Streamlines and Pressure Distribution on Arbitrary Ship Hulls at Zero Froude Number

1968 ◽  
Vol 12 (03) ◽  
pp. 231-236
Author(s):  
E. O. Tuck ◽  
C. von Kerczek
Keyword(s):  
Conformal Mapping ◽  
Froude Number ◽  
Potential Flow ◽  
Hydrodynamic Pressure ◽  
Polynomial Functions ◽  
Forward Motion ◽  
Mapping Functions ◽  
Ship Hulls ◽  
Longitudinal Coordinate ◽  
Quantities Of Interest

A method is presented for computing the streamlines and the hydrodynamic pressure along the streamlines on a slender ship in steady forward motion at zero Froude number. The ship is represented by conformal mapping functions whose coefficients are polynomial functions of the longitudinal coordinate of the ship. The potential flow about the ship is obtained in terms of the coefficients of the surface equation of the ship and all flow quantities of interest are computed directly from these coefficients.

The Representation of Ship Hulls by Conformal Mapping Functions

1969 ◽  
Vol 13 (04) ◽  
pp. 284-298
Author(s):  
C. von Kerczek ◽  
E. O. Tuckk
Keyword(s):  
Conformal Mapping ◽  
Cross Sections ◽  
Design Procedure ◽  
Mapping Function ◽  
Polynomial Functions ◽  
Mapping Functions ◽  
Ship Hulls ◽  
Longitudinal Coordinate ◽  
Hydrodynamic Calculations ◽  
Hull Design

A method is described by which an arbitrary hull surface may be approximated by ananalytic function. The cross sections of the ship are represented by conformal mapping functions whose coefficients are polynomial functions of the longitudinal coordinate of the ship. Such a representation is intended to be used primarily for hydrodynamic calculations. However, the procedure used in generating the mapping function representation of the hull surface can, with some slight modifications, be used to freely form a hull surface. This could possibly be the basis of a mathematical hull design procedure.

The Representation of Ship Hulls by Conformal Mapping Functions: Fractional Maps

1983 ◽  
Vol 27 (03) ◽  
pp. 158-159
Author(s):  
C. von Kerczek
Keyword(s):  
Conformal Mapping ◽  
Cross Sections ◽  
Polynomial Interpolation ◽  
Spline Interpolation ◽  
Longitudinal Direction ◽  
Interpolation Scheme ◽  
Mapping Functions ◽  
Ship Hulls ◽  
The Cross ◽  
High Degree

The method for analytically representing ship hulls by conformal mapping functions of the cross sections and lengthwise polynomial interpolation of the mappings, which was developed by von Kerczek and Tuck [1], has found useful applications to ship hydrodynamics (see references [2] and [3]) as well as ship design [4]. In both such applications, however, there have been two major criticisms of this type of representation of the underwater portion of the ship hull. The first criticism concerned the occurrence of undesirable waviness in the longitudinal direction of the cross sections of the ship. This waviness is due to fitting high-degree polynomials to very slowly varying data. This defect of the surface representation can be removed easily by abandoning the polynomial interpolation and substituting some form of spline interpolation. It has been found that interpolation by simple Hermite cubic splines works very well. Such modifications of the lengthwise interpolation scheme are well known and need no elaboration.

Modeling of Finite-span Ram Wings Moving Above Water at Finite Froude Numbers

2014 ◽  
Vol 58 (03) ◽  
pp. 146-156
Author(s):  
Konstantin I. Matveev
Keyword(s):  
Potential Flow ◽  
Ground Effect ◽  
Flow Theory ◽  
Solid Surfaces ◽  
Forward Motion ◽  
Variable Parameters ◽  
Finite Span ◽  
Effect Theory ◽  
Lifting Surfaces ◽  
Strong Ground

Power-augmented ram wings can be used for very fast transportation of heavy cargo over water and relatively flat solid surfaces. This article describes a coupled aerohydrodynamic model for a ram wing in steady forward motion. Effects of a finite wingspan and finite Froude numbers are accounted for by the extreme ground effect theory for airflow and a linearized potential flow theory for water. Representative results showing the influence of several variable parameters of the vehicle geometry and operational regimes are demonstrated for a selected ram-wing configuration. The developed method can be applied for modeling of airborne lifting surfaces operating in the strong ground effect on a variety of fast marine craft.

Conformal mapping for potential flow about airfoils with attached flap.

1973 ◽  
Vol 10 (1) ◽  
pp. 60-62 ◽  
Author(s):  
Vernon J. Rossow
Keyword(s):  
Conformal Mapping ◽  
Potential Flow

Theoretical Range and Trajectory of a Water Jet

2015 ◽  
Author(s):  
Ben Trettel ◽  
Ofodike A. Ezekoye
Keyword(s):  
Experimental Data ◽  
Froude Number ◽  
Analytical Model ◽  
Droplet Size ◽  
Fire Protection ◽  
Potential Flow ◽  
Water Jet ◽  
Simple Analytical Model ◽  
Qualitative Understanding ◽  
Vertical Height

The trajectory of a water jet is important in many applications, including fire protection, irrigation, and decorative fountains. Increasing the maximum distance the jet travels by changing the nozzle or other variables is often desirable. This distance could be the horizontal range (also often called the reach or throw) or the maximum vertical height. Which factors control the trajectory are unclear. Consequently, a simple analytical model is developed which provides a qualitative understanding of the system. This model differs significantly from previous models. Previous models either used a dragless trajectory, which is correct according to potential flow theory if the jet does not break into droplets, or treated the trajectory as if droplets formed immediately upon leaving the nozzle. Both approaches have been noted to be unsatisfactory by past researchers. Our model compares favorably against available experimental data. Using our model, we show that the range decreases as the nozzle Froude number increases and that range increases as breakup length and droplet size increase.

Research on Trailing Cavity of Underwater Vehicles Based on Potential Flow Theory

2018 ◽  
Author(s):  
Zeyu Shi ◽  
Xiongliang Yao ◽  
Jiaolong Zhao ◽  
Longquan Sun ◽  
Yue Tian
Keyword(s):  
Froude Number ◽  
Potential Flow ◽  
Flow Theory ◽  
Research Problem ◽  
Underwater Vehicles ◽  
Calculation Model ◽  
Cavitation Number ◽  
Polar Coordinates ◽  
Hydrodynamic Characteristics ◽  
Potential Flow Theory

In the exceeding water process of underwater vehicles, the existing of trailing cavity will have distinct effects on the hydrodynamic characteristics of vehicles. Recent researches mostly leave gravity effect out of consideration, while the gravity will affect trailing cavity characteristics and then affect the hydrodynamic characteristics of vehicles. In this study, we research the effect of gravity on the trailing cavity of underwater vehicles. Firstly, a complex boundary model which taken partial cavity into consideration is established based on potential flow theory and a program according to this model is written. Because all flow parameter has nothing to do with the radial location, the research problem can be simplified as a two-dimensional problem and studied in polar coordinates. With regularization of the length of the navigation calculation model, infinity to flow velocity and the distance pressure, research domain can be represented by plane in the containing slit. The program is proved to be effective by comparison the results with the data in existing papers. Finally, we calculate the trailing cavity forms of a cone and an underwater vehicle under different cavitation numbers and Froude numbers to study the rules of trailing cavity forms changing with cavitation number and Froude number. Under the same number of Froude, the cavity size of the rear part of vehicle gradually decreases with the increasing cavitation number, and the maximum radius of the cavity equals to the biggest size of the tail radius of the vehicle. Under the same cavitation number bodies, vehicle trailing cavity length gradually increases with the increase of Froude number, but radius of the cavity of the vehicle changed little, the largest radius is equivalent to the tail radius of the vehicle.

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