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Micro-combustion modelling with RBF-FD: A high-order meshfree method for reactive flows in complex geometries
Applied Mathematical Modelling ( IF 5 ) Pub Date : 2021-02-03 , DOI: 10.1016/j.apm.2021.01.032
Víctor Bayona , Mario Sánchez-Sanz , Eduardo Fernández-Tarrazo , Manuel Kindelan

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.



中文翻译:

使用RBF-FD进行微燃烧建模:复杂几何中反应流的高阶无网格方法

诸如无人机或微型机器人之类的新型微型设备已经增加了对新一代小型燃烧动力系统的需求,其超出了电池或燃料电池的能量密度限制。停留时间短和热量散失大的特性降低了基于燃烧的设备的效率,这是一项关键的因素,需要做出认真的建模工作才能理解妨碍其高效运行的竞争性理化现象。考虑到这一目标,本文致力于开发一种高阶无网格方法,该模型使用径向基函数生成的基于有限次方样条(PHS)的多元多项式增广的有限差分(RBF-FD)来建模复杂几何形状内的燃烧(PHS + poly)。在我们的模型中 微型旋转式发动机的燃烧室是通过一个非稳态反应扩散方程组与稳定流动通过一个细长的二维狭窄通道的系统进行模拟的。转换效率的特征是识别出随点火点而变化的不同燃烧方式。我们证明,基于PHS + poly的RBF-FD能够在分散的节点分布上实现高阶代数收敛,从而能够在流域的关键区域进行节点优化。此功能使其特别适用于将不规则几何形状的问题与诸如反应性前沿或冲击波之类的前沿解决方案集成在一起。进行了几次数值测试,以证明我们的方法的准确性和有效性。

更新日期:2021-02-16
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