American Journal of Applied Mathematics

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Derivation of Turbulent Energy in Presence of Dust Particles

Received: 14 October 2013    Accepted:     Published: 10 November 2013
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Abstract

Energy equation for dusty fluid turbulent flow has been derived in terms of correlation tensors of second order. In presence of dust particles, mathematical modeling of turbulent energy is discussed including the correlation between the pressure fluctuations and velocity fluctuations at two points of the flow field, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between the two points, one point has been taken as origin of the coordinate system.

DOI 10.11648/j.ajam.20130104.15
Published in American Journal of Applied Mathematics (Volume 1, Issue 4, October 2013)
Page(s) 71-77
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Energy Equation, Turbulent Flow, Dust Particle, Two-point Correlation, Correlation Tensor

References
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[2] Ahmed, S.F. and Sarker, M.S.A., (2011). Fiber suspensions in turbulent flow with two-point correlation. Bangladesh Journal of Scientific and Industrial Research, 46(2): pp. 265-270.
[3] Bosse, T. and Kleiser, L., (2006). Small particles in homogeneous turbulence: Settling velocity enhancement by two-way coupling. Physics of Fluids, 18: pp. 027102-17.
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[5] Chandrasekhar, S., (1955). Hydro magnetic turbulence. II. An elementary theory. Proceedings of the Royal Society, 233: pp. 330-350.
[6] Crowe, C.T., Troutt, T.R. and Chung, J.N., (1996). Numerical models for two-phase turbulent flows. Annual Review of Fluid Mechanics, 28: pp.11-43.
[7] Havnes, O. and Kassa, M., (2009). On the sizes and observable effects of dust particles in polar mesospheric winter echoes. Journal of Geophysical Research, DOI: 10.1029/2008JD011276, 114: D09209.
[8] Hinze, J.O., (1975). Turbulence, New York: McGraw-Hill Book Company.
[9] Hodgson, L.S. and Brandenburg, A. 1998. Turbulence effects in planetesimal formation. Astronomy and Astrophysics. 330: 1169-1174.
[10] Hussainov, M., Kartushinsky, A., Rudi, U., Shcheglov, I., Kohnen, G. and Sommerfeld M., (2000). Experimental investigation of turbulence modulation by solid particles in a grid-generated vertical flow. International Journal of Heat and Fluid Flow, 21: pp. 365-373.
[11] Johansen, A., Henning,T. and Klahr, H., (2006). Dust sedimentation and self-sustained kelvin-helmholtz turbulence in protoplanetary disk midplanes. The Astrophysical Journal, 643: pp. 1219-1232.
[12] Kishore, N. and Sarker, M.S.A., (1990). Rate of change of vorticity covariance in MHD turbulent flow of dusty incompressible fluid. International Journal of Energy Research, 14(5): pp. 573–577.
[13] Kvasnak, W., Ahmadi, G., Bayer, R. and Gaynes, M., (1993). Experimental investigation of dust particle deposition in a turbulent channel flow. Journal of Aerosol Science, 24: pp. 795-815.
[14] Nickovic, S., Kallos G., Papadopoulos, A. and Kakaliagou, O., (2001). A model for prediction of desert dust cycle in the atmosphere. Journal of Geophysical Research, 106: pp. 18113-18129.
[15] Oakey, N.S., (1982). Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements. Journal of Physical Oceanography, 12: pp. 256-271.
[16] Okuzumi, S. and Hirose, S., (2011). Modeling magnetorotational turbulence in protoplanetary disks with dead zones. The Astrophysical Journal, DOI:10.1088/0004-637X/742/2/65, 742: 65.
[17] Pakhomov, M.A., Protasov, M.V., Terekhov, V.I. and Varaksin, A.Y., (2007). Experimental and numerical investigation of downward gas-dispersed turbulent pipe flow. International Journal of Heat and Mass Transfer, 50: pp. 2107–2116.
[18] Pan, L., Padoan, P., Scalo, J., Kritsuk, A.G. and Norman, M.L., (2011). Turbulent clustering of protoplanetary dust and planetesimal formation. The Astrophysical Journal, DOI: 10.1088/0004-637X/740/1/6, 740(1):6.
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Author Information
  • Senior Lecturer in Mathematics, Prime University, Dhaka, Bangladesh

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    Shams Forruque Ahmed. (2013). Derivation of Turbulent Energy in Presence of Dust Particles. American Journal of Applied Mathematics, 1(4), 71-77. https://doi.org/10.11648/j.ajam.20130104.15

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    Shams Forruque Ahmed. Derivation of Turbulent Energy in Presence of Dust Particles. Am. J. Appl. Math. 2013, 1(4), 71-77. doi: 10.11648/j.ajam.20130104.15

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    Shams Forruque Ahmed. Derivation of Turbulent Energy in Presence of Dust Particles. Am J Appl Math. 2013;1(4):71-77. doi: 10.11648/j.ajam.20130104.15

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  • @article{10.11648/j.ajam.20130104.15,
      author = {Shams Forruque Ahmed},
      title = {Derivation of Turbulent Energy in Presence of Dust Particles},
      journal = {American Journal of Applied Mathematics},
      volume = {1},
      number = {4},
      pages = {71-77},
      doi = {10.11648/j.ajam.20130104.15},
      url = {https://doi.org/10.11648/j.ajam.20130104.15},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.20130104.15},
      abstract = {Energy equation for dusty fluid turbulent flow has been derived in terms of correlation tensors of second order. In presence of dust particles, mathematical modeling of turbulent energy is discussed including the correlation between the pressure fluctuations and velocity fluctuations at two points of the flow field, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between the two points, one point has been taken as origin of the coordinate system.},
     year = {2013}
    }
    

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    AB  - Energy equation for dusty fluid turbulent flow has been derived in terms of correlation tensors of second order. In presence of dust particles, mathematical modeling of turbulent energy is discussed including the correlation between the pressure fluctuations and velocity fluctuations at two points of the flow field, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between the two points, one point has been taken as origin of the coordinate system.
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