Large eddy simulation of turbulent premixed

Journal of Turbulence

ISSN: (Print) 1468-5248 (Online) Journal homepage: http://www.tandfonline.com/loi/tjot20

Large eddy simulation of turbulent premixed combustion using tabulated detailed chemistry and presumed probability density function Hongda Zhang, Chao Han, Taohong Ye & Zhuyin Ren To cite this article: Hongda Zhang, Chao Han, Taohong Ye & Zhuyin Ren (2016) Large eddy simulation of turbulent premixed combustion using tabulated detailed chemistry and presumed probability density function, Journal of Turbulence, 17:3, 327-355, DOI: 10.1080/14685248.2015.1096364 To link to this article: http://dx.doi.org/10.1080/14685248.2015.1096364

Published online: 13 Nov 2015.

Submit your article to this journal

Article views: 85

View related articles

View Crossmark data

Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=tjot20 Download by: [East China University of Science and Technology]

Date: 23 February 2016, At: 00:40

JOURNAL OF TURBULENCE,  VOL. , NO. , – http://dx.doi.org/./..

Downloaded by [East China University of Science and Technology] at 00:40 23 February 2016

Large eddy simulation of turbulent premixed combustion using tabulated detailed chemistry and presumed probability density function Hongda Zhanga , Chao Hana,b , Taohong Yea and Zhuyin Renc a

Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, China; b School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, USA; c Center for Combustion Energy and School of Aerospace, Tsinghua University, Beijing, China

ABSTRACT

ARTICLE HISTORY

A method of chemistry tabulation combined with presumed probability density function (PDF) is applied to simulate piloted premixed jet burner flames with high Karlovitz number using large eddy simulation. Thermo-chemistry states are tabulated by the combination of auto-ignition and extended auto-ignition model. To evaluate the predictive capability of the proposed tabulation method to represent the thermo-chemistry states under the condition of different fresh gases temperature, a-priori study is conducted by performing idealised transient one-dimensional premixed flame simulations. Presumed PDF is used to involve the interaction of turbulence and flame with beta PDF to model the reaction progress variable distribution. Two presumed PDF models, Dirichlet distribution and independent beta distribution, respectively, are applied for representing the interaction between two mixture fractions that are associated with three inlet streams. Comparisons of statistical results show that two presumed PDF models for the two mixture fractions are both capable of predicting temperature and major species profiles, however, they are shown to have a significant effect on the predictions for intermediate species. An analysis of the thermo-chemical state-space representation of the sub-grid scale (SGS) combustion model is performed by comparing correlations between the carbon monoxide mass fraction and temperature. The SGS combustion model based on the proposed chemistry tabulation can reasonably capture the peak value and change trend of intermediate species. Aspects regarding model extensions to adequately predict the peak location of intermediate species are discussed.

Received  March  Accepted  September  KEYWORDS

Piloted premixed jet burner; well-stirred reactor regime; large eddy simulation; tabulated chemistry; presumed probability density function

1. Introduction Recently, more stringent emission regulations are pushing toward the development of more fuel-efficient and low-emission gas turbine systems. Turbulent fuel-lean premixed combustion plays a predominant role in reducing NOx emission due to the low flame temperatures.[1] The key concern for many fuel-lean operated combustion devices is flame stability and stabilisation,[2,3] which are commonly achieved by the use of bluff-body,[4,5] CONTACT Taohong Ye ©  Taylor & Francis

[email protected]


328

H. ZHANG ET AL.

swirling flows [6,7] and piloted flames.[8,9] These shear-driven flows may result in unprecedented levels of turbulent fluctuations, such that turbulence eddies can penetrate into the flame front, modify the inner flame structure and even lead to local extinction, rendering the flamelet assumption invalid.[10] The intense interaction of turbulence and chemistry, and transport of potentially hundreds of species over a broad range of scales makes accurately predicting the flame characteristics of fuel-lean premixed combustion devices with high Karlovitz number a significant challenge for many numerical modelling. The Sydney Piloted Premixed Jet Burner (PPJB) was recently developed to investigate turbulence-chemistry interactions at lean and highly turbulent conditions without additional geometrical complexity and swirling flow,[9,11,12] of which the three streams are jet, pilot and co-flow, respectively. A series of flames, which differ only in the bulk velocity of the central jet with the bulk velocities of 50, 100, 150 and 200 m/s, respectively, has been experimentally investigated. As the jet bulk velocity increases, the luminosity is observed to vary differently in the axial direction and be reduced, with the two high jet velocity flames exhibiting local extinction and reignition. Detailed measurements of both velocity and scalar statistics have been reported for these four flames in [9,11,12] to develop the suitable combustion model. Several research groups have carried out numerical simulations of PPJB flames. Rowinski and Pope [13] employed Reynolds-averaged Navier-Stokes (RANS)-PDF model to calculate PPJB flames. The predictions of temperature and mass fractions of major species were in close agreement with experimental data, while the reaction progress was overpredicted in the region where local extinction exists. They identified that the mixing model may be responsible for the discrepancy. Duwig et al. [14] used implicit large eddy simulation (LES) method to directly solve the composition transport equations where the reaction rates were obtained from an Arrhenius expression. They investigated the sensitivity of the simulation results to different reaction mechanisms and found that a 20-species skeletal mechanism is required to capture the measurements at least. They also stated that the interaction between turbulence and chemistry plays an important role in PPJB flames, which agrees with the view of Dunn et al. [12] and Rowinski and Pope.[13] Chen and Ihme [15] performed LES calculation using a steady flamelet-progress variable (FPV) combustion model to predict PPJB flames with high Karlovitz number to evaluate the ability of combustion model based on the assumption of flamelet regime. Comparisons of statistical results show that mass fractions of major species are in reasonable agreement with the measurements, however, mass fractions of some intermediate compositions has clear discrepancy with experimental data. In recent years, the chemistry tabulation method, which decouples the flow and chemical reactions through the construction of chemistry tables, has been successfully used in the simulation of turbulent premixed flames.[16–18] In this study, a sub-grid scale (SGS) combustion model by combining chemistry tabulation with presumed probability density function (PDF) is developed for turbulent premixed flames with high Karlovitz number, in which the thermo-chemistry states are tabulated by utilising the combination of autoignition (AI) and extended auto-ignition (EAI) [19] model. The proposed SGS combustion model in conjunction with LES is then employed for the simulations of PPJB flames. As an outline of the paper, in Section 2, the PPJB experimental setup and operating conditions are presented. The methodology including the chemistry tabulation approach, presumed PDF

JOURNAL OF TURBULENCE

329


Table . Operating conditions for the piloted premixed jet burner. Inlet

D/mm

Jet (PPJB) Jet (PPJB) Pilot Coflow

. . . .

U/(m/s)

T /K

Mixture

Equivalence ratio

Re

Ka

  . .

   

CH4 –Air CH4 –Air CH4 –Air H2 –Air

. . . .

, , – –

  – –

model and SGS combustion closure are discussed in Section 3. A description of the numerical setup is included in Section 4. In Section 5, the overall LES results are evaluated with respect to the experiments in terms of the influence of different grids, the predictive capability of different chemistry tabulation approaches, and the evaluation of different presumed PDF models. Finally, the paper finishes with discussions and conclusions in Section 6.

2. The Sydney piloted premixed jet burner In the PPJB, a fuel-lean methane/air mixture is supplied through the central pipe with a 4 mm inside diameter at room temperature. Surrounding the fuel-stream is a pilot-stream using a stoichiometric methane/air combustion products and radicals to stabilise the flame. The fuel-lean hydrogen/air combustion product coflow-stream has a diameter of 197 mm which is large enough to isolate the flame from ambient air to eliminate potential reactionquenching and dilution effects.[11] Detailed measurements of both velocity and scalar statistics have been carried out by Dunn and co-workers.[9,11,12] The abundant database could be used to validate the combustion model. By varying the central fuel-stream velocity and keeping all other conditions constant, a series of flames, PPJB50 and PPJB100, are investigated using LES in the present work. The operating conditions of two different flames, PPJB50 and PPJB100, are summarised in Table 1.

3. Methodology 3.1. Chemistry tabulation approach ... Three-stream auto-ignition model In high Karlovitz number PPJB flames,[9,11,12] turbulent eddies smaller than the flame thickness can penetrate the flame front, resulting in intense small-scale mixing between reactants and products. Since mixing is fast and the overall reaction rate is limited by chemistry, one may attempt to represent the local reaction brush as a collection of homogeneous reactors. Duwig and Dunn [16] has performed LES of the Sydney premixed jet burner with high Karlovitz number by using the tabulation approach based on the assumption of homogeneous reactor. The ability of the AI tabulation technique to capture the non-flamelet structure is carefully discussed and the predictive capability of the AI model is established. The choice of homogeneous reactors differs from the popular method of utilising freely propagating one-dimensional laminar flames [20], where the diffusion contribution in the elementary laminar flames is retained which results in a reactive–diffusive balance. The intense mixing associated with high Karlovitz number suggests the possibility of neglecting

330

H. ZHANG ET AL.


the diffusion contribution for constructing the chemistry table. A typical scenario describing homogeneous reactors has been discussed by Duwig and co-workers.[16,21] Representing the reactions in this scenario as an unsteady homogeneous reactor, the governing equations [22] describing this idealised process can be written as ⎧ dYi ⎪ ⎪ = ωi ⎨ρ dt i = 1, . . . , N. ⎪ ⎪ ⎩ ρ dT = ωT dt

(1)

The initial conditions of the N species for solving Equation (1) are defined by the formula (2). Meanwhile, the initial condition of temperature is obtained from sensible enthalpy which also has the following formula: ⎤ Y1 ⎢...⎥

⎥ X (t = 0) = ⎢ ⎣ YN ⎦ = Z1 X f + (1 − Z1 ) Z2 Xc + (1 − Z2 ) Xp , hs ⎡

(2)

where X represents the mass fraction Yi and sensible enthalpy hs , ωi is the reaction rate corresponding to species i, ωT is the heat release due to combustion; the subscripts f , p and c denote the fuel-stream, pilot-stream and coflow-stream, respectively. The mixture fraction Z1 is equal to 1 in central fuel-stream and 0 in the other two streams, the secondary mixture fraction Z2 is 1 in coflow-stream and 0 in the rest of streams. By solving ordinary differential equation (1) under different mixture fraction Z1 and Z2 , all the thermo-chemistry quantities ϕ, such as mass fractions of species, temperature, reacting source term and other necessary quantities can be parameterised by mixture fraction and time coordinate, namely ϕ = ϕ(Z1 , Z2 , t ). Since we do not solve a transport equation for the evolving time t relative to the reaction parcel, it is suitable to replace it with a transported variable. The only condition is that the new variable should satisfy a one-to-one correspondence with evolving time t. A possible choice is the reaction progress variable Yc , which is defined by a total mass fraction of four major species Yc = YCO2 + YCO + YH2 O + YH2 . Hence, the chemistry table ϕ(Z1 , Z2 , t ) can be re-parameterised by the mixture fraction and the reaction progress variable to establish the AI-table ϕ AI (Z1 , Z2 , Yc ). Ignition delay versus mixture fraction Z1 under the condition Z2 = 0 is plotted in Figure 1 with GRI 3.0 [23] to describe the methane/air chemical reaction mechanism. Ignition delays τig increase rapidly with mixture fraction Z1 after achieving the minimum value which is found almost at Z1 ≈ 0.14. It is noticed that the initial temperature decreases gradually by increasing mixture fraction Z1 . As the initial temperature given by Equation (2) is lower than the AI temperature of methane/air premixed gases, the numerical solution of Equation (1) could not converge and the chemistry table could not be established between Z1 ∈ (Zright , 1). For the value of Z1 larger than Zright ≈ 0.76, the chemistry table is usually generated using linear interpolation (LI) along the direction of the reaction progress variable. The overall chemistry table ϕ AI−LI (Z1 , Z2 , Yc ) is generated by the combination of AI



331

Figure . Characteristic time scale versus mixture fraction.

model and LI: ϕ

AI−LI

(Z1 , Z2 , Yc ) =

ϕ AI (Z1 , Z2 , Yc ) ϕ LI (Z1 , Z2 , Yc )

i f Z1 ∈ (0, Zright ] . i f Z1 ∈ (Zright , 1)

(3)

In this study, instead of the LI approach, an EAI model is established next. ... Extended auto-ignition model Since the species and heat diffusion contribution in the homogeneous reactor is neglected, the combustion process is solely controlled by chemistry. However, when the initial temperature of mixture is lower than the AI temperature, auto-ignition process does not occur. Therefore, the EAI model instead of LI may be a good choice to contain the diffusion terms which presents transport effect of species and energy. The governing equations of the EAI model [19] can be written as ⎧ d ρDi dYi dYi ⎪ ⎪ + ωi ⎨ ρu = dt dt S2L dt i = 1, . . . , N. (4) d ρDT dT dT ⎪ ⎪ ⎩ ρu = + ωT dt dt S2L dt The boundary conditions of the species mass fraction of Equation (4) are defined by the formula (5). Meanwhile, the boundary condition of temperature is obtained from sensible enthalpy which also has the following formula: ⎧ ⎡ ⎤ ⎪ Y1 ⎪ ⎪ ⎪ ⎢

⎪ ...⎥ ⎪ ⎥ ⎨ X (t → −∞) = ⎢ ⎣ YN ⎦ = Z1 X f + (1 − Z1 ) Z2 Xc + (1 − Z2 ) Xp , (5) ⎪ hs ⎪ ⎪ ⎪

⎪ dX ⎪ ⎩ t → +∞ = 0 dt where ρu is the fresh gases density, SL is the laminar flame propagation speed with respect to the fresh gases, Di is the diffusion coefficient of species i, DT is the heat diffusion coefficient and a time scale t is obtained from spatial dimension x (t = x/SL ). By solving Equation (4) under different mixture fraction Z1 and Z2 , all the needed thermo-chemistry states can be parameterised by mixture fraction and time scale, namely ϕ = ϕ(Z1 , Z2 , t ). The reaction


332

H. ZHANG ET AL.

progress variable increases with time scale monotonously, then ϕ(Z1 , Z2 , t ) is mapped to ϕ(Z1 , Z2 , Yc ). Similar to the chemistry table obtained from the AI model, all the necessary thermo-chemistry quantities are stored in the EAI-table ϕ EAI (Z1 , Z2 , Yc ). Actually, Equation (4) can be derived from freely propagating one-dimensional laminar flames, with the only simplification being that Equation (4) uses assumptions on the species heat capacities, namely all species have the same heat capacity. An important physical effect of the diffusion term [16] in Equation (4) is to allow transport of intermediate species which are produced in the reaction front by setting t = t1 in t space. Due to the transport of intermediate species, the concentration of intermediate species (or chemical reactivity) increases in the fresh gases region (t < t1 ). Therefore, in the case of low initial temperature, the reaction process can still occur by utilising the EAI model. ... Combination of AI and EAI model By using Equation (5) to set the fresh gases conditions, one-dimensional freely propagating premixed flame characteristic time scale, τ p f = δL /SL , versus mixture fraction Z1 under the condition Z2 = 0 is shown in Figure 1. The laminar flame thickness δL can be evaluated from the maximum gradient of temperature δL = (Tb − Tu )/max(dT /dx), where the subscripts b and u denote the burnt and unburnt state, respectively. The characteristic time scale τ p f varies monotonously with mixture fraction Z1 . When the mixture fraction Z1 is smaller than Zleft ≈ 0.46, the mixture evolution is governed by rapid AI due to the higher initial temperature and a so-called freely propagating flame cannot be observed.[19] For the value of Z1 larger than Zright , premixed flame propagation can occur when the AI process is not successful. In the range of Z1 ∈ (Zleft , Zright ), it is noticed that both AI and premixed flame propagation may coexist. The similarities and differences between AI and premixed propagating flame are discussed below within the range of Z1 ∈ (Zleft , Zright ). Figure 2 shows the thermo-chemistry quantities versus the normalised reaction progress variable c in AI and EAI chemistry tables at three mixture fractions Z1 = 0.5, 0.6, 0.7, respectively. The definition of c is described in Section 3.2. The temperature, YO2 , and YH2 O trajectories provided by AI-table and EAI-table are almost similar (other values of mixture fraction Z1 also have similar results that are not shown in this paper). However, some differences in magnitude of the shapes of YCO2 , YCO and reaction source term trajectories are observed. Compared to the EAI-table, the AI-table returns higher concentration of carbon monoxide, lower concentration of carbon dioxide and lower reaction rate of Yc in c-space. The differences are linked to the absence of molecular diffusion in AI model, which have been discussed by Domingo et al.[19] The analysis of AI and premixed propagating flame suggests that the AI model can be used to tabulate the behaviour of rapid AI of the fresh mixtures within the range of Z1 ∈ (0, Zleft ). When the value of Z1 is higher than Zcross (the intersection of characteristic time scale given by the AI and EAI model in Figure 1, if the intersection does not exist under the condition of different values of Z2 , the value of Zcross is equal to Zleft ), τig > τ p f , AI is less likely to be the major controlling phenomenon and EAI tabulation is regarded as a more appropriate choice. In the range of Z1 ∈ (Zleft , Zcross ), combustion may start following two scenarios associated with AI and premixed propagating flame. Accounting for all the above observations, as a first attempt, the overall chemistry table ϕ AI−EAI (Z1 , Z2 , Yc ) is tabulated



333

Figure . Chemistry quantities trajectories for various mixture fraction.

by utilising the combination of the AI and EAI model: ϕ

AI−EAI

(Z1 , Z2 , Yc ) =

ϕ AI (Z1 , Z2 , Yc ) i f Z1 ∈ (0, Zcross ] . ϕ EAI (Z1 , Z2 , Yc ) i f Z1 ∈ (Zcross , 1)

(6)

In this study, the chemistry table ϕ AI−EAI (Z1 , Z2 , Yc ) is tabulated from the AI model simply within the range of Z1 ∈ (Zleft , Zcross ). It should be noted that Domingo et al. [19] has performed LES of a lifted methane jet flame in a vitiated coflow by using the tabulation approach based on a linear decomposition of AI and premixed propagating flame. More discussion of the predictive capability of this tabulation approach can be found in [19]. A-priori tests could be performed to estimate the prediction capabilities of two chemistry tabulation approaches, Equation (3) and Equation (6), respectively, by computing a series of unsteady one-dimensional premixed reacting flows in the next section. ... A-priori study: comparison between two chemistry tabulation approaches To evaluate the predictive capability of the proposed tabulation approach to represent the thermo-chemistry states within the range of Z1 ∈ (Zleft , Zright ), a-priori study is conducted by performing idealised transient one-dimensional premixed flame simulations using

334

H. ZHANG ET AL.

Fresh Mixture Symmetry Boundary Condition (x = 0 mm)

SL Pressure Outlet (x = 50 mm)


Figure . Unsteady one-dimensional premixed flame configuration diagram.

Figure . Reaction source term versus normalised reaction progress variable for different mixture fraction; grey symbols correspond to simulations of unsteady one-dimensional premixed flames; solid lines correspond to the AI-EAI chemistry database; and dotted–dashed lines correspond to the AI-LI chemistry database.

ANSYS Fluent. The schematic of the configuration is shown in Figure 3. The methane/air chemical reaction mechanism is described by the GRI 3.0.[23] The fresh gases temperature could be varied with different mixture fraction Z1 so that either AI or premixed flame propagation could be the leading phenomena. Figure 4 shows reaction source term versus the normalised reaction progress variable by setting Z1 = 0.5, 0.6, 0.7, respectively, 1D under the condition Z2 = 0. Here, scatter data ωYc corresponds to simulations of unsteady AI−EAI AI−LI one-dimensional premixed flame, the other two lines are ωYc and ωYc given by the AI-EAI and AI-LI chemistry table. For a certain value of normalised reaction progress variable at Z1 = 0.5, the same value of reaction source term can be obtained from two chemistry tables. The chemistry table tabulated by the AI model can reasonably represent the



335

peak value and change trend of the reaction source term. On both sides of the maximum of reaction source term, the tabulated responses deviate slightly from simulations of unsteady one-dimensional premixed flame. This deviation may be attributed to the occurrence of molecular diffusion effects that are not included in the present chemistry tabulation. For Z1 = 0.6 and Z1 = 0.7, the reaction source term exhibits great differences between two AI−EAI AI−LI is much greater than ωYc and closer chemistry tables. It clearly indicates that ωYc 1D to ωYc . It is reasonable because AI is less likely to be the major controlling phenomenon which has larger time scale than premixed flame characteristic propagation scale. These preliminary tests constitute a very severe evaluation of chemistry tabulation. The results indicate that, as a first attempt, the AI-EAI chemistry table could reasonably represent the reaction path under different fresh gases temperature. Later, the validation of two chemistry tabulation approaches in conjunction with LES would be completed by comparison to experiments.

3.2. Presumed PDF closure In the LES of the turbulent combustion, the sub-grid flame structure is modelled by presumed PDF for two mixture fractions and the reaction progress variable: ϕ˜ =

ϕ (Z1 , Z2 , Yc ) P˜ (Z1 , Z2 , Yc ) dZ1 dZ2 dYc ,

(7)

˜ 1 , Z2 , Yc ) is the filtered joint probability density function. However, the distriwhere P(Z ˜ 1 , Z2 , Yc ) is difficult to assume due to the dependence between the mixture bution of P(Z fraction and the reaction progress variable. In order to solve this issue, a normalised reaction progress variable is defined, c = (Yc − Yc min )/(Yceq − Yc min ), where Yc min and Yceq are the minimum and equilibrium value of the reaction progress, respectively. Under this nor˜ 1 , Z2 , c) malisation, c could be assumed to be independent of the mixture fraction, and P(Z can be written as P˜ (Z1 , Z2 , c) = P˜ (Z1 , Z2 ) P˜ (c).

(8)

The PDF of c does not have a general form for numerical simulation of turbulent combustion, it is usually modelled as a delta function.[24,25] More adequate PDF of c, such as a beta function or the statistically most-likely distribution has also been employed.[26] Here, a beta PDF defined by a filtered reaction progress variable c˜ and sub-grid variance 2 is used to model the reaction progress variable distribution. More in-depth discussion c ˜ is a subject of future work and not considered here. The beta function [27] has about P(c) been shown to provide an adequate description of the PDF of mixture fraction, however, there is less study on the joint PDF of two mixture fractions, more detailed discussions will be shown next.

336

H. ZHANG ET AL.


... Dirichlet distribution Girimaji [28] introduced the Dirichlet distribution for modelling multivariate joint PDF, and it is successfully used in numerical simulation of turbulent combustion.[29,30] Substantially, the Dirichlet distribution is a multivariate beta PDF, and has the following definition: K K i=1 βi β −1 (9) P˜ (φ1 , . . . , φK ) = K

φi i ,

i=1 (βi ) i=1 where is the Gamma function, and βi is the model parameter. Equation (9) is valid when βi ≥ 0 is satisfied for i = 1, 2, . . . , K. If K = 2, the Dirichlet distribution can be reduced to a standard beta distribution. For K = 3, the Dirichlet distribution for two mixture fractions can then be written as P˜ (Z1 , Z2 ) =

(a + b + c) Z1 a−1 (1 − Z1 − Z2 )b−1 Z2 c−1 , (a) (b) (c)

(10)

where the parameters have to satisfy, Z1 ≥ 0, Z2 ≥ 0, Z1 + Z2 ≤ 1. The coefficients a, b and 2 c are determined as functions of filtered mixture fraction Z˜ 1 , Z˜ 2 and sub-grid variance Z 1 : Z˜ 1 (1 − Z˜ 1 ) − 1 Z˜ 1 , a= 2 Z 1 Z˜ 1 (1 − Z˜ 1 ) − 1 (1 − Z˜ 1 − Z˜ 2 ), b= 2 Z 1 Z˜ 1 (1 − Z˜ 1 ) − 1 Z˜ 2 . c= 2 Z 1

(11) (12) (13)

The sub-grid variance of the secondary mixture fraction and covariance are obtained from [15] Z˜ 2 (1 − Z˜ 2 ) 2 Z12 Z 2 = ˜ ˜ Z1 (1 − Z1 ) 2 Z˜ Z Z = − 2 1 . Z 1 2 1 − Z˜ 1

(14) (15)

˜ 1 , Z2 ) for mixture fraction Z1 , and Z2 Figure 5 shows four typical distributions of P(Z which is associated with the values of three coefficients a, b and c. Here, a sub-grid variance 2 2 2 2 σ is defined by the sum of Z 1 and Z2 , namely σ = Z1 + Z2 . For a small value of σ , ˜ 1 , Z2 ) is approaching a Guassian PDF.[28] This is the case (a) for σ = 0.0036, which P(Z is practically identical to the two-dimensional Guassian distribution. With increasing σ , the three coefficients a, b and c decrease. As long as all coefficients of a, b and c are greater ˜ 1 , Z2 ) is zero at all boundaries and has a than or equal to 1, as shown in Figure 5(b), P(Z ˜ 1 , Z2 ) becomes singular maximum in between. If any one of a, b and c is less than 1, P(Z at the corresponding boundary but remains integrable. This is the case (c) for a = 0.484,



337

˜ 1 , Z2 ) for mixture fraction Z , and Z . Figure . Distributions of P(Z

˜ 1 , Z2 ) is singular at the boundary of Z1 . As for the case (d) there is a very large value P(Z ˜ 1 , Z2 ) is approximate to delta function σ for a given set of filtered values Z˜ 1 and Z˜ 2 , P(Z located at the three corner points of the mixture fraction domain. ˜ 1 , Z2 ) is modelled as Dirichlet distribution, and a beta function is used to When P(Z ˜ model P(c), the filtered thermo-chemistry quantities ϕ˜ can be expressed in terms of five parameters: 2 2 ϕ˜ = ϕ( ˜ Z˜ 1 , Z˜ 2 , Z 1 , c˜, c ).

(16)

The filtered chemistry tabulation approach requires the solution of governing equations for 2 2 Z˜ 1 , Z˜ 2 , Z 1 , c˜ and c , and the transport equations are presented in Section 3.3. ... Independent beta distribution In general, in order to reduce the difficulty of numerical integration, mixture fraction Z1 ˜ 1 , Z2 ) could be assumed to be independent of the secondary mixture fraction Z2 , then P(Z can be written as P˜ (Z1 , Z2 ) = P˜ (Z1 ) P˜ (Z2 ) .

(17)


338

H. ZHANG ET AL.

As the cold jet gas is initially surrounded by the pilot-stream which is at a temperature of 2274 K, the interaction of the jet and the high-temperature pilot gases could result in relatively vigorous reactions in the thin shear layer between the jet-stream and pilot-stream. The effect of the coflow-stream into the jet region is existent only in the downstream. The main role of the coflow-stream is to isolate the flame from ambient air to eliminate potential reaction-quenching and dilution effects. Based on these considerations, a beta function 2 ˜ defined by filtered mixture fraction Z˜ 1 and sub-grid variance Z 1 is used to model P(Z1 ), ˜ 2 ) is modelled as a delta distribution. Under this assumption, the filtered thermoand P(Z chemistry quantities ϕ˜ can still be expressed in terms of five parameters: 2 2 ϕ˜ = ϕ( ˜ Z˜ 1 , Z˜ 2 , Z 1 , c˜, c ).

(18)

It should be noted that the constraint Z1 + Z2 ≤ 1 is not satisfied in the independent beta distribution. The above two presumed PDF models are applied to study the PPJB flames, respectively.

3.3. LES governing equations In addition to the solution of the transport equations for mass and momentum, the lowMach number, variable-density LES-formulation requires the solution of five extra trans 2 2 port equations for scalars Z˜ 1 , Z˜ 2 , Z 1 , c˜, c . Because too many unclosed terms exist in the 2 2 equations of c˜, c and are difficult to be modelled, here the unnormalised quantities Y˜c , Y c 2 are solved instead of c˜, c . These modelled equations can be written as ∂ ρ¯ u˜i Z˜ 1 ∂ ρ¯ Z˜ 1 ∂ + = ∂t ∂xi ∂xi

∂ Z˜ 1 ρ¯ D˜ ∂xi

+

∂τZres ˜ 1

∂xi ∂τZres ˜

(19)

∂ ρ¯ u˜i Z˜ 2 ∂ ∂ Z˜ 2 ∂ ρ¯ Z˜ 2 2 + = (20) ρ¯ D˜ + ∂t ∂xi ∂xi ∂xi ∂xi ∂τ res 2 2 2 2 ˜ ∂ ρ¯ Z ∂ ρ ¯ u ∂ ∂ Z˜ 1 ∂ Z Z Z i 1 1 1 + = + 2τZres − ρ¯ χ˜Zres1 (21) ρ¯ D˜ 1 + ˜1 ∂t ∂xi ∂xi ∂xi ∂xi ∂xi ∂τY˜res ˜c ∂ ρ¯ u˜iY˜c ∂ Y ∂ ∂ ρ¯Y˜c c + ρ¯ D˜ + = + ρ¯ ω˜ Yc (22) ∂t ∂xi ∂xi ∂xi ∂xi res ∂τ 2 2 2 ˜ Y ∂ ρ ¯ u ∂ ∂Y˜c ∂ Y ∂ ρ¯Y Yc2 i c c c res ˜c ω˜ Yc . ˜ + = + 2τY˜res − ρ ¯ χ ˜ + 2 ρ ¯ Y ω − Y ρ¯ D + c Y c Y c c ∂x ∂t ∂xi ∂xi ∂xi ∂xi i (23) res ˜ ˜ The residual turbulent fluxes τφres ˜ (τφ˜ = ρ¯ ui φ − ρ¯ ui φ) are approximated using the eddy diffusivity model:

˜

¯ tφ τφres ˜ = ρD

∂ φ˜ , ∂xi

with

˜

Dtφ = Cφ 2 (2S˜i j S˜i j )1/2 ,

(24)


339

where the coefficients Cφ is estimated using the dynamic procedure.[31] The residual scalar dissipation rate of mixture fraction χ˜Zres1 is expressed with a linear relaxation hypothesis:[32]


χ˜Zres1 =

CχzCε νt Z2 , Cu Sct 2 1

(25)

where the constant value Cχz = 2, Cε /Cu = 2, and turbulent Schmidt number Sct = 0.4.[33] The SGS eddy viscosity νt is obtained from the dynamic Smagorinsky closure. The residual scalar dissipation rate of the reaction progress variable χ˜Yres deserves a careful treatc ment, since Y˜c is not a conservative scalar and sensitive to chemistry. As a first attempt, the direct transposition of the linear relaxation hypothesis to the reaction progress variable is employed in this study. The relation is also written as χ˜Yres = c

CχYc Cε νt Y 2 , Cu Sct 2 c

(26)

where the constant value CχYc = 2, Cε /Cu = 2, and Sct = 0.4. The reaction source terms ω˜ Yc and Y c ωYc are precomputed and stored in the filtered chemistry table. The unsolved 2 are obtained from the resolved reaction progress variable Y ˜c and its variance quantities c˜, c 2 Yc through the following definitions: Y˜c − Y c min Yceq − Yc min 2 1 Y 1 2 c 2 c c = . +Y − 2 2 2 Y Y Y ceq ceq ceq c˜ =

(27) (28)

4. Numerical setup The filtered governing equations are solved in a cylindrical coordinate system. The computational cylindrical domain has 60 and 20 D in axial and radial direction, respectively, where D is the diameter of the central fuel-stream. The computational domain is discretised by structured grid. A grid convergence study is carried out for PPJB flames with two refinement levels. The coarse mesh consists of 216 non-uniform grid points in the axial direction and 176 non-uniform grid points in the radial direction and 64 equidistant grid points in the circumferential direction. The total number of the coarse mesh is about 2.44 million. The fine mesh consists of 343 non-uniform grid points in axial direction, 205 non-uniform grid points in radial direction and 64 equidistant grid points in circumferential direction. The total number of the fine mesh is about 4.5 million. Two sets of mesh are both refined in the shear layer and the nozzle-near region to ensure high precision solutions. The solution of a turbulent periodic pipe-flow simulation is used for prescribing the inflow velocity profile in the fuel-stream, the experimentally reported bulk-flow velocity is used for describing the inlet velocity profiles in the pilot-stream and coflow-stream. The non-slip boundary condition is implemented on the wall, and the convective boundary condition is used for the outflow condition.

340

H. ZHANG ET AL.

Table . Eight simulation cases for PPJB flames. Case


LES- LES- LES- LES- LES- LES- LES- LES-

Description

Grid

Chemistry tabulation

Presumed PDF model

Reference LES Grid convergence study Presumed PDF effects Tabulation evaluation Reference LES Grid convergence study Presumed PDF effects Tabulation evaluation

Coarse Fine Coarse Coarse Coarse Fine Coarse Coarse

AI-EAI AI-EAI AI-EAI AI-LI AI-EAI AI-EAI AI-EAI AI-LI

Dirichlet distribution Dirichlet distribution Independent beta distribution Dirichlet distribution Dirichlet distribution Dirichlet distribution Independent beta distribution Dirichlet distribution

The filtered governing equations are solved using a finite difference scheme. The convection terms of the momentum equations are discretised using a second-order energy conserving scheme. The convection terms of the scalar equations are discretised using the third-order WENO scheme. The diffusion terms of all transport equations are discretised using the second-order central differences scheme. Temporal discretisation is implemented using the Crank–Nicolson scheme. The discretised equations are solved using the Newton– Raphson iterations. The time step is dynamically adjusted to ensure the Courant number less than 0.5. Table 2 presents a summary of the eight simulation cases in this study. Each LES case is running over 5τ (the corresponding time scale τ = L/U , where L = 60D, and U = UPilot ) to obtain statistically converged results, and taking statistic ensembling average for 5τ . The chemistry table is generated using GRI 3.0 mechanism (53 species, 325 reactions),[23] which has been verified properly for PPJB flames.[15] By balancing the storage and precision, the chemistry table is discretised by 50 × 50 × 25 × 50 × 25 grid points in 2 2 2 2 the directions of Z˜ 1 × Z˜ 2 × Z 1 × c˜ × c . The gridstretching is employed in the Z1 − c directions to increase the resolution, and the grid is uniform in the rest of directions.

5. Results and discussions 5.1. Statistical results ... Velocity results Figure 6 shows the radial profiles of the mean and root-mean-square (rms) axial velocity at four axial locations for PPJB50. The simulation results show that the mean axial velocity are in good agreement with experimental data, meanwhile, the simulations capture the trend of the rms axial velocity profiles. Although the inflowcondition from a turbulent periodic pipe-flow simulation with specified bulk-flow was used, some differences between experiments and predictions can be observed. The rms axial velocity is slightly overpredicted near the inner shear layer which is due to the velocity difference between the fuel-stream and pilot-stream. At x = 140 mm, good agreement between experiments and predictions for rms axial velocity is obtained. Comparisons of mean and rms profiles for the axial velocity of PPJB100 are shown in Figure 7. The simulation results are in reasonable agreement with experiments at all measurement locations. The discrepancies are mostly confined to the centreline at x = 100 mm, where the rms axial velocity are slightly underpredicted.



341

Figure . Radial distributions of mean and rms axial velocity, PPJB.

... Mixture fraction results Comparisons of mean and rms profiles for two mixture fractions at different axial locations are presented in Figures 8 and 9. Good agreement between measurements and simulations for mean values of Z1 is obtained at all measurement locations for PPJB50 and PPJB100. While discrepancies for the low-speed case PPJB50 become apparent at x = 100 mm, the simulation results overpredict the radical spreading. Shown on the second column of Figures 8 and 9 are the rms values of Z1 for PPJB50 and PPJB100, it can be seen that the location and peak value are adequately predicted by the simulations. Radial profiles of the secondary mixture fraction Z2 are shown in the last two columns. The major difference between measurements and simulations is observed at x = 10 mm, and similar results have been reported by Chen and Ihme.[15] By increasing the downstream distance, the prediction results for secondary mixture fraction improve. At the last measurement location, the mean and rms values for secondary mixture fraction are well predicted. ... Temperature results Comparisons of the temperature fields at four measurement locations are presented in Figures 10 and 11. At x = 10 mm, differences on the outer side of the pilot-stream are attributed to heat losses, which have been discussed by Chen and Ihme.[15] Apart from this discrepancy, the simulation results for PPJB50 and PPJB100 are in excellent agreement with experiments. With the increasing downstream distance, the mean temperature profiles


342

H. ZHANG ET AL.

Figure . Radial distributions of mean and rms axial velocity, PPJB.

are in good agreement with measurements on the outer side of the pilot-stream. However, the rms temperature results are slightly underpredicted near the inner shear layer. At x = 30 mm, it can be seen that the peak value of mean temperature are well predicted, however, the mean temperature gradient has slight discrepancy with experimental data near the inner shear layer. A possible reason for this discrepancy may be attributed to the present SGS models that inadequately capture the flame position. Such effect could be incorporated into the modelling of SGS scalar dissipation rate and presumed PDF model of the reaction progress variable, which were discussed by Chumakov [34] and Ihme and Pitsch [26]. At the last two measurement locations, the location and peak value of mean temperature are adequately predicted by the simulations, particularly for PPJB100. ... Species results Comparisons of Favre-averaged mass fractions of CH4 , H2 O, CO2 for PPJB50 at different axial locations are presented in Figure 12. Good agreement between experiments and predictions is obtained for CH4 and H2 O at all measurement locations for PPJB50. The discrepancies are mostly confined to the centreline at x = 100 mm, where the mass fraction of CH4 is slightly underpredicted and H2 O is slightly overpredicted. Apart from a slight discrepancy in the region corresponding to the outer side of the pilot-stream at x = 10 mm, the simulation results for CO2 are in excellent agreement with experiments throughout the flame. On the outer side of the pilot-stream at x = 10 mm, the mass fraction of CO2 is

343



Figure . Radial distributions of mean and rms mixture fraction, PPJB.

slightly overpredicted, which can be attributed to the assumption of homogeneous scalar inflow conditions in the pilot-stream and coflow-stream.[15] Further improvements can be expected by accommodating variable scalar profiles. Figure 13 shows the Favre-averaged results for mass fractions of major species for PPJB100. At x = 10 mm, differences on the

H. ZHANG ET AL.


344

Figure . Radial distributions of mean and rms mixture fraction, PPJB.

outer side of the pilot-stream are observed for CO2 which are also due to the homogeneous scalar inflow conditions. Apart from this discrepancy, predictions for CH4 , H2 O, CO2 are in reasonable agreement with experiments throughout the flame. However, due to the higher



345

Figure . Radial distributions of mean and rms temperature, PPJB.

reaction progress, CH4 is underpredicted and CO2 is overpredicted at the last measurement location for PPJB100, and similar results also have been reported by Rowinski and Pope [13] and Chen and Ihme.[15] Comparisons of Favre-averaged mass fractions of CO for PPJB50 and PPJB100 are shown in Figures 12 and 13. The predicted mass fractions of CO for cases LES50-1 and LES50-2 are much better than the one for case LES50-3 which indicates that the presumed PDF model has a significant effect on the predictions for intermediate species, and the Dirichlet distribution could reasonably approximate the distributions of the two mixture fractions. The agreement between experiments and predictions for PPJB100 is comparable to the results that were obtained for PPJB50. Note also that the cases LES50-4 and LES100-4 over-predict the peak value of CO, and the differences between the AI-LI-based simulations and experiments increase when travelling downstream. The SGS combustion model based on the AI-EAI chemistry tabulation can reasonably capture the peak value and change trend of CO. However, it should be noted that the present predictions for the peak location of CO have clear discrepancy with experiments which may also be attributed to the present SGS models that inadequately capture the flame position as discussed in Section 5.1.3. In the present simulations, the LES results based on a method of AI-EAI chemistry tabulation combined with presumed PDF are capable of predicting temperature and species


346

H. ZHANG ET AL.

Figure . Radial distributions of mean and rms temperature, PPJB.

profiles, meanwhile, the simulation results based on fine grid are similar to coarse grid. Therefore, the following analysis of the flame structure is based on the results obtained by cases LES50-1 and LES100-1. The proposed SGS combustion model in conjunction with LES has also been employed for the simulations of PPJB150 and PPJB200. For brevity, the LES results for temperature and mass fractions of major species at different measurement locations have been moved to Appendix. With increasing downstream distance, the present model over-predicts the reactivity in the region where local extinction exists. The two high jet velocity flames are predicted to be wider and longer. A potential reason for this discrepancy can be attributed to the SGS combustion model to capture local extinction and re-ignition. Such effects could be incorporated into the chemistry tabulation technique by utilising a strained counter-flow premixed flame and more appropriate PDF distribution of the reaction progress variable.

5.2. Scatter data An analysis of the thermo-chemical state-space representation of the SGS combustion model is performed by comparing correlations between YCO and temperature. Comparisons between experiments and simulations for PPJB50 and PPJB100 at different axial locations are presented in Figure 14. The scatter data are extracted along the radial direction until 4D

347



Figure . Radial distributions for mass fractions of major species, PPJB.

away from the centreline. Chen and Ihme [15] performed LES calculations using a steady FPV combustion model to predict PPJB flames. From Figure 14, significant differences are observed for the peak value. First, the simulations of Chen and Ihme [15] under-predict the peak value of YCO throughout the flame. Second, the AI-LI-based simulations over-predict

H. ZHANG ET AL.


348

Figure . Radial distributions for mass fractions of major species, PPJB.

the peak value, and the differences between AI-LI predictions and experiments increase when travelling downstream. The SGS combustion model based on the AI-EAI chemistry tabulation can reasonably capture the peak value of YCO and change in the trend between



349

Figure . Comparisons of correlation data at different axial locations; grey symbols are experimental data; solid lines are experimental mean profiles; dashed lines are the AI-EAI-based simulation results; dotted–dashed lines correspond to simulations of Chen and Ihme;[] and dashed-double-dotted lines are the AI-LI-based simulation results.

YCO and temperature, even though slightly over-predict the peak value at the last measurement location. It should be noted that the presumed PDF of the two mixture fractions in the present simulations is similar to the one of Chen and Ihme.[15] Based on the above, one can draw a conclusion that the type of chemistry tabulation dramatically influences the prediction of intermediate species but does not have the same effect on the major species prediction.


350

H. ZHANG ET AL.

Figure . Distributions of the reaction source term obtained by two presumed PDF models.

5.3. Comparison of two presumed PDF models Many SGS models, employed for the reaction source term in the filtered scalar transport equations, have been developed to predict turbulent premixed combustion. In the present simulations, the filtered reaction source term was precomputed and stored in the filtered chemistry table, which is obtained by integrating the laminar chemistry library using the presumed PDF. Therefore, presumed PDF models are expected to have a great effect on the simulation results. For the given values of the mixture fraction Z1 and Z2 , Figure 15 shows the distributions of the reaction source term obtained by two presumed PDF models, Dirichlet distribution (model 1) and independent beta distribution (model 2). The shapes of the curves are quite similar for both models, but some differences in the location and peak value of reaction source term are observed, which has a significant effect on the predictions of CO mass fractions shown in Section 5.1.4. 5.4. Flame structure Figure 16 shows the predicted instantaneous CO mass fraction fields for PPJB50 and PPJB100, respectively. It can be seen that the flame structure consists of two regions for all the two flames. The first region features a relatively thin reaction layer and is not subject to turbulent eddies. The second region locates the downstream flow field, and it shows strong intermittent behaviour with turbulent eddies shaping the reaction layer.[16] Due to the high speed jet of cold gas being initially surrounded by the pilot-stream which is at a temperature of 2274 K, the interaction of the jet and the high-temperature pilot gases could result in relatively vigorous reactions in the thin shear layer between the jet-stream and pilot-stream. Therefore, the CO mass fraction fields exhibit a thin peak in the shear layer close to the jet exit. This thin band is wrinkled by turbulent motions, but turbulence is not able to affect the inner structure. With increasing downstream distance, one could observe



351

Figure . Snapshots of instantaneous CO mass fraction fields.

an effect of the vortices with pockets of high CO complementing the thin band. Further downstream, the pattern evolves as a collection of large pockets with high CO mass fraction. These pockets are located in the shear layer and travel downstream. By increasing the turbulence intensity, the effect of the turbulent eddies on the flame structure becomes more evident, and at the same axial position, the size of these pockets for PPJB100 is larger than PPJB50.

6. Conclusions LESs are performed for two PPJB flames utilising a tabulated chemistry and a presumed PDF approach to model the turbulence flame interactions under high Karlovitz number. The following conclusions can be drawn from the present investigation. (1) Comparisons of statistical results show that the two presumed PDF models of mixture fraction are both capable of predicting temperature and major species profiles. However, they are shown to have a significant effect on the predictions for intermediate species. Compared to an independent beta distribution, the Dirichlet distribution has been found to reasonably approximate the distributions of the two mixture fractions. (2) An analysis of the thermo-chemical state-space representation of the SGS combustion model is performed by comparing correlations between the carbon monoxide mass fraction and temperature. The type of chemistry tabulation dramatically influences the prediction of intermediate species. The SGS combustion model based on the AI-EAI chemistry tabulation can reasonably capture the peak value of the carbon monoxide and change in the trend between the carbon monoxide and temperature. (3) The present predictions for the peak location of intermediate species have apparent discrepancy with experimental data. A possible reason for this discrepancy may be attributed to the present SGS combustion model that inadequately captures the flame position. Such effect could be incorporated into the modelling of the SGS scalar dissipation rate and the presumed PDF model of the reaction progress variable, and further exploration is required to improve the present simulation results. (4) For PPJB150 and PPJB200, the present model over-predicts the reactivity, which can be attributed to the local extinction process. This effect could be incorporated in the chemistry tabulation technique by utilising a strained counter-flow premixed flame and more appropriate PDF distribution of the reaction progress variable.

352

H. ZHANG ET AL.

Acknowledgments The authors would like to acknowledge the funding of the Program (Grant Nos. 51176178, 91441117 and 91441202), and the Key Program (Grant No. 50936005) of National Natural Science Foundation of China. We want to express our gratitude to Prof. Assaad Masri for sharing the experimental data. The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of University of Science and Technology of China.


Disclosure statement No potential conflict of interest was reported by the authors.

Funding The authors would like to acknowledge the funding of the Program [grant no. 51176178], [grant no. 91441117], [grant no. 91441202], and the Key Program [grant no. 50936005] of National Natural Science Foundation of China.

References [1] Lefebvre AH. Gas turbine combustion. Hoboken: CRC Press; 1998. [2] Lefebvre A. The role of fuel preparation in low-emission combustion. J Eng Gas Turbines Power. 1995;117:617–654. [3] Correa SM. Power generation and aeropropulsion gas turbines: from combustion science to combustion technology. Symp Combust. 1998;27:1793–1807. [4] Pitz R, Daily J. Experimental study of combustion in a turbulent free shear layer formed at a rearward facing step. In: 19th AIAA Aerospace Sciences Meeting; St. Louis, USA; 1981. [5] Sanquer S, Bruel P, Deshaies B. Some specific characteristics of turbulence in the reactive wakes of bluff bodies. AIAA J. 1998;36:994–1001. [6] Duwig C, Fuchs L. Study of flame stabilization in a swirling combustor using a new flamelet formulation. Combust Sci Technol. 2005;177:1485–1510. [7] Anacleto P, Fernandes E, Heitor M, et al. Swirl flow structure and flame characteristics in a model lean premixed combustor. Combust Sci Technol. 2003;175:1369–1388. [8] Chen Y-C, Peters N, Schneemann G, et al. The detailed flame structure of highly stretched turbulent premixed methane-air flames. Combust Flame. 1996;107:223–224. [9] Dunn MJ, Masri AR, Bilger RW, et al. Finite rate chemistry effects in highly sheared turbulent premixed flames. Flow Turbul Combust. 2010;85:621–648. [10] Peters N. The turbulent burning velocity for large-scale and small-scale turbulence. J Fluid Mech. 1999;384:107–132. [11] Dunn MJ, Masri AR, Bilger RW. A new piloted premixed jet burner to study strong finite-rate chemistry effects. Combust Flame. 2007;151:46–60. [12] Dunn MJ, Masri AR, Bilger RW, et al. The compositional structure of highly turbulent piloted premixed flames issuing into a hot coflow. Proc Combust Inst. 2009;32:1779– 1786. [13] Rowinski DH, Pope SB. PDF calculations of piloted premixed jet flames. Combust Theory Model. 2011;15:245–266. [14] Duwig C, Nogenmyr K-J, Chan C-k, et al. Large eddy simulations of a piloted lean premix jet flame using finite-rate chemistry. Combust Theory Model. 2011;15:537–568. [15] Chen Y, Ihme M. Large-eddy simulation of a piloted premixed jet burner. Combust Flame. 2013;160:2896–2910. [16] Duwig C, Dunn MJ. Large eddy simulation of a premixed jet flame stabilized by a vitiated co-flow: Evaluation of auto-ignition tabulated chemistry. Combust Flame. 2013;160:2879– 2895.



353

[17] Domingo P, Vervisch L, Payet S, et al. DNS of a premixed turbulent V flame and LES of a ducted flame using a FSD-PDF subgrid scale closure with FPI-tabulated chemistry. Combust Flame. 2005;143:566–586. [18] Proch F, Kempf AM. Numerical analysis of the Cambridge stratified flame series using artificial thickened flame LES with tabulated premixed flame chemistry. Combust Flame. 2014;161:2627–2646. [19] Domingo P, Vervisch L, Veynante D. Large-eddy simulation of a lifted methane jet flame in a vitiated coflow. Combust Flame. 2008;152:415–432. [20] Van Oijen J, Lammers F, De Goey L. Modeling of complex premixed burner systems by using flamelet-generated manifolds. Combust Flame. 2001;127:2124–2134. [21] Duwig C, Fuchs L. Large eddy simulation of a H2/N2 lifted flame in a vitiated co-flow. Combust Sci Technol. 2008;180:453–480. [22] Galpin J, Angelberger C, Naudin A, et al. Large-eddy simulation of h2–air auto-ignition using tabulated detailed chemistry. J Turbul. 2008;9:1–21. [23] Smith G, Golden D, Frenklach M, et al. GRI-Mech 3.0, 2000. Available from: http://www.me.berkeley.edu/gri_mech [24] Pierce CD, Moin P. Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion. J Fluid Mechan. 2004;504:73–97. [25] Ihme M, Cha CM, Pitsch H. Prediction of local extinction and re-ignition effects in nonpremixed turbulent combustion using a flamelet/progress variable approach. Proc Combust Inst. 2005;30:793–800. [26] Ihme M, Pitsch H. Prediction of extinction and reignition in nonpremixed turbulent flames using a flamelet/progress variable model: 1. A priori study and presumed PDF closure. Combust Flame. 2008;155:70–89. [27] Wall C, Boersma BJ, Moin P. An evaluation of the assumed beta probability density function subgrid-scale model for large eddy simulation of nonpremixed, turbulent combustion with heat release. Phys Fluids. 2000;12:2522–2529. [28] Girimaji S. Assumed β-pdf model for turbulent mixing: Validation and extension to multiple scalar mixing. Combust Sci Technol. 1991;78:177–196. [29] Baurle R, Girimaji S. Assumed PDF turbulence-chemistry closure with temperaturecomposition correlations. Combust Flame. 2003;134:131–148. [30] Hasse C, Peters N. A two mixture fraction flamelet model applied to split injections in a DI diesel engine. Proc Combust Inst. 2005;30:2755–2762. [31] Pierce CD, Moin P. A dynamic model for subgrid-scale variance and dissipation rate of a conserved scalar. Phys Fluids. 1998;10:3041–3044. [32] Ihme M, Pitsch H. Prediction of extinction and reignition in nonpremixed turbulent flames using a flamelet/progress variable model: 2. Application in LES of Sandia flames D and E. Combust Flame. 2008;155:90–107. [33] Pitsch H, Steiner H. Large-eddy simulation of a turbulent piloted methane/air diffusion flame (Sandia flame D). Phys Fluids. 2000;12:2541–2554. [34] Chumakov SG. Subgrid models for large eddy simulation: Scalar flux, scalar dissipation and energy dissipation [dissertation for the doctoral degree]. Madison, WI: University of Wisconsin Madison; 2005.

Appendix. Radial profiles of temperature and mass fractions for major species The radial profiles of temperature and mass fractions of CH4 , CO2 , CO are shown in Figures 17 and 18.

H. ZHANG ET AL.


354

Figure . Radial distributions for temperature and mass fractions of major species, PPJB.



Figure . Radial distributions for temperature and mass fractions of major species, PPJB.

355