A sub-grid air entrainment model for breaking bow waves and naval surface ships

Moraga, Francisco; Carrica, Pablo M.; Drew, Donald A.; Lahey, R.T.

doi:10.1016/j.compfluid.2007.06.003

Cited by 52 publications

(54 citation statements)

References 35 publications

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“…Herep is filtered pressure which is identical in phases following the neglect of interfacial surface tension, B b k is the source for the kth bubble group due to air entrainment and S b k is the intergroup mass transfer which only accounts for bubble breakup in the present study (Moraga et al 2008, Ma et al 2011. The bubble breakup model proposed by Martínez-Bazán et al (1999a,b, 2010 …”

Section: The Filtered Two-fluid Equationsmentioning

confidence: 99%

“…In the continuous type models, instead, the interface between an individual bubble and the liquid is not resolved, and the interfacial momentum transfers are considered using the closure models. A critical issue in this approach, especially under breaking waves, is accurately introducing air bubbles into a model using a bubble entrainment formulation (Moraga et al 2008, Shi et al 2010, Ma et al 2011.…”

Section: Introductionmentioning

confidence: 99%

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Bubble entrainment and liquid–bubble interaction under unsteady breaking waves

Derakhti

Kirby

2014

J. Fluid Mech.

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Liquid–bubble interaction, especially in complex two-phase bubbly flow under breaking waves, is still poorly understood. In the present study, we perform a large-eddy simulation using a Navier–Stokes solver extended to incorporate entrained bubble populations, using an Eulerian–Eulerian formulation for a polydisperse bubble phase. The volume-of-fluid method is used for free-surface tracking. We consider an isolated unsteady deep water breaking event generated by a focused wavepacket. Bubble contributions to dissipation and momentum transfer between the water and air phases are considered. The model is shown to predict free-surface evolution, mean and turbulent velocities, and integral properties of the entrained dispersed bubbles fairly well. We investigate turbulence modulation by dispersed bubbles as well as shear- and bubble-induced dissipation, in both spilling and plunging breakers. We find that the total bubble-induced dissipation accounts for more than 50 % of the total dissipation in the breaking region. The average dissipation rate per unit length of breaking crest is usually written as $b{\it\rho}g^{-1}c_{b}^{5}$, where ${\it\rho}$ is the water density, $g$ is the gravitational acceleration and $c_{b}$ is the phase speed of the breaking wave. The breaking parameter, $b$, has been poorly constrained by experiments and field measurements. We examine the time-dependent evolution of $b$ for both constant-steepness and constant-amplitude wavepackets. A scaling law for the averaged breaking parameter is obtained. The exact two-phase transport equation for turbulent kinetic energy (TKE) is compared with the conventional single-phase transport equation, and it is found that the former overpredicts the total subgrid-scale dissipation and turbulence production by mean shear during active breaking. All of the simulations are also repeated without the inclusion of a dispersed bubble phase, and it is shown that the integrated TKE in the breaking region is damped by the dispersed bubbles by approximately 20 % for a large plunging breaker to 50 % for spilling breakers. In the plunging breakers, the TKE is damped slightly or even enhanced during the initial stage of active breaking.

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Section: The Filtered Two-fluid Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bubble entrainment and liquid–bubble interaction under unsteady breaking waves

Derakhti

Kirby

2014

J. Fluid Mech.

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“…2 approach (Drew, 1983). Two-fluid models are used to model the polydisperse two-fluid bubbly flow based on mixture theory (Carrica et al 1999;Moraga et al, 2008, Shi et al, 2010Ma et al 2011;Derakhti & Kirby, 2014). A first attempt to use a continuum type model for studying bubbly flow under surface breaking waves was made by Shi et al (2010).…”

Section: Introductionmentioning

confidence: 99%

Are breaking waves, bores, surges and jumps the same flow?

Lubin

Chanson

2016

Environ Fluid Mech

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The flow structure in the aerated region of the roller generated by breaking waves remains a great challenge to study, with large quantities of entrained air and turbulence interactions making it very difficult to investigate in details. A number of analogies were proposed between breaking waves in deep or shallow water, tidal bores and hydraulic jumps. Many numerical models used to simulate waves in the surf zone do not implicitly simulate the breaking process of the waves, but are required to parameterise the wave-breaking effects, thus relying on experimental data. Analogies are also assumed to quantify the roller dynamics and the energy dissipation. The scope of this paper is to review the different analogies proposed in the literature and to discuss current practices. A thorough survey is offered and a discussion is developed an aimed at improving the use of possible breaking proxies. The most recent data are revisited and scrutinised for the use of most advanced numerical models to educe the surf zone hydrodynamics. In particular, the roller dynamics and geometrical characteristics are discussed. An open discussion is proposed to explore the actual practices and propose perspectives based on the most appropriate analogy, namely the tidal bore.

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“…The two phase blended k ‐ ε / k ‐ ω SST turbulence model is used to model turbulence . All the boundaries have no‐slip wall boundary conditions.…”

Section: Evaluation Tests and Discussionmentioning

confidence: 99%

A pressure–velocity coupling approach for high void fraction free surface bubbly flows in overset curvilinear grids

Castro

Carrica

2015

Numerical Methods in Fluids

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Summary A methodology for improved robustness in the simulation of high void fraction free surface polydisperse bubbly flows in curvilinear overset grids is presented. The method is fully two‐way coupled in the sense that the bubbly field affects the continuous fluid and vice versa. A hybrid projection approach is used in which staggered contravariant velocities at cell faces are computed for transport and pressure–velocity coupling while the momentum equation is solved on a collocated grid arrangement. Conservation of mass is formulated such that a strong coupling between void fraction, pressure, and velocity is achieved within a partitioned approach, solving each field separately. A pressure–velocity projection solver is iterated together with a predictor stage for the void fraction to achieve a robust coupling. The implementation is described for general curvilinear grids detailing particulars in the neighborhood to overset interfaces or a free surface. A balanced forced method to avoid the generation of spurious currents is extended for curvilinear grids. The overall methodology allows simulation of high void fraction flows and is stable even when strong packing forces accounting for bubble collisions are included. Convergence and stability in one‐dimensional (1D) and two‐dimensional (2D) configurations is evaluated. Finally, a full‐scale simulation of the bubbly flow around a flat‐bottom boat is performed demonstrating the applicability of the methodology to complex problems of engineering interest. Copyright © 2015 John Wiley & Sons, Ltd.

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A sub-grid air entrainment model for breaking bow waves and naval surface ships

Cited by 52 publications

References 35 publications

Bubble entrainment and liquid–bubble interaction under unsteady breaking waves

Bubble entrainment and liquid–bubble interaction under unsteady breaking waves

Are breaking waves, bores, surges and jumps the same flow?

A pressure–velocity coupling approach for high void fraction free surface bubbly flows in overset curvilinear grids

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