Simulation of the Dynamic Behavior of Ships Based on Slender-Body Theory (SBT)

2013 ◽  
Author(s):  
Oscar D. Tascon ◽  
Jaime D. Mora ◽  
Roberto J. Algarin
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Dynamic Performance ◽  
Slender Body ◽  
Computational Time ◽  
Slender Body Theory ◽  
Shipbuilding Industry ◽  
Technology Corporation ◽  
The Mathematical Model ◽  
Body Theory

One of the aims of the Colombian Ministry of Defense in the field of science and technology is to develop and build in-house simulators for training. An important prerequisite in the development of these types of simulators is to have accurate knowledge about the forces that act on the particular type of ship being considered. In the pursuit of this objective, the Science & Technology Corporation for the Development of the Shipbuilding Industry in Colombia — COTECMAR has established a research program for the development of physics-based models to predict the generalized forces acting on maneuvering ships. The following article proposes a mathematical model capable of providing the simulator with calculations for the hydrodynamic forces acting on three types of ships: displacement ships, submarines and planning hulls. Derived from slender-body theory (SBT), the mathematical model presented minimizes computational time and eliminates the need for experimental data, making it possible to use the calculation of hydrodynamics forces at the initial stages of design when the geometry of the ship is constantly revised and the effect of those changes in the dynamic performance of the ship needs to be assessed. The article explains the mathematical model proposed and its modular nature, compares existing numerical and experimental data with results obtained from this study for the three case studies selected: displacement ships, submarines and planing hulls.

scholarly journals Metachronal Swimming with Rigid Arms near Boundaries

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 24 ◽  
Author(s):  
Rintaro Hayashi ◽  
Daisuke Takagi
Keyword(s):  
Mathematical Model ◽  
Stokes Flow ◽  
Experimental System ◽  
Phase Delay ◽  
Slender Body ◽  
Inertial Effects ◽  
Slender Body Theory ◽  
Measured Displacement ◽  
Body Theory ◽  
Over Time

Various organisms such as crustaceans use their appendages for locomotion. If they are close to a confining boundary then viscous as opposed to inertial effects can play a central role in governing the dynamics. To study the minimal ingredients needed for swimming without inertia, we built an experimental system featuring a robot equipped with a pair of rigid slender arms with negligible inertia. Our results show that directing the arms to oscillate about the same time-averaged orientation produces no net displacement of the robot each cycle, regardless of any phase delay between the oscillating arms. The robot is able to swim if the arms oscillate asynchronously around distinct orientations. The measured displacement over time matches well with a mathematical model based on slender-body theory for Stokes flow. Near a confining boundary, the robot with no net displacement every cycle showed similar behavior, while the swimming robot increased in speed closer to the boundary.

Note on the swimming of slender fish

1960 ◽  
Vol 9 (2) ◽  
pp. 305-317 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Swimming Speed ◽  
Critical Value ◽  
Slender Body ◽  
Vortex Wake ◽  
Frictional Drag ◽  
Slender Body Theory ◽  
Propulsive Efficiency ◽  
Deformable Bodies ◽  
Work Done ◽  
Body Theory

The paper seeks to determine what transverse oscillatory movements a slender fish can make which will give it a high Froude propulsive efficiency, $\frac{\hbox{(forward velocity)} \times \hbox{(thrust available to overcome frictional drag)}} {\hbox {(work done to produce both thrust and vortex wake)}}.$ The recommended procedure is for the fish to pass a wave down its body at a speed of around $\frac {5} {4}$ of the desired swimming speed, the amplitude increasing from zero over the front portion to a maximum at the tail, whose span should exceed a certain critical value, and the waveform including both a positive and a negative phase so that angular recoil is minimized. The Appendix gives a review of slender-body theory for deformable bodies.

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
Author(s):  
Joseph B. Keller ◽  
Sol I. Rubinow
Keyword(s):  
Integral Equation ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Unit Length ◽  
The Body ◽  
Slender Body ◽  
Slow Flow ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

Application of a Bubble-Induced Turbulence Model to Subcooled Boiling in a Vertical Pipe

1999 ◽  
Author(s):  
Mahmut D. Mat ◽  
Yüksel Kaplan ◽  
Olusegun J. Ilegbusi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Liquid Phase ◽  
Turbulence Model ◽  
Transport Equations ◽  
Subcooled Boiling ◽  
Vertical Pipe ◽  
Void Fractions ◽  
Turbulence Production ◽  
The Mathematical Model

Abstract Subcooled boiling of water in a vertical pipe is numerically investigated. The mathematical model involves solution of transport equations for vapor and liquid phase separately. Turbulence model considers the turbulence production and dissipation by the motion of the bubbles. The radial and axial void fractions, temperature and velocity profiles in the pipe are calculated. The estimated results are compared to experimental data available in the literature. It is found that while present study satisfactorily agrees with experimental data in the literature, it improves the prediction at lower void fractions.

Analytical Study of Hydro-Pneumatic Processes for Gorlov's Power System

1994 ◽  
Vol 208 (1) ◽  
pp. 67-70
Author(s):  
A I Ryazanov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Power System ◽  
Analytical Study ◽  
Model Tests ◽  
Air Pressure ◽  
Pneumatic Power ◽  
Time Required ◽  
The Mathematical Model

This paper describes the aerohydrodvnamics of processes in chambers of Gorlov's hydro-pneumatic power system. The mathematical model is developed to determine the main parameters of the processes: water and air velocities, air pressure in the chamber, the periods of time required to fill and empty the chambers and the output of energy during the cycle. The results obtained are in agreement with experimental data and model tests.

Rods falling near a vertical wall

1977 ◽  
Vol 83 (2) ◽  
pp. 273-287 ◽  
Author(s):  
W. B. Russel ◽  
E. J. Hinch ◽  
L. G. Leal ◽  
G. Tieffenbruck
Keyword(s):  
Integral Equation ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Vertical Wall ◽  
Numerical Results ◽  
Slender Body ◽  
Asymptotic Results ◽  
Slender Body Theory ◽  
Friction Coefficients ◽  
Body Theory

As an inclined rod sediments in an unbounded viscous fluid it will drift horizontally but will not rotate. When it approaches a vertical wall, the rod rotates and so turns away from the wall. Illustrative experiments and a slender-body theory of this phenomenon are presented. In an incidental study the friction coefficients for an isolated rod are found by numerical solution of the slender-body integral equation. These friction coefficients are compared with the asymptotic results of Batchelor (1970) and the numerical results of Youngren ' Acrivos (1975), who did not make a slender-body approximation.

scholarly journals MATHEMATICAL MODELING OF LEACHING PROCESS OF RED MUD IN ORDER TO OBTAIN THE KINETICS PARAMETERS

2015 ◽  
Vol 14 (2) ◽  
pp. 90 ◽  
Author(s):  
K. L. M. Dos Passos ◽  
B. M. Viegas ◽  
E. N. Macêdo ◽  
J. A. S. Souza ◽  
E. M. Magalhães
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Red Mud ◽  
Mineralogical Composition ◽  
Raw Material ◽  
Data Conversion ◽  
Kinetics Parameters ◽  
Leaching Process ◽  
Iron Leaching ◽  
The Mathematical Model

The use of the waste of the Bayer process, red mud, is due to its chemical and mineralogical composition that shows a material rich in oxides of iron, titanium and aluminum. Some studies conducted show that this waste can be applied as a source of alternative raw material for concentration and subsequent recovery of titanium compounds from an iron leaching process, which is present in higher amounts, about 30% by weight. To obtain a greater understanding about the leaching kinetics, the information of the kinetic data of this process is very important. In this context, the main objective of this work is the development of a mathematical model that is able to fit the experimental data (conversion / extraction iron, titanium and aluminum) of the leaching process by which is possible to obtain the main kinetic parameters such as the activation energy and the velocity of chemical reactions as well as the controlling step of the process. The development of the mathematical model was based on the model of core decreasing. The obtained model system of ordinary differential equations was able to fit the experimental data obtained from the leaching process, enabling the determination of the controlling step, the rate constants and the activation energies of the leaching process.

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