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. 2018 May 21;32(10):10121–10131. doi: 10.1021/acs.energyfuels.8b01001

Assessment of On-the-Fly Chemistry Reduction and Tabulation Approaches for the Simulation of Moderate or Intense Low-Oxygen Dilution Combustion

Zhiyi Li †,‡,*, Michał T Lewandowski §, Francesco Contino ‡,∥, Alessandro Parente †,‡,*
PMCID: PMC6196345  PMID: 30364430

Abstract

The current paper focuses on the numerical simulation of the Delft jet in hot co-flow (DJHC) burner, fed with natural gas and biogas, using the eddy dissipation concept (EDC) model with dynamic chemistry reduction and tabulation, i.e., tabulated dynamic adaptive chemistry (TDAC). The central processing unit (CPU) time saving provided by TDAC is evaluated for various EDC model constants and chemical mechanisms of increasing complexity, using a number of chemistry reduction approaches. Results show that the TDAC method provides speed-up factors of 1.4–2.0 and more than 10 when using a skeletal mechanism (DRM19) and a comprehensive kinetic mechanism (POLIMIC1C3HT), respectively. The directed relation graph with error propagation (DRGEP), dynamic adaptive chemistry (DAC), and elementary flux analysis (EFA) reduction models show superior performances when compared to other approaches, such as directed relation graph (DRG) and path flux analysis (PFA). All of the reduction models have been adapted for run-time reduction. Furthermore, the contribution of tabulation is more important with small mechanisms, while reduction plays a major role with large ones.

Introduction

Moderate or intense low-oxygen dilution (MILD) combustion technology has gained increasing attention in the past few decades.1−3 It is characterized by very strong mixing between reactants and products. As a result, the fuel conversion rate is higher and the temperature field is more uniform than in conventional combustion, thereby reducing CO, soot, and NOx emissions.1,2 As a result of the intensive mixing and reduced temperature peaks, reactivity in MILD combustion is reduced to the point that the overall oxidation process is controlled by chemical kinetics.4 Thus, combustion models which consider finite-rate chemistry are required when modeling such a combustion regime. In the present work, the eddy dissipation concept (EDC) combustion model5 is used.

The number of species and reactions in a reaction mechanism grows with the number of carbon atoms in the fuel component. As a consequence, the central processing unit (CPU) time associated with chemistry resolution can be very significant for industrial applications involving realistic fuels. In this framework, the use of pre-reduced or pre-tabulated mechanisms may not be able to capture the dynamic phenomena, such as extinction and re-ignition, accurately. Therefore, on-the-fly/dynamic chemistry reduction/tabulation methods are essential to alleviate the calculation burden for finite-rate chemistry approaches. Various investigations based on the use of on-the-fly chemistry reduction techniques are reported in the literature. Tosatto et al.6 used a transport-flux-based directed relation graph (DRG) model in a two-dimensional simulation of axisymmetric co-flow flames. A speed-up factor of about 5 was reported for a steady case, while a factor ranging from 10 to 20 was obtained for a time-dependent oscillating flame. Yang et al.7 investigated the use of dynamic adaptive chemistry (DAC) for efficient chemistry calculations in turbulent reacting flow modeling. The incurred errors in the predicted temperature and species concentrations were effectively controlled, and a speed-up of 3–6 times was achieved. Zhang et al.8 and He et al.9 conducted homogeneous charge compression ignition (HCCI) engine simulations with the element flux analysis (EFA) approach. The size of the kinetic scheme was significantly reduced while maintaining reliable accuracy. A new adaptive reduction method that emphasizes solution error control was proposed by Oluwayemisi et al.10 and tested in combustion computational fluid dynamics (CFD) with autoignition [one-dimensional (1D), zero-dimensional (0D)] and two-dimensional (2D) laminar flame examples. They concluded that the proposed decoupled species and reaction reduction (DSRR) model is as fast as the directed relation graph (DRG) model. Moreover, DSRR offers improved solution accuracy control. In 2016, Xie et al.11 introduced a Jacobian-aided rate analysis (TSRA) approach. The chemical species are categorized through this approach plus time scale, and no problem-dependent parameters, such as starting species, are required. They drew the conclusion that the TSRA method yields more accurate predictions of ignition delay time and composition compared to DRG based DAC approach.

The dynamic reduction method allows for significant CPU savings; however, the cost associated with the direct ordinary differential equation (ODE) integration can still be significant if the number of species in the reduced mechanisms is non-negligible. This is especially important in some non-conventional or engine combustion applications, where detailed chemistry is necessary and the number of species set is still large, even after reduction. The coupling with the dynamic tabulation approach provides a solution to this issue. Tang et al.12 combined chemistry dimension reduction and tabulation with a methodology called in situ adaptive tabulation–rate-controlled constrained equilibrium (ISAT–RCCE). The chemistry reduction with RCCE is performed by specifying a set of represented species, and the selection of species is performed using a new greedy algorithm with local improvement (GALI). The ISAT–RCCE calculations show good agreement with the direct integration approach without reduction, and a significant speed-up factor of about 500 is obtained in comparison to direct integration. Ren et al.13 and Contino et al.14 coupled the DAC approach with ISAT in engine simulations, achieving speed-up factors of the order of 100. The chemistry reduction model expedites the reaction substep in the operator-splitting scheme through local skeletal reduction, whereas ISAT expedites the calculations by reducing the number of direct ODE integrations through tabulating and reusing the solutions, thus making the use of detailed chemistry in CFD simulations more achievable.14

The current investigation focuses on the simulation of MILD combustion with the tabulated dynamic adaptive chemistry (TDAC)14 approach, where several conventional reduction methods are adjusted to be dynamic and coupled with the dynamic tabulation method of ISAT. The study is motivated by the specific features of such a combustion regime: indeed, there is a general consensus about the need of detailed kinetics in MILD combustion, yet it is not clear to which extent a chemical mechanism can be reduced without loss of accuracy. The Delft jet in hot co-flow (DJHC) burner15−18 is chosen as validation test case. Two fuels, Dutch natural gas and biogas, and three chemical mechanisms, DRM19,19 GRI3.0,20 and POLIMIC1C3HT,21 are chosen to assess the speed-up achieved with TDAC. The EDC constants are adjusted to optimize simulation results following recent studies.22−26 Several reduction approaches are benchmarked against DAC, and the contribution of reduction and tabulation in the TDAC approach is assessed. The objective of the present work is to provide an overall assessment of the TDAC method under MILD conditions. All of the numerical models are implemented in the OpenFOAM development version without external libraries.

Numerical Models

In this section, the EDC combustion model and the TDAC approach for chemistry reduction and tabulation are presented in detail.

Eddy Dissipation Concept

The EDC model, proposed by Magnussen,5 assumes that combustion happens in the fine structures, where energy dissipation takes place. In the original model formulation, the fine structures are described as perfectly stirred reactors (PSRs). However, some software packages (for example, ANSYS Fluent) treat them as plug flow reactors (PFRs) mainly for numerical convenience. A previous work has shown that there are no distinguishable differences when using PSRs and PFRs.27 Therefore, the PFR treatment is selected in the current study. Each computational cell is separated into a fine structure region and surrounding fluid region. The mass fraction of the fine structures (γλ) and the mean residence time of the fluid inside the fine structures (τ*) are described as

graphic file with name ef-2018-01001x_m001.jpg 1

and

graphic file with name ef-2018-01001x_m002.jpg 2

where ν is the kinematic viscosity and ε is the dissipation rate of kinetic energy, k. Cγ and Cτ are two model parameters, set to 2.1377 and 0.4083, respectively. Finally, the mean reaction rate of species i is expressed as

graphic file with name ef-2018-01001x_m003.jpg 3

This expression of the EDC model was proposed by Magnussen in 2005 and, therefore, denoted as EDC2005 in the present work. The term Ỹi in eq 3 is the mean mass fraction of species i between the fine structures, Yi*, and the surrounding fluid, Yi. The mass fraction Yi* of species i inside the fine structures is estimated solving a PFR equation, with the residence time of τ*. A detailed kinetic mechanism is used in the PFR calculation. In the present study, the DRM19 (19 species + N2 and AR, 58 reactions),19 GRI3.0 (53 species, 325 reactions),20 and POLIMIC1C3HT (107 species, 2642 reactions)21 mechanisms are used.

The EDC2005 model has been reported to overpredict peak temperatures in MILD combustion conditions.23,24 Adjustments of the Cγ and Cτ constants have been proposed to correct this behavior.22−26 Among them, the adjustment proposed by De et al.25 focused on the DJHC flame, for which Cτ was increased to 3.0 or Cγ decreased to 1.0.

Tabulation of Dynamic Adaptive Chemistry

TDAC couples a modified in situ adaptive tabulation (ISAT)28 algorithm and chemical mechanism reduction methods,14,29−33 including DRG,34 directed relation graph with error propagation (DRGEP),35 DAC,36 elementary flux analysis (EFA),37 and path flux analysis (PFA).38 The TDAC process is visualized in Figure 1. ISAT stores the initial composition and the solution of the ODE integration with so-called “leafs” and retrieves them with a linear approximation when the composition space is within an ellipsoid of accuracy (EOA), avoiding the need for a direct integration. When ISAT needs growth or addition instead of retrieve, it provides first the composition ψq to the mechanism reduction method, which simplifies the mechanism and provides a reduced set of species compositions ψaq to the ODE solver. The solver computes the reaction mapping R(ψa), and then ISAT builds the full reaction mapping R(ψq) from R(ψaq).14 If the differences between the existing and newly build reaction mappings are within the user-defined tolerance of εISAT, the EOA will grow to include the new mapping. Otherwise, a new “leaf” will be added to include the newly computed mappings. Furthermore, a time-step-specific scale factor is defined, to give more control on the time-step variations.39

Figure 1.

Figure 1

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TDAC method flowchart. This figure was adjusted with permission from ref (14). Copyright 2011 Elsevier.

The five different reduction approaches (DRG, DRGEP, DAC, PFA, and EFA) implemented in the TDAC code are all based on a network graph assumption, in which the relationship between various species or reactions are linked with weights. An error ε is evaluated when a species or reaction is removed and compared to the maximum acceptable value εmax, predefined by the user. If ε is larger than the maximum error εmax, this means that the species/reaction is important for the network graph and cannot be removed. The DRG, DRGEP, and PFA methods that were initially developed for mechanism preprocessing have been adapted for dynamic reduction in the TDAC method.14,30−32

In DRG,34 the error ε is expressed via an interaction coefficient rAB representing the contribution of species B to the production rate of species A

graphic file with name ef-2018-01001x_m004.jpg 4

where νA,i is the stoichiometric coefficient of species A, ωi represents the reaction rate in each reaction, nR is the number of reactions, and δBi is defined as

graphic file with name ef-2018-01001x_m005.jpg 5

Later, Pepiot-Desjardins and Pitsch35 proposed the DRGEP model. They argued that a more accurate way to consider the contribution of species B to species A is to use the net contribution, instead of evaluating production and consumption individually. Therefore, a new definition of the direct interaction coefficient is introduced

graphic file with name ef-2018-01001x_m006.jpg 6

in which PA and CA denote the production and consumption of species A, respectively. They are expressed with

graphic file with name ef-2018-01001x_m007.jpg 7

and

graphic file with name ef-2018-01001x_m008.jpg 8

Furthermore, the effect of removing a group of species is also included, since the previously removed species are considered as well. Most importantly, the notion of error propagation is brought up in DRGEP. When evaluating the error rAB, the length of the path the error has to propagate, from B to A, is considered.

graphic file with name ef-2018-01001x_m009.jpg 9

Instead, only the weakest contribution is taken in DRG

graphic file with name ef-2018-01001x_m010.jpg 10

In eqs 9 and 10, S1 = A, Sn = B, and p denotes a certain path that links two species A and B. Finally

graphic file with name ef-2018-01001x_m011.jpg 11

The DAC method implemented in the TDAC code is very similar to the DRGEP approach discussed above, except that the contribution of removing a group of species is neglected.29,36 With regard to the PFA model based on the DRG and DRGEP methods, both the directly linked (first generation) and undirectly linked (higher generation) species contributions are evaluated,38 resulting in an interaction coefficient rAB with information from multiple generations. For the EFA approach, the error evaluation is focused on removing individual reactions, expressed as37

graphic file with name ef-2018-01001x_m012.jpg 12

where ri and rik are the individual reaction rates before and after removing a reaction k from the network. The variance sk is defined as

graphic file with name ef-2018-01001x_m013.jpg 13

where r̅k is the averaged reaction rate of the remaining reactions after reaction k is removed.

graphic file with name ef-2018-01001x_m014.jpg 14

Table 1 shows the differences and similarities of the five reduction models explained.

Table 1. Differences and Similarities of the Reduction Models in TDAC.

reduction model DRG DRGEP DAC PFA EFA
graph network yes yes yes yes yes
species group effect no yes no    
error propagation no yes yes    
error evaluation based on species species species species reaction
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Validation Cases

The DJHC burner15,17 is chosen as a validation case to test the EDC2005 model and the TDAC potential for CPU time saving. The DJHC burner has a central fuel jet with an inner diameter of 4.5 mm. The hot co-flow is provided by a secondary burner mounted in an outer tube with the inner diameter of 82.8 mm. A schematic 2D drawing of the DJHC burner is shown in Figure 2. A detailed description of the DJHC jet can be found in the studies of Oldenhof et al.15 and Sarras et al.17

Figure 2.

Figure 2

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2D schematic drawing of the DJHC burner. This figure was adjusted with permission from ref (15). Copyright 2011 Elsevier.

The mean and variance of the temperature and velocity experimental values are available for validation. Both Dutch natural gas15 and biogas17 are used as central jet fuel. The Dutch natural gas case is classified as “DJHC-I” with Re = 4100 and biogas as “biogas” with Re = 4000 in the research work of Sarras et al.17 The differences on the fuel component are listed in Table 2.

Table 2. Central Jet Fuel Content for the Dutch Natural Gas and Biogas Cases15,17.

molar content (%) CH4 N2 C2H6 CO2
Dutch natural gas 81 15 4  
biogas 56.7 10.5 2.8 30
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Further properties of the fuel and co-flow streams are presented in Table 3.

Table 3. Physical Properties of the Natural Gas and Biogas Flames15,17.

case V̇fuel,mean (nL/min) Tco-flow,max (K) Yco-flow,O2 Refuel
Dutch natural gas 16.1 1540 0.076 4100
biogas 15.3 1436 0.095 4000
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Numerical Settings

Unsteady Reynolds-averaged Navier–Stokes (URANS) simulations with local time stepping (LTS) were performed, using the standard k–ε turbulence model. Previous work conducted by Lewandowski and Ertesvåg40 has shown that the standard k–ε gives the best prediction on jet mean velocity decay among the other modified k–ε model variations for DJHC flames with a low Reynolds number. The simulation domain is extended 225 mm axially (z) downstream of the burner exit and 80 mm toward the radial direction (r). The whole domain is discretized with a structured 2D axisymmetric mesh. After a grid independence study,40 the mesh with 14 400 cells is chosen. The inlet boundary conditions for the temperature and velocity were taken from experimental values measured 3 mm downstream of the jet exit, as proposed by De et al.25 The reactingFoam solver is used. The time discretization is handled with a first-order local Euler scheme, and second-order schemes are used for all spatial discretization. The DRM19,19 GRI3.0,20 and POLIMIC1C3HT21 mechanisms are selected, because they are characterized by an increasing complexity, i.e., number of species and reactions. According to Contino,29 the value of 10–4 is commonly used for the ISAT tabulation tolerance if the test case is not highly inhomogeneous. Bourgeois tested several choices of reduction tolerance of DAC,39 showing that the cases with reduction tolerances of 1 × 10–4 and 1 × 10–5 show almost identical ignition delay time as the case with DAC turned off. However, using 1 × 10–4 is able to largely reduce the active species. Therefore, TDAC is used with a tolerances for both reduction and tabulation of 1 × 10–4.

The seulex solver is used for ODE integration, and the absolute tolerance of 1 × 10–11 and relevant tolerance of 1 × 10–5 are chosen. Seulex uses an extrapolation algorithm, and it is based on the linearly implicit Euler method with step size control and order selection.41 The target species of CO, CH4, and HO2 are chosen for reduction methods after a sensitivity analysis.

The standard EDC parameters are first used for the simulation of both natural gas and biogas cases. Looking at eq 2, it is clear that increasing Cτ leads to an increased residence time in the fine structures. This results in a higher CPU time required for the ODE integration. Preliminary simulations confirmed this, indicating that setting Cτ to 3.0 results in a simulation time 2.6 times higher than with standard constants. Therefore, we chose to adjust first the value of Cγ to 1.0, as suggested by De et al.,25 and then modify the constant Cτ,22,24,25 to improve the prediction. This approach was chosen since the focus of the present work is on dynamic chemistry reduction and tabulation. However, more advanced EDC extensions have been proposed for MILD combustion, such as the use of functional expressions accounting for local flow conditions24 or using a variable reacting fraction of the fine structures.40

Results and Discussion

In the present section, numerical simulations of the DJHC burner fed with natural gas and biogas are validated against experimental data. The reduction and tabulation efficiency, which is represented with CPU time saving, provided by TDAC is demonstrated. The influence of the chemical mechanism and reduction methods on TDAC performances is also discussed. Finally, reduction and tabulation in TDAC are tested separately, to identify their contributions to speed-up.

Natural Gas Flame Modeling

For the natural gas case, the mean radial and axial temperature and velocity profiles are used for validation. The axial locations for the radial profiles are z = 15/30/60/120/150 mm. The mean temperature profile is first presented in Figure 3. The corresponding values of Cτ and Cγ are listed in Table 4.

Figure 3.

Figure 3

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Mean temperature profiles obtained with the EDC2005 model, using standard and adjusted constants, compared to the experimental data. Kinetic mechanism: DRM19. TDAC with DAC reduction model. Fuel: Dutch natural gas.

Table 4. Standard and Adjusted EDC Constants.

constant standard adjust 1 adjust 2 adjust 3
Cγ 2.1377 1.0 1.0 1.0
Cτ 0.4083 0.4083 1.47 3.0
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In Figure 3, the effect of the EDC model parameters become clear at axial locations above 30 mm. At z = 60 mm, a pronounced temperature peak, by over 300 K higher than the experimental value, is obtained using the standard and first set of modified constants (adjust1). With the second set of modified constants (adjust2), this overprediction is alleviated to 100 K. Further downstream, at z = 120 and 150 mm, a slightly shifted temperature peak is observed for all of the cases, with the case using the adjust2 set closer to the measured values. For the centerline profile, applying the second set of constants helps correct the overprediction of the temperature downstream (z ≥ 100 mm) of the jet. Overall, the second set of constants better capture the experimental temperatures for the DJHC natural gas flame case. Using the third set of modified constants (adjust3) leads to an extinguished flame. Thus, the corresponding profiles are not shown here. The reduced peak temperature value from standard constants to first set of constants is due to the decrease of Cγ, which leads to the reduction of the mass fraction of the reacting zone in each computational cell, as shown in eq 1. Going from the first to the third set of constants, Cγ is kept constant and Cτ is increased. As a result, a higher residence time τ* and lower mean reaction rates are obtained, as indicated by eq 3. Therefore, the temperature peak is further alleviated with the second set of constants, and the flame is extinguished with the third.

The velocity profiles are presented in Figure 4. Using different parameter sets results in negligible differences at almost all locations. However, the case with standard constants shows earlier decay, as indicated by the centerline profile. Generally, the prediction of the radial velocity profiles is quite accurate, at all axial locations. The centerline profile shows, however, an underprediction of velocity after z = 30 mm, by 13.5% at z = 60 mm. This means that the jet downstream decay rate is slightly overpredicted by the model.

Figure 4.

Figure 4

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Mean velocity profiles obtained with the EDC2005 model using standard and adjusted constants compared to the experimental data. Kinetic mechanism: DRM19. TDAC with DAC reduction model. Fuel: Dutch natural gas.

As far as the computational savings are concerned, the relative, normalized CPU time of the simulations, with and without TDAC, is shown in Table 5. The normalization is based on the CPU time consumption of the base case, defined as the simulation with standard EDC and without TDAC. A speed-up of 1.4–2 times is obtained using the DRM19 mechanism, depending upon the set of adjusted constants used for the natural gas flame. The mean temperature and velocity profile obtained using TDAC are virtually identical to the results obtained without TDAC; therefore, they are not shown here.

Table 5. Normalized Time Consumption with/without TDAC and Using Various EDC Sets of Constantsa.

constant set standard adjust1 adjust2 adjust3
without TDAC 1.00 0.72 1.94  
with TDAC 0.51 0.50 1.26  
speed-up 1.96 1.44 1.54  
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a

TDAC with DAC reduction model applied. Fuel: Dutch natural gas.

Biogas Flame Modeling

For the biogas case, the radial profiles at axial locations z = 65/110/140/170 mm are used for temperature validation, while the experimental data at z = 30/60/90/120 mm are available to compare to computed velocities. In Figure 5, the mean numerical and experimental temperature profiles are compared, using several EDC2005 parameter settings. The trend is very similar to what is observed for the natural gas case. A clear overprediction of temperature levels is obtained using the standard and adjust 1 sets of constants. The level of agreement is significantly improved using the second and third sets of constants, although some overpredictions (10–20%) can still be observed at z = 140/170 mm using the third set. Figure 6 shows the comparison between the measured and computed velocity profiles. The agreement is very satisfactory, with the maximum difference always being below 1.0 m/s, and no distinctive difference can be observed between the profiles provided by the different EDC constant sets.

Figure 5.

Figure 5

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Mean temperature profiles obtained with the EDC2005 model using standard and adjusted constants compared to the experimental data. Kinetic mechanism: DRM19. TDAC with DAC reduction model. Fuel: biogas.

Figure 6.

Figure 6

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Mean velocity profiles obtained with the EDC2005 model using standard and adjusted constants compared to the experimental data. Kinetic mechanism: DRM19. TDAC with DAC reduction model. Fuel: biogas.

The normalized time consumption factor with and without TDAC is shown in Table 6. Together with the data from the natural gas case in Table 5, a conclusion can be drawn that the total CPU time is indeed increased with the increased Cτ value. Furthermore, the speed-up factor still lies in the range between 1.4 and 2.0. Almost no visual difference can be observed between the results obtained with and without TDAC.

Table 6. Normalized Time Consumption with/without TDAC and Using Various EDC Sets of Constantsa.

constant set standard adjust1 adjust2 adjust3
without TDAC 1.0 1.34 1.58 1.88
with TDAC 0.55 0.78 1.03 1.14
speed-up 1.82 1.72 1.53 1.65
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a

TDAC with DAC reduction model applied. Fuel: biogas.

Influence of Chemical Mechanisms

The natural gas flame is chosen for the current and following sections, to demonstrate the influence of chemical kinetics and reduction algorithm on the simulation speed-up as well as to clarify the role of tabulation and reduction in TDAC. In the study of De et al.,25 the DRM19 mechanism was found to perform satisfactorily for the DJHC natural gas flame. However, to test the potential speed-up of the TDAC method, two additional mechanisms of increasing size are chosen, namely, GRI3.0 and POLIMIC1C3HT. At the same time, the effect of the mechanism on the accuracy of the predictions is assessed as well. Figure 7 compares the temperature profiles provided by the different mechanisms plotted against the experimental data. The second set of constants (adjust2) is employed for all simulations. The profiles provided by the different mechanisms do not show major differences. Nevertheless, using a more detailed mechanism at downstream axial distances, z = 120 mm, helps reduce the temperature overprediciton by 30–40 K.

Figure 7.

Figure 7

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Mean temperature profiles obtained with the EDC2005 model using the DRM19, GRI3.0, and POLIMIC1C3HT mechanisms compared to the experimental data. EDC2005 constant: adjust2. TDAC with DAC reduction model. Fuel: Dutch natural gas.

In Table 7, a trend of increasing speed-up is observed when more complicated mechanisms are chosen. The CPU time consumption normalization is based on the case with the DRM19 mechanism and without TDAC. Using the POLIMIC1C3HT mechanism requires 27.43 times the CPU required for the DRM19 case when neither reduction nor tabulation is applied. Using the TDAC method reduces the gap to 4.12 times, which corresponds to roughly 10 times speed-up. The use of a mechanism as complicated as POLIMIC1C3HT might not be necessary for the present case. However, the significant CPU time saving achieved using TDAC is very promising for the application of the method to more complex cases and regimes, with no a priori knowledge about the appropriateness of a pre-reduced mechanism (as DRM19).

Table 7. Normalized Time Consumption with/without TDAC and Various Chemical Mechanismsa.

mechanism DRM19 GRI3.0 POLIMIC1C3HT
without TDAC 1.0 4.01 27.43
with TDAC 0.65 2.10 2.68
speed-up 1.54 1.91 10.24
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a

TDAC with DAC reduction model. Fuel: Dutch natural gas.

Finally, the number of active species distribution for the various chemical mechanisms in the domain is presented in Figure 8. The number of active species indicates the species left after removing unimportant species. We can observe that almost 100% of the species are used in both the reaction zone and the downstream (z ≥ 100 mm) area of the simulation domain when the DRM19 mechanism is chosen. Away from these regions, the number of active species drops, thus saving computational resources. This effect is magnified with two other chemical mechanisms. With GRI3.0, around 75% of the species are necessary in the active zone close to the centerline. Upstream and far from the centerline region, the number of active species is further reduced to around 20–30. With the POLIMIC1C3HT mechanism, approximately 56% of the species set is retained, leading to the observed speed-up factor of 10.24, as indicated in Table 7. The reason for the low reduction potential on the DRM19 mechanism is that it is already a small (skeletal) mechanism with less than 20 species (inert species excluded). In the MILD non-conventional combustion regime, most of the species and reactions are necessary to include to account for the complex turbulence/chemistry interactions. However, for a large mechanism, such as POLIMIC2C3HT, there are much more species and reactions. Some of them are important only for a certain area of the domain; thus, more reduction on CPU time is obtained.

Figure 8.

Figure 8

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Contour plot of the number of active species (nActiveSpecies) obtained using the EDC2005 model with the DRM19, GRI3.0, and POLIMIC1C3HT mechanisms. EDC2005 constant: adjust2. TDAC with DAC reduction model applied. Fuel: Dutch natural gas. Axis unit: m.

Influence of the Chemistry Reduction Approach

In the present section, the speed-up factor of various chemistry reduction models (DRG, DRGEP, DAC, PFA, and EFA) are compared using both the skeletal and comprehensive mechanisms. The mean temperature and species mass fraction profiles obtained from the five different reduction models with the DRM19 mechanism show only minor differences, as indicated in the Supporting Information. In Table 8, the speed-up factors are listed and compared. Minor differences are observed for the DRM19 case, using the different chemistry reduction approaches. This can be explained with the help of Figure 8. Indeed, the DRM19 mechanism is already a reduced mechanism, and this implies that the margins for further reduction are tight. On the other hand, using the POLIMIC1C3HT mechanism, larger differences are identified between the five methods. The DRGEP, DAC, and EFA models have speed-up factors around 3 times higher than those obtained using DRG and PFA models. Using a more complicated mechanism helps to better evaluate the efficiency of the various approaches.

Table 8. Simulation Speed-up with Various Reduction Methodsa.

reduction model DRG DRGEP DAC PFA EFA
speed-up with DRM19 1.57 1.55 1.55 1.58 1.55
speed-up with POLIMIC1C3HT 3.9 10.90 10.22 3.2 9.6
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a

Tabulation turned on. Fuel: Dutch natural gas.

In Figure 9, a contour plot of the number of active species in the simulation domain is again presented when the POLIMIC1C3HT mechanism is applied. The reduction ability of DRG, DRGEP, DAC, PFA, and EFA models can thus be analyzed. The DRG and PFA reduction models provide very weak reduction ability. Approximately only 10% of the whole species set are removed for the reaction area and regions nearby, whereas the other three approaches, DRGEP, DAC, and EFA, present a significantly reduced set of species, around 40% by estimation. Among them, the DRGEP model provides the most reduced set of species in the whole domain. Moreover, the reactive area is well-identified with DRGEP, DAC, and EFA models as well.

Figure 9.

Figure 9

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Contour plot of the number of active species (nActiveSpecies) obtained using the EDC2005 model with the DRM19, GRI3.0, and POLIMIC1C3HT mechanisms. EDC2005 constant: adjust2. TDAC with DAC reduction model applied. Fuel: Dutch natural gas. Axis unit: m.

CH2O is a key precursor in the initiation process of the reaction for fuel molecules with carbon atoms, especially in MILD combustion.42−45 Therefore, it is adopted here in combination with the temperature to identify the reactive region in the flame. The regions with a high temperature and high CH2O mass fraction are highlighted in Figure 10. When DRGEP, DAC, or EFA methods are chosen, a larger number of active species is identified in these regions (Figure 9), which is not the case when the DRG or PFA methods are used. The latter identifies a large number of active species far from the centerline, after z = 100 mm, where low temperature and CH2O levels are observed. This proves that the DRG and PFA models are not as efficient and accurate as the other reduction approaches in selecting the appropriate active species in the relevant regions of the flame.

Figure 10.

Figure 10

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Contour plot of the mean CH2O mass fraction and mean temperature obtained using the EDC2005 model. Kinetic mechanism: POLIMIC1C3HT. EDC2005 constant: adjust2. Tabulation turned on. DAC reduction models. Fuel: Dutch natural gas. Axis unit: m.

Influence of Reduction/Tabulation

Because the TDAC method is a combination of chemistry tabulation and reduction, it is interesting to quantify how much they contribute to the speed-up separately. In Table 9, the normalized CPU time is listed considering both tabulation and reduction, only reduction, only tabulation, and without reduction/tabulation. Both DRM19 and POLIMIC1C3HT mechanisms were used. The base case for normalization is the case with both tabulation and reduction for a given mechanism used. A vertical comparison of normalized CPU time is not possible. From Table 9, it can be observed that, using a small mechanism, such as DRM19, the tabulation contribution is more significant, whereas with a large mechanism, such as POLIMIC1C3HT, the reduction step plays the major role. For a detailed mechanism, such as POLIMIC1C3HT, the reduction of the number of species significantly speed-up the ODE integration step. When it comes to the DRM19 case, the mechanism is already very light (the number of species smaller than 20, inert species excluded) and the reduction potential is much lower. Therefore, tabulation is the key step under such conditions.

Table 9. Normalized Time Consumption with/without Reduction and Tabulationa.

model no TDAC TDAC only reduction only tabulation
DRM19 1.55 1.0 1.41 1.03
POLIMIC1C3HT 10.22 1.0 2.38 6.33
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a

DAC reduction model. Fuel: Dutch natural gas. Comparison between the normalized times is possible only horizontally.

A contour plot of the averaged tabulation results (TabulationResultsMean) is shown in Figure 11. Because it is averaged data, the results are presented in decimals between 0 and 2, instead of integers of 0 (add), 1 (grow), and 2 (retrieve). The retrieve (solution directly recovered with linear approximation), grow (ellipsoid of accuracy expanded to include the new mapping), and add (new “leaf” added) in each computational cell can be identified with red, green, and blue colors. Most regions that are far away from the centerline are marked with retrieve for both mechanisms. In the reactive region, as identified from Figure 10, it is characterized mostly by green (grow), indicating an expansion of the EOA. One can also appreciate that the POLIMIC1C3HT mechanism is able to capture the interaction of co-flow and air streams in the upstream area, which is colored with green, whereas the DRM19 mechanism predicted the same area to be closer to retrieve. Using two mechanisms, the reaction system is described with different reactions and species. Therefore, the contributions of reactions and dominating phenomenon in local regions are different as well, showing inconsistency on the tabulation results.

Figure 11.

Figure 11

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Contour plot of the tabulation results (TabulationResultsMean) obtained using the EDC2005 model with DRM19 and POLIMIC1C3HT mechanisms. EDC2005 constant: adjust2. Reduction model: DAC. Fuel: Dutch natural gas. Axis unit: m.

Conclusion

In the current paper, the DJHC burner was numerically investigated by means of Reynolds-averaged Navier–Stokes (RANS) simulations with detailed kinetic mechanisms and dynamic chemistry reduction/tabulation. Two fuels, Dutch natural gas and biogas, were selected for the preliminary model validation. The speed-up potential of TDAC is assessed using three mechanisms (DRM19, GRI3.0, and POLIMIC1C3HT) and different chemistry reduction models (DRG, DRGEP, DAC, PFA, and EFA). Moreover, the contributions of tabulation and reduction are investigated separately. The followings conclusions are summarized: (1) The current EDC model implementation in OpenFOAM with a modified set of constants (using Cγ = 1.0 and Cτ = 1.47) provide satisfactory predictions for mean temperature profiles of the natural gas flame, while the lower reactivity of the biogas flame make the use of Cγ = 1.0 and Cτ = 3.0 more accurate. The mean velocity distribution is well-predicted for both flames with all of the model settings. A speed-up factor of 1.4–2.0 is obtained using the TDAC method with the DRM19 mechanism. (2) Using a more complicated chemical mechanism, such as GRI3.0 or POLIMIC1C3HT, slightly improves temperature predictions and leads to significantly increased CPU time with respect to the DRM19 case (27.4 times for POLIMIC1C3HT) when TDAC is turned off. However, with TDAC, a 10 times speed-up is obtained for the POLIMIC1C3HT mechanism, reducing the CPU time gap between POLIMIC1C3HT and DRM19 to 4.16 times. (3) The DRGEP, DAC, and EFA reduction approaches are more efficient and accurate compared to the DRG and PFA models. (4) When a small mechanism is used (DRM19), tabulation is the main contributor to computational saving. With more complex mechanisms (POLIMIC1C3HT), chemistry reduction plays the main role.

The current investigation validates the application of the EDC model in combination with the TDAC method under MILD regime using the open-source software OpenFOAM. The time saving using TDAC with complex chemistry is very promising, thus making it feasible to extend it to industrial or semi-industrial applications.

Acknowledgments

This project has received funding from the European Union’s Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie Grant Agreement 643134. The research of Alessandro Parente is sponsored by the European Research Council, Starting Grant 714605, and from the Fédération Wallonie-Bruxelles, via “Les Actions de Recherche Concertée (ARC)” call for 2014–2019. The authors are indepted to Professor Dirk Roekaerts at Delft University of Technology (TU Delft) for his courtesy to provide the experimental data of DJHC flames.

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.8b01001.

  • Mean temperature and species mass fraction profiles from the five cases with different reduction methods (DRG, DRGEP, DAC, EFA, and PFA) compared to the case in which the reduction is turned off (PDF)

The authors declare no competing financial interest.

Supplementary Material

ef8b01001_si_001.pdf (163KB, pdf)

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Supplementary Materials

ef8b01001_si_001.pdf (163KB, pdf)

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