L. Luo, Y.C. Liu, "Variation of gas phase combustion properties of complex fuels during vaporization: comparison for distillation and droplet scenarios," Proceedings of the Combustion Institute 38 (2021) 3287-3294.

Surrogate mixtures for modelling real fuels are formulated based on gaseous combustion property targets and liquid physical properties. A batch distillation model was developed to evaluate the vaporization characteristics of some existing surrogates for Jet-A. Chinese aviation fuel RP-3 was then used as a target to experimentally obtain distillation curves and variation of chemical functional groups. A 24-component surrogate was formulated mainly to capture the distillation behavior of RP-3. This surrogate was then used in two droplet vaporization models (Finite Thermal Conductivity/Finite Diffusivity (FTC/FD), Infinite Thermal Conductivity/Infinite Diffusivity (ITC/ID)) to investigate the effects of preferential vaporization on gaseous combustion properties of a complex real fuel. The results obtained from FTC/FD and ITC/ID provide regional bounds for droplets in a vaporizing spray. Four combustion property targets (Molecular Weight (MW), Hydrogen to Carbon ratio (H/C), Derived Cetane Number (DCN) and Threshold Sooting Index (TSI)) were employed as indicators of gas combustion properties. It was found that due to a wide distribution of compounds’ volatility, gaseous combustion properties vary significantly during droplet vaporization. The results suggest development of vaporization models that well capture preferential vaporization of a target real fuel for further spray modelling.

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L. Luo, Y.C. Liu, "An "artificial" activity coefficient modelling approach for emulating combustion and physical property variations during distillation of real complex fuel", Combustion and Flame 230 (2021) 111446.

       Real complex fuels consist of hundreds of species and hence are difficult to model in numerical simulation. There have been many methods to formulate simple surrogate suite composed of several compounds. While these surrogates emulate gaseous combustion properties with acceptable fidelity, due to insufficient number of surrogate components comprehensive distillation behaviors of simple surrogates exhibit considerable discrepancy compared to that of real complex fuels. In this work, we demonstrated a new methodology for representing complex fuel economically. Firstly, we obtained information about functional group evolution of a complex fuel (Chinese aviation fuel, RP-3) from distillation experiments and formulated a rather complex surrogate mixture. Then, a Functional Group Matching (FGM) method was applied to convert the complex surrogate to a target 4-component surrogate mixture with an “artificial” activity coefficient model (AACM) such that distillation of real complex fuels can be accurately replicated. This “artificial” activity coefficient model was validated in batch distillation simulation in comparison with the complex surrogate with conventional phase equilibrium model (UNIQUAC Functional-group Activity Coefficient (UNIFAC)). Results showed that chemical functional groups, combustion property targets (CPTs) and physical properties (density, surface tension, and dynamic viscosity) during a distillation process of the simple surrogate well represented those of the complex surrogate. Also, the computational efficiency of this 4-component surrogate with AACM method was verified, which was thousands of times faster than 24-component mixture with UNIFAC. The “artificial” activity coefficient model for a simple surrogate mixture therefore contained the most authentic physics from the distillation experiments of a real complex fuel with potential to improve the computational efficiency and to couple with the chemical kinetics mechanisms available to the simple surrogate.

T. Chen, S. Yu, Y.C. Liu, "Effects of pressure on propagation characteristics of methane-air edge flames within two-dimensional mixing layers: A numerical study", Fuel 301 (2021) 120857.

The effects of pressure on propagation of laminar edge flames were numerically investigated using an OpenFOAM-6 platform developed with multicomponent transport properties. With various equivalence ratio gradients (∇ϕ) as inlet conditions, propagation of non-stationary edge flames in two-dimensional mixing layers at three pressures (0.5 bar, 1.0 bar and 2.0 bar) were studied. The heat release rate increases with increasing pressure and decreases with increasing ∇ϕ due to flame curvature and stretch. The linearity between flame curvature K and ∇ϕ is revealed. The K and slope of this linearity are both larger under high pressure. Flame stretch is dominated by flow strain and flame curvature rather than unsteady flame motion. With increasing ∇ϕ and pressure, stretch rate κ shows increasing feature due to larger curvature and stronger flow strain. The obvious negative linear dependence of local flame speed Sd on κ is revealed under three pressures. The range of Karlovitz number under three pressures are 0.2∼ 1.4, indicating that edge flames are weakly stretched and the linear correlation between Sd and κ could be explained by weakly stretched flame theory. Compared with positive dependence of mass diffusion term Sd d on K, the dominating negative dependence of reaction term Sr d on K leads to negative correlation of Sd with K. Global flame speed UF shows non-monotonic feature with increasing ∇ϕ under three pressures, which is mainly due to non-monotonic upstream velocity reduction Udrop. Flame stretch is important for the shift from critical gradient ∇ϕdc (for maximum Udrop) to smaller ∇ϕFc (for maximum UF) and stronger decreasing feature of UF thanUdrop under large ∇ϕ.

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T. Chen, S. Yu, Y.C. Liu, "Soret effects on the diffusion-chemistry interaction of hydrogen-air edge flames propagating in transverse gradient evolving mixing layers", Fuel 315 (2022) 123014.

The effects of Soret diffusion (SD) on the hydrogen-air edge ame propagation and the diffusion-chemistry interaction are investigated through simulation facilitated by the numerical code MultiDiffFOAM. The edge ames in this study gradually develop from a ame kernel into a tri-brachial structure in a hydrogen-air mixing layer that temporally evolves due to transverse reactant concentration gradient. We demonstrate that the responses of ame displacement speed Sd to ame curvature K, stretch rate  and scalar dissipation rate  are distinctly influenced by SD. For the linear Sd-K and Sd-X correlations, SD would result in a smaller Markstein length. Moreover, SD is shown to lead to shifting of the Sd-X curve towards the regime with larger X. Compared with the weak influences of SD on the tangential diffusion component Sd;t and normal diffusion component Sd;n, the chemical reaction component Sd;r is significantly weakened by SD. The important chemical reactions for edge ame propagation are identified based on sensitivity analysis and their rates are found to be smaller when SD is considered. For the local composition at the ame marker, the mass fraction of H2 is slightly larger and that of H is obviously smaller when SD is considered. The SD flux of H2 jSD H2 and that of H jSDH are both coupled with the driving force grad(lnT) along the mixture fraction coordinate. However, the jSD H2 is mainly concentrated on the unburnt side while the jSD H is on the burnt side. The analyses on decomposed uxes of H2 and H along the flame normal direction further suggest that SD would enhance the H2 mass diusion but weaken the H mass diffusion. Such opposite effects stem from the distribution features that H2 is mainly on the unburnt side while H on the burnt side.

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T. Chen, S. Yu, Y.C. Liu, "Flow strain and curvature Markstein numbers of edge flame in the counterflow configuration", International Journal of Hydrogen Energy (2022) in press.

Based on the counterflow configuration, the Markstein numbers of one-dimensional pre-mixed flame and two-dimensional edge flame of hydrogen-air system are numerically studied and compared with each other. By varying the inlet velocity and mixing layer thickness, the proportional relationship between flame stretch caused by flow strain (Ka s) and by flame curvature (Ka c) disappears, and therefore two corresponding Markstein numbers Ma s and Ma c at different flame markers (or iso-contours of temperature) within flame front could be obtained through linear fitting between normalized flame displacement speed S * d and bivariate (Ka s ; Ka c). With the flame marker shifting from unburnt to burnt side, Ma c profile of edge flame exhibits a decreasing trend while Ma s profiles of premixed flame and edge flame both display an increasing trend with its sign changing from negative to positive. Moreover, a good agreement of Ma s profiles between two kinds of flames is observed while the discrepancy begins to appear when normalized temperature q !5, which should be attributed to the shift of flame marker from premixed branch into diffusion branch rather than the decrease of heat release rate. The comparison between simulation and theory reveals differences of Ma s values except for 2.5 < q < 4 and those of Ma c values except for q ¼ 2.5, which might be accounted for a moderate Zel'dovich number Ze, i.e. 3.9, based on detailed hydrogen-air chemical mechanism. Therefore, the "larger activation energy" assumed in asymptotic theory may not be valid for hydrogen-air flames whose equivalence ratio is 1.6 in this study.

H. Zhou, W. Zhang, Y.C. Liu, "A cell model analysis for droplets inside non-dilute n-heptane droplet clouds near autoignition limit", International Journal of Heat and Mass Transfer 175 (2021) 121189.

Vaporization and two-stage autoignition of single droplets inside the droplet clouds were numerically studied using a spherical cell model. We aimed to investigate the behaviors of individual droplets in a moderately hot ambient (600-800 K) under the influence of surrounding droplets at atmospheric pressure. For a given ratio of distance between droplets L and the droplet diameter D₀, autoignition only occurs when D₀ is above certain critical value. Exemplar cases with L/D₀ = 10 were used for detailed discussion as they are found to be near the autoignition limit. For droplets smaller than 400 mm, no ignition occurs and the surrounding gas phase is saturated by fuel vapor before the droplet completely vaporizes. A simple model of final saturation state was established. With this model, it was observed that when the gas phase in the droplet cloud is saturated, the temperature and fuel concentration distributions are insensitive to the distance between droplets. For droplets larger than 500 mm, a variety of autoignition processes including first stage ignition, cool flame burning, second stage ignition, and diffusional extinction are observed. Unlike single isolated droplets, such behaviors are primarily due to heat accumulation and limited supply of oxidizer that pertains to the scenario of non-dilute droplet cloud. Autoignition of individual droplets in a cloud only happens in the region where chemical time scale is smaller than the physical time scale for vaporization and diffusion. The temperature range of autoignition is broadened with increasing initial droplet diameter. Two potential mechanisms were identified for such broadening. Analyses of ‘probable droplet cloud autoignition (PDCA)’ region were found to qualitatively predict the state switch of vaporization, cool flame ignition, and second stage ignition.

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H. Zhou, Y.C. Liu, "External group combustion of droplet clouds under two-stage autoignition conditions", Combustion and Flame 234 (2021) 111689.

The present study aims to extend the understanding of the external group combustion for droplet clouds under two-stage autoignition conditions. First, an exemplar case has been chosen to analyze the two-stage ignition behavior and flame structure. It was found that the fuel vapor transport of the droplet cloud is mainly supported by the thin vaporization layer near the edge of the cloud, which is the dominant factor of the ignition process. The case shows that a typical two-stage ignition includes the following detailed processes: first stage ignition, quasi-steady non-premixed cool flame, second stage ignition, and premixed hot flame. Three possible ignition modes for droplet clouds were identified through parametric studies, i.e. no ignition, single-stage ignition, and two-stage ignition. The transition between these modes is mainly controlled by the competition between chemical reaction and the vaporization of a thin layer of fuel droplets. Phase diagrams of different ignition modes at different ambient temperatures and sub parameters of the group number were presented. The previous group number G = 2πndR_c² demonstrated unsatisfactory prediction in the ignition modes of the droplet clouds. Basing on the vaporization layer feature of the droplet clouds, a new dimensionless group ignition number with much better predictability is first proposed in this work, i.e. G_ig = 4πn^2/3d². The physical meaning of G_ig is the dimensionless total surface area of droplets within a local layer.

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H. Zhou, Y.C. Liu, "Internal group combustion of dropelt clouds and its transition to external group combustion under two-stage ignition conditions", Proceedings of the Combustion Institute (2022) in press.

The present study is an extension of our prior study on the external group combustion (EGC) of droplet clouds under two-stage autoignition conditions [Zhou and Liu, Combust. Flame 234 (2021) 111689]. Effects of droplet heating and different n-alkane fuel candidates have been further considered. By comparing numerical results from n-heptane and n-dodecane, it was found that the fuel volatility has little effect on the combustion modes of droplet clouds. Among all the computed cases, internal group combustion (IGC) occurs for relatively low value of group ignition number G_ig (= 4πn^2/3d², n and d are the droplet number density and diameter, respectively). When G_ig further increases, the combustion mode can switch to EGC. IGC modes can be sustained by cool or hot flame. IGC of cool flame exhibits a partial burning structure, while IGC of hot flame is firstly premixed, followed by non-premixed structure. These flame structures were analyzed in details. A regime diagram based on G_ig and ambient temperature T_a was developed for all the IGC modes. It was found that for high T_a (1500 K), G_ig can be used to predict ICG modes, but for low T_a (900 K) and intermediate T_a (1200 K), additional parameters might be needed for the prediction, especially for the cases when G_ig is around 0.03. The inapplicability is due to the strong interaction between droplet behavior (droplet heating and vaporization) and chemical kinetics (low and high temperature reaction) that were not inherent to description of G_ig. To clarify the interaction, time scale analysis of these processes was performed for better complementation of the regime diagram characterized by G_ig and T_a for various IGC modes.

In this study, a 1-step and a 2-step globalized model are used to investigate the competition between chemical kinetics and volumetric expansion. Parametric studies have been conducted to better understand how the critical Damköhler numbers (Da_cr) are related to characteristic chemical time scales: the induction and excitation times. Results show that a gas particle can be cooled down to only 30% of the original temperature and ignite due to strong chemical heat release. For the 1-step model, the contour for Da_cr exhibits bifurcation behaviors for Da_cr > 1. Results for the 2-step model demonstrates a ‘saddle-like’ structure of Da_cr in the q₁-q₂ space (q_i is the reduced activation energy of the i^th chemical step) which disappears as q increases. The Da_cr contours are symmetric about the q₁ = q₂ line. The increase of chemical endothermicity within the induction period leads to an increase of Da_cr.