Spatio-temporal dynamics in pipe flow
Moxey, David C. (2011) Spatio-temporal dynamics in pipe flow. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2585059~S1
When fluid flows through a channel, pipe or duct, there are two basic forms of motion: smooth laminar flow and disordered turbulent motion. The transition between these two states is a fundamental and open problem which has been studied for over 125 years. What has received far less attention are the intermittent dynamics which possess qualities of both turbulent and laminar regimes. The purpose of this thesis is therefore to investigate large-scale intermittent states through extensive numerical simulations in the hopes of further understanding the transition to turbulence in pipe flow. We begin by reviewing the spectral-element code Semtex which is used to perform the simulations. We discuss modifications to this code to impose a constant flowrate to the flow through a pipe and to improve the computational efficiency on certain multicore architectures. We then move on to examine the reverse transition from turbulence to laminar flow in a long, 125 diameter periodic pipe, which unlike the forward transition does not depend on finiteamplitude perturbations to the flow and thus captures the natural dynamics contained within the transition. The Reynolds number Re is reduced from Re = 2,800 to Re = 2,250 over a long timescale, and by investigating the resultant spatio-temporal dynamics we discover that the transition can be characterised by three fundamentally different states separated by two Reynolds numbers. Below Rec <= 2,300, turbulence takes the form of equilibrium puffs which eventually decay. Above Rei = 2,600, flow remains uniformly turbulent throughout the domain. Between these two values, the dynamics are an intermitent mixture of both turbulent and laminar regimes which take the form of unsteady alternating laminar-turbulent bands. Finally, we concentrate on finding a more exact value for Rec, which marks the onset of sustained turbulence in pipe flow. We examine the process through which isolated turbulent puffs split and find that, like decay, this process is stochastic and memoryless. By drawing comparisons with other simple stochastically driven systems – in particular, directed percolation – we compare the timescales for decay and splitting, and ascertain that Rec = 2,040 +- 10.
|Item Type:||Thesis or Dissertation (PhD)|
|Subjects:||Q Science > QA Mathematics|
|Library of Congress Subject Headings (LCSH):||Tubes -- Fluid dynamics, Multiphase flow, Turbulence|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute|
|Sponsors:||Engineering and Physical Sciences Research Council (EPSRC)|
|Extent:||xiii, 147 leaves : illustrations, charts|
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