Centre for Complexity Science and Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.
Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, United Kingdom.
Phys Rev E. 2019 Feb;99(2-1):023314. doi: 10.1103/PhysRevE.99.023314.
Smoldering is the slow, low-temperature, flameless burning of porous fuels and the most persistent type of combustion phenomena. It is a complex physical process that is not yet completely understood, but it is known that it is driven by heat transfer, mass transfer, and fuel chemistry. A specific case of high interest and complexity is fingering behavior. Fingering is an instability that occurs when a thin fuel layer burns against an oxygen current. These instabilities appear when conduction rather than convection is the dominant mode of heat transfer to the fuel ahead and the availability of oxygen is limited during the combustion of a thin fuel, such as paper. The pattern of the fingers can be characterized through the distance between them and their width, and can be classified into three different regimes: isolated fingers, tip-splitting fingers, or no fingers forming and a smooth continuous front. In this paper, a multilayer cellular automaton based on three governing principles (heat, oxygen, and fuel) is shown to reproduce all the regimes and the details of finger structures observed in previous experiments. It is shown how when oxygen is not limited, a smooth smoldering front is formed. If the oxygen speed decreases beyond a critical value, fingers appear first as tip-splitting fingers and later as isolated fingers, increasing the distance between them and decreasing their thickness. The oxygen consumed during oxidation influences these critical values with a positive correlation. This cellular automaton provides an alternative approach to simulate smoldering combustion in large systems over long times. That the model is able to reproduce the complex pattern formation seen in a fingering experiment validates the model. In the future, we could apply the model in various other geometries to make predictions on the outcome of smoldering combustion processes.
闷烧是多孔燃料的慢速、低温、无焰燃烧，是最持久的燃烧现象之一。它是一个复杂的物理过程，尚未完全理解，但已知它是由热传递、质量传递和燃料化学驱动的。一个特别有趣和复杂的情况是指状行为。指状是当薄燃料层在氧气流中燃烧时发生的不稳定性。当热传递到前方燃料的主导模式是传导而不是对流，并且在薄燃料（如纸张）燃烧时氧气供应有限时，就会出现这些不稳定性。可以通过它们之间的距离和宽度来描述指状物的模式，并可以将其分为三个不同的区域：孤立的指状物、尖端分裂的指状物或没有形成指状物并且有一个平滑连续的前沿。在本文中，展示了一种基于三个控制原理（热、氧和燃料）的多层元胞自动机，它可以再现以前实验中观察到的所有区域和指状物结构的细节。它展示了当氧气不受限制时，如何形成平滑的闷烧前沿。如果氧气速度降低到临界值以下，首先会出现尖端分裂的指状物，然后是孤立的指状物，增加它们之间的距离并减小它们的厚度。氧化过程中消耗的氧气与这些临界值呈正相关。这种元胞自动机提供了一种模拟大系统长时间闷烧燃烧的替代方法。该模型能够再现指状实验中看到的复杂图案形成，验证了该模型。将来，我们可以将该模型应用于各种其他几何形状，以对闷烧燃烧过程的结果进行预测。
