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首页> 外文期刊>Applied Mathematical Modelling >Micro-combustion modelling with RBF-FD: A high-order meshfree method for reactive flows in complex geometries
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Micro-combustion modelling with RBF-FD: A high-order meshfree method for reactive flows in complex geometries

机译：具有RBF-FD的微燃烧模拟：复杂几何形状中的反应流量的高阶网格综合方法

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摘要

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 physico-chemical 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.
机译：新的微型器件，如无人驾驶飞行器或微机器人，增加了新一代小型燃烧动力系统的需求，这些小型燃烧电力系统超出了电池或燃料电池的能量密度限制。特点短暂停留时间和强烈的热量损失降低了基于燃烧的设备的效率，这是需要急性建模努力的关键因素，了解妨碍妨碍其有效操作的竞争物理化学现象。通过这一目标，本文致力于使用径向基础函数产生基于多球多态花键（RBF-FD）的复杂几何模型模拟复杂几何模型燃烧的高阶Meshfree方法。 （pHS + poly）。在我们的模型中，微旋转发动机的燃烧室通过耦合的不稳定反应扩散方程的系统模拟，该系统耦合的稳定流动通过较大的细长狭窄的狭窄通道。转换效率的特征在于识别作为点火点的函数出现的不同燃烧状态。我们表明PHS + POT基RBF-FD能够在散射节点分布上实现高阶代数会聚，从而能够在流体域的关键区域中提供节点细化。该特征使其特别适合于将不规则几何形状的问题与正面的解决方案相结合，例如反应前线或冲击波。进行了几种数值测试以证明我们方法的准确性和有效性。

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