Towards Experimental Inflow Conditions for Direct Numerical Simulations from Data Assimilation

我们建议开发一种方法来提取时间分辨，全三维进口条件在所有流量的可压缩湍流实验。目的是数据驱动的湍流直接数值模拟。关键部分是数据同化，它适应直接数值模拟的边界和初始条件，直到它最小化模拟生成的合成图像与高速相机生成的纹影图像之间的差异。这种差异的最小化，即所谓的“损失函数”是该方法的核心，并通过计算非平稳数值进口条件下的梯度的伴随公式来实现。然后使用梯度来找到损失函数的一个平稳点。紊流在很大程度上取决于进口条件。在紊流的直接数值模拟中，它们是未知的，只能近似或指定为平均符合某些标准。有时，手头的问题不需要完全匹配的进口条件，但在其他情况下，所讨论的数量在很大程度上取决于它。我们想集中讨论后一种情况。该项目基于之前所有关键成分的工作：直接数值模拟、可压缩高速流的数据同化和以前DNS计算的现有数据集。这些工具是经过测试的，我们可以使用。我们成功地在其他合成测试案例中使用了这种方法，并且在以前的工作中也对声学问题进行了粒子图像速度和压力测量。然而，在这里，我们将不进行新的实验来获得上述纹影图像。我们更愿意发展理论框架，并将回答以下问题：(i)原则上可以从纹影图像中获得哪些数据，（ii）是否可以从标量场中获得矢量场，以及我们将（iii）验证湍流场数据上的三维数据同化。这些步骤将完成，(i)理论上应用Kovasznay的经典研究（他对热线做了这个，我们想对纹影法做这个），（ii）通过扩展我们对从温度测量中提取速度数据的模式可观测性的研究（我们将再次对纹影进行研究，并将分析从2D扩展到3D）和（iii）通过从先前模拟撞击射流的现有dns数据中综合提取双纹影图像，并对该数据进行数据同化以进行验证。

We propose to develop a method to extract time-resolved, fully three dimensional inlet conditions in all flow quantities from a compressible turbulent experiment. The aim is a data driven Direct Numerical Simulation of turbulent flow. The key component is a data assimilation, which adapts boundary and initial conditions of a Direct Numerical Simulation until it minimizes the difference between synthetic images, generated from the simulation, and Schlieren images from high speed cameras. The minimization of this difference, the so called "loss function" is the heart of the method and is achieved by an adjoint formulation for the calculation of the gradient with respect to the non-stationary numerical inlet conditions. The gradient is then used in finding a stationary point of the loss function. Turbulent flows crucially depend on the inlet conditions. In direct numerical simulations of a turbulent flow they are unknown and can only be approximated or specified to match certain criteria on average. Sometimes exactly matching inlet conditions are not needed for the problem at hand but in other cases, the quantity in question very much depends on it. We want to concentrate on the latter case. The project is based on previous work in all key ingredients: direct numerical simulation, as well as data assimilation for compressible high-speed flows and an existing dataset from previous DNS calculations. These tools are tested and available us. We successfully used this method in other synthetic test cases but also with Particle Image Velocimerty as well as pressure measurements for acoustic problems in previous work. Here, however, no new experiments to obtain the mentioned Schlieren images will we performed. We rather develop the theoretical framework and will answer among others the following questions: (i) What data can in principle be obtained from the Schlieren images, (ii) whether a vector field can be obtained from a scalar field and we will (iii) validate the 3D data assimilation on a turbulent field data. These steps will be done, (i) theoretically by applying a classical investigation by Kovasznay (he did this for a hot wire and we want to do it for the Schlieren method), (ii) by extending a study on the observability of modes we did for extracting velocity data from temperature measurements (we will do again both for Schlieren and to extend the analysis from 2D to 3D) and (iii) by synthetically extracting double Schlieren images from existing DNS-data of a previous simulation of an impinging jet and performing the data assimilation to this data for validation.