4 results
The turbulent bubble break-up cascade. Part 2. Numerical simulations of breaking waves
- Wai Hong Ronald Chan, Perry L. Johnson, Parviz Moin, Javier Urzay
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- Journal:
- Journal of Fluid Mechanics / Volume 912 / 10 April 2021
- Published online by Cambridge University Press:
- 16 February 2021, A43
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Breaking waves generate a distribution of bubble sizes that evolves over time. Knowledge of how this distribution evolves is of practical importance for maritime and climate studies. The analytical framework developed in Part 1 (Chan, Johnson & Moin, J. Fluid Mech., vol. 912, 2021, A42) examined how this evolution is governed by the bubble-mass flux from large- to small-bubble sizes which depends on the rate of break-up events and the distribution of child bubble sizes. These statistics are measured in Part 2 as ensemble-averaged functions of time by simulating ensembles of breaking waves, and identifying and tracking individual bubbles and their break-up events. The large-scale break-up dynamics is seen to be statistically unsteady, and two intervals with distinct characteristics were identified. In the first interval, the dissipation rate and bubble-mass flux are quasi-steady, and the theoretical analysis of Part 1 is supported by all observed statistics, including the expected $-10/3$ power-law exponent for the super-Hinze-scale size distribution. Strong locality is observed in the corresponding bubble-mass flux, supporting the presence of a super-Hinze-scale break-up cascade. In the second interval, the dissipation rate decays, and the bubble-mass flux increases as small- and intermediate-sized bubbles become more populous. This flux remains strongly local with cascade-like behaviour, but the dominant power-law exponent for the size distribution increases to $-8/3$ as small bubbles are also depleted more quickly. This suggests the emergence of different physical mechanisms during different phases of the breaking-wave evolution, although size-local break-up remains a dominant theme. Parts 1 and 2 present an analytical toolkit for population balance analysis in two-phase flows.
Shock-induced heating and transition to turbulence in a hypersonic boundary layer
- Lin Fu, Michael Karp, Sanjeeb T. Bose, Parviz Moin, Javier Urzay
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- Journal:
- Journal of Fluid Mechanics / Volume 909 / 25 February 2021
- Published online by Cambridge University Press:
- 21 December 2020, A8
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The interaction between an incident shock wave and a Mach-6 undisturbed hypersonic laminar boundary layer over a cold wall is addressed using direct numerical simulations (DNS) and wall-modelled large-eddy simulations (WMLES) at different angles of incidence. At sufficiently high shock-incidence angles, the boundary layer transitions to turbulence via breakdown of near-wall streaks shortly downstream of the shock impingement, without the need of any inflow free-stream disturbances. The transition causes a localized significant increase in the Stanton number and skin-friction coefficient, with high incidence angles augmenting the peak thermomechanical loads in an approximately linear way. Statistical analyses of the boundary layer downstream of the interaction for each case are provided that quantify streamwise spatial variations of the Reynolds analogy factors and indicate a breakdown of the Morkovin's hypothesis near the wall, where velocity and temperature become correlated. A modified strong Reynolds analogy with a fixed turbulent Prandtl number is observed to perform best. Conventional transformations fail at collapsing the mean velocity profiles on the incompressible log law. The WMLES prompts transition and peak heating, delays separation and advances reattachment, thereby shortening the separation bubble. When the shock leads to transition, WMLES provides predictions of DNS peak thermomechanical loads within $\pm 10\,\%$ at a computational cost lower than DNS by two orders of magnitude. Downstream of the interaction, in the turbulent boundary layer, the WMLES agrees well with DNS results for the Reynolds analogy factor, the mean profiles of velocity and temperature, including the temperature peak, and the temperature/velocity correlation.
Diffusion-flame ignition by shock-wave impingement on a supersonic mixing layer
- César Huete, Antonio L. Sánchez, Forman A. Williams, Javier Urzay
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- Journal:
- Journal of Fluid Mechanics / Volume 784 / 10 December 2015
- Published online by Cambridge University Press:
- 30 October 2015, pp. 74-108
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Ignition in a supersonic mixing layer interacting with an oblique shock wave is investigated analytically and numerically under conditions such that the post-shock flow remains supersonic. The study requires consideration of the structure of the post-shock ignition kernel that is found to exist around the point of maximum temperature, which may be located either near the edge of the mixing layer or in its interior, depending on the profiles of the fuel concentration, temperature and Mach number across the mixing layer. The ignition kernel displays a balance between the rates of chemical reaction and of post-shock flow expansion, including the acoustic interactions of the chemical heat release with the shock wave, leading to increased front curvature. The analysis, which adopts a one-step chemistry model with large activation energy, indicates that ignition develops as a fold bifurcation, the turning point in the diagram of the peak perturbation induced by the chemical reaction as a function of the Damköhler number providing the critical conditions for ignition. While an explicit formula for the critical Damköhler number for ignition is derived when ignition occurs in the interior of the mixing layer, under which condition the ignition kernel is narrow in the streamwise direction, numerical integration is required for determining ignition when it occurs at the edge, under which condition the kernel is no longer slender. Subsequent to ignition, for the Arrhenius chemistry addressed, the lead shock will rapidly be transformed into a thin detonation on the fuel side of the ignition kernel, and, under suitable conditions, a deflagration may extend far downstream, along with the diffusion flame that must separate the rich and lean reaction products. The results can be helpful in describing supersonic combustion for high-speed propulsion.
Asymptotic theory of the elastohydrodynamic adhesion and gliding motion of a solid particle over soft and sticky substrates at low Reynolds numbers
- JAVIER URZAY
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- Journal:
- Journal of Fluid Mechanics / Volume 653 / 25 June 2010
- Published online by Cambridge University Press:
- 05 May 2010, pp. 391-429
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This analysis makes use of asymptotic analyses and numerical methods to address, in the limit of small Reynolds and ionic Péclet numbers and small clearances, the canonical problem of the forces exerted on a small solid spherical particle undergoing slow translation and rotation in an incompressible fluid moving parallel to an elastic substrate, subject to electric double-layer and van der Waals intermolecular forces, as a representative example of particle gliding and the idealized swimming dynamics of more complex bodies near soft and sticky surfaces in a physiological solvent. The competition of the hydrodynamic, intermolecular and surface-deformation effects induces a lift force, and drag-force and drift-force perturbations, which do not scale linearly with the velocities, and produce a non-additivity of the intermolecular effects by reducing the intensity of the repulsive forces and by increasing the intensity of the attractive forces. The lift force enhances a reversible elastohydrodynamic adhesion regime in both ionized and deionized solvents, in which lateral motion and lift-off from the substrate can occur. An irreversible elastohydrodynamic adhesion regime, produced by elastic instabilities in the form of surface bifurcations in the substrate, is found to exist for both positive and negative lift forces and is enhanced by small gliding velocities and large substrate compliances, for which critical thresholds are calculated for both ionized and deionized solvents. Elastohydrodynamic corrections are derived for the critical coagulation concentration of electrolyte predicted by the Derjaguin–Landau–Verwey–Overbeek (DLVO) standard theory of colloid stabilization. The corrected DLVO critical concentration is unable to describe the adhesion process when the substrate is sufficiently compliant or when the solvent is deionized. These effects may have consequences on the lateral motility and adhesion of small particles and swimming micro-organisms to soft and sticky substrates, in which the reversible or irreversible character of the adhesion process may be influenced not only by the solvent ionic strength, as described by the DLVO theory, but also by the motion kinematics and the substrate mechanical properties.