The oblique ascent of a viscous vortex pair toward a free surface

1992 ◽  
Vol 236 ◽  
pp. 461-476 ◽  
Author(s):  
Hans J. Lugt ◽  
Samuel Ohring
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Vortex Pair ◽  
Nonlinear Boundary Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Directional Change ◽  
Secondary Vortices

The problem of a vortex pair, rising obliquely at an angle of 45° toward a deformable free surface in a viscous, incompressible fluid, is solved with the aid of the Navier—Stokes equations. The full nonlinear boundary conditions at the free surface are applied. The oblique interaction of the vortex pair with the free surface results in a number of novel features that have not been observed for the special case of a vertical rise, reported earlier. These features include the directional change of trajectories near the free surface and the occurrence of waves driven by the vortex pair. Moreover, surface tension can completely change the flow characteristics such as the direction of the trajectories and the generation of secondary vortices. Numerical solutions are presented for selected Reynolds, Froude, and Weber numbers.

Interaction of a viscous vortex pair with a free surface

1991 ◽  
Vol 227 ◽  
pp. 47-70 ◽  
Author(s):  
Samuel Ohring ◽  
Hans J. Lugt
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Vortex Pair ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Flow Situation ◽  
Vortex Centre ◽  
Secondary Vortices ◽  
Nonlinear Free Surface

A vortex pair in a viscous, incompressible fluid rises vertically toward a deformable free surface. The mathematical, description of this flow situation is a time-dependent nonlinear free-surface problem that has been solved numerically for a two-dimensional laminar flow with the aid of the Navier-Stokes equations by using boundary-fitted coordinates. For a number of selected flow parameters, results are presented on the decay of the primary vortices and their paths, the generation of surface vorticity and secondary vortices, the development and final stage of the disturbed free surface, and the influence of surface tension. High and low Froude numbers represent the two extremes of free-surface yielding and stiffness, respectively. For an intermediate Froude number, a special rebounding due to the presence of secondary vortices has been observed: the path of the primary vortex centre portrays a complete loop.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

Numerical and asymptotic methods for certain viscous free-surface flows

1992 ◽  
Vol 340 (1656) ◽  
pp. 1-45 ◽  
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Lubrication Approximation ◽  
Navier Stokes Equations ◽  
Flow Rates

This paper concerns the two-dimensional motion of a viscous liquid down a perturbed inclined plane under the influence of gravity, and the main goal is the prediction of the surface height as the fluid flows over the perturbations. The specific perturbations chosen for the present study were two humps stretching laterally across an otherwise uniform plane, with the flow being confined in the lateral direction by the walls of a channel. Theoretical predictions of the flow have been obtained by finite-element approximations to the Navier-Stokes equations and also by a variety of lubrication approximations. The predictions from the various models are compared with experimental measurements of the free-surface profiles. The principal aim of this study is the establishment and assessment of certain numerical and asymptotic models for the description of a class of free-surface flows, exemplified by the particular case of flow over a perturbed inclined plane. The laboratory experiments were made over a range of flow rates such that the Reynolds number, based on the volume flux per unit width and the kinematical viscosity of the fluid, ranged between 0.369 and 36.6. It was found that, at the smaller Reynolds numbers, a standard lubrication approximation provided a very good representation of the experimental measurements but, as the flow rate was increased, the standard model did not capture several important features of the flow. On the other hand, a lubrication approximation allowing for surface tension and inertial effects expanded the range of applicability of the basic theory by almost an order of magnitude, up to Reynolds numbers approaching 10. At larger flow rates, numerical solutions to the full equations of motion provided a description of the experimental results to within about 4% , up to a Reynolds number of 25, beyond which we were unable to obtain numerical solutions. It is not known why numerical solutions were not possible at larger flow rates, but it is possible that there is a bifurcation of the Navier-Stokes equations to a branch of unsteady motions near a Reynolds number of 25.

Numerical Simulations of Three-Dimensional Flows in a Cubic Cavity With an Oscillating Lid

1993 ◽  
Vol 115 (4) ◽  
pp. 680-686 ◽  
Author(s):  
Reima Iwatsu ◽  
Jae Min Hyun ◽  
Kunio Kuwahara
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Navier Stokes Equations ◽  
Sinusoidal Oscillations ◽  
Dependent Flow

Numerical studies are made of three-dimensional flow of a viscous fluid in a cubical container. The flow is driven by the top sliding wall, which executes sinusoidal oscillations. Numerical solutions are acquired by solving the time-dependent, three-dimensional incompressible Navier-Stokes equations by employing very fine meshes. Results are presented for wide ranges of two principal physical parameters, i.e., the Reynolds number, Re ≤ 2000 and the frequency parameter of the lid oscillation, ω′ ≤ 10.0. Comprehensive details of the flow structure are analyzed. Attention is focused on the three-dimensionality of the flow field. Extensive numerical flow visualizations have been performed. These yield sequential plots of the main flows as well as the secondary flow patterns. It is found that the previous two-dimensional computational results are adequate in describing the main flow characteristics in the bulk of interior when ω′ is reasonably high. For the cases of high-Re flows, however, the three-dimensional motions exhibit additional complexities especially when ω′ is low. It is asserted that, thanks to the recent development of the supercomputers, calculation of three-dimensional, time-dependent flow problems appears to be feasible at least over limited ranges of Re.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

Simulation of the Gap Resonance Between Two Rectangular Barges in Regular Waves by a Free Surface Viscous Flow Solver

2013 ◽  
Author(s):  
B. Elie ◽  
G. Reliquet ◽  
P.-E. Guillerm ◽  
O. Thilleul ◽  
P. Ferrant ◽  
...  
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Viscous Flow ◽  
Stokes Equations ◽  
Resonance Phenomenon ◽  
Navier Stokes ◽  
Regular Waves ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Gap Resonance

This paper compares numerical and experimental results in the study of the resonance phenomenon which appears between two side-by-side fixed barges for different sea-states. Simulations were performed using SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach and results are compared with experimental data on two fixed barges with different headings and bilges. Numerical results, obtained using the SWENSE approach, are able to predict both the frequency and the magnitude of the RAO functions.

scholarly journals Mathematical Model for the Electrokinetic Instability of Electrolyte Flow

2019 ◽  
Vol 224 ◽  
pp. 02003
Author(s):  
Andrey Shobukhov
Keyword(s):  
Electric Potential ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Steady State Solution ◽  
Stability Loss ◽  
Navier Stokes ◽  
Ion Distribution ◽  
Navier Stokes Equations ◽  
Dilute Aqueous Solution

We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.

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