Reconstruction of Scalar Source Intensity Based on Sensor Signal in Turbulent Channel Flow

We consider a turbulent channel flow, where a scalar point source with a time-harmonic intensity releases a substance that can be modeled as a passive scalar. With the source location known, our objective is to estimate the time history of the source intensity based on sensor measurements at different locations downstream of the source by adopting an adjoint approach. It is shown that the proposed algorithm reproduces the original coherent sinusoidal wave of the scalar source accurately from the chaotic scalar signals measured by our sensors. By systematically changing the source-sensor distance and the pulsation frequency of the source, we clarify how these two factors affect the estimation accuracy. The proposed scheme is also applicable to estimation with multiple sensors. We demonstrate that increasing the number of sensors improves the estimation greatly when the scalar is released from a source away from the wall, where large-scale eddies dominate the scalar dispersion. In contrast, the estimation performance remains poor even with multiple sensors when the scalar source is located near the wall, where the source information is quickly lost due to the strong turbulence activity and the scalar diffusion in the near-wall region.