Investigation of numerical resolution requirements of the Eulerian Stochastic Fields and the Thickened Stochastic Field approach

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. An investigation into numerical resolution requirements is conducted through simulation of a series of one-dimensional stochastic fields simulations of freely-propagating turbulent premixed flames. The investigation involved various stochastic field simulations at different combustion regimes and numerical resolutions. It was concluded that the conventional approach of using a numerical grid spacing equal to the filter scale can yield substantial numerical error; specifically towards the flamelet regime. However, using a numerical 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 thesis in order to provide physically and numerically-accurate solutions of the stochastic fields equations with reduced compute time compared to a fully resolved simulations. The Thickened Stochastic Fields formulation bridges between the conventional stochastic fields and conventional Thickened-Flame approaches depending on the sub-filter combustion regime and numerical grid spacing utilised. One-dimensional stochastic fields simulations of freely-propagating turbulent premixed flames are used in order to obtain a 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

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 transported Probability Density Function modelling 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, implying that the usual practice of setting the LES filter length scale equal to grid spacing leads to severe under-resolution, to numerical thickening of the flame, and to substantial error in the turbulent flame speed. The under-resolution is worst for low Karlovitz number combustion, where the thickness of the Stochastic Fields flame structures is similar to 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 Bunsen flame LES results confirm that setting the LES filter length scale equal to the grid spacing gives substantial numerical error, and that this error affects the Stochastic Fields solution to a greater extent than it affects the flow field solution. The present results have important implications for application of the Stochastic Fields approach to simulation of high-pressure industrial premixed combustion systems where the grid spacing is necessarily much larger than the laminar flame thickness and suggests that some amount of artificial flame thickening might be needed in order to make such simulations numerically accurate

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 Eddys 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 Partially-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 Partially-Thickened Stochastic Fields formulation bridges between the conventional Stochastic Fields and conventional Thickened-Flame approaches depending on the numerical grid spacing utilised, and converges towards Direct Numerical Simulation in the limit of full-resolution. 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 Bunsen flame, demonstrating that the method leads to numerically-converged simulations that agree with results of conventional Stochastic Fields simulations using orders of magnitude more grid points. The present development therefore facilitates the accurate application of the Stochastic Fields approach to industrially-relevant combustion systems

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 Eddys 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 Partially-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 Partially-Thickened Stochastic Fields formulation bridges between the conventional Stochastic Fields and conventional Thickened-Flame approaches depending on the numerical grid spacing utilised, and converges towards Direct Numerical Simulation in the limit of full-resolution. 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 Bunsen flame, demonstrating that the method leads to numerically-converged simulations that agree with results of conventional Stochastic Fields simulations using orders of magnitude more grid points. The present development therefore facilitates the accurate application of the Stochastic Fields approach to industrially-relevant combustion systems

Data for "Resolution Requirements in Stochastic Field Simulation of Turbulent Premixed Flames"

Raw data used in production of the published article (also presented at Mediterranean Combustion Symposium, Naples, Italy): Picciani, M. A., Richardson, E. S., &amp; Navarro-martinez, S. (2018). Resolution requirements in stochastic field simulation of turbulent premixed flames. Flow Turbulence and Combustion, 1-16. </span

Data for &quot;A Thickened Stochastic Fields Approach For Turbulent Combustion Simulation&quot;

Raw data used for preparation of the published manuscript (also presented at Tenth Mediterranean Combustion Symposium, Napoli, Italy.): Picciani, M. A., Richardson, E. S., &amp; Navarro-martinez, S. (2018). A thickened stochastic fields approach for turbulent combustion simulation. Flow Turbulence and Combustion, 1-18.</span