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Abstract:Prediction of NOx and OH is one of the challenging problems in turbulent combustion. In the present study a large eddy simulation (LES) of a CH4/H2/N2 diffusion .ame is carried out at a Reynolds number of 15,200 with special emphasis on the NOx prediction. A steady state .amelet model is used as a combustion closure model. A steady state .amelet either based on the scalar dissipation or progress variable approach is not appropriate for prediction of NOx. In the present study a transport equation for the NOx is solved, where source term is estimated from the .amelet tables as a function of mixture fraction, its variance and scalar dissipation rate. In LES the in.ow boundary condition affects the entire .ow .eld, and its effects become more important in combustion. In the present study effect of not accounting a suitable in.ow boundary condition is studied and its effect is quanti.ed in terms of nozzle diameter. The NOx prediction depends on the chemical mechanism, in the present study three mechanism GRI-Mech 3.0, GRI-Mech
2.11 and San Diego mechanism are studied. The present study showed that the .amelet model predicted very good agreement with measurements for temperature and major species with all the reaction mechanisms. However, for predictions of minor species such as NOx the San Diego mechanism performs better than the other reaction mechanisms. The study showed the potential of steady .amelet model for predicting the kinetically controlled reaction such as NOx. The present study did not account the radiation, which would reduce the global temperature and subsequently performance of the chemical mechanisms.
Combustion of a fuel with oxidizer having N2 leads to formation of NOx, especially at high temperatures. The NOx emissions contribute to the formation of .ne particles and ozone smog. NOx also causes acid rain leading to low Ph that degrades water quality and harms .sh. NOx emissions also contribute to haze air pollution in our environment. Fundamental understanding of the emission of hazardous species such as NOx during a combustion process is critically important. Development of a low NOx burner requires a better understanding of the interaction of the turbulence and chemistry. NOx forma
tion in turbulent .ames is a complex process that requires accurate modeling of chemistry, turbulence, and their interactions. Large Eddy Simulation (LES) is one of the viable tools for predicting turbulent .ows at comparatively reduced cost. LES resolves larger eddies on the grid scales, and the role of smaller more universal eddies are modeled. Combustion takes place on the .ne unresolved small structures. However, LES does not resolve these reactive .ne structures, and the turbulence-chemistry interactions need to be modeled using a model. LES combustion models do not differ considerably from already existing RANS model but LES itself captures the instantaneous quantities and mixing more accurately. The turbulence combustion closure models for LES have been studied over the decades.
Solving a transport equation along with a source term is very computationally expensive for LES. Tabulation approaches both for premixed and non-premixed .ames have been proposed to overcome this dif.culty.1 The conserved scalar variable approach can be applied to reaction system where the reaction rates are very fast and the reaction zone thickness is small. When the reaction time becomes larger than the Kolmogorov time the reaction interface with .ames, and .ames becomes disturbed and the conserved scalar variable has limitation for these .ames. Nevertheless, the conserved scalar approach is widely used in turbulent combustion. The conserved variable approach was proposed by Peters.2, 3 The method have been tested and used widely for Reynolds Averaged Navier Stoke (RANS) simulation. The extension of the RANS based .amelet modeling to the LES is straightforward. A LES subgrid combustion model based on .amelet was presented by Cook and Riley4 and they carried out a LES simulation of a hydrogen diffusion .ame. Kempf et al.1 presented LES of Sandia Flame D, Bluff Body .ame, Hydrogen diffusion Flame and counter .ow diffusion .ame using the steady state .amelet model and they obtained satisfactory agreement with experiments. Pitsch and Steiner5 carried out a LES of the piloted Sandia-D .ame using an unsteady Lagrangian .amelet model and they achieved an excellent agreement even for minor species.
The .amelet approach is an attractive way for modeling turbulent .ames, because of the low computational cost. In the .amelet approach the chemistry is decoupled from the mean .ow. Though the .amelet approach is widely accepted for the prediction of major and global temperature, the validity of the .amelet approach for NOx prediction is questionable.6 A detailed study was carried out by Vranos et al.7 on NOx formation and differential diffusion in a turbulent CH4/H2 diffusion .ame. Their study showed a large discrepancies between the .amelet results and the measured NOx levels. It was concluded that transient behavior and .amelet interactions are signi.cant contributor. It was speculated that the shift and deviations from the experiments were attributed largely to premixing and homogeneous reaction effects, transients, and .amelet interactions. The effect of the radiation heat loss was insigni.cant in their study, because of the lower .ame height. The effect of the radiative heat loss on NOx is important and has been studied by Chen and Changa.8 They carried out the joint scalar probability density function (PDF) approach and the traditional .amelet model for modeling of NOx formation in a turbulent, non-premixed jet .ame. The importance of various effects such as transients, .ame-interaction, preferential diffusion, and radiative heat loss on NOx formation were evaluated. They concluded that the radiative heat loss was important for NOx predictions in the far .eld, and it can lower the predicted values by a factor of 3 leading to a better agreement with the experimental data. The effect of preferential diffusion was not much for the over-prediction in the NOx levels, which is similar .nding to Vranos et al.7 In the present study radiation and preferential diffusion effects are not studied. However, the effect of not accounting the radiation on .ame temperature is mentioned. A previous Reynolds Averaged Navier Stokes (RANS) study of .ame DLR by Lee and Choi9 showed that the inclusion of radiation caused the reduction of the temperature in the far .eld region of the jet and leading to a better agreement with the experimental data.
Since the steady state .amelet approach is not the solution, then the alternatives have to be worked out. The current state of the art for NOx prediction are unsteady .amelet model, PDF transport, a transport equation of NOx with source term from the precalculated tables, progress variable approach, Eddy Dissipation Concept (EDC) etc. In the present method a transport equation for NOx is solved with a source term from the .amelet table. A similar approach have been studied by Ravikanti et al.10 for RANS based approach for bluff body burner. In the present study LES approach is used. Another important issue while simulating the NOx is the effects of the chemical kinetic mechanism. The effect of the three chemical kinetic mechanism, GRI-Mech 3.0, GRI-Mech 2.11 and San Diego mechanism are studied. In the present study LES of .ame DLR is carried out at a Reynolds number of 15,200. In LES selecting a proper in.ow boundary condition is a challenge. In present study effect of the in.ow boundary condition is quanti.ed in terms of the nozzle diameter.
Governing Filtered Equations
The governing .ltered equation for LES are The continuity equation
+ =0 (1)
The momentum equation
u iu j .p
+= - +
.t .xj .xj
. .u i uj .tsgs
+ . -
The mixture fraction equation
+ Z = .Di(3)
.t .xj .xj.xj
is a .ltered density,u i is a .ltered velocity component, p
is .ltered pressure, is the dynamic viscosity, t is time, tsgs is subgrid stress andZ is the Favre .ltered mixture fraction. The governing equations were discretized with the .nite volumes technique on a staggered cylindrical grid. The convective and diffusive terms in the momentum equation were discretized using a second order central differencing scheme. The convective term in species transport equation were discretized using the Total Variation Diminishing(TVD) schemes. A scheme is said to be TVD if it does not increase the
total variation of the solution TV(u= TV(un), where n+1)
TV(u= Lj |uj+1 -uj |. The concept of TVD was introduced by Harten.11 The TVD schemes are bounded schemes, which do not produce undershoot and overshoot in the mass fractions. The Charm limiter1 is used in this study. The Sub Grid Stress (SGS) term was closed with Smagorinsky subgrid model. The numerical accuracy of current .nite volume technique is an order of two in space. The transport equations were integrated in time by an explicit low storage three stage Runge-Kutta method. An incompressible version of the code was used. A projection method was used for pressure velocity correction. For further details please refer.1
Modeling of the Filtered Reaction Rates .amelet approach.
The laminar .amelet modeling is employed here for the turbulent chemistry coupling. The model is based on the conserved variable approach, where mixture fraction represents the mixedness of the fuel and oxidizer or local equivalence ratio. The .amelet approach decouple the chemistry from the mean .ow, and the effect of the chemistry on the .ow is modeled through the density and viscosity as a function of mixture fraction, its variance and scalar dissipation rate or progress variable. While implementing the .amelet model the species and energy governing equations are transformed in the mixture fraction space. The reduced form of the equations are solved in the mixture fraction space. The local turbulent .ame structures is assumed as a thin laminar .amelets, which is characterized by the .ltered mixture fraction, it variance and scalar dissipation rate. The sub grid variance of the reactive scalars is a parameter which is used to account for the turbulence-chemistry interaction. In LES instantaneous information is available then a simple algebraic models is suf.cient to estimate the subgrid variance. A model developed by Forkel12 is used in present simulations. The .ltered rate of scalar dissipation .can be derived from the effective viscosity (ef f = + t), the resolved
mixture fraction gradient .xj and the Schmidt-number (s, st).4
..t .f .f
. =2 + (4)
sst .xj .xj
The subgrid distribution of the mixture fraction is described by a presumed-shape PDF and for the scalar dissipation rate is described by a Dirac peak. The chemical state (density, viscosity, species mass fraction, temperature, production/destruction of species etc.) is a function of the .ltered mixture fraction Z, the subgrid variance Z ' , and the .ltered scalar dissipation rate ..
The .amelet library was generated by using the FlameMaster code of Pitsch.13 FlameMaster solves the governing .amelet equations on the mixture fraction space. The effect of differential diffusion of species and radiation heat loss were neglected. Equal diffusivity for all the species were assumed. As it was mentioned that the usual way of using the .amelet approach for predicting the NOx is inappropriate. In the present study, a transport equation for the NOx mass fraction was solved. The source term in the transport equation was modeled with the where, YNOx and .NOx are .ltered NOx mass fraction and source term. The
..YNOx + ..YNOxuj =
.t .xj (5)
. .xj .DNOx .YNOx .xj + ..NOx
18 11 ' '
.NOx = .NOx (Z,Z ; .)P (Z,Z )P (.) dZd. (6) W00
The source term .T in equation (6) was evaluated from the
.amelet table as a function of mixture fraction Z, its variance Z ' and scalar dissipation rates .. The source term .NOx in equation (5) was obtained by integrating the .amelet source term .T with presumed PDFs for mixture fraction and scalar
Results and Discussion
Geometrical and Numerical Con.guration of Test Case
LES of Flame DLR1416 was carried out. Flame DLR has a fuel nozzle with a diameter (D) of 8mm which was surrounded by an air co-.ow of 0.2m/s.The central jet contains 22.1 % CH4, 33.2 %H2, and 44.7 % N2 by volume. The fuel bulk velocity was
42.2 m/s which gave a Reynolds number of 15,200 based on the nozzle diameter D. Hydrogen was added to stabilize the .ame and Nitrogen was added to reduce thermal radiation and to improve the signal quality of the Raman scattering technique.1416 For the numerical simulation a cylindrical computational domain with 120D in axial direction and 30D in radial direction were employed. The numerical grids of 1024 32 57 were used axially, circumferentially and radially respectively. The grid nodes were equidistant in the axial and circumferential directions. Five cells were used in nozzle, otherwise the grid was stretched radially.
GRI-Mech 2.1121 and the San Diego mechanism,22 hereafter
0.08SD, were used in the present study. GRI-Mech Version 2.11
0.07is a successor to GRI-Mech 1.2 and contains 277 elementary
chemical reactions with 49 species. The Version 2.11 was not
optimized for modeling pure nitrogen-hydrogen-oxygen GRI
Mech 3.0 is an optimized mechanism designed to model natural
gas combustion, including NO formation and reburn chemistry.
It consist of 325 elementary reactions with 53 species. The San
Diego mechanism comprises 52 species with 454 reactions. It
Figure 2: Centerline pro.les of mean and RMS value of mixture fraction
Effect of In.ow Boundary Condition
The in.ow boundary condition was Dirichlet condition where velocity pro.les , mixture fraction and NOx species mass fraction were speci.ed.1417 Velocities .uctuations with speci.ed length scales were generated using a turbulence in.ow generator developed by Klein et al.18 and these .uctuations were superimposed over mean velocity pro.le.19 On the downstream (out.ow boundary) zero gradient conditions (.ui/.xi =0.0) was posed. On the annular surface of the computational domain .xed absolute values of pressure and zero gradients for velocity components were speci.ed.
is relatively new and includes detailed nitrogen chemistry.
LES predicts spreading more accurately than the RANS, however a major disadvantage with LES is a proper speci.cation of the in.ow boundary conditions. As it was mentioned that the in.ow boundary condition was generated using the pseudo in.ow turbulence generator. The turbulence generator generates the in.ow pro.le with the speci.ed length scales, which does not have the proper turbulent length and velocities scales. In addition to that it does not represent the actual experimental conditions, where mixing and burning leads to the sudden expansion of the gases due to the heat release, which affects the .ow parameters at inlet. In the present numerical simulation the in.ow boundary condition is the .xed Dirichlet boundary, which does not allow the sudden changes in the velocities due to sudden heat release. Forkel and Janica23 have studied the in
.uences of the in.ow boundary conditions on H2 diffusion jet
The jet axial velocity can be represented by an origin and an
empirical constant. For non-reacting round jets the inverse of
centerline axial velocity with respect to the axial distance is a
400 200straight line. Then, the axial velocity distribution with respect to the axial distance can be easily represented by the origin and
0the empirical constant.24
Figure 3: Centerline pro.les of mean and RMS value of temperature 0.04
X/D Figure 5: Centerline pro.les of H2 O and H2 Figure 4: Centerline pro.les of CO2 and CO
However, this practice is normally not used in case of reacting Three hydrocarbons kinetic mechanisms, GRI-Mech 3.020 , jets. In the present simulation a similar method was adopted to understand the effect of the in.ow boundary condition. Fig-0.0012ure 1 shows the centerline distribution of the inverse of the ax
ial velocity, speci.cally, UB /U0(x), where UB is the jet bulk
velocity and U0(x) is the centerline axial velocity. Figure 1
shows three data, experimental, calculation without shift(LES
actual prediction) and calculation with shift (LES actual prediction shifted by 5D in axial direction). It is observed that the slopes of three data set are the same except there is a slight offset between the original LES prediction and experiments. In order to compensate the offset the LES predictions were shifted by 5D. The effect of in.ow boundary condition was quanti.ed
0.0004 0.0002 0
Figure 7: Centerline pro.les of OH
in terms of the nozzle diameter D. In the present simulation 5D 0.00018shift was required to compensate in.ow uncertainty. However, 0.00016it will vary from a case to case and detailed validations are re-0.00014quired which is not covered in the present study. All the scalar 0.00012
ations of mixture fraction, the predictions are in satisfactory
agreement with experimental data. There is a slight discrepancy between RMS of mixture fraction and experiments because of 0 0 20 40 60 80 100 120 the nozzle problem.X/D
Figure 8: Centerline pro.les of NOx retrieved from the .amelet table
and velocities data were shifted by 5D, with this shifting the
predictions are in very good agreement with the experiments.
Figure 2 shows the centerline pro.le of the mean and .uctu-
X/D Figure 9: Centerline pro.les of NOx obtained by solving a transport Figure 6: Centerline pro.les of CH4 and O2 equation for NOx mass fraction
Figure 3 shows the mean and RMS of temperature centerline pro.les. The predictions are in excellent agreement with experiments. Figure 4 shows the centerline pro.les of the CO2 and CO. It is observed that the CO2 was underpredicted close to the stoichiometric regime, and the CO was overpredicted in this regime. Figure 5 shows the centerline pro.les of the H2O and H2. It is observed that H2O was underpredicted close to the stoichiometric regime, and H2 was overpredicted in this regime. Figure 6 shows centerline pro.les of the CH4 and O2. Near to the stoichiometric region CO2 and H2O were under predicted, whereas CO and H2 were overpredicted as shown in Figures 4 and 5. It is also observed that the O2 was overpredicted near to the stoichiometric regions as shown in Figure 6.
The exothermic reactions such as CO + O2 =. CO2 and H2 + O2 =. H2O will lead to further increase in the temperature in stoichiometric region. However, in the present study effect of radiation was not accounted, otherwise with radiation temperature would have been underpredicted. Accounting of the radiation increases the computational time and dimensions of the .amelet table. A previous RANS study by Lee and Choi9 of same .ame showed that the radiation reduced the temperature in the far .eld region of the jet. Figure 7 shows the centerline pro.le of the OH. The OH is slightly over predicted in stoichiometric regime. It is concluded that the effect of the used mechanism have insigni.cant effect on the major species and global temperature.
A major objective of the present study was to establish a methodology for NOx prediction using the steady state .amelet approach, and also understand the in.uences of the chemical mechanism on NOx predictions. Figures 8 and 9 show the centerline pro.les of the NOx with and without retrieving NOx concentration from the .amelet table. It is observed that the conventional way of NOx prediction from .amelet tables over-predicted the NOx, on the other hand solving a transport equation for the NOx mass fraction gave a considerably better agreement. The effect of chosen mechanism is signi.cant on the NOx predictions. This is because, the each hydrocarbon mechanism have different subsets for NOx chemistry. In addition to that the formation of NOx largely depends on the free radical such as O and H.
RANS study10 of bluff body .ame showed that the GRI-Mech
2.11 predicts better than the other two mechanisms.
Figures. 10, 11 and 12 show the radial pro.les of mean and RMS of axial velocity at R/D = 10, R/D = 20, and R/D = 40 respectively. Figure 10 shows the mean velocity is predicted well but the .uctuations are quite high close to nozzle, because of the nozzle problem and central differencing scheme used for discretization of the convective terms in momentum equations. At R/D = 20 and R/D = 40 the prediction of mean and RMS of axial velocity are in satisfactory agreement.
20 5 0 010
0 2 4 6 8 10R/D
0Figure 12: Radial pro.le of mean and RMS of the axial velocity at
R/D = 40
Figure 10: Radial pro.le of mean and RMS of the axial velocity at
Figs. 13, 14 and 15 show the mean and .uctuation radial mix-
R/D = 10
ture fraction at R/D = 10, R/D = 20, and R/D = 40 respectively. Both the mean and .uctuations are in satisfactory agreement with the experimental data. Though RMS of axial veloci
ties were overpredicted close to nozzle (see Figure 10), RMS of the mixture fraction are predicted well as shown in Figure 13.
Because the TVD scheme was used for the discretization of the
convective term in mixture fraction equation, which is numerically diffusive compared to the central differencing schemes.
0 1 2 3 4 5
R/D = 20 0.7
Three routes have been found important for NOx formation in
hydrocarbon and non-hydrocarbon fuel. These are the thermal route, the N2O route, and the the prompt mechanisms. The GRI-Mech 2.11 mechanism underpredicts the NOx level near.eld and the GRI-Mech 3.0 mechanisms overpredict the NOx level by a large margin in the far.eld region. It is observed that the SD mechanism predicted more accurately than the GRI-Mech 3.0 and GRI-Mech 2.11. However, A previous
Figure 13: Radial pro.le of mean and RMS of the mixture fraction at
R/D = 10
Figure 16: Radial pro.les of NOx at R/D
Figure 14: Radial pro.le of mean and RMS of the mixture fraction at X/D R/D = 20 Figure 17: Radial pro.les of NOx at R/D = 20
Figs. 16, 17, 18 and 19 show the mean radial pro.les of NOx at R/D = 10, R/D = 20, R/D = 40, and R/D = 80 respectively. At R/D = 10 and R/D = 20, for R/D = 1 the NOx predictions are reasonable well with SD mechanism, whereas for R/D = 1 the predictions with GRI-Mech 3.0 performed better than other mechanisms. At R/D = 40 the GRI-Mech 3.0 mechanism predicted reasonably well compared to the other mechanism. At R/D = 80 the SD mechanism pre
0 2 4 6 8 10
dicted reasonably well compared to the other mechanism. The R/D present study shows that the SD mechanism predicts reasonably Figure 18: Radial pro.les of NOx at R/D = 40
well compared to the other mechanism in throughout the .ame 0.00012regime.
0 5 10 15 20 R/D
Figure 15: Radial pro.le of mean and RMS of the mixture fraction at
LES of the .ame DLR is carried out using a steady .amelet
R/D = 40
combustion model. The present study showed that for NOx pre
dictions a conventional approach of retrieving from the .amelet
tables is not appropriate due to large difference in chemical
times scales. A methodology based on the transportation of
the NOx with a source term from the .amelet table is proposed. The method predicted more accurately than the conventional
method. To account the nozzle problems all the scalar and ve
locities data were shifted by 5 nozzle diameter, with this ad
justment the predictions are in satisfactory agreements. The
effect of not accounting the radiation is also studied. The ef-R/D fects of three well known hydrocarbons mechanism are studied.
The NOx values are overpredicted for all three studied mechanism. The N/H/O subsets from the GRI-Mech 3.0 gives over-prediction in NOx value, the SD mechanism gives a good estimates compared to the other mechanism. However, the in.uences of a mechanism will vary from the case to case. Present study conclude that it would be advisable to use more than one mechanism for accurate NOx estimation.