Rotating disks and cones a centennial of von Kármán’s 1921 paper

Abstract

It is now more than 100 years since the work of von Kármán (1921) on the boundary-layer flow over a rotating disk was published in the first volume of Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM, Vol. 1(4), pp 233-252). Recently, there has been a large amount of work undertaken addressing the instability and transition of the boundary-layer flows over rotating disks and cones using theoretical, numerical and experimental techniques. Here we will discuss some different methods to analyze experimental data that can give insight into the instability and transition to turbulence of boundary-layer flows over rotating slender and broad cones (including the disk). At first, we discuss the pdf-method (probability density function) that allows a simple way to determine regions of instability growth, transition and fully developed turbulence. Secondly, we look at various ways to use spectral information to investigate the boundary layers giving a deeper understanding of the transition process. Finally, a method to determine the most probable flow structure leading up to fully developed turbulence is discussed. We envisage that some of these methods can be useful in analyzing instability and transition also in other flow cases.

Keywords

• slender cones
• broad cones
• cross-flow instability
• centrifugal instability
• pdf-plot
• spectral plot
• flow-structure reconstruction