Air trapping at impact of a rigid sphere onto a liquid

2012 ◽  
Vol 695 ◽  
pp. 310-320 ◽  
Author(s):  
P. D. Hicks ◽  
E. V. Ermanyuk ◽  
N. V. Gavrilov ◽  
R. Purvis
Keyword(s):  
Free Surface ◽  
Excellent Agreement ◽  
Spherical Body ◽  
Axisymmetric Body ◽  
Boundary Integral ◽  
Theoretical Modelling ◽  
Rigid Sphere ◽  
Air Trapping ◽  
Air Pocket ◽  
Surface Profiles

AbstractAn experimental and theoretical investigation of the air trapping by a blunt, locally spherical body impacting onto the free surface of water is conducted. In the parameter regime previously studied theoretically by Hicks & Purvis (J. Fluid Mech., vol. 649, 2010, pp. 135–163), excellent agreement between experimental data and theoretical modelling is obtained. Earlier predictions of the radius of the trapped air pocket are confirmed. A boundary element method is used to consider air cushioning of an impact of an axisymmetric body into water. Efficient computational methods are obtained by analytically integrating the boundary integral equation over the azimuthal variable. The resulting numerically computed free-surface profiles predict an annular touchdown region in excellent agreement with the experiments.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

Free-surface flows with two stagnation points

1996 ◽  
Vol 324 ◽  
pp. 393-406 ◽  
Author(s):  
J.-M. Vanden-Broeck ◽  
F. Dias
Keyword(s):  
Free Surface ◽  
Infinite Number ◽  
Wave Breaking ◽  
Free Surface Flows ◽  
Number Of Solutions ◽  
Surface Flows ◽  
Stagnation Points ◽  
Surface Profiles ◽  
Countably Infinite

Symmetric suction flows are computed. The flows are free-surface flows with two stagnation points. The configuration is related to the modelling of wave breaking at the bow of a ship. It is shown that there is a countably infinite number of solutions and that the free-surface profiles are characterized by waves.

New solutions for periodic interfacial gravity waves

2021 ◽  
Vol 928 ◽  
Author(s):  
X. Guan ◽  
J.-M. Vanden-Broeck ◽  
Z. Wang
Keyword(s):  
Integral Equation ◽  
Excellent Agreement ◽  
Gravity Waves ◽  
Global Bifurcation ◽  
Integral Equation Method ◽  
Finite Depth ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Fourier Expansions ◽  
Wave Profiles

Two-dimensional periodic interfacial gravity waves travelling between two homogeneous fluids of finite depth are considered. A boundary-integral-equation method coupled with Fourier expansions of the unknown functions is used to obtain highly accurate solutions. Our numerical results show excellent agreement with those already obtained by Maklakov & Sharipov using a different scheme (J. Fluid Mech., vol. 856, 2018, pp. 673–708). We explore the global bifurcation mechanism of periodic interfacial waves and find three types of limiting wave profiles. The new families of solutions appear either as isolated branches or as secondary branches bifurcating from the primary branch of solutions.

A B-Spline Based BEM for Unsteady Free-Surface Flows

1999 ◽  
Vol 43 (01) ◽  
pp. 13-24
Author(s):  
M. Landrini ◽  
G. Grytøyr ◽  
O. M. Faltinsen
Keyword(s):  
Free Surface ◽  
Evolution Equations ◽  
Boundary Integral Equations ◽  
Fluid Dynamic ◽  
Domain Boundary ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
Surface Flows ◽  
B Spline ◽  
Nonlinear Free Surface

Fully nonlinear free-surface flows are numerically studied in the framework of the potential theory. The problem is formulated in terms of boundary integral equations which are solved by means of an arbitrary high-order boundary element method based on B-Spline representation of both the geometry and the fluid dynamic variables along the domain boundary. The solution is stepped forward in time either by following Lagrangian points attached to the free surface or by a less conventional scheme in which evolution equations for the B-Spline coefficients are integrated in time. Numerical examples for inner and outer free-surface flows are shown. The accuracy of the numerical solution is assessed either by checking mass and energy conservation or by comparing with reference solutions. Good results are generally obtained. Extended use of the developed algorithm to more applied problems in the context of naval hydrodynamics is now under development.

scholarly journals Modelling of the behaviour of metal foams under shock compression

2018 ◽  
Vol 183 ◽  
pp. 01041
Author(s):  
Nicolas Jacques ◽  
Romain Barthélémy
Keyword(s):  
Experimental Data ◽  
Excellent Agreement ◽  
Strain Curve ◽  
Metal Foams ◽  
Cellular Materials ◽  
Theoretical Modelling ◽  
Stress Strain Curve ◽  
Open Cell ◽  
Proposed Model ◽  
Shock Response

A theoretical modelling is proposed to describe the shock response of foam materials. This model is based on micromechanical and energetic arguments, and takes into account the contribution of microscale inertia. Within this framework, an analytical expression of the Hugoniot stress-strain curve is proposed for elastic-plastic cellular materials. The predictions derived from the proposed model are in excellent agreement with experimental data for open-cell aluminium foams. The case of viscoplastic foams is also considered.

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