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.

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.

scholarly journals Sustained gravity currents in a channel

2016 ◽  
Vol 798 ◽  
pp. 853-888 ◽  
Author(s):  
Andrew J. Hogg ◽  
Mohamad M. Nasr-Azadani ◽  
Marius Ungarish ◽  
Eckart Meiburg
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Analytical Techniques ◽  
Direct Numerical Simulations ◽  
Density Difference ◽  
Water Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Shallow Layer ◽  
Dense Fluid

Gravitationally driven motion arising from a sustained constant source of dense fluid in a horizontal channel is investigated theoretically using shallow-layer models and direct numerical simulations of the Navier–Stokes equations, coupled to an advection–diffusion model of the density field. The influxed dense fluid forms a flowing layer underneath the less dense fluid, which initially filled the channel, and in this study its speed of propagation is calculated; the outflux is at the end of the channel. The motion, under the assumption of hydrostatic balance, is modelled using a two-layer shallow-water model to account for the flow of both the dense and the overlying less dense fluids. When the relative density difference between the fluids is small (the Boussinesq regime), the governing shallow-layer equations are solved using analytical techniques. It is demonstrated that a variety of flow-field patterns are feasible, including those with constant height along the length of the current and those where the height varies continuously and discontinuously. The type of solution realised in any scenario is determined by the magnitude of the dimensionless flux issuing from the source and the source Froude number. Two important phenomena may occur: the flow may be choked, whereby the excess velocity due to the density difference is bounded and the height of the current may not exceed a determined maximum value, and it is also possible for the dense fluid to completely displace all of the less dense fluid originally in the channel in an expanding region close to the source. The onset and subsequent evolution of these types of motions are also calculated using analytical techniques. The same range of phenomena occurs for non-Boussinesq flows; in this scenario, the solutions of the model are calculated numerically. The results of direct numerical simulations of the Navier–Stokes equations are also reported for unsteady two-dimensional flows in which there is an inflow of dense fluid at one end of the channel and an outflow at the other end. These simulations reveal the detailed mechanics of the motion and the bulk properties are compared with the predictions of the shallow-layer model to demonstrate good agreement between the two modelling strategies.

Partially Averaged Navier-Stokes Turbulence Modeling of Flow in 5x5 PWR Fuel Assembly With Spacer Grid

2018 ◽  
Author(s):  
Giacomo Busco ◽  
Yassin A. Hassan
Keyword(s):  
Large Eddy Simulation ◽  
Numerical Simulations ◽  
Stokes Equations ◽  
Direct Numerical Simulations ◽  
Navier Stokes ◽  
Spacer Grid ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Reynolds Averaged Navier Stokes

The highly turbulent flow inside a pressurized water reactor makes unpractical the use of scale resolving simulations, due to the large number of space and time turbulent structures. The high computational cost associated with typical large eddies simulations or direct numerical simulations techniques is unsuitable due to the large spatiotemporal resolution required. Partially averaged Navier-Stokes turbulence model is presented as bridging model between Reynolds averaged Navier-Stokes equations and direct numerical simulations. As filtered representation of the Navier-Stokes equations, the model is able to continuously shift its energy-based filter, inside the turbulence spectrum, being able to resolve the turbulent scales of interest. The choice of energy based cut-off filters gives the chance to directly impose the degree of needed resolution, where the most important large scales unsteadiness are resolved at minimal computational expenses. The partially averaged Navier-Stokes modelling approach has been tested for a Reynolds number of 14,000, inside a 5 × 5 fuel bundle, with a single spacer grid and split-type mixing vanes. Four different filters have been tested, whose resolution ranged from Reynolds averaged Navier-Stokes and large eddy simulation. A comparison with large eddy simulation will be presented. The results show that the partially averaged Navier-Stokes modeling produces results comparable to those of large eddy simulation when the appropriate cut-off energy filter is chosen. The turbulence models results will be compared with the available particle image velocimetry experimental data.

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.

Computations of Boiling Flows

Volume 3 ◽  
2004 ◽  
Author(s):  
Gre´tar Tryggvason ◽  
Asghar Esmaeeli
Keyword(s):  
Numerical Simulations ◽  
Phase Boundary ◽  
Energy Equation ◽  
Stokes Equations ◽  
Accurate Solution ◽  
Direct Numerical Simulations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Average Heat ◽  
Long Time

Numerical simulations of boiling flows are discussed. The change of phase from liquid to vapor and vice-versa usually takes place in a highly unsteady manner where the phase boundary is very convoluted. Direct numerical simulations therefore require the accurate solution of the Navier-Stokes equations and the energy equation in each phase and the correct incorporation of the unsteady phase boundary. Such simulations, where the motion of an unsteady phase boundary is followed for a sufficiently long time to allow computation of average heat transfer are very recent. Here, we will describe one method that has been used successfully to simulate boiling flows and show a few examples of studies using the method.

Fluidelastic Instability in Tube Arrays Subject to Two-Phase Cross Flow: A Porous Medium Approach

2015 ◽  
Author(s):  
Eliott Tixier ◽  
Cédric Béguin ◽  
Stéphane Étienne ◽  
Dominique Pelletier ◽  
Alexander Hay ◽  
...  
Keyword(s):  
Porous Medium ◽  
Numerical Simulations ◽  
Power Plants ◽  
Single Phase ◽  
Stokes Equations ◽  
Direct Numerical Simulations ◽  
Two Phase ◽  
Coupled Equations ◽  
Integration Schemes ◽  
Fluidelastic Instability

In nuclear power plants, heat exchangers undergo important flow induced vibrations, fluidelastic instability (FEI) being the most damaging one. Direct numerical simulations of such a phenomenon is currently an impossible task because of the considerable number of tubes and the two-phase nature of the flow. The novelty of the present approach is to use a porous medium to model the tube bundle and the surrounding flow. The Navier-Stokes equations are averaged on a control volume and the tubes materialized by a porosity field and source terms that model the interactions between the fluid and the solid. New sets of fully coupled equations were developed and solved with a finite element solver using high order time integration schemes. The unsteady porous medium approach already developed for single-phase flow is extended to the Euler-Euler formulation to describe the two-phase mixture. Validation and calibration of the parameters are achieved by comparing the critical flow rate and the forces acting on the tubes with results from direct numerical simulations and experimental data for single-phase flows.

Bound-state formation in interfacial turbulence: direct numerical simulations and theory

2013 ◽  
Vol 716 ◽  
Author(s):  
M. Pradas ◽  
S. Kalliadasis ◽  
P.-K. Nguyen ◽  
V. Bontozoglou
Keyword(s):  
Numerical Simulations ◽  
State Formation ◽  
Stokes Equations ◽  
Bound State ◽  
Direct Numerical Simulations ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Oscillatory Dynamics ◽  
Low Dimensional

AbstractWe examine pulse interaction and bound-state formation in interfacial turbulence using the problem of a falling liquid film as a model system. We perform direct numerical simulations (DNSs) of the full Navier–Stokes equations and associated wall and free-surface boundary conditions and we examine both analytically and numerically a low-dimensional (LD) model for the film. For a two-pulse system, DNSs reveal the existence of very rich and complex pulse interactions, characterized by either overdamped, underdamped or self-sustained oscillating behaviours, all of them found to be in excellent agreement with LD results. Having demonstrated the reliability of the LD model for two-pulse systems/smaller domains, we use it to investigate larger domains with many interacting pulses, where DNSs are computationally expensive. We demonstrate that such systems are likely to be dominated by a self-sustained oscillatory dynamics.

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 A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

Sign in / Sign up

Export Citation Format

Share Document