On Wave Diffraction of a Two-Dimensional Moonpool in a Two-Layer Fluid in Finite Water Depth

2018 ◽  
Author(s):  
Xingyu Song ◽  
Xin Xu ◽  
Xinshu Zhang ◽  
Yunxiang You
Keyword(s):  
Free Surface ◽  
Resonance Frequency ◽  
Internal Wave ◽  
Wave Mode ◽  
Resonance Frequencies ◽  
Exciting Forces ◽  
Wave Exciting Forces ◽  
Free Surface Wave ◽  
Piston Mode ◽  
Wave Elevations

This paper studies the wave diffraction of a two-dimensional moonpool in a two-layer fluid in finite water depth by using a domain decomposition scheme and an eigenfunction matching method. The formulae of the wave exciting forces, the free surface and internal wave elevations at zero-frequency are derived. Numerical convergence has been assessed by repeating the computations for increasing values of the truncation orders. The present model has been validated by comparing a limiting case with a single-layer fluid case and the comparisons are in general satisfactory. Although the wave exciting forces and free surface wave elevations around resonance frequency are overestimated, the piston mode resonance frequency is well predicted. Two typical configurations with different moonpool widths are selected for computations in both free surface and internal wave modes. It is found that, the wave exciting forces, free surface and internal wave elevations in internal wave mode are much smaller than those in free surface wave mode. In addition, the wave exciting forces in internal wave mode attenuate to zero quickly as incident wave frequency increases. For moonpool with small width, only piston mode resonance can be observed. The piston mode resonance frequencies identified in free surface and internal wave modes are the same. The characteristics of piston mode resonance can also be observed in the horizontal and vertical wave exciting forces. Around the piston mode resonance frequency, the wave exciting forces reach their local maximums. It is revealed that, as moonpool width increases, the piston mode resonance frequency decreases. Meanwhile, it shows that more asymmetric and symmetric sloshing mode resonances appear alternately and occur at higher frequencies than the piston mode resonance. Moreover, the predicted sloshing mode resonance frequencies are compared with those estimated by a simple approximate formula.

Vibration-induced drop atomization and bursting

2003 ◽  
Vol 476 ◽  
pp. 1-28 ◽  
Author(s):  
A. J. JAMES ◽  
B. VUKASINOVIC ◽  
MARC K. SMITH ◽  
A. GLEZER
Keyword(s):  
Free Surface ◽  
Resonance Frequency ◽  
Capillary Waves ◽  
Dynamical Process ◽  
Entire Volume ◽  
Droplet Ejection ◽  
Basic Physics ◽  
Free Surface Wave ◽  
Secondary Droplets ◽  
Diaphragm System

A liquid drop placed on a vibrating diaphragm will burst into a fine spray of smaller secondary droplets if it is driven at the proper frequency and amplitude. The process begins when capillary waves appear on the free surface of the drop and then grow in amplitude and complexity as the acceleration amplitude of the diaphragm is slowly increased from zero. When the acceleration of the diaphragm rises above a well-defined critical value, small secondary droplets begin to be ejected from the free-surface wave crests. Then, quite suddenly, the entire volume of the drop is ejected from the vibrating diaphragm in the form of a spray. This event is the result of an interaction between the fluid dynamical process of droplet ejection and the vibrational dynamics of the diaphragm. During droplet ejection, the effective mass of the drop–diaphragm system decreases and the resonance frequency of the system increases. If the initial forcing frequency is above the resonance frequency of the system, droplet ejection causes the system to move closer to resonance, which in turn causes more vigorous vibration and faster droplet ejection. This ultimately leads to drop bursting. In this paper, the basic phenomenon of vibration-induced drop atomization and drop bursting will be introduced, demonstrated, and characterized. Experimental results and a simple mathematical model of the process will be presented and used to explain the basic physics of the system.

scholarly journals The Close Relationship between Internal Wave and Ocean Free Surface Wave

2021 ◽  
Vol 9 (12) ◽  
pp. 1330
Author(s):  
Bang-Fuh Chen ◽  
Yi-Jei Huang
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Wave Height ◽  
Water Surface ◽  
Simple Method ◽  
Wave Signal ◽  
Close Relationship ◽  
Free Surface Wave

A numerical model was used to simulate the propagation of internal waves (IW) along the surface layer. The results show that strong water exchange during IW propagation results in strong free surface flow and produces small but distinct free surface waves. We found a close relationship between the internal and ocean surface waves. Our intuitive reaction is that by training the relationship between the water surface wave height and the internal wave waveform, the internal wave waveform can be reversed from the water surface wave height value. This paper intends to validate our intuition. The artificial neural network (ANN) method was used to train the Fluent simulated results, and then the trained ANN model was used to predict the inner waves below by the free surface wave signal. In addition, two linear internal wave equations (I and II) were derived, one based on the Archimedes principle and the other based on the long wave and Boussinesq approximation. The prediction by equation (II) was superior to the prediction of equation (I), which is independent of depth. The predicted IW of the proposed ANN method was in good agreement with the simulated results, and the predicted quality was much better than the two linear wave formulas. The proposed simple method can help researchers infer the magnitude of IW from the free surface wave signal. In the future, the spatial distribution of IW below the sea surface might be obtained by the proposed method without costly field investigation.

Dynamic Characteristics of a Submerged, Flexible Cylinder Vibrating in Finite Water Depths

1992 ◽  
Vol 36 (02) ◽  
pp. 154-167
Author(s):  
A. Ergin ◽  
W. G. Price ◽  
R. Randall ◽  
P. Temarel
Keyword(s):  
Free Surface ◽  
Resonance Frequency ◽  
Water Depth ◽  
Dynamic Characteristics ◽  
Mode Shapes ◽  
Flexible Cylinder ◽  
Rigid Boundary ◽  
Fluid Structure ◽  
Resonance Frequencies ◽  
Theoretical Predictions

This paper presents experimental data and theoretical predictions of the dynamic characteristics (natural and resonance frequencies, mode shapes) of a flexible cylinder vibrating in air and at fixed positions below a free surface in water of finite depth. The flat-ended, thin cylindrical shell of overall length 1284 mm, external radius 180 mm, thickness 3 mm is made of mild steel. In the experiments, the shell was tethered (i) at 0.21, 0.23, and 0.68 m depths below the free surface in water of depth 1.6 m and (ii) at 0.25, 1.5, and 3.5 m depths in 4 m of water. The resonance frequency data recorded provide measures of the influences of free surface, cylinder position, rigid boundary, water depth, etc. occurring in the fluid-structure interaction process. The theoretical predictions are derived from a three-dimensional hydroelastic mathematical model which, through the calculations of the generalized fluid loadings, accounts for the influence of free surface and rigid boundaries, position of submerged cylinder, neutral buoyancy or, as in the present case, with tethers and buoyancy effects. An extensive comparison of results is included. The experimental restrictions of water depth, cylinder position, etc. and the fluid-structure interactions are assessed and illustrated through the calculated resonance frequency values.

Topology Optimized Design of Functionally Graded Piezoelectric Resonators with Specified Resonance Frequencies

2009 ◽  
Vol 631-632 ◽  
pp. 305-310
Author(s):  
Wilfredo Montealegre Rubio ◽  
Emílio Carlos Nelli Silva ◽  
Glaucio H. Paulino
Keyword(s):  
Finite Element ◽  
Resonance Frequency ◽  
Functionally Graded ◽  
Single Frequency ◽  
Continuum Approximation ◽  
Continuous Change ◽  
Piezoelectric Resonators ◽  
Resonance Frequencies ◽  
Functionally Graded Piezoelectric ◽  
Piston Mode

This work explores the design of piezoelectric resonators based on functionally graded material (FGM) concept. The goal is to design single-frequency Functionally Graded Piezoelectric Resonators (FGPR) subjected to the following requirements: (i) an assurance of the specified resonance frequency, and (ii) for most acoustic wave generation applications, the FGPR is required to oscillate in the piston mode. Several approaches can be used to achieve these goals; however, a novel approach is to design the piezoelectric transducer by using Topology Optimization Method. Accordingly, in this work, the optimal material gradation of an FGPR is found, which maximizes a specified and single resonance frequency subjected to a volume constraint. To track the desirable piston mode, a mode-tracking method utilizing the modal assurance criterion (MAC) is applied. The continuous change of piezoelectric, dielectric, and elastic properties is achieved by using the graded finite element (GFE) concept, where these material properties are interpolated inside the finite element using interpolation functions. The optimization algorithm is constructed based on sequential linear programming (SLP), and the concept of the Continuum Approximation of Material Distribution (CAMD) is considered. The software is implemented in MATLAB language. In addition, to illustrate the method, a two-dimensional FGPR is designed with plane strain assumption. Performance of designed FGPR is compared with non-FGPR performance.

scholarly journals Wave-induced response of a floating two-dimensional body with a moonpool

2015 ◽  
Vol 373 (2033) ◽  
pp. 20140109 ◽  
Author(s):  
Arnt G. Fredriksen ◽  
Trygve Kristiansen ◽  
Odd M. Faltinsen
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Resonance Frequency ◽  
Hybrid Method ◽  
Two Dimensional ◽  
Body Boundary ◽  
Flow Domain ◽  
Wave Induced ◽  
Piston Mode ◽  
Nonlinear Hybrid

Regular wave-induced behaviour of a floating stationary two-dimensional body with a moonpool is studied. The focus is on resonant piston-mode motion in the moonpool and rigid-body motions. Dedicated two-dimensional experiments have been performed. Two numerical hybrid methods, which have previously been applied to related problems, are further developed. Both numerical methods couple potential and viscous flow. The semi-nonlinear hybrid method uses linear free-surface and body-boundary conditions. The other one uses fully nonlinear free-surface and body-boundary conditions. The harmonic polynomial cell method solves the Laplace equation in the potential flow domain, while the finite volume method solves the Navier–Stokes equations in the viscous flow domain near the body. Results from the two codes are compared with the experimental data. The nonlinear hybrid method compares well with the data, while certain discrepancies are observed for the semi-nonlinear method. In particular, the roll motion is over-predicted by the semi-nonlinear hybrid method. Error sources in the semi-nonlinear hybrid method are discussed. The moonpool strongly affects heave motions in a frequency range around the piston-mode resonance frequency of the moonpool. No resonant water motions occur in the moonpool at the piston-mode resonance frequency. Instead large moonpool motions occur at a heave natural frequency associated with small damping near the piston-mode resonance frequency.

scholarly journals Measurement of material volumes in a cylindrical silo using acoustic wave and resonance frequency analysis

2020 ◽  
Vol 9 (4) ◽  
pp. 1585-1594
Author(s):  
Chukiet Sodsri
Keyword(s):  
Resonance Frequency ◽  
Frequency Analysis ◽  
Acoustic Waves ◽  
Standing Waves ◽  
Wave Mode ◽  
Rice Grain ◽  
Resonance Frequency Analysis ◽  
Resonance Frequencies ◽  
Material Volume ◽  
Time Invariant

This work presents an approach for measuring material volumes in a closed cylindrical silo by using acoustic waves and resonance frequency analysis of silo’s acoustic systems. With an assumption that the acoustical systems were linear and time-invariant, frequency responses of the systems were identified via measurement. A sine sweep was generated, amplified and fed to a loudspeaker inside the silo. Acoustic waves were picked up by a microphone and processed to yield the silo's frequency response. Resonance frequencies and wave mode numbers of standing waves in the frequency range below 900 Hz were analyzed and used for calculation of air-cavity lengths. With known silo's dimension, the material volume estimations were achieved. Sets of experiments for estimating volumes of sand, cement, water, rice grain, and stone flakes in a closed silo, were done. It was found that the approach could successfully estimate the volumes of sand, cement, and water with a satisfactory accuracy. Percent errors of the estimations were less than 3% from the actual volumes. However, the approach could not estimate the volume of rice grain and stone flakes, since their sound refractions were neither resulted in standing waves nor acoustical modes in the silo.

scholarly journals Study on the applicability of the microtremor HVSR method to support seismic microzonation in the town of Idrija (W Slovenia)

2017 ◽  
Vol 17 (6) ◽  
pp. 925-937 ◽  
Author(s):  
Andrej Gosar
Keyword(s):  
Seismic Hazard ◽  
Resonance Frequency ◽  
Complex Geometry ◽  
Free Field ◽  
Seismic Microzonation ◽  
Clear Correlation ◽  
S Wave ◽  
Resonance Frequencies ◽  
Hvsr Method ◽  
The Town

Abstract. The town of Idrija is located in an area with an increased seismic hazard in W Slovenia and is partly built on alluvial sediments or artificial mining and smelting deposits which can amplify seismic ground motion. There is a need to prepare a comprehensive seismic microzonation in the near future to support seismic hazard and risk assessment. To study the applicability of the microtremor horizontal-to-vertical spectral ratio (HVSR) method for this purpose, 70 free-field microtremor measurements were performed in a town area of 0.8 km2 with 50–200 m spacing between the points. The HVSR analysis has shown that it is possible to derive the sediments' resonance frequency at 48 points. With the remaining one third of the measurements, nearly flat HVSR curves were obtained, indicating a small or negligible impedance contrast with the seismological bedrock. The isofrequency (a range of 2.5–19.5 Hz) and the HVSR peak amplitude (a range of 3–6, with a few larger values) maps were prepared using the natural neighbor interpolation algorithm and compared with the geological map and the map of artificial deposits. Surprisingly no clear correlation was found between the distribution of resonance frequencies or peak amplitudes and the known extent of the supposed soft sediments or deposits. This can be explained by relatively well-compacted and rather stiff deposits and the complex geometry of sedimentary bodies. However, at several individual locations it was possible to correlate the shape and amplitude of the HVSR curve with the known geological structure and prominent site effects were established in different places. In given conditions (very limited free space and a high level of noise) it would be difficult to perform an active seismic refraction or MASW measurements to investigate the S-wave velocity profiles and the thickness of sediments in detail, which would be representative enough for microzonation purposes. The importance of the microtremor method is therefore even greater, because it enables a direct estimation of the resonance frequency without knowing the internal structure and physical properties of the shallow subsurface. The results of this study can be directly used in analyses of the possible occurrence of soil–structure resonance of individual buildings, including important cultural heritage mining and other structures protected by UNESCO. Another application of the derived free-field isofrequency map is to support soil classification according to the recent trends in building codes and to calibrate Vs profiles obtained from the microtremor array or geophysical measurements.

Response of Liquid in Cylindrical Tank with Rigid Annual Baffle Considering Damping Effect

2011 ◽  
Vol 255-260 ◽  
pp. 3687-3691 ◽  
Author(s):  
Jia Dong Wang ◽  
Ding Zhou ◽  
Wei Qing Liu
Keyword(s):  
Free Surface ◽  
Dynamic Response ◽  
Potential Function ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Cylindrical Tank ◽  
Generalized Coordinates ◽  
Damping Effect ◽  
Total Potential ◽  
Free Surface Wave

Sloshing response of liquid in a rigid cylindrical tank with a rigid annual baffle under horizontal sinusoidal loads was studied. The effect of the damping was considered in the analysis. Natural frequencies and modes of the system have been calculated by using the Sub-domain method. The total potential function under horizontal loads is assumed to be the sum of the tank potential function and the liquid perturbed function. The expression of the liquid perturbed function is obtained by introducing the generalized coordinates. Substituting potential functions into the free surface wave conditions, the dynamic response equations including the damping effect are established. The damping ratio is calculated by Maleki method. The liquid potential are obtained by solving the dynamic response equations of the system.

Theory of Short Wave Excitation

1986 ◽  
Vol 30 (03) ◽  
pp. 147-152
Author(s):  
Yong Kwun Chung
Keyword(s):  
Incident Wave ◽  
Characteristic Length ◽  
Finite Depth ◽  
Short Wave ◽  
The Body ◽  
Wave Number ◽  
Floating Body ◽  
Wave Excitation ◽  
Exciting Forces ◽  
Wave Exciting Forces

When the wavelength of the incident wave is short, the total surface potential on a floating body is found to be 2∅ i & O (m-l∅ i) on the lit surface and O (m-l∅ j) on the shadow surface where ~b i is the potential of the incident wave and m the wave number in water of finite depth. The present approximation for wave exciting forces and moments is reasonably good up to X/L ∅ 1 where h is the wavelength and L the characteristic length of the body.

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