RATE-CONTROLLED CONSTRAINED EQUILIBRIUM: A BASIS FOR EFFECTIVE COUPLING OF COMPREHENSIVE CHEMICAL KINETICS AND CFD

燃烧过程的模拟仍然是一个突出的技术问题，具有广泛的影响，科学和实践。到目前为止，我们能源的最大比例是通过燃烧设备产生的，如汽车的内燃机，飞机的涡轮机或发电的工业燃烧器。这些过程还导致产生各种各样的污染物，如NOx和烟尘，以及产生温室气体。人们普遍承认，改进这些工艺有很大的潜力，可带来巨大的环境效益。燃烧建模需要流体动力学方程的耦合，通过计算流体动力学（CFD）代码数值求解，具有全面的化学动力学模型。实际的燃烧装置总是紊流的，这就需要另一个要素，即燃烧-化学相互作用模型。耦合所有这些元素导致了一个艰巨的计算问题，瓶颈的主要原因是计算的化学动力学部分。综合化学动力学包括非常大量的物种和反应：即使是最简单的燃料，如甲烷，也需要50多个物种，而对于商业燃料，可以很容易地存在数百个物种和反应。每个物种都向问题引入了额外的微分方程，并且此类系统通常表现出的过度刚度进一步阻碍了积分。然而，如果要预测污染物的形成，就必须纳入全面的机制。燃烧的数学模型可以大大简化，利用时间尺度分离的优势，假设快速反应，通常与中间物种，是在一个局部平衡状态。本研究将探索一种基于时间尺度分离的低维模型：速率控制约束平衡（RCCE）。在这种方法中，动力学控制的物种被允许根据包括原始详细机制的化学动力学的相关微分方程来演化，而平衡物种通过最小化混合物的自由能来确定，受到附加约束（除了质量守恒之外，能量和元素），动力学控制的物质必须保持由其控制方程的解给出的浓度。作者以前的工作提供的证据表明，RCCE有可能发展成为一种方法，在理论上严格和实际可行的大型化学机制到CFD代码的实施。在建立了概念证明之后，现在需要进一步开展工作，使RCCE进入准备应用于实际问题的阶段。此外，关于RCCE的基本原理的几个重要问题仍然没有答案，例如它与其他机制简化方法的关系，例如计算奇异摄动（CSP）。这两种方法是互补的，它们的结合可能会证明是一个非常强大的工具。

Modelling of combustion processes remains an outstanding technical problem with wide implications, both scientific and practical. By far the largest percentage of our energy is produced via combustion equipment such as internal combustion engines for cars, turbines for aircraft or industrial burners for power generation. These processes also account for the generation of a wide variety of pollutants, such as NOx and soot, as well as for the generation of greenhouse gases. It is widely acknowledged that there is large potential for improvement of those processes, resulting in great environmental benefits. Combustion modelling requires the coupling of fluid dynamics equations, solved numerically through a Computational Fluid Dynamics (CFD) code, with a comprehensive chemical kinetics model. Practical combustion devices are invariably turbulent, which necessitates a further element, the turbulence-chemistry interaction model. Coupling all of these elements results in a formidable computational problem, and the main cause of the bottleneck is the chemical kinetics part of the calculation. Comprehensive chemical kinetics include very large numbers of species and reactions: even for the simplest fuels, such as methane, more than 50 species are necessary, while for commercial fuels hundreds of species and reactions can easily be present. Each species introduces an additional differential equation to the problem, and integration is further hampered by the excessive stiffness that is often exhibited by such systems. Yet the incorporation of comprehensive mechanisms is essential if the formation of pollutants is to be predicted. The mathematical modelling of combustion can be significantly simplified by taking advantage of the time scale separation to assume that fast reactions, typically associated with intermediate species, are in a state of local equilibrium. The proposed research will explore a promising concept for deriving the low-dimensional models on the basis of time-scale separation: Rate-Controlled Constrained Equilibrium (RCCE). In this approach, the kinetically controlled species are allowed to evolve according to the relevant differential equations including the chemical kinetics of the original detailed mechanism, whilst the equilibrated species are determined by minimising the free energy of the mixture, subject to the additional constraints (apart from conservation of mass, energy and elements) that the kinetically controlled species must retain the concentrations given by the solution of their governing equations. Previous work by the authors has provided evidence that RCCE has the potential to develop into a method that is both theoretically rigorous and practically feasible for the implementation of large chemical mechanisms into CFD codes. Having established proof of concept, further work is now required to bring RCCE to the stage where it is ready for application in practical problems. Furthermore, several important questions about the fundamentals of RCCE remain unanswered, such as its relation to other methods of mechanism reduction such as Computational Singular Perturbation (CSP). The two methods are complementary and it is possible that a combination of them will prove a very powerful tool.