Variational Data Assimilation for Stationary Euler-Euler Spray Simulation

Simulations of flow and transport in sprays are computationally expensive and rely on models to incorporate the interaction between the different phases. Here, we employ the Euler-Euler multi-fluid approach with a finite number of liquid phases to simulate the evolution of sprays downstream of primary and secondary break-up.

To compensate for model uncertainties and to reduce discrepancies between simulation results and experimental reference data we perform variational data assimilation in a two-step process. In particular, after identifying optimal boundary conditions, the eddy viscosity of the continuous phase and the drag coefficient fields are adapted by the discrete adjoint method. This method provides a cost function gradient at computational cost independent of the number of parameters. A gradient based optimizer is then applied to update the parameter values.

An OpenFOAM Euler-Euler multi-fluid solver is extended to solve the corresponding adjoint equations for the gradients of the parameter fields and the inlet boundary conditions. This solver is based on an analogous solver for the stationary RANS equations, presented earlier.

We present results for different spray configurations. An emphasis is put on the analysis of the reference data distribution and regularization.