OJFD  Vol.6 No.4 , December 2016
Analysis of High Concentration Spikes Appearing in Mass Plume in Nearly Homogeneous Turbulent Flow Based on the PDF Transport Equation
Abstract: To evaluate the pollutant dispersion in background turbulent flows, most researches focus on statistical variation of concentrations or its fluctuations. However, those time-averaged quantities may be insufficient for risk assessment, because there emerge many high-intensity pollutant areas in the instantaneous concentration field. In this study, we tried to estimate the frequency of appearance of the high concentration areas in a turbulent flow based on the Probability Density Function (PDF) of concentration. The high concentration area was recognized by two conditions based on the concentration and the concentration gradient values. We considered that the estimation equation for the frequency of appearance of the recognized areas consisted of two terms based on each condition. In order to represent the two terms with physical quantities of velocity and concentration fields, simultaneous PIV (Particle Image Velocimetry) and PLIF (Planar Laser-Induced Fluorescence) measurement and PLIF time-serial measurement were performed in a quasi-homogeneous turbulent flow. According to the experimental results, one of the terms, related to the condition of the concentration, was found to be represented by the concentration PDF, while the other term, by the streamwise mean velocity and the integral length scale of the turbulent flow. Based on the results, we developed an estimation equation including the concentration PDF and the flow features of mean velocity and integral scale of turbulence. In the area where the concentration PDF was a Gaussian one, the difference between the frequencies of appearance estimated by the equation and calculated from the experimental data was within 25%, which showed good accuracy of our proposed estimation equation. Therefore, our proposed equation is feasible for estimating the frequency of appearance of high concentration areas in a limited area in turbulent mass diffusion.
Cite this paper: Endo, M. , Shao, Q. , Tsukahara, T. and Kawaguchi, Y. (2016) Analysis of High Concentration Spikes Appearing in Mass Plume in Nearly Homogeneous Turbulent Flow Based on the PDF Transport Equation. Open Journal of Fluid Dynamics, 6, 472-495. doi: 10.4236/ojfd.2016.64034.

[1]   Takemura, T., Nakamura, H., Takigawa, M., Kondo, H., Satomura, T., Miyasaka, T. and Nakajima, T. (2011) A Numerical Simulation of Global Transport of Atmospheric Particles Emitted from the Fukushima Daiichi Nuclear Power Plant. SOLA, 7, 101-104.

[2]   Terada, H. and Chino, M. (2008) Development of an Atmospheric Dispersion Model for Accidental Discharge of Radionuclides with the Function of Simultaneous Prediction for Multiple Domains and its Evaluation by Application to the Chernobyl Nuclear Accident. Journal of Nuclear Science and Technology, 45, 920-931.

[3]   Chino, M., Nakamura, H., Nagai, H., Terada, H., Katata, G. and Yamazawa, H. (2011) Preliminary Estimation of Release Amounts of 131I and 137Cs Accidenrally Discharged from the Fulushima Daiichi Nuclear Power Plant into the Atmosphere. Journal of Nuclear Science and Technology, 48, 1129-1134.

[4]   Gifford, F.A. (1959) Statistical Properties of a Fluctuating Plume Model. Advances in Geophysics, 6, 117-137.

[5]   Sykes, R.I., Lewellen, W.S. and Parker, S.F. (1984) A Turbulent-Transport Model for Concentration Fluctuations and Fluxes. Journal of Fluid Mechanics, 139, 193-218.

[6]   Brown, M.J. and Palarya, S. (1997) Plume Descriptors Derived from a Non-Gaussian Concentration Model. Atmospheric Environment, 31, 183-189.

[7]   Page, J.L., Dickman, B.D., Webster, D.R. and Weissburg, M.J. (2011) Getting Ahead: Context-Dependent Responses to Odorant Filaments Drive Along-Stream Progress during Odor Tracking in Blue Crabs. Journal of Experiment Biology, 214, 1498-1512.

[8]   Webster, D.R., Volyanskyy, K.Y. and Weissburg, M.J. (2011) Sensory-Mediated Tracking Behavior in Turbulent Chemical Plumes. Proceedings of the 7th International Symposium on Turbulence and Shear Flow Phenomena, Canada, 28-31 July 2011, 1-6.

[9]   Endo, M., Tsukahara, T. and Kawaguchi, Y. (2015) Relationship between Diffusing-Ma-terial Lumps and Organized Structures in Turbulent Flow. Proceedings of the 5th International AJK Joint Fluids Engineering Conference, Korea, 26-31 July 2015, 1747-1753.

[10]   Endo, M., Shao, Q., Tsukahara, T. and Kawaguchi, Y. (2016) Diffusion Process of High Concentration Spikes in a Quasi-Homogeneous Turbulent Flow. Open Journal of Fluid Dynamics. (In Press)

[11]   Holzer, M. and Siggia, E.D. (1994) Turbulent Mixing of a Passive Scalar. Physics of Fluids, 6, 1820-1837.

[12]   Buch, K.A. and Dahm, W.J.A. (1996) Experimental Study of the Fine-Scale Structure of Conserved Scalar Mixing in Turbulent Shear Flow. Journal of Fluid Mechanics, 317, 21-71.

[13]   Pope, S.B. (1985) PDF Methods for Turbulent Reactive Flows. Progress in Energy and Combustion Science, 11, 119-192.

[14]   Ferchichi, M. and Tavoularis, S. (2002) Scalar Probability Density Function and Fine Structure in Uniformly Sheared Turbulence. Journal of Fluid Mechanics, 461, 155-182.

[15]   Jayesh and Warhaft, Z. (1992) Probability Distribution, Conditional Dissipation, and Transport of Passive Temperature Fluctuation in Grid-generated Turbulence. Physics of Fluids, 4, 2292-2307.

[16]   Fox, R.O. (1996) On Velocity-Conditioned Scalar Mixing in Homogeneous Turbulence. Physics of Fluids, 8, 2678-2691.

[17]   Hu, H., Saga, T., Kobayashi, T. and Taniguchi, N., (2002) Simultaneous Velocity and Concentration Measurements of a Turbulent Jet Mixing Flow. Annual of the New York Academy of Science, 972, 254-259.

[18]   Diez, F.J., Bernal, L.P. and Faeth, G.M. (2005) PLIF and PIV Measurements of the Self-Preserving Structure of Steady Round Buoyant Turbulent Plumes in Crossflow. International Journal of Heat and Fluid Flow, 26, 873-882.

[19]   Janzen, J.G., Herlina, H., Jirka, G.H., Schulz, H.E. and Gulliver, J.S. (2010) Estimation of Mass Transfer Velocity Based on Measured Turbulence Parameters. AIChE Journal, 56, 2005-2017.

[20]   Pope, S.B. (2000) Turbulent Flows. Cambridge University Press, Cambridge, 305-308.

[21]   Overholt, M.R. and Pope, S.B. (1996) Direct Numerical Simulation of a Passive Scalar with Imposed Mean Gradient in Isotropic Turbulence. Physics of Fluids, 8, 3128-3148.

[22]   Brethouwer, G. and Nieuwstadt, F.T.M. (2001) DNS of Mixing and Reaction of Two Species in a Turbulent Channel Flow: A Validation of the Conditional Moment Closure. Flow, Turbulence and Combustion, 66, 209-239.

[23]   Brown, R.J. and Bilger, R.W. (1996) An Experimental Study of a Reactive Plume in Grid Turbulence. Journal of Fluid Mechanics, 312, 373-407.

[24]   Meyers, R.E. and O’brien, E.E. (1981) The Joint PDF of a Scalar and Its Gradient at a Point in a Turbulent Fluid. Combustion Science and Technology, 26, 123-134.