Virtual Replica of a Towing Tank Experiment to Determine the Kelvin Half-Angle of a Ship in Restricted Water

The numerical simulation of ship flows has evolved into a highly practical approach in naval architecture. In typical virtual towing tanks, the principle of Galilean relativity is invoked to maintain the ship as fixed, while the surrounding water is prescribed to flow past it. This assumption may be identified, at least partly, as being responsible for the wide-scale adoption of computational solutions within practitioners’ toolkits. However, it carries several assumptions, such as the levels of inlet turbulence and their effect on flow properties. This study presents an alternative virtual towing tank, where the ship is simulated to advance over a stationary fluid. To supplement the present work, the free surface disturbance is processed into Fourier space to determine the Kelvin half-angle for an example case. The results suggest that it is possible to construct a fully unsteady virtual towing tank using the overset method, without relying on Galilean relativity. Differences between theoretical and numerical predictions for the Kelvin half-angle are predominantly attributed to the assumptions used by the theoretical method. The methods presented in this work can potentially be used to validate free-surface flows, even when one does not have access to experimental wave elevation data.

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A Potential Field Description for Gravity-Driven Film Flow over Piece-Wise Planar Topography

Fluids ◽

10.3390/fluids4020082 ◽

2019 ◽

Vol 4 (2) ◽

pp. 82 ◽

Cited By ~ 3

Author(s):

Markus Scholle ◽

Philip H. Gaskell ◽

Florian Marner

Keyword(s):

Free Surface ◽

Potential Field ◽

Numerical Solutions ◽

Film Flow ◽

First Integral ◽

Characteristic Parameter ◽

Numerical Predictions ◽

Planar Substrate ◽

Surface Disturbance ◽

Gravity Driven

Models based on a potential field description and corresponding first integral formulation, embodying a reduction of the associated dynamic boundary condition at a free surface to one of a standard Dirichlet-Neumann type, are used to explore the problem of continuous gravity-driven film flow down an inclined piece-wise planar substrate in the absence of inertia. Numerical solutions of the first integral equations are compared with analytical ones from a linearised form of a reduced equation set resulting from application of the long-wave approximation. The results obtained are shown to: (i) be in very close agreement with existing, comparable experimental data and complementary numerical predictions for isolated step-like topography available in the open literature; (ii) exhibit the same qualitative behaviour for a range of Capillary numbers and step heights/depths, becoming quantitively similar when both are small. A novel outcome of the formulation adopted is identification of an analytic criteria enabling a simple classification procedure for specifying the characteristic nature of the free surface disturbance formed; leading subsequently to the generation of a related, practically relevant, characteristic parameter map in terms of the substrate inclination angle and the Capillary number of the associated flow.

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The cauchy-poisson waves in an inviscid rotating stratified liquid

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953390000053 ◽

1990 ◽

Vol 3 (1) ◽

pp. 57-64

Author(s):

Lokenath Debnath ◽

Uma B. Guha ◽

Manjusri Basu

Keyword(s):

Free Surface ◽

Gravity Waves ◽

Large Time ◽

Boussinesq Approximation ◽

Free Surface Flows ◽

Phase Method ◽

Stationary Phase Method ◽

Initial Value ◽

Surface Disturbance ◽

Stratified Liquid

Based upon the Boussinesq approximation, an initial value investigation is made of the axisymmetric free surface flows generated in an inviscid rotating stratified liquid of infinite depth by the prescribed free surface disturbance. The asymptotic analysis of the integral solution is carried out by the stationary phase method to describe the solution for large time and large distance from the source of the disturbance. The asymptotic solution is found to consist of the classical free surface gravity waves and the internal-inertial waves.

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A Simple Verification Test for Nonlinear Flow Calculations Around a Ship Hull Steadily Advancing in Calm Water

Journal of Ship Research ◽

10.5957/jsr.2012.56.3.162 ◽

2012 ◽

Vol 56 (03) ◽

pp. 162-169

Author(s):

Francis Noblesse ◽

Lijue Wang ◽

Chi Yang

Keyword(s):

Free Surface ◽

Boundary Conditions ◽

Free Surface Flows ◽

Wave Profile ◽

Surface Flows ◽

Ship Hulls ◽

Euler Flow ◽

Numerical Predictions ◽

Calm Water ◽

Analytical Relations

Simple analytical relations that can readily be applied to verify a critical aspect of numerical predictions of fully nonlinear free-surface flows around ship hulls steadily advancing in calm water are given. The relations do not involve the flow field equations; that is, they are only based on the boundary conditions at the ship hull surface and at the free surface. These boundary conditions have a predominant influence on free-surface flows around advancing ship hulls. The analytical relations are exact for inviscid flows, and can be applied to numerical methods that solve either the Laplace equation (potential-flow methods) or the Euler flow equations (CFD Euler-flow methods). They provide a simple test to verify if numerical predictions given by nonlinear potential-flow or Euler-flow methods correctly satisfy the hull-surface and free-surface boundary conditions along the contact curve between the hull surface and the free surface. The relations might also be used to verify CFD methods that solve the RANS equations if they are applied at the edge of the viscous boundary layer. The analytical test can identify an inconsistency, which might point to a "method issue" related to a feature of a numerical method (e.g., a numerical-differentiation scheme) or an "implementation issue" in the implementation of the method (e.g., a poor discretization). For purposes of illustration, the test is applied to predictions of flows around the Wigley parabolic hull given by two CFD methods that solve the Euler equations with fully nonlinear boundary conditions at the free surface. This illustrative example demonstrates that the test can indeed be useful to identify numerical inaccuracies. The analytical relations can also be used to determine experimental values of the flow velocity at a ship wave profile that correspond to measurements of the wave profile.

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