A Model Comparison of Different Flamelet Generated Manifolds for Analysis of Strained Hydrogen Flames

Abstract

To reduce humanity’s dependency on fossil fuels, hydrogen is increasingly investigated as a promising energy carrier. When converting the chemical energy of hydrogen to the desired form, hydrogen reacts with oxygen to form water. This makes hydrogen very promising for achieving net-zero carbon emissions. For the aviation sector, hydrogen combustion has been suggested as a possible solution.
As with any technology, challenges remain. Whilst combustion modelling using Computational Fluid Dynamics (CFD) is not a solved problem to begin with, hydrogen combustion is made more complex by differential diffusion. This occurs when different species do not diffuse at the same rate. Hydrogen tends to diffuse faster than other species, causing local changes in mixture fraction, in addition to super-adiabatic temperatures and super-equilibrium product concentrations. This effect is stronger in strained or curved flames. Flame strain and curvature also influences the local reaction rate. These phenomena occur on a very small length and time scale. To simulate this directly, very fine meshes and very precise transport equations for each species are required. This can be prohibitively expensive for large scale designs or for design iteration.
In cases where simulating this behaviour directly is not possible, an alternative model is required. In this paper, five variants of such a model are assessed. These models are based on the assumption that the flame can be approximated as an ensemble of 1-dimensional flamelets. These flamelets can be analysed before the CFD simulations are performed. The results are then parametrized by a number of control variables, using a presumed filtered probability density function which aims to include sub-grid scale effects. By changing the flamelet conditions and control variable definition, different manifolds can be generated. In this paper, a number of these Flamelet-Generated Manifolds (FGMs) are compared to a higher fidelity model (using an Eulerian Stochastic Fields (ESF) approach). These FGMs use the mixture fraction, the progress variable and their sub-grid variances as control variables. Five different FGMs are tested, characterized by the progress variable definition (water vs hydrogen mass fraction) and flamelet strain rate (0 (unstrained) vs 3000 vs 6000 vs 13000 s^-1.
The performance of these models is assessed by means of a Large Eddy Simulation (LES) of a combustor with a bluff-body, using the open source CFD software OpenFOAM. The bluff-body causes a recirculation zone in its wake. Additionally, it causes a strain on the flame front, where differential diffusion is expected to cause super-adiabatic temperatures and super-equilibrium mixture fractions.
The results show that the FGMs give a good prediction of the conditionally averaged reaction rates. They are also capable of qualitatively predicting the increase in mixture fraction, super-adiabatic temperature and super-equilibrium product mass fractions. They can therefore be used in a strained combustor setting with lean, premixed hydrogen. However, there are challenges regarding the prediction of temperature, especially for FGMs using a hydrogen based progress variable. This should be investigated in the future. Furthermore, the FGMs predict the reaction rate well despite over-predicting the local effects of strain and differential diffusion.