Hydrodynamic similitude

A dynamic similitude embodies both hydrodynamic and thermodynamic similitudes. A hydrodynamic similitude requires a similar flow pattern and similar veloc-... 

A technique which can assist in the scale-up of commercial plants designs is the use of scale models. A scale model is an experimental model which is smaller than the hot commercial bed but which has identical hydrodynamic behavior. Usually the scale model is fluidized with air at ambient conditions and requires particles of a different size and density than those used in the commercial bed. The scale model relies on the theory of similitude, sometimes through use of Buckingham s pi theorem, to design a model which gives identical hydrodynamic behavior to the commercial bed. Such a method is used in the wind tunnel testing of small model aircraft or in the towing tank studies of naval vessels. 

For point particles governed by Stokes law, the Stokes number is the only criterion other than geometry that determines similitude for the shape of the particle trajectories. To ensure hydrodynamic similarity, in general, the collector Reynolds number also must be preserved, as well as the ratio I = R/a, called the interception parameter. Then, the collection efficiency of particles hitting an obstacle such as a cylinder has the form ... 

Birkhoff, Garrett. Hydrodynamics A Study in Logic, Fact, and Similitude. 

Anonymous (1980). Birkhoff to dehver von Neumann Lecture. SIAM News 13(6) 1. P Birkhoff, G. (1950). Hydrodynamics-. A study in logic, fact and similitude. University Press Princeton NJ, 2 . ed. 1960. 

Safoniuk, M, Grace JR, Hackman L, McKnight CA. Use of dimensional similitude for scale-up of hydrodynamics in three-phase fluidized beds. Chem Eng Sci 54 4961-4966, 1999. 

Sanchez et al. (2008) tested the scale-up method for three-phase fluidized bed hydrodynamics proposed by Safoniuk et al. (1999), based upon the principles of dynamic similitude. The authors matched several systems operated at pressures in the range of 0.79-15.6MPa (prototype) with model systems operated at atmospheric pressure. Experiments were carried out to test this technique by comparing global phase holdups, and flow regime in systems where the five dimensionless groups were matched operated at significantly different pressures. 

In scaling-down of EBR, it has to be assured that hydrodynamic characteristics be identical, maintaining phase holdups unchanged. The key parameters in scaling-down are catalyst particle diameter, reactor diameter, as well as liquid and gas superficial velocities. For scaling-up, methods based on geometric and dynamic similitude are very useful. 

Sanchez, J.L., Ruiz, R.S., Alonso, R, Ancheyta, J. 2008. Evaluation of the hydrodynamics of high-pressure ebullated beds based on dimensional similitude. Catal. Today 130 519-526. 

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