Modeling Phase Transition during Primary Breakup of Turbulent Liquid Jets and Sheets

我们考虑了一个大表面结构（Large Surface Structure， LSS）模型，在三维空间上对湍流液体射流或薄片初次破裂过程中的相变进行了数值模拟。为了开发和验证LSS模型，将进行直接数值模拟（DNS）研究初级破裂期间的相变效应。为此，水平集/涡流表（LSVS）方法将被扩展到包括相位变化的影响。本文将分析两种具有工程应用代表性且与LSS模型的大涡模拟（LES）方法相一致的情景：a)相变速度在亚网格尺度上是一个常数；b)亚网格尺度上的相变速度是局部亚网格湍流输送和剪切的函数。第一个场景代表了典型的LES建模方法，其中子网格相变速度仅是已分解尺度量的函数。因此，它的局部子网格PDF是一个delta函数。在第二种情况下，考虑了由于亚网格湍流输送和剪切波动引起的局部亚网格相变速度变化。如果证明这些结果与第一种情况产生显著不同的DNS结果，则需要使用依赖于传输和剪切的PDF或力矩的相变速度的非δ函数子网格PDF来关闭LSS模型。为了在DNS研究中获得足够的精度，将使用不连续伽辽金方法或采用高阶WENO格式的精细化水平集网格方法对偏微分方程进行数值求解。将采用两种互补的策略来解决问题中存在的广泛的长度尺度。在接近相位界面的区域进行网格细化，确保处理比柯尔莫哥洛夫尺度小一个数量级的结构。这样或更小尺寸的结构被转移到拉格朗日喷雾模型中。虽然局部窄带方法将确保计算成本保持可行，但整个算法的并行化将允许访问现代并行计算机系统的高计算能力，以便执行广泛的DNS计算。最后的LSS方法的实际用途将意味着一种统计方法。湍流建模需要开发适当的基于界面的滤波器，并对未封闭的子网格项进行建模。在上述两种相变情况下，可以直接应用为预混湍流燃烧开发的建模策略来推导这些闭合模型。生成的LSVS DNS数据将受到相同的过滤器的约束，以便验证闭包假设。此外，LSVS方法和最终的LSS模型将使用不同数值方法获得的数值数据，特别是法国合作伙伴的VOF计算，以及研究组获得的实验数据和文献报道的数据进行验证。

We consider a Large Surface Structure (LSS) model for the numerical simulation of phase transition during primary breakup of turbulent liquid jets or sheets in three dimensions. To develop and verify the LSS model, Direct Numerical Simulations (DNS) studies of the phase transition effects during primary breakup will be performed. To this end the Level Set/Vortex Sheet (LSVS) method will be extended to include the effects of phase change. Two scenarios representative of engineering applications and consistent with the Large Eddy Simulation (LES) approach of the LSS model will be analyzed: a) the phase change velocity is a constant on the subgrid scale and b) the phase change velocity on the subgrid scale is a function of local subgrid turbulent transport and shear.The first scenario represents a typical LES modeling approach, in that the subgrid phase change velocity is a function of resolved scale quantities only. Its local subgrid PDF is thus a delta function. In the second scenario, local subgrid variations of the phase change velocity due to fluctuations in the subgrid turbulent transport and shear are taken into account. Should these prove to yield significant different DNS results than the first scenario, the use of a non-delta function subgrid PDF of the phase change velocity, dependent on the PDFs, or moments, of transport and shear are required for the LSS model closure.In order to achieve sufficient accuracy for the DNS studies, the partial differential equations will be solved numerically using either a Discontinuous Galerkin method or a Refined Level Set Grid approach employing high-order WENO schemes. Two complimentary strategies will be employed to resolve the wide range of length scales present in the problem. Mesh refinement in the region close to the phase interface ensures the handling of structures of size about one order of magnitude smaller than the Kolmogorov scale. Structures of this or smaller size are then transferred into a Lagrangian spray model. While a localized narrow band approach will ensure that the computational cost remains feasible, parallelization of the whole algorithm will allow access to the high computational power of modern parallel computer systems in order to perform extensive DNS calculations.Practical usefulness of the final LSS method will imply a statistical approach. Turbulence modeling requires the development of appropriate interface based filters and modeling of the unclosed subgrid terms. In the two phase transition cases described above, the modeling strategies developed for premixed turbulent combustion can be applied directly to derive these closure models. The generated LSVS DNS data will be subjected to the same filters in order to validate the closure assumptions. Furthermore, the LSVS method and the final LSS model will be validated using both numerical data obtained by different numerical approaches, specifically the VOF calculations of the French partner, as well as experimental data obtained in the research group and as reported in the literature.