Sparse-Lagrangian Particle Methods for Spray Combustion

应发展随机粒子法来模拟湍流喷雾燃烧。如果一个相可以理解为连续体，而另一个相可以用离散的液滴来表示，那么随机粒子方法适合于两相流的建模。这些条件在初级喷雾破裂后的大多数燃烧室中都成立，拉格朗日方法可以用于液滴守恒方程的建模。此外，我们使用基于粒子的蒙特卡罗方法逼近气相化学成分的联合概率密度函数（PDF）。每个蒙特卡罗粒子表示流体单元的瞬时局部解，避免了经典矩法的闭合问题，并以闭合形式给出了化学源项。因此，粒子方法非常适合于模拟反应性两相流。借助大涡模拟，在欧拉框架下求解了速度场的守恒方程。提出的工作的新颖之处在于使用稀疏粒子方法计算气相组成PDF。传统的粒子方法需要每个LES细胞20到50个粒子，它们的数值解可能非常昂贵。当使用稀疏方法时，粒子数可以降低到每10个LES细胞小于1个粒子，并且对于具有复杂化学性质的情况，模拟时间可以减少多达2个数量级。然而，跨相界面的质量和热传递建模，即分散的液滴和PDF（气相）颗粒之间的传递是一个重大挑战，需要新的建模方法。闭包不容易从传统的（密集的）粒子方法中适应。在第一个资助期内，使用液滴加载双剪切层配置的直接数值模拟（DNS）研究了各种替代闭包。只有DNS允许对粒子配对（即选择从液滴中接收质量的气相粒子）和两相之间的混合速度（即混合时间尺度）进行明确（和孤立）的分析，并且这种对某些物理过程的隔离有助于开发新的闭包。然而，实验室喷雾火焰的MMC-LES仍然具有与实验数据明显偏差的特点，因为真实的喷雾火焰不太可能在非预混燃烧状态下完全燃烧，液滴可能不会到处分散。因此，在第二个资助期内，这些模型将扩展至涵盖不同的工艺和火焰条件，例如部分预混火焰和密集喷雾火焰，然后将借助现有的实验数据对模型进行验证。

Stochastic particle methods shall be developed for the modelling of turbulent spray combustion. Stochastic particle methods are suited for the modelling of two-phase flows if one phase can be understood as a continuum and the other phase can be represented by discrete droplets. These conditions hold in most combustion chambers after primary spray breakup, and a Lagrangian method can be used for the modelling of the droplets’ conservation equations. In addition, we use a particle-based Monte Carlo method for the approximation of the joint probability density function (PDF) of the chemical composition of the gas phase. Every Monte Carlo (PDF) particle represents an instantaneous, local solution of a fluid element, the closure problems of classical moment methods can be avoided, and the chemical source term is given in closed form. Particle methods are therefore ideally suited for the modelling of reactive two-phase flows. The conservation equations for the velocity field are solved in an Eulerian framework with the aid of large-eddy simulations (LES). The novelty of the proposed work is the use of a sparse particle method for the computation of the gas phase composition PDF. Conventional particle methods require between 20 and 50 particles per LES cell and their numerical solution can be extremely costly. The particle number can be lowered to less than 1 particle per 10 LES cells when using sparse methods, and simulation times can be reduced by up to 2 orders of magnitude for cases with complex chemistry. The modelling of mass and heat transfer across the phase interface, i.e. the transfer between the disperse liquid droplets and the PDF (gas phase) particles is, however, a significant challenge and requires novel modelling approaches. Closures cannot easily be adapted from conventional (dense) particle methods. A variety of alternative closures has been investigated in the first funding period using direct numerical simulations (DNS) of a droplet laden double shear layer configuration. Only DNS allows for an explicit (and isolated) analysis of particle pairing (i.e. selection of the gas phase particle to receive the mass from the droplet) and the speed of the mixing between (i.e. the mixing time scale) between the two phases, and this isolation of certain physical processes facilitates the development of new closures. MMC-LES of laboratory spray flames continue, however, to feature distinct deviations from experimental data since real spray flames are unlikely to burn entirely within the non-premixed combustion regimes and droplets may not be dispersed everywhere. In the second funding period, the models shall therefore be extended to cover a variety of process and flame conditions such as partially premixed flames and dense spray flames, and they will then be validated with the aid of available experimental data.