Separated inviscid sheet flows

2011 ◽  
Vol 678 ◽  
pp. 511-534 ◽  
Author(s):  
BUM-SANG YOON ◽  
YURIY A. SEMENOV
Keyword(s):  
Free Surface ◽  
Free Surface Flows ◽  
Bottom Surface ◽  
Free Boundaries ◽  
Trailing Edge ◽  
Hodograph Method ◽  
Inviscid Incompressible Fluid ◽  
Wide Range ◽  
Finite Distance ◽  
Supercritical Flows

A steady sheet flow of an inviscid incompressible fluid along a curvilinear surface ending with a rounded trailing edge is considered in the presence of gravity. The effect of surface tension is ignored. The formulation of the problem is applicable to the study of free-surface flows over obstacles in channels, weirs and spillways, and pouring flows. An advanced hodograph method is employed for solving the problem, which is reduced to a system of two integro-differential equations in the velocity modulus on the free surface and in the slope of the bottom surface. These equations are derived from the dynamic and kinematic boundary conditions. The Brillouin–Villat criterion is applied to determine the location of the point of flow separation from the rounded trailing edge. Results showing the effect of gravity on the flow detachment and the geometry of the free boundaries are presented over a wide range of Froude numbers including both subcritical and supercritical flows. For supercritical flows two families of solutions for an arbitrary bottom shape are reproduced. It is shown that the additional condition requiring the free surface to be flat at a finite distance from the end of the channel selects a unique solution for a given bottom height and geometry for supercritical flows. This solution is continuous in going from the subcritical to the supercritical flow regime.

Advanced CFD Simulations of free-surface flows around modern sailing yachts using a newly developed openFOAM solver

2016 ◽  
Author(s):  
Janek Meyer ◽  
Hannes Renzsch ◽  
Kai Graf ◽  
Thomas Slawig
Keyword(s):  
Free Surface ◽  
Large Scale ◽  
Breaking Waves ◽  
Free Surface Flows ◽  
Body Motion ◽  
Computational Time ◽  
Efficient Computation ◽  
Surface Flows ◽  
Scale Free ◽  
Wide Range

While plain vanilla OpenFOAM has strong capabilities with regards to quite a few typical CFD-tasks, some problems actually require additional bespoke solvers and numerics for efficient computation of high-quality results. One of the fields requiring these additions is the computation of large-scale free-surface flows as found e.g. in naval architecture. This holds especially for the flow around typical modern yacht hulls, often planing, sometimes with surface-piercing appendages. Particular challenges include, but are not limited to, breaking waves, sharpness of interface, numerical ventilation (aka streaking) and a wide range of flow phenomenon scales. A new OF-based application including newly implemented discretization schemes, gradient computation and rigid body motion computation is described. In the following the new code will be validated against published experimental data; the effect on accuracy, computational time and solver stability will be shown by comparison to standard OF-solvers (interFoam / interDyMFoam) and Star CCM+. The code’s capabilities to simulate complex “real-world” flows are shown on a well-known racing yacht design.

Free-surface flows past a surface-piercing object of finite length

1994 ◽  
Vol 273 ◽  
pp. 109-124 ◽  
Author(s):  
J. Asavanant ◽  
J.-M. Vanden-Broeck
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
Three Solutions ◽  
Surface Flows ◽  
Sharp Crest ◽  
Supercritical Flows

Steady two-dimensional flows past a parabolic obstacle lying on the free surface in water of finite depth are considered. The fluid is treated as inviscid and incompressible and the flow is assumed to be irrotational. Gravity is included in the free-surface condition. The problem is solved numerically by using boundary integral equation techniques. It is shown that there are solutions for which the flow is supercritical both upstream and downstream and others for which the flow is subcritical both upstream and downstream. These flows have continuous tangents at both ends of the obstacle at which separation occurs. For supercritical flows, there are up to three solutions corresponding to the same value of the Froude number when the obstacle is concave and up to two solutions when the obstacle is convex. For subcritical flows, there are solutions with waves behind the obstacle. As the Froude number decreases, these waves become steeper and the numerical calculations suggest that they, ultimately, reach limiting configurations with a sharp crest forming a 120° angle.

scholarly journals Splash jet generated by collision of two liquid wedges

2013 ◽  
Vol 737 ◽  
pp. 132-145 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu ◽  
J. M. Oliver
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Hodograph Method ◽  
Pressure Distributions ◽  
Wide Range ◽  
Self Similar Solution ◽  
Gravity Effects ◽  
Self Similar ◽  
The Impact ◽  
Analytical Expressions

AbstractA complete nonlinear self-similar solution that characterizes the impact of two liquid wedges symmetric about the velocity direction is obtained assuming the liquid to be ideal and incompressible, with negligible surface tension and gravity effects. Employing the integral hodograph method, analytical expressions for the complex potential and for its derivatives are derived. The boundary value problem is reduced to two integro-differential equations in terms of the velocity modulus and angle to the free surface. Numerical results are presented in a wide range of wedge angles for the free surface shapes, streamline patterns, and pressure distributions. It is found that the splash jet may cause secondary impacts. The regions with and without secondary impacts in the plane of the wedge angles are determined.

The nonlinear problem of a gliding body with gravity

2013 ◽  
Vol 727 ◽  
pp. 132-160 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Body Surface ◽  
Breaking Waves ◽  
The Body ◽  
Surface Shape ◽  
Parameter Plane ◽  
Hodograph Method ◽  
Wide Range ◽  
Free Surface Shape ◽  
Analytical Expressions

AbstractAnalysis based on the velocity potential free flow theory with the fully nonlinear boundary condition is made for the steady flow generated by a body gliding along a free surface. Employing the integral hodograph method, we derive analytical expressions for the complex velocity and for the derivative of the complex potential with the coordinate of a parameter plane. The boundary value problem is transformed into a system of two integro-differential equations for the velocity modulus on the free surface and for the slope of the wetted body surface in the parameter plane. The same slope and curvature of the free surface and the body surface at the intersection are adopted to determine the separation points of the flow and from the body. Numerical results are provided for a gliding flat plate and a circular cylinder. The pressure distribution along the body and the free surface shape are presented for a wide range of Froude numbers, within the limit for which the solution corresponding to non-breaking waves downstream can be obtained.

Inviscid free-surface flow over a periodic wall

1991 ◽  
Vol 226 ◽  
pp. 189-203 ◽  
Author(s):  
V. Bontozoglou ◽  
S. Kalliadasis ◽  
A. J. Karabelas
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Surface Shape ◽  
Flow Parameters ◽  
Material Deposition ◽  
Straightforward Method ◽  
Wide Range ◽  
Free Surface Shape

A numerical method is described, based on the hodograph formulation, for analysing in viscid, free-surface flows over a periodic wall. An efficient implementation of the wall boundary condition results in a straightforward method, accurate for a wide range of bottom undulation heights and flow parameters. It is demonstrated that a series of resonances is possible between the bottom undulations and the free surface. The steady, free-surface profiles are accurately calculated for a wide range of current velocities and are shown to be significantly dimpled by higher harmonics. A study of the flow field indicates that the free-surface shape strongly affects the velocities close to the wall, leading to distributions which change dramatically with current velocity. Some implications of the new results on the phenomena of wall dissolution or material deposition, Bragg scattering of surface waves and sediment transport in rivers, are discussed.

The effect of gravity and cavitation on a hydrofoil near the free surface

2008 ◽  
Vol 597 ◽  
pp. 371-394 ◽  
Author(s):  
ODD M. FALTINSEN ◽  
YURIY A. SEMENOV
Keyword(s):  
Free Surface ◽  
Numerical Procedure ◽  
Free Boundaries ◽  
Complex Flow ◽  
Initial Flow ◽  
Closed Cavity ◽  
Flow Parameters ◽  
Wide Range ◽  
Wake Model

A nonlinear analysis has been made to determine the effects of the free surface and transverse gravity field on the steady cavity flow past a shaped hydrofoil beneath the free surface. A closed cavity wake model has been proposed, and a method for the determination of an analytical function from its modulus and argument on the region boundary has been employed to derive the complex flow potential in a parameter plane. The boundary-value problem is reduced to a system of integral and integro-differential equations in the velocity modulus along the free boundaries and the velocity angle along the hydrofoil surface, both written as a function of parametric variables. The system of equations is solved through a numerical procedure, which is validated in the cases of a cavitating flat plate and non-cavitating shaped hydrofoils by comparison with data available in the literature. The results are presented in a wide range of Froude numbers and depths of submergence in terms of the cavity and free-surface shapes and force coefficients. The influences of the free surface and gravity on the aforementioned quantities are discussed. The limiting cavity size corresponding to zero cavitation number in the presence of gravity is found for various initial flow parameters.

scholarly journals Viscous free-surface flows past cylinders

2020 ◽  
Vol 5 (8) ◽  
Author(s):  
Edward M. Hinton ◽  
Andrew J. Hogg ◽  
Herbert E. Huppert
Keyword(s):  
Free Surface ◽  
Free Surface Flows ◽  
Surface Flows

scholarly journals Frequency Division Multiplexing of Terahertz Waves Realized by Diffractive Optical Elements

2021 ◽  
Vol 11 (14) ◽  
pp. 6246
Author(s):  
Paweł Komorowski ◽  
Patrycja Czerwińska ◽  
Mateusz Kaluza ◽  
Mateusz Surma ◽  
Przemysław Zagrajek ◽  
...  
Keyword(s):  
Frequency Division Multiplexing ◽  
Diffractive Optical Elements ◽  
Frequency Division ◽  
Terahertz Waves ◽  
Optical Elements ◽  
Telecommunication Systems ◽  
Wide Range ◽  
The Future ◽  
Wireless Telecommunication ◽  
Finite Distance

Recently, one of the most commonly discussed applications of terahertz radiation is wireless telecommunication. It is believed that the future 6G systems will utilize this frequency range. Although the exact technology of future telecommunication systems is not yet known, it is certain that methods for increasing their bandwidth should be investigated in advance. In this paper, we present the diffractive optical elements for the frequency division multiplexing of terahertz waves. The structures have been designed as a combination of a binary phase grating and a converging diffractive lens. The grating allows for differentiating the frequencies, while the lens assures separation and focusing at the finite distance. Designed structures have been manufactured from polyamide PA12 using the SLS 3D printer and verified experimentally. Simulations and experimental results are shown for different focal lengths. Moreover, parallel data transmission is shown for two channels of different carrier frequencies propagating in the same optical path. The designed structure allowed for detecting both signals independently without observable crosstalk. The proposed diffractive elements can work in a wide range of terahertz and sub-terahertz frequencies, depending on the design assumptions. Therefore, they can be considered as an appealing solution, regardless of the band finally used by the future telecommunication systems.

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