35,847 research outputs found

    On Lagrangian and vortex-surface fields for flows with Taylor–Green and Kida–Pelz initial conditions

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    For a strictly inviscid barotropic flow with conservative body forces, the Helmholtz vorticity theorem shows that material or Lagrangian surfaces which are vortex surfaces at time t = 0 remain so for t > 0. In this study, a systematic methodology is developed for constructing smooth scalar fields φ(x, y, z, t = 0) for Taylor–Green and Kida–Pelz velocity fields, which, at t = 0, satisfy ω·∇φ = 0. We refer to such fields as vortex-surface fields. Then, for some constant C, iso-surfaces φ = C define vortex surfaces. It is shown that, given the vorticity, our definition of a vortex-surface field admits non-uniqueness, and this is presently resolved numerically using an optimization approach. Additionally, relations between vortex-surface fields and the classical Clebsch representation are discussed for flows with zero helicity. Equations describing the evolution of vortex-surface fields are then obtained for both inviscid and viscous incompressible flows. Both uniqueness and the distinction separating the evolution of vortex-surface fields and Lagrangian fields are discussed. By tracking φ as a Lagrangian field in slightly viscous flows, we show that the well-defined evolution of Lagrangian surfaces that are initially vortex surfaces can be a good approximation to vortex surfaces at later times prior to vortex reconnection. In the evolution of such Lagrangian fields, we observe that initially blob-like vortex surfaces are progressively stretched to sheet-like shapes so that neighbouring portions approach each other, with subsequent rolling up of structures near the interface, which reveals more information on dynamics than the iso-surfaces of vorticity magnitude. The non-local geometry in the evolution is quantified by two differential geometry properties. Rolled-up local shapes are found in the Lagrangian structures that were initially vortex surfaces close to the time of vortex reconnection. It is hypothesized that this is related to the formation of the very high vorticity regions

    Adhesion and detachment fluxes of micro-particles from a permeable wall under turbulent flow conditions

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    We report a numerical investigation of the deposition and re-entrainment of Brownian particles from a permeable plane wall. The tangential flow was turbulent. The suspension dynamics were obtained through direct numerical simulation of the Navier–Stokes equations coupled to the Lagrangian tracking of individual particles. Physical phenomena acting on the particles such as flow transport, adhesion, detachment and re-entrainment were considered. Brownian diffusion was accounted for in the trajectory computations by a stochastic model specifically adapted for use in the vicinity of the wall. Interactions between the particles and the wall such as adhesion forces and detachment were modeled. Validations of analytical solutions for simplified cases and comparisons with theoretical predictions are presented as well. Results are discussed focusing on the interplay between the distinct mechanisms occurring in the fouling of filtration devices. Particulate fluxes towards and away from the permeable wall are analyzed under different adhesion strengths

    Roughness effects in turbulent forced convection

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    We conducted direct numerical simulations (DNSs) of turbulent flow over three-dimensional sinusoidal roughness in a channel. A passive scalar is present in the flow with Prandtl number Pr=0.7Pr=0.7, to study heat transfer by forced convection over this rough surface. The minimal channel is used to circumvent the high cost of simulating high Reynolds number flows, which enables a range of rough surfaces to be efficiently simulated. The near-wall temperature profile in the minimal channel agrees well with that of the conventional full-span channel, indicating it can be readily used for heat-transfer studies at a much reduced cost compared to conventional DNS. As the roughness Reynolds number, k+k^+, is increased, the Hama roughness function, ΔU+\Delta U^+, increases in the transitionally rough regime before tending towards the fully rough asymptote of κm1log(k+)+C\kappa_m^{-1}\log(k^+)+C, where CC is a constant that depends on the particular roughness geometry and κm0.4\kappa_m\approx0.4 is the von K\'arm\'an constant. In this fully rough regime, the skin-friction coefficient is constant with bulk Reynolds number, RebRe_b. Meanwhile, the temperature difference between smooth- and rough-wall flows, ΔΘ+\Delta\Theta^+, appears to tend towards a constant value, ΔΘFR+\Delta\Theta^+_{FR}. This corresponds to the Stanton number (the temperature analogue of the skin-friction coefficient) monotonically decreasing with RebRe_b in the fully rough regime. Using shifted logarithmic velocity and temperature profiles, the heat transfer law as described by the Stanton number in the fully rough regime can be derived once both the equivalent sand-grain roughness ks/kk_s/k and the temperature difference ΔΘFR+\Delta \Theta^+_{FR} are known. In meteorology, this corresponds to the ratio of momentum and heat transfer roughness lengths, z0m/z0hz_{0m}/z_{0h}, being linearly proportional to z0m+z_{0m}^+, the momentum roughness length [continued]...Comment: Accepted (In press) in the Journal of Fluid Mechanic

    Coalescence of Liquid Drops: Different Models Versus\ud Experiment

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    The process of coalescence of two identical liquid drops is simulated numerically in the framework of two essentially different mathematical models, and the results are compared with experimental data on the very early stages of the coalescence process reported recently. The first model tested is the ‘conventional’ one, where it is assumed that coalescence as the formation of a single body of fluid occurs by an instant appearance of a liquid bridge smoothly connecting the two drops, and the subsequent process is the evolution of this single body of fluid driven by capillary forces. The second model under investigation considers coalescence as a process where a section of the free surface becomes trapped between the bulk phases as the drops are pressed against each other, and it is the gradual disappearance of this ‘internal interface’ that leads to the formation of a single body of fluid and the conventional model taking over. Using the full numerical solution of the problem in the framework of each of the two models, we show that the recently reported electrical measurements probing the very early stages of the process are better described by the interface formation/disappearance model. New theory-guided experiments are suggested that would help to further elucidate the details of the coalescence phenomenon. As a by-product of our research, the range of validity of different ‘scaling laws’ advanced as approximate solutions to the problem formulated using the conventional model is\ud established

    Drag reduction induced by superhydrophobic surfaces in turbulent pipe flow

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    The drag reduction induced by superhydrophobic surfaces is investigated in a turbulent pipe flow. Wetted superhydrophobic surfaces are shown to trap gas bubbles in their asperities. This stops the liquid from coming in direct contact with the wall in that location, allowing the flow to slip over the air bubbles. We consider a well-defined texture with streamwise grooves at the walls in which the gas is expected to be entrapped. This configuration is modeled with alternating no-slip and shear-free boundary conditions at the wall. With respect to the classical turbulent pipe flow, a substantial drag reduction is observed which strongly depends on the grooves’ dimension and on the solid fraction, i.e., the ratio between the solid wall surface and the total surface of the pipe’s circumference. The drag reduction is due to the mean slip velocity at the wall which increases the flow rate at a fixed pressure drop. The enforced boundary conditions also produce peculiar turbulent structures which on the contrary decrease the flow rate. The two concurrent effects provide an overall flow rate increase as demonstrated by means of the mean axial momentum balance. This equation provides the balance between the mean pressure gradient, the Reynolds stress, the mean flow rate, and the mean slip velocity contribution
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