Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth

2002 ◽  
Vol 470 ◽  
pp. 319-357 ◽  
Author(s):  
ODD M. FALTINSEN ◽  
ALEXANDER N. TIMOKHA
Keyword(s):  
Finite Depth ◽  
Modal System ◽  
Full Account ◽  
Inviscid Flows ◽  
State Response ◽  
Linear Damping ◽  
Convergence Problems ◽  
Run Up ◽  
Fourth Order Polynomial ◽  
Good Agreement

The modal system describing nonlinear sloshing with inviscid flows in a rectangular rigid tank is revised to match both shallow fluid and secondary (internal) resonance asymptotics. The main goal is to examine nonlinear resonant waves for intermediate depth/breadth ratio 0.1 [lsim ] h/l [lsim ] 0.24 forced by surge/pitch excitation with frequency in the vicinity of the lowest natural frequency. The revised modal equations take full account of nonlinearities up to fourth-order polynomial terms in generalized coordinates and h/l and may be treated as a modal Boussinesq-type theory. The system is truncated with a high number of modes and shows good agreement with experimental data by Rognebakke (1998) for transient motions, where previous finite depth modal theories failed. However, difficulties may occur when experiments show significant energy dissipation associated with run-up at the walls and wave breaking. After reviewing published results on damping rates for lower and higher modes, the linear damping terms due to the linear laminar boundary layer near the tank's surface and viscosity in the fluid bulk are incorporated. This improves the simulation of transient motions. The steady-state response agrees well with experiments by Chester & Bones (1968) for shallow water, and Abramson et al. (1974), Olsen & Johnsen (1975) for intermediate fluid depths. When h/l [lsim ] 0.05, convergence problems associated with increasing the dimension of the modal system are reported.

scholarly journals Statistics of Simulated Storm Waves over Bathymetry

2021 ◽  
Vol 9 (7) ◽  
pp. 784
Author(s):  
Arnida Lailatul Latifah ◽  
Durra Handri ◽  
Ayu Shabrina ◽  
Henokh Hariyanto ◽  
E. van Groesen
Keyword(s):  
Water Waves ◽  
Open Water ◽  
Storm Events ◽  
Extreme Waves ◽  
Marine Structures ◽  
Wave Statistics ◽  
Storm Waves ◽  
Different Types ◽  
Run Up ◽  
Good Agreement

This paper shows simulations of high waves over different bathymetries to collect statistical information, particularly kurtosis and crest exceedance, that quantifies the occurrence of exceptionally extreme waves. This knowledge is especially pertinent for the design and operation of marine structures, safe ship trafficking, and mooring strategies for ships near the coast. Taking advantage of the flexibility to perform numerical simulations with HAWASSI software, with the aim of investigating the physical and statistical properties for these cases, this paper investigates the change in wave statistics related to changes in depth, breaking and differences between long- and short-crested waves. Three different types of bathymetry are considered: run-up to the coast with slope 1/20, waves over a shoal, and deep open-water waves. Simulations show good agreement in the examined cases compared with the available experimental data and simulations. Then predictive simulations for cases with a higher significant wave height illustrate the changes that may occur during storm events.

scholarly journals INTERACTION OF IDEALIZED URBAN INFRASTRUCTURE AND LONG WAVES DURING RUN-UP AND ON-LAND FLOW PROCESS IN COASTAL REGIONS

2012 ◽  
Vol 1 (33) ◽  
pp. 18 ◽  
Author(s):  
Nils Goseberg ◽  
Torsten Schlurmann
Keyword(s):  
Shock Wave ◽  
Urban Infrastructure ◽  
Coastal Regions ◽  
Flow Process ◽  
Long Wave ◽  
Roughness Elements ◽  
Shock Wave Generation ◽  
Run Up ◽  
Sloping Beach ◽  
Good Agreement

This paper reports experimental results of long wave run-up climbing up a 1:40 sloping beach. The resulting maximum run-up is compared with analytical results and a good agreement is found for single sinusoidal waves with uniform wave period and varying amplitude. Subsequently, the interaction with macro-roughness elements on the beach is investigated for different long-shore obstruction ratios. The reduction in wave run-up is expressed by means of a nomogram relating the wave run-up without macro-roughness elements present to those cases where on-land flow is modified by macro-roughness. The presented results mainly focus on a non-staggered and non-rotated macro-roughness configuration. In addition to the run-up reduction, surface elevation profiles on the shore are presented, that address the shock wave generation when the wave tongue approaches the first row of macro-roughness elements.

The reaction-diffusion (RD) theory of wool (hair) follicle initiation and development. II. Original secondary follicles

1995 ◽  
Vol 46 (2) ◽  
pp. 357 ◽  
Author(s):  
BN Nagorcka
Keyword(s):  
Early Stage ◽  
Fibre Diameter ◽  
Reaction Diffusion ◽  
Future Generations ◽  
Chemical Components ◽  
Full Account ◽  
System Equations ◽  
And Diffusion ◽  
Total P ◽  
Good Agreement

In an accompanying paper it was shown that a spatial prepattern mechanism based on a biochemical reaction referred to as a reaction-diffusion (RD) system is able to account for many aspects of the initiation and development of primary (P) wool follicles. In this paper the same RD system is applied to the initiation and development of original secondary (SO) follicles. Prepatterns are generated by solving the equations describing the reaction and diffusion of the chemical components of the RD system in early stage follicles. It is demonstrated that the prepattern mechanism can account for the loss of a sweat gland causing a change from P follicle initiation to SO follicle initiation. The RD system equations are also solved in the epidermis. The time sequence of prepatterns obtained in the epidermis account for the tendency of SO follicles to group with P follicles, by initiating in-between members of the trio group of P follicles as well as in between existing SO follicles. The prepatterns obtained did not account for the tendency of secondary follicles to initiate on the posterior side of the trio group. Good agreement was obtained between the predicted increase in total follicle density and the increase in follicle density observed during follicle initiation by Carter and Hardy (1947), provided full account was taken of the interaction between existing follicles and each new future generations of follicles. The prepattern mechanism provides a fundamental basis for an inverse genetic correlation between total P and SO follicle density and fibre diameter.

VIBRATION OF CIRCULAR BLADED DISK WITH IMPERFECTIONS

2011 ◽  
Vol 21 (10) ◽  
pp. 2893-2904 ◽  
Author(s):  
LADISLAV PŮST ◽  
LUDĚK PEŠEK
Keyword(s):  
Dynamic Properties ◽  
Single Point ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Fe Model ◽  
Rotating Disks ◽  
Response Curves ◽  
State Response ◽  
Bladed Disk ◽  
Linear Damping

The steady state response of a model of circular bladed disk with imperfection is investigated. Disk imperfection results from additional two groups of damping heads fixed on opposite ends of one diameter. These damping heads are introduced into the computing model as additional point mass, damping and stiffness. Such type of imperfection causes the bifurcation of double eigenfrequencies into pairs of close eigenfrequencies. The effect of imperfection is examined both numerically on three-dimensional nonrotating FE-model and analytically on a simplified split 2DOF model of rotating disk excited by single point harmonic force. Nonlinear friction connection is analyzed and equivalent linear damping coefficient is derived and used in the calculation procedure. It is shown that nonproportional distribution of damping strongly influences the high of resonance peaks. Some examples of response curves illustrate the dynamic properties of stationary and rotating disks with mass-damping-stiffness imperfection.

The Maximum Transient Resonance Response of Rotating Blades With Regard to Centrifugal Force and Non-Linear Damping Effects

1997 ◽  
Author(s):  
Horst D. Irretier
Keyword(s):  
Centrifugal Force ◽  
Natural Frequencies ◽  
Linear Change ◽  
Rotating Blades ◽  
Operation Process ◽  
Non Linear ◽  
Linear Damping ◽  
Pass Through ◽  
Run Up ◽  
Approximate Formulas

During the operation process in many types of fluid flow machines the rotating blades pass through various resonances e.g. during run-up or run-down or other transient conditions. Therefore, for the high cycle fatigue problem of the blades it might be important to consider the transient vibratory response of the blades during these passages through resonance and to get knowledge about the occuring maximum vibratory stresses. In the paper, approximate formulas are presented which allow the estimation of the maximum transient response of the blades. Thereby, the influence of the change of the natural frequencies due to the increasing or decreasing centrifugal force field during the run-up or run-down, respectively, is taken into consideration. Basically, the approximate formulas are based on a linear change of the natural frequencies versus time and on a linear viscous type of damping. Extensions to account for parabolic changes which are more realistic for centrifugal effects and for non-linear damping models e.g. friction damping or turbulence damping are discussed.

scholarly journals Nonlinear run-ups of regular waves on sloping structures

2012 ◽  
Vol 12 (12) ◽  
pp. 3811-3820 ◽  
Author(s):  
T.-W. Hsu ◽  
S.-J. Liang ◽  
B.-D. Young ◽  
S.-H. Ou
Keyword(s):  
Boussinesq Equations ◽  
Irregular Waves ◽  
Coastal Structures ◽  
Regular Waves ◽  
Wave Flume ◽  
Coastal Risk ◽  
Run Up ◽  
Two Parameters ◽  
Prediction Capability ◽  
Good Agreement

Abstract. For coastal risk mapping, it is extremely important to accurately predict wave run-ups since they influence overtopping calculations; however, nonlinear run-ups of regular waves on sloping structures are still not accurately modeled. We report the development of a high-order numerical model for regular waves based on the second-order nonlinear Boussinesq equations (BEs) derived by Wei et al. (1995). We calculated 160 cases of wave run-ups of nonlinear regular waves over various slope structures. Laboratory experiments were conducted in a wave flume for regular waves propagating over three plane slopes: tan α =1/5, 1/4, and 1/3. The numerical results, laboratory observations, as well as previous datasets were in good agreement. We have also proposed an empirical formula of the relative run-up in terms of two parameters: the Iribarren number ξ and sloping structures tan α. The prediction capability of the proposed formula was tested using previous data covering the range ξ ≤ 3 and 1/5 ≤ tan α ≤ 1/2 and found to be acceptable. Our study serves as a stepping stone to investigate run-up predictions for irregular waves and more complex geometries of coastal structures.

Three-Dimensional Numerical and Experimental Simulation of Wave Run-Up Due to Wave Impact With a Vertical Surface

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Armin Bodaghkhani ◽  
Yuri S. Muzychka ◽  
Bruce Colbourne
Keyword(s):  
Vertical Surface ◽  
The Body ◽  
Experimental Simulation ◽  
Processing Unit ◽  
Plate Model ◽  
Wave Impact ◽  
Central Processing ◽  
Break Up ◽  
Run Up ◽  
Good Agreement

This paper describes a numerical simulation of the interaction of a single nonlinear wave with a solid vertical surface in three dimensions. A coupled volume of fluid (VOF) and level set method (LSM) is used to simulate the wave-body interaction. A Cartesian-grid method is used to model immersed solid boundaries with constant grid spacing for simplicity and lower storage requirements. Mesh refinement is implemented near the wall boundaries due to the complex behavior of the free surface around the body. The behavior of the wave impact, the water sheet, and the high-speed jet arising from the wave impact are all captured with these methods. The numerical scheme is implemented using parallel computing due to the high central processing unit and memory requirements of this simulation. The maximum wave run-up velocity, instant wave run-up velocity in front of the vertical surface, the sheet break-up length, and the maximum impact pressure are computed for several input wave characteristics. Results are compared with a laboratory experiment that was carried out in a tow tank in which several generated waves were impacted with a fixed flat-shaped plate model. The numerical and experimental data on sheet breakup length are further compared with an analytical linear stability model for a viscous liquid sheet, and good agreement is achieved. The comparison between the numerical model and the experimental measurements of pressure, the wave run-up velocity, and the break-up length in front of the plate model shows good agreement.

scholarly journals Computation of the Diffraction Transfer Matrix and the Radiation Characteristics in the Open-Source BEM Code NEMOH

2016 ◽  
Author(s):  
Francesc Fàbregas Flavià ◽  
Cameron McNatt ◽  
François Rongère ◽  
Aurélien Babarit ◽  
Alain H. Clément
Keyword(s):  
Open Source ◽  
Transfer Matrix ◽  
Body Wave ◽  
Finite Depth ◽  
Interaction Theory ◽  
Floating Bodies ◽  
Radiation Characteristics ◽  
Speed Up ◽  
Multi Body ◽  
Good Agreement

Until now, widely available boundary element method (BEM) codes did not allow the calculation of two non-conventional hydrodynamic operators, which characterize the way a body diffracts and radiates waves, known as Diffraction Transfer Matrix and Radiation Characteristics respectively. When embedded into the finite-depth interaction theory developed by [1], they drastically speed up the computation of the added mass, damping and excitation force coefficients of a group (“farm”) of floating bodies. This paper presents the implementation of their computation in the open source BEM solver NEMOH using the methodology proposed by [2]. Results for two different geometries, a cylinder and a square box, are presented and compared to an alternative computational approach developed by [3]. A very good agreement between them is found. In addition, the hydrodynamic operators of the cylinder are compared to a semi-analytical solution available in the literature showing a good match. Results obtained using the finite-depth interaction theory are shown for a generic multi-body wave energy converter (WEC) demonstrating how the capabilities added to the BEM software NEMOH can facilitate the numerical modeling of the hydrodynamic interactions in large arrays of bodies.

Autoparametric Resonances of Elastic Structures Coupled With Two Sloshing Modes in a Square Liquid Tank

2011 ◽  
Author(s):  
Takashi Ikeda ◽  
Masaki Takashima ◽  
Yuji Harata
Keyword(s):  
Vibration Suppression ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Liquid Level ◽  
Tuned Liquid Damper ◽  
Response Curves ◽  
Small Deviations ◽  
Sloshing Mode ◽  
Linear Damping ◽  
Good Agreement

Nonlinear vibrations of an elastic structure coupled with liquid sloshing in a square tank subjected to vertical sinusoidal excitation are investigated. Previous studies examined the vibrations of a structure coupled with only one sloshing mode in a rectangular tank. However, square tanks are expected to work more efficiently as a vibration suppression device (Tuned Liquid Damper, TLD) because two sloshing modes, (1,0) and (0,1) modes, simultaneously appear when the internal resonance ratio 2:1:1 is satisfied. In reality, it is impossible to build a perfectly square tank. Therefore, a nearly square liquid tank is also considered when the tuning condition is slightly deviated. In the theoretical analysis, the fluid in the tank is assumed to be perfect. The modal equations of motion for seven sloshing modes are derived using Galerkin’s method, considering the nonlinear terms. The linear damping terms are then incorporated into the modal equations to consider the damping effect of sloshing. The frequency response curves are determined using van der Pol’s method (based on the harmonic balance method). From these response curves, the influences of the liquid level, the aspect ratio of the tank cross section, and the deviation of the tuning condition are investigated. For a square tank it is found that (1,0) and (0,1) modes are nonlinearly coupled. When the liquid level is high, there are three patterns for sloshing: (I) both (1,0) and (0,1) sloshing modes appear at identical amplitudes; (II) these two modes appear at different amplitudes; and (III) either (1,0) or (0,1) mode appears. Compared with the performance of a rectangular TLD, a square TLD works more efficiently when the liquid level is low. Small deviations of the tuning condition may cause amplitude modulated motion to appear. Bifurcation sets are also calculated to illustrate the influence of the system parameters on the performance of the TLD. Experiments were also conducted in order to confirm the validity of the theoretical results. These results were in good agreement with the experimental data.

Comparison of Wave Run-Up Formulas by Flume Experiments

2014 ◽  
Vol 556-562 ◽  
pp. 4151-4154
Author(s):  
Lei Wang ◽  
Shou Xian Zhu ◽  
Xun Qiang Li ◽  
Wen Jing Zhang ◽  
Wen Chao Wang
Keyword(s):  
Significant Error ◽  
Flume Experiments ◽  
Mathematical Equations ◽  
Run Up ◽  
Steep Slopes ◽  
Good Agreement

The wave run-up formulas from the Code of Hydrology for Sea Harbour (CHSH), the Code for design of levee project (CDLP) and Hunt are all widely used, but they are in different forms of mathematical equations. In this paper, some flume experiments for wave run-up are made to examine these formulas. The tests show that the wave run-up formula from Hunt is in good agreement with the experiments. The wave run-up formula from CDLP has been usually used in steep slopes, while the tests show that it is also in good agreement with the experiments in the small slope flume. The wave run-up formula from CHSH is also used mainly in steep slopes, it brings significant error of the wave run-up calculation contrasting with the experiments.

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