Wave Forces on a Stationary Platform of Elliptical Shape

1973 ◽  
Vol 17 (02) ◽  
pp. 61-71
Author(s):  
H. S. Chen ◽  
C. C. Mei
Keyword(s):  
Diffraction Problem ◽  
Wave Length ◽  
Practical Interest ◽  
Vertical Cylinder ◽  
Present Theory ◽  
Wave Forces ◽  
Mathieu Functions ◽  
Body Type ◽  
Elliptical Cross ◽  
Long Wave

Exciting forces and moments due to plane incident waves on a stationary platform are studied in this paper. The platform is a vertical cylinder with a finite draft and elliptical cross section. The mathematical solution to the diffraction problem is obtained on the basis of the linearized long wave approximation. Numerical results via Mathieu functions are presented for a shiplike body with beam-to-length ratio Various draft-to-depth ratios and angles of incidence are considered. Results have been checked with the limiting case of a circular cylinder for the long-wave length range. Aside from its own practical interest, the present theory provides a basis for comparison with other approximate theories of slender-body type and serves as a prelude to the corresponding calculations for arbitrary wavelengths.

Calculation of Wave Forces on Cylindrical Piles Using a 3D Numerical Wave Tank

2013 ◽  
Author(s):  
Arun Kamath ◽  
Hans Bihs ◽  
Øivind A. Arntsen
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Practical Interest ◽  
Vertical Cylinder ◽  
Free Water ◽  
Wave Force ◽  
Weno Scheme ◽  
Wave Forces ◽  
Single Cylinder ◽  
Cylindrical Piles

Offshore constructions generally include a large number of vertical cylinders in the support structure. The calculation of wave forces on a vertical cylinder and hydrodynamic effects on it in the presence of neighbouring cylinders is of practical interest. In this paper, a 3D numerical model is used to calculate wave forces on bottom fixed cylindrical piles. Two cases are considered in this study: a single cylinder and a pair of tandem cylinders. A scenario with multiple cylindrical structures in close proximity introduces complex wave-structure interactions and would be of great interest to observe this in detail in a three-dimensional simulation. The wave force exerted on a cylindrical pile is numerically calculated by integrating the pressure and the wall shear stress around the surface of the cylinder. In the case of the single cylinder, the force calculated by the model is compared to the force predicted by the Morison formula and MacCamy-Fuchs theory. In the second case, the pair of cylinders is aligned in the direction of the incoming waves. The numerically calculated inline wave force on each cylinder is compared to the analytical solution for this setup and a good agreement is seen. The Reynolds-Averaged Navier-Stokes equations are used as the governing equations for the fluid flow in the numerical model. The convective terms are discretized using a 5th-order conservative finite difference WENO scheme. A 3rd-order accurate TVD Range-Kutta scheme is used for time discretization. Chorin’s projection method is used to discretize the pressure. The Poisson equation for pressure is solved using a preconditioned BiCGStab algorithm. The level set method is used to obtain a sharp representation of the free water surface. Turbulence in the flow is simulated using the k-ω model. The numerical model is adapted to parallel processing using the MPI library to improve the computing performance of the code.

scholarly journals Wave loadings on a vertical cylinder due to heave motion

1995 ◽  
Vol 18 (1) ◽  
pp. 151-170 ◽  
Author(s):  
D. D. Bhatta ◽  
M. Rahman
Keyword(s):  
Velocity Potential ◽  
Diffraction Problem ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Wave Forces ◽  
Wave Loads ◽  
Exterior Region ◽  
Calm Water ◽  
Heave Motion ◽  
Fixed Structure

Wave forces and moments due to scattering and radiation for a vertical circular cylinder heaving in water of finite depth are derived analytically. These are derived from the total velocity potential which can be decomposed as two velocity potentials; one due to scattering in the presence of an incident wave on fixed structure (diffraction problem), and the other due to radiation by the heave motion on calm water (radiation problem). For each part, the velocity potential is derived by considering two regions, namely, interior region and exterior region. The complex matrix equations are solved numerically to determine the unknown coefficients to compute the wave loads. Some numerical results are presented for different depth to radius and draft to radius ratios.

Properties of Ebonite. XXIX. The Absorption Spectrum of Ebonite

1949 ◽  
Vol 22 (1) ◽  
pp. 231-232
Author(s):  
E. H. Dock ◽  
B. D. Porritt ◽  
W. H. Willott
Keyword(s):  
Absorption Spectrum ◽  
Present Note ◽  
Wave Length ◽  
Thin Sheet ◽  
Practical Interest ◽  
Inert Gas ◽  
Long Wave ◽  
Absorption Of Light ◽  
Molten Sulfur ◽  
Deposited Film

Abstract The absorption spectrum of ebonite has some practical interest, because the absorption of light causes the surface to deteriorate. A knowledge of the absorption spectrum should help in discovering which are the harmful rays. Published information hitherto appears to be limited to radiation of long wave length, i.e., thermal or infrared. The present note describes experiments on rubber-sulfur (65:35 or 68:32) compositions vulcanized for about 5 hours at 155° C. Owing to the great opacity of ebonite, it is necessary to work with very thin specimens. Various methods of obtaining these suggest themselves: (1) grinding down a small thin sheet; (2) cutting thin shavings; (3) vulcanizing as of a thin film between glass or quartz plates; (4) vulcanizing a film of rubber, deposited on glass or quartz, by immersion in molten sulfur; (5) vulcanizing a deposited film of a rubber-sulfur mix by heating in an inert gas. Methods (1), (2) and (5) have so far been found the most satisfactory. In method (2) it is advantageous to soften the material by swelling, e.g., in nitrobenzene; the swelling liquid can then be removed by extraction with a volatile solvent. Methods (1) and (2) have the advantage of enabling specimens to be obtained from larger pieces that can be analyzed or submitted to other tests.

Stresses and Deformations of Toroidal Shells of Elliptical Cross Section: With Applications to the Problems of Bending of Curved Tubes and of the Bourdon Gage

1952 ◽  
Vol 19 (1) ◽  
pp. 37-48
Author(s):  
R. A. Clark ◽  
T. I. Gilroy ◽  
E. Reissner
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Closed Shell ◽  
Open Shell ◽  
Elliptical Cross Section ◽  
Axially Symmetric ◽  
Elliptical Cross ◽  
Two Parameters ◽  
Toroidal Shells

Abstract This paper is concerned with the application of the theory of thin shells to several problems for toroidal shells with elliptical cross section. These problems are as follows: (a) Closed shell subjected to uniform normal wall pressure. (b) Open shell subjected to end bending moments. (c) Combination of the results for the first and second problems in such a way as to obtain results for the stresses and deformations in Bourdon tubes. In all three problems the distribution of stresses is axially symmetric but only in the first problem are the displacements axially symmetric. The magnitude of stresses and deformations for given loads depends in all three problems on the magnitude of the two parameters bc/ah and b/c where b and c are the semiaxes of the elliptical section, a is the distance of the center of the section from the axis of revolution, and h is the thickness of the wall of the shell. For sufficiently small values of bc/ah trigonometric series solutions are obtained. For sufficiently large values of bc/ah asymptotic solutions are obtained. Numerical results are given for various quantities of practical interest as a function of bc/ah for the values 2, 1, 1/2, 1/4 of the semiaxes ratio b/c. It is suggested that the analysis be extended to still smaller values of b/c and to cross sections other than elliptical.

STABILITY ANALYSIS OF THE THIN POWER LAW LIQUID FILM FLOWING DOWN ON A VERTICAL CYLINDER

2006 ◽  
Vol 30 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Po-Jen Cheng ◽  
Kuo-Chi Liu
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Flow Index ◽  
Free Film ◽  
Long Wave ◽  
Lateral Curvature ◽  
The Stability ◽  
Film Interface

The paper investigates the stability theory of a thin power law liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized linear kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The analysis results also indicate that by increasing the flow index and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

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