An a priori study of different tabulation methods for turbulent pulverised coal combustion

In many practical pulverised coal combustion systems, different oxidiser streams exist, e.g. the primary- and secondary-air streams in the power plant boilers, which makes the modelling of these systems challenging. In this work, three tabulation methods for modelling pulverised coal combustion are evaluated through an a priori study. Pulverised coal flames stabilised in a three-dimensional turbulent counterflow, consisting of different oxidiser streams, are simulated with detailed chemistry first. Then, the thermo-chemical quantities calculated with different tabulation methods are compared to those from detailed chemistry solutions. The comparison shows that the conventional two-stream flamelet model with a fixed oxidiser temperature cannot predict the flame temperature correctly. The conventional two-stream flamelet model is then modified to set the oxidiser temperature equal to the fuel temperature, both of which are varied in the flamelets. By this means, the variations of oxidiser temperature can be considered. It is found that this modified tabulation method performs very well on prediction of the flame temperature. The third tabulation method is an extended three-stream flamelet model that was initially proposed for gaseous combustion. The results show that the reference gaseous temperature profile can be overall reproduced by the extended three-stream flamelet model. Interestingly, it is found that the predictions of major species mass fractions are not sensitive to the oxidiser temperature boundary conditions for the flamelet equations in the a priori analyses.     

Flame structure analysis and flamelet progress variable modelling of strained coal flames

Strained two-phase pulverised coal flames in a counterflow configuration are investigated numerically. Three operating conditions with different coal-to-primary-air ratios and inlet velocities were evaluated in order to establish different flame regimes. At first, the two-phase flow of the fully resolved reference cases is calculated solving the transport equation for the species and directly evaluating the reaction rates. Different flame structures are identified using the heat release rate and the chemical explosive mode as markers, showing that complex structures with a combination of lean premixed and non-premixed flames can be observed in strained counterflow coal flames. In addition to the fully resolved simulation, the suitability of the Flamelet-Progress Variable (FPV) model is investigated. Both premixed and non-premixed tables are employed. At first, the suitability of the look-up tables is evaluated by means of an a priori analysis, using the fully resolved simulations as reference solutions, showing that the non-premixed flamelet table correctly predicts the structure of the strained coal flames, while the premixed table shows sensible deviations in terms of temperature and species, especially at rich conditions. Finally, the a posteriori analysis shows that the fully coupled FPV model with a non-premixed flamelet look-up table can accurately predict strained coal flames.     

A quantitative method for a priori evaluation of combustion reaction models

In recent years, direct numerical simulations have been used increasingly to evaluate the validity and performance of combustion reaction models. This study presents a new, quantitative method to determine the ideal model performance attainable by a given parameterization of the state variables. Data from direct numerical simulation (DNS) of unsteady CO/H₂–air jet flames is analysed to determine how well various parameterizations represent the data, and how well specific models based on those parameterizations perform. Results show that the equilibrium model performs poorly relative to an ideal model parameterized by the mixture fraction. The steady laminar flamelet model performs quite well relative to an ideal model parameterized by mixture fraction and dissipation rate in some cases. However, at low dissipation rates or at dissipation rates exceeding the steady extinction limit, the steady flamelet model performs poorly. Interestingly, even in many cases where the steady flamelet model fails (particularly at low dissipation rate), the DNS data suggests that the state may be parameterized well by the mixture fraction and dissipation rate. A progress variable based on the CO₂ mass fraction is proposed, together with a new model based on the CO₂ progress variable. This model performs nearly ideally, and demonstrates the ability to capture extinction with remarkable accuracy for the CO/H₂ flames considered.     

Modeling curvature effects in turbulent autoigniting non-premixed flames using tabulated chemistry

Turbulent flames are intrinsically curved. In the presence of preferential diffusion, curvature effects either enhance or suppress molecular diffusion, depending on the diffusivity of the species and the direction of the flame curvature. When a tabulated chemistry type of modeling is employed, curvature-preferential diffusion interactions have to be taken into consideration in the construction of manifolds. In this study, we employ multistage stage flamelet generated manifolds (MuSt-FGM) method to model autoigniting non-premixed turbulent flames with preferential diffusion effects included. The conditions for the modeled flame are in MILD combustion regime. To model the above-mentioned curvature-preferential diffusion interactions, a new mixture fraction which has a non-unity Lewis number is defined and used as a new control variable in the manifold generation. 1D curved flames are simulated to create the necessary flamelets. The resulting MuSt-FGM tables are used in the simulation of 1D laminar flames, and then also applied to turbulent flames using 2D direct numerical simulations (DNS). It was observed that when the curvature effects are included in the manifold, the MuSt-FGM results agree well with the detailed chemistry results; whereas the results become unsatisfactory when the curvature effects are ignored.     

An efficient approach of unsteady flamelet modeling of a cross-flow-jet combustion system using LES

Steady flamelet models have been widely used in turbulent combustion simulations because of their simplicity, efficiency, yet physics-based nature. They are, however, unable to handle slow chemical and physical processes such as pollutant formation. Unsteady flamelet models have been shown to be able to provide accurate predictions especially for pollutants, but their implementations are usually not as straightforward as for the steady models, and additional assumptions are involved. One relatively straightforward approach of implementing the unsteady flamelet model is to tabulate the time history of unsteady flamelet solutions. This often leads to flamelet libraries of large sizes because of increased dimensions for the new physics. The purpose of this paper is to introduce a new and efficient approach of tabulating unsteady flamelet solutions in the LES of complex systems, here demonstrated in simulations of a cross-flow-jet combustion system. This approach employs Taylor series expansions to represent the time history of unsteady flamelet solutions. Compared with other approaches, the new approach retains the efficiency and simplicity benefits of steady flamelet models but possesses the accuracy of unsteady flamelet models. Various issues associated with the formulation and implementation of this approach are discussed, which include the selection of the base solution, the order of accuracy of the expansion, and the treatment of simultaneous wall heat losses and heat transfer through thermal radiation. This approach is validated in large eddy simulations of a cross-flow-jet combustion system. Good agreement with experiments is obtained for both temperature and NO concentration, as well as for major species.     

Propagation speed of combustion and invasion waves in stochastic simulations with competitive mixing

We consider the propagation speeds of steady waves simulated by particles with stochastic motions, properties and mixing (Pope particles). Conventional conservative mixing is replaced by competitive mixing simulating invasion processes or conditions in turbulent premixed flames under the flamelet regime. The effects of finite correlation times for particle velocity are considered and wave propagation speeds are determined for different limiting regimes. The results are validated by stochastic simulations. If the correlation time is short, the model corresponds to the KPP–Fisher equation, which is conventionally used to simulate invasion processes. If the parameters of the simulations are properly selected, the model under consideration is shown to be consistent with existing experimental evidence for propagation speeds of turbulent premixed flames.     

Unsteady response of chain-branching premixed-flames to pressure waves

Motivated by some recent experimental results that are incompatible with the standard one-step model, we present an analytical study of the unsteady response of flames to acoustic waves in the framework of a simple two-step chemistry model, using conditions that are appropriate to approximately describe lean methane–air flames. The calculated response functions are qualitatively different from those obtained with the standard one-step model. The results are sufficiently encouraging to suggest that the analysis should be extended in the near future to more detailed kinetics schemes.     

Unsteady flamelet/progress variable approach for non-premixed turbulent lifted flames

The unsteady flamelet/progress variable approach has been developed for the prediction of a lifted flame to capture the extinction and re-ignition physics. In this work inclusion of the time variant behavior in the flamelet generation embedded in the large eddy simulation technique, allows better understanding of partially premixed flame dynamics. In the process sufficient simulations to generate unsteady laminar flamelets are performed, which are a function of time. These flamelets are used for the generation of the look-up table and the flamelet library is produced. This library is used for the calculation of temperature and other species in the computational domain as the solution progresses. The library constitutes filtered quantities of all the scalars as a function of mean mixture fraction, mixture fraction variance and mean progress variable. Mixture fraction and progress variable distributions are assumed to be β-PDF and δ-PDF respectively. The technique used here is known as the unsteady flamelet progress variable (UFPV) approach. One of the well known lifted flames is considered for the present modeling which shows flame lift-off. The results are compared with the experimental data for the mixture fraction and temperature. Lift off height is predicted from the numerical calculations and compared with the experimentally given value. Comparisons show a reasonably good agreement and the UFPV combustion model appears to be a promising technique for the prediction of lifted and partially premixed flames.     

湍流扩散燃烧的数值研究-PDF方法和火焰面模型的性能比较

采用标量概率密度函数(PDF)方法、稳态和非稳态火焰面模型三种方法对一个值班湍流CH_4/O_2/N_2射流扩散火焰(Sandia Flame D)进行数值计算,以比较不同燃烧模型的性能。PDF方法通过计算反应标量的PDF输运方程来得到标量分布,而火焰面模型只求解单标量混合物分数的PDF方程,组分和温度分布通过火焰面方程的求解或者火焰面数据库的插值得到。计算结果和实验数据对比表明PDF方法计算结果最好但计算量相当大,稳态火焰面模型则反之。综合而言,非稳态火焰面模型的预测结果相对稳态模型有了非常大的改进,而计算量仍然容易接受,非常适合工程应用。     

Thermoacoustic response of fully compressible counterflow diffusion flames to acoustic perturbations

The goal of this research is to study the thermoacoustic response of diffusion flames due to their relevance in applications such as rocket engines. An in-house code is extended to solve the fully compressible counterflow diffusion flame equations, allowing for a spatially- and temporally-varying pressure field. Various hydrogen-air flames with a range of strain rates are simulated using detailed chemistry. After introducing sinusoidal pressure perturbations at the inlet, the gain and phase of various quantities of interest are extracted. As the frequency is increased, the gain of the temperature source term transitions from the perturbed steady flamelet value to a first plateau at intermediate frequencies, and finally to a second plateau at the highest frequencies. At these high frequencies, the gain of the integrated heat release decays to zero, underscoring the importance of compressibility. These three regimes can be identified and explained through a linearization and frequency domain analysis of the governing equations. The validity of the low Mach number assumption and importance of detailed chemistry are assessed.     

Characteristic boundary conditions for direct simulations of turbulent counterflow flames

Improved Navier–Stokes characteristic boundary conditions (NSCBC) are formulated for the direct numerical simulations (DNS) of laminar and turbulent counterflow flame configurations with a compressible flow formulation. The new boundary scheme properly accounts for multi-dimensional flow effects and provides nonreflecting inflow and outflow conditions that maintain the mean imposed velocity and pressure, while substantially eliminating spurious acoustic wave reflections. Applications to various counterflow configurations demonstrate that the proposed boundary conditions yield accurate and robust solutions over a wide range of flow and scalar variables, allowing high fidelity in detailed numerical studies of turbulent counterflow flames.     

Validation of a mixture-averaged thermal diffusion model for premixed lean hydrogen flames

The mixture-averaged thermal diffusion model originally proposed by Chapman and Cowling is validated using multiple flame configurations. Simulations using detailed hydrogen chemistry are done on one-, two-, and three-dimensional flames. The analysis spans flat and stretched, steady and unsteady, and laminar and turbulent flames. Quantitative and qualitative results using the thermal diffusion model compare very well with the more complex multicomponent diffusion model. Comparisons are made using flame speeds, surface areas, species profiles, and chemical source terms. Once validated, this model is applied to three-dimensional laminar and turbulent flames. For these cases, thermal diffusion causes an increase in the propagation speed of the flames as well as increased product chemical source terms in regions of high positive curvature. The results illustrate the necessity for including thermal diffusion, and the accuracy and computational efficiency of the mixture-averaged thermal diffusion model.     

A three mixture fraction flamelet model for multi-stream laminar pulverized coal combustion

A three mixture fraction flamelet model is proposed for multi-stream laminar pulverized coal combustion. The technique of coordinate transformation is utilized to map the flamelet solutions from a unit pyramid space into a unit cubic space to improve the stability of the simulation. The validity of the three mixture fraction flamelet model was assessed on different configurations, including a laminar counterflow pulverized coal/methane flame and a laminar piloted pulverized coal jet flame. The flamelet predictions were compared to the reference results of the detailed chemistry solutions. For the counterflow flame, it was found that the flame temperature and major species mass fractions are correctly predicted by the three mixture fraction flamelet model. However, discrepancies are observed for combustion-mode-sensitive species such as CO and H₂ in the premixed combustion region. The thermo-chemical quantities in the char surface reaction zone cannot be correctly predicted if the mixing between the char off-gas stream and other streams is neglected. For the piloted jet flame, it was shown that the stable thermo-chemical variables can be correctly predicted at the upper and middle stream locations. However, at the downstream location, discrepancies can be observed in certain regions. Overall, the validity of the three mixture fraction flamelet model for multi-stream pulverized coal combustion is confirmed and its performance in turbulent pulverized coal combustion will be tested in future work.     

Direct numerical simulations of rich premixed turbulent n-dodecane/air flames at diesel engine conditions

Rich premixed turbulent n-dodecane/air flames at diesel engine conditions are analyzed using direct numerical simulations. The conditions correspond to a parametric variation of the Engine Combustion Network Spray A (pressure 60 atm; oxidizer oxygen level and temperature 21% and 900 K, respectively; fuel temperature 363 K). Three simulations with equivalence ratios of 3, 5, and 7 are performed with a Karlovitz number (Ka, based on flame time) of order 100 to match the estimated Ka of the rich premixed combustion region in Spray A. At these conditions, the reference laminar flames exhibit a complex structure which involves both low-temperature chemistry (LTC) and high-temperature chemistry over a wide range of length scales. In the presence of turbulence, the flame structure is strongly affected in physical space and the reaction zone exhibits a very complex structure in which broken, distributed, and thin regions co-exist, especially for the leanest case. However, the contribution of the LTC pathway is only weakly affected by turbulence. In progress variable space, the mean flame structure, including the chemical source terms, is found to match remarkably well that of the corresponding unity Lewis number laminar flame, particularly for the $?=$ 3 and 5 cases. This behavior is attributed to the strong turbulent mixing occurring throughout the flames/reaction zones, which suppresses differential diffusion effects. Nevertheless, large conditional fluctuations around the mean chemical source terms are identified. These are found to correlate very well with radical species mass fractions such as OH. In addition, a similar functional dependence is obtained from counterflow laminar flames. As such, it appears from these results that laminar flame models have a potential to be used to represent the thermochemical state of rich premixed turbulent flames under diesel engine conditions.     

钝体驻定湍流扩散火焰的数值研究——燃烧模型比较

分别采用标量联合的概率密度函数方法、稳态火焰面模型、Euler非稳态火焰面模型和基于有限体积/Monte Carlo混合算法的完备PDF模型对钝体驻定的Sydney湍流扩散火焰HM1进行数值模拟,以比较不同燃烧模型的性能,并比较标量联合的概率密度函数方法和Euler非稳态火焰面模型对氮氧化物排放预测的差异.计算结果和实验数据的比较表明,采用概率密度函数方法计算化学反应可以得到更好的结果但计算量较大,而用火焰面模型求解计算量较小,在接近完全燃烧的情形下,其计算结果比较合理.     

湍流扩散火焰的非稳态火焰面模拟

采用稳态的和非稳态的火焰面模型同时对一个湍流甲烷射流扩散火焰进行了数值模拟,比较了两者对湍流平均火焰结构、活性自由基和污染物(氮氧化物)排放的模拟效果。速度场采用κ-ε模型计算,守恒标量混合物分数的分布通过其概率密度函数(PDF)输运方程的求解得到。稳态的火焰面结构由查询火焰面数据库得到,而非稳态的火焰面结构由火焰面方程和流场方程耦合求解来计算。采用详细的GRI—Mech 3.0机理描述甲烷的氧化和氮氧化物的形成。数值模拟结果和实验数据作了广泛的对比,验证了火焰面模型对湍流扩散燃烧的定量模拟能力。     

A hybrid EDC/Flamelet approach for modelling biomass combustion of grate-firing furnace

This paper proposes a new combustion model for the simulation of biomass combustion. It is developed based on the framework of the well-known Eddy Dissipation Concept (EDC) approach, which has the ability to incorporate chemical kinetics in turbulent reacting flows and thus makes it suitable for modelling gas-phase combustion. However, its high computational cost when using detailed chemistry has made it impractical for modelling large/industrial setups. To address this handicap, the proposed approach decouples the real-time calculation of chemical and mixing processes by importing a pre-calculated steady laminar flamelet library into EDC. The development of this new model is performed based on a modified version of EDC (called Extended EDC), which is capable of modelling the gas-phase of biomass combustion over a wide range of turbulent flow conditions. The proposed model is validated by simulating the well-documented experiment of the piloted jet flames of Barlow and Frank. The performance of the model is then evaluated by simulating a small-scale grate firing biomass furnace. The results show that, overall, the proposed model can be used to model biomass combustion at substantially low computational cost.     

Cellular and sporadic flame regimes of low-Lewis-number stretched premixed flames

3D structure and dynamical behavior of low-Lewis-number stretched premixed flames are numerically simulated within the framework of a thermo-diffusive model with one-step chemical reaction. The results are compared with microgravity experiments at qualitative level. The influence of Lewis number, equivalence ratio, and heat loss intensity on flame structure is investigated. It is experimentally and numerically found that lean counterflow flames can appear as a set of separate ball-like flames in a state of chaotic motion. It is shown that the time averaged flame balls coordinate may be considered as important characteristic similar to coordinate of continuous flame front. Numerical simulations reveal essential incompleteness of combustion at high level of heat losses. This incompleteness occurs in the process of lean mixtures combustion and is caused by fuel leakage through the gaps among ball-like flames.     

Prediction of NO in turbulent diffusion flames using Eulerian particle flamelet model

The combustion characteristics for the turbulent diffusion flames using the unsteady flamelet concept have been numerically investigated. The Favre-averaged Navier–Stokes equations are solved by a finite volume method of SIMPLE type that incorporates the laminar flamelet concept with a modified k ? ε turbulence model. The NO formation is estimated by solving the Eulerian particle transport equations in a postprocessing mode. Two test problems are considered: CH₄/H₂/N₂ jet flame and CH₄/H₂ stabilised bluff body flame. The temperature and species profiles are well captured by the flamelet model. Two different chemical mechanisms (GRI 2.11 and 3.0) give nearly identical results for temperature and species except NO. The GRI 3.0 gives significantly higher NO levels compared to the GRI 2.11. This is mainly attributed to the difference in NO formation by the prompt mechanism. The NO formation is sensitive to the number of flamelet particles. The NO levels for two test flames do not change when the flamelet particle number exceeds six.