Licentiate seminar

Direct numerical simulations of the rotating-disk boundary-layer flow

Defendant Main Advisor Extra Advisor Date
Ellinor Appelquist Philipp Schlatter Henrik Alfredsson 2014-09-03

Christopher Davies, Cardiff University

Evaluation committee


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 are mostly limited to linear instabilities derived from direct numerical simulations (DNS) but with the objective that further work will focus on the nonlinear regime, providing greater insights into the transition route to turbulence.
The numerical code Nek5000 has been chosen for the DNS using a spectral-element method in an effort to reduce spurious effects from low-order discretizations. Large-scale parallel simulations have been used to obtain the present results.
The known similarity solution of the Navier–Stokes equation for the rotating-disk flow, also called the von Karman flow, is investigated and can be reproduced with good accuracy by the DNS. With the addition of small roughnesses on the disk surface, convective instabilities appear and data from the DNS are analysed and compared with experimental and theoretical data. A theoretical analysis is also presented using a local linear-stability approach, where two stability solvers have been developed based on earlier work. A good correspondence between DNS and theory is found and the DNS results are found to explain well the behaviour of the experimental boundary layer within the range of Reynolds numbers for small amplitude (linear) disturbances. The comparison between the DNS and experimental results, presented for the first time here, shows that the DNS allows (for large azimuthal domains) a range of unstable azimuthal wavenumbers ? to exist simultaneously with the dominant ? varying, which is not accounted for in local theory, where ? is usually fixed for each Reynolds number at which the stability analysis is applied.
Furthermore, the linear impulse response of the rotating-disk boundary layer is investigated using DNS. The local response is known to be absolutely unstable. The global response is found to be stable if the edge of the disk is assumed to be at infinity, and unstable if the domain is finite and the edge of the domain is placed such that there is a large enough pocket region for the absolute instability to develop. The global frequency of the flow is found to be determined by the edge Reynolds number.
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