Flow Around a Suddenly Start Rotating Circular Cylinder and Introduce a New Paradox

Abstract

There have been many misunderstanding about the flow around vortices for example a stationary and/or moving vortex pair. The authors have pointed out that no fluid dynamics textbooks have accepted the existence of stationary or arbitral speed moving vortices. About the vortex flow, recently the authors have found a new analytic solution of the Navier-Stokes equations for two-dimensional flow around a suddenly start rotating circular cylinder. This analytic solution explains the velocity distribution, vorticity distribution with change in time, and boundary layer thickness close to a vortex filament because of the action of viscosity. The resulting solutions are involved simple exponential function. Authors present a new construction for the solution of the Navier-Stokes equations for suddenly start rotating circular cylinder. New solution is based on the concept of the similarity solution approach using similarity variable, dimensional analysis, initial, & boundary conditions. A brief theoretical discussion is presented about the suddenly start rotating circular cylinder. The second part of the paper deals with the analytic solution being compared with experimental results in various Reynolds number. A typical measurement is that of relaxation of rotational velocities when the cylinder is subjected only to the viscous resistance. To measure the velocity distribution of the flow the experiments were made with the help of tracer particle (aluminum powder and 150-grain diameter meshes) for water and oil (Super Mulpus 68). The effects of the Reynolds number on the laminar asymmetric flow structure in the flow region are studied. The induced speed distribution in the rotation of cylinder (diameter 10 mm) circumference has examined about the Reynolds number from 26 to 522 for water consequent cylinder rpm 10, 25, 50, 75, 100 and 0.12 to 2.32 for Super Mulpus 68 Oil consequent cylinder rpm 5, 10, 25, 50, 75, 100. The relation between the induced speeds after the time had passed enough and the various cylinder rotational speeds for both analytical and experimental results are shown. At lower Reynolds number experimental results are closer to theoretical results for a finite time condition, at that time there is exist vorticity around the cylinder. We can also establish that more difference between experimental and theoretical results with higher Reynolds number. An interesting phenomenon has been observed in the flow patterns at various Reynolds number and is discussed. Finally, authors have explained the significant difference between experimental and theoretical results and a new paradox has been introduced.