Lock-in and quasiperiodicity in a forced hydrodynamically self-excited jet

The ability of hydrodynamically self-excited jets to lock into strong external forcing is well known. Their dynamics before lock-in and the specific bifurcations through which they lock in, however, are less well known. In this experimental study, we acoustically force a low-density jet around its natural global frequency. We examine its response leading up to lock-in and compare this to that of a forced van der Pol oscillator. We find that, when forced at increasing amplitudes, the jet undergoes a sequence of two nonlinear transitions: (i) from periodicity to T{double-struck}2 quasiperiodicity via a torus-birth bifurcation; and then (ii) from T{double-struck}2 quasiperiodicity to 1:1 lock-in via either a saddle-node bifurcation with frequency pulling, if the forcing and natural frequencies are close together, or a torus-death bifurcation without frequency pulling, but with a gradual suppression of the natural mode, if the two frequencies are far apart. We also find that the jet locks in most readily when forced close to its natural frequency, but that the details contain two asymmetries: the jet (i) locks in more readily and (ii) oscillates more strongly when it is forced below its natural frequency than when it is forced above it. Except for the second asymmetry, all of these transitions, bifurcations and dynamics are accurately reproduced by the forced van der Pol oscillator. This shows that this complex (infinite-dimensional) forced self-excited jet can be modelled reasonably well as a simple (three-dimensional) forced self-excited oscillator. This result adds to the growing evidence that open self-excited flows behave essentially like low-dimensional nonlinear dynamical systems. It also strengthens the universality of such flows, raising the possibility that more of them, including some industrially relevant flames, can be similarly modelled. © 2013 Cambridge University Press.

Inkjet printing of weakly elastic polymer solutions

Fluid assessment methods, requiring small volumes and avoiding the need for jetting, are particularly useful in the design of functional fluids for inkjet printing applications. With the increasing use of complex (rather than Newtonian) fluids for manufacturing, single frequency fluid characterisation cannot reliably predict good jetting behaviour, owing to the range of shearing and extensional flow rates involved. However, the scope of inkjet fluid assessments (beyond achievement of a nominal viscosity within the print head design specification) is usually focused on the final application rather than the jetting processes. The experimental demonstration of the clear insufficiency of such approaches shows that fluid jetting can readily discriminate between fluids assessed as having similar LVE characterisation (within a factor of 2) for typical commercial rheometer measurements at shearing rates reaching 104rads-1.Jetting behaviour of weakly elastic dilute linear polystyrene solutions, for molecular weights of 110-488. kDa, recorded using high speed video was compared with recent results from numerical modelling and capillary thinning studies of the same solutions.The jetting images show behaviour ranging from near-Newtonian to "beads-on-a-string". The inkjet printing behaviour does not correlate simply with the measured extensional relaxation times or Zimm times, but may be consistent with non-linear extensibility L and the production of fully extended polymer molecules in the thinning jet ligament.Fluid test methods allowing a more complete characterisation of NLVE parameters are needed to assess inkjet printing feasibility prior to directly jetting complex fluids. At the present time, directly jetting such fluids may prove to be the only alternative. © 2014 The Authors.

On the laminar-turbulent transition of the rotating-disk flow: The role of absolute instability

© 2014 Cambridge University Press. This paper describes a detailed experimental study using hot-wire anemometry of the laminar-turbulent transition region of a rotating-disk boundary-layer flow without any imposed excitation of the boundary layer. The measured data are separated into stationary and unsteady disturbance fields in order to elaborate on the roles that the stationary and the travelling modes have in the transition process. We show the onset of nonlinearity consistently at Reynolds numbers, R, of ∼ 510, i.e. at the onset of Lingwood's (J. Fluid Mech., vol. 299, 1995, pp. 17-33) local absolute instability, and the growth of stationary vortices saturates at a Reynolds number of ∼ 550. The nonlinear saturation and subsequent turbulent breakdown of individual stationary vortices independently of their amplitudes, which vary azimuthally, seem to be determined by well-defined Reynolds numbers. We identify unstable travelling disturbances in our power spectra, which continue to grow, saturating at around R=585, whereupon turbulent breakdown of the boundary layer ensues. The nonlinear saturation amplitude of the total disturbance field is approximately constant for all considered cases, i.e. different rotation rates and edge Reynolds numbers. We also identify a travelling secondary instability. Our results suggest that it is the travelling disturbances that are fundamentally important to the transition to turbulence for a clean disk, rather than the stationary vortices. Here, the results appear to show a primary nonlinear steep-fronted (travelling) global mode at the boundary between the local convectively and absolutely unstable regions, which develops nonlinearly interacting with the stationary vortices and which saturates and is unstable to a secondary instability. This leads to a rapid transition to turbulence outward of the primary front from approximately R=565 to 590 and to a fully turbulent boundary layer above 650.

A comparison of winter pre-heating requirements for natural displacement and natural mixing ventilation

In winter, natural ventilation can be achieved either through mixing ventilation or upward displacement ventilation (P.F. Linden, The fluid mechanics of natural ventilation, Annual Review of Fluid Mechanics 31 (1999) pp. 201-238). We show there is a significant energy saving possible by using mixing ventilation, in the case that the internal heat gains are significant, and illustrate these savings using an idealized model, which predicts that with internal heat gains of order 0.1 kW per person, mixing ventilation uses of a fraction of order 0.2-0.4 of the heat load of displacement ventilation assuming a well-insulated building. We then describe a strategy for such mixing natural ventilation in an atrium style building in which the rooms surrounding the atrium are able to vent directly to the exterior and also through the atrium to the exterior. The results are motivated by the desire to reduce the energy burden in large public buildings such as hospitals, schools or office buildings centred on atria. We illustrate a strategy for the natural mixing ventilation in order that the rooms surrounding the atrium receive both pre-heated but also sufficiently fresh air, while the central atrium zone remains warm. We test the principles with some laboratory experiments in which a model air chamber is ventilated using both mixing and displacement ventilation, and compare the energy loads in each case. We conclude with a discussion of the potential applications of the approach within the context of open plan atria type office buildings.