Similarity solution for oblique water entry of an expanding paraboloid

2014 ◽  
Vol 745 ◽  
pp. 398-408 ◽  
Author(s):  
G. X. Wu ◽  
S. L. Sun
Keyword(s):  
Free Surface ◽  
Boundary Element Method ◽  
Nonlinear Boundary ◽  
Velocity Potential ◽  
Numerical Solutions ◽  
Nonlinear Boundary Conditions ◽  
Water Entry ◽  
Similarity Solutions ◽  
Pressure Distributions ◽  
Flow Features

AbstractSimilarity solutions based on velocity potential theory are found to be possible in the case of an expanding paraboloid entering water when gravity is ignored. Numerical solutions are obtained based on the boundary element method. Iteration is used for the nonlinear boundary conditions on the unknown free surface, together with regular remeshing. Results are obtained for paraboloids with different slenderness (or bluntness). Flow features and pressure distributions are discussed along with the physical implications. It is also concluded that similarity solutions may be possible in more general cases.

Numerical Investigation of Air Cavity Formation During the High-Speed Vertical Water Entry of Wedges

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
Jingbo Wang ◽  
Odd M. Faltinsen
Keyword(s):  
Free Surface ◽  
High Speed ◽  
Nonlinear Boundary ◽  
Water Entry ◽  
Similarity Solutions ◽  
Free Surface Flows ◽  
Cavity Formation ◽  
Air Cavity ◽  
Numerical Instabilities ◽  
Entry Velocity

In this paper, a nonlinear boundary element method (BEM) is developed for investigating air cavity formation during the high-speed water entry of wedges. A technique is proposed for dynamic re-gridding of free surface boundaries. This technique applies to both equally and nonequally spaced grids, and it is able to suppress the numerical instabilities encountered using a BEM for simulating free surface flows. The authors also develop a purely numerical method to simulate nonviscous flow separation, which occurs when the flow reaches the knuckle of the wedge. The present nonlinear BEM has been verified by comparisons with similarity solutions. We also compare numerical results with experimental results. Finally, we give a numerical prediction of the evolution of the cavity until the closure of the cavity, and the influence of the initial entry velocity, wedge mass, and deadrise angle on the characteristics of the transient cavities is investigated.

scholarly journals Water entry of an expanding wedge/plate with flow detachment

2016 ◽  
Vol 797 ◽  
pp. 322-344 ◽  
Author(s):  
Yuriy A. Semenov ◽  
Guo Xiong Wu
Keyword(s):  
Free Surface ◽  
General Solution ◽  
Water Entry ◽  
Hodograph Method ◽  
Fixed Length ◽  
Pressure Distributions ◽  
Initial Stage ◽  
Special Cases ◽  
Wedge Plate ◽  
Special Case

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to ${\rm\pi}$. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions.

Nonlinear Boundary Conditions in Simulations of Electrochemical Experiments Using the Boundary Element Method.

2007 ◽  
Author(s):  
Markus Träuble ◽  
Carolina Nunes Kirchner ◽  
Gunther Wittstock ◽  
Theodore E. Simos ◽  
George Maroulis
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Element Method

On the interaction of a collapsing cavity and a compliant wall

1991 ◽  
Vol 226 ◽  
pp. 401-423 ◽  
Author(s):  
J. H. Duncan ◽  
S. Zhang
Keyword(s):  
Vertical Velocity ◽  
Nonlinear Boundary ◽  
Velocity Potential ◽  
Unit Area ◽  
Nonlinear Boundary Conditions ◽  
Fluid Density ◽  
Membrane Tension ◽  
Cavity Size ◽  
Compliant Wall ◽  
As If

The collapse of a spherical vapour cavity in the vicinity of a compliant boundary is examined numerically. The fluid is treated as a potential flow and a boundary-element method is used to solve Laplace's equation for the velocity potential. Full nonlinear boundary conditions are applied on the surface of the cavity. The compliant wall is modelled as a membrane with a spring foundation. At the interface between the fluid and the membrane, the pressure and vertical velocity in the flow are matched to the pressure and vertical velocity of the membrane using linearized conditions. The results of calculations are presented which show the effect of the parameters describing the flow (the initial cavity size and position, the fluid density and the pressure driving the collapse) and the parameters describing the compliant wall (the mass per unit area, membrane tension, spring constant and coating radius) on the interaction between the two. When the wall is rigid, the collapse of the cavity is characterized by the formation of a re-entrant jet that is directed toward the wall. However, if the properties of the compliant wall are chosen properly, the collapse can be made to occur spherically, as if the cavity were in an infinite fluid, or with the reentrant jet directed away from the wall, as if the cavity were adjacent to a free surface. This behaviour is in qualitative agreement with the experiments of Gibson & Blake (1982) and Shima, et al. (1989). Calculations of the transfer of energy between the flow and the coating are also presented.

Numerical Simulation of the Water Entry of a Wedge Based on the Complex Variable Boundary Element Method

2011 ◽  
Vol 90-93 ◽  
pp. 2507-2510 ◽  
Author(s):  
Jie Gao ◽  
Yong Hu Wang ◽  
Ke An Chen
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Complex Variable ◽  
Similarity Solution ◽  
Velocity Potential ◽  
Initial Conditions ◽  
Time Derivative ◽  
Water Entry ◽  
Variable Boundary ◽  
Element Method

The water entry problem of a wedge is simulated based on the velocity potential theory in time domain. The Complex Variable Boundary Element Method (CVBEM) is used in the stretched coordinate system. Before the simulation, the similarity solution is taken as the initial conditions. The auxiliary function scheme in conjunction with the same CVBEM is used to obtain the accurate time derivative of velocity potential and pressure distribution on wedge surface. The time marching solution is matched with the jet special treatment. Finally, the simulation results are compared with the similarity solution, which shows that the jet linear approximation can simulate the jet well.

Numerical solution for two-dimensional flow under sluice gates using the natural element method

2010 ◽  
Vol 37 (12) ◽  
pp. 1550-1559 ◽  
Author(s):  
Farhang Daneshmand ◽  
S.A. Samad Javanmard ◽  
Tahereh Liaghat ◽  
Mohammad Mohsen Moshksar ◽  
Jan F. Adamowski
Keyword(s):  
Free Surface ◽  
Numerical Technique ◽  
Surface Profile ◽  
Nonlinear Boundary Conditions ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Natural Element Method ◽  
Natural Element ◽  
Surface Profiles ◽  
Element Method

Fluid loads on a variety of hydraulic structures and the free surface profile of the flow are important for design purposes. This is a difficult task because the governing equations have nonlinear boundary conditions. The main objective of this paper is to develop a procedure based on the natural element method (NEM) for computation of free surface profiles, velocity and pressure distributions, and flow rates for a two-dimensional gravity fluid flow under sluice gates. Natural element method is a numerical technique in the field of computational mechanics and can be considered as a meshless method. In this analysis, the fluid was assumed to be inviscid and incompressible. The results obtained in the paper were confirmed via a hydraulic model test. Calculation results indicate a good agreement with previous flow solutions for the water surface profiles and pressure distributions throughout the flow domain and on the gate.

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.

A Fast New Algorithm for Solving a Nonlinear Beam Equation under Nonlinear Boundary Conditions

2017 ◽  
Vol 72 (5) ◽  
pp. 397-400 ◽  
Author(s):  
Chein-Shan Liu ◽  
Botong Li
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Nonlinear Boundary Conditions ◽  
Beam Equation ◽  
Test Functions ◽  
Nonlinear Beam ◽  
Expansion Coefficients ◽  
Sinusoidal Functions

AbstractFor the problem of a nonlinear beam equation under nonlinear boundary conditions of moments, a fast iterative method is developed by transforming the ordinary differential equation into an integral one. The sinusoidal functions are used subtly as test functions as well as the bases of numerical solution in the calculation. Due to the orthogonality of the sinusoidal functions, the expansion coefficients of numerical solution in closed form can be found easily. Hence, the iterative scheme converges very fast to find numerical solutions with high accuracy.

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