Advancements in Lattice Boltzmann Methods for Combustion Modeling: Addressing Compressibility and Species Transport Challenges

The lattice Boltzmann method is a relatively novel approach within CFD, originating from the lattice gas automata (LGA) models developed in the 1980s. Unlike traditional CFD methods, which directly solve the Navier-Stokes equations, LBM operates on a mesoscopic scale, using a discrete lattice grid to simulate the distribution of particle velocities. This allows LBM to capture the microscopic behavior of fluids, providing a bridge between kinetic theory and continuum fluid mechanics. Its inherent advantages include simplicity in algorithm implementation, locality of interactions, and the ability to efficiently handle complex boundary conditions and parallel computations.  The application of LBM to combustion modeling, however, has been challenging due to the method’s initial limitations in handling compressible flows and complex chemical kinetics. Combustion processes involve a wide range of temporal and spatial scales, making the accurate simulation of these phenomena particularly demanding. Traditional LBM was originally designed for incompressible, isothermal flows, which are inadequate for capturing the compressible and reactive nature of combustion.

New expert review study published in Progress in Energy and Combustion Science and conducted by Seyed Ali Hosseini, Pierre Boivin, Dominique Thévenin, and led by Professor Ilya Karlin from the Department of Mechanical and Process Engineering, ETH Zurich from Switzerland addressed these challenges by discussing various advancements in LBM that have been developed to extend its applicability to combustion simulations. The authors provide a comprehensive overview of the different strategies employed to overcome the limitations of traditional LBM in this context. One of the primary hurdles in applying LBM to combustion is the accurate modeling of compressibility. Traditional LBM is inherently incompressible due to its reliance on a low-Mach number assumption. However, combustion processes often involve high-Mach number flows where compressibility effects cannot be ignored. To address this, researchers have developed several modifications to the LBM framework, such as the introduction of pressure and temperature equations that are consistent with compressible fluid dynamics.

The authors highlights the development of the double distribution function (DDF) approach, where two distribution functions are used: one for the density and momentum and another for the energy. This method allows the LBM to simulate thermal flows by incorporating temperature-dependent variables and ensuring the conservation of both momentum and energy. The DDF approach is crucial for accurately modeling the energy balance in combustion processes, which is governed by the complex interplay between heat conduction, convection, and chemical reactions. Combustion involves the interaction of multiple chemical species, each with its own transport properties and reaction kinetics. Accurately modeling these interactions within the LBM framework requires extensions that can handle multi-species flows and complex reaction mechanisms. The authors discuss the development of kinetic models for species transport, such as the thermal mixture-averaged model, which accounts for the diffusion of individual species based on their molecular properties. Additionally, the study explores the integration of detailed chemical kinetics into the LBM framework. This includes the implementation of reaction source terms within the LBM evolution equation, allowing the method to capture the dynamics of chemical reactions alongside fluid flow. These advancements are crucial for simulating combustion processes where the rate of chemical reactions significantly influences the flow field and vice versa. Another critical challenge in extending LBM to combustion simulations is maintaining numerical stability and accuracy. Combustion processes are characterized by sharp gradients in temperature, pressure, and species concentration, which can lead to numerical instabilities in traditional LBM implementations. The study reviews various techniques that have been developed to enhance the stability of LBM for combustion, such as the introduction of advanced collision models and the use of higher-order lattice structures. The authors emphasize the importance of selecting appropriate lattice configurations and collision operators to ensure that the LBM can accurately capture the macroscopic behavior of the flow while maintaining numerical stability. The entropic LBM, which introduces an entropy constraint to the collision process, is highlighted as a particularly effective approach for enhancing stability in highly non-linear flow regimes, such as those encountered in combustion.

The advancements in LBM discussed in this study have led to its successful application in a wide range of combustion scenarios, from simple laminar flames to more complex turbulent combustion systems. The ability of LBM to handle complex geometries and boundary conditions makes it particularly well-suited for simulating combustion in real-world engineering applications, such as internal combustion engines, gas turbines, and industrial furnaces. The study also outlines several areas where further research is needed to fully realize the potential of LBM for combustion modeling. One of the key challenges identified is the need for more efficient and accurate methods for coupling LBM with other numerical techniques, such as direct numerical simulation and large eddy simulation, which are commonly used in combustion research. Additionally, the development of more sophisticated models for handling complex chemical kinetics and turbulence within the LBM framework is highlighted as a critical area for future work.

In conclusion, Professor Ilya Karlin and his team represents a significant step forward in the application of the lattice Boltzmann method to combustion modeling. By addressing the challenges of compressibility, species transport, and numerical stability, the authors have demonstrated the viability of LBM as a powerful tool for simulating combustion processes. The continued development of LBM in this area holds great promise for advancing our understanding of combustion and improving the design of combustion-based technologies. As the field of computational combustion continues to evolve, the lattice Boltzmann method is poised to play an increasingly important role in providing accurate and efficient simulations of complex reactive flows. The authors  provides a solid foundation for future research and development in this exciting and rapidly growing area of computational science.