Acceleration techniques for efficient and accurate particle PDF simulations of large-scale turbulent combustion

Abstract

In this time of severe climate change, there is an increasing need for sophisticated simulation tools to facilitate more efficient fossil-fuel based combustion devices with low pollutant and greenhouse gas emissions. In particular, to simulate a turbulent reacting flow, a proper prediction of the interactions between turbulence and chemistry is extremely important. Probability density function (PDF) methods have been shown to capture this strong turbulence chemistry interaction accurately. However, one of the biggest disadvantages of PDF methods is its significantly higher computational cost of solving the chemistry in its exact form compared to other simpler methods, such as flamelet-based models. This necessitates the development of strategies to reduce the cost of PDF type approaches without losing the level of accuracy. Two different categories of techniques to accelerate the process are explored in this thesis. The use of analytical Jacobian is observed to be a promising step to accelerate the chemistry source term integration compared to using numerical Jacobian. Here, a generalized projection-based analytical Jacobian framework is provided that considers all species mass fractions and temperature in the state vector while satisfying the mass conservation constraint consistently. The use of a projection matrix with the analytical Jacobian ensures that the mass fraction vector never goes off its realizable simplex, defined by the constraint, at any time step. This approach provides an accurate solution with different types of solvers, and also predicts the spectral properties of the corresponding dynamical system within round-off errors. Next, the algorithm for generating the analytical Jacobian is combined with a dimension reduction technique, the quasi-steady species (QSS) assumption. An automated algorithm package is developed, which provides the analytical expression of the Jacobian with QSS species, properly integrating all the additional derivatives corresponding to the QSS-derived algebraic expressions, and can be readily implemented in any high-fidelity turbulent simulation. Combining these two techniques (analytical Jacobian and QSS) has shown a significant reduction in the computational cost of a partially stirred reactor (PaSR) simulation. Adaptive chemistry approaches, which tailor the fidelity and size of the kinetic models used for reaction integration to the local flame conditions, have reduced the cost of PDF-type methods due to their ability to accurately describe the relevant combustion kinetics with significantly fewer variables and equations. In this work, two new adaptive chemistry algorithms are developed. The first addresses a key challenge of efficiently capturing the secondary chemistry pathways, such as pollutant formation, in an existing pre-partitioned adaptive chemistry (PPAC) approach. This new algorithm, PPAC-Additive, decouples the secondary chemistry from primary chemistry pathways (fuel oxidation), thus developing smaller reduced kinetic models compared to PPAC. In PPAC-Additive, the reduced models are generated first for main oxidation targets only, and then the important secondary pathways, demonstrated with NOx prediction, are dealt with afterwards in a separate stage. Both PPAC and PPAC-Additive generate the reduced models based on a sample set of compositions in an offline stage, which are then used adaptively during the simulation of interest. In contrast to the current adaptive frameworks, which require extensive pre-processing analysis and assumption, the second algorithm, dynamically partitioned adaptive chemistry (DPAC), is a completely stand-alone adaptive approach with limited need for user input. DPAC generates the reduced models during the adaptive simulation based on the encountered compositions at runtime. DPAC updates the reduced kinetic models continuously as the flame and its compositions evolve in time, making it more flexible and efficient than other existing adaptive chemistry approaches. Both PPAC-Additive and DPAC have shown significant gain in CPU cost and memory requirement compared to a detailed simulation and PPAC in the context of large-scale LES-PDF simulations.