Numerical study of multicomponent spray flame propagation

A computational study of one dimensional multicomponent laminar JetA/air spray flames is presented. The objective is to understand the effect of various spray parameters (diameter, droplet velocity, liquid loading) on the spray flame structure and propagation. Simulation of the Eulerian gas phase is coupled with a Lagrangian tracking of the dispersed liquid phase. Jet-A surrogate of n-dodecane, methyl-cyclohexane and xylene is considered. A discrete multicomponent model for spray vapourisation is used along with an analytically reduced chemistry for computing the gas phase reactions. Both overall lean and rich cases are examined and compared with existing literature for single component spray flames. The preferential evaporation effect, unique to multicomponent fuels cause a variation of fuel vapour composition on both sides of the flamefront and this has a direct impact on the spray flame structure and propagation speed. In rich cases, multiple flame structures exist due to the staged release of vapours across the reactive zone. Spray flame speed correlations proposed for single component fuels are ex∗Corresponding author Email address: varun.shastry@cerfacs.fr (Varun Shastry) Preprint submitted to Proceedings of the Combustion Institute May 7, 2020 tended to the multicomponent case, for both zero and high relative velocity between the liquid and gas. The correlations are able to accurately predict the effective equivalence ratio at which the flame burns and hence the laminar spray flame speeds of multicomponent fuels for all cases studied in this work.


Introduction
Spray formation and combustion have been extensively studied due to the wide ranging application in propulsion and power generation [1]. The various mechanisms involved, occurring at different length and time scales lead to a very complex combustion process with multiple flame structures and combustion regimes [2]. Large Eddy Simulations coupled with detailed 5 chemistry descriptions have been recently performed to get an insight into these highly coupled systems. However a single component representation of the liquid fuel has been mostly utilised [3][4][5].
Real fuels used in these combustion systems contain a large number of components belonging to a range of hydrocarbon families. Differences in their 10 volatilities cause a spatio-temporal variation of the reactive gas phase mixture as the spray evolves. Additionally, preferential evaporation significantly affects the mixture reactivity specially when vaporisation and autoignition time-scales are comparable and in the presence of turbulent structures [6,7].
To address these, a detailed study of multicomponent spray flame structure 15 and propagation is thus necessary in understanding turbulent combustion of fuel blends and developing corresponding models in addition to the existing LES studies [8].
To the authors knowledge, little literature exists on multicomponent laminar spray flames and the parameters influencing it. The one dimensional lam-20 inar premixed spray flame configuration using a single component fuel has been studied to understand the main propagation mechanisms. For lean and stoichiometric mixtures, Ballal and Lefebvre [9] experimentally showed that compared to a gaseous premixed laminar flame at the same overall equivalence ratio, increasing droplet diameter reduces the laminar spray flame 25 speed. This is due to the vapourisation of smaller droplets before reaching the flamefront, which increases the equivalence ratio seen by the flame. For rich mixtures, Hayashi et al. [10] observed an enhanced flame speed over a specific range of droplet diameters in rich mixtures. Here the partial evaporation causes the mixture to burn at stoichiometric conditions enhancing the 30 flame speed. Based on detailed chemistry simulations, Neophytou and Mastorakos [11] marginally correlated the laminar spray flame speed trends with an effective equivalence ratio φ ef f seen by the flame. All of these studies were performed for zero relative velocity between the liquid and the gas phases.
However recently, Rochette et al. [12] performed one dimensional n-heptane 35 laminar spray flame simulations using a two-step chemistry and showed that the relative velocity between the liquid phase and the carrier gas phase also has significant impact on φ ef f and hence the propagation speed. They also derived correlations for the estimation of φ ef f and the laminar spray flame speed as a function of the spray parameters.

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This work aims to analyse the effect of a multicomponent fuel on spray flames, including evaporation and chemistry effects. It is the first attempt to include both Analytically Reduced Chemistry (ARC) and multicomponent evaporation in one dimensional numerical simulations to understand the effect of various spray parameters (diameter, liquid loading, relative velocity 45 and equivalence ratio) on the structure and propagation of a multicomponent spray flame.

Numerical setup
Computations are performed using the CFD code AVBP with a Lagrangian point particle formulation to represent the spray. Source terms 50 for transfer of mass, momentum and energy from the liquid to gaseous phase are distributed to the closest nodes in the Eulerian gas phase in a two-way coupling approach (http://cerfacs.fr/avbp7x/).

Chemical Mechanism
In this work, the surrogate for Jet-A proposed by Narayanaswamy et al.

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[13] is reduced. The three components of the surrogate are n-dodecane (NDC), methyl-cyclohexane (MCH) and a xylene (XYL) species that represents the three possible isomers (ortho-, para-and meta-xylene). The mole fractions of each component in the fuel are X N DC = 0.451, X M CH = 0.268 and X XY L = 0.281. The detailed mechanism with 230 species and 4868 60 reversible reactions of [14] has been reduced with reduction code ARCANE (https://chemistry.cerfacs.fr/en/arcane/) based on YARC [15]

Droplet Evaporation Model
The droplet evaporation is modelled using a quasi steady state assumption. Detailed description of the evaporation model can be found in earlier studies [3,12]. The multicomponent extension is discussed here. The Spalding mass transfer number B M and the fraction of vapour i for an individual component i are calculated as [1]: where Y i is the mass fraction of the individual component i and the subscripts 70 surf and ∞ denote the droplet surface and far-field locations respectively.
Only the components present in the liquid phase are considered in Eq. 1.
Vapour liquid equilibrium Eq. 2 is used to obtain the mole fractions of the fuel components at the droplet surface (X i,surf ) using the liquid mole fractions (X i,liq ) and the vapour pressure (P sat,i (T )) of the different components. Calculating the surface mass fractions Y i surf to be used in Eq. 1 is then straightforward.
Using the above equations, the evaporation rate m i p of an individual component can be calculated using the total evaporation rate of the dropletṁ p and the fraction of vapour i as: The unsteady effects encountered in the multicomponent evaporation include the heat diffusion and mass diffusion in the liquid phase.Time scales for droplet heating(τ H ) and droplet evaporation (τ ev ) can be compared using the specific heat capacities (c) and thermal conductivity (λ) of the liquid(liq) and gaseous(gas) phases as For droplets exposed to high temperature, τ H < τ ev , causing the droplet to reach the steady wet bulb temperature. A similar analysis comparing the mass diffusion inside the liquid (τ dif f ) with the droplet evaporation (τ ev ) in terms of the diffusion coefficient (D) and density(ρ) yields Since D liq D F the time scales in this case be comparable. The more volatile components on the droplet surface quickly evaporate in the high temperatures. This sets up a very strong gradient especially for the small 75 droplets and a flux from the centre to surface. For droplet diameters of 100µm (greater than range used in this work) little differences in the evaporation trends was observed for multicomponent droplets modelled with these unsteady effects [16] and an infinite liquid diffusivity(used here).
The implemented is able to capture the major trends of multicompo- In the flame zone with B comb M of 3.3 we obtain d f ≈ 12d p . When the interdroplet distance S < d f , the isolated droplet burning regime is not reached. the sum of gaseous and liquid equivalence ratios (φ tot = φ gas + φ liq ).
Cases A to C have been set-up to cover a wide range of typical burning regimes observed in real combustors where preferential concentration may lead to a variety of both local liquid loadings and gaseous equivalence ratios.
Moreover, the effect of relative velocity has been investigated to get even 110 closer to real operating conditions where the relative velocity between the gas and droplets can be high as the air and liquid fuel injections are separate.
Inlet gas temperature is 400K and droplets are injected at 300K. The flame speeds and structures are computed over a range of droplet diameters ranging from d p = 5µm to 80µm. For a given droplet diameter, the number 115 of injected droplets is adjusted to fulfil the targeted equivalence ratio. The isolated burning droplet regime is unreachable in this set-up as the interdroplet distance is less than d f introduced previously. The relative velocity between the phases is taken into account by introducing a velocity ratio u * = u liq /u gas [12].  In Fig. 4 for Case A and u * = 1 MCH is shown to evaporate completely in the main flame region followed by XYL and finally NDC. The preferential 130 evaporation of MCH and its complete consumption within the main premixed flame zone shown in Fig. 4b causes a slight increase in φ ef f compared to φ gas .
As the droplets move through the main flamefront gradually they contain only XYL and NDC, and finally only NDC, whose evaporation rate reaches a maximum in the post-flame high temperature region. Due to the lower 135 volatility and longer evaporation distance of NDC, a secondary consumption zone with very low but non-zero reaction rates exist as seen in Fig. 4c.
Increasing the droplet velocity so that u * = 30 shifts the evaporation zone behind the main flamefront as shown in Fig. 5. In Case A two limiting regimes may be encountered. The first corresponds 145 to droplets small or slow enough to evaporate completely in the main reaction zone leading to φ ef f = φ tot while in the second limit large or fast droplets contribute very little to the flame propagation and φ ef f = φ gas . As the flame is overall lean, this leads to the spray flame speed limits for Case A to lie between S L φgas ≤ S L T P ≤ S L φ tot .  The spatial profiles of HR, Γ F and −ω F for Case B are shown in Fig. 6 and      n-heptane case [12]. To extend these correlations to the present case, it is necessary to consider the varying evaporation rates and contributions of the where d p 0 , ρ liq and ρ gas are the initial droplet diameter, liquid and gas density respectively. D F is the diffusion coefficient of the fuel vapour, Sc is the Schmidt number of the surrounding gas and Re p is the Reynolds number of 200 the droplet. k is a factor whose value is taken as 0.6. [1].
For droplets with high relative velocity, it is important to take into account drag force acting on them. Using the droplet relaxation time τ p = ρ liq d 2 p0 /18µ gas (µ gas is the dynamic viscosity of the surrounding gas) and the flame time τ f = δ 0 S L /S 0 L , a flame Stokes number is identified as St f = τ p /τ f . A droplet injected with a velocity u p 0 reaches after crossing the flame thickness the velocity u p : The evaporation length for each component i is then given by δ i ev = u p τ i ev . Following Rochette et al. [12] and using the above expressions, φ ef f is In Eq. 9, s is the stoichiometric ratio. For a hydrocarbon fuel C x H y , s =   For the evaporation controlled flames of Case C (Fig. 13), correlation follows the trend but with some deviation from the simulation results. It is observed in Fig. 13 that a flame can be sustained for gaseous equivalence ratios lower than the flammability limit if droplets have low or zero relative 225 velocities. As was observed in Fig. 8 and