Spatial reconstruction of steady scalar sources from remote measurements in turbulent flow

Identifying the source of passive scalar transported in a turbulent environment from remote measurements is an ill-posed problem due to the irreversibility of diffusive processes. A significant difficulty of the source reconstruction is due to different potential source locations generating very highly correlated signals at the sensor. A variational algorithm is formulated, which utilizes high-fidelity simulations to reconstruct the spatial distribution of the source. A cost functional is defined based on the difference between the true measurements and their prediction from the simulations with the estimated source. Using forward-adjoint looping, the gradient of the cost functional with respect to the source distribution is evaluated, and the estimate of the source is updated. The adjoint-variational approach naturally accommodates measurements from multiple sensors, with essentially the same computational cost. The algorithm is evaluated for scalar dispersion in turbulent channel flow. When a single sensor is placed directly downstream of the source, the reconstruction is accurate in the cross-stream directions and is elongated in the streamwise direction. The estimated source, however, can reproduce the measurements and the scalar plume downstream of the sensor location. In the channel centre and log layer, the scalar fields are dominated by dispersion, and therefore the reconstruction is better than in the near-wall regions, where the scalar fields are dominated by diffusion. When a sensor is placed near the wall, the accuracy of the source recovery deteriorates due to diffusive effects. By using more sensors that span the plume cross-section, improvement of performance can be demonstrated despite an enlarged domain of dependence.