Prediction of Drag Coefficient for Accelerated Single Sphere in Power Law Fluids

Abstract

In the present study a single sphere accelerated in Polyacrylamide solution with different concentration (0.01, 0.03, 0.05 and 0.07) wt% as non Newtonian fluid within the considered range of power law index (0.6 – 1) and water as Newtonian fluid. Different types and sizes of spheres (stainless steel, glass and plastic) were used. Reynolds number (Re) and generated Reynolds number (Regn) varied between (1-888). Various equations for drag coefficient of a single sphere falling through Newtonian and non Newtonian fluid have been tested for different sizes and densities .It was found that a very similar Re–CD behavior. It is also clear that the most accurate correlation is the one proposed by Lali giving a 0.001619 RMS_ CD value. Archimedes' number was calculated for sphere motion at accelerated velocity and when it reached it's terminal velocity, and it was found that there was an uncertainty relation between Ar and Regn (R2= 0.572) for accelerated motion but there is a good relation between Ar and Regn (R2= 0.935) for sphere at its terminal velocity. The predicted values of Regn depended on Ar and showed a good relationship with the experimental values (R2= 0.958) as well as the measured drag coefficient.