4 results
Surface gravity wave-induced drift of floating objects in the diffraction regime
- Q. Xiao, R. Calvert, S.Q. Yan, T.A.A. Adcock, T.S. van den Bremer
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- Journal:
- Journal of Fluid Mechanics / Volume 980 / 10 February 2024
- Published online by Cambridge University Press:
- 01 February 2024, A27
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Floating objects will drift due to the action of surface gravity waves. This drift will depart from that of a perfect Lagrangian tracer due to both viscous effects (non-potential flow) and wave–body interaction (potential flow). We examine the drift of freely floating objects in regular (non-breaking) deep-water wave fields for object sizes that are large enough to cause significant diffraction. Systematic numerical simulations are performed using a hybrid numerical solver, qaleFOAM, which deals with both viscosity and wave–body interaction. For very small objects, the model predicts a wave-induced drift equal to the Stokes drift. For larger objects, the drift is generally greater and increases with object size (we examine object sizes up to $10\,\%$ of the wavelength). The effects of different shapes, sizes and submergence depths and steepnesses are examined. Furthermore, we derive a ‘diffraction-modified Stokes drift’ akin to Stokes (Trans. Camb. Phil. Soc., vol. 8, 1847, pp. 411–455), but based on the combination of incident, diffracted and radiated wave fields, which are based on potential-flow theory and obtained using the boundary element method. This diffraction-modified Stokes drift explains both qualitatively and quantitatively the increase in drift. Generally, round objects do not diffract the wave field significantly and do not experience a significant drift enhancement as a result. For box-shape objects, drift enhancement is greater for larger objects with greater submergence depths (we report an increase of $92\,\%$ for simulations without viscosity and $113\,\%$ with viscosity for a round-cornered box whose size is $10\,\%$ of the wavelength). We identify the specific standing wave pattern that arises near the object because of diffraction as the main cause of the enhanced drift. Viscosity plays a small positive role in the enhanced drift behaviour of large objects, increasing the drift further by approximately $20\,\%$.
Bag film breakup of droplets in uniform airflows
- K. Tang, T.A.A. Adcock, W. Mostert
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- Journal:
- Journal of Fluid Mechanics / Volume 970 / 10 September 2023
- Published online by Cambridge University Press:
- 29 August 2023, A9
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We present novel numerical simulations investigating the bag breakup of liquid droplets. We first examine the viscous effect on the early-time drop deformation, comparing with theory and experiment. Next, a bag film forms at late time and is susceptible to spurious mesh-induced breakup in numerical simulations, which has prevented previous studies from reaching grid convergence of fragment statistics. We therefore adopt the manifold death (MD) algorithm which artificially perforates thin films once they reach a prescribed critical thickness independent of the grid size, controlled by a numerical parameter $L_{sig}$. We show grid convergence of fragment statistics when utilising the MD algorithm, and analyse the fragment behaviour and bag film disintegration mechanisms including ligament breakup, node detachment and rim destabilisation. Our choice of the critical thickness parameter $L_{sig}$ is limited by numerical constraints and thus has not been matched to experiment or theory; consequently, the current simulations yield critical bag film perforation thicknesses larger than experimentally observed. The influence of the MD algorithm configuration on the bag breakup phenomena and statistics will be investigated in future work. We also study the effects of moderate liquid Ohnesorge number ($0.005 \leqslant Oh \leqslant 0.05$) on the bag breakup process and fragment statistics, where a non-monotonic dependency of the average diameter of bag film fragments on $Oh$ is found. These results highlight the utility of the MD algorithm in multiphase simulations involving topological changes, and pave the way for physics-based numerical investigations into spume generation at the air–sea interface.
Wave breaking and jet formation on axisymmetric surface gravity waves
- M.L. McAllister, S. Draycott, T. Davey, Y. Yang, T.A.A. Adcock, S. Liao, T.S. van den Bremer
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- Journal:
- Journal of Fluid Mechanics / Volume 935 / 25 March 2022
- Published online by Cambridge University Press:
- 25 January 2022, A5
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Axisymmetric standing waves occur across a wide range of free surface flows. When these waves reach a critical height (steepness), wave breaking and jet formation occur. For travelling surface gravity waves, wave breaking is generally considered to limit wave height and reversible wave motion. In the ocean, the behaviour of directionally spread waves lies between the limits of purely travelling (two dimensions) and axisymmetric (three dimensions). Hence, understanding wave breaking and jet formation on axisymmetric surface gravity waves is an important step in understanding extreme and breaking waves in the ocean. We examine an example of axisymmetric wave breaking and jet formation colloquially known as the ‘spike wave’, created in the FloWave circular wave tank at the University of Edinburgh, UK. We generate this spike wave with maximum crest amplitudes of 0.15–6.0 m (0.024–0.98 when made non-dimensional by characteristic radius), with wave breaking occurring for crest amplitudes greater than 1.0 m (0.16 non-dimensionalised). Unlike two-dimensional travelling waves, wave breaking does not limit maximum crest amplitude, and our measurements approximately follow the jet height scaling proposed by Ghabache et al. (J. Fluid Mech., vol. 761, 2014, pp. 206–219) for cavity collapse. The spike wave is predominantly created by linear dispersive focusing. A trough forms, then collapses producing a jet, which is sensitive to the trough's shape. The evolution of the jets that form in our experiments is predicted well by the hyperbolic jet model proposed by Longuet–Higgins (J. Fluid Mech., vol. 127, 1983, pp. 103–121), previously applied to jets forming on bubbles.
Fractal-like actuator disc theory for optimal energy extraction
- D. Dehtyriov, A.M. Schnabl, C.R. Vogel, S. Draper, T.A.A. Adcock, R.H.J. Willden
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- Journal:
- Journal of Fluid Mechanics / Volume 927 / 25 November 2021
- Published online by Cambridge University Press:
- 30 September 2021, A40
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The limit of power extraction by a device which makes use of constructive interference, i.e. local blockage, is investigated theoretically. The device is modelled using actuator disc theory in which we allow the device to be split into arrays and these then into sub-arrays an arbitrary number of times so as to construct an $n$-level multi-scale device in which the original device undergoes $n-1$ sub-divisions. The alternative physical interpretation of the problem is a planar system of arrayed turbines in which groups of turbines are homogeneously arrayed at the smallest $n\mathrm {th}$ scale, and then these groups are homogeneously spaced relative to each other at the next smallest $n-1\mathrm {th}$ scale, with this pattern repeating at all subsequent larger scales. The scale-separation idea of Nishino & Willden (J. Fluid. Mech., vol. 708, 2012b, pp. 596–606) is employed, which assumes mixing within a sub-array occurs faster than mixing of the by-pass flow around that sub-array, so that in the $n$-scale device mixing occurs from the inner scale to the outermost scale in that order. We investigate the behaviour of an arbitrary level multi-scale device, and determine the arrangement of actuator discs ($n\mathrm {th}$ level devices) which maximises the power coefficient (ratio of power extracted to undisturbed kinetic energy flux through the net disc frontal area). We find that this optimal arrangement is close to fractal, and fractal arrangements give similar results. With the device placed in an infinitely wide channel, i.e. zero global blockage, we find that the optimum power coefficient tends to unity as the number of device scales tends to infinity, a 27/16 increase over the Lanchester–Betz limit of $0.593$. For devices in finite width channels, i.e. non-zero global blockage, similar observations can be made with further uplift in the maximum power coefficient. We discuss the fluid mechanics of this energy extraction process and examine the scale distribution of thrust and wake velocity coefficients. Numerical demonstration of performance uplift due to multi-scale dynamics is also provided. We demonstrate that bypass flow remixing and ensuing energy losses increase the device power coefficient above the limits for single devices, so that although the power coefficient can be made to increase, this is at the expense of the overall efficiency of energy extraction which decreases as wake-scale remixing losses necessarily rise. For multi-scale devices in finite overall blockage two effects act to increase extractable power; an overall streamwise pressure gradient associated with finite blockage, and wake pressure recoveries associated with bypass-scale remixing.