Micro-combustion modelling with RBF-FD: A high-order meshfree method for reactive flows in complex geometries

Abstract

New micro-devices, such as unmanned aerial vehicles or micro-robots, have increased the demand of a new generation of small-scale combustion power system that go beyond the energy-density limitations of batteries or fuel cells. The characteristics short residence times and intense heat losses reduce the efficiency of combustion-based devices, a key factor that requires of an acute modelling effort to understand the competing physicochemical phenomena that hamper their efficient operation. With this objective in mind, this paper is devoted to the development of a high-order meshfree method to model combustion inside complex geometries using radial basis functions-generated finite differences (RBF-FD) based on polyharmonic splines (PHS) augmented with multivariate polynomials (PHS+poly). In our model, the combustion chamber of a micro-rotary engine is simulated by a system of unsteady reaction-diffusion equations coupled with a steady flow passing a bidimensional stenotic channel of great slenderness. The conversion efficiency is characterized by identifying the different combustion regimes that emerged as a function of the ignition point. We show that PHS+poly based RBF-FD is able to achieve high-order algebraic convergence on scattered node distributions, enabling for node refinement in key regions of the fluid domain. This feature makes it specially well adapted to integrate problems in irregular geometries with front-like solutions, such as reactive fronts or shock waves. Several numerical tests are carried out to demonstrate the accuracy and effectiveness of our approach.