

	Mekanik In English

Doktorsdisputation

The rotating-disk boundary-layer flow studied through numerical simulations


Respondent	Huvudhandledare	Bihandledare	Datum
Ellinor Appelquist	Philipp Schlatter	Henrik Alfredsson & Rebecca Lingwood	2017-02-24

Opponent
Benoît Pier, École centrale de Lyon

Betygsnämd

Abstract

This thesis deals with the instabilities of the incompressible boundary-layer flow that is induced by a disk rotating in otherwise still fluid. The results presented include both work in the linear and nonlinear regime and are derived from direct numerical simulations (DNS). Comparisons are made both to theoretical and experimental results providing new insights into the transition route to turbulence. The simulation code Nek5000 has been chosen for the DNS using a spectral-element method (SEM) with a high-order discretization, and the results were obtained through large-scale parallel simulations. The known similarity solution of the Navier--Stokes equations for the rotating-disk flow, also called the von Kármán rotating-disk flow, is reproduced by the DNS. With the addition of modelled small simulated roughnesses on the disk surface, convective instabilities appear and data from the linear region in the DNS are analysed and compared with experimental and theoretical data, all corresponding very well. A theoretical analysis is also presented using a local linear-stability approach, where two stability solvers have been developed based on earlier work. Furthermore, the impulse response of the rotating-disk boundary layer is investigated using DNS. The local response is known to be absolutely unstable and the global response, on the contrary, is stable if the edge of the disk is assumed to be at radius infinity. Here comparisons with a finite domain using various boundary conditions give a global behaviour that can be both linearly stable and unstable, however always nonlinearly unstable. The global frequency of the flow is found to be determined by the Reynolds number at the confinement of the domain, either by the edge (linear case) or by the turbulence appearance (nonlinear case). Moreover, secondary instabilities on top of the convective instabilities induced by roughness elements were investigated and found to be globally unstable. This behaviour agrees well with the experimental flow and acts at a smaller radial distance than the primary global instability. The sharp line corresponding to transition to turbulence seen in experiments of the rotating disk can thus be explained by the secondary global instability. Finally, turbulence data were compared with experiments and investigated thoroughly.