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Technical Briefs

# Particle Deposition Onto Rough Surfaces

[+] Author and Article Information
Giovanni Lo Iacono1

Rothamsted Research, Harpenden, Hertfordshire AL5 2JQ, UKgiovanni.loiacono@bbsrc.ac.uk

Andy M. Reynolds

Rothamsted Research, Harpenden, Hertfordshire AL5 2JQ, UK

Paul G. Tucker

Whittle Laboratory, University of Cambridge, Cambridge CB3 0DY, UK

1

Corresponding author.

J. Fluids Eng 130(7), 074501 (Jun 25, 2008) (5 pages) doi:10.1115/1.2948359 History: Received January 15, 2007; Revised April 02, 2008; Published June 25, 2008

## Abstract

Predictions for the number of particles depositing from fully developed turbulence onto a fully roughened $k$-type surface are obtained from the results of large-eddy simulations for a ribbed-channel flow. Simulation data are found to provide only partial support for the “mass-sink hypothesis,” i.e., the notion that all particles entering a mass sink, a volume of fluid extending vertically from the deposition surface, are captured and eventually deposited. The equality of the number of particles entering the mass sink and the number of particles depositing is attained, and a qualitative agreement with the empirical model of Wood (1981, “A Simple Method for the Calculation of Turbulent Deposition to Smooth and Rough Surfaces  ,” J. Aerosol Sci., 12(3), pp. 275–290) for the height of this mass sink is obtained. However, a significant proportion of particles escapes from the mass sink and the equality of numbers is attained only because many particles deposit onto rib surfaces above the mass sink, without first entering the mass sink.

###### FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
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## Figures

Figure 1

(a) To estimate the height Σ+, above the ribbed surface, six different regions limited by the wall itself and by (x-z) planes parallel to the wall have been identified. Region 1 coincides with the region when the LES modeled stress tensor is reduced to, it extends from y+∕h+=0 to y+∕h+=0.1, regions 2, 3, 4, 5, and 6 extend from y+∕h+=0 to y+∕h+=0.2,0.4,0.6,0.8,1.0, respectively. (b) Particles can move away to the central area of the channel; they can deposit onto the walls or onto any face of the rib. At any time t, we counted: the number of particles that have entered (but not deposited) a certain region i, Nient(t); the number of particles that have escaped the region i, Niesc, the number of particles that have reentered (but not deposited) the region i, NiR; the number of particles that, being in a region i, directly have deposited onto the left face of the rib DiL, the right face of the rib DiR, and the top face of the rib DT (of course, those particles can come only from the central region of the channel, above the rib); the number of particles that have deposited on the bottom wall Db (inevitably, they deposit directly from region 1); the total number of particles that have deposited onto the rough wall Diw=DiL+DiR+DT+Db; the number of particles that, being outside the region i, still have deposited onto the left face of the rib DiLout, the right face of the rib DiRout, the top face of the rib DTout, and the total number of particles Diwout=DiLout+DiRout+DTout, the total number of particles that have reached the Region i regardless of their final condition, i.e., deposited, escaped, reentered, etc. Ni=Nient(t)+NiR+Niesc+Diw. Then, from Ni and Diw+Diwout we extrapolated the value of Σ+ that satisfies N(Σ+)=Dw(Σ+)+Dwout(Σ+), i.e., when the total number of particles N(Σ+) that have reached a region of height Σ+ is equal to the total number of particles that have deposited. This height was defined as mass sink.

Figure 2

Averaged streamwise velocity profile along the spanwise (z) and the streamwise (x) direction and in the time interval t+−t0+=3500. The velocity and position are normalized, respectively, by the maximum velocity umax and by the channel width Ly. (○) experiment of Hanjalic and Launder (14) (pitch ratio 10), – current LES. The predicted mass flow for y∕Ly≲0.2 is necessarily consistent with experiments, despite the absence of measurements for this region. It is found that (not shown here) the velocity exhibits a clear logarithmic profile in the region y∕h≳1.5, where the normal direction is divided by the rib height h(14). The friction velocity u* is determined by fitting the current LES according to the same parametrization of Hanjalic and Launder (14), which results in u*=0.5950, e+∼1, h+=245. The inset shows the velocity profile plotted in universal coordinates compared with the modified “law of the wall” for rough surfaces (dashed line) u+(y+)=1∕κlog(y+−e+)+C−Δu+. The value of Δu+ is in agreement with the prediction of Perry (5) that Δu+=κ−1lnh++2.2=15.3 (for large w+) and with other values found in literature (see e.g., Refs. 15-16). This corresponds to a fully rough regime with equivalent sand grain roughness kseq+ of the order of O(3)(17).

Figure 3

Ratios Ri=Diw∕Ni(t) of deposited particles (τp+=610) over particles present in the regions identified by levels y+∕h+=0.1 and y+∕h+=1.0. Similar profiles have been observed for different regions and for τp+=29.2. Particles are released at the horizontal central plane of the channel, then they will enter the six regions shown in Fig. 1 and deposit. An equilibrium phase occurs when the flux of depositing particles is proportional to the flux of particles entering the said region and the trend of Ri is roughly constant. Statistics are extracted upon establishment of constant particle fluxes.

Figure 4

Fraction of depositing particles within a region. ○ refers to τp+=610. ◻ refers to τp+=29.2. Same nomenclature as in Fig. 1.

Figure 5

Fraction of escaping particles from a region. ○ refers to τp+=610. ◻ refers to τp+=29.2. Same nomenclature as in Fig. 1.

Figure 6

Fraction of particles depositing on the portion of rib wall outside a region. ○ refers to τp+=610. ◻ refers to τp+=29.2. Same nomenclature as in Fig. 1.

Figure 7

The total number of particles depositing onto the rough wall. ○ refers to τp+=610. ◻ refers to τp+=29.2. Same nomenclature as in Fig. 1.

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