A broad range of engineering applications involves helical flow of non-Newtonian fluids between two eccentric cylinders. These applications often require estimation of the frictional pressure losses along the axes of the cylinders. Laboratory flow loops are commonly used to study the flow characteristics at smaller scales of investigation. This study uses the laws of similarity and dimensional analysis to obtain a set of scaling equations between the laboratory and prototype scales of the described annular flow. These equations are derived for four types of fluid rheology including Newtonian, power-law, Bingham-plastic, and yield power-law.

Results are expressed through a set of closed-form formulae that would determine the flow rate and rotational speed of the inner pipe in the laboratory model in terms of the flow rate and pipe rotation speed, as well as other flow parameters of the prototype. The specific forms of these scaling equations are developed in such a way that the dimensionless friction factors of the annular flows at the laboratory model and prototype scales become identical. In the case of the yield power-law fluid, a complete similitude between the two scales requires using a fluid in the laboratory model that is different from the prototype fluid. As such, application of the obtained equations in minimizing the laboratory flow loop size is demonstrated. It is shown that proper selection of the rheological parameters of the fluid in the flow loop model would enable substantial reduction in the geometric scale of the similitude.

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Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.