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Sub-micron particle deposition on an isothermal horizontal rod in a turbulent flow system

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Summary

The available theoretical models for particulate fouling were reviewed and used to explain some of limited fouling data which have been reported. An experimental measurement of the thermophoretic deposition of sub-micron particles on the smooth wall of a circular rod and a simple approximation of a two-dimensional method for predicting the thermophoretic effects on sub-micron particles are introduced. The particles were moving under fully developed turbulent flow conditions, and the investigation focusses on diffusive deposition of sub-micron particles ofd p=0.05 μm andd p=0.25 μm in diameter.

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Abbreviations

A d :

area of deposition

C :

particle concentration

D :

Brownian diffusion coeffcient,K BT/3δμd p

d p :

particle diameter

de :

effective diameter of channel

f :

friction factor

k :

universal constant

K B :

Boltzmann constant, 1.38×10−23 J/K

Le :

Entrance transition length

m c :

total mass collected on the filter

m d :

total mass deposited on the wall surface

N :

particle flux,D ∂c/∂y

Pr:

Prandtl number

Q :

volumetric air flow rate

r :

radius co-ordinate

r i :

radius of central rod

r o :

radius of outside pipe

Re:

Reynolds number

Sc:

Schmidt number

t c :

time for each sampling in seconds

t d :

total time of a run in seconds

T :

absolute temperature

u :

velocity inx-direction

u * :

friction velocity

v :

velocity iny-direction

v t :

thermophoretic velocity

V d :

deposition velocity of particle

x :

distance along the wall

y :

distance from the wall

τ:

shear stress of fluid

ϱ:

density of fluid

ε:

υ t δ d /2D

ξ:

δ d /δ

β:

nondimensional temperature,T w−T∞/Tw

μ:

viscosity of fluid

v :

kinematic viscosity

α:

coefficient of thermal reflection or 630/37 (Eq. (25))

δ:

boundary layer thickness

o :

reference conditions

w :

wall conditions

∞:

conditions far from the surface

+:

nondimensional values

References

  1. Beal, S. K.: Deposition of particles in turbulent flow on channel or pipe walls. Nucl. Sci. Engng40, 1–11 (1970).

    Google Scholar 

  2. Gardner, G. C.: Events leading to erosion in the steam turbine. Proc. Instn. Mech. Engrs.178, Pt. 1, No. 23 (1963–1964).

  3. Parker, G. J., Ryley, D. J.: Equipment and techniques for studying the deposition of sub-micron particles on turbine blades. Proc. Instn. Mech. Engrs.184, (3c), 45–51 (1969–1970).

    Google Scholar 

  4. Vermes, G.: Thermophoresis-enhanced deposition rate in combustion turbine blade passages. J. Eng. Power101, 542–548 (1979).

    Google Scholar 

  5. Gokoglu, S. A., Rosner, D. E.: Thermophoretically enhanced mass transport rates to solid and transpiration-cooled walls across turbulent (law-of-the-wall) boundary-layers. Ind. Eng. Chem. Fundam.24, 208–213 (1985).

    Google Scholar 

  6. Ryley, D. J., Al-Azzawi, H. K.: Suppression of the deposition of nucleated fog droplets on the steam turbine stator blades by blade heating. Int. J. Heat Fluid Flow4, 207–216 (1983).

    Google Scholar 

  7. Lin, C. S., Moulton, R. W., Putnam, G. L.: Mass transfer between solid wall and fluid streams. Ind. Eng. Chem.45, 636–640 (1953).

    Google Scholar 

  8. Wells, A. C., Chamberlain, A. C.: Transport of small particles to vertical surface. Brit. J. Appl. Phys.18, 1793–1799 (1967).

    Google Scholar 

  9. Liu, B. Y. H., Illori, T. A.: Inertial deposition of aerosol particles in turbulent pipe flow. In: ASME Symposium on Flow Studies in Air and Water Pollution, atlanta, Georgia, pp. 103–113 (1973).

  10. Liu, B. Y. H., Agarwal, J. K.: Experimental observation of aerosol deposition in turbulent flow. J. Aerosol Sci.5, 145–155 (1974).

    Google Scholar 

  11. El-Shobokshy, M. S., Ismail, I. A.: Deposition of aerosol particles from turbulent fluid onto rough pipe wall. Atmospheric Environment14, 297–304 (1980).

    Google Scholar 

  12. Davies, C. N.: Deposition of aerosol from turbulent flow through pipes. Proc. Roy. Soc. A289, 235–246 (1966).

    Google Scholar 

  13. Laufer, J.: The structure of turbulence in fully developed pipe flow. NACA Report 1174.

  14. Cleaver, J. W., Yates, B.: The effect of re-entrainment of particle deposition. Chem. Engng Sci.31, 147–151 (1976).

    Google Scholar 

  15. Yung, B. P. K., Merry, H., Boff, T. R.: The role of turbulent bursts in particle reentrainment in equeous systems. Chem. Engng Sci.44, 873–882 (1989).

    Google Scholar 

  16. Rashidi, M., Hetsron, G., Banerjee, S.: Particle-turbulence interaction in a boundary-layer. Int. J. Multiphase Flow16, 935–949 (1990).

    Google Scholar 

  17. Gardner, G. C.: Deposition of particles from a gas flowing parallel to a surface. Int. J. Multiphase Flow2, 213–246 (1975).

    Google Scholar 

  18. Owen, I., El-Kady, A. A., Cleaver, J. W.: Deposition of sub-micrometre particles onto a heated surface with widely spaced roughness elements. J. Aerosol Sci.20, 671–681 (1989).

    Google Scholar 

  19. Castilld, J. L., Rosner, D. E.: Theory of surface deposition from a unary dilute vapor-containing stream allowing for condensation within the laminar boundary-layer. Chem. Engng Sci.44, 925–937 (1989).

    Google Scholar 

  20. Brown, T. D.: The deposition of sodium sulphate from combustion gases. J. Inst. Fuel39, 378–385 (1966).

    Google Scholar 

  21. Byers, R. L., Calvert, S.: Particle deposition from turbulent streams by means of thermal force. Ind. Eng. Chem. Fundam.8, 646–655 (1979).

    Google Scholar 

  22. Singh, B., Byers, R. L.: Particle deposition due to thermal force in the transition and near-continuum regimes. Ind. Eng. Chem. Fundam.11, 127–133 (1972).

    Google Scholar 

  23. Nishio, G., Kitani, S., Takahashi, K.: Thermophoretic deposition of aerosol particles in a heatexchanger pipe. Ind. Eng. Chem. Process Des. Develop.13, 408–415 (1974).

    Google Scholar 

  24. Whitmore, P. J., Meisen, A.: Estimation of thermo- and diffusionsphoretic particle deposition. Canadian J. Chem. Engng.55, 279–285 (1977).

    Google Scholar 

  25. Ryley, D. J., Davies, J. B.: Effect of thermophoresis on fog droplet deposition on low pressure steam turbine guide blades. Int. J. Heat Fluid Flow4, 163–167 (1983).

    Google Scholar 

  26. Rosner, D. E., Atkins, R. M.: Experimental studies of salt/ash deposition rates from combustion products using optical techniques. In: Fouling and stagging resulting from impurities in combustion gases (Bryers, R., ed.). p. 469. New York: The Engrg. Foundation 1983.

    Google Scholar 

  27. Eisner, A. D., Rosner, D. E.: Experimental and theoretical studies of submicron particle thermophoresis in combustion gases. PCH Physico Chemical Hydrodynamics7, 91–100 (1986).

    Google Scholar 

  28. Hinze, J. O.: Turbulence. 2nd ed., p. 717, New York: McGraw-Hill 1975.

    Google Scholar 

  29. Kelly, B. T.: A particulate model for low temperature deposition in advanced gascooled reactors. UKAEA Report ND-M-2537(s) (1935).

  30. Clauser, F. H.: Turbulent boundary-layer in adverse pressure gradient. J. Aeronaut. Sci.21, 91–108 (1954).

    Google Scholar 

  31. Özisik, M. N.: Heat transfer, a basic approach. New York: McGraw Hill 1985.

    Google Scholar 

  32. Deissler, R. G.: Analytical and experimental investigation of adiabatic turbulent flow in smooth tubes. NACA TN 2138 (1950).

  33. Otani, Y., Enii, H., Kanaoka, C., Kato, K.: Determination of deposition velocity onto a waferforparticles in the size range between 0.03 and 0.8pm. J. Aerosol Sci.20, 787–796 (1989).

    Google Scholar 

  34. Parker, G. J., Ryley, D. J.: Equipment and techniques for studying the deposition of sub-micron particles on turbine blades. Proc. Instn. Mech. Engrs.184, 3c, 45–51 (1969–1970)

    Google Scholar 

  35. Al-Azzawi, H. K., Owen, I.: Measuring the thermal conductivity of uranine. Int. J. Heat and Fluid Flow5, 1, 57–59 (1984).

    Google Scholar 

  36. Hanratty, T. J.: Turbulent exchange of heat and momentum with a boundary A.I.Ch.E. J.2, 359–362 (1956).

    Google Scholar 

  37. Corino, E. R., Brodkey, R. S.: A visual investigation of the wall region on turbulent flow. J. Fluid Mech37, 1–30 (1969).

    Google Scholar 

  38. Harriott, P.: A random eddy modification of the penetration theory. Chem. Engng Sci.17, 149–154 (1962).

    Google Scholar 

  39. Thomas, L. C., Gingo, P. S., Chung, B. T. F.: The surface rejuvenation model for turbulent convective transport-an exact solution. Ind. Eng. Chem. Fund.10, 1239–1242 (1975).

    Google Scholar 

  40. Bullin, J. A., Dukler, A. E.: Random eddy models for surface renewal: formulation as a stochastic process. Chem. Engng Sci.27, 439–442 (1972).

    Google Scholar 

  41. Rajagopal, R., Thomas, L. C.: Adaptation of the stochastic formulation of the surface rejuvenation model to turbulent convective heat transfer. Chem. Engng Sci.29, 1639–1644 (1974).

    Google Scholar 

  42. Pinczewski, W. V., Sideman, S.: A model for mass (heat) transfer in turbulent tube flow, moderate and high Schmidt (Prandtl) number. Chem. Engng Sci.29, 1969–1976 (1974).

    Google Scholar 

  43. Schlichting, H.: Boundary-layer theory, 7th ed. New York: McGraw-Hill 1979.

    Google Scholar 

  44. Davies, J. T.: Turbulence phenomena, an introduction to the eddy transfer of momentum, mass, and heat, particularly at interfaces. New York: Academic Press 1972.

    Google Scholar 

  45. Shaw, D. A., Hanratty, J. T.: Turbulent mass transfer rates to a wall for large Schmidt numbers. A.I.O.h.E. J.23, 1, 28–36 (1977).

    Google Scholar 

  46. Beal, S. K.: Deposition of particles in turbulent flow on channel or pipe walls. Nuclear Sci. Engng40, 1–11 (1970).

    Google Scholar 

  47. Kneen, T., Strauss, W.: Deposition of dust from turbulent gas stream. Atmospheric Environment3, 55–67 (1969).

    Google Scholar 

  48. Montgomery, T. L., Corn, M.: Aerosol deposition in a pipe with turbulent airflow. Aerosol Sci1, 185–213 (1970).

    Google Scholar 

  49. Sehmel, G. A.: Aerosol deposition from turbulent air streams in vertical conduits. AEC Res. and Dev. Rpt. BNWL-579 (1968).

  50. Hinze, J. O.: Turbulence, 2nd ed., p. 621. New York: McGraw-Hill 1975.

    Google Scholar 

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Author notes

  1. M. -C. Chiou

    Present address: Department of Vehicle Engineering, National Huwei Institute of Technology, 64 Wenhua Road, Huwei, Yunlin, Taiwan

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    Chiou, M.C. Sub-micron particle deposition on an isothermal horizontal rod in a turbulent flow system. Acta Mechanica 145, 135–158 (2000). https://doi.org/10.1007/BF01453649

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    • DOI: https://doi.org/10.1007/BF01453649

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