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Steady‐state and decay dynamics for impellers of varying aspect ratio in unbaffled tanks
Author(s) -
Maynes D.,
Butcher M.
Publication year - 2002
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690480106
Subject(s) - impeller , mechanics , radius , reynolds number , torque , slip factor , physics , range (aeronautics) , steady state (chemistry) , volume (thermodynamics) , momentum (technical analysis) , control theory (sociology) , materials science , thermodynamics , turbulence , chemistry , computer security , control (management) , management , finance , composite material , computer science , economics
Hydrodynamic torque measurements on impellers of square cross section were conducted for 33 different impellers in 3 different cylindrical unbaffled tanks. The tanks differed in volume by two orders of magnitude, and the Reynolds number range of the data was 10 4 –10 5 . A wide range of impeller sizes and aspect ratios was investigated, focusing on the decay regime where the tank walls impacted the torque measurement, and the steady state where the torque is constant on average. The number of revolutions required for spin‐up to steady state is a function of the tank radius and height and the impeller radius and height, and an expression is presented that describes the spin‐up time in terms of these variables and is valid for all of the data. At steady state and for a Reynolds number of 10 5 , the torque coefficient or power number depended primarily on the height of the impeller and tank, but not on the impeller radius. During the decay regime, the measured torque coefficient decreases with a power‐law relation and is proportional to the number of revolutions raised to the k power. The k value did not depend on the height of the tank, but only on the impeller radius, impeller height, and tank radius. Expressions relating the steady‐state torque coefficient and the decay exponent, k, to the geometric variables model all of the data quite well. With these relations, the effects of the varying impeller aspect ratios on the energy required for mixing of momentum, and on the time required for mixing to occur, can be quantified.