Derivation of Morison’s Force Coefficients by Three Alternative Forms of the Method of Moments

2016 ◽  
Author(s):  
N. I. Mohd Zaki ◽  
M. K. Abu Husain ◽  
G. Najafian
Keyword(s):  
Conventional Method ◽  
Method Of Moments ◽  
Particle Velocity ◽  
Field Experiments ◽  
Inertial Force ◽  
Wave Force ◽  
Wave Load ◽  
Sampling Variability ◽  
Water Particle ◽  
Empirical Coefficients

Morison’s equation is the most widely used method of predicting wave forces on slim cylindrical members of offshore structures. The equation assumes that the wave force is composed of two components: a drag force and an inertial force, where the drag component is due to water particle velocity and the inertial component is due to water particle acceleration. Morison’s equation has two empirical coefficients, which are usually referred to as the drag and inertia coefficients. The values of these empirical coefficients are determined from laboratory and/or field experiments. In a typical wave load investigation, the wave force together with corresponding water particle velocity and acceleration are measured. The measured data is then analysed to calculate constant values for drag and inertia coefficients. One of the methods used in derivation of these coefficients is the (conventional) method of moments. However, the coefficients obtained from this method show considerable scatter due to large sampling variability. The purpose of this paper is to compare the sampling variability of drag and inertia coefficients from the conventional method of moments with those derived from two alternative forms of the method, i.e. methods of linear and low-order moments. Simulated data has been used to compare the efficiency of the three methods of moments. The results indicate that in most cases, the method of linear moments is superior to the other two methods. This is particularly true for drag-dominated forces.

A More Efficient Form of the Method of Moments for Derivation of Morison’s Force Coefficients

2007 ◽  
Author(s):  
G. Najafian
Keyword(s):  
Method Of Moments ◽  
Particle Velocity ◽  
Field Experiments ◽  
Inertial Force ◽  
New Method ◽  
Total Force ◽  
Wave Load ◽  
Sampling Variability ◽  
Water Particle ◽  
Empirical Coefficients

Morison’s equation is the most widely used method of predicting wave forces on slim cylindrical members of offshore structures. The equation assumes that the total force of the fluid is made up of a drag force and an inertial force, where the drag component is due to water particle velocity and the inertial component is due to water particle acceleration. In practice, the force uses two empirical coefficients, which are usually referred to as the drag and inertia coefficients. The values of these empirical coefficients are determined from laboratory and/or field experiments. In a typical wave load investigation, the wave force together with corresponding water particle velocity and acceleration are measured. The measured data is then analysed to calculate constant values for drag and inertia coefficients. One of the methods used in derivation of these coefficients is the method of moments. However, the coefficients obtained from this method show considerable scatter due to large sampling variability. The purpose of this paper is to introduce a more efficient form of the method of moments, which will lead to more accurate estimates of Morison’s coefficients by reducing their sampling variability. Simulated data has been used to compare the new method of moments with the conventional one. The results indicate that the new method is superior to the conventional one. This is particularly the case for drag-dominated forces.

scholarly journals The Effects on Water Particle Velocity of Wave Peaks Induced by Nonlinearity under Different Time Scales

2021 ◽  
Vol 9 (7) ◽  
pp. 748
Author(s):  
Aifeng Tao ◽  
Shuya Xie ◽  
Di Wu ◽  
Jun Fan ◽  
Yini Yang
Keyword(s):  
Particle Velocity ◽  
Modulation Instability ◽  
Wave Train ◽  
Quadratic Function ◽  
Offshore Structures ◽  
Stokes Wave ◽  
Wave Load ◽  
Freak Waves ◽  
Water Particle ◽  
Generation Mechanisms

The water particle velocity of the wave peaks is closely related to the wave load borne by offshore structures. It is of great value for marine disaster prevention to study the water particle velocity of nonlinear extreme waves represented by Freak waves. This study applies the High-order Spectral Method (HOS) numerical model to analyze the characteristics and influencing factors of the water particle velocity of Freak wave peak with two different generation mechanisms under the initial condition of a weakly modulated Stokes wave train. Our results show that the water particle velocity of the wave peak increases linearly with wave height and initial wave steepness in the evolution stage of modulation instability. While in the later stage, the relationship becomes exponential. Under the condition of similar wave heights, the deformation degrees of Freak waves with different generation mechanisms are distinct, the deformation degree of modulation instability stage is smaller than that of the later stage. The water particle velocity of the wave peaks increases with the deformation degrees. Furthermore, the correlation between wave peak height and water particle velocity is a quadratic function. This provides a theoretical basis for further understanding of nonlinear waves and the prediction of marine disasters.

scholarly journals DEVELOPMENT OF WAVE POWER GENERATION SYSTEM SUITABLE FOR INNER BAY

2020 ◽  
pp. 39
Author(s):  
Rioko Hirota ◽  
Takaaki Shigematsu ◽  
Kenji Katoh ◽  
Tatsuro Wakimoto ◽  
Shinya Yoshioka
Keyword(s):  
Power Generation ◽  
Particle Velocity ◽  
High Energy ◽  
Wave Power ◽  
Generation System ◽  
Water Particle ◽  
Water Turbine ◽  
Power Generation System ◽  
The Relationship ◽  
Wave Power Generation

With the increasing demand for renewable energy in the world, research contributing to the improvement of the technology level of wave power generation is essential. The authors have been developed a wave power generation system using port facilities in inner bays with high energy-consuming cities. In this study, the relationship between the rotational characteristics of a Savonius water turbine and the water particle velocity was quantitatively evaluated under the calm conditions of the inner bay, such as wave motion, flow, and coexistence of wave and current. According to the experimental results, it is found that the relationship between the rotational circumferential speed and the water particle velocity of the water turbine installed in a wave field tends to be different from that in a flow field and is evaluated by different equations. In addition, the relationship between circumferential velocity and the water particle velocity has also been formulated when installed in a wave-current coexistence field.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/KX0XBFuao48

scholarly journals KINEMATICS OF BREAKING WAVES

1976 ◽  
Vol 1 (15) ◽  
pp. 25 ◽  
Author(s):  
Edward B. Thornton ◽  
James J. Galvin ◽  
Frank L. Bub ◽  
David P. Richardson
Keyword(s):  
Solitary Waves ◽  
Particle Velocity ◽  
Asymptotic Expression ◽  
Breaking Waves ◽  
The Body ◽  
Time Dependent ◽  
Wave Crest ◽  
Periodic Waves ◽  
Water Particle ◽  
Highly Nonlinear

The sight and sound of breaking waves and surf is so familiar and enjoyable that we tend to forget how little we really understand about them. Why is it, that compared to other branches of wave studies our knowledge of breaking waves is so empirical and inexact? The reason must lie partly in the difficulty of finding a precise mathematical description of a fluid flow that is in general nonlinear and time-dependent. The fluid accelerations can no longer be assumed t o be small compared t o gravity, as in Stokes's theory for periodic waves and the theory of cnoidal waves in shallow water, nor is the particle velocity any longer small compared to the phase velocity. The aim of this paper is to bring together s ome recent contributions to the calculation both of steep symmetric waves and of time-dependent surface waves. These have a bearing on the behaviour of whitecaps in deep water and of surf in the breaker zone . Since spilling breakers in gently shoaling water closely resemble solitary waves, we begin with the description of solitary waves of limiting amplitude, then discuss steep waves of arbitrary height. The observed intermittency of whitecaps is discussed in terms of the energy maximum, as a function of wave steepness, In Sections 6 and 7 a simpler description of steady symmetric waves is proposed, using an asymptotic expression for the flow near the wave crest. Finally we describe a new numerical technique (MEL, or mixed Eulerian-Lagrangian) with which it has been found possible to follow the development of periodic waves past the point when overturning takes place. Measurement of waves, and vertical and horizontal water particle velocities were made of spilling, plunging and surging breakers at sandy beaches in the vicinity of Monterey, California. The measured breaking waves, derived characteristically from swell-type waves, can be described as highly nonlinear. Spectra and cross spectra were calculated between waves and velocities. Secondary waves were noted visually and by the strong harmonics in the spectra. The strength of the harmonics is related to the beach steepness, wave height and period. The phase difference between waves and horizontal velocities indicates the unstable crest of the wave leads the velocities on the average by 5-20 degrees. Phase measurements between wave gauges in a line perpendicular to the shore show breaking waves to be frequency nondispersive indicating phase-coupling of the various wave components. The coherence squared values between the sea surface elevation and the horizontal water particle velocity were high in all runs, ranging above 0.8 at the peak of the spectra. The high coherence suggests that most of the motion in the body of breaking waves is wave-induced and not turbulent.

scholarly journals Experimental Investigation on Hydrodynamic Coefficients of a Column-Stabilized Fish Cage in Waves

2019 ◽  
Vol 7 (11) ◽  
pp. 418
Author(s):  
Zhao ◽  
Chen ◽  
Bi ◽  
Cui
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Drag Force ◽  
Inertial Force ◽  
Element Model ◽  
Wave Force ◽  
Hydrodynamic Coefficients ◽  
Horizontal Wave ◽  
Horizontal Wave Force ◽  
The Finite Element Model

This study on hydrodynamic coefficients of a column-stabilized fish cage under wave action plays an important role in the anti-wave design of cages. The regular wave test was used to study the horizontal wave force of the jacket and column-stabilized fish cage under different wave heights, periods, and incident angles; the finite element model of the jacket and the column-stabilized fish cage was established according to the test model. On the basis of the calculation of the finite element model, combined with the wave force obtained from the experiment, the hydrodynamic coefficients of the structure was fitted by the least squares method, and then the drag force, inertial force, and total force of the structure under different conditions were calculated. The results show that the hydrodynamic coefficients of the jacket and netting under the wave condition were more obvious with the change of the KC number and wave incident angles. And as the wave height increased, the drag force, the inertial force, and the proportion of the drag force to the horizontal wave force both increased. When the wavelength was large, the same trend occured as the wave period increased. When the wave incident angles were different, the forces of the jacket and the column-stabilized fish cage were always small in lateral low-frequency waves, which is consistent with the change law of hydrodynamic coefficients of the jacket and netting.

Field Observation of the Wave-Induced Water Particle Velocity in the Surf Zone

1980 ◽  
Vol 23 (1) ◽  
pp. 81-89 ◽  
Author(s):  
Masaru Mizuguchi ◽  
Masahiko Isobe ◽  
Shintaro Hotta ◽  
Kiyoshi Horikawa
Keyword(s):  
Particle Velocity ◽  
Field Observation ◽  
Surf Zone ◽  
Water Particle ◽  
Wave Induced

scholarly journals VORTEX FORMATION IN PLUNGING BREAKER

1986 ◽  
Vol 1 (20) ◽  
pp. 54 ◽  
Author(s):  
T. Sakai ◽  
T. Mizutani ◽  
H. Tanaka ◽  
Y. Tada
Keyword(s):  
Flow Visualization ◽  
Particle Velocity ◽  
Vortex Formation ◽  
Water Particle ◽  
Mac Method ◽  
Long Wave ◽  
Wave Celerity ◽  
Maximum Water ◽  
Slope Beach ◽  
Plunging Breaker

By a flow visualization of a plunging breaker on 1/20 slope beach in a wave tank, an existence of 2nd and 3rd horizontal vortices(Miller, 1976) and slanting vortex (Nadaoka et al., 1986) is confirmed. A MAC method is applied to simulate a violent motion after an impinging of a jet from a crest of a plunging breaker on the trough surface. The calculated maximum water particle velocity in the jet is found to reach three times the linear long wave celerity. Values of circulation of the first four horizontal vortices are calculated and their changes in time are discussed.

scholarly journals Growth parameters and yield attributing characters of PR-118 (V1) and PR-116 (V2) varieties of rice (Oryza sativa L.) as influenced by different planting methods

2014 ◽  
Vol 6 (2) ◽  
pp. 755-762
Author(s):  
Amandeep Kaur ◽  
L. K. Dhaliwal
Keyword(s):  
Conventional Method ◽  
Field Experiments ◽  
Growth Parameters ◽  
Oryza Sativa L ◽  
Dry Weight ◽  
Growth And Yield ◽  
Rice Varieties ◽  
Area Index ◽  
Planting Methods ◽  
Planting Method

Field experiments were conducted at Punjab Agricultural University, Ludhiana (Punjab) to study the effect of different agronomic aspects of bed planting on growth and yield of rice during Kharif seasons of 2012 and 2013. The 30 days old seedlings of both rice varieties PR-118 (V1) and PR-116 (V2) were transplanted on 15th June (D1), 30th June (D2) and 15th July (D3). The two rice varieties were transplanted under bed planting (M1) and conventional planting (M2) methods respectively. The results showed that growth parameters like number of tillers per plant, dry weight per plant leaf area index (LAI) and plant height were significantly higher in bed planting than conventional method. In bed planting method, grain yield of rice (48.82q/h) was found to be more than the conventional method (35.74 q/h) during 2012.Varieties PR-118 yielded 47.61q/h more than PR-116 (39.97 q/h) in bed planting. Yield contributing characters like number of effective tillers, number of grains per plant and 1000-grain weight of rice were more in bed planting than conventional method. Harvest index and biological yield was also found to be more in bed planting method than conventional planting. Rice transplanted on 15th June yielded (50.15q/h) more than 30th June (41.45q/h) and 15th July (35.27q/h). Similar results were found in Kharif 2013. Interaction between dates of transplanting and varieties and between varieties and planting methods were found significant.

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