Estimation method to identify scalar point source in turbulent flow based on Taylor’s diffusion theory

Abstract

We introduce a new approach to diffusion-source estimation for quick identification of the unknown source, based on Taylor's diffusion theory for turbulent transport of passive scalar from a fixed point source. In order to evaluate the method, we used planar laser-induced fluorescence to measure the concentration field of fluorescent dye in water flowing in a channel. We considered two kinds of datasets: basis data and observed data. The former is used to determine the basis functions characterizing the streamwise dependence of variances for three statistics: the mean concentration, root-mean-square (RMS) of fluctuations in the concentration, and RMS of the temporal gradient of the fluctuating concentration. Consistent with Taylor's theory, we found that the lateral distribution of each statistic was basically Gaussian, and their standard deviations increased as a function of the square root of the distance from the emitted point. Based on these facts, a basis function can be formulated and expected to be valid for estimation of unknown sources. Source estimation was performed with the observed data, which corresponded to limited available information about the concentration from an unknown point source. We confirmed a good prediction accuracy of the proposed method with an averaged bias as small as the turbulent integral scale. Better precision was achieved by employing several statistics simultaneously. In this case, the standard deviation of the estimated source position was assessed at 14 % of the mean distance between the source and measurement points, after 100 source-estimate trials with different datasets. The methodology tested in this paper is expected to be applicable more general and complex environmental diffusion issues involving anisotropic turbulent dispersion, and space-time variable mainstream systems; but its versatility in such systems is currently under investigation.

Study on the Shear Effect on Dye Patches Diffused in Wall-Bounded Shear Flow

“…For comparison, results for dye injection in homogeneous turbulent flow are firstly given. The related experiment in our group can be seen in [7]. Seven diffusion distances are chosen in the homogeneous case, which are X* = 5, 10, 25, 30, 35, 40, and 60.…”

“…Webster et al [6] inspired by food or mate locating of animals, proposed a bilateral comparison method for tracking turbulent chemical plume source, besides, the integral spanwise length scale was also indicated to be suitable for source localization. Tsukahara et al [7] used the time-averaged concentration and root mean square of concentration fluctuations to conduct inverse source localization of dye release based on the Taylor's diffusion theory. Their source-locating method was tested in the framework of a water channel-flow experiment providing a rather homogeneous turbulent field in the channel central region.…”

Applicability of Convolutional Neural Network for Estimation of Turbulent Diffusion Distance from Source Point

“…Wang et al [2] stated that the data resolution in the streamwise or time direction should satisfy the criteria, based on the Taylor microscale in the streamwise direction. Tsukahara et al [3] evaluated a simple method based on the Taylor diffusion theory for the turbulent transport of a passive scalar from a fixed-point source. As the Taylor diffusion theory is essentially based on the statistical properties of turbulence, their estimation from instantaneous information resulted in large errors.…”

Inverse Source Locating Method Based on Graphical Analysis of Dye Plume Images in a Turbulent Flow

“…Based on those previous researches [8]- [16], many quantities are found to be related with the diffusion distance of dye plumes: these quantities includes time-average concentration, plume width, concentration fluctuation quantities, intermittency, concentration burst quantities, spatial correlation, and integral length. Some inverse estimation methods for source localization have been proposed based on these diffusion-distance-related quantities [16] [17].…”