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

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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.

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References

  1. Fernando HJS, Lee SM, Anderson J, Princevac M, Pardyjak E, Grossman-Clarke S (2001) Urban fluid mechanics: air circulation and contaminant dispersion in cities. Environ Fluid Mech 1:107–164

    Article  Google Scholar 

  2. Hayashi Y (2011) An analysis of the Great East Japan Earthquake by scientific information asymmetry models. In: Proceedings of the 8th international conference on innovation and management, pp 497–505

  3. Yamashita S, Suzuki S (2013) Risk of thyroid cancer after the Fukushima Nuclear Power Plant accident. Respir Investig 51(3):128–133

    Article  Google Scholar 

  4. Chino M, Kitabata H (1999) Development of the emergency system for radioactive source term estimation. JAERI-Data/Code 99-012. Japan Atomic Energy Research Institute (in Japanese)

  5. Furuno A, Chino M, Yamazawa H (2006) Development of a source term estimation method for nuclear emergency by long-range atmospheric dispersion simulations. J At Energy Soc Jpn 5(3):229–240

    Google Scholar 

  6. Bagtzoglou AC, Dougherty DE, Tompson AFB (1992) Application of particle methods to reliable identification of groundwater pollution sources. Water Resour Manag 6:15–23

    Article  Google Scholar 

  7. Ababou R, Bagtzoglou AC, Mallet A (2010) Anti-diffusion and source identification with the ‘RAW’ scheme: a particle-based censored random walk. Environ Fluid Mech 10:41–76

    Article  Google Scholar 

  8. Islam M (1999) Application of a Gaussian plume model to determine the location of an unknown emission source. Water Soil Pollut 112:241–245

    Article  Google Scholar 

  9. Ebrahimi M, Jahangirian A (2013) New analytical formulations for calculation of dispersion parameters of Gaussian model using parallel CFD. Environ Fluid Mech 13:125–144

    Article  Google Scholar 

  10. U.S. Environmental Protection Agency (1977) User’s manual for single source (CRSTER) model. EPA 450/2-77-0.3. U.S. Environmental Protection Agency, Research Triangle Park

  11. Weil JC, Brower RP (1984) An updated Gaussian plume model for tall stacks. J Air Pollut Control Assoc 34(8):818–827

    Article  Google Scholar 

  12. Abe S, Kato S (2010) A study on improving the numerical stability in reverse simulation. J Environ Eng (Trans AIJ) 75(656):891–897 (in Japanese)

    Article  Google Scholar 

  13. Abe S, Kato S, Hamba F, Kitazawa D (2012) Study on the dependence of reverse simulation for identifying a pollutant source on grid resolution and filter width in cavity flow. J Appl Math 2012:1–16

    Article  Google Scholar 

  14. Hamba F, Abe S, Kitazawa D, Kato S (2012) Filtering for the inverse problem of convection–diffusion equation with a point source. J Phys Soc Jpn 81:1–8

    Article  Google Scholar 

  15. Houweling S, Kaminski T, Dentener F, Lelieveld J, Heimann M (1999) Inverse modeling of methane sources and sinks using the adjoint of a global transport model. J Geophys Res Atmos 104:26137–26160

    Article  Google Scholar 

  16. Caya A, Sun J, Snyder C (2005) A comparison between the 4DVAR and the ensemble Kalman filter techniques for radar data assimilation. Mon Weather Rev 133:3081–3094

    Article  Google Scholar 

  17. Rao KS (2007) Source estimation methods for atmospheric dispersion. Atmos Environ 41:6964–6973

    Article  Google Scholar 

  18. Sharan M, Issartel JP, Singh SK, Kumar P (2009) An inversion technique for the retrieval of single-point emissions from atmospheric concentration measurements. Proc R Soc Lond A. doi:10.1098/rspa.2008.0402

  19. Hinze JO (1959) Turbulence. McGraw-Hill, New York, pp 324–352

    Google Scholar 

  20. McComb WD (1990) The physics of fluid turbulence. Oxford University Press, Oxford, pp 437–441

    Google Scholar 

  21. Davidson PA (2004) Turbulence: an introduction for scientists and engineers. Oxford University Press, Oxford, pp 273–276

    Google Scholar 

  22. Kosugi K, Makita H, Haniu H (2014) Experimental investigation on turbulent diffusion phenomena of meandering plume in the quasi-isotropic turbulent field (variation of mean concentration properties for turbulent Reynolds numbers). Trans JSME 80(810):1–14 (in Japanese)

    Google Scholar 

  23. Webster DR (2007) Structure of turbulent chemical plumes. In: Trace chemical sensing of explosives. Wiley, New York, pp 109–129

  24. Motozawa M, Kurosawa T, Otsuki T, Iwamoto K, Ando H, Senda T, Kawaguchi Y (2012) PLIF measurement of turbulent diffusion in drag-reducing flow with dosed polymer solution from a wall. J Therm Sci Technol 7:272–287

    Article  Google Scholar 

  25. Moser RD, Kim J, Mansour NN (1999) Direct numerical simulation of turbulent channel flow up to \({\rm {Re}}_{\tau } = 590\). Phys Fluids 11:943–945

    Article  Google Scholar 

  26. Bradley EF, Antonia RA, Chambers AJ (1981) Turbulence Reynolds number and the turbulent kinetic energy balance in the atmospheric surface layer. Bound Layer Meteorol 21:183–197

    Article  Google Scholar 

  27. Webster DR, Rahman S, Dasi LP (2003) Laser-induced fluorescence measurements of a turbulent plume. J Eng Mech 129:1130–1137

    Article  Google Scholar 

  28. Crimald JP (2008) Planar laser induced fluorescence in aqueous flows. Exp Fluids 44:851–863

    Article  Google Scholar 

  29. Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge, pp 305–308

    Book  Google Scholar 

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Acknowledgments

We express our appreciation to Messrs. Shotaro Hatsutani and Junichiro Hasegawa, who were master’s students at Tokyo University of Science, for their support in experiments and discussions.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Tokyo University of Science, 2641 Yamazaki, Noda-shi, Chiba, 278-8510, Japan

    Takahiro Tsukahara, Kana Oyagi & Yasuo Kawaguchi

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  1. Takahiro Tsukahara
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  2. Kana Oyagi
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  3. Yasuo Kawaguchi
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Correspondence to Takahiro Tsukahara.

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Tsukahara, T., Oyagi, K. & Kawaguchi, Y. Estimation method to identify scalar point source in turbulent flow based on Taylor’s diffusion theory. Environ Fluid Mech 16, 521–537 (2016). https://doi.org/10.1007/s10652-015-9436-x

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  • DOI: https://doi.org/10.1007/s10652-015-9436-x

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