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Direct numerical simulations of the rotating-disk boundary-layer flow
KTH, School of Engineering Sciences (SCI), Mechanics.
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

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 developedbased 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 β to exist simultaneously with the dominantβ varying, which is not accounted for in local theory, where β 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.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. , viii, 30 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2014:17
Keyword [en]
Fluid mechanics, boundary layer, rotating disk, laminar-turbulent transition, convective instability, absolute instability, secondary instability, crossflow instability, direct numerical simulations
National Category
Engineering and Technology
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-146087ISBN: 978-91-7595-202-4 (print)OAI: oai:DiVA.org:kth-146087DiVA: diva2:722222
Presentation
2014-09-03, Faxen, Teknikringen 8, KTH, Stoockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20140708

Available from: 2014-07-08 Created: 2014-06-05 Last updated: 2014-07-08Bibliographically approved
List of papers
1. Global linear instability and the radial boundary of the rotating-disk flow
Open this publication in new window or tab >>Global linear instability and the radial boundary of the rotating-disk flow
(English)Manuscript (preprint) (Other academic)
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-146877 (URN)
Note

QS 2014

Available from: 2014-06-17 Created: 2014-06-17 Last updated: 2014-07-08Bibliographically approved
2. Simulating the linear behaviour of the flow over a rotating disk due to roughness elements
Open this publication in new window or tab >>Simulating the linear behaviour of the flow over a rotating disk due to roughness elements
Show others...
2014 (English)Report (Other academic)
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-146879 (URN)
Note

QC 20140617

Available from: 2014-06-17 Created: 2014-06-17 Last updated: 2014-07-08Bibliographically approved
3. Simulating the laminar von Karman flow in Nek5000
Open this publication in new window or tab >>Simulating the laminar von Karman flow in Nek5000
2014 (English)Report (Other academic)
Abstract [en]

The laminar incompressible boundary layer over a rotating disk, also called the von Karman flow, is investigated. The goal is to set up a direct numericalsimulation (DNS) environment for further use to investigate the transition from laminar to turbulent flow for this boundary layer. For this the spectral-element code Nek5000 is used. A set of ODE-equations are first derived from the incompressible cylindrical Navier–Stokes equations, which are solved for the exact von Karman solution. Further, Nek5000 is prepared to solve for the same laminar solution. Comparing the two solutions give a quantification of the accuracy of the DNS solver Nek5000. Different scalings of the equations are investigated, together with quantifications of how good the different available boundary conditions are, also investigating different reference frames and grid dependency of the solution. The general conclusion is that the von K ́rm ́na aflow is possible to simulate in Nek5000. The method was robust when it cameto using different scalings, reference frames and resolutions.

Keyword
Fluid mechanics, boundary layer, rotating disk
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-146080 (URN)
Note

QC 20140617

Available from: 2014-06-05 Created: 2014-06-05 Last updated: 2014-07-08Bibliographically approved
4. Revisiting the stability analysis of the flow over a rotating disk
Open this publication in new window or tab >>Revisiting the stability analysis of the flow over a rotating disk
2014 (English)Report (Other academic)
Abstract [en]

Local linear stability analysis applied to the rotating-disk flow is discussed.This flow case is an exact similarity solution to the cylindrical incompressibleNavier–Stokes equations also called the von Karman flow. The laminar mean velocity profiles are obtained by solving the resulting ordinary differential equa-tions assuming the flow is axisymmetric and time independent. Two stability-analyses methods are used to investigate the local linear stability of this flow: i)the ‘shooting method’; and ii) the ‘Chebyshev polynomial method’. This the-oretical investigation focuses on convectively unstable disturbances. Resultsobtained from the two methods are compared and the methods are shown togive similar results. These theoretical results are also compared with directnumerical simulations and experimental results showing good agreement.

Publisher
128 p.
Keyword
Fluid mechanics, boundary layer, rotating disk, laminar-turbulent transition
National Category
Mechanical Engineering
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-146079 (URN)
Note

QC 20140617

Available from: 2014-06-05 Created: 2014-06-05 Last updated: 2017-02-03Bibliographically approved

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