S. Navarro-Martinez

A dynamic model for the Lagrangian stochastic dispersion coefficient

A stochastic sub-grid model is often used to accurately represent particle dispersion in turbulent flows using large eddy simulations. Models of this type have a free parameter, the dispersion coefficient, which is not universal and is strongly grid-dependent. In the present paper, a dynamic model for the evaluation of the coefficient is proposed and validated in decaying homogeneous isotropic turbulence. The grid dependence of the static coefficient is investigated in a turbulent mixing layer and compared to the dynamic model. The dynamic model accurately predicts dispersion statistics and resolves the grid-dependence. Dispersion statistics of the dynamically calculated constant are more accurate than any static coefficient choice for a number of grid spacings. Furthermore, the dynamic model produces less numerical artefacts than a static model and exhibits smaller sensitivity in the results predicted for different particle relaxation times.

Analysis of extinction in a non-premixed turbulent flame using large eddy simulation and the chemical explosion mode analysis

The paper presents computational results of a turbulent non-premixed flame with large extinction, using the large eddy simulation probability density function methodology. The simulation captures local flame extinction at different flame locations, and major species predictions show good agreement with experimental data. A chemical explosive mode analysis is used to determine the flame structure including the explosive modes and the Damköhler number distribution. Due to the nature of the turbulence combustion model, statistical information on the sub-grid flame structure is available: such as sub-grid explosive modes. The analysis suggests that, in the present flame, sub-grid structures are only relevant close to the inlet nozzle, and that downstream extinction is governed by large-scale interactions.

Analysis of Stabilization Mechanisms in Lifted Flames

Flame stabilization and the mechanisms that govern the dynamics at the flame base have been subject to numerous studies in recent years. Recent results using a combined Large Eddy Simulation‐Conditional Moment Closure (LES‐CMC) approach to model the turbulent flow field and the turbulence‐chemistry interactions has been successful in predicting flame ignition and stabilization by auto‐ignition, but LES‐CMCs capability of the accurate modelling of the competition between turbulent quenching and laminar and turbulent flame propagation at the anchor point has not been resolved. This paper will consolidate LES‐CMC results by analysing a wide range of lifted flame geometries with different prevailing stabilization mechanisms. The simulations allow a clear distinction of the prevailing stabilization mechanisms for the different flames, LES‐CMC accurately predicts the competition between turbulence and chemistry during the auto‐ignition process, however, the dynamics of the extinction process and turbulent flame...

Resolution Requirements in Stochastic Field Simulation of Turbulent Premixed Flames

The spatial resolution requirements of the Stochastic Fields probability density function approach are investigated in the context of turbulent premixed combustion simulation. The Stochastic Fields approach is an attractive way to implement a transported Probability Density Function modelling framework into Large Eddy Simulations of turbulent combustion. In premixed combustion LES, the numerical grid should resolve flame-like structures that arise from solution of the Stochastic Fields equation. Through analysis of Stochastic Fields simulations of a freely-propagating planar turbulent premixed flame, it is shown that the flame-like structures in the Stochastic Fields simulations can be orders of magnitude narrower than the LES filter length scale. The under-resolution is worst for low Karlovitz number combustion, where the thickness of the Stochastic Fields flame structures is on the order of the laminar flame thickness. The effect of resolution on LES predictions is then assessed by performing LES of a laboratory Bunsen flame and comparing the effect of refining the grid spacing and filter length scale independently. The usual practice of setting the LES filter length scale equal to grid spacing leads to severe under-resolution and numerical thickening of the flame, and to substantial error in the turbulent flame speed. The numerical resolution required for accurate solution of the Stochastic Fields equations is prohibitive for many practical applications involving high-pressure premixed combustion. This motivates development of a Thickened Stochastic Fields approach (Picciani et al. Flow Turbul. Combust. X, YYY (2018) in order to ensure the numerical accuracy of Stochastic Fields simulations.

Assessment of Conventional Droplet Evaporation Models for Spray Flames

The present work investigates droplet evaporation rates in inert and reactive environments using fully resolved Direct Numerical Simulation (DNS). The droplets are arranged in regular droplet layers and the evaporation of two different fuels, n-heptane and kerosene, is investigated under engine like conditions. It is found that the performance of standard models fort he evaporation rate strongly depends on the modelling of the representative properties. The conventional 1/3-rule for their computation does not necessarily lead to good agreement between model and DNS. This holds for droplet evaporation in non-reacting and reacting environments. Conditions at the droplet surface would need to be more heavily weighted for better model performance. The droplet loading has a minor effect on the validity of the standard single droplet evaporation models.

Gas-Phase Mixing in Droplet Arrays

Droplet evaporation is usually modelled as a subgrid process and induces local inhomogeneities in the mixture fraction probability density function (PDF) and its scalar dissipation. These inhomogeneities are usually neglected, however, they can be significant and determine the combustion regime. In the present work, Direct Numerical Simulations (DNS) of fully resolved evaporating methanol droplets are analysed, assessing fuel vapour mixing in laminar and turbulent flows. The results show that scalar probability distributions and scalar dissipation vary greatly depending on the position relative to the droplet position, on droplet loading and on flow conditions. The β-PDF seems to capture the global behaviour for laminar flows around droplet arrays with low droplet density, however, mixing characteristics for higher droplet densities in stagnant and turbulent flows cannot be approximated by a β-PDF, and modelling approaches based on cell mean values will lead to erroneous results.

A Thickened Stochastic Fields Approach for Turbulent Combustion Simulation

The Stochastic Fields approach is an effective way to implement transported Probability Density Function modelling into Large Eddy Simulation of turbulent combustion. In premixed turbulent combustion however, thin flame-like structures arise in the solution of the Stochastic Fields equations that require grid spacing much finer than the filter scale used for the Large Eddy Simulation. The conventional approach of using grid spacing equal to the filter scale yields substantial numerical error, whereas using grid spacing much finer than the filter length scale is computationally-unaffordable for most industrially-relevant combustion systems. A Thickened Stochastic Fields approach is developed in this study in order to provide physically-accurate and numerically-converged solutions of the Stochastic Fields equations with reduced compute time. The Thickened Stochastic Fields formulation bridges between the conventional Stochastic Fields and conventional Thickened-Flame approaches depending on the numerical grid spacing utilised. One-dimensional Stochastic Fields simulations of freely-propagating turbulent premixed flames are used in order to obtain criteria for the thickening factor required, as a function of relevant physical and numerical parameters, and to obtain a model for an efficiency function that accounts for the loss of resolved flame surface area caused by applying the thickening transformation to the Stochastic Fields equations. The Thickened Stochastic Fields formulation is tested by performing LES of a laboratory premixed Bunsen flame. The results demonstrate that the Thickened Stochastic Fields method produces accurate predictions even when using a grid spacing equal to the filter scale. The present development therefore facilitates the accurate application of the Stochastic Fields approach to industrially-relevant combustion systems.

Detailed simulation of air-assisted spray atomization: effect of numerical scheme at intermediate Weber number

Numerical simulations are often used to understand spray atomisation and estimate the size of the liquid fragments. Several techniques (Level Set, Volume of Fluid, Smooth Particle Hydrodynamics, among others) exist to compute multiphase flows and potentially represent liquid-break-up. However, the complexity of the breakup process and the wide range of scales prevents the use of an unified approach to simulate the complete spray. Numerical techniques face different challenges depending on the spray characteristics. The incorrect representation of surface forces in capillary dominated flows, creates large parasitic currents that distort and in some cases destroy the interface. Methods that perform well in the capillary regime aim to capture the interface directly and the surface radius cur- vature is therefore larger than the mesh size. However, this creates large constrains on the mesh resolution and limits its applications to low Weber number flows, when there is no extensive atomization. Methods that simulate large Weber number flows (typical of industrial injectors) do not resolve the interface directly and the mesh is larger than the smallest radius of curvature. These models often have numerical or artificial diffusion that destroys small scale structures and alters the break-up. However, even at large Weber flows, the spray formation can be affected by errors due to the local imbalance between pressure and surface tension forces and interface curvature errors. Numerical schemes work around these problems by adjusting the amount of numerical diffusion of the scheme depending on the spray application. Intermediate Weber number sprays are well suited to study the performance of numerical methods as they exhibit hybrid behaviour between capillary flows and full atomization. In the present work an intermediate gas Weber of a laboratory air-blast atomiser is investigated using a volume of fluid approach. The amount of numerical diffusion is controlled by a compressive factor in the volume of fluid transport equation. The effect of the compressive term on spray atomization and droplet size distribution is explored. The results suggest that the optimal amount of diffusion depends on the local Weber number.

Scalar Mixing in Droplet Arrays in Stagnant and Convective Environments

Droplet evaporation is usually modelled as a subgrid process and induces local inhomogeneities in the mixture fraction probability density function (PDF) and its scalar dissipation. These inhomogeneities are usually neglected, however, they can be significant and determine the combustion regime. In the present work, Direct Numerical Simulations (DNS) of fully resolved evaporating methanol droplets are analysed, assessing fuel vapour mixing in laminar and turbulent flows. The results show that scalar probability distributions and scalar dissipation vary greatly depending on the position relative to the droplet position, on droplet loading and on flow conditions. The β-PDF seems to capture the global behaviour for laminar flows around droplet arrays with low droplet density, however, mixing characteristics for higher droplet densities in stagnant and turbulent flows cannot be approximated by a β-PDF, and modelling approaches based on cell mean values will lead to erroneous results.