scholarly journals NUMERICAL CALCULATION OF WAVE FORCES ON STRUCTURES

1976 ◽  
Vol 1 (15) ◽  
pp. 131
Author(s):  
B.D. Nichols ◽  
C.W. Hirt
Keyword(s):  
Stokes Equations ◽  
Numerical Technique ◽  
Ocean Waves ◽  
Navier Stokes ◽  
Wave Forces ◽  
Transient Wave ◽  
Dynamic Interactions ◽  
Navier Stokes Equations ◽  
Calculational Method ◽  
Moving Bodies

A finite-difference technique for solving the Navier-Stokes equations for an incompressible fluid is used to calculate transient wave forces experienced by fixed and moving bodies. The numerical technique is based on the Marker-and-Cell (MAC) method developed by Harlow and Welch (1965). This new technique uses an especially simple solution algorithm that is designed for persons with little or no experience in numerical fluid dynamics. Originally conceived as an instructional tool, it has proven to be an extremely useful and versatile calculational method. Many useful calculations are possible with the publicly available code, SOLA-SURF, which is briefly described in Sec. II; however, the outstanding feature of this numerical scheme is the ease with which it can be modified to handle more complex problems. Reported here, in Sec. Ill, are examples to illustrate the utility of this new calculational tool for investigating the dynamic interactions between ocean waves and coastal structures.

Symmetry-breaking bifurcations in spherical Couette flow

1996 ◽  
Vol 310 ◽  
pp. 293-324 ◽  
Author(s):  
Oleg Yu. Zikanov
Keyword(s):  
Symmetry Breaking ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Basic Equilibrium ◽  
Spherical Couette ◽  
Pseudo Spectral

The solutions of the nonlinear and linearized Navier-Stokes equations are computed to investigate the instabilities and the secondary two- and three-dimensional regimes in the flow of an incompressible viscous fluid in a thin gap between two concentric differentially rotating spheres. The numerical technique is finite difference in the radial direction, spectral in the azimuthal direction, and pseudo-spectral in the meridional direction. The study follows the experiments by Yavorskaya, Belyaev and co-workers in which a variety of steady axisymmetric and three-dimensional travelling wave secondary regimes was observed in the case of a thin layer and both boundary spheres rotating. In agreement with the experimental results three different types of symmetry-breaking primary bifurcations of the basic equilibrium are detected in the parameter range under consideration.

Numerical Study of Wave Slamming on an Oscillating Flap

2014 ◽  
Author(s):  
Yanji Wei ◽  
Alan Henry ◽  
Olivier Kimmoun ◽  
Frederic Dias
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Flow Characteristics ◽  
Ocean Waves ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Numerical Studies ◽  
Wave Slamming ◽  
Volume Method

Bottom hinged Oscillating Wave Surge Converters (OWSCs) are efficient devices for extracting power from ocean waves. There is limited knowledge about wave slamming on such devices. This paper deals with numerical studies of wave slamming on an oscillating flap to investigate the mechanism of slamming events. In our model, the Navier–Stokes equations are discretized using the Finite Volume method with the Volume of Fluid (VOF) approach for interface capturing. Waves are generated by a flap-type wave maker in the numerical wave tank, and the dynamic mesh method is applied to model the motion of the oscillating flap. Basic mesh and time step refinement studies are performed. The flow characteristics in a slamming event are analysed based on numerical results. Various simulations with different flap densities, water depths and wave amplitudes are performed for a better understanding of the slamming.

A Theoretical and Experimental Study of Confined Vortex Flow

1969 ◽  
Vol 36 (4) ◽  
pp. 687-692 ◽  
Author(s):  
G. J. Farris ◽  
G. J. Kidd ◽  
D. W. Lick ◽  
R. E. Textor
Keyword(s):  
Flow Field ◽  
Radial Flow ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Tangential Velocity ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
General Validity ◽  
Wide Range

The interaction of a vortex with a stationary surface was studied both theoretically and experimentally. The flow field examined was that produced by radially inward flow through a pair of concentric rotating porous cylinders that were perpendicular to, and in contact with, a stationary flat plane. The complete Navier-Stokes equations were solved over a range of tangential Reynolds numbers from 0–300 and a range of radial Reynolds numbers from 0 to −13, the minus sign indicating radially inward flow. In order to facilitate the solution, the original equations were recast in terms of a dimensionless stream function, vorticity, and third variable related to the tangential velocity. The general validity of the numerical technique was demonstrated by the agreement between the theoretical and experimental results. Examination of the numerical results over a wide range of parameters showed that the entire flow field is very sensitive to the amount of radial flow, especially at the transition from zero radial flow to some finite value.

Prediction of Cascade Performance Using an Incompressible Navier-Stokes Technique

1990 ◽  
Author(s):  
G. V. Hobson ◽  
B. Lakshminarayana
Keyword(s):  
Stokes Equations ◽  
Control Volume ◽  
Numerical Technique ◽  
Skin Friction Coefficient ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Distribution Boundary ◽  
Turbulence Effects ◽  
Good Agreement

A fully elliptic, control volume solution of the two-dimensional incompressible Navier-Stokes equations for the prediction of cascade performance over a wide incidence range is presented in this paper. The numerical technique is based on a new pressure substitution method. A Poisson equation is derived from the pressure weighted substitution of the full momentum equations into the continuity equation. The analysis of a double circular arc compressor cascade is presented, and the results are compared with the available experimental data at various incidence angles. Good agreement is obtained for the blade pressure distribution, boundary layer and wake profiles, skin friction coefficient, losses and outlet angles. Turbulence effects are simulated by the Low-Reynolds-Number version of the k-ε turbulence model.

On the Numerical Solution of Two-Dimensional, Laminar Compressible Flows With Imbedded Shock Waves

1972 ◽  
Vol 94 (4) ◽  
pp. 765-769 ◽  
Author(s):  
W. D. Goodrich ◽  
J. P. Lamb ◽  
J. J. Bertin
Keyword(s):  
Shock Waves ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Leading Edge ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Numerical Experimentation ◽  
Explicit Finite Difference

The complete, time-dependent Navier-Stokes equations are expressed in conservation form and solved by employing an explicit finite difference numerical technique which incorporates artificial viscosity terms of the form first suggested by Rusanov for numerical stability in the vicinity of shock waves. Surface boundary conditions are developed in a consistent and unique manner through the use of a physically oriented extrapolation procedure. From numerical experimentation an extended range for the explicit stability parameter is established. Also employed is an additional convergence parameter which relates incremental spatial steps. Convergence of the transient solution to a steady state flow was obtained after 400 to 500 time steps. Sample solutions are presented for supersonic flow of air over the leading edge of a slightly blunted flat plate, past a backward facing step, and in the near wake of a blunt trailing edge. Free-stream Mach numbers from 2 to 10 are included in the sample computations.

Application of a Viscous Flow Methodology to the NREL Phase VI Rotor

2002 ◽  
Author(s):  
Guanpeng Xu ◽  
Lakshmi N. Sankar
Keyword(s):  
Stokes Equations ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Local Flow ◽  
Navier Stokes Equations ◽  
Horizontal Axis Wind Turbines ◽  
Blade Tip ◽  
Bladed Rotor ◽  
Stall Angle

A numerical technique has been developed for efficiently simulating fully three-dimensional viscous fluid flow around horizontal axis wind turbines (HAWT). In this approach, the viscous region surrounding the blades is modeled using 3-D unsteady Navier-Stokes equations. The inviscid region away from the boundary layer and the wake is modeled using potential flow. The concentrated vortices that emanate from the blade tip are treated as piecewise straight line segments that are allowed to deform and convect at the local flow velocity. Biot-Savart law is used to estimate the velocity field associated with these vortices. Calculations are presented under axial wind conditions for a NREL two-bladed rotor, known as the Phase VI rotor, tested at the NASA Ames Research Center. Good agreement with the measurements is found. The computed results are used to develop improved engineering models for the loss of lift at the blade tip, and for the delay in the stall angle at inboard locations. The improved models are incorporated in a blade element-momentum (BEM) analysis to study the post-stall behavior of a three-bladed rotor tested at NREL.

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