Direct numerical simulation of the droplet evaporation and combustion using a discontinuous Galerkin scheme
Final Report Abstract
The work carried out in the present work period is part of the development of a numerical solver that allows the simulation of the evaporation and combustion of a fuel droplet using the DGM. During the present period, the focus remained on the realization of an adequate implementation that allows the simulation of reactive flows in a single phase in an efficient and robust way. The discretized set of equations of continuity, momentum, energy, and chemical species are solved in a fully coupled manner, using specialized linear solvers and adequate preconditioning. The temperature and concentration dependence of the density, heat capacity, and transport parameters is considered. An one-step chemical model with variable kinetic parameters is used for the representation of the chemical reaction. A mixed-order formulation was used for the spatial discretization, meaning that velocity, temperature, and mass fraction fields are approximated with polynomials of degree k, and the pressure with k − 1. The implementation of a globalized Newton algorithm, a homotopy strategy, together with other specialized convergence-supporting strategies permitted the simulation of the tightly coupled nonlinear equations. An additional strategy was used in the case of steady reacting flows, which allowed the simulation of several classical steady-state diffusion flame configurations. This strategy makes use of a simplified set of equations obtained under the assumption of an infinitely fast chemical reaction. The implemented solver was thoroughly tested and validated for the stationary and transient regimes, using test cases at increasing levels of complexity. Starting with incompressible flow systems, then variable density flows, and finally variable density flows with chemical reactions. The test cases allowed us to assess the accuracy of the method and validate the solver against various benchmark solutions. Additionally, h-convergence studies were performed in various flow settings, which allowed us to confirm that the expected convergence rates of k + 1 for velocities, temperature and mass fractions, and k for the pressure are obtained. Stability problems were observed in transient simulations of low Mach flows in which density exhibits large variations. The extension of the solver for multiphase flows remains to be realized. Preliminary work in this regard has been done, showing the potential of the present fully coupled approach.
Publications
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A fully coupled high‐order discontinuous Galerkin method for diffusion flames in a low‐Mach number framework. International Journal for Numerical Methods in Fluids, 94(4), 316-345.
Gutiérrez‐Jorquera, Juan & Kummer, Florian
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A Fully Coupled Discontinuous Galerkin Method for Diffusion Flames Embedded in a Low-Mach Solver Framework. PhD thesis, Technische Universität Darmstadt, Darmstadt
Gutiérrez Jorquera, J.
