Numerical analysis of laminar methane–air side-wall-quenching

Combustion and Flame 186 (2017) 299–310

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Numerical analysis of laminar methane–air side-wall-quenching Sebastian Ganter a,∗, Arne Heinrich a, Thorsten Meier a, Guido Kuenne a, Christopher Jainski b, Martin C. Rißmann b, Andreas Dreizler b, Johannes Janicka a a b

Institute of Energy and Power Plant Technology, TU Darmstadt, Jovanka-Bontschits-Strasse 2, Darmstadt 64287, Germany Institute Reactive Flows and Diagnostics, TU Darmstadt, Jovanka-Bontschits-Strasse 2, Darmstadt 64287, Germany

a r t i c l e

i n f o

Article history: Received 30 March 2017 Revised 6 July 2017 Accepted 23 August 2017

Keywords: Premixed Methane Detailed chemistry Flame-wall-interaction Side-wall-quenching

a b s t r a c t Flame-wall-interaction (FWI) is investigated numerically using a premixed stoichiometric Side-WallQuenching configuration. Within the 2D fully resolving laminar simulation, detailed chemistry is used to study the stationary quenching of a methane–air (CH4 ) flame at an isothermal inert wall of 300 K. The investigation is related to a recent experimental study that revealed that the carbon-monoxide distribution substantially differs in the near-wall region when compared to an undisturbed flame. Simulations are carried out using different reaction mechanisms (GRI and Smooke) as well as diffusion treatments (unity Lewis and mixture averaged transport) and the results are compared to the measured temperature and CO concentrations. Specifically regarding the latter, being an important pollutant, recent attempts based on tabulated chemistry failed in predicting its near-wall accumulation. Accordingly, within this work the detailed chemistry simulations are used to investigate the origin of CO near the wall. Therefore, a Lagrangian analysis is applied to quantify the contribution of chemical production and consumption as well as diffusion to understand the root mechanism of the high CO concentrations measured. The analysis revealed that the high CO concentrations near the wall results from a transport originating from CO produced at larger wall distances. In that region being not submitted to large heat losses, a high chemical activity and corresponding CO production is found. Accordingly, a diffusion process is initiated towards the wall where the chemical sources itself were actually found to be negative. © 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction The investigation of flame-wall-interaction (FWI) constitutes an important research field since in many technical combustors the reaction zone approaches the enclosing walls. In some applications flames are in direct contact with a relatively cold wall which can have an influence on the efficiency of the combustor and also on the formation of pollutants [1]. Downsizing concepts as found in IC engines which increase the surface to volume ratio may further amplify the importance of wall effects [2]. In order to optimize combustors, an understanding of the dominating phenomena in the close proximity of walls is essential. This work aims to contribute to a deeper insight in this research field. Many publications concentrate on the prediction and measurement of quenching distances and wall heat fluxes. Popp and Baum [3] investigated the Head-On-Quenching (HOQ) of a methane flame using a one-dimensional detailed chemistry (DC) simulation. Ezekoye et al. [4] experimentally studied the HOQ of methane and

∗

Corresponding author. E-mail address: [email protected] (S. Ganter).

propane flames using a constant volume chamber. Both works concluded that single step mechanisms and simplified chemical transport models can not predict the FWI correctly since low activation energy recombination reactions have a significant contribution during the quenching. Sidewall quenching (SWQ) was studied by Alshaalan and Rutland [5,6] within a three-dimensional direct numerical simulation (DNS) of a V-shaped flame in a turbulent Couette flow. They also used a single step reaction approach and therefore could not account for radical recombination effects near the wall. A turbulent three-dimensional DNS applying detailed chemistry has been carried out by Gruber et al. [7], who simulated an anchored V-shaped hydrogen flame within a channel flow. One of their major findings was that the flame speed does not drop to zero despite a vanishing reaction rate. Accordingly Gruber et al. [7] concluded an increasing importance of the diffusional contribution onto the flame speed at the wall. The role of the diffusion processes is also the central issue of this work. Chauvy et al. [8] performed detailed chemistry simulations in order to study the formation of unburnt hydrocarbon (HC). They considered the HOQ scenario as well as combustion in crevices and applied a skeletal mechanism mimicking iso-octane combustion. By contrast the current work focuses on the SWQ scenario and a methane–air flame.

http://dx.doi.org/10.1016/j.combustflame.2017.08.017 0010-2180/© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

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This work continues the investigation of SWQ that was evaluated experimentally by Jainski et al. [9] using a premixed methane Side-Wall-Quenching burner. During his work extensive measurements regarding flow field, OH- and CO-distribution, and temperature were performed. Jainski et al. [9] observed an increased CO mass fraction at low temperatures near the wall when compared with a freely propagating flame. The measured data could not provide an adequate explanation for this behavior. First numerical simulations were carried out by Heinrich et al. [10], which covered the full SWQ burner configuration. Using the Flamelet Generated Manifold (FGM) chemistry reduction approach which allows for simulations of large computational domains they found that their simulation accomplishes to predict the major structures such as the distribution of CO2 and temperature, but fails in predicting pollutants such as CO. Since the origin of the CO accumulation near the wall remained unclear the current work aims to explain the underlying phenomena. As a first preparing step it will be shown how the configuration which is basically three-dimensional can be approximated by a generic two-dimensional sub-domain in order to reduce the computational effort. The focus is then shifted to the thermo-chemical state during the quenching phenomenon in the vicinity of the cold wall, which requires a more detailed treatment of the chemical processes. Being a laminar configuration, the SWQ burner fulfills an essential condition for the reduction to the twodimensional sub-domain since turbulence is an inherently threedimensional phenomenon. Using this sub-domain enables the application of detailed kinetics in order to predict the chemical states in the quenching region near the wall. Furthermore, a Lagrangian description method is used to analyze the role of diffusion processes and chemical reactions for the CO distribution in the flame quenching region. Accordingly, the objectives of this work are: • Assess the reliability of detailed chemistry simulations regarding the thermo-chemical states in a SWQ configuration using experimental data. • Investigate the influence of the reaction mechanism and the diffusion treatment on the thermo-chemical state. • Analyze the origin of the enhanced CO mass fraction in the close vicinity of the wall during quenching. This work is organized as follows: In Section 2, the governing equations are introduced and the numerical methods are presented. The configuration is then described in Section 3, which also provides the justification to use a reduced simulation domain. In Section 4, the reliability of the simulation is assessed by a comparison with experimental results. Furthermore, an investigation of the occurring phenomena is performed in order to explain the measured data. The paper ends with a concluding section. 2. Numerical methods and modeling All simulations are performed with the academic CFD code Fastest. The incompressible, variable density finite volume code uses a block-structured boundary fitted hexahedral mesh. The spatial interpolation of the velocity is based on the Taylor series expansion of Lehnhäuser and Schäfer [11] to maintain second order accuracy on non-regular cells. Boundedness of scalar quantities is assured by the total variation diminishing scheme suggested by Zhou et al. [12]. The code uses a cell centered variable arrangement on a non-staggered grid with selective interpolation of the mass fluxes as proposed by Rhie and Chow [13]. The time integration is done with an explicit three-stage Runge–Kutta scheme [14] combined with a pressure correction procedure to satisfy continuity. The SWQ configuration is simulated using tabulated as well as detailed chemistry. For the tabulated chemistry simulation the FGM approach is applied as detailed by van Oijen and de Goey [15] and Ketelheun et al. [16,17]. Beside the reaction progress variable the

enthalpy is used to account for the enthalpy losses to the wall. The main results of this work are obtained from detailed chemistry simulations that were performed using different reaction mechanisms as well as diffusion treatments. Further description of the detailed chemistry implementation is provided below and can be found in [18,19]. 2.1. Governing equations The (laminar) flow is described by the conservation equation for mass and momentum neglecting volume forces:

∂ρ ∂ρ ui + =0 ∂t ∂ xi    ∂uj ∂ρ u j ∂  ∂ ∂p + − ρν ρ ui u j = ∂t ∂ xi ∂ xi ∂ xi ∂xj

(1) (2)

where ρ , ui , ν and p denote the density, velocity, kinematic viscosity and pressure, respectively. Detailed kinetics involves solving a transport equation for all species that are considered depending on the reaction mechanism applied:

  ∂ρYk ∂   + ρ ui + Vk,i Yk = ω˙ k ∂t ∂ xi

(3)

where Yk and Vk, i are the mass fractions and the diffusion velocities, respectively. The transport equation for enthalpy hs is solved in its sensible formulation:

  ∂ρ hs ∂ ∂ λ ∂ hs + + ω˙ T ( ρ u i hs ) = ∂t ∂ xi ∂ xi cp ∂ xi

(4)

where the sensible enthalpy hs and its source term ω˙ T can be formulated by the enthalpy h, the standard enthalpies of formation h0f k of all species, their mass fractions Yk and their source terms ω˙ k as:

hs = h −



h0fkYk

(5)

h0fk ω˙ k

(6)

k

ω˙ T = −

 k

2.2. Species, momentum and enthalpy transport properties In the case of mixture averaged diffusion modeling (MixAvg) the diffusion velocities in Eq. (3) are replaced by

Vk,i = −

ρ Dk ∂ (YkW ) W ∂ xi

(7)

[1] where W denote the average molar mass leading to

  ∂ρYk ∂ ∂ ρ Dk ∂ (YkW ) + ρ u Y = + ω˙ k ( i k) ∂t ∂ xi ∂ xi W ∂ xi

(8)

The scalar diffusion coefficients Dk are approximated using binary diffusion coefficients Dkj and the mixing rule [20]

1 − Yk Dk =  Xj

(9)

j=k Dk j

where Xj denotes the mole fractions. The binary diffusion coefficients Dkj are derived from the kinetic theory of gases as done by Hirschfelder et al. [21]. The kinematic viscosity ν and the thermal conductivity λ that occur in Eqs. (2) and (4) are obtained from the viscosities and thermal conductivities of pure gases using the mixing rule for viscosities [22]:



ν=

n  i=1

1+

νi

1+

1 Xi

 j=n j=1, j=i

X j φi j

with

φi j =

 12  14 2 νi νj

Mj Mi

√

(4/ 2 ) 1 + (Mi /M j ) (10)

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Fig. 1. 1D Head-On-Quenching. Left: Normalized wall heat flux over normalized time τ = t/tF where tF = δF /sl is the flame time with δ F and sl being the flame thickness and the laminar flame speed, respectively. Right: CO mass fraction over wall distance for the six instances marked within the wall heat flux evolution.

and Mi and Mj being the molar masses and the mixing rule for thermal conductivities [23]:

⎛

n 

1 λ= ⎝ 2

Xi λi +

i=1

n 

−1 ⎞ ⎠ (Xi /λi )

(11)

i=1

As done for the diffusivity, the pure gas viscosity ν i and conductivity λi is derived from the kinetic theory of gases. Beside the mixture averaged diffusion treatment also the unity Lewis number assumption (Lewis 1) is used. In the latter case a constant molar mass of the mixture throughout the reaction is assumed which simplifies Eq. (8) to the following formulation [24]:

  ∂ρYk ∂ ∂ ∂ Yk ρ + ρ u Y = D + ω˙ k . ( i k) ∂t ∂ xi ∂ xi ∂ xi

(12)

Furthermore an empirical model for the thermal conductivity λ and the dynamic viscosity μ is used [18,25,26]:

λ cp

μ cp

= 2.58 · 10−5

= 1.67 · 10−8

 T 0.69 298K

 T 0.51 298K

kg m−1 s−1

2

kg J−1 m−1 s−1

(13)

(14)

where the heat capacity cp is calculated from Nasa polynomials [27–29]. These expressions are reasonable for methane–air combustion where the fresh and the burned gas is mostly characterized by nitrogen such that a pure temperature dependence can be assumed. The coefficient for the species diffusion D in Eq. (12) is calculated from the thermal conductivity using the Lewis number definition.

Fig. 2. SWQ-Burner and fields of measurements with the numerical sub-domain magnified on the right. The latter shows the inlet velocity profile of the fresh mixture (blue) and burned gas (red), the flame by an isoline of the CO2 source term (black) and streamlines (black dashed). The four black horizontal lines near the flame tip denote the extraction lines for the CO and temperature data. Their streamwise positions xq = −0.550, −0.050, 0.450 and 0.950 mm are defined relative to the quenching point as detailed in Section 3.2. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

2.3. Chemical source term The chemical source term ω˙ k of the species k is defined as sum of the contribution of all elementary reactions Nr [1]. These contributions depend on the concentrations ci of the species i and the molar stoichiometric coefficients νij and νij of species i of reaction j for the forward reaction and the backward reaction respectively as given in Eq. (15). Furthermore the contributions depend on the stoichiometric coefficient ν kj of species j of reaction k. The forward reaction constant kf is modeled using the modified Arrhenius law [30] (Eq. (16)) whereas the backward reaction constant kb is calculated using the equilibrium constant Kc which depends on the Gibbs free energy change of reaction at standard conditions R G0j and the atmospheric pressure pa (Eq. (17)).

ω˙ k = Wk

Nr 

νk j

Ns Ns   ν ν  kf, j ci ji − kb, j ci ji i=1

j=1

 kf, j = A j T β j exp

Kc, j =

Ea, j − RT

s ν  p Nk=1 kj

a

RT

(15)

i=1

 ,

 exp



Kc, j =

−R G0j RT

kf, j kb, j

(16)

 (17)

The parameters that occur in the Arrhenius law are taken from reaction mechanisms.

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Fig. 3. OH distribution based on measurements of Jainski et al. [9] and flame front for the complete measurement plane (left) and a magnified region (right): Experimental ), 3D FGM [10] ( ), generic configuration DC GRI Lewis 1 ( ), and FGM GRI Lewis 1 ( ) conditioned for quenching point, the computation domain of the ( generic configuration is sketched as dark blue rectangle in the left figure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Comparison of the FGM performed in the 2D sub-domain ( xq = −0.550 (), −0.050 (), 0.450 (∗ ), 0.950 () mm.

) with the 3D FGM (

2.4. Choice of reaction mechanisms The conduction of detailed chemistry simulations requires the selection of a suitable reaction mechanism that depends on the considered fuel and the configuration as well as on the quantities of interest such as global flame properties or specific species. Popp and Baum used four different mechanisms (WIIP, Coffe with C1 chemistry, Coffe with C2 chemistry and Smooke with 82 reactions) simulating a 1D HOQ configuration. They found that all mechanisms agreed regarding global results for the flame-wallinteraction. In this work the reduced mechanism of Smooke and Giovangigli [25] (16 species and 25 reactions) as well as the GRI 3.0 mechanism [31] (53 species and 325 reactions) were used. This choice was done since GRI is an established and widely used mechanism for methane–air combustion. Similarly, the Smooke mechanism is commonly used to significantly lower the computing costs due to its reduced number of species considered. To judge on the sensitivity of this choice with respect to the CO prediction being the quantity of interest, we compared these mechanism in

) of the full configuration of Heinrich et al. [10]. Symbols denote the position

a 1D HOQ simulation in advance to the SWQ analysis. Results are given in Fig. 1 showing the temporal evolution of the wall heat flux on the left where several instances of time are defined whose corresponding CO profiles are given on the right. Due to its reduced set of species, the Smooke mechanism predicts a slightly larger peak value at the first instant before the quenching  1 . This remains visible throughout the quenching process until the results approach each other towards the last instant being close to the chemical equilibrium  6 . Overall the result shows a weak sensitivity with respect to the chemical mechanism for this near wall reaction. It should be noted, that also larger differences were observed for other minor species. But regarding the CO prediction being the quantity of interest, the Smooke mechanism is close to the GRI reference giving confidence for this study. 3. Configuration and numerical setup The configuration that is analyzed in this work is sketched in Fig. 2. A stoichiometric methane–air mixture issues from the noz-

S. Ganter et al. / Combustion and Flame 186 (2017) 299–310

Fig. 5. Top: OH mass fraction in the quenching region with location of maximum value (white line). Bottom: Normalized auxilliary function.

Fig. 6. CO2 mass fraction in the near wall region (top) and directly along the wall (bottom).

zle at ambient conditions (p = 1 atm, T = 300 K) and passes a rod (ø 1 mm) where a V-flame stabilizes. The nozzle flow Reynolds number is about 50 0 0. The left flame branch approaches the wall at an angle of approximately 10 degrees where the SWQ takes place. The wall temperature slightly varies along the water-cooled wall and is estimated to be within 300 and 350 K based on thermocouples measurements beneath the wall surface [9,32]. The burner has a thermal power of approximately 9.3 kW. 3.1. Computational domain and boundary conditions The FGM simulation of Heinrich et al. [10] covered a large part of the geometry including the rod using Artificial Flame Thickening (ATF) in order to reduce the grid resolution requirements. In

303

this work, however, a reduced two-dimensional sub-domain gray in Fig. 2 is considered. This enables to investigate the processes by means of detailed chemistry simulations. The sub-domain which covers about 80% of the considered flame branch is magnified on the right of Fig. 2. Based on the experimental estimation the wall is assumed to have a constant temperature of 300 K, whereby no-slip condition is applied. Catalytic effects were not included since they are negligible at these wall temperatures [3]. The sub-domain is initially simulated using the FGM approach to obtain results that can be compared with the 3D simulation of Heinrich et al. [10]. However, as detailed therein, like in the real configuration, the velocity field of the 3D simulation shows a certain divergence into the z-direction such that the inflow boundary condition need to be adjusted in the 2D simulation to obtain the correct flame attachment angle. Accordingly, a parabolic velocity profile (blue in Fig. 2 is adapted in order to cover the global flame shape that was obtained experimentally by Jainski et al. [9]. Figure 3 shows the good congruence of the flame fronts of the experiment and sub-domain simulation. The 3D FGM shows a certain offset compared to the experiment which is caused by the artificial thickening. In order to assess the reduction of the computational domain, the temperature and the CO mass fraction are plotted in Fig. 4 along the extraction lines that are depicted in Fig. 2. For this comparison the spatial profiles (Fig. 4 middle and right) of the 3D ATF simulation are re-transformed by the thickening factor. As can be seen the sub-domain simulation yields the same results. With this finding the reduced domain is considered as verified and will be used for the detailed chemistry simulations aiming for the analyses of the physical processes during the SWQ. Since no rod is included in the 2D sub-domain the flame is stabilized by hot burned exhaust gas under equilibrium conditions that is injected in a 0.5 mm wide section of the inlet as marked with red color in Fig. 2. In order to compensate partially for the difference in the density of the burned and unburned gas (and with that also in the mass flux), the inlet velocity of the burned gas is set larger than the inlet velocity of the unburned gas by a factor of 2.244. The simulation is carried out on an equidistant Cartesian grid using a cell size of 50 μm resulting in 72,0 0 0 cells and y+ below 0.5 throughout the whole domain. It has been verified that the stoichiometric methane–air flame of thickness 0.5 mm is sufficiently resolved for both reaction mechanisms considered. As mentioned in Section 2.2 the detailed chemistry simulations either uses the unity Lewis number assumption or mixture averaged diffusion. In the case of unity Lewis number assumption a bulk inlet velocity of 1.7 m/s was used which corresponds to the inlet velocity of the 2-dimensional FGM simulation being also based on the unity Lewis number assumption. Since the laminar

Fig. 7. 1D adiabatic flamelet simulated with Chem1D: CO mass fraction (blue and red line) and CO source term (colored areas) over space (left) and over temperature (right) for stoichiometric conditions. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 8. Temperature and CO mass fraction profiles. Experimental data [9] ( ), experimental mean values (), FGM ( ) and MixAvg ( ). DC GRI with Lewis 1 (

flame speed in the case with mixture averaged diffusion is significantly higher, the inlet velocities were increased in order to retain the flame shape. Table 1 lists the laminar flame speeds and the bulk inflow velocities, respectively. 3.2. Definition of the SWQ reference system Although a laminar configuration is considered, the flame attachment point slightly fluctuated in streamwise direction during the experimental measurements due to acoustic Helmholtz resonances. Furthermore the individual detailed chemistry simulations show marginally different position of the quenching point. Since the thermo-chemical state within the quenching region strongly

), DC SMO with Lewis 1 (

) and MixAvg (

Table 1 Laminar flame speed for stoichiometric methane–air flames and the bulk inlet velocities used for the subdomain simulations.

FGM Lewis 1 GRI Lewis 1 SMO Lewis 1 GRI MixAvg SMO MixAvg

slaminar (m/s)

ubulk (m/s)

0.279 0.281 0.290 0.371 0.367

1.7 1.7 1.7 2.244 2.151

),

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305

depends on the streamwise position, the profiles are compared after introducing a relative coordinate system which is depicted in Fig. 5. In contrast with Fig. 2 and 3 the configuration in Fig. 5 is rotated by 90 degrees, such that the streamwise direction is orientated horizontally and the wall is located at the upper boundary as well as in all subsequent graphs. The relative coordinate system uses the quenching point as coordinate origin whereby y remains the wall distance and xq denotes the wall parallel coordinate pointing in downstream direction. There are two criteria used to determine the quenching point depending on the data that is available for the considered results. Regarding the experimental data the OH distribution is used to calculate a quenching point based on the drop of the OH-gradient. Since the FGM can not predict the OH distribution correctly, the CO2 evolution along the wall is used for the quenching point definition. In order to compare FGM and experimental results, the detailed chemistry that provides CO2 as well as OH, is used to build the bridge between the quenching point definition for the experiments on one side and the quenching point definition for the FGM simulation on the other side. To determine the quenching point that is based on the OH distribution which is exemplary shown in Fig. 5 (top) first an auxiliary function g(x) is defined as

g( x ) =



max

y∈[0,6]mm

|∇YOH (x, y )|



(18) x=const

which gives the maximum of the Euclidean norm of the OH gradient along the y-axis for every x-position. This auxiliary function is then normalized by its maximum resulting in

gn ( x ) =

g( x ) maxx [g(x )]

(19)

as shown in Fig. 5 (bottom). The quenching point xOH is then defined as the x-position where the normalized auxiliary function gn (x) reaches 0.5:

xOH = {x | gn (x ) = 0.5}

(20)

The CO2 based criterion defines the quenching point as the streamwise position where the CO2 mass fraction at the wall has reached a value of YCO2 ,half being defined to be the half of the maximum CO2 mass fraction of the detailed chemistry simulation (GRI, Lewis 1). Figure 6 shows the mass fraction of CO2 in the quenching region and at the wall, respectively. The CO2 based criterion reads

xCO2 = {x | YCO2 (x, y = 0 ) = YCO2 ,half }.

(21)

The OH based quenching point for the FGM xOH, FGM is then reconstructed by

xOH,FGM := xCO2 ,FGM + xOH,DC − xCO2 ,DC .





0.15 mm



(22)

Herein the detailed chemistry values are taken from the simulation using the GRI mechanism and Lewis 1 diffusion treatment to be consistent with the FGM table generation. However, the sensitivity of the reconstructed quenching point with respect to the mechanism as well as the diffusion treatment was below half a flame thickness and it has been verified to have a negligible effect onto the results. By means of the two quenching point definitions and their linking by detailed chemistry results (Eq. (22)) the experimental data and the FGM results can be conditioned consistently to the quenching point position. 4. Results 4.1. The thermo-chemical state near the wall: CO and temperature profiles In the following section, the detailed chemistry simulations are compared with experimental data as well as FGM results. Based

Fig. 9. CO mass fraction against temperature. Experimental data [9] ( ), adiabat ), FGM ( ), DC SMO with Lewis 1 ( ) flamelet simulation by Chem1D ( ), DC GRI with Lewis 1 ( ) and MixAvg ( ). and MixAvg (

on these comparisons an assessment of the detailed chemistry approach is deduced. First of all the chemical processes of an adiabatic flamelet is recapitulated considering a one dimensional stoichiometric detailed chemistry simulation using the Chem1D solver [24]. Figure 7 illustrates the result of a one dimensional simulation represented by the mass fraction and the source term of CO plotted over space (left). The range with a positive and a negative source term is denoted as production and oxidation branch, respectively. The figure reveals mainly an increasing CO mass fraction within the production branch and a decreasing CO mass within the oxidation branch. The beginning decline within the production branch is caused by diffusion. The maximal CO mass fraction is about 0.048,

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S. Ganter et al. / Combustion and Flame 186 (2017) 299–310

Fig. 10. Left: Source, diffusion and convection term for CO2 corresponding to Eq. (23). Right: Integrals of the source and diffusion term corresponding to Eqs. (26) and (25) as well as the CO2 mass fraction. For orientation the temperature (gray) and the heat release (qualitative, dashed gray) is added on the right y-axis.

Fig. 11. Left: Source, diffusion and convection term for CO corresponding to Eq. (23). Right: Integrals of the source and diffusion term corresponding to Eqs. (26) and (25) as well as the CO mass fraction. For orientation the temperature (gray) and the heat release (qualitative, dashed gray) is added on the right y-axis.

the equilibrium is about 0.009. Figure 7 (right) shows the results plotted over temperature since this kind of presentation is used in the subsequent sections. This behavior is also observed by Jainski et al. [9] in the most upstream measurement (xq =−0.550 mm) presented in Figs. 8 and Fig. 9 (last graphs in each figure). The adiabatic flamelet result is also plotted in Fig. 9 for orientation. Near the quenching point at xq = −0.050 mm the experimental results of Jainski et al. [9] reveal an increased CO mass fraction near the wall of about 0.03. At this position the maximum CO value has flatten to about 0.38 compared to the maximum in the undisturbed flame. The equilibrium amount of CO far from the wall remains at roughly 0.01. Downstream of the quenching point (xq = 0.950 mm) Jainski et al. [9] observed that the CO mass fraction falls to its equilibrium value close to the wall as well as at the wall distance where the CO maximum was observed in the most upstream measurement. Regarding the FGM results a reasonable good agreement of the CO mass fraction as well as the temperature can be found upstream of the quenching point (xq = −0.550 mm) where the flame is almost adiabatic. As mentioned in the introduction, however, the FGM can capture the temperature but not the CO mass fraction in the region of flame-wall-interaction (xq = −0.050 mm, 0.450 mm

and 0.950 mm) [10]. Although the FGM predicts a falling maximum value, it does not exhibit the rise of CO near the wall at xq = −0.050. These results which represent the reproduction of the 3D simulation of Heinrich et al. [10] show that the FGM chemistry reduction approach based on burner stabilized flamelets as detailed in van Oijen and de Goey [15] and Ketelheun et al. [16], 17] is not able to predict the CO mass fraction near the wall. As outlined in Heinrich et al. [10] the reasons for this deficiency requires further investigations but is likely linked to the influence of diffusive fluxes of CO that are not accounted for within the FGM table generation. As described in the subsequent sections these fluxes indeed have a significant contribution to the CO concentrations near the wall. It should be noted, that this deficiency is limited to the near wall region and, as visible in Fig. 3, does not affect the global flame topology which is determined by adiabatic flame propagation being predicted very accurately by the FGM (see e.g., xq = −0.550 mm in Fig. 8). The detailed chemistry simulations that were performed within this work show a significantly better result for all positions of xq than the FGM simulations. As can be seen in Figs. 8 and 9, they are all within the experimental scatter with a moderate influence of the reaction mechanism and diffusion treatment. Even though

S. Ganter et al. / Combustion and Flame 186 (2017) 299–310

307

Fig. 12. Source term (top left), diffusion term (top right), integrated source term (bottom left), integrated diffusion term (bottom right) with temperature isolines in Kelvin ), quenching point position ( ) and streamwise positions xq ( ). (

the simulation results are close, a certain trend can be observed showing an improved prediction quality towards the more complete approaches (larger mechanism, mixture averaged diffusion treatment). Looking for example at the CO profile at the quenching point (xq = −0.050 mm in Fig. 8) it is visible, that the simulations with Lewis 1 (solid lines) predict the peak value farther away from the wall compared to the experimental mean. Both, the GRI and Smooke mechanism peak at the same wall distance. The maximum value seems more accurate with the Smooke mechanism but as we will see, it is rather a compensation of errors. A systematic difference can be observed when going over to the results obtained with mixture averaged diffusion treatment (dashed lines). Since the diffusivity of CO is now smaller compared to Lewis 1 the peak value increases. At the same time it moves closer to the wall and the spatial position coincided with the measurements for both mechanisms. However, the simulation with the Smooke mechanism now overestimates the peak value while the results with the GRI mechanism follow the measurements very accurately. This deficiency of the Smooke mechanism is in agreement with the preliminary HOQ results shown in Fig. 1. Accordingly, combining the information of the peak value and its position, the most elaborated approach performs best. The same hold for the more upstream position xq = −0.550 mm. Further downstream the peaks collapsed into the wall and the Lewis 1 simulations now show the higher amount of CO at which they are closer to the experiment but only in the direct vicinity of the wall. This near wall value seems to be very sensitive to the axial location since the measurements show a strong reduction of CO into the axial direction such that only the

mixture averaged transport predicts the correct value at the wall for the most downstream position (xq = 0.950 mm). Since the detailed chemistry simulations are in good agreement with the experimental results, these are used to investigate the dominating phenomena near the wall which neither could be done experimentally nor using the FGM chemistry reduction approach.

4.2. Description of Langrangian method using a 1D example In order to investigate the process that underlies the results shown in the previous section the data of the detailed chemistry simulation are used to determine the influence of chemical sources and diffusion within the flame-wall-interaction. In the following the question of the origin of enhanced CO near the wall is addressed. In a first step however a 1D laminar flamelet using GRI and mixture averaged diffusion treatment is considered in order to introduce the method that will be used subsequently to investigate the Side-Wall-Quenching data. Furthermore the method is first demonstrated for CO2 instead of CO since the results for CO2 can be depicted more clearly. Thereafter the method is demonstrated for CO accordingly, as it is done for the SWQ analyses. Considering Eq. (3) that can be formulated as

  ∂ Yk ∂Y 1 ∂ ω˙ k ρ Dk ∂ (YkW ) = −ui k + + ∂t ∂ xi ρ ∂ xi W ∂ xi ρ        convection

diffusion : d

source : q

(23)

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the convection term, the source term q and the diffusion term d of CO2 across a steady state 1D flamelet are plotted in Fig. 10 (left). The preheat zone is dominated by diffusion and convection whereas reaction and convection are dominant in the reaction zone. In order to obtain the CO2 mass fraction and its compounds regarding diffusive and chemically formed CO2 across the flamelet, the Lagrangian perspective is chosen. By integrating the diffusive term d and the source term q along the trajectory of an notional particle that follows the flow perfectly (according to Eqs. (24)– (26)), the two accumulated CO2 mass fractions D and Q are obtained (Fig. 10 (right)).

x p (t ) =



t

t0

D(x p (t )) =

Q (x p (t )) =

 dt + x0 u 

t

t0



t

t0

(24)

d (x p (t ))dt + D0

(25)

q(x p (t ))dt + Q0

(26)

Since the convective term does not occur in the conservation equation in Lagrangian form, consistency of the integrated terms can be proven by

Y =Q +D

(27)

which is fulfilled as shown in Fig. 10 (right). Figure 11 shows the corresponding terms and the accumulated terms according to Eqs. (26) and (25) for the CO mass fraction. 4.3. SWQ analysis using the Lagrangian method In this section the Lagrangian analysis method is applied to the SWQ simulation in order to explain the high CO mass fraction near the wall by analyzing the contribution of chemical sources and diffusion. For this purpose the most realistic simulation based on the GRI reaction mechanism and mixture averaged diffusion treatment is used. For the integration of the source- and the diffusion term shown in the upper graphs of Fig. 12, Eqs. (24)–(26) were integrated along 500 streamlines based on the explicit Euler scheme within the whole computational domain. The time step was chosen to be one tenth of the grid spacing divided by the local velocity ending up with an averaged time step size below 10−4 s. The particles are initialized at the inflow of the computational domain and the integration constants, i.e the initial amount of CO originating from diffusion as well as chemical reaction, are set to zero. For the region where the inflow composition is equal to the equilibrium values the assumption of an integration constant that equals zero is obviously wrong but those streamlines do not reach the region of interest. Interpolating the integrated terms from the streamlines one obtains the fields shown in the lower graphs of Fig. 12, i.e., for a given location those maps show how much of the CO found originated from source or diffusion. To bring the results of the analysis into the context of the measured CO and temperature data, wall normal lines at the positions xq = −0.550 , −0.050 , 0.450 and 0.950 mm are extracted (marked in Fig. 12 with dashed lines) and provided in Fig. 13 showing the CO mass fraction and its compounds in temperature space. We will use these two representations in combination with Eq. (27) to outline the root mechanism causing the high CO concentrations measured near the wall. Starting at xq = −0.550 mm, the flame is still almost unaffected by the wall and we find the common structure of a freely propagating flame: As visible in Fig. 13, Q has a large contribution in the high temperature region where Y is maximal. According to their physical significance, the diffusive fluxes redistribute the quantity

Fig. 13. Wall normal lines of integrated source term Q ( ), integrated diffusion ), and total amount of CO Y ( ) over temperature with experimenterm D ( tal data ( ).

without a net contribution in a global sense. Accordingly, similar to the evolution outlined on the right of Fig. 11, in the preheating zone (T<10 0 0 K), Y originates exclusively from diffusion (D) which in turn has a negative contribution in the reaction zone. A significant, and decisive change of these evolutions can be observed at the second position (xq = −0.050 mm) being very close to the quenching point. Here Fig. 13, shows large values of CO even

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309

Fig. 14. Diffusive flux as streamlines based on ∇ (W · YCO ).

at the lowest temperatures, i.e., towards the wall. It is visible, that the contribution of the source is still qualitatively the same while the diffusion is strongly increased. Following the graphs and Eq. (27) it is apparent that it dominates the accumulated value of CO. This result is also visible in Fig. 12 showing that the increased CO near the wall, when approaching the quenching point from the upstream direction, is dominated by D with no contribution from Q. To understand this observation, we add Fig. 14 to explain why D is the dominating quantity. It contains streamlines but not along the convection direction but along the diffusion velocity, i.e., this diffusion streamlines are obtained by integrating the gradient ∇ (W · YCO ) which is parallel to the diffusion velocity given by Eq. (7). Within the FWI region two mechanism act: First, the diffusion normal to the flame. As mentioned, this is obviously also present in the adiabatic region as given by the diffusion lines leaving the flame orthogonal in Fig. 14. However, close to the wall the gradients steepen and there is no longer a large region of unburnt gases into which the diffusion can take place. Instead, within an area of the flame-wall alignment angle the wall blocks the diffusion. This first mechanism would also act in a HOQ scenario. The second reason for the large diffusion observed in Figs. 12 and 13 is very visible in Fig. 14. Close to the wall the diffusion lines no longer leave the flame into the normal direction. In that region the low temperature reduced the chemical formation of CO such that gradients also form in the flame tangential direction. The resulting diffusive flux from the region of chemical formation towards the wall is apparent in Fig. 14. Combined with the quantification by means of the Lagrangian analysis (Figs. 12 and 13) this outlines the majority of the mechanism to explain the large concentrations measured at the wall. There are small remaining processes in the more downstream region (xq = 0.450 and 0.950 mm) to complete the picture. Here CO reduces again. This is caused by two overlapping processes. The first one is diffusion. Farther away from the wall, there is a large pool of equilibrium state (YCO ≈ 0.01, see e.g., xq = −0.550 mm in Fig. 13) originating from the adiabatic flame. In the absence of significant production by chemical reaction, diffusive fluxes are initiated towards this region as indicated by the diverging diffusion lines visible in the near-wall region downstream of the quenching point in Fig. 14. However, this global process is obviously rather slow and cannot explain the CO evolution on its own as is obvious from the quantification in Fig. 13. At xq = 0.450 mm, D indeed reduced compared to xq = −0.050 mm1 but close to the wall Y is actually below D indicating that it reduced at a rate above 1 To avoid confusion one should be reminded, that Fig. 12 bottom and Fig. 13 represents accumulated values, i.e., even though D is still positive at xq = −0.450 mm the reduction compared to xq = −0.050 mm indicates that locally the diffusion has a negative contribution as outlined.

the diffusive flux. Even more significant is the evolution towards xq = 0.950 mm. Here, Y strongly reduced close to the wall while D even increased in the near wall vicinity. This evolution arises from the second process, developing right near the wall: a negative contribution is added by the chemical source Q. Chemically this negative contribution is caused by the fact that an increasing amount of gases is cooled down by the wall. Several elementary reactions describe the reversible process of CO2 formation based on CO. The net sum of these reactions is, that the equilibrium values shift towards CO2 with decreasing temperatures. It is visible in the bottom left of Fig. 12, that this accumulates to an overall negative contribution close to the wall towards xq = 0.450 mm and even stronger at xq = 0.950 mm as also visible in Fig. 13 explaining the final state of the CO mass fraction. 5. Conclusion This work considered the side-wall-quenching process as it has been experimentally investigated recently by Jainski et al. [9]. In order to analyze the species distribution being noticeably different when compared to an undisturbed flame, we performed detailed chemistry simulations in a sub-domain of the original configuration. Contrary to tabulated chemistry, the detailed chemistry simulations used here were able to reproduce the measured CO accumulation close to the wall. All simulations could predict the qualitative evolution with a certain sensitivity related to the chemical reaction mechanism and approximations of diffusive fluxes. Within this moderate variation the prediction quality improved with increasing complexity of the approaches (larger mechanism, differential diffusion transport) with a remaining uncertainty due to the experimental scatter. In order to understand the underlying mechanism of the measured CO accumulation, a Lagrangian analysis has been introduced to evaluate the contribution of diffusive fluxes and chemical sources to this process. It is revealed, that the high CO concentrations near the wall results from a transport originating from CO produced at larger wall distances. In that region being not submitted to large heat losses, a high chemical activity and corresponding CO production is found. Accordingly, a diffusion process is initiated towards the wall where the chemical sources itself were actually found to be negative. Acknowledgments Financial support by Deutsche Forschungsgemeinschaft (DFG) through grants SFB/TRR 150 and in the framework of the Excellence Initiative, Darmstadt Graduate School of Excellence Energy Science and Engineering (GSC 1070) is gratefully acknowledged. All computations were performed on the Lichtenberg High Performance Computer of TU Darmstadt.

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