Towards Experimental Inflow Conditions for Direct Numerical Simulations from Data Assimilation

• Applicant: Professor Dr. Jörn Lothar Sesterhenn
• Subject Area: Fluid Mechanics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 542503842

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.

• DFG Programme: Research Grants