To this date, simulating the dynamics of a fluid remain extremely expensive for most practical design prob- lems. The large range of length and time scales to be resolved makes it especially computationally heavy. In engineering applications, the standard is still the RANS approach for CFD modelling. Most commonly the so- called two-equation models are used. The use of CFD in the aerospace design process is still severely limited by the inability to accurately and reliably predict turbulent flows with significant regions of separation. More accurate modelling approaches including LES are often not practical to use in engineering applications.
In the recent work of Deltares, such problems also arise. Research has been performed on water flow be- hind an underflow gate. The flow phenomenon that occurs closely resembles that of a wall-bounded jet. The reason such research has been performed is to better predict the turbulent behaviour of the jet downstream to predict possible damage to sediment. Seven weirs on the Meuse are planned to be renovated or replaced. Currently, bed protection is designed using physical scale models. Ultimately numerical models are to be the new standard for designing bed protection behind an underflow weir.
In their work experiments have been performed to acquire PIV data of the velocity field. This has been compared to their results of multiple CFD simulations which have been performed with different levels of fidelity. Several gate openings, changing the effective Reynolds number, have been used to compare the experimental results with the simulations. They concluded that although the velocity field solution of the simulations is good enough for engineering practices, all simulations show a mismatch in the area of the shear layer between the jet and the main flow.
In recent years more and more research has been done in the applications of machine learning. The capabilities of ML have increased rapidly and are now also used in closure modelling. Alongside this are the continuously improving experimental capabilities which allow for much higher resolution information. The combination can be used for data-driven techniques to improve upon current RANS models.
In recent work, the paradigm of field inversion has been proposed. Here instead of calibrating the mod- elling coefficients, a corrective field is used to effectively address the modelling deficiency. The correction field has been applied to the production term of the specific turbulent dissipation rate transport equation. To infer the values of the highest probability for the corrective field inverse methods are proposed. The method proposed uses Bayesian inversion, which includes an optimisation process. As the problem consists of a large number of variables normal optimisation processes are too expensive. Therefore, the adjoint method is proposed to compute gradients efficiently.
In this work, the goal is to extend upon the recent work on field inversion. The paradigm will be applied to the underflow weir case of Deltares. The experimental data will be used to infer a spatially varying corrective field used to correct the simulations to improve their predictive capabilities. As the density of data points is often far smaller than the density of simulation cells, and often data sets do not cover the whole simulation domain the paradigm is extended to accept imperfect data.
It was found that with these extensions a correction field could be found that can lower the cost function by a factor of two. The prediction of flow features behind the weir were predicted more accurately using the newly found corrected model.