Combustion of fossil fuels is still widely used around the globe for various services both at the industrial and residential levels. This chemical reaction emits pollutants that can have environmental impacts, such as NOx and CO₂. Therefore, there is interest in developing next-generation combustion technologies, such as hydrogen-based combustion, and there is also a need for improving or retrofitting existing equipment ^[1]. MILD combustion ^[2], also known as colorless ^[3] or flameless combustion ^[4] is a promising technology for these purposes.

The concept of flameless combustion was first introduced by Wünning ^{[4], [5]}. This regime is achieved by preheating and diluting the fresh air-fuel mixture with hot flue gases. Significant dilution with these gases results in a reaction without a visible flame front and a uniform temperature distribution with low NOx emissions. The critical parameter for achieving flameless combustion is the recirculation factor Kv, defined as a ratio of recirculated mass flow to the input mass flow to the furnace ^[2]. In such studies, a flameless regime for methane was achieved with Kv values ranging from approximately 3 and 8, for furnace temperatures above the self-ignition temperature of the flammable mixture.

Cavaliere and de Joannon later formally defined MILD combustion regime ^{[2], [6]}. MILD is an acronym that refers to a “Moderate or Intense Low-oxygen Dilution” regime where two conditions must be satisfied: First, the reactive mixture must be above self-ignition temperature. Second, the temperature increases inside the furnace due to reaction (∆T) must be lower than the self-ignition temperature (T _si ). This definition was obtained using a perfectly stirred reactor analysis. Flameless can be regarded as a practical way to obtain a MILD combustion regime, where strong dilution due to recirculation leads to a lower oxygen concentration in reactants and a lower temperature increase in the furnace. If the temperature of the reactive mixture is above self-ignition temperature, MILD conditions are satisfied.

Both definitions of flameless and MILD combustion are the subject of intense debate, suggesting that the underlying physics of this phenomenon is not yet completely understood ^[7]-[9]. The parameter Kv, which is used to characterize the recirculation intensity in MILD combustion, has several limitations as identified in literature. It can be easily calculated for an external gas recirculation (EGR) case if fuel, oxidizer, and recirculated gas mass flow rates are measured. However, in several furnaces, internal gas recirculation (IGR) is used, where high impulse jet flows create recirculating swirls. In such cases, measuring the aerodynamic Kv is challenging and it is usually estimated by CFD simulations ^[10].

For an IGR case, there are several Kv values inside the furnace due to the variation in mass flow being recirculated from point to point ^[10]. A common assumption is to report the maximum Kv value ^{_{[8], [11]}} . Furthermore, Kv can also vary depending on whether the fuel and oxidizer flows are premixed or non-premixed before the reaction ^[7]. Despite its drawbacks, Kv is still a widely used parameter for studying flameless combustion.

This work aims to bridge the gap between MILD and flameless combustion definitions by proposing a parameter based on mass balance called recirculation ratio Z. With this parameter, the critical point for establishing the MILD combustion regime unconditionally is evaluated. This study includes numerical simulations of reactor networks considering CH₄ and C₂H₆, and the calculation of reactor temperatures using an energy balance of C₃H₈ and H₂. An algorithm for constructing combustion maps is presented, and the unconditional MILD critical point is identified and analyzed in connection to Kv, Z, and oxygen concentration.

Figure 4 presents a map of MILD combustion regime for the case of CH₄-air mixture at stoichiometric equivalence ratio (ϕ=1), simulated using the GRI-Mech 3.0 mechanism. The oxidizer in this simulation is synthetic air, which is a mixture of oxygen and nitrogen only. The results obtained in this work are consistent with previous results reported in the literature, which were performed using Chemkin-pro ^[21]. This work focuses on the critical point that results from the intersection of the T _si line and the ∆T = T _si line. For the CH₄-air case at ϕ=1, this critical point is at an oxygen mole fraction of 9.7 %. This means that any reactive mixture with an oxygen mole fraction above 9.7 % and a temperature above T _si will exhibit MILD combustion, and this zone is identified as UMC. It is worth noting that it is not necessary to reach such low oxygen levels for achieving MILD in this case, but simulations were performed up to an oxygen mole fraction of 1 % to investigate the behavior in extremely dilute conditions. Below this oxygen level, combustion becomes very difficult to establish, and the self-ignition line converges to the extinction line in Figure 4.

Figure. 4 Source: Created by the authors.

Figure 5 presents the oxygen mole fraction in the oxidizer as a function of the recirculation factor Kv for CH₄ and C₂H₆ cases at three different equivalence ratios. These results consider flue gas recirculation obtained after simulating the reactor network, rather than using synthetic air. In all cases, an increase in recirculation factor Kv leads to dilution of the mixture, resulting in a decrease in the oxygen mole fraction before the reaction. This decrease in oxygen concentration is more pronounced at lower Kv values, between 0 and 2. Beyond Kv = 2, oxygen concentration still decreases with a less steep slope. The results also show that achieving extremely low oxygen levels, such as 1 %, would require a recirculation factor Kv higher than 8 at stoichiometric conditions for methane. This indicates that a significant amount of flue gas recirculation would be needed to achieve such low oxygen levels in the oxidizer for methane combustion.

Figure. 5 Source: Created by the authors.

Achieving mixtures with very low oxygen concentrations through internal aerodynamic recirculation can be challenging, as pointed out in experiments reported in the literature ^[25].

Therefore, mixtures with deficient O₂ concentrations (i.e., 1 %) would be only possible by the creation of synthetic air in a laboratory by mixing O₂ and N₂ at a fixed amount, instead of using actual recirculation of combustion gases for lean or stoichiometric equivalence ratios.

Figure 6 shows a comparison between two different combustion mechanisms, namely “GRI-Mech 3.0” and “Polimi”. The same map of MILD combustion regime presented in Figure 4 is redrawn with both mechanisms. Both mechanisms present similar results, although the critical point in the case of “Polimi” is higher, closer to 10 % oxygen. The “Polimi” mechanism is known to have updated kinetics and can be used for a broader range of fuels compared to GRI-Mech 3.0. However, GRI-Mech is used for simulations of all fuels considered in this work as it requires lower computational power compared to Polimi mechanism.

Figure. 6 Source: Created by the authors.

Figure 7 shows the map of MILD combustion constructed using two different approaches: synthetic air (discontinuous line) and recirculating flue gases (continuous line). Synthetic air, a mixture of O₂ and N₂, is commonly used as the oxidizer for building this kind of map ^[21]. This mixture assumes that all dilutants are nitrogen. However, when actual flue gas is recirculated, the composition of dilutants may also include other substances such as carbon dioxide (CO₂) or water (H₂O). When accounting for flue gas recirculation, the critical point for UMC shifts to a higher O₂ mole fraction, in this case, to 10.6 %. Furthermore, the maximum mole fraction is no longer 21 % as in air, only about 18.9 %, because even when there is no recirculation (Kv = 0), air is premixed and diluted with fuel. Therefore, caution must be exercised when comparing critical points from different combustion maps, as not all maps are constructed in the same way, and the oxygen fractions may be either from oxidizer (as in synthetic air maps) or from flue gas/fuel/air mixture before reaction (as proposed in this study).

Figure. 7 Source: Created by the authors.

Figure 8 presents combustion maps for CH₄ and C₂H₆ at three different equivalence ratios: 1, 0.8 and 0.6. For both fuels, the critical point changes significantly: in the case of methane, it shifts from 10.6 % at ϕ=1 to about 15.5 % at ϕ=6.0, which is consistent with previous studies ^[21]. However, an interesting observation that has not been reported before is the critical recirculation factor Kv that corresponds to each case. For CH₄, it decreases from Kv = 0.86 at ϕ=1 to Kv = 0.59 at ϕ=0.6. This implies that as the equivalence ratio decreases, the requirements for mass recirculation also decrease. In other words, it becomes easier to establish MILD combustion by recirculation at leaner equivalence ratios.

Figure. 8 Source: Created by the authors.

In the case of C₂H₆, critical Kv is significantly higher compared to CH₄. For example, at ϕ=1, critical Kv for ethane is more than three times what is required for methane. This demonstrates that the critical Kv or O₂ level for UMC is dependent on both fuel type and equivalence ratio and can vary considerably.

It is also noteworthy that the self-ignition temperature changes with oxygen mole fraction and may either increase or decrease with Kv. However, at ϕ=0.6 for both fuels, it becomes almost horizontal, meaning that T _si does not change significantly with oxygen concentration. This implies that under such conditions, UMC can be achieved for a wide range of recirculation factors. In the lean equivalence ratio, which involves an excess of air, this excess aids in diluting the mixture effectively while maintaining sufficient oxygen for the reaction to initiate and sustain.

Figure 9 shows the relationship between recirculation ratio Z and recirculation factor Kv, which was determined through numerical analysis. It is observed that this relationship does not change with fuel or equivalence ratio. A recirculation ratio Z of 0.5 signifies that half of the combustion gases are being recirculated back into the reactor, corresponding to Kv = 1. However, as Kv further increases, Z increases slowly, suggesting that Z converges to unity for an infinite Kv. In practical applications, achieving a Kv value higher than eight through aerodynamic recirculation is challenging ^[25].

Figure. 9 Source: Created by the authors.

Figure 10 presents the critical recirculation ratio Z _c as a function of fuel and equivalence ratio. Across all fuels, the trend is consistent: as the equivalence ratio increases, a higher recirculation ratio is necessary. Notably, among the fuels simulated, methane requires the lowest Z _c , while hydrogen necessitates the highest Z _c . This observation is noteworthy as hydrogen combustion does not produce carbon dioxide as the other fuels investigated.

Figure. 10 Source: Created by the authors.

For alkanes such as CH₄, C₂H₆ and C₃H₈, the maximum ∆Z _c for any given, lean equivalence ratio is only 0.1. This indicates that the requirements for achieving unconditional MILD combustion, as measured by Z _c , are similar among these fuels. However, for H₂, due to the lack of CO₂ production during combustion, it becomes challenging to achieve unconditional MILD combustion for equivalence ratios above 0.7 as it would require a significantly large Z _c (and Kv as well). This provides a theoretical basis for diluting pure hydrogen combustion with CO₂ to reduce the requirements of internal gas recirculation for achieving UMC at virtually any lean equivalence ratio considered in this work. Furthermore, Figure 10 includes data points from previous literature for MILD combustion experiments with methane ^[26] and propane ^[8]. The results presented in Figure 10 agree with the findings from these previous studies, as Z is higher than the theoretical Z _c calculated in this work for both methane and propane cases.

This work analyzed the conditions for establishing the unconditional MILD combustion regime under flue gas recirculation, using numerical simulations for lean combustion of CH₄, C₂H₆, C₃H_8, and H₂. The critical point that marks the start of such regime can be identified by the self-ignition temperature and a particular oxygen concentration in the mixture before the reaction. This point changes significantly from fuel to fuel and depends on the global equivalence ratio.

A parameter called recirculation ratio Z was introduced based on mass balance. According to the results, Z better captures the critical recirculation requirements of UMC regime compared to the standard recirculation factor Kv, for most of the fuels considered within a Z _c = 0.1 for any of the lean equivalence ratios studied.

In all cases studied, the critical ratio Z _c diminishes with the equivalence ratio. Methane requires the lowest Z _c while hydrogen requires the highest. In fact, for H₂, unconditional MILD combustion could only be obtained for equivalence ratios below 0.7 and at Z _c between 0.5 and 0.8. H₂ does not have CO₂ as a dilutant in flue gases compared to the other fuels studied; therefore, this result suggests that performing dilution with CO₂ could reduce recirculation requirements for MILD combustion of pure hydrogen.

Further work could focus on the extension of the analysis to other fuels and conditions such as investigation of the effect of different dilutants on recirculation requirements for unconditional MILD combustion.