scholarly journals Is the Volume-of-Fluid Method Coupled with a Sub-Grid Bubble Equation Efficient for Simulating Local and Continuum Aeration?

Water ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1535
Author(s):  
Lourenço Sassetti Mendes ◽  
Javier L. Lara ◽  
Maria Teresa Viseu
Keyword(s):  
Stokes Equations ◽  
Computational Cost ◽  
Air Entrainment ◽  
Volume Of Fluid ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Volume Of Fluid Method ◽  
Navier Stokes Equations ◽  
Engineering Standards ◽  
The One

Air entrainment is common in free surface flows in large hydraulic structures (e.g., spillways, chutes, energy dissipation structures) and must be considered to assure an effective and safe operation. Due to the large size of the prototype structures, it is infeasible to model individual air bubbles. Therefore, using the OpenFOAM toolbox, an efficient simulation model for aerated flows is developed for engineering purposes. The Reynolds-averaged Navier–Stokes equations and the volume-of-fluid method are coupled with a sub-grid bubble population model that simulates entrainment and transport. A comprehensive assessment of the effectiveness, computational cost, and reliability is performed. Local and continuum bubble entrainment are evaluated in two distinct flows: an impinging jet and along a spillway chute. Aeration is induced, respectively, by a shear flow and by the thickening of the turbulent boundary layer. Moreover, a detailed sensitivity analysis of the model’s parameters is conducted. Calibration and validation are performed against experimental and prototype data. Among the analyzed entrainment formulations, the one depending exclusively on the turbulent kinetic energy is the only applicable to different flow types. Good accuracy is found, meeting engineering standards, and the additional computation cost is marginal. Results depend primarily on the volume-of-fluid method ability to reproduce the interface. Calibration is straightforward in self-aeration but more difficult for local aeration.

An Improved Volume of Fluid Method for Two-Phase Flow Computations on Collocated Grid System

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Dong-Liang Sun ◽  
Yong-Ping Yang ◽  
Jin-Liang Xu ◽  
Wen-Quan Tao
Keyword(s):  
Two Phase Flow ◽  
Stokes Equations ◽  
Volume Of Fluid ◽  
Vof Method ◽  
Navier Stokes ◽  
Phase Flow ◽  
Volume Of Fluid Method ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Collocated Grid

An improved volume of fluid method called the accurate density and viscosity volume of fluid (ADV-VOF) method is proposed to solve two-phase flow problems. The method has the following features: (1) All operations are performed on a collocated grid system. (2) The piecewise linear interface calculation is used to capture interfaces and perform accurate estimations of cell-edged density and viscosity. (3) The conservative Navier–Stokes equations are solved with the convective term discretized by a second and third order interpolation for convection scheme. (4) A fractional-step method is applied to solve the conservative Navier–Stokes equations, and the BiCGSTAB algorithm is used to solve the algebraic equations by discretizing the pressure-correction equation. The above features guarantee a simple, stable, efficient, and accurate simulation of two-phase flow problems. The effectiveness of the ADV-VOF method is verified by comparing it with the conventional volume of fluid method with rough treatment of cell-edged density and viscosity. It is found that the ADV-VOF method could successfully model the two-phase problems with large density ratio and viscosity ratio between two phases and is better than the conventional volume of fluid method in this respect.

On Offset Placement of a Compound Droplet in a Channel Flow

2021 ◽  
Author(s):  
Jagannath Mahato ◽  
Dhananjay Kumar Srivastava ◽  
Dinesh Kumar Chandraker ◽  
Rajaram Lakkaraju
Keyword(s):  
Viscosity Ratio ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Flow Direction ◽  
Navier Stokes ◽  
Volume Of Fluid Method ◽  
Lateral Migration ◽  
Navier Stokes Equations ◽  
Deformation Patterns ◽  
Compound Droplet

Abstract Investigations on flow dynamics of a compound droplet have been carried out in a two-dimensional fully-developed Poiseuille flow by solving the Navier-Stokes equations with the evolution of the droplet using the volume of fluid method with interface compression. The outer droplet undergoes elongation similar to a simple droplet of same size placed under similar ambient condition in the flow direction, but, the inner droplet evolves in compressed form. The compound droplet is varied starting from the centerline towards the walls of the channel. The simulations showed that on applying an offset, asymmetric slipper-like shapes are observed as opposed to symmetric bullet-like shapes through the centerline. Temporal dynamics, deformation patterns, and droplet shell pinch-off mode vary with the offset, with induction of lateral migration. Also, investigations are done on the effect of various parameters like droplet size, Capillary number, and viscosity ratio on the deformation magnitude and lateral migration.

scholarly journals Do the Volume-of-Fluid and the Two-Phase Euler Compete for Modeling a Spillway Aerator?

Water ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 3092
Author(s):  
Lourenço Sassetti Mendes ◽  
Javier L. Lara ◽  
Maria Teresa Viseu
Keyword(s):  
Stokes Equations ◽  
Cost Benefit ◽  
Volume Of Fluid ◽  
Navier Stokes ◽  
Type Model ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Entrained Air ◽  
Computational Resources ◽  
Mesh Convergence

Spillway design is key to the effective and safe operation of dams. Typically, the flow is characterized by high velocity, high levels of turbulence, and aeration. In the last two decades, advances in computational fluid dynamics (CFD) made available several numerical tools to aid hydraulic structures engineers. The most frequent approach is to solve the Reynolds-averaged Navier–Stokes equations using an Euler type model combined with the volume-of-fluid (VoF) method. Regardless of a few applications, the complete two-phase Euler is still considered to demand exorbitant computational resources. An assessment is performed in a spillway offset aerator, comparing the two-phase volume-of-fluid (TPVoF) with the complete two-phase Euler (CTPE). Both models are included in the OpenFOAM® toolbox. As expected, the TPVoF results depend highly on the mesh, not showing convergence in the maximum chute bottom pressure and the lower-nappe aeration, tending to null aeration as resolution increases. The CTPE combined with the k–ω SST Sato turbulence model exhibits the most accurate results and mesh convergence in the lower-nappe aeration. Surprisingly, intermediate mesh resolutions are sufficient to surpass the TPVoF performance with reasonable calculation efforts. Moreover, compressibility, flow bulking, and several entrained air effects in the flow are comprehended. Despite not reproducing all aspects of the flow with acceptable accuracy, the complete two-phase Euler demonstrated an efficient cost-benefit performance and high value in spillway aerated flows. Nonetheless, further developments are expected to enhance the efficiency and stability of this model.

The turning couples on an elliptic particle settling in a vertical channel

1994 ◽  
Vol 271 ◽  
pp. 1-16 ◽  
Author(s):  
Peter Y. Huang ◽  
Jimmy Feng ◽  
Daniel D. Joseph
Keyword(s):  
Shear Stress ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Vertical Channel ◽  
Navier Stokes ◽  
Front Face ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Back Face ◽  
The One

We do a direct two-dimensional finite-elment simulation of the Navier–Stokes equations and compute the forces which turn an ellipse settling in a vertical channel of viscous fluid in a regime in which the ellipse oscillates under the action of vortex shedding. Turning this way and that is induced by large and unequal values of negative pressure at the rear separation points which are here identified with the two points on the back face where the shear stress vanishes. The main restoring mechanism which turns the broadside of the ellipse perpendicular to the fall is the high pressure at the ‘stagnation point’ on the front face, as in potential flow, which is here identified with the one point on the front face where the shear stress vanishes.

Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments

2015 ◽  
Vol 767 ◽  
pp. 364-393 ◽  
Author(s):  
P. Lubin ◽  
S. Glockner
Keyword(s):  
Stokes Equations ◽  
Early Stage ◽  
Flow Direction ◽  
Three Dimensional ◽  
Air Entrainment ◽  
Breaking Waves ◽  
Navier Stokes ◽  
Vortex Filaments ◽  
Navier Stokes Equations ◽  
Main Flow Direction

AbstractThe scope of this work is to present and discuss the results obtained from simulating three-dimensional plunging breaking waves by solving the Navier–Stokes equations, in air and water. Recent progress in computational capabilities has allowed us to run fine three-dimensional simulations, giving us the opportunity to study for the first time fine vortex filaments generated during the early stage of the wave breaking phenomenon. To date, no experimental observations have been made in laboratories, and these structures have only been visualised in rare documentary footage (e.g. BBC 2009 South Pacific. Available on YouTube, 7BOhDaJH0m4). These fine coherent structures are three-dimensional streamwise vortical tubes, like vortex filaments, connecting the splash-up and the main tube of air, elongated in the main flow direction. The first part of the paper is devoted to the presentation of the model and numerical methods. The air entrainment occurring when waves break is then carefully described. Thanks to the high resolution of the grid, these fine elongated structures are simulated and explained.

Numerical Modeling of Flow Over a Dam Spillway

2006 ◽  
Author(s):  
Iraj Saeedpanah ◽  
M. Shayanfar ◽  
E. Jabbari ◽  
Mohammad Haji Mohammadi
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Iterative Solution ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Continuity Equations ◽  
Water Jets ◽  
Pressure Fields ◽  
Good Agreement

Free surface flows are frequently encountered in hydraulic engineering problems including water jets, weirs and around gates. An iterative solution to the incompressible two-dimensional vertical steady Navier-Stokes equations, comprising momentum and continuity equations, is used to solve for the priori unknown free surface, the velocity and the pressure fields. The entire water body is covered by a unstructured finite element grid which is locally refined. The dynamic boundary condition is imposed for the free surface where the pressure vanishes. This procedure is done continuously until the normal velocities components vanish. To overcome numerical errors and oscillations encountering in convection terms, the SUPG (streamline upwinding Petrov-Galerkin) method is applied. The solution method is tested for different discharges onto a standard spillway geometries. The results shows good agreement with available experimental data.

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