scholarly journals An axisymmetric non-hydrostatic model for double-diffusive water systems

2016 ◽  
Author(s):  
Koen Hilgersom ◽  
Marcel Zijlema ◽  
Nick van de Giesen
Keyword(s):  
Shallow Water ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Water Layer ◽  
Free Surface Flow ◽  
Momentum Conservation ◽  
Water Systems ◽  
Surface Flow ◽  
Navier Stokes ◽  
Double Diffusive

Abstract. The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In systems that approach axisymmetry around a central location, computation times can be reduced by applying a quasi 3-D axisymmetric model setup. This article applies the Navier-Stokes equations described in cylindrical coordinates, and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite volume model can be easily extended to this quasi 3-D framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature and salinity dependent densities, molecular diffusivities, and kinematic viscosity. Four qualitative case studies demonstrate a good behaviour with respect to expected density and diffusivity driven flow and stratification in shallow water bodies. A fifth case study involves a new validation method that quantifies the radial expansion of a dense water layer developing from a central inflow at the bottom of a shallow water body.

scholarly journals An axisymmetric non-hydrostatic model for double-diffusive water systems

2018 ◽  
Vol 11 (2) ◽  
pp. 521-540 ◽  
Author(s):  
Koen Hilgersom ◽  
Marcel Zijlema ◽  
Nick van de Giesen
Keyword(s):  
Case Studies ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Water Layer ◽  
Free Surface Flow ◽  
Momentum Conservation ◽  
Water Systems ◽  
Surface Flow ◽  
Diffusive Processes ◽  
Double Diffusive

Abstract. The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In 3-D systems that approach axisymmetry around a central location, computation times can be reduced by applying a 2-D axisymmetric model set-up. This article applies the Reynolds-averaged Navier–Stokes equations described in cylindrical coordinates and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite-volume model can be easily extended to the developed framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature- and salinity-dependent densities, molecular diffusivities, and kinematic viscosity. One quantitative case study, based on an analytical solution derived for the radial expansion of a dense water layer, and two qualitative case studies demonstrate a good behaviour of the model for seepage inflows with contrasting salinities and temperatures. Four case studies with respect to double-diffusive processes in a stratified water body demonstrate that turbulent flows are not yet correctly modelled near the interfaces and that an advanced turbulence model is required.

A Three Dimensional Non-Hydrostatic Numerical Model for Free Surface Flow and Mass Transportation

2013 ◽  
Vol 353-356 ◽  
pp. 2496-2501
Author(s):  
Biao Lv
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Navier Stokes ◽  
Mass Transportation ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Good Agreement

A three dimensional non-hydrostatic numerical model is presented based on the incompressible Navier-Stokes equations and mass transport equations. An unstructured finite-volume technique is used to discretized the governing equations with good adaptable to complicated boundary. A conservative scalar transport algorithm is also applied in this model. An integral method of the top- layer pressure is applied to reduce the number of vertical layers. Three classical examples including periodic waves propagating over a submerged bar and non-hydrostatic lock exchange are used to demonstrate the capability and efficiency of the model. The simulation results are in good agreement with the analytical solution and experimental data.

3D Volume-of-Fluid (VOF) Based Simulation of Water Impact Problem Using Navier-Stokes Computations

2015 ◽  
Author(s):  
Van-Tu Nguyen ◽  
Warn-Gyu Park
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Free Surface Flow ◽  
Volume Of Fluid ◽  
Water Entry ◽  
Surface Flow ◽  
Dam Break ◽  
Navier Stokes ◽  
Water Impact ◽  
Impact Problem

In this paper, a three-dimensional (3D) numerical investigation of dam-break and water entry problems with emphasis on the water impact loading is presented. Flow fields of incompressible viscous fluids are solved using unsteady Navier-Stokes equations (NS). Pseudo-time derivatives are introduced into the equations to improve computational efficiency. The interface between two phases is tracked using a volume-of-fluid (VOF) interface tracking algorithm developed in a generalized curvilinear coordinate system. The accuracy and capability of the numerical model for free surface flow simulations are demonstrated by using experiments of the dam-break flow over a horizontal dry bed. The water impact problem has been analyzed by free falling water entry of a hemisphere and a cone. Comparisons between the obtained solutions, the experimental data and the results of other numerical simulations in the literature are presented exhibiting good agreement.

scholarly journals A Computational Fluid Dynamics Model for a Water Vortex Power Plant as Platform for Etho- and Ecohydraulic Research

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 639
Author(s):  
Dennis Powalla ◽  
Stefan Hoerner ◽  
Olivier Cleynen ◽  
Nadine Müller ◽  
Jürgen Stamm ◽  
...  
Keyword(s):  
Power Plant ◽  
Numerical Model ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Field Measurements ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Navier Stokes ◽  
Two Phase

The objective of the present paper is to develop a validated numerical model of a water vortex power plant that serves as a digital twin for further studies such as assessments of the ethohydraulic characteristics or the performance of such devices. The reference for the validation process is a large-scale hydraulic installation equipped with a full-scale water vortex power plant prototype installed in Dresden (Germany), where flow field measurements were carried out using three-dimensional Acoustic Doppler Velocimetry. The numerical model was implemented within the software package Star-CCM+. The unsteady, two-phase flow was solved with the Reynolds-Averaged Navier–Stokes equations in a Eulerian Multiphase approach, deploying a Volume of Fluid method to describe the free-surface flow. Water level and flow velocities were systematically compared in key areas of the device, demonstrating that the simulation is in good agreement with experimental observations. Relative differences are limited to at most 4% regarding water height in the system, and even the much more challenging velocity fields are reproduced with typical relative errors of roughly 10%. This validates the ability of the model to model the challenging flow conditions found in a water vortex power plant, enabling subsequent studies of the characteristics of this power plant concerning fish migration.

scholarly journals Congested shallow water model: roof modeling in free surface flow

2018 ◽  
Vol 52 (5) ◽  
pp. 1679-1707 ◽  
Author(s):  
Edwige Godlewski ◽  
Martin Parisot ◽  
Jacques Sainte-Marie ◽  
Fabien Wahl
Keyword(s):  
Shallow Water ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Hyperbolic Equations ◽  
Mechanical Energy ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Water Model ◽  
Shallow Water Model ◽  
Time Step

We are interested in the modeling and the numerical approximation of flows in the presence of a roof, for example flows in sewers or under an ice floe. A shallow water model with a supplementary congestion constraint describing the roof is derived from the Navier-Stokes equations. The congestion constraint is a challenging problem for the numerical resolution of hyperbolic equations. To overcome this difficulty, we follow a pseudo-compressibility relaxation approach. Eventually, a numerical scheme based on a finite volume method is proposed. The well-balanced property and the dissipation of the mechanical energy, acting as a mathematical entropy, are ensured under a non-restrictive condition on the time step in spite of the large celerity of the potential waves in the congested areas. Simulations in one dimension for transcritical steady flow are carried out and numerical solutions are compared to several analytical (stationary and non-stationary) solutions for validation.

Free Surface Flow Past Ships in Shallow Water

2002 ◽  
Author(s):  
A. Ganguly ◽  
V. Shigunov ◽  
O. Turan
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Near Field ◽  
Free Surface Flow ◽  
Steady State Solution ◽  
Surface Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Medium Speed ◽  
Measured Resistance

A finite volume method with a multiphase type free surface description is employed to calculate the flow around ships in shallow and restricted channels. The flows at critical and supercritical depth Froude numbers (Fnd = 1.0 and Fnd = 1.18) are calculated for Series–60 monohull and a medium speed catamaran. A steady state solution for Reynolds-averaged Navier-Stokes equations with a k-ε turbulence model is obtained by time marching. Computed wave profiles are in good agreement with model tests in the near field of the ship. The computed and measured resistance agree fairly well.

Simulation of Three-Dimensional Shear Flow Around a Nozzle-Afterbody at High Speeds

1992 ◽  
Vol 114 (2) ◽  
pp. 178-185 ◽  
Author(s):  
Oktay Baysal ◽  
Wendy B. Hoffman
Keyword(s):  
Shear Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Surface Flow ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Duct Flow ◽  
Navier Stokes Equations ◽  
Eddy Viscosity Model ◽  
Pressure Distributions

Turbulent shear flows at supersonic and hypersonic speeds around a nozzle-afterbody are simulated. The three-dimensional, Reynolds-averaged Navier-Stokes equations are solved by a finite-volume and implicit method. The convective and the pressure terms are differenced by an upwind-biased algorithm. The effect of turbulence is incorporated by a modified Baldwin-Lomax eddy viscosity model. The success of the standard Baldwin-Lomax model for this flow type is shown by comparing it to a laminar case. These modifications made to the model are also shown to improve flow prediction when compared to the standard Baldwin-Lomax model. These modifications to the model reflect the effects of high compressibility, multiple walls, vortices near walls, and turbulent memory effects in the shear layer. This numerically simulated complex flowfield includes a supersonic duct flow, a hypersonic flow over an external double corner, a flow through a non-axisymmetric, internal-external nozzle, and a three-dimensional shear layer. The specific application is for the flow around the nozzle-afterbody of a generic hypersonic vehicle powered by a scramjet engine. The computed pressure distributions compared favorably with the experimentally obtained surface and off-surface flow surveys.

A Stable Semi-Implicit Method for Free Surface Flows

2005 ◽  
Vol 73 (6) ◽  
pp. 940-947 ◽  
Author(s):  
Cassio M. Oishi ◽  
José A. Cuminato ◽  
Valdemir G. Ferreira ◽  
Murilo F. Tomé ◽  
Antonio Castelo ◽  
...  
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Free Surface Flow ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Navier Stokes ◽  
Variable Order ◽  
Implicit Methods ◽  
Time Lagged

The present work is concerned with a semi-implicit modification of the GENSMAC method for solving the two-dimensional time-dependent incompressible Navier-Stokes equations in primitive variables formulation with a free surface. A projection method is employed to uncouple the velocity components and pressure, thus allowing the solution of each variable separately (a segregated approach). The viscous terms are treated by the implicit backward method in time and a centered second order method in space, and the nonlinear convection terms are explicitly approximated by the high order upwind variable-order nonoscillatory scheme method in space. The boundary conditions at the free surface couple the otherwise segregated velocity and pressure fields. The present work proposes a method that allows the segregated solution of free surface flow problems to be computed by semi-implicit schemes that preserve the stability conditions of the related coupled semi-implicit scheme. The numerical method is applied to both the simulation of free surface and to confined flows. The numerical results demonstrate that the present technique eliminates the parabolic stability restriction required by the original explicit GENSMAC method, and also found in segregated semi-implicit methods with time-lagged boundary conditions. For low Reynolds number flows, the method is robust and very efficient when compared to the original GENSMAC method.

scholarly journals WAVE MOTION NEAR A BREAKWATER ROUNDHEAD

2012 ◽  
Vol 1 (33) ◽  
pp. 71
Author(s):  
Takahide Honda ◽  
Peter Wellens ◽  
Marcel Van Gent
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Flow Model ◽  
Stokes Equations ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Physical Model Tests

COMFLOW is a general 3D free-surface flow solver. The numerical method is based on the Navier-Stokes equations in a porous medium, with additional force terms to represent the (turbulent) interaction of the flow with the medium. The free surface is displaced by means of the Volume-Of-Fluid method. The main objective in this paper is to validate the permeable flow model in 3D. Tailor-made physical model tests were performed for this purpose. In the experiment surface elevations are measured inside and around a permeable structure with 18 wave gauges in total. The measurements are represented well by the simulation results.

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