The emission requirements for jet engines are becoming more stringent and the combustion process determines pollutant emissions. Therefore, we model the distribution of fuel drops generated by a fuel injector in a jet engine, which can be assumed to be a five‐dimensional problem in terms of drop size, x‐position, y‐position, x‐velocity and y‐velocity. The data are generated by numerical simulations of the fuel atomization process for several jet engine operating conditions. In combustion simulations, the variables are usually assumed to be independent at the start of the simulation, which is clearly not so as our data show. The dependence between some of the variables is non‐monotone and asymmetric, which makes the modelling task difficult. Our aim is to provide a realistic parametric model for the dependence structure. For this, we employ vine copulas which provide a flexible way to construct a multivariate distribution function. However, we need to use non‐standard bivariate copulas as building blocks. Using this copula representation enables us to create realistic samples of fuel spray droplets which improve the prediction of the combustion process and the pollutant emissions. Moreover, this approach is significantly faster than solving the set of differential equations describing fuel disintegration.

中文翻译：

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使用藤蔓copulas模拟喷气发动机中的喷油器喷雾特性

喷气发动机的排放要求越来越严格，燃烧过程决定了污染物的排放。因此，我们对喷气发动机中喷油器产生的燃油滴的分布进行建模，就其尺寸，x位置，y位置，x速度和y而言，可以认为是一个五维问题。-速度。数据是通过几种喷气发动机工况的燃料雾化过程的数值模拟生成的。在燃烧模拟中，通常假定变量在模拟开始时是独立的，这显然与我们的数据所示的情况不同。一些变量之间的依赖关系是非单调的和不对称的，这使得建模任务很困难。我们的目的是为依赖结构提供一个现实的参数模型。为此，我们采用藤蔓菌柄，它们提供了构建多元分布函数的灵活方法。但是，我们需要使用非标准的双变量copulas作为构建基块。使用这种copula表示，我们可以创建逼真的燃料喷雾液滴样本，从而改善对燃烧过程和污染物排放的预测。