Passive makes perfect - reconstructing mean velocity and passive scalar fields from limited observations

Flows with passive scalars are common in many engineering and industrial applications. One current challenge, which involves pollutants as the passive scalar, is modelling and predicting urban air quality. Simulating these flows requires vast computational resources and modelling assumptions whereas experimental measurements are sparse and incomplete. To improve predictions of mean (time-averaged) velocity and passive scalar concentration, a data assimilation (DA) framework is developed which minimizes the discrepancy between a RANS simulation and partial observations of mean velocity and passive scalar fields. In doing so, the DA infers unknown forcing terms in the momentum and advection diffusion equations corresponding to Reynolds stress gradients and scalar fluxes, respectively. The algorithm is demonstrated on the laminar flow past a heated cylinder, i.e. temperature is the passive scalar. DA successfully reconstructs the mean velocity and temperature fields even with limited input data. It is also shown that with just temperature data as the input, DA improves predictions of the mean velocity fields.