scholarly journals Displacement flows under elastic membranes. Part 1. Experiments and direct numerical simulations

2015 ◽  
Vol 784 ◽  
pp. 487-511 ◽  
Author(s):  
Draga Pihler-Puzović ◽  
Anne Juel ◽  
Gunnar G. Peng ◽  
John R. Lister ◽  
Matthias Heil
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Theoretical Models ◽  
Navier Stokes ◽  
Elastic Membrane ◽  
Two Phase ◽  
Constant Flow Rate ◽  
Viscous Forces ◽  
Elastic Membranes ◽  
Set Up

The injection of fluid into the narrow liquid-filled gap between a rigid plate and an elastic membrane drives a displacement flow that is controlled by the competition between elastic and viscous forces. We study such flows using the canonical set-up of an elastic-walled Hele-Shaw cell whose upper boundary is formed by an elastic sheet. We investigate both single- and two-phase displacement flows in which the localised injection of fluid at a constant flow rate is accommodated by the inflation of the sheet and the outward propagation of an axisymmetric front beyond which the cell remains approximately undeformed. We perform a direct comparison between quantitative experiments and numerical simulations of two theoretical models. The models couple the Föppl–von Kármán equations, which describe the deformation of the thin elastic membrane, to the equations describing the flow, which we model by (i) the Navier–Stokes equations or (ii) lubrication theory. We identify the dominant physical effects that control the behaviour of the system and critically assess modelling assumptions that were made in previous studies. The insight gained from these studies is then used in Part 2 of this work, where we formulate an improved lubrication model and develop an asymptotic description of the key phenomena.

scholarly journals Evaluation of the Turbulence Model Influence on the Numerical Simulations of Unsteady Cavitation

2003 ◽  
Vol 125 (1) ◽  
pp. 38-45 ◽  
Author(s):  
O. Coutier-Delgosha ◽  
R. Fortes-Patella ◽  
J. L. Reboud
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Simple Algorithm ◽  
Numerical Code ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Cavitating Flows ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Compressibility Effects

Unsteady cavitation in a Venturi-type section was simulated by two-dimensional computations of viscous, compressible, and turbulent cavitating flows. The numerical model used an implicit finite volume scheme (based on the SIMPLE algorithm) to solve Reynolds-averaged Navier-Stokes equations, associated with a barotropic vapor/liquid state law that strongly links the density variations to the pressure evolution. To simulate turbulence effects on cavitating flows, four different models were implemented (standard k-ε RNG; modified k-ε RNG; k-ω with and without compressibility effects), and numerical results obtained were compared to experimental ones. The standard models k-ε RNG and k-ω without compressibility effects lead to a poor description of the self-oscillation behavior of the cavitating flow. To improve numerical simulations by taking into account the influence of the compressibility of the two-phase medium on turbulence, two other models were implemented in the numerical code: a modified k-ε model and the k-ω model including compressibility effects. Results obtained concerning void ratio, velocity fields, and cavitation unsteady behavior were found in good agreement with experimental ones. The role of the compressibility effects on turbulent two-phase flow modeling was analyzed, and it seemed to be of primary importance in numerical simulations.

Lagrangian transport by breaking surface waves

2017 ◽  
Vol 829 ◽  
pp. 364-391 ◽  
Author(s):  
Luc Deike ◽  
Nick Pizzo ◽  
W. Kendall Melville
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Wave Packets ◽  
Direct Numerical Simulations ◽  
Stokes Drift ◽  
Navier Stokes ◽  
Two Phase ◽  
Lagrangian Transport ◽  
Tracer Particles ◽  
Simple Scaling

The Lagrangian transport due to non-breaking and breaking focusing wave packets is examined. We present direct numerical simulations of the two-phase air–water Navier–Stokes equations describing focusing wave packets, investigating the Lagrangian drift by tracking tracer particles in the water before, during and after the breaking event. The net horizontal transport for non-breaking focusing packets is well described by the classical Stokes drift, both at the surface and in the bulk of the fluid, where the e-folding scale of the evanescent vertical profile is given by the characteristic wavenumber. For focusing wave packets that lead to breaking, we observe an added drift that can be ten times larger than the classical Stokes drift for a non-breaking packet at the surface, while the initial depth of the broken fluid scales with the wave height at breaking. We find that the breaking induced Lagrangian transport scales with the breaking strength. A simple scaling argument is proposed to describe this added drift and is found to be consistent with the direct numerical simulations. Applications to upper ocean processes are discussed.

Numerical Modeling of Evolution of Boundary Between Incompressible Gas and Liquid in Two-Dimensional Region

2006 ◽  
Vol 4 ◽  
pp. 224-236
Author(s):  
A.S. Topolnikov
Keyword(s):  
Numerical Modeling ◽  
Interphase Boundary ◽  
Incompressible Liquid ◽  
Stokes Equations ◽  
Numerical Code ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Incompressible Media ◽  
Good Agreement

The paper is devoted to numerical modeling of Navier–Stokes equations for incompressible media in the case, when there exist gas and liquid inside the rectangular calculation region, which are separated by interphase boundary. The set of equations for incompressible liquid accounting for viscous, gravitational and surface (capillary) forces is solved by finite-difference scheme on the spaced grid, for description of interphase boundary the ideology of Level Set Method is used. By developed numerical code the set of hydrodynamic problems is solved, which describe the motion of two-phase incompressible media with interphase boundary. As a result of numerical simulation the solutions are obtained, which are in good agreement with existing analytical and experimental solutions.

scholarly journals Experimental and Numerical Study on Water Filling and Air Expelling Process in a Pipe with Multiple Air Valves under Water Slow Filling Condition

Water ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2511
Author(s):  
Jintao Liu ◽  
Di Xu ◽  
Shaohui Zhang ◽  
Meijian Bai
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Practical Method ◽  
Navier Stokes ◽  
Physical Processes ◽  
Two Phase ◽  
Saint Venant Equations ◽  
Water Filling ◽  
Air Valve

This paper investigates the physical processes involved in the water filling and air expelling process of a pipe with multiple air valves under water slow filling condition, and develops a fully coupledwater–air two-phase stratified numerical model for simulating the process. In this model, the Saint-Venant equations and the Vertical Average Navier–Stokes equations (VANS) are respectively applied to describe the water and air in pipe, and the air valve model is introduced into the VANS equations of air as the source term. The finite-volume method and implicit dual time-stepping method (IDTS) with two-order accuracy are simultaneously used to solve this numerical model to realize the full coupling between water and air movement. Then, the model is validated by using the experimental data of the pressure evolution in pipe and the air velocity evolution of air valves, which respectively characterize the water filling and air expelling process. The results show that the model performs well in capturing the physical processes, and a reasonable agreement is obtained between numerical and experimental results. This agreement demonstrates that the proposed model in this paper offers a practical method for simulating water filling and air expelling process in a pipe with multiple air valves under water slow filling condition.

scholarly journals Development of Hybrid Airlift-Jet Pump with Its Performance Analysis

2018 ◽  
Vol 8 (9) ◽  
pp. 1413 ◽  
Author(s):  
Dan Yao ◽  
Kwongi Lee ◽  
Minho Ha ◽  
Cheolung Cheong ◽  
Inhiug Lee
Keyword(s):  
Boundary Conditions ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Jet Pump ◽  
Two Phase

A new pump, called the hybrid airlift-jet pump, is developed by reinforcing the advantages and minimizing the demerits of airlift and jet pumps. First, a basic design of the hybrid airlift-jet pump is schematically presented. Subsequently, its performance characteristics are numerically investigated by varying the operating conditions of the airlift and jet parts in the hybrid pump. The compressible unsteady Reynolds-averaged Navier-Stokes equations, combined with the homogeneous mixture model for multiphase flow, are used as the governing equations for the two-phase flow in the hybrid pump. The pressure-based methods combined with the Pressure-Implicit with Splitting of Operators (PISO) algorithm are used as the computational fluid dynamics techniques. The validity of the present numerical methods is confirmed by comparing the predicted mass flow rate with the measured ones. In total, 18 simulation cases that are designed to represent the various operating conditions of the hybrid pump are investigated: eight of these cases belong to the operating conditions of only the jet part with different air and water inlet boundary conditions, and the remaining ten cases belong to the operating conditions of both the airlift and jet parts with different air and water inlet boundary conditions. The mass flow rate and the efficiency are compared for each case. For further investigation into the detailed flow characteristics, the pressure and velocity distributions of the mixture in a primary pipe are compared. Furthermore, a periodic fluctuation of the water flow in the mass flow rate is found and analyzed. Our results show that the performance of the jet or airlift pump can be enhanced by combining the operating principles of two pumps into the hybrid airlift-jet pump, newly proposed in the present study.

NUMERICAL SIMULATION OF ISOTHERMAL AND THERMAL TWO-PHASE FLOWS USING PHASE-FIELD MODELING

2007 ◽  
Vol 18 (04) ◽  
pp. 536-545 ◽  
Author(s):  
NAOKI TAKADA ◽  
AKIO TOMIYAMA
Keyword(s):  
Phase Field ◽  
Stokes Equations ◽  
Density Ratio ◽  
Navier Stokes ◽  
Phase Field Modeling ◽  
Two Phase Flows ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Field Modeling ◽  
High Density Ratio

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, we examined the applicability of two versions of computational fluid dynamics method, NS-PFM, combining Navier-Stokes equations with phase-field modeling for interface based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

scholarly journals A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution

2020 ◽  
pp. 1-35
Author(s):  
Christian Rohde ◽  
Lars von Wolff
Keyword(s):  
Phase Field ◽  
Stokes Equations ◽  
Solid Phase ◽  
Immiscible Fluids ◽  
Sharp Interface ◽  
Ion Concentration ◽  
Navier Stokes ◽  
Interface Model ◽  
Sharp Interface Model ◽  
Two Phase

We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase-field approach is suggested that couples the Navier–Stokes equations and the solid’s ion concentration transport equation with the Cahn–Hilliard evolution for the phase fields. The model is shown to preserve the fundamental conservation constraints and to obey the second law of thermodynamics for a novel free energy formulation. An extended analysis for vanishing interfacial width reveals that in this limit the sharp interface model is recovered, including all relevant transmission conditions. Notably, the new phase-field model is able to realize Navier-slip conditions for solid–fluid interfaces in the limit.

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.

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