scholarly journals Numerical Simulation of Air–Water Two-Phase Flow on Stepped Spillways Behind X-Shaped Flaring Gate Piers under Very High Unit Discharge

Water ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1956 ◽  
Author(s):  
Dong ◽  
Wang ◽  
Vetsch ◽  
Boes ◽  
Tan
Keyword(s):  
Two Phase Flow ◽  
Stokes Equations ◽  
Air Entrainment ◽  
Stepped Spillway ◽  
Phase Flow ◽  
Air Concentration ◽  
Two Phase ◽  
Unit Discharge ◽  
Stepped Spillways ◽  
Very High

Stepped spillways are commonly used under relatively low unit discharge, where cavitation pitting can be avoided by self-aerated flow. However, there are several dams in China with stepped spillways in combination with X-shaped flaring gate piers with unit design discharge considerably larger than specified in the available guidelines. Consequently, air–water two-phase flow on stepped spillway behind X-shaped flaring gate piers under very high unit discharge was investigated using Computational Fluid Dynamics (CFD) simulations. The 3-D Reynolds-averaged Navier–Stokes equations were solved, including sub-grid models for air entrainment, density evaluation, and drift-flux, to capture self-aerated free-surface flow over the spillway. The pressure on the vertical step faces was compared with laboratory data. In addition, the air–water two-phase flow characteristics and prototype step failure of the simulated prototype spillway were analyzed based on the numerical results of velocity, pressure, and air concentration. Moreover, an optimized bottom-aeration was further studied. The results reveal that the involved models can predict the air concentration near the steps. The cavitation index at the stepped surface is below the threshold value, and the air concentration is insufficient under high unit discharges. Moreover, with the proposed optimization of the aerator air entrainment can be improved and thereby cavitation erosion risk can be reduced.

scholarly journals Studies of Two-Phase Flow at a Chute Aerator with Experiments and CFD Modelling

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Penghua Teng ◽  
James Yang ◽  
Michael Pfister
Keyword(s):  
Two Phase Flow ◽  
Fluid Model ◽  
Air Entrainment ◽  
Phase Flow ◽  
Air Concentration ◽  
Cfd Modelling ◽  
Two Phase ◽  
Air Bubble ◽  
Two Fluid Model ◽  
Two Fluid

The chute aerator of a spillway is a structure in such a sense that air is, in the intense emulsification, entrained into the high-velocity water flow. Correctly predicting the air entrainment and two-phase flow pattern at the aerator would contribute to reliable spillway operation. Based on experimental data, 2D numerical simulations are preformed to predict streamwise air concentrations in the aerated flow, in which a two-fluid model is used. Depending on the air bubble size, relatively good agreement is seen with the experiments in the air cavity zone. The simulations give rise to higher air concentration downstream of the cavity, which is presumably due to underestimation of the interfacial forces in the two-fluid model.

scholarly journals A two-phase flow model for three-dimensional breaking waves over complex topography

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150101 ◽  
Author(s):  
Zhihua Xie
Keyword(s):  
Wave Breaking ◽  
Flow Model ◽  
Two Phase Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Air Entrainment ◽  
Breaking Waves ◽  
Phase Flow ◽  
Complex Topography ◽  
Two Phase

A two-phase flow model has been developed to study three-dimensional breaking waves over complex topography, including the wave pre-breaking, overturning and post-breaking processes. The large-eddy simulation approach has been adopted in this study, where the model is based on the filtered Navier–Stokes equations with the Smagorinsky sub-grid model being used for the unresolved scales of turbulence. The governing equations have been discretized using the finite volume method, with the PISO algorithm being employed for the pressure–velocity coupling. The air–water interface has been captured using a volume of fluid method and the partial cell treatment has been implemented to deal with complex topography in the Cartesian grid. The model is first validated against available analytical solutions and experimental data for solitary wave propagation over constant water depth and three-dimensional breaking waves over a plane slope, respectively. Furthermore, the model is used to study three-dimensional overturning waves over three different bed topographies, with three-dimensional wave profiles and surface velocities being presented and discussed. The overturning jet, air entrainment and splash-up during wave breaking have been captured by the two-phase flow model, which demonstrates the capability of the model to simulate free surface flow and wave breaking problems over complex topography.

On convergent schemes for two-phase flow of dilute polymeric solutions

2018 ◽  
Vol 52 (6) ◽  
pp. 2357-2408 ◽  
Author(s):  
Stefan Metzger
Keyword(s):  
Finite Element ◽  
Two Phase Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Phase Flow ◽  
Two Phase ◽  
Extra Stress Tensor ◽  
Spring Force ◽  
Polymeric Solutions ◽  
Fokker Planck

We construct a Galerkin finite element method for the numerical approximation of weak solutions to a recent micro-macro bead-spring model for two-phase flow of dilute polymeric solutions derived by methods from nonequilibrium thermodynamics ([Grün, Metzger, M3AS 26 (2016) 823–866]). The model consists of Cahn-Hilliard type equations describing the evolution of the fluids and the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three spatial dimensions for the velocity and the pressure of the fluids with an elastic extra-stress tensor on the right-hand side in the momentum equation which originates from the presence of dissolved polymer chains. The polymers are modeled by dumbbells subjected to a finitely extensible, nonlinear elastic (FENE) spring-force potential. Their density and orientation are described by a Fokker-Planck type parabolic equation with a center-of-mass diffusion term. We perform a rigorous passage to the limit as the spatial and temporal discretization parameters simultaneously tend to zero, and show that a subsequence of these finite element approximations converges towards a weak solution of the coupled Cahn-Hilliard-Navier-Stokes-Fokker-Planck system. To underline the practicality of the presented scheme, we provide simulations of oscillating dilute polymeric droplets and compare their oscillatory behaviour to the one of Newtonian droplets.

scholarly journals Slug Regime Transitions in a Two-Phase Flow in Horizontal Round Pipe. CFD Simulations

2020 ◽  
Vol 10 (23) ◽  
pp. 8739
Author(s):  
Vitaly Sergeev ◽  
Nikolai Vatin ◽  
Evgeny Kotov ◽  
Darya Nemova ◽  
Svyatoslav Khorobrov
Keyword(s):  
Pressure Drop ◽  
Flow Regime ◽  
Two Phase Flow ◽  
Stokes Equations ◽  
Bubbly Flow ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Technical Solution ◽  
Phase Flow ◽  
Two Phase

The main objective of the study is to propose a technical solution integrated into the pipeline for the transition of the flow regime from slug to bubbly two-phase flow. The object of research is isothermal two-phase gas–Newtonian-liquid flow in a horizontal circular pipeline. There is local resistance in the pipe in the form of a streamlined transverse mesh partition. The mesh partition ensures the transition of the flow from the slug regime to the bubbly regime. The purpose of the study is to propose a technical solution integrated into the pipeline for changing the flow regime of a two-phase flow from slug to bubbly flow. The method of research is a simulation using computational fluid dynamics (CFD) numerical simulation. The Navier–Stokes equations averaged by Reynolds describes the fluid motion. The k-ε models were used to close the Reynolds-averaged Navier–Stokes (RANS) equations. The computing cluster «Polytechnic—RSK Tornado» was used to solve the tasks. The results of simulation show that pressure drop on the grid did not exceed 10% of the pressure drop along the length of the pipeline. The mesh partition transits the flow regime from slug to layered one, which will help to increase the service life and operational safety of a real pipeline at insignificant energy costs to overcome the additional resistance integrated into the pipeline.

Liquid Jet Impingement on a Free Liquid Surface: PIV Study of the Turbulent Bubbly Two-Phase Flow

2010 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Flow Field ◽  
Two Phase Flow ◽  
Jet Impingement ◽  
Flow Region ◽  
Air Entrainment ◽  
Continuous Phase ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Field Characteristics ◽  
Inflow Conditions

The turbulent two-phase flow arising from the normal impingement of a round free-surface water jet on a horizontal air-water interface was experimentally studied. Due to the weakly viscous nature of the flow system under consideration, external perturbations or small variations in jet inflow conditions can lead to drastically different flow field characteristics under seemingly similar test conditions. In the current study, a fully developed turbulent jet, exiting a long pipe, ensured properly characterized inflow conditions. The study considered two jet inflow conditions; one entrained air and created a bubbly two-phase flow field while the other did not. Particle image velocimetry (PIV) was used to characterize the flow field beneath the interface, with and without air entrainment, for various nozzle-to-interface separation distances. Turbulent velocity fields of the continuous-phase and dispersed-phase were simultaneously measured in the developing flow region and presented using Reynolds decomposition into mean and fluctuating components. The mean and RMS velocities of the two-phase flow field were compared with velocity measurements obtained under single-phase conditions.

Coupled solution of the Boltzmann and Navier–Stokes equations in gas–liquid two phase flow

2013 ◽  
Vol 71 ◽  
pp. 283-296 ◽  
Author(s):  
Sudarshan Tiwari ◽  
Axel Klar ◽  
Steffen Hardt ◽  
Alexander Donkov
Keyword(s):  
Two Phase Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Phase Flow ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Coupled Solution

Steady and Dynamic Models of Fuel and Air Flow in Carburetors for Small Engines

2005 ◽  
Vol 127 (4) ◽  
pp. 778-786 ◽  
Author(s):  
Diego A. Arias ◽  
Timothy A. Shedd
Keyword(s):  
Dynamic Models ◽  
Two Phase Flow ◽  
Stokes Equations ◽  
Small Diameter ◽  
Phase Flow ◽  
Flow Conditions ◽  
Dynamic Flow ◽  
Complex Flow ◽  
Two Phase ◽  
Small Engines

This work presents the mathematical model of a complex flow network containing short metering orifices, compressible flow, and two-phase flow in small diameter pipes. It has been developed to study the steady and dynamic flows in a carburetor for small engines. It extends the previously published models by incorporating a detailed review of two-phase flow pressure drop, the effect of the fuel well on the control of air-bleed flow, and dynamic flow. The homogeneous two-phase flow model, which is commonly used in previous models, was compared to an empirical correlation derived from experiments in small pipes and found to be in poor agreement. In order to assess dynamic flow conditions, the model was extended by solving instantaneous one-dimensional Navier-Stokes equations in single-phase pipes. This strategy proved successful in explaining the mixture enrichment seen under pulsating flow conditions. The model was also used to derive a sensitivity analysis of geometries and physical properties of air and fuel.

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.

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