In a recent experiment Paoletti [Phys. Rev. Lett. 101, 154501 (2008)]10.1103/PhysRevLett.101.154501 monitored the motion of tracer particles in turbulent superfluid helium and inferred that the velocity components do not obey the Gaussian statistics observed in ordinary turbulence. Motivated by their experiment, we create a small 3D turbulent state in an atomic Bose-Einstein condensate, compute directly the velocity field, and find similar nonclassical power-law tails. We obtain similar results in 2D trapped and 3D homogeneous condensates, and in classical 2D vortex points systems. This suggests that non-Gaussian turbulent velocity statistics describe a fundamental property of quantum turbulence. We also track the decay of the vortex tangle in the presence of the thermal cloud.

Turbulent combustion of mono-disperse droplet-mist has been analysed based on three-dimensional Direct Numerical Simulations (DNS) in canonical configuration under decaying turbulence for a range of different values of droplet equivalence ratio (φ d ), droplet diameter (a d ) and root-mean-square value of turbulent velocity (u ). The fuel is supplied in liquid phase and the evaporation of droplets gives rise to gaseous fuel for the flame propagation into the droplet-mist. It has been found that initial droplet diameter, turbulence intensity and droplet equivalence ratio can have significant influences on the volume-integrated burning rate, flame surface area and burning rate per unit area. The droplets are found to evaporate predominantly in the preheat zone, but some droplets penetrate the flame front, reaching the burned gas side where they evaporate and some of the resulting fuel vapour diffuses back towards the flame front. The combustion process in gaseous phase takes place predominantly in fuel-lean mode even for φ d > 1. The probability of finding fuel-lean mixture increases with increasing initial droplet diameter because of slower evaporation of larger droplets and this predominantly fuel-lean mode of combustion exhibits the attributes of low Damköhler number combustion and gives rise to thickening of flame with increasing droplet diameter. The chemical reaction is found to take place under both premixed and non-premixed modes of combustion and the relative contribution of non-premixed combustion to overall heat release increases with increasing droplet size. Combust (2016) 96:573-607 of the flame propagation and mode of combustion have been analysed in detail and detailed physical explanations have been provided for the observed behaviour.

Three-dimensional Direct Numerical Simulations (DNS) in canonical configuration have been employed to study the combustion of mono-disperse droplet-mist under turbulent flow conditions. A parametric study has been performed for a range of values of droplet equivalence ratio φ d , droplet diameter a d and root-mean-square value of turbulent velocity u . The fuel is supplied entirely in liquid phase such that the evaporation of the droplets gives rise to gaseous fuel which then facilitates flame propagation into the dropletmist. The combustion process in gaseous phase takes place predominantly in fuel-lean mode even for φ d > 1. The probability of finding fuel-lean mixture increases with increasing initial droplet diameter because of slower evaporation of larger droplets. The chemical reaction is found to take place under both premixed and non-premixed modes of combustion: the premixed mode ocurring mainly under fuel-lean conditions and the non-premixed mode under stoichiometric or fuel-rich conditions. The prevalence of premixed combustion was seen to decrease with increasing droplet size. Furthermore, droplet-fuelled turbulent flames have been found to be thicker than the corresponding turbulent stoichiometric premixed flames and this thickening increases with increasing droplet diameter. The flame thickening in droplet cases has been explained in terms of normal strain rate induced by fluid motion and due to flame normal propagation arising from different components of displacement speed. The statistical behaviours of the effective normal strain rate and flame stretching have been analysed in detail and detailed physical explanations have been provided for the observed behaviour. It has been found that the droplet cases show higher probability of finding positive effective normal strain rate (i.e. combined contribution of fluid motion and flame propagation), and negative values of stretch rate than in the stoichiometric premixed flame under similar flow conditions, which are responsible for higher flame thickness and smaller flame area generation in droplet cases.

The distributions of flow topologies within the flames representing the corrugated flamelets, thin reaction zones, and broken reaction zone regimes of premixed turbulent combustion are investigated using direct numerical simulation data of statistically planar turbulent H 2 -air flames with an equivalence ratio φ = 0.7. It was found that the diminishing influence of dilatation rate with increasing Karlovitz number has significant influences on the statistical behaviors of the first, second, and third invariants (i.e., P , Q, and R) of the velocity gradient tensor. These differences are reflected in the distributions of the flow topologies within the flames considered in this analysis. This has important consequences for those topologies that make dominant contributions to the scalar-turbulence interaction and vortexstretching terms in the scalar dissipation rate and enstrophy transport equations, respectively. Detailed physical explanations are provided for the observed regime dependences of the flow topologies and their implications on the scalar dissipation rate and enstrophy transport.

Enstrophy is an intrinsic feature of turbulent flows, and its transport properties are essential for the understanding of premixed flame-turbulence interaction. The interrelation between the enstrophy transport and flow topologies, which can be assigned to eight categories based on the three invariants of the velocity-gradient tensor, has been analysed here. The enstrophy transport conditional on flow topologies in turbulent premixed flames has been analysed using a Direct Numerical Simulation database representing the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) combustion regimes. The flame in the CF regime exhibits considerable flame-generated enstrophy, and the dilatation rate and baroclinic torque contributions to the enstrophy transport act as leading order sink and source terms, respectively. Consequently, flow topologies associated with positive dilatation rate values, contribute significantly to the enstrophy transport in the CF regime. By contrast, enstrophy decreases from the unburned to the burned gas side for the cases representing the TRZ and BRZ regimes, with diminishing influences of dilatation rate and baroclinic torque. The enstrophy transport in the TRZ and BRZ regimes is governed by the vortex-stretching and viscous dissipation contributions, similar to non-reacting flows, and topologies existing for all values of dilatation rate remain significant contributors.

Motivated by experiments performed in superfluid helium, we study numerically the motion of toroidal bundles of vortex filaments in an inviscid fluid. We find that the evolution of these large-scale vortex structures involves the generalised leapfrogging of the constituent vortex rings. Despite three dimensional perturbations in the form of Kelvin waves and vortex reconnections, toroidal vortex bundles retain their coherence over a relatively large distance (compared to their size), in agreement with experimental observations.Comment: 22 pages, 12 figure

Superfluid helium consists of two inter-penetrating fluids, a viscous normal fluid and an inviscid superfluid, coupled by a mutual friction. We develop a two-fluid shell model to study superfluid turbulence. We investigate the energy spectra and the balance of fluxes between the two fluids as a function of temperature in continuously forced turbulence, and, in the absence of forcing, the decay of turbulence. We furthermore investigate deviations from the k −5/3 spectrum caused by the mutual friction force. We compare our results with experiments and existing calculations.We find that, at sufficiently low temperatures a build-up of energy develops at high wavenumbers suggesting the need for a further dissipative effect, such as the Kelvin wave cascade and phonon emission.

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