Fully Nonlinear Potential/RANSE Simulation of Wave Interaction With Ships and Marine Structures

2008 ◽  
Author(s):  
Pierre Ferrant ◽  
Lionel Gentaz ◽  
Bertrand Alessandrini ◽  
Romain Luquet ◽  
Charles Monroy ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Irregular Waves ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Fully Nonlinear ◽  
Nonlinear Potential ◽  
6 Degrees Of Freedom

This paper documents recent advances of the SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach, a method for simulating fully nonlinear wave-body interactions including viscous effects. The methods efficiently combines a fully nonlinear potential flow description of undisturbed wave systems with a modified set of RANS with free surface equations accounting for the interaction with a ship or marine structure. Arbitrary incident wave systems may be described, including regular, irregular waves, multidirectional waves, focused wave events, etc. The model may be fixed or moving with arbitrary speed and 6 degrees of freedom motion. The extension of the SWENSE method to 6 DOF simulations in irregular waves as well as to manoeuvring simulations in waves are discussed in this paper. Different illlustative simulations are presented and discussed. Results of the present approach compare favorably with available reference results.

scholarly journals A Numerical Study on the Aerodynamics of Freely Falling Planar Ice Crystals

2018 ◽  
Vol 75 (9) ◽  
pp. 2849-2865 ◽  
Author(s):  
Joseph J. Nettesheim ◽  
Pao K. Wang
Keyword(s):  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Numerical Study ◽  
Flow Fields ◽  
Terminal Velocity ◽  
Ice Crystals ◽  
Navier Stokes ◽  
Empirical Formulas ◽  
Navier Stokes Equations ◽  
6 Degrees Of Freedom

Abstract Fluid flow fields and fall patterns of falling planar ice crystals are studied by numerically solving the unsteady, incompressible Navier–Stokes equations using a commercially available computational fluid dynamics package. The ice crystal movement and orientation are explicitly simulated based on hydrodynamic forces and torques representing the 6 degrees of freedom. This study extends the current framework by investigating four planar-type ice crystals: crystals with sector-like branches, crystals with broad branches, stellar crystals, and ordinary dendritic crystals. The crystals range from 0.2 to 5 mm in maximum dimension, corresponding to Reynolds number ranges from 0.2 to 384. The results indicate that steady flow fields are generated for flows with Reynolds numbers less than 100; larger plates generate unsteady flow fields and exhibit horizontal translation, rotation, and oscillation. Empirical formulas for the drag coefficient, 900-hPa terminal velocity, and ventilation effect are given. Fall trajectory, pressure distribution, wake structure, vapor field, and vorticity field are examined.

A Cartesian Explicit Solver for Complex Hydrodynamic Applications

2014 ◽  
Author(s):  
P. Bigay ◽  
A. Bardin ◽  
G. Oger ◽  
D. Le Touzé
Keyword(s):  
Level Set ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Flow Past A Cylinder ◽  
Explicit Solver

In order to efficiently address complex problems in hydrodynamics, the advances in the development of a new method are presented here. This method aims at finding a good compromise between computational efficiency, accuracy, and easy handling of complex geometries. The chosen method is an Explicit Cartesian Finite Volume method for Hydrodynamics (ECFVH) based on a compressible (hyperbolic) solver, with a ghost-cell method for geometry handling and a Level-set method for the treatment of biphase-flows. The explicit nature of the solver is obtained through a weakly-compressible approach chosen to simulate nearly-incompressible flows. The explicit cell-centered resolution allows for an efficient solving of very large simulations together with a straightforward handling of multi-physics. A characteristic flux method for solving the hyperbolic part of the Navier-Stokes equations is used. The treatment of arbitrary geometries is addressed in the hyperbolic and viscous framework. Viscous effects are computed via a finite difference computation of viscous fluxes and turbulent effects are addressed via a Large-Eddy Simulation method (LES). The Level-Set solver used to handle biphase flows is also presented. The solver is validated on 2-D test cases (flow past a cylinder, 2-D dam break) and future improvements are discussed.

Fekete-Gauss Spectral Elements for Incompressible Navier-Stokes Flows: The Two-Dimensional Case

2013 ◽  
Vol 13 (5) ◽  
pp. 1309-1329 ◽  
Author(s):  
Laura Lazar ◽  
Richard Pasquetti ◽  
Francesca Rapetti
Keyword(s):  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Schur Complement ◽  
Spectral Element ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Flow Past A Cylinder ◽  
Accuracy Study

AbstractSpectral element methods on simplicial meshes, say TSEM, show both the advantages of spectral and finite element methods, i.e., spectral accuracy and geometrical flexibility. We present aTSEM solver of the two-dimensional (2D) incompressible Navier-Stokes equations, with possible extension to the 3D case. It uses a projection method in time and piecewise polynomial basis functions of arbitrary degree in space. The so-called Fekete-Gauss TSEM is employed,i.e., Fekete (resp. Gauss) points of the triangle are used as interpolation (resp. quadrature) points. For the sake of consistency, isoparametric elements are used to approximate curved geometries. The resolution algorithm is based on an efficient Schur complement method, so that one only solves for the element boundary nodes. Moreover, the algebraic system is never assembled, therefore the number of degrees of freedom is not limiting. An accuracy study is carried out and results are provided for classical benchmarks: the driven cavity flow, the flow between eccentric cylinders and the flow past a cylinder.

Viscosity Effects on the Radiation Hydrodynamics of Horizontal Cylinders

1991 ◽  
Vol 113 (4) ◽  
pp. 334-343 ◽  
Author(s):  
R. W. Yeung ◽  
C.-F. Wu
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Small Body ◽  
Low Frequency ◽  
Body Motion ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Horizontal Cylinders

The problem of a body oscillating in a viscous fluid with a free surface is examined. The Navier-Stokes equations and boundary conditions are linearized using the assumption of small body-motion to wavelength ratio. Generation and diffusion of vorticity, but not its convection, are accounted for. Rotational and irrotational Green functions for a divergent and a vorticity source are presented, with the effects of viscosity represented by a frequency Reynolds number Rσ = g2/νσ3. Numerical solutions for a pair of coupled integral equations are obtained for flows about a submerged cylinder, circular or square. Viscosity-modified added-mass and damping coefficients are developed as functions of frequency. It is found that as Rσ approaches infinity, inviscid-fluid results can be recovered. However, viscous effects are important in the low-frequency range, particularly when Rσ is smaller than O(104).

Numerical Simulations of Nonlinear Post-Critical Vibrations of an Airfoil After Flutter Instability

2011 ◽  
Author(s):  
Jaromi´r Hora´cˇek ◽  
Miloslav Feistauer ◽  
Petr Sva´cˇek
Keyword(s):  
Numerical Simulations ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Mass Matrix ◽  
Vertical Direction ◽  
Navier Stokes ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Classical Flutter

The contribution deals with the numerical simulation of the flutter of an airfoil with three degrees of freedom (3-DOF) for rotation around an elastic axis, oscillation in the vertical direction and rotation of a flap. The finite element (FE) solution of two-dimensional (2-D) incompressible Navier-Stokes equations is coupled with a system of nonlinear ordinary differential equations describing the airfoil vibrations with large amplitudes taking into account the nonlinear mass matrix. The time-dependent computational domain and a moving grid are treated by the Arbitrary Lagrangian-Eulerian (ALE) method and a suitable stabilization of the FE discretization is applied. The developed method was successfully tested by the classical flutter computation of the critical flutter velocity using NASTRAN program considering the linear model of vibrations and the double-lattice aerodynamic theory. The method was applied to the numerical simulations of the post flutter regime in time domain showing Limit Cycle Oscillations (LCO) due to nonlinearities of the flow model and vibrations with large amplitudes. Numerical experiments were performed for the airfoil NACA 0012 respecting the effect of the air space between the flap and the main airfoil.

Effects of Non-Dimensional Parameters on Formation and Break Up of Cylindrical Droplets

2004 ◽  
Author(s):  
Mohammad Taeibi-Rahni ◽  
Shervin Sharafatmand
Keyword(s):  
Stokes Equations ◽  
Fluid Model ◽  
Time Dependent ◽  
Navier Stokes ◽  
Ohnesorge Number ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Dimensional Parameters ◽  
Break Up ◽  
Eotvos Number

The consistent behavior of non-dimensional parameters on the formation and break up of large cylindrical droplets has been studied by direct numerical simulations (DNS). A one-fluid model with a finite difference method and an advanced front tracking scheme was employed to solve unsteady, incompressible, viscous, immiscible, multi-fluid, two-dimensional Navier-Stokes equations. This time dependent study allows investigation of evolution of the droplets in different cases. For moderate values of Atwood number (AT), increasing Eotvos number (Eo) explicitly increases the deformation rate in both phenomena. Otherwise, raising the Ohnesorge number (Oh) basically amplifies the viscous effects.

scholarly journals The emergence of localized vortex–wave interaction states in plane Couette flow

2013 ◽  
Vol 721 ◽  
pp. 58-85 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall ◽  
Andrew Walton
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Critical Layer ◽  
Navier Stokes ◽  
Turbulent Spots ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractThe recently understood relationship between high-Reynolds-number vortex–wave interaction theory and computationally generated self-sustaining processes provides a possible route to an understanding of some of the underlying structures of fully turbulent flows. Here vortex–wave interaction (VWI) theory is used in the long streamwise wavelength limit to continue the development found at order-one wavelengths by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). The asymptotic description given reduces the Navier–Stokes equations to the so-called boundary-region equations, for which we find equilibrium states describing the change in the VWI as the wavelength of the wave increases from $O(h)$ to $O(Rh)$, where $R$ is the Reynolds number and $2h$ is the depth of the channel. The reduced equations do not include the streamwise pressure gradient of the perturbation or the effect of streamwise diffusion of the wave–vortex states. The solutions we calculate have an asymptotic error proportional to ${R}^{- 2} $ when compared to the full Navier–Stokes equations. The results found correspond to the minimum drag configuration for VWI states and might therefore be of relevance to the control of turbulent flows. The key feature of the new states discussed here is the thickening of the critical layer structure associated with the wave part of the flow to completely fill the channel, so that the roll part of the flow is driven throughout the flow rather than as in Hall & Sherwin as a stress discontinuity across the critical layer. We identify a critical streamwise wavenumber scaling, which, when approached, causes the flow to localize and take on similarities with computationally generated or experimentally observed turbulent spots. In effect, the identification of this critical wavenumber for a given value of the assumed high Reynolds number fixes a minimum box length necessary for the emergence of localized structures. Whereas nonlinear equilibrium states of the Navier–Stokes equations are thought to form a backbone on which turbulent flows hang, our results suggest that the localized states found here might play a related role for turbulent spots.

scholarly journals Coriolis effect and the attachment of the leading edge vortex

2017 ◽  
Vol 820 ◽  
pp. 312-340 ◽  
Author(s):  
T. Jardin
Keyword(s):  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Coriolis Effect ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Leading Edge Vortex ◽  
Edge Vortex ◽  
Vorticity Transport ◽  
Rotating Wing

The role of the Coriolis effect on the attachment of the leading edge vortex (LEV) is investigated. Toward that end, the Navier–Stokes equations are solved in the non-inertial reference frame of a high angle of attack $\unicode[STIX]{x1D6FC}$ rotating wing with the Coriolis term being artificially tuned. Reynolds numbers in the range $Re\in [100;750]$ are considered to identify the interplay between Coriolis and viscous effects. Similarly, artificial tuning of the centrifugal term is achieved to identify the interplay between Coriolis and centrifugal effects. It is shown that (i) the Coriolis effect is the key element in LEV stability for $Re>200$, (ii) viscous effects are the key element for $Re<200$ and (iii) centrifugal effects have a marginal role. The Coriolis effect is found to promote spanwise flow in the core and behind the LEV, which is known to promote outboard vorticity transport and presumably contributes to stabilizing the aft boundary layer. These mechanisms of LEV stabilization have increased authority as $\unicode[STIX]{x1D6FC}$ decreases.

scholarly journals A Massively Parallel Hybrid Finite Volume/Finite Element Scheme for Computational Fluid Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2316
Author(s):  
Laura Río-Martín ◽  
Saray Busto ◽  
Michael Dumbser
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Finite Element ◽  
Mach Number ◽  
Finite Volume ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Massively Parallel ◽  
Navier Stokes ◽  
Navier Stokes Equations

In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular for the approximate solution of the incompressible and compressible Navier-Stokes equations, as well as for the shallow water equations on staggered unstructured meshes in two and three space dimensions. The key features of the method are the use of an edge-based/face-based staggered dual mesh for the discretization of the nonlinear convective terms at the aid of explicit high resolution Godunov-type finite volume schemes, while pressure terms are discretized implicitly using classical continuous Lagrange finite elements on the primal simplex mesh. The resulting pressure system is symmetric positive definite and can thus be very efficiently solved at the aid of classical Krylov subspace methods, such as a matrix-free conjugate gradient method. For the compressible Navier-Stokes equations, the schemes are by construction asymptotic preserving in the low Mach number limit of the equations, hence a consistent hybrid FV/FE method for the incompressible equations is retrieved. All parts of the algorithm can be efficiently parallelized, i.e., the explicit finite volume step as well as the matrix-vector product in the implicit pressure solver. Concerning parallel implementation, we employ the Message-Passing Interface (MPI) standard in combination with spatial domain decomposition based on the free software package METIS. To show the versatility of the proposed schemes, we present a wide range of applications, starting from environmental and geophysical flows, such as dambreak problems and natural convection, over direct numerical simulations of turbulent incompressible flows to high Mach number compressible flows with shock waves. An excellent agreement with exact analytical, numerical or experimental reference solutions is achieved in all cases. Most of the simulations are run with millions of degrees of freedom on thousands of CPU cores. We show strong scaling results for the hybrid FV/FE scheme applied to the 3D incompressible Navier-Stokes equations, using millions of degrees of freedom and up to 4096 CPU cores. The largest simulation shown in this paper is the well-known 3D Taylor-Green vortex benchmark run on 671 million tetrahedral elements on 32,768 CPU cores, showing clearly the suitability of the presented algorithm for the solution of large CFD problems on modern massively parallel distributed memory supercomputers.

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