Abstract
Non-equilibrium effects resulting from the slow relaxation of inertial particles to statistical equilibrium with flow fluctuations in turbulence are known to have important consequences, but they are not readily incorporated into models. Here, a simple analysis of these effects predicts −2/3 power-law dependence of the particle deposition rate on Stokes number (normalized particle inertia) in the far field of a confined turbulent flow, and a weaker near-field dependence. Near-field measurements and numerical simulations exhibit this weaker dependence, as do models that are generally viewed as validated by this result, but the models fail to capture the newly identified far-field behavior due to their equilibrium assumptions. Quantification of these qualitative observations is obtained by incorporating particle response to fluid motion into ‘one-dimensional turbulence’ (ODT), a stochastic computational model of turbulence.
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Chen, M., McLaughlin, J.B.: A new correlation for the aerosol deposition rate in vertical ducts. J. Colloid Interface Sci. 169, 437–455 (1995)
DeGraaff, D.B., Eaton, J.K.: Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346 (2000)
Farmer, R.A.: Liquid droplet trajectories in two phase flow. Ph.D. Dissertation, MIT (1969)
Gioia, G., Chakraborty, P.: Turbulent friction in rough pipes and the energy spectrum of the phenomenological theory. Phys. Rev. Lett. 96, 44502.1–4 (2006)
Graham, D.I.: Development of particle dispersion characteristics from arbitrary initial conditions in isotropic turbulence. J. Fluid Mech. 501, 149–168 (2004)
Graham, D.I., James, P.W.: Turbulent dispersion of particles using eddy interaction models. Int. J. Multiph. Flow 22, 157–175 (1996)
Guha, A.: Transport and deposition of particles in turbulent and laminar flow. Annu. Rev. Fluid Mech. 40, 311–341 (2008)
Hoyas, S., Jimenez, J.: Scaling of the velocity fluctuations in turbulent channels up to Re τ =2003. Phys. Fluids 18, 11702.1–4 (2006)
Kalda, J., Morozenko, A.: Turbulent mixing: the roots of intermittency. New J. Phys. 10, 093003.1–11 (2008)
Kerstein, A.R.: Linear-eddy modeling of turbulent transport. Part VI: Microstructure of diffusive scalar mixing fields. J. Fluid Mech. 231, 361–394 (1991)
Kerstein, A.R.: One-dimensional turbulence: Model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows. J. Fluid Mech. 392, 277–334 (1999)
Kerstein, A.R.: ODT: Stochastic simulation of multi-scale dynamics. Lect. Notes Phys. 756, 291–333 (2009)
Kerstein, A.R., Krueger, S.K.: Clustering of randomly advected low-inertia particles: A solvable model. Phys. Rev. E 73, 25302.1–4 (2006)
Kerstein, A.R., Ashurst, W.T., Nilsen, V., Wunsch, S.E.: One-dimensional turbulence: Vector formulation and application to free shear flows. J. Fluid Mech. 447, 85–109 (2001)
Liu, B.Y., Agarwal, J.K.: Experimental observation of aerosol deposition in turbulent flow. J. Aerosol Sci. 5, 145–148 (1974)
McCoy, D.D., Hanratty, T.J.: Rate of deposition of droplets in annular two-phase flow. Int. J. Multiph. Flow 3, 319–331 (1977)
McLaughlin, J.B.: Aerosol particle deposition in numerically simulated channel flow. Phys. Fluids A 1, 1211–1224 (1989)
Rowe, P.N.: The drag coefficient of a sphere. Trans. Inst. Chem. Eng. 39, 175–181 (1961)
Schmidt, J.R.: Trajectories of evaporating droplets in a turbulent combustor using the One Dimensional Turbulence model. M.S. Thesis, Univ. of Arizona (2000)
Schmidt, J.R.: Stochastic models for the prediction of individual particle trajectories in One Dimensional Turbulence flows. Ph.D. Dissertation, Univ. of Arizona (2004)
Schmidt, R.C., Kerstein, A.R., Wunsch, S.E., Nilsen, V.: Near-wall LES closure based on One-Dimensional Turbulence modeling. J. Comput. Phys. 186, 317–355 (2003)
Schmidt, J.R., Wendt, J.O.L., Kerstein, A.R.: A novel method for the prediction of particle-laden turbulent channel flow using the One Dimensional Turbulence model. In: Proc. 4th Int. Conf. on Heat Transf., Fluid Mech., and Thermo., Cairo, Egypt (2005)
Schmidt, J.R., Wendt, J.O.L., Kerstein, A.R.: Prediction of particle laden turbulent channel flow using One Dimensional Turbulence. In: Balachandar, S., Prosperetti, A. (eds.) Computational Approaches to Multiphase Flow, pp. 433–441. Springer, Berlin (2006)
Shin, M., Lee, J.W.: Memory effect in the Eulerian particle deposition in a fully developed turbulent channel flow. J. Aerosol Sci. 32, 675–693 (2001)
Shin, M., Kim, D.S., Lee, J.W.: Deposition of inertia-dominated particles inside a turbulent boundary layer. Int. J. Multiph. Flow 29, 893–926 (2003)
Uijttewaal, W.S.J., Oliemans, R.V.A.: Particle dispersion and deposition in direct numerical and large eddy simulations of vertical pipe flows. Phys. Fluids 8, 2590–2604 (1996)
Wang, Q., Squires, K.D., Chen, M., McLaughlin, J.B.: On the role of the lift force in turbulence simulations of particle deposition. Int. J. Multiph. Flow 23, 749–763 (1996)
Young, J., Leeming, A.: A theory of particle deposition in turbulent pipe flow. J. Fluid Mech. 340, 129–159 (1997)
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Schmidt, J.R., Wendt, J.O.L. & Kerstein, A.R. Non-equilibrium Wall Deposition of Inertial Particles in Turbulent Flow. J Stat Phys 137, 233 (2009). https://doi.org/10.1007/s10955-009-9844-8
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DOI: https://doi.org/10.1007/s10955-009-9844-8