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Research Papers: Heat and Mass Transfer

# The Effect of Naturally Developing Roughness on the Mass Transfer in Pipes Under Different Reynolds Numbers

[+] Author and Article Information
D. Wang, D. Ewing

Department of Mechanical Engineering,
McMaster University,

C. Y. Ching

Department of Mechanical Engineering,
McMaster University,
e-mail: chingcy@mcmaster.ca

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 30, 2016; final manuscript received April 27, 2017; published online June 6, 2017. Assoc. Editor: Jim A. Liburdy.

J. Heat Transfer 139(10), 102005 (Jun 06, 2017) (8 pages) Paper No: HT-16-1615; doi: 10.1115/1.4036728 History: Received September 30, 2016; Revised April 27, 2017

## Abstract

The local mass transfer over dissolving surfaces was measured at pipe Reynolds number of 50,000, 100,000, and 200,000. Tests were run at multiple time periods for each Reynolds number using 203 mm diameter test sections that had gypsum linings dissolving to water in a closed flow loop at a Schmidt number of 1200. The local mass transfer was calculated from the decrease in thickness of the gypsum lining that was measured using X-ray-computed tomography (CT) scans. The range of Sherwood numbers for the developing roughness in the pipe was in good agreement with the previous studies. The mass transfer enhancement (Sh/Shs) was dependent on both the height ($ep−v$) and spacing ($λstr$) of the roughness scallops. For the developing roughness, two periods of mass transfer were present: (i) an initial period of rapid increase in enhancement when the density of scallops increases till the surface is spatially saturated with the scallops and (ii) a slower period of increase in enhancement beyond this point, where the streamwise spacing is approximately constant, and the roughness height grows more rapidly. The mass transfer enhancement was found to correlate well with the parameter ($ep−v/λstr$)0.2, with a weak dependence on Reynolds number.

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## Figures

Fig. 1

Schematic of test facility

Fig. 2

Pictures of the experimental facility showing (a) lower part of the flow loop including the pump and valves and (b) top part of the flow loop including the test section and reservoir

Fig. 3

Local distribution of Sherwood number in different time periods for surfaces exposed to flow with: (a) Re = 50,000, (b) Re = 100,000, and (c) Re = 200,000 (times are given in modified time)

Fig. 4

Variation of Sherwood number averaged in sampling areas as a function of normalized peak to valley roughness height for the three Reynolds numbers

Fig. 5

Illustration of estimating Sherwood number in nearly smooth region where the ratio of peak to valley roughness and streamwise spacing is smaller than 0.01

Fig. 6

Comparison of the range of mass transfer rates averaged in each sampling area measured in current experiments with the previous studies for both smooth and rough surfaces

Fig. 7

Variation of mass transfer enhancement (Sh/Shs) as afunction of normalized peak to valley roughness height andcomparison with mass transfer results from Dawson andTrass [4]

Fig. 8

Variation of mass transfer (Sh/Shs) enhancement as a function of height to spacing (pitch) ratio

Fig. 9

Variation of Sherwood number as a function of height to spacing (pitch) ratio

Fig. 10

Variation of roughness height to spacing ratio as a function of normalized height with a best fit power correlation between them

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