Minimising wave drag for free surface flow past a two-dimensional stern

2011 ◽  
Vol 23 (7) ◽  
pp. 072101 ◽  
Author(s):  
Osama Ogilat ◽  
Scott W. McCue ◽  
Ian W. Turner ◽  
John A. Belward ◽  
Benjamin J. Binder
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Wave Drag ◽  
Surface Flow ◽  
Two Dimensional ◽  
Flow Past

scholarly journals Steady Two-Dimensional Free-Surface Flow Past Disturbances in an Open Channel: Solutions of the Korteweg–De Vries Equation and Analysis of the Weakly Nonlinear Phase Space

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 24 ◽  
Author(s):  
Benjamin Binder
Keyword(s):  
Free Surface ◽  
Open Channel ◽  
Kdv Equation ◽  
Bottom Topography ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Two Dimensional ◽  
Model Approximation ◽  
Flow Past ◽  
Channel Bottom

Two-dimensional free-surface flow past disturbances in an open channel is a classical problem in hydrodynamics—a problem that has received considerable attention over the last two centuries (e.g., see Lamb’s Treatise, 1879). With traces back to Russell’s experimental observations of the Great Wave of Translation in 1834, Korteweg and de Vries (1895), and others, derived an unforced equation to describe the balance between nonlinearity and dispersion required to model the solitary wave. More recently, Akylas (1984) derived a forced KdV equation to model a pressure distribution on the free-surface (e.g., a ship). Since then, the forced KdV equation has been shown to be a useful model approximation for two-dimensional flow past disturbances in an open channel. In this paper, we review the stationary solutions of the forced KdV equation for four types of localised disturbances: (i) a flat plate separating two free surfaces; (ii) a compact bump, or dip in the channel bottom topography; (iii) a compact distribution of pressure on the free surface and (iv) a step-wise change in the otherwise constant horizontal level of the channel bottom topography. Moreover, Dias and Vanden-Broeck (2002) developed a phase plane method to analyse flow over a bump, and this general approach has also been applied to the three other types of forcing (see Binder et al., 2005–2015, and others). In this study, we use eleven basic flow types to classify the steady solutions of the forced KdV equation using the phase plane method. Additionally, considering solutions that are wave-free both far upstream and far downstream, we compare KdV model approximations of the uniform flow conditions in the far-field with exact solutions of the full problem. In particular, we derive a new KdV model approximation for the upstream dimensionless flow-rate which is conveniently given in terms of the known downstream dimensionless flow-rate.

SPLASH Nonlinear and Unsteady Free-Surface Analysis Code for Grand Prix Yacht Design

1997 ◽  
Author(s):  
Bruce S. Rosen ◽  
Joseph P. Laiosa
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Inviscid Flow ◽  
Wave Drag ◽  
Surface Flow ◽  
Viscous Drag ◽  
Accurate Estimation ◽  
Following Seas ◽  
Induced Drag ◽  
Lifting Surfaces

The SPLASH free-surface potential flow panel code computer program is presented. The 3D flow theory and its numerical implementation are discussed. Some more conventional applications are reviewed, for steady flow past solid bodies, and for classical linearized free-surface flow. New free-surface capabilities are also described, notably, steady nonlinear solutions, and novel unsteady partially­nonlinear solutions in the frequency domain. The inviscid flow method treats both free-surface waves and lifting surfaces. The calculations yield predictions for complex interactions at heel and yaw such as wave drag due to lift, the effect of the free­surface on lift and lift-induced drag, and unsteady motions and forces in oblique or following seas. These are in addition to the usual predictions for the simpler effects considered separately, for example double-body lift and induced drag, and upright steady wave resistance or added resistance in head seas. For prediction of total resistance, the use of computed variable wetted areas and wetted lengths in a standard semi-empirical, handbook-type "viscous stripping" algorithm provides a more accurate estimation of viscous drag than is possible otherwise. Results from a variety of IACC and IMS yacht design studies, including comparisons with experimental data, support the conclusion that the free­surface panel code can be used for reliable and accurate prediction of sailboat performance.

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