Based on the forecast in the International Energy Outlook (2011), most energy will still be generated by burning of fossil fuel for the foreseeable future. Increasing efficiency and eliminating pollution are the compelling challenges in the energy industry in the 21st century. In order to achieve the “sustainable development” defined in the United Nations Framework Convention on Climate Change (UNFCC, 1992), study on combustion, especially turbulent combustion modelling, is of great importance.
For the development of the modern combustion system, computer simulations need to be incorporated into the design process to speed up the turnover time and reduce the cost. A high quality combustion simulation requires a good turbulent combustion model and usually comes with a significant computational cost. For most practical turbulent combustion systems the success of a simulation depends on finding a model which provides a high quality result at an affordable cost. The aim of the study in this thesis is to provide such a turbulent combustion model.
In recent years, the Large Eddy Simulation (LES) approach which resolves the large scales of turbulence motions and models the small scales has been widely adopted in turbulence studies. As combustion reactions subject to small-scale variations, the LES technique alone does not solve the turbulent combustion problem, and a turbulent combustion model is still required (Peters, 2000). Among all the available combustion models, the more general transport Probability Destiny Function (PDF) model (Pope, 1985), or transport Filtered Density Function (FDF) (Pope, 1991a) model in the LES context, provides an exact closure for the reaction source term in combustion modelling, although an additional model is still needed to account for the conditional mixing. However, the high dimensionality of the transport PDF/FDF equations makes it a very expensive model.
The Multiple Mapping Conditioning (MMC) model proposed by Klimenko and Pope (2003), which inherits the nature of the PDF model (Pope, 1985), and reduces the particle resolution by the employment of the conditional moment closure hypothesis (Klimenko and Bilger, 1999), appears to be a promising model for combustion simulation. With the advanced MMC mixing model, the hybrid sparse-Lagrangian simulation can be performed using fewer Pope particles (Klimenko and Cleary, 2010) than LES grid cells. The improvement in computational efficiency has been shown to reach up to two to three orders of magnitude (Cleary et al., 2009). As sparse-Lagrangian simulation is a relatively new modelling approach, there are still some issues which need to be addressed. All knowledge about the model is presented in this thesis.
When the sparse model was first introduced by Cleary et al. (2009), density was not coupled. This has limited the application of the sparse model and numerical consistency of the hybrid model was not ensured. To solve this problem, a dynamic conditioning method (Ge et al., 2009, 2011b) was adapted from the equivalent enthalpy method suggested by Muradoglu et al. (2001). At the same time a new time scale model controlling the conditional fluctuations has been raised. Adopting these models, good matches between simulation results and experiments in the simulation of strong local extinction and re-ignition in Sandia flame E has been demonstrated.
The MMC mixing model enforces mixing in an extended space consisting of physical location and reference variables that link to the composition. In the previous sparse-Lagrangian simulations, this localization was controlled by an arbitrary ratio between physical and reference mixture fraction scales. In this thesis, a fractal/gradient model is introduced to link the two scales in the current MMC mixing model. This model enforces consistent control of localization structure over a range of particle number densities (Ge et al., 2012).
In the investigation of the universality of the sparse model, sparse-Lagrangian simulation has been applied to the Sandia flame series D-F. With only one set of parameters, simulation results have demonstrated that sparse-Lagrangian simulation is robust and can be applied to certain combustion conditions without tuning. In the same study, the issue regarding separating the numerical and model parameters has been investigated as well. Unlike other mixing models, the particle number density in the MMC mixing model is both a numerical and model parameter. The study indicates that extra caution is needed when implementing and applying sparse-Lagrangian simulation.
To fully explore the potential of the sparse-Lagrangian simulation, an open platform based on OpenFOAM (OpenCFD Ltd, 1999) is developed. A hybrid Eulerian LES/ stochastic Lagrangian scheme has been implemented onto the OpenFOAM C++ toolbox. By fully utilizing advanced features of the object oriented programming and the existing OpenFOAM code, a new Pope particle class and PDF turbulent mixing/combustion solver has been developed. With the new implementation and a specifically designed algorithm, a stringent one-step chemistry problem for PDF mixing models is studied to demonstrate the numerical convergence of the sparse method. It is hoped that with the well established OpenFOAM component, the new code will allow the sparse-Lagrangian simulation to be applied to a wider range of complex practical problems.