation below [36]. 0:0266T Dab ¼ P MWab s2ab UD
(29)
With the following associated units: Dab ¼ ½ m2 =s; T ¼ ½ K; P ¼ Pa and sab ¼ ½ A , the remaining terms are defined below: MWab ¼ 2½ð1=MWa Þ þ ð1=MWb Þ1:
(30)
MWa and MWa are molecular weights of the chemical species a and b, respectively. Also sab ¼ ðsa þ sb Þ = 2:
(31)
where sa and sa are the hard-sphere collision diameter of species a and b, respectively. And collision integral UD is defined from the following equation: 1:06036 0:19300 1:03587 þ þ * * ðT* Þ0:15610 expð0:47635 T Þ expð1:52996 T Þ 1:76474 þ expð3:89411 T* Þ
UD ¼
k=ε dL =SL
(33)
where kB is the Boltzmann constant. and value of the characteristic Lennard-Jones, εn ðn ¼ a; bÞ, are also tabulated in Table 1 [37].
Turbulent combustion flow regime In this research, the Reynolds number based on the height of step, is Re ¼ 1:35 104 , The height of the step is half the height of the combustion chamber. Therefore, the Reynolds number is expressed on the basis of the hydraulic diameter. The critical Reynolds number for an internal flow is almost 2300 based on a hydraulic diameter. The Reynolds number is related to _ the inverse of the dynamic viscosity Re ¼ ðm=mLÞ . The dynamic viscosity of gases is directly proportional to the
rCp SL
(35)
In this equation, there are numerical, analytical and experimental methods for computing SL [38]. For the methane flame with an equivalence ratio of 0.9, the value of SL is approximately 0.3 m/s at the standard temperature and pressure [38]. In the choice of the combustion model, the Damkohler number plays an important role. At flows where Da[1, the chemical reaction time is faster than the turbulence mixing time and the combustion parameters are controlled by the turbulence mixing of the flow, the assumption of fast chemical reaction is true in these combustion currents [39e41]. The EDM method is one of the models of fast chemistry reaction and is suitable for combustion areas with Damkohler numbers higher than one. Another important dimensionless number is the Karlovitz number, defined as the ratio of the combustion time scale to the Kolmogorov time scale. Ka ¼
and where the dimensionless temperature T is defined by,
(34)
In this equation, dL is the laminar flame thickness, and SL is the one-dimensional laminar flame velocity. The laminar flame thickness can be estimated from the following equation [38].
(32)
*
kB T kB T ¼ εab ðεa εb Þ0:5
Da ¼
dL z l
1:5
T* ¼
temperature ma ¼ ma0 ðT=T0 Þ0:7 [28]. In the present study, the maximum combustion temperature is almost 2200 K. Therefore, the dynamic viscosity will change with the maximum values ratio ðT=T0 Þ0:7 ¼ ð2200=298Þ0:7 y4: inside the combustion chamber. The Reynolds number is inverse to the viscosity. The Reynolds number will reach its number Re ¼ ð1:35 104 Þ =4 ¼ 3375 at its lowest value. Because of 2300 < ðRe ¼ 3375Þ, the flow relatively is located in the low Reynolds area. The Reynolds number of flow, based on the block height at the inlet of the combustion chamber is Re ¼ 1:35 104 . The Damkohler number is also defined as the ratio of the turbulence integral time scale to the combustion time scale [38].
dL =SL
(36)
ðy=εÞ0:5
In this equation, y is the fluid kinematics. Considering the conditions at inlet, according to Ref. [7], the values of Da and Ka are obtained as approximately 380 and 0.07, respectively. In the case where the combustion temperature is at its maximum value of 2200 K, the lowest value of the Reynolds is calculated as 3375 K and at this temperature, the gas viscosity will be 4 times of its previous value. In this region, new values of Daz300 and Kaz0.2 are calculated, indicating that the
Table 1 e Lennard-Jones parameters for chemical species. ε ε ½¼K Chemical s½¼ A ½¼K Chemical s½¼ A kB kB species species CH4 CO CO2 H2O
3.758 3.690 3.941 2.641
148.6 91.7 195.2 809.1
NO N2 O2
3.492 3.798 3.467
116.7 71.4 106.7
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Fig. 1 e Temperature changes (a) on the cenerline at Y ¼ 20 mm (b) At the outlet of the chamber at X ¼ 470 mm, in terms of the number of the grid points. Changes of (c) xþ , (d) yþ : based on variations in distance on the walls of the enclosure. flame is always in the laminar wrinkled or the laminar corrugated regimes [32]. Thus, a fast chemical reaction takes place inside the combustion chamber and the combustion parameters are controlled by turbulent mixing. Many researchers have used this model with a one-step or two-step global reaction mechanisms [42e45]. In the laminar wrinkled regime, the laminar flame thickness dl is much smaller than the Kolmogorov scale. Damkohler number is larger than one. Therefore, the turbulence of the stream can only wrinkle the flame front and has no effect on the chemical reaction inside the flame front. In the laminar corrugated regime, the structure is very similar to the wrinkled regime, except that the intensity of turbulence in the wavy region is greater than the velocity of the laminar flame SL . In this region, due to the turbulence intensity of the flow, large eddies can move faster than the laminar flame velocity [38]. The sum of laminar wrinkled and corrugated regimes is called the flamelets regime. Therefore, in the flamelets regime, the chemical reaction time is much faster than the turbulence time of the flow. As previously stated, the correctness assumption of the EDM model, which is due to the high speed of the chemical reaction is true here. Therefore, in order to simulate the turbulent pre-mixed combustion with the combustion chamber conditions of ref. [7], the low Reynolds model, Launder Sharma EDM is utilized. In addition to simplicity, this model has good convergence and low computational cost to run the
written code. Run-time and convergence in this study utilizing the EDM low Reynolds simulation by a computer with the specifications of 4 GB of RAM Core i3-370 M, one-core processor, takes about 2 min, while the convergence time for simulation with T-PCMC method with a computer with the specifications of four Xeon E5650 hex-core processors and 24 GB of RAM takes about 11 h [32].
Grid study After checking the accuracy of the program, grid analysis was performed. For this purpose, one state of the combustion chamber with boundary conditions of ref. [22] was considered. In order to select the appropriate grid for simulating our combustion chamber, we investigated the effect of changing the number of points on the temperature distribution along the centerline at y ¼ 20 mm, shown in Fig. 1(a). Moreover, as depicted in Fig. 1(b), the effect of changing the number of points on the temperature distribution at the outlet of the combustion chamber at x ¼ 470 mm was investigated. Due to low discrepancy between grid of 20 70 and smaller grids, this grid was chosen for further simulations. þ As illustrated in Fig. 1(a), (b), the yþ top and ybottom of the first point of the grid of the upper and lower walls and xþ of the first point of the grid of the side wall, are selected such that this point can be located in the viscous sublayer [46]. The model of near wall turbulent flow are as follows [46,47]:
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Fig. 2 e (a) Temperature profiles, (b) mean axial velocity, (c) mean CO2% volume concentrations, (d) mean CO % volume concentrations. (A) Experimental [22], (B) LS-LRN-k¡ε/EDM model utilized in the present paper with proper coefficients, (C) T-PCMC [49] and (D) Fluent three-step EDM Reynolds stress model [50]. y 0:5 yþ ¼ r Cm k m
0:5 x xþ ¼ r Cm k m
(37)
In these equations, y indicated the distance between the first node and the upper (and lower) wall and x presents the longitudinal distance of the first node from the side wall. K is kinetic energy of the turbulent flow. In the simulation of turbulence flow, the exact grid of the near-wall region is very important. Its distance to the combustion chamber’s walls can affect the accuracy of the simulation results. In the low Reynolds regime, placing the first near-wall node close to 1 and less is very desirable [48]. Fig. 1(c), (d) shows the variation of xþ for the first node close to the vertical wall and yþ for the first node close to the lower and upper walls in terms of x and y changes, respectively. As shown in these figures, the first node near the wall is located in the viscous sublayer.
Numerical scheme The governing equations are solved in Cartesian coordinates by using FORTRAN 90 programming, that has been used in LSLRN-kε/EDM framework. The turbulenceecombustion interaction in the flame field is numerically studied with better coefficients implemented in our code. A finite volume method (FVM) with staggered grids is used and SIPMLE algorithm was chosen for the coupling between the velocity and the pressure. For all simulations presented in this paper. Moreover, a Power Law Scheme (PLS) was used for the conservation equation of momentum, turbulent kinetic energy, turbulent dissipation rate, spices chemical. While the NOx and CO concentrations were obtained through applying the Zeldovich and Westbrook-Dryer mechanisms, respectively.
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Fig. 3 e Experimental [22] ( ), T-PCMC [49]( ) and LS-LRN-k¡ε/EDM model utilized in the present paper with proper coefficients ( ) (a) x=h ¼ 17:5 ðCO2%Þ , (b) x=h ¼ 17:5 ðUHC%Þ, (c) x=h ¼ 24: ðCO2%Þ , (d) x=h ¼ 24: ðUHC%Þ .
The system of governing equations is solved simultaneously using numerical or TDMA (Tri-Diagonal Matrix Algorithm) finite difference methods. The turbulent intensity of the input flow is 7%. Under Relaxation factor values considered are as follow: for momentum 0.6, for k and ε turbulent equation (0.8), for energy 0.4 and for rest of equation (0.5). The criterion of convergence is the summation of residual mass sources less than 104 for the other terms of the transport equations and is 106 for the energy equation is 105 .
Validation Fig. 2 illustrates the validity of the written code by comparison of our results with the experimental results of ref. [22] and numerical results of ref. [49] and ref. [50]. These diagrams depict temperature graph, average axial velocity, mean CO2
and CO concentrations. From these diagrams, it can be observed that the combustion model in our work, using LSLRN-kε/EDM with appropriate coefficients (A ¼ 1, B ¼ 0.5) has better results than those reported by Ref. [49] and ref. [50]. Therefore, this method is more accurate in determining the temperature field and velocity of chemical species production. The temperature profiles are depicted in Fig. 2(a). It is obvious that both numerical methods, LS-LRN-kε/EDM and T-PCMC, have good results in the combustion field modeling. The maximum combustion temperature is 1900 K, illustrating an appropriate distribution of temperature, which confirms with the experimental results. The same trend can be seen in the graphs of mean axial velocity profile, mean CO2% volume concentrations and mean CO % volume concentrations (Fig. 2(b)e(d), respectively). In the modeling of chemical species such as CO2 and CO, both methods, LS-LRN-kε/EDM and T-PCMC, have been successful to identify flow vortices at the corners of the enclosure. As shown, the LS-LRN- kε/EDM
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Fig. 4 e Effect of H₂O dilution on the temperature distribution at (b) outlet and (a) centerline of the combustion chamber.
Fig. 5 e Effect of H₂O dilution on produced NO concentration at the (b) outlet and (a) centerline of the combustion chamber.
model, utilized in the present work, with appropriate coefficients is far better in comparison with the T-PCMC model and provides proper results compared with experimental results. It should be noted that the results of three-step EDM, Reynolds stress [50] are weaker than those of the other results. Fig. 3 illustrates comparison of the values of H2O and UHC in different locations of the combustion chamber from the experimental results [22] and the numerical results [49] and the present study. As can be seen in the diagrams, the selection of the LS-LRN-kε/EDM modeling model with assumed coefficients A ¼ 1 and B ¼ 0.5 gives very good results that are very close to the experimental results. Thus, in the following sections of the paper, the distribution of temperature, velocity and concentration of combustion species are studied by introducing H2O as diluent, utilizing the aforementioned LS-
LRN-kε/EDM model. Furthermore, the distribution of CO and NOx are carefully investigated.
Results and discussion Effect of H2O dilution Fig. 4 and Fig. 6 depict the effect of H2O dilution on temperature distribution, NO concentration, mass distribution of CO at the outlet of the chamber at x ¼ 470 mm and at y ¼ 20 mm, along the centerline of the combustion chamber. As shown in Fig. 4(a), along the centerline at y ¼ 20 mm, close to the inlet of the combustion chamber before the location of the maximum temperature, with increasing H2O diluent, temperature increase with a steep slope can be
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Fig. 6 e Effect of H₂O dilution on produced CO concentration at (a) centerline (b) outlet of the combustion chamber.
observed, such that by dilute injection to the fuel and air mixture, the temperature reaches its maximum value immediately close to the inlet. Then the temperature decreases along the longitudinal direction, towards the outlet of the chamber, which is due to the absorption of combustion energy from the combustion by the water diluent. This, in turn, causes the temperature of the fluid to decrease as a result of the increase of H2O diluent, as shown in Fig. 4(b) at the outlet of the combustion chamber at x ¼ 470 mm. However, due to the limited injection of H2O diluent, the abovementioned effect at the outlet of the combustion chamber is not very significant. Fig. 5(a) illustrates that by increasing concentration of H2O, concentration of NO increases at the outlet of the combustion chamber from bottom and then gradually decreases to the top of the cross section. As shown in Fig. 5(b), concentration of NO increases along the length of chamber in the centerline initially, then becomes approximately constant after reaching a maximum point. Moreover, by adding H2O to the combustion chamber, an increment is observed in the concentration of NO in the beginning of the combustion chamber. It is inverted after a while, the concentration of NO decreases by increasing H2O at the ending part of the chamber. Moreover, with increasing H2O dilution in the combustion chamber, we see a decrease in the production of NO pollutants. The effect of the H2O diluent increase on the NOx pollutant reduction is extremely severe, such that with a slight increase in the amount of H2O diluent, a sharp reduction in the amount of this pollutant can be observed. Regarding the amount of H2O diluent, the slope of this reduction is very high. Fig. 6(a) illustrates that by adding H2O, the concentration of CO decreases at the outlet of the combustion chamber from bottom to top. As shown in Fig. 6(b), the concentration of CO increases along the length of chamber in the centerline initially and decreases after reaching a maximum point. However, by increasing the concentration of H2O, an increasing is observed in the concentration of CO initially. It is
inverted after a while, so the concentration of CO decreases by increasing H2O at the ending part of the chamber. Fig. 6(a) shows that the location of the most concentrated pollutant of CO is at the inlet of the combustion chamber. Before the location of the maximum temperature in the combustion chamber. As H2O diluent increases, the peak of produced pollutant emission CO increases, and the higher the amount of diluent, the higher the amount of peak and the inclination towards the inlet of the combustion chamber. Regarding the fact that, by increasing the H2O diluent, CO stays longer in the combustion chamber. As we move towards the outlet of the combustion chamber, the pollutant CO reacts more with other species and its mass fraction decreases. Therefore, according to the diagrams of Fig. 6(b), we see a decrease in the production of CO pollutant by the injection of H2O diluent. However, for a specific value of the H2O diluent, the increase in the combustion chamber length does not have a significant effect on the reduction of the CO pollutant. In the profiles of Fig. 7(a)e(c), the distribution of the temperature based on Kelvin, the distribution of NO concentration based on PPM and the distribution of mass fraction of CO in the combustion chamber versus changes in the H2O diluents values are depicted, respectively. As indicated by the temperature distribution (Fig. 7(a)), increasing the mass fraction of H2O as a diluent reduces the high temperature area in the combustion chamber. This, in turn, reduces NO concentration in the combustion chamber (Fig. 7(b)). At the chamber inlet, the concentration of CO production increases with increasing in the concentration of H2O but along the combustion chamber, CO reacts as fuel gradually and reduces by increasing the H2O (Fig. 7(c)). This suggests that in order to reduce the concentration of CO produced in the combustion chamber by adding H2O, the length of the chamber should be long enough; otherwise, adding H₂O has an inverted result. As the temperature distribution is shown in Fig. 7(a), an increase in the mass fraction of H2O as a diluent decreases the temperature at the outlet of the combustion chamber,
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Fig. 7 e Distribution of: (a) the temperature based on Kelvin (b) NO concentration based on PPM and (c) mass fraction of CO; for A(S ¼ 0.0), B(S ¼ 0.01), C(S ¼ 0.02) and D(S ¼ 0.03).
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although this temperature decrease is not very remarkable, but as shown in Fig. 7(b), increasing H2O diluent leads to extreme reduction of NOx concentration, mainly found at the outlet of the combustion chamber. The contours in Fig. 7(c) illustrates how the concentration of CO pollutant in the combustion chamber is affected by the increase in the amount of H2O in the fuel and air. As indicated by the profiles, as the H2O diluent increases, the pollutant CO increases at the combustion chamber inlet. As shown in the case A of Fig. 7(c), the amount of CO reaches its minimum value after the location of the maximum temperature in the combustion chamber and before the outlet. This indicates that the combustion chamber length should not be less than a specific value, (in this case, without diluent about 300 mm), but increasing the length after this critical point has little effect on CO reduction.
Conclusion We have performed a numerical investigation of the effect of diluents of H2O on NOx and CO formation in turbulent premixed methane-air flame. In this work, we utilized a finite volume method (FVM) with staggered grids for discretizing the set of governing equations. SIMPLE algorithm was implemented using a fine grid resolution. Discretization of the convective terms was done using Power Law Scheme (PLS). In order to simulate the interaction of turbulence and reaction in the flame, the eddy dissipation and kε turbulence models were applied. The implemented LS-LRN-kε/EDM method with the new coefficients depicted excellent agreement with previously published experimental measurements. The results of the research show that T-PCMC advanced models can not accurately model weak turbulent flows. The kε model with wall functions cannot simulate the temperature distribution and turbulent combustion flow patterns, accurately. Because the corrections made to them are not efficient for combustion flows. In these cases, the LRN models provide fairly better answers. Finally, in this work, LS-LRN-kε/EDM model has been used to study the distribution of temperature and distribution of NOx and CO pollutants in a turbulent premixed flame. The following results were obtained: 1. By increasing the H2O dilution in the pre-mixed turbulent combustion process, the temperature increases. Furthermore, concentrations of NOx and CO pollutants along the centerline of the combustion chamber increase close to the inlet of the combustion chamber. However, after the location of the maximum temperature in the combustion chamber along the centerline towards the outlet of the combustion chamber, we see a sharp decrease in temperature, a decrease in the NOx and CO pollutants in the combustion chamber due to the absorption of combustion energy by H2O. 2. With a slight increase in the H2O diluent, we see a slight decrease in temperature compared with the significant reduction of NOx and CO emissions from the combustion chamber.
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3. By increasing the H2O diluent, the maximum amount of CO emission is directed towards the inlet of the combustion chamber. This is because of inadequate burning of methane in the presence of H2O, which H2O as an intermediate molecule causes effective collision of methane molecules with oxygen molecules. 4. At a specific value of the H2O diluent at a given location, the amount of CO is suddenly reduced to the lowest value. Therefore, the combustion chamber must always be selected such that its length will not be less than a certain value. Since in this case it causes more emission of CO pollutant into the environment. 5. The length of the combustion chamber should be long enough in order to reduce the produced CO due to H₂O injection. Otherwise, the injection of H₂O will have an adverse effect on the production of NO and CO, which has not been reported in previous studies. 6. Increasing the mass fraction of H₂O as a diluent, reduces the high temperature region in the combustion chamber. This, in turn, reduces NO concentration in the combustion chamber.
Declaration of competing interest The authors declare no conflict of interest.
references
[1] Lieuwen T, Zinn BT. The role of equivalence ratio oscillations in driving combustion instabilities in low NOx gas turbines. In: Symposium (International) on combustion, 27. Elsevier; 1998 Jan 1. p. 1809e16. [2] Poinsot T. Prediction and control of combustion instabilities in real engines. Proc Combust Inst 2017;36(1):1e28. [3] Telesca A, et al. Use of oxyfuel combustion ash for the production of blended cements: a synergetic solution toward reduction of CO2 emissions. Fuel Process Technol 2017;156:211e20. [4] Zaidaoui H, Boushaki T, Sautet JC, Chauveau C, Sarh B, € kalp I. Effects of CO2 dilution and O2 enrichment on nonGo premixed turbulent CH4-air flames in a swirl burner. Combust Sci Technol 2018;190(5):784e802. [5] Ma T, Takeuchi K. Technology choice for reducing NOx emissions: an empirical study of Chinese power plants. Energy Policy 2017;102:362e76. [6] Wang H-f, Chen Y-l, Chen H-l, Liu M-h. A numerical analysis ~ 2/N ~ 2 laminar of instantaneous response of the CH~ 4/O flamelet. Chin J Comput Phys 2006;23(2):193. [7] Ilbas M, Yılmaz I, Veziroglu TN, Kaplan Y. Hydrogen as burner fuel: modelling of hydrogenehydrocarbon composite fuel combustion and NOx formation in a small burner. Int J Energy Res 2005;29(11):973e90. _ Kaplan Y. Investigations of hydrogen and [8] Ilbas M, Yılmaz I, hydrogenehydrocarbon composite fuel combustion and NOx emission characteristics in a model combustor. Int J Hydrogen Energy 2005;30(10):1139e47. [9] Lopez-Parra F, Turan A. Computational study on the effects of non-periodic flow perturbations on the emissions of soot and NOx in a confined turbulent methane/air diffusion flame. Combust Sci Technol 2007;179(7):1361e84.
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 5 ( 2 0 2 0 ) 1 0 8 8 2 e1 0 8 9 4
[10] Wetzel F, Habisreuther P, Zarzalis N. Numerical investigation of lean blow out of a model gas turbine combustion chamber using a presumed JPDF-reaction model by taking heat loss processes into account. In: ASME Turbo Expo 2006: Power for Land, Sea, and Air. American Society of Mechanical Engineers; 2006 Jan 1. p. 41e9. [11] Hahn WA, Wendt JOL. NOx formation in flat, laminar, opposed jet methane diffusion flames. In: Symposium (International) on Combustion, 18; 1981. p. 121e31. no. 1. [12] Saqr KM, Aly HS, Sies MM, Wahid MA. Effect of free stream turbulence on NOx and soot formation in turbulent diffusion CH4-air flames. Int Commun Heat Mass Transf 2010;37(6):611e7. [13] Shaw H. The effects of water, pressure, and equivalence ratio on nitric oxide production in gas turbines. J Eng Power 1974;96(3):240e6. [14] Greeves G, Khan IM, Onion G. Effects of water introduction on diesel engine combustion and emissions. In: Symposium (International) on combustion, 16; 1977. p. 321e36. no. 1. [15] Burnham JB, Giuliani MH, Moeller DJ. Development, installation and operating results of a steam injection system (STIG™) in a general electric LM5000 gas generator. In: ASME 1986 international gas turbine conference and exhibit. vol. 10. American Society of Mechanical Engineers; 1986. p. 257e62. V004T10A019-V004T10A019. [16] Feitelberg AS, Tangirala VE, Elliott RA, Pavri RE, Schiefer RB. Reduced NOx diffusion flame combustors for industrial gas turbines. In: ASME turbo expo 2000: power for land, sea, and air. vol. 123. American Society of Mechanical Engineers; 2000. p. 757e65. V002T02A006-V002T02A006. € ke S, et al. Influence of steam dilution on the combustion [17] Go of natural gas and hydrogen in premixed and rich-quenchlean combustors. Fuel Process Technol 2013;107:14e22. [18] Cheng I. Power systems. Cheng Power Syst 2015. http://www. chengpower.com/. [19] Xue R, Hu C, Sethi V, Nikolaidis T, Pilidis P. Effect of steam addition on gas turbine combustor design and performance. Appl Therm Eng 2016;104:249e57. [20] Pugh DG, et al. Dissociative influence of H2O vapour/spray on lean blowoff and NOx reduction for heavily carbonaceous syngas swirling flames. Combust Flame 2017;177:37e48. [21] Dai C, Shu Z, Li P, Mi J. Combustion characteristics of a methane jet flame in hot oxidant coflow diluted by H2O versus the case by N2. Energy Fuels 2018;32(1):875e88. 2018/ 01/18. [22] El Banhawy Y, Sivasegaram S, Whitelaw JH. Premixed, turbulent combustion of a sudden-expansion flow. Combust Flame 1983;50:153e65. orie des eaux courantes. Impr. [23] Boussinesq J. Essai sur la the nationale; 1877. [24] Sarkar S, Lakshmanan B. Application of a Reynolds stress turbulence model to the compressible shear layer. AIAA J 1991;29(5):743e9. 1991/05/01. [25] Launder BE, Sharma BI. Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett Heat Mass Transf 1974/11/01/ 1974;1(2):131e7. [26] Launder BE, Spalding DB. The numerical computation of turbulent flows. In: Numerical prediction of flow, heat transfer, turbulence and combustion. Pergamon; 1983. p. 96e116. [27] Peters N. Turbulent combustion. Cambridge university press; 2000. [28] Magnussen BF, Hjertager BH. On mathematical modeling of turbulent combustion with special emphasis on soot
[29] [30]
[31]
[32]
[33]
[34]
[35] [36] [37] [38] [39]
[40] [41] [42]
[43]
[44]
[45]
[46]
[47] [48] [49]
[50]
formation and combustion. Symposium (international) on Combustion, 16. Elsevier; 1977 Jan 1. p. 719e29. Zeldovich J. The oxidation of nitrogen in combustion and explosions. Eur Phys J A Hadrons Nucl 1946;21:577e628. Hanson RK, Salimian S. Survey of rate constants in the N/H/O system. In: Gardiner WC, editor. Combustion chemistry. New York, NY: Springer New York; 1984. p. 361e421. Miller JA, Bowman CT. Mechanism and modeling of nitrogen chemistry in combustion. Prog Energy Combust Sci 1989;15(4):287e338. Raine RR, Stone CR, Gould J. Modeling of nitric oxide formation in spark ignition engines with a multizone burned gas. Combust Flame 1995;102(3):241e55. Brewster BS, Cannon SM, Farmer JR, Meng F. Modeling of lean premixed combustion in stationary gas turbines. Prog Energy Combust Sci 1999;25(4):353e85. Westbrook CK, Dryer FL. Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames. Combust Sci Technol 1981;27(1e2):31e43. Turns SR. An introduction to combustion. New York: McGraw-hill; 1996. Reid RC, Prausnitz JM, Poling BE. The properties of gases and liquids, 4; 1987. p. 450e575. Svehla RA. Estimated viscosities and thermal conductivities of gases at high temperatures. 1962. Poinsot T, Veynante D. Theoretical and numerical combustion. RT Edwards, Inc.; 2005. s J, Gil A, Corte s C, Herce C. Numerical study of coPallare firing coal and Cynara cardunculus in a 350 MWe utility boiler. Fuel Process Technol 2009;90(10):1207e13. Veynante D, Vervisch L. Turbulent combustion modeling. Prog Energy Combust Sci 2002;28(3):193e266. Stephen R. An introduction to combustion: concepts and applications. McGraw-hill; 1996. Li M, Christofides PD. Computational study of particle inflight behavior in the HVOF thermal spray process. Chem Eng Sci 2006;61(19):6540e52. Li M, Christofides PD. Multi-scale modeling and analysis of an industrial HVOF thermal spray process. Chem Eng Sci 2005;60(13):3649e69. Dolatabadi A, Mostaghimi J, Pershin V. Effect of a cylindrical shroud on particle conditions in high velocity oxy-fuel (HVOF) spray process. J Mater Process Technol 2003;137(1e3):214e24. Khan MN, Shamim T. Effect of particle and injection parameters on the performance of a dual-stage high-velocity oxygen fuel thermal spray system. J Therm Spray Technol 2015;24(5):807e16. Versteeg HK, Malalasekera W. An introduction to computational fluid dynamics: the finite volume method. Pearson education; 2007. Pope SB. Turbulent flows. IOP Publishing; 2001. Gerasimov A. Modeling turbulent flows with fluent. Sheffield, UK: Ansys Inc; 2006. Velez C, Martin S, Jemcov A, Vasu S. LES simulation of an enclosed turbulent reacting methane jet with the tabulated premixed CMC method. 2015. no. 56697, p. V04BT04A055. Martin SM, Kramlich JC, Riley JJ. The premixed conditional moment closure method applied to idealized lean premixed gas turbine combustors. In: ASME Turbo Expo 2002: Power for Land, Sea, and Air. American Society of Mechanical Engineers; 2002 Oct. p. 573e80.
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Numerical study of the effect of H2O diluents on NOx and CO formation in turbulent premixed methane-air flame Mohsen Nasiri Soloklou, Ali Akbar Golneshan* Thermo-fluids department school of mechanical engineering, Shiraz University, Shiraz, Fars, 71348-51154, Iran
highlights kε/EDM framework is used to study turbulence combustion. The energy absorbed by H2O leads to a severe decrease in temperature. Using H2O diluent leads to reduction in the amount of NOx and CO emissions. By increasing the H2O diluent, enclosures with smaller length can be utilized.
article info
abstract
Article history:
The interaction of turbulenceecombustion inside the flame field is studied in a Launder-
Received 19 July 2019
Sharma Low Reynolds Number (LS-LRN) kε/EDM framework, while suitable coefficients
Received in revised form
have been utilized in the code. A finite volume method (FVM) with staggered grids was
1 October 2019
applied to discrete set of governing equations. SIMPLE algorithm is applied with a fine grid
Accepted 3 October 2019
resolution. The convective terms are discretized using Power Law Scheme (PLS). The sys-
Available online 4 March 2020
tem of governing equations is solved simultaneously using numerical or TDMA finite difference methods (Tri-Diagonal Matrix Algorithm). By implementation of the Zeldovich and
Keywords:
Westbrook-Dryer mechanisms, NOx and CO concentrations were obtained, respectively. It
Turbulent flame
is illustrated that the implemented LS-LRN-kε/EDM method with the new coefficients by
H2O diluent
shorter runtimes has very good agreement with previously published experimental mea-
Pollutant reduction
surements. Increasing the H2O diluent at the inlet leads to an increase in the temperature,
Launder-sharma low Reynolds kε/
which increases the NOx and CO near the entrance, but gradually towards the outlet of the
EDM
combustion chamber. The energy absorbed by H2O leads to a severe decrease in temperature and subsequent reduction in the amount of NOx and CO emissions. With increasing H2O diluent, changes in temperature are not very significant, while changes in pollutants CO and especially NOx, are remarkable. With the increase of H2O diluent, the maximum amount of CO emission displaces towards the inlet of the combustion chamber. However, it should be noted that, at a specific value of H2O diluent, the length of the combustion chamber should not be less than critical value, causing the exhaust of the pollutant with large volume to the environment. After the critical point, the increase in the length of the chamber has little effect on reduction of the pollutant exhaust. However, by increasing the H2O diluent, enclosures with smaller length can be utilized. © 2019 Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.
* Corresponding author. E-mail address: [email protected] (A.A. Golneshan). https://doi.org/10.1016/j.ijhydene.2019.10.083 0360-3199/© 2019 Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.
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Introduction In recent decades more attention has been payed to the need for cleaner combustion systems satisfying the energy requirements of human being. By premixing the fuel and oxidizer uniformly prior to combustion, premixed combustion systems lead to improved combustion efficiency and fewer formations of NOx. Improvement of the combustion systems is very significant, specially to avoid combustion instabilities [1,2] and reduction of the pollutant emissions [3e5]. Numerous studies have reported the NOx formation in various combustion regimes [6e10]. Hahn and Wendt [11] examined the flame thickness and NO formation rate of non-premixed methane jet flames. The flame thickness and NO formation rate of non-premixed methane jet flames. They stated that NOx formation rate is a function of the flame stretching. Saqr et al. [12] conducted a numerical study of the effect of free stream turbulence on the NOx in the turbulent flame of CH4air. It was shown that the increase of turbulence intensity in the air stream results in the reduction of the formation rate of pollutants. Shaw [13] studied the effect of dilution with water and the simultaneous effect of pressure on combustion parameters and production of nitrogen monoxide in both kinetic and equilibrium states. He argued that in some cases with processes based on equilibrium, calculations are not valid and contradict the results of kinetic states. In addition, it was shown that increasing the water vapor causes a reduction in the production of nitrogen monoxide in the combustion chamber. Greeves et al. [14] carried out an experimental investigation of carbon monoxide and nitrogen monoxide reduction by injection of water into the combustion chamber in three ways of injecting water into the air, injecting water into fuel and injecting water directly into the compartment. They showed that injection of water in fuel have had more effect on reducing the amount of carbon monoxide and nitrogen monoxide compared to injection of water in air or direct water injection into the combustion chamber. Burnham et al. [15] aimed to reduce the emission of pollutants by an experimental investigation of water vapor injection into a gas turbine, containing natural gas. Their results showed that water vapor injection is an effective and practical way to reduce the production of carbon monoxide in the combustion chamber. Two-tube nozzles were used in this experiment. Vapor and fuel were introduced into the combustion zone through the external nozzles and through the inner nozzles, respectively. Feitelberg et al. [16] investigated the effect of excessive vapor and air on the combustion emissions. They reduced the temperature in the combustion chamber by diluting the fuel with additional air. They observed that the amount of nitrogen monoxide contaminants was decreased. Moreover, these experiments carried out by injection of vapor as the diluent. Comparison of the results in the cases of with and without injection of water vapor indicated that vapor injection at high temperatures reduces the NOx production, remarkably. Gokke et al. [17] examined the combustion of natural gas and hydrogen in the conditions of with and without vapor injection in different equivalence ratios in the turbulent pre-mixed flame. They measured the shape and position of the flame experimentally. They showed that the
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addition of water vapor to the fuel has a significant effect on reducing the emissions of nitrogen monoxide in the combustion chamber. The method of vapor injection into a premixed flame is called Cheng Low NOx (CLN) method. This method was first introduced by Cheng [18]. Cheng claimed that the pre-mixing of water vapor with fuel, in addition to reducing the temperature, diminishes the combustion zone of nitrogen oxide formation and consequently, reduces the mass fraction of nitrogen oxide compared to the method of water vapor injection into the non-premixed flame. Zhou et al. [19] investigated the effect of adding water vapor into the combustion chamber on pressure, temperature and local Mach number parameters by the method of equilibrium analysis. They showed that by injecting water vapor, the temperature of every point through the combustion chamber reduces. In their paper, it was shown that an increase in the amount of injected water vapor has a small effect on reducing the temperature of the chamber and under these conditions, the temperature drop occurs with a slight slope. They also showed that decreasing the temperature leads to decreasing the amount of nitrogen monoxide produced in the combustion chamber. Pugh et al. [20] investigated the effect of water vapor injection into a pre-mixed turbulent flame. Their examination was carried out in the range of equivalence ratio from 0.6 to 0.8. They showed that water vapor injection has a significant effect on the fuel consumption and flame velocity. They also showed that the injection of water vapor reduces the temperature of the chamber. Consequently, it reduces NOx production in the combustion chamber. Dai et al. [21] studied combustion characteristics of a methane flame in hot co-flow diluted by H₂O versus the case by N2. It was shown that by changing the diluent from N2 to H₂O, both the temperature and the dimension of the flame reduce remarkably. Our aim in this work is to predict the pollutants of a turbulent flame by utilizing a code written based on eddy dissipation model (EDM) based on the new coefficients. Our code is able to model turbulent and premixed CH4 flame with reasonable runtimes and it shows good agreement with previously reported experimental results in a RANS environment. In this study, the k ε/EDM combustion model (LS-LRN) was used to model the combustion chamber, which has not been reported in other studies. For the first time, we have investigated the details of the temperature distribution and the modifications of both CO and NOx pollutants simultaneously by injecting different amounts of H2O diluent in the dilution range of zero to 0.03. Moreover, by varying the diluent values, the geometrical relationship between the combustion chamber and the distribution of CO and NOx pollutants is depicted. Furthermore, the effect of H₂O dilution on the temperature distribution, axial velocity, NOx and CO concentrations through the combustion chamber has been examined.
Problem statement and mathematical formulation In this work, we have considered the combustion chamber studied by Banhawy et al. [22] with a rectangular cross section. The mixture of air and fuel methane enters a mixing compartment with various equivalence ratios and goes
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through a flow strainer before entering the combustion chamber. The dimensions of the combustion chamber are 0.47 m 0.157 m 0.04 m, with a h ¼ 0.02 m step at the entry of the combustion chamber, causing the expansion of the flow. The Reynolds number of the mixture, based on the step height as characteristic length is 1:35 104 . The mixture of gas and air entering the combustion chamber with temperature of 300 K. The top and bottom walls cool down by water and maintained at a constant temperature of 300 K. Due to much longer channel width compared to its height, the studied flow can be considered as two-dimensional. The following assumptions are considered in this work: 1. The flow is steady-state and two-dimensional. 2. The pressure inside the combustion chamber is considered to be constant. 3. The ideal gas state equation is governed for every species of reactants and products. 4. Thermodynamic properties of species, density and viscosity of fluid are functions of temperature. 5. The effect of buoyancy is neglected. 6. It is assumed that no radiation heat transfer exists. 7. The walls are maintained at a constant temperature of 300 K. 8. Using the Boussinesq.approximation [23] that the momentum transfer caused by turbulent eddies can be modeled with an eddy viscosity. After considering the mentioned simplifications, the governing equations will be as follows: v rUj ¼ 0: v Xj
Continuity
v rUi Uj vP v ¼ þ v Xj v Xi v Xj v Ui Conservation of momentum ðm þ mt Þ v Xj
(1)
(2)
v r Ya Uj v m v Ya ¼ rDam þ t v Xj v Xj sy v Xj þ u_ a
Mass conservation for species i
p ¼ rRT
Conservation of energy X Ya Ma
State equation
v rUj k v m vk ¼ mþ t þ Pk r ε Dt rD v Xj sk v Xj v Xj
(6)
Turbulent dissipation rate
v rUj ε v m vε ε ¼ mþ t þ f 1 Cε1 Pk f 2 Cε2 r ε þ rE vXj k sε vXj vXj
(7)
Relations (6) and (7) contain a set of variables whose values are calculated from the following relationships. 2
mt ¼ r C m f m
k ε
εk Dt ¼ 2r gRT
pffiffiffi!2 2 2 v k v Ui E ¼ 2yyt vXj vXk vXj vUj vUi vUj Pk ¼ mt þ v Xi v Xj v Xi
D ¼ 2y
(8)
D and E are included in the low Reynolds closure models in order to render the models valid to the wall. And mt , Dt and Pk are turbulent viscosity, Compressibility effect and turbulent kinetic energy produced items, respectively.where: 2
Rt ¼
k ; yε
3:4
f 1 ¼ 1:
f 2 ¼ 1 0:3exp R2t ;
2 Rt 1þ 50
f m ¼ exp (9)
In this case, y and yt are Molecular kinematic viscosity and Turbulence kinematic viscosity, respectively. And g is specific heat ratio. And Dt is defined as the turbulent dilatation dissipation term. f m , f 1 and f 2 are vary with the given models, which f m , f 1 and f 2 are the local turbulent model damping functions. The constants used in this model are as follows [24]: Cm ¼ 0:09 Cε1 ¼ 1:44 Cε2 ¼ 1:92 sε ¼ 1:3 sy ¼ 0:7 st ¼ 0:9
(10)
where Cm , Cε1 , Cε2 , sε , sy and st are the same empirical constant found in the Launder-Sharma Low Reynolds model [23]. (3)
Boundary conditions
N v r Uj T v l mt v T 1 X ¼ þ u_ i v Xj Cp st v Xj Cp i¼1 v Xj 0 hf;a
Launder-Sharma Low Reynolds model [24] leads to the turbulent kinetic energy. Fluid compressibility properties alter only in the dissipation of turbulent kinetic energy [25] due to the assumption of ideal gas for the fluid. Turbulent kinetic energy:
(4)
(5)
In this case, i and j are coordinate components along X and Y. And Uj , T, Ya and u_ a , respectively, are the average velocity, average pressure, average temperature, average of mass fraction of the species, and the average of net production rate of the chemical component. Also r: density, Ya mass fraction of chemical species a, Cp : average specific heat capacity at constant pressure, l: thermal conductivity coefficient, R: constant gases for a species, Ma : molecular mass of species a, 0 hf;a : enthalpy Formation of the standard of the a species.
The boundary conditions for the domain in the combustion chamber, surrounded by solid wall are as follows [26]: Inlet ð0 y 0:02 mÞ ðx ¼ 0Þ : Tin ¼ 300: K
YinCH4 ¼
0:055 S þ 1: S S þ 1:
Re ¼ 1:35 104
YinH2 O ¼
Iinlet ¼ 0:16Re0:125
YinCO2 ¼ 0:0
3 0:22 kinlet ¼ ðuinlet Iinlet Þ2 YinO2 ¼ 2 S þ 1: 1:5
εinlet ¼
0:164 kinlet 0:07Dh
YinN2 ¼
0:725 S þ 1:
(11)
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Definition of S for H2O as diluents: S ¼ f0:0; 0:01; 0:02; 0:03g QUOTE Side wall of combustion chamber ð0:02 m y 0:04 mÞ ux ¼ 0;
uy ¼ 0;
T ¼ 300 K;
vYa vx ¼ 0 ; a ¼ 1; 2; …; I
(12)
Outlet of combustion chamber ðx ¼ 0:470 mÞ : uy ¼ 0;
vux vx ¼ 0;
vT vx ¼ 0;
vYa vx ¼ 0 ; a ¼ 1; 2; …; I (13)
Walls ðy ¼ 0:0 mÞ and ðy ¼ 0:04 mÞ ux ¼ 0;
uy ¼ 0;
T ¼ 300 K;
vYa vx ¼ 0 ; i ¼ 1; 2; …; I
(14)
The values of kinlet and εinlet , respectively, are the inlet kinetic energy of turbulence and the inlet kinetic energy dissipation of turbulence. In the above equations Iinlet is the turbulence intensity and the Dh is hydraulic diameter. Re is also the Reynolds number of the input current. And Yin is the value of concentration of species at inlet. All of the units are based on meters and Kelvin.
Combustion modeling The eddy dissipation model is applied for the calculation of the effect of turbulent chemical reaction rate. The minimum of the following rates as the local average reaction rate in equation is taken [27]: Net mean rate of the fuel: u_ F ¼ rAYF
ε k
(15)
by Zeldovich mechanism [29]. and rate constants for these reactions are calculated by Hanson and Salimian [30]. The first reaction shows the Chemical breakdown of the nitrogen molecule. The second reaction has high activation energy and the limiting factor of the reaction rate in the Zeldovich mechanism. The third reaction is important under conditions of rich fuel and close to stoichiometric values. Due to the strength of the triple bond in the nitrogen molecule, high energy is needed to break this bond and this is the main cause of NOx thermal production at high temperatures. Also, if there is enough oxygen in the fuel with high temperatures the combined nitrogen and oxygen demand increases and a pseudo-equilibrium state for free nitrogen production and consumption is obtained. This pseudo-equilibrium assumption in dilute fuels is assumed to be correct. Therefore, the NO formation rate can be calculated as follows.
2
k2 ½NO 1 kk1 1 ½N2 k2 ½O2
d½NO ¼ 2k1 ½O½N2 dt ½NO 1 þ k2 ½Ok1 2 þk3 ½OH
(20)
In this equation, a partial equilibrium method is used to determine the concentration of O and OH radicals and the values of these concentrations are calculated as follows [31,32]. 27123 ½O ¼ 36:34T0:5 ½O2 0:5 exp T
(21)
4595 ½OH ¼ 2:129 103 T0:57 ½O0:5 ½H2 O0:5 exp T
(22)
Net mean rate of the oxidizer: (16)
Net mean rate of the production: u_ Pr ¼ r
A:B ε YPr 1 þ St k
(17)
YF is Mass fraction of fuel, YOx is Oxidizing mass fraction, YPr is mass fraction of combustion products, St is Stoichiometric ratio of oxidizing mass to fuel mass. A is a fixed model with a standard value of 4. In this paper, this numerical constant is equal to 1. And B is fixed at 0.5 [28].
To include NO formation for this type of flame, the thermal mechanisms are employed [36]. The transport equation for NO can be written as follows: (18)
in which, YNO , De , and SNO are mass fraction, effective diffusion, and the source term, respectively. SNO can be calculated by the relation: SNO ¼ MNO
d½NO dt
CO prediction model The two-step model of Westbrook and Dryer is used [34] for simulation of the chemical reaction of methane combustion, CH4 þ 3 2O2 /CO2 þ 2H2 O
(23)
CO þ 1 2O2 /CO2
(24)
=
NOx prediction model
V:ðrVYNO Þ ¼ V:ðrDe VYNO Þ þ SNO
The NOx thermal mechanism has the greatest effect on NOx production at high temperatures. Increased nitrogen monoxide production has a direct relationship with increasing temperature [33]. Therefore, in this study, due to the fact that combustion occurs at atmospheric pressure and high temperatures, a developed Zeldovich mechanism is used to predict NOx produced in the combustion chamber.
(19)
where MNO is the molecular weight of NO and d½NO is calculated dt
=
YOx ε u_ Ox ¼ rA St k
Thermodynamic relations Viscosity, specific heats coefficient and thermal conductivity are evaluated as: k¼
I X a¼1
Ya ka ;
Cp ¼
I X a¼1
Ya Cpa ;
m¼
I X
Ya ma
(25)
a¼1
Furthermore, the viscosity of species, thermal conductivity and effective diffusion coefficient of species vary in terms of temperatures which can be given as [28]:
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ma ¼ ma0
T T0
0:7
;
ka ¼ ka0
T T0
0:7 (26)
where ma0 and ka0 are viscosity and thermal conductivity coefficient of species, calculated at T0 ¼ 298 K and atmospheric pressure. Furthermore, specific heat coefficient of species are predicted by Ref. [35]: Cpa ¼ a1a þ a2a T þ a3a T2 þ a4a T3 þ a5a T4 RT
(27)
Also effective binary diffusion coefficients Dam are written as [35]: Dam ¼ PI
1 Xa
(28)
bsa ðXb =Dab Þ
In which Xa ; Dab are mole fraction and ordinary multicomponent diffusion coefficients. To use the above equation, the mass transfer coefficient of each chemical species must be calculated relative to each other. The dual mass transfer coefficient for the pair of chemical species a and b is obtained from the simplified relation below [36]. 0:0266T Dab ¼ P MWab s2ab UD
(29)
With the following associated units: Dab ¼ ½ m2 =s; T ¼ ½ K; P ¼ Pa and sab ¼ ½ A , the remaining terms are defined below: MWab ¼ 2½ð1=MWa Þ þ ð1=MWb Þ1:
(30)
MWa and MWa are molecular weights of the chemical species a and b, respectively. Also sab ¼ ðsa þ sb Þ = 2:
(31)
where sa and sa are the hard-sphere collision diameter of species a and b, respectively. And collision integral UD is defined from the following equation: 1:06036 0:19300 1:03587 þ þ * * ðT* Þ0:15610 expð0:47635 T Þ expð1:52996 T Þ 1:76474 þ expð3:89411 T* Þ
UD ¼
k=ε dL =SL
(33)
where kB is the Boltzmann constant. and value of the characteristic Lennard-Jones, εn ðn ¼ a; bÞ, are also tabulated in Table 1 [37].
Turbulent combustion flow regime In this research, the Reynolds number based on the height of step, is Re ¼ 1:35 104 , The height of the step is half the height of the combustion chamber. Therefore, the Reynolds number is expressed on the basis of the hydraulic diameter. The critical Reynolds number for an internal flow is almost 2300 based on a hydraulic diameter. The Reynolds number is related to _ the inverse of the dynamic viscosity Re ¼ ðm=mLÞ . The dynamic viscosity of gases is directly proportional to the
rCp SL
(35)
In this equation, there are numerical, analytical and experimental methods for computing SL [38]. For the methane flame with an equivalence ratio of 0.9, the value of SL is approximately 0.3 m/s at the standard temperature and pressure [38]. In the choice of the combustion model, the Damkohler number plays an important role. At flows where Da[1, the chemical reaction time is faster than the turbulence mixing time and the combustion parameters are controlled by the turbulence mixing of the flow, the assumption of fast chemical reaction is true in these combustion currents [39e41]. The EDM method is one of the models of fast chemistry reaction and is suitable for combustion areas with Damkohler numbers higher than one. Another important dimensionless number is the Karlovitz number, defined as the ratio of the combustion time scale to the Kolmogorov time scale. Ka ¼
and where the dimensionless temperature T is defined by,
(34)
In this equation, dL is the laminar flame thickness, and SL is the one-dimensional laminar flame velocity. The laminar flame thickness can be estimated from the following equation [38].
(32)
*
kB T kB T ¼ εab ðεa εb Þ0:5
Da ¼
dL z l
1:5
T* ¼
temperature ma ¼ ma0 ðT=T0 Þ0:7 [28]. In the present study, the maximum combustion temperature is almost 2200 K. Therefore, the dynamic viscosity will change with the maximum values ratio ðT=T0 Þ0:7 ¼ ð2200=298Þ0:7 y4: inside the combustion chamber. The Reynolds number is inverse to the viscosity. The Reynolds number will reach its number Re ¼ ð1:35 104 Þ =4 ¼ 3375 at its lowest value. Because of 2300 < ðRe ¼ 3375Þ, the flow relatively is located in the low Reynolds area. The Reynolds number of flow, based on the block height at the inlet of the combustion chamber is Re ¼ 1:35 104 . The Damkohler number is also defined as the ratio of the turbulence integral time scale to the combustion time scale [38].
dL =SL
(36)
ðy=εÞ0:5
In this equation, y is the fluid kinematics. Considering the conditions at inlet, according to Ref. [7], the values of Da and Ka are obtained as approximately 380 and 0.07, respectively. In the case where the combustion temperature is at its maximum value of 2200 K, the lowest value of the Reynolds is calculated as 3375 K and at this temperature, the gas viscosity will be 4 times of its previous value. In this region, new values of Daz300 and Kaz0.2 are calculated, indicating that the
Table 1 e Lennard-Jones parameters for chemical species. ε ε ½¼K Chemical s½¼ A ½¼K Chemical s½¼ A kB kB species species CH4 CO CO2 H2O
3.758 3.690 3.941 2.641
148.6 91.7 195.2 809.1
NO N2 O2
3.492 3.798 3.467
116.7 71.4 106.7
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Fig. 1 e Temperature changes (a) on the cenerline at Y ¼ 20 mm (b) At the outlet of the chamber at X ¼ 470 mm, in terms of the number of the grid points. Changes of (c) xþ , (d) yþ : based on variations in distance on the walls of the enclosure. flame is always in the laminar wrinkled or the laminar corrugated regimes [32]. Thus, a fast chemical reaction takes place inside the combustion chamber and the combustion parameters are controlled by turbulent mixing. Many researchers have used this model with a one-step or two-step global reaction mechanisms [42e45]. In the laminar wrinkled regime, the laminar flame thickness dl is much smaller than the Kolmogorov scale. Damkohler number is larger than one. Therefore, the turbulence of the stream can only wrinkle the flame front and has no effect on the chemical reaction inside the flame front. In the laminar corrugated regime, the structure is very similar to the wrinkled regime, except that the intensity of turbulence in the wavy region is greater than the velocity of the laminar flame SL . In this region, due to the turbulence intensity of the flow, large eddies can move faster than the laminar flame velocity [38]. The sum of laminar wrinkled and corrugated regimes is called the flamelets regime. Therefore, in the flamelets regime, the chemical reaction time is much faster than the turbulence time of the flow. As previously stated, the correctness assumption of the EDM model, which is due to the high speed of the chemical reaction is true here. Therefore, in order to simulate the turbulent pre-mixed combustion with the combustion chamber conditions of ref. [7], the low Reynolds model, Launder Sharma EDM is utilized. In addition to simplicity, this model has good convergence and low computational cost to run the
written code. Run-time and convergence in this study utilizing the EDM low Reynolds simulation by a computer with the specifications of 4 GB of RAM Core i3-370 M, one-core processor, takes about 2 min, while the convergence time for simulation with T-PCMC method with a computer with the specifications of four Xeon E5650 hex-core processors and 24 GB of RAM takes about 11 h [32].
Grid study After checking the accuracy of the program, grid analysis was performed. For this purpose, one state of the combustion chamber with boundary conditions of ref. [22] was considered. In order to select the appropriate grid for simulating our combustion chamber, we investigated the effect of changing the number of points on the temperature distribution along the centerline at y ¼ 20 mm, shown in Fig. 1(a). Moreover, as depicted in Fig. 1(b), the effect of changing the number of points on the temperature distribution at the outlet of the combustion chamber at x ¼ 470 mm was investigated. Due to low discrepancy between grid of 20 70 and smaller grids, this grid was chosen for further simulations. þ As illustrated in Fig. 1(a), (b), the yþ top and ybottom of the first point of the grid of the upper and lower walls and xþ of the first point of the grid of the side wall, are selected such that this point can be located in the viscous sublayer [46]. The model of near wall turbulent flow are as follows [46,47]:
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Fig. 2 e (a) Temperature profiles, (b) mean axial velocity, (c) mean CO2% volume concentrations, (d) mean CO % volume concentrations. (A) Experimental [22], (B) LS-LRN-k¡ε/EDM model utilized in the present paper with proper coefficients, (C) T-PCMC [49] and (D) Fluent three-step EDM Reynolds stress model [50]. y 0:5 yþ ¼ r Cm k m
0:5 x xþ ¼ r Cm k m
(37)
In these equations, y indicated the distance between the first node and the upper (and lower) wall and x presents the longitudinal distance of the first node from the side wall. K is kinetic energy of the turbulent flow. In the simulation of turbulence flow, the exact grid of the near-wall region is very important. Its distance to the combustion chamber’s walls can affect the accuracy of the simulation results. In the low Reynolds regime, placing the first near-wall node close to 1 and less is very desirable [48]. Fig. 1(c), (d) shows the variation of xþ for the first node close to the vertical wall and yþ for the first node close to the lower and upper walls in terms of x and y changes, respectively. As shown in these figures, the first node near the wall is located in the viscous sublayer.
Numerical scheme The governing equations are solved in Cartesian coordinates by using FORTRAN 90 programming, that has been used in LSLRN-kε/EDM framework. The turbulenceecombustion interaction in the flame field is numerically studied with better coefficients implemented in our code. A finite volume method (FVM) with staggered grids is used and SIPMLE algorithm was chosen for the coupling between the velocity and the pressure. For all simulations presented in this paper. Moreover, a Power Law Scheme (PLS) was used for the conservation equation of momentum, turbulent kinetic energy, turbulent dissipation rate, spices chemical. While the NOx and CO concentrations were obtained through applying the Zeldovich and Westbrook-Dryer mechanisms, respectively.
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Fig. 3 e Experimental [22] ( ), T-PCMC [49]( ) and LS-LRN-k¡ε/EDM model utilized in the present paper with proper coefficients ( ) (a) x=h ¼ 17:5 ðCO2%Þ , (b) x=h ¼ 17:5 ðUHC%Þ, (c) x=h ¼ 24: ðCO2%Þ , (d) x=h ¼ 24: ðUHC%Þ .
The system of governing equations is solved simultaneously using numerical or TDMA (Tri-Diagonal Matrix Algorithm) finite difference methods. The turbulent intensity of the input flow is 7%. Under Relaxation factor values considered are as follow: for momentum 0.6, for k and ε turbulent equation (0.8), for energy 0.4 and for rest of equation (0.5). The criterion of convergence is the summation of residual mass sources less than 104 for the other terms of the transport equations and is 106 for the energy equation is 105 .
Validation Fig. 2 illustrates the validity of the written code by comparison of our results with the experimental results of ref. [22] and numerical results of ref. [49] and ref. [50]. These diagrams depict temperature graph, average axial velocity, mean CO2
and CO concentrations. From these diagrams, it can be observed that the combustion model in our work, using LSLRN-kε/EDM with appropriate coefficients (A ¼ 1, B ¼ 0.5) has better results than those reported by Ref. [49] and ref. [50]. Therefore, this method is more accurate in determining the temperature field and velocity of chemical species production. The temperature profiles are depicted in Fig. 2(a). It is obvious that both numerical methods, LS-LRN-kε/EDM and T-PCMC, have good results in the combustion field modeling. The maximum combustion temperature is 1900 K, illustrating an appropriate distribution of temperature, which confirms with the experimental results. The same trend can be seen in the graphs of mean axial velocity profile, mean CO2% volume concentrations and mean CO % volume concentrations (Fig. 2(b)e(d), respectively). In the modeling of chemical species such as CO2 and CO, both methods, LS-LRN-kε/EDM and T-PCMC, have been successful to identify flow vortices at the corners of the enclosure. As shown, the LS-LRN- kε/EDM
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Fig. 4 e Effect of H₂O dilution on the temperature distribution at (b) outlet and (a) centerline of the combustion chamber.
Fig. 5 e Effect of H₂O dilution on produced NO concentration at the (b) outlet and (a) centerline of the combustion chamber.
model, utilized in the present work, with appropriate coefficients is far better in comparison with the T-PCMC model and provides proper results compared with experimental results. It should be noted that the results of three-step EDM, Reynolds stress [50] are weaker than those of the other results. Fig. 3 illustrates comparison of the values of H2O and UHC in different locations of the combustion chamber from the experimental results [22] and the numerical results [49] and the present study. As can be seen in the diagrams, the selection of the LS-LRN-kε/EDM modeling model with assumed coefficients A ¼ 1 and B ¼ 0.5 gives very good results that are very close to the experimental results. Thus, in the following sections of the paper, the distribution of temperature, velocity and concentration of combustion species are studied by introducing H2O as diluent, utilizing the aforementioned LS-
LRN-kε/EDM model. Furthermore, the distribution of CO and NOx are carefully investigated.
Results and discussion Effect of H2O dilution Fig. 4 and Fig. 6 depict the effect of H2O dilution on temperature distribution, NO concentration, mass distribution of CO at the outlet of the chamber at x ¼ 470 mm and at y ¼ 20 mm, along the centerline of the combustion chamber. As shown in Fig. 4(a), along the centerline at y ¼ 20 mm, close to the inlet of the combustion chamber before the location of the maximum temperature, with increasing H2O diluent, temperature increase with a steep slope can be
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Fig. 6 e Effect of H₂O dilution on produced CO concentration at (a) centerline (b) outlet of the combustion chamber.
observed, such that by dilute injection to the fuel and air mixture, the temperature reaches its maximum value immediately close to the inlet. Then the temperature decreases along the longitudinal direction, towards the outlet of the chamber, which is due to the absorption of combustion energy from the combustion by the water diluent. This, in turn, causes the temperature of the fluid to decrease as a result of the increase of H2O diluent, as shown in Fig. 4(b) at the outlet of the combustion chamber at x ¼ 470 mm. However, due to the limited injection of H2O diluent, the abovementioned effect at the outlet of the combustion chamber is not very significant. Fig. 5(a) illustrates that by increasing concentration of H2O, concentration of NO increases at the outlet of the combustion chamber from bottom and then gradually decreases to the top of the cross section. As shown in Fig. 5(b), concentration of NO increases along the length of chamber in the centerline initially, then becomes approximately constant after reaching a maximum point. Moreover, by adding H2O to the combustion chamber, an increment is observed in the concentration of NO in the beginning of the combustion chamber. It is inverted after a while, the concentration of NO decreases by increasing H2O at the ending part of the chamber. Moreover, with increasing H2O dilution in the combustion chamber, we see a decrease in the production of NO pollutants. The effect of the H2O diluent increase on the NOx pollutant reduction is extremely severe, such that with a slight increase in the amount of H2O diluent, a sharp reduction in the amount of this pollutant can be observed. Regarding the amount of H2O diluent, the slope of this reduction is very high. Fig. 6(a) illustrates that by adding H2O, the concentration of CO decreases at the outlet of the combustion chamber from bottom to top. As shown in Fig. 6(b), the concentration of CO increases along the length of chamber in the centerline initially and decreases after reaching a maximum point. However, by increasing the concentration of H2O, an increasing is observed in the concentration of CO initially. It is
inverted after a while, so the concentration of CO decreases by increasing H2O at the ending part of the chamber. Fig. 6(a) shows that the location of the most concentrated pollutant of CO is at the inlet of the combustion chamber. Before the location of the maximum temperature in the combustion chamber. As H2O diluent increases, the peak of produced pollutant emission CO increases, and the higher the amount of diluent, the higher the amount of peak and the inclination towards the inlet of the combustion chamber. Regarding the fact that, by increasing the H2O diluent, CO stays longer in the combustion chamber. As we move towards the outlet of the combustion chamber, the pollutant CO reacts more with other species and its mass fraction decreases. Therefore, according to the diagrams of Fig. 6(b), we see a decrease in the production of CO pollutant by the injection of H2O diluent. However, for a specific value of the H2O diluent, the increase in the combustion chamber length does not have a significant effect on the reduction of the CO pollutant. In the profiles of Fig. 7(a)e(c), the distribution of the temperature based on Kelvin, the distribution of NO concentration based on PPM and the distribution of mass fraction of CO in the combustion chamber versus changes in the H2O diluents values are depicted, respectively. As indicated by the temperature distribution (Fig. 7(a)), increasing the mass fraction of H2O as a diluent reduces the high temperature area in the combustion chamber. This, in turn, reduces NO concentration in the combustion chamber (Fig. 7(b)). At the chamber inlet, the concentration of CO production increases with increasing in the concentration of H2O but along the combustion chamber, CO reacts as fuel gradually and reduces by increasing the H2O (Fig. 7(c)). This suggests that in order to reduce the concentration of CO produced in the combustion chamber by adding H2O, the length of the chamber should be long enough; otherwise, adding H₂O has an inverted result. As the temperature distribution is shown in Fig. 7(a), an increase in the mass fraction of H2O as a diluent decreases the temperature at the outlet of the combustion chamber,
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Fig. 7 e Distribution of: (a) the temperature based on Kelvin (b) NO concentration based on PPM and (c) mass fraction of CO; for A(S ¼ 0.0), B(S ¼ 0.01), C(S ¼ 0.02) and D(S ¼ 0.03).
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although this temperature decrease is not very remarkable, but as shown in Fig. 7(b), increasing H2O diluent leads to extreme reduction of NOx concentration, mainly found at the outlet of the combustion chamber. The contours in Fig. 7(c) illustrates how the concentration of CO pollutant in the combustion chamber is affected by the increase in the amount of H2O in the fuel and air. As indicated by the profiles, as the H2O diluent increases, the pollutant CO increases at the combustion chamber inlet. As shown in the case A of Fig. 7(c), the amount of CO reaches its minimum value after the location of the maximum temperature in the combustion chamber and before the outlet. This indicates that the combustion chamber length should not be less than a specific value, (in this case, without diluent about 300 mm), but increasing the length after this critical point has little effect on CO reduction.
Conclusion We have performed a numerical investigation of the effect of diluents of H2O on NOx and CO formation in turbulent premixed methane-air flame. In this work, we utilized a finite volume method (FVM) with staggered grids for discretizing the set of governing equations. SIMPLE algorithm was implemented using a fine grid resolution. Discretization of the convective terms was done using Power Law Scheme (PLS). In order to simulate the interaction of turbulence and reaction in the flame, the eddy dissipation and kε turbulence models were applied. The implemented LS-LRN-kε/EDM method with the new coefficients depicted excellent agreement with previously published experimental measurements. The results of the research show that T-PCMC advanced models can not accurately model weak turbulent flows. The kε model with wall functions cannot simulate the temperature distribution and turbulent combustion flow patterns, accurately. Because the corrections made to them are not efficient for combustion flows. In these cases, the LRN models provide fairly better answers. Finally, in this work, LS-LRN-kε/EDM model has been used to study the distribution of temperature and distribution of NOx and CO pollutants in a turbulent premixed flame. The following results were obtained: 1. By increasing the H2O dilution in the pre-mixed turbulent combustion process, the temperature increases. Furthermore, concentrations of NOx and CO pollutants along the centerline of the combustion chamber increase close to the inlet of the combustion chamber. However, after the location of the maximum temperature in the combustion chamber along the centerline towards the outlet of the combustion chamber, we see a sharp decrease in temperature, a decrease in the NOx and CO pollutants in the combustion chamber due to the absorption of combustion energy by H2O. 2. With a slight increase in the H2O diluent, we see a slight decrease in temperature compared with the significant reduction of NOx and CO emissions from the combustion chamber.
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3. By increasing the H2O diluent, the maximum amount of CO emission is directed towards the inlet of the combustion chamber. This is because of inadequate burning of methane in the presence of H2O, which H2O as an intermediate molecule causes effective collision of methane molecules with oxygen molecules. 4. At a specific value of the H2O diluent at a given location, the amount of CO is suddenly reduced to the lowest value. Therefore, the combustion chamber must always be selected such that its length will not be less than a certain value. Since in this case it causes more emission of CO pollutant into the environment. 5. The length of the combustion chamber should be long enough in order to reduce the produced CO due to H₂O injection. Otherwise, the injection of H₂O will have an adverse effect on the production of NO and CO, which has not been reported in previous studies. 6. Increasing the mass fraction of H₂O as a diluent, reduces the high temperature region in the combustion chamber. This, in turn, reduces NO concentration in the combustion chamber.
Declaration of competing interest The authors declare no conflict of interest.
references
[1] Lieuwen T, Zinn BT. The role of equivalence ratio oscillations in driving combustion instabilities in low NOx gas turbines. In: Symposium (International) on combustion, 27. Elsevier; 1998 Jan 1. p. 1809e16. [2] Poinsot T. Prediction and control of combustion instabilities in real engines. Proc Combust Inst 2017;36(1):1e28. [3] Telesca A, et al. Use of oxyfuel combustion ash for the production of blended cements: a synergetic solution toward reduction of CO2 emissions. Fuel Process Technol 2017;156:211e20. [4] Zaidaoui H, Boushaki T, Sautet JC, Chauveau C, Sarh B, € kalp I. Effects of CO2 dilution and O2 enrichment on nonGo premixed turbulent CH4-air flames in a swirl burner. Combust Sci Technol 2018;190(5):784e802. [5] Ma T, Takeuchi K. Technology choice for reducing NOx emissions: an empirical study of Chinese power plants. Energy Policy 2017;102:362e76. [6] Wang H-f, Chen Y-l, Chen H-l, Liu M-h. A numerical analysis ~ 2/N ~ 2 laminar of instantaneous response of the CH~ 4/O flamelet. Chin J Comput Phys 2006;23(2):193. [7] Ilbas M, Yılmaz I, Veziroglu TN, Kaplan Y. Hydrogen as burner fuel: modelling of hydrogenehydrocarbon composite fuel combustion and NOx formation in a small burner. Int J Energy Res 2005;29(11):973e90. _ Kaplan Y. Investigations of hydrogen and [8] Ilbas M, Yılmaz I, hydrogenehydrocarbon composite fuel combustion and NOx emission characteristics in a model combustor. Int J Hydrogen Energy 2005;30(10):1139e47. [9] Lopez-Parra F, Turan A. Computational study on the effects of non-periodic flow perturbations on the emissions of soot and NOx in a confined turbulent methane/air diffusion flame. Combust Sci Technol 2007;179(7):1361e84.
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[10] Wetzel F, Habisreuther P, Zarzalis N. Numerical investigation of lean blow out of a model gas turbine combustion chamber using a presumed JPDF-reaction model by taking heat loss processes into account. In: ASME Turbo Expo 2006: Power for Land, Sea, and Air. American Society of Mechanical Engineers; 2006 Jan 1. p. 41e9. [11] Hahn WA, Wendt JOL. NOx formation in flat, laminar, opposed jet methane diffusion flames. In: Symposium (International) on Combustion, 18; 1981. p. 121e31. no. 1. [12] Saqr KM, Aly HS, Sies MM, Wahid MA. Effect of free stream turbulence on NOx and soot formation in turbulent diffusion CH4-air flames. Int Commun Heat Mass Transf 2010;37(6):611e7. [13] Shaw H. The effects of water, pressure, and equivalence ratio on nitric oxide production in gas turbines. J Eng Power 1974;96(3):240e6. [14] Greeves G, Khan IM, Onion G. Effects of water introduction on diesel engine combustion and emissions. In: Symposium (International) on combustion, 16; 1977. p. 321e36. no. 1. [15] Burnham JB, Giuliani MH, Moeller DJ. Development, installation and operating results of a steam injection system (STIG™) in a general electric LM5000 gas generator. In: ASME 1986 international gas turbine conference and exhibit. vol. 10. American Society of Mechanical Engineers; 1986. p. 257e62. V004T10A019-V004T10A019. [16] Feitelberg AS, Tangirala VE, Elliott RA, Pavri RE, Schiefer RB. Reduced NOx diffusion flame combustors for industrial gas turbines. In: ASME turbo expo 2000: power for land, sea, and air. vol. 123. American Society of Mechanical Engineers; 2000. p. 757e65. V002T02A006-V002T02A006. € ke S, et al. Influence of steam dilution on the combustion [17] Go of natural gas and hydrogen in premixed and rich-quenchlean combustors. Fuel Process Technol 2013;107:14e22. [18] Cheng I. Power systems. Cheng Power Syst 2015. http://www. chengpower.com/. [19] Xue R, Hu C, Sethi V, Nikolaidis T, Pilidis P. Effect of steam addition on gas turbine combustor design and performance. Appl Therm Eng 2016;104:249e57. [20] Pugh DG, et al. Dissociative influence of H2O vapour/spray on lean blowoff and NOx reduction for heavily carbonaceous syngas swirling flames. Combust Flame 2017;177:37e48. [21] Dai C, Shu Z, Li P, Mi J. Combustion characteristics of a methane jet flame in hot oxidant coflow diluted by H2O versus the case by N2. Energy Fuels 2018;32(1):875e88. 2018/ 01/18. [22] El Banhawy Y, Sivasegaram S, Whitelaw JH. Premixed, turbulent combustion of a sudden-expansion flow. Combust Flame 1983;50:153e65. orie des eaux courantes. Impr. [23] Boussinesq J. Essai sur la the nationale; 1877. [24] Sarkar S, Lakshmanan B. Application of a Reynolds stress turbulence model to the compressible shear layer. AIAA J 1991;29(5):743e9. 1991/05/01. [25] Launder BE, Sharma BI. Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett Heat Mass Transf 1974/11/01/ 1974;1(2):131e7. [26] Launder BE, Spalding DB. The numerical computation of turbulent flows. In: Numerical prediction of flow, heat transfer, turbulence and combustion. Pergamon; 1983. p. 96e116. [27] Peters N. Turbulent combustion. Cambridge university press; 2000. [28] Magnussen BF, Hjertager BH. On mathematical modeling of turbulent combustion with special emphasis on soot
[29] [30]
[31]
[32]
[33]
[34]
[35] [36] [37] [38] [39]
[40] [41] [42]
[43]
[44]
[45]
[46]
[47] [48] [49]
[50]
formation and combustion. Symposium (international) on Combustion, 16. Elsevier; 1977 Jan 1. p. 719e29. Zeldovich J. The oxidation of nitrogen in combustion and explosions. Eur Phys J A Hadrons Nucl 1946;21:577e628. Hanson RK, Salimian S. Survey of rate constants in the N/H/O system. In: Gardiner WC, editor. Combustion chemistry. New York, NY: Springer New York; 1984. p. 361e421. Miller JA, Bowman CT. Mechanism and modeling of nitrogen chemistry in combustion. Prog Energy Combust Sci 1989;15(4):287e338. Raine RR, Stone CR, Gould J. Modeling of nitric oxide formation in spark ignition engines with a multizone burned gas. Combust Flame 1995;102(3):241e55. Brewster BS, Cannon SM, Farmer JR, Meng F. Modeling of lean premixed combustion in stationary gas turbines. Prog Energy Combust Sci 1999;25(4):353e85. Westbrook CK, Dryer FL. Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames. Combust Sci Technol 1981;27(1e2):31e43. Turns SR. An introduction to combustion. New York: McGraw-hill; 1996. Reid RC, Prausnitz JM, Poling BE. The properties of gases and liquids, 4; 1987. p. 450e575. Svehla RA. Estimated viscosities and thermal conductivities of gases at high temperatures. 1962. Poinsot T, Veynante D. Theoretical and numerical combustion. RT Edwards, Inc.; 2005. s J, Gil A, Corte s C, Herce C. Numerical study of coPallare firing coal and Cynara cardunculus in a 350 MWe utility boiler. Fuel Process Technol 2009;90(10):1207e13. Veynante D, Vervisch L. Turbulent combustion modeling. Prog Energy Combust Sci 2002;28(3):193e266. Stephen R. An introduction to combustion: concepts and applications. McGraw-hill; 1996. Li M, Christofides PD. Computational study of particle inflight behavior in the HVOF thermal spray process. Chem Eng Sci 2006;61(19):6540e52. Li M, Christofides PD. Multi-scale modeling and analysis of an industrial HVOF thermal spray process. Chem Eng Sci 2005;60(13):3649e69. Dolatabadi A, Mostaghimi J, Pershin V. Effect of a cylindrical shroud on particle conditions in high velocity oxy-fuel (HVOF) spray process. J Mater Process Technol 2003;137(1e3):214e24. Khan MN, Shamim T. Effect of particle and injection parameters on the performance of a dual-stage high-velocity oxygen fuel thermal spray system. J Therm Spray Technol 2015;24(5):807e16. Versteeg HK, Malalasekera W. An introduction to computational fluid dynamics: the finite volume method. Pearson education; 2007. Pope SB. Turbulent flows. IOP Publishing; 2001. Gerasimov A. Modeling turbulent flows with fluent. Sheffield, UK: Ansys Inc; 2006. Velez C, Martin S, Jemcov A, Vasu S. LES simulation of an enclosed turbulent reacting methane jet with the tabulated premixed CMC method. 2015. no. 56697, p. V04BT04A055. Martin SM, Kramlich JC, Riley JJ. The premixed conditional moment closure method applied to idealized lean premixed gas turbine combustors. In: ASME Turbo Expo 2002: Power for Land, Sea, and Air. American Society of Mechanical Engineers; 2002 Oct. p. 573e80.