General formulas for drag coefficient and settling velocity of sphere based on theoretical law
The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number (Re) range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws,...
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doaj-6eab48d996db441a84062e94bb68b6d92020-11-25T00:42:35ZengElsevierInternational Journal of Mining Science and Technology2095-26862015-03-01252219223General formulas for drag coefficient and settling velocity of sphere based on theoretical lawHongli Yang0Minqiang Fan1Airong Liu2Lianping Dong3Department of Mineral Processing, College of Mining Engineering, Taiyuan University of Technology, Taiyuan 030024, ChinaCorresponding author. Tel.: +86 351 6014776.; Department of Mineral Processing, College of Mining Engineering, Taiyuan University of Technology, Taiyuan 030024, ChinaDepartment of Mineral Processing, College of Mining Engineering, Taiyuan University of Technology, Taiyuan 030024, ChinaDepartment of Mineral Processing, College of Mining Engineering, Taiyuan University of Technology, Taiyuan 030024, ChinaThe settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number (Re) range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the Stokes law, the Oseen law, and the Goldstein law, were developed and fitted using 480 groups of experimental data (Re < 2 × 105). The results show that the 2nd approximation of a rational function containing only one parameter can describe CD–Re relationship accurately over the whole Re range of 0–2 × 105. The new developed formulas containing five parameters show higher goodness over wide Re range than presently existing equations. The introduction of the Oseen law is helpful for improving the fitting goodness of the empirical formulas. On the basis of one of the Oseen-based CD–Re formulas giving the lowest sum of squared relative errors Q over the whole Re range (Re < 2 × 105), a general formula for settling velocity ut based on dimensionless parameters was proposed showing high goodness. Keywords: Sphere, Drag coefficient, Settling velocity, Reynolds number, Theoretical equationhttp://www.sciencedirect.com/science/article/pii/S2095268615000178 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Hongli Yang Minqiang Fan Airong Liu Lianping Dong |
spellingShingle |
Hongli Yang Minqiang Fan Airong Liu Lianping Dong General formulas for drag coefficient and settling velocity of sphere based on theoretical law International Journal of Mining Science and Technology |
author_facet |
Hongli Yang Minqiang Fan Airong Liu Lianping Dong |
author_sort |
Hongli Yang |
title |
General formulas for drag coefficient and settling velocity of sphere based on theoretical law |
title_short |
General formulas for drag coefficient and settling velocity of sphere based on theoretical law |
title_full |
General formulas for drag coefficient and settling velocity of sphere based on theoretical law |
title_fullStr |
General formulas for drag coefficient and settling velocity of sphere based on theoretical law |
title_full_unstemmed |
General formulas for drag coefficient and settling velocity of sphere based on theoretical law |
title_sort |
general formulas for drag coefficient and settling velocity of sphere based on theoretical law |
publisher |
Elsevier |
series |
International Journal of Mining Science and Technology |
issn |
2095-2686 |
publishDate |
2015-03-01 |
description |
The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number (Re) range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the Stokes law, the Oseen law, and the Goldstein law, were developed and fitted using 480 groups of experimental data (Re < 2 × 105). The results show that the 2nd approximation of a rational function containing only one parameter can describe CD–Re relationship accurately over the whole Re range of 0–2 × 105. The new developed formulas containing five parameters show higher goodness over wide Re range than presently existing equations. The introduction of the Oseen law is helpful for improving the fitting goodness of the empirical formulas. On the basis of one of the Oseen-based CD–Re formulas giving the lowest sum of squared relative errors Q over the whole Re range (Re < 2 × 105), a general formula for settling velocity ut based on dimensionless parameters was proposed showing high goodness. Keywords: Sphere, Drag coefficient, Settling velocity, Reynolds number, Theoretical equation |
url |
http://www.sciencedirect.com/science/article/pii/S2095268615000178 |
work_keys_str_mv |
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