scholarly journals Mathematical Modeling of Partial-Porous Circular Cylinders with Water Waves

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Min-Su Park ◽  
Weoncheol Koo
Keyword(s):  
Water Waves ◽  
Body Wave ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Expansion Method ◽  
The Body ◽  
Circular Cylinders ◽  
Exterior Region ◽  
Eigenfunction Expansion Method ◽  
Body Regions

The interaction of water waves with partially porous-surfaced circular cylinders was investigated. A three-dimensional numerical modeling was developed based on the complete mathematical formulation of the eigenfunction expansion method in the potential flow. Darcy’s law was applied to describe the porous boundary. The partial-porous cylinder is composed of a porous-surfaced body near the free surface, and an impermeable-surfaced body with an end-capped rigid bottom below the porous region. The optimal ratio of the porous portion to the impermeable portion can be adopted to design an effective ocean structure with minimal hydrodynamic impact. To scrutinize the hydrodynamic interactions inNpartial-porous circular cylinders, the computational fluid domain is divided into three regions: an exterior region,Ninner porous body regions, andNregions beneath the body. Wave excitation forces and wave run-up on multibodied partial-porous cylinders are calculated and compared for various porous-portion ratios and wave conditions, all of which significantly influence the hydrodynamic property.

scholarly journals Theoretical Hydrodynamic Analysis of a Surface-Piercing Porous Cylindrical Body

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 320
Author(s):  
Dimitrios N. Konispoliatis ◽  
Ioannis K. Chatjigeorgiou ◽  
Spyridon A. Mavrakos
Keyword(s):  
Water Waves ◽  
Wave Attenuation ◽  
Three Dimensional ◽  
Cylindrical Body ◽  
Expansion Method ◽  
Wave Theory ◽  
Linear Wave ◽  
Wave Loads ◽  
Dimensional Solution ◽  
Eigenfunction Expansion Method

In the present study, the diffraction and the radiation problems of water waves by a surface-piercing porous cylindrical body are considered. The idea conceived is based on the capability of porous structures to dissipate the wave energy and to minimize the environmental impact, developing wave attenuation and protection. In the context of linear wave theory, a three-dimensional solution based on the eigenfunction expansion method is developed for the determination of the velocity potential of the flow field around the cylindrical body. Numerical results are presented and discussed concerning the wave elevation and the hydrodynamic forces on the examined body for various values of porosity coefficients. The results revealed that porosity plays a key role in reducing/controlling the wave loads on the structure and the wave run-up, hence porous barriers can be set up to protect a marine structure against wave attack.

Study on Dynamic Stability of Single Floating Pier Under Waves

2021 ◽  
Author(s):  
Yikuan He ◽  
Bing Han ◽  
Wenyu Ji
Keyword(s):  
Dynamic Stability ◽  
Expansion Method ◽  
Diffraction Effect ◽  
Exterior Region ◽  
Factors Affecting ◽  
Eigenfunction Expansion Method ◽  
Floating Bridge ◽  
Response Equation ◽  
Floating Pier ◽  
Wave Excitation Force

Abstract Considering the upper structure restraint effect of the floating bridge, the diffraction effect and radiation effect of linear monochromatic waves, the dynamic response equation of floating pier is derived and the factors affecting the dynamic stability of the floating pier are analyzed in this paper. Based on the theory of potential flow, the calculation domain is divided into the interior region and the exterior region. The wave diffraction and radiation problems are solved by the matched eigenfunction expansion method (MEEM). After obtaining the wave excitation force, additional mass and radiation damping coefficient, considering the restraint effect of the upper structure of the floating bridge, the motion differential equation of the floating pier is established, and the response amplitude operator (RAOs) of the floating pier is obtained. The effects of span, mass and stiffness of upper structure, as well as the draft depth, size and net height of floating pier on dynamic stability of floating pier under wave are analyzed. The results show that the increase in the span of upper structure will significantly increase the peak RAOs of sway and heave, and the increase in stiffness is helpful to reduce the peak RAOs of sway and heave. The increase of the floating pier radius can reduce the heave RAO, and the net height on the water surface of the floating pier increases the heave and roll.

Effective Estimation of Water Waves Scattering by Double-Row Pile Breakwaters

2012 ◽  
Author(s):  
Omid Nejadkazem ◽  
Ahmad Reza Mostafa Gharabaghi
Keyword(s):  
Water Waves ◽  
Wave Length ◽  
Expansion Method ◽  
Optimum Number ◽  
Intermediate Water ◽  
Double Row ◽  
Eigenfunction Expansion Method ◽  
Efficient Performance ◽  
Efficient Calculation ◽  
Efficient Prediction

This paper describes various hydraulic characteristic of double-row pile breakwaters (DPB). Applying an eigenfunction expansion method, a numerical method have been developed that can compute wave transmission, reflection, and other hydraulic characteristics. To verify the validity of developed prediction, laboratory experiments of Isaascson et al. (1999) have been utilized. Then for an efficient calculation, optimum number of necessary evanescent waves for an effective and efficient prediction is discussed for various hydraulic quantities of interest. In a nutshell, for an effective and efficient performance of the DPB, intermediate water wave and porosity range of [0.2 0.3] are recommended. Relative distance between two barriers must be set depending on significant wave length of design.

Hydrodynamic Interactions of the Truncated Porous Vertical Circular Cylinder With Water Waves

2018 ◽  
Author(s):  
Charaf Ouled Housseine ◽  
Sime Malenica ◽  
Guillaume De Hauteclocque ◽  
Xiao-Bo Chen
Keyword(s):  
Circular Cylinder ◽  
Porous Body ◽  
Wave Diffraction ◽  
Water Waves ◽  
Expansion Method ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Diffraction Radiation ◽  
Linear Potential ◽  
Eigenfunction Expansion Method

Wave diffraction-radiation by a porous body is investigated here. Linear potential flow theory is used and the associated Boundary Value Problem (BVP) is formulated in frequency domain within a linear porosity condition. First, a semi-analytical solution for a truncated porous circular cylinder is developed using the dedicated eigenfunction expansion method. Then the general case of wave diffraction-radiation by a porous body with an arbitrary shape is discussed and solved through Boundary Integral Equation Method (BIEM). The main goal of these developments is to adapt the existing diffraction-radiation code (HYDROSTAR) for that type of applications. Thus the present study of the porous cylinder consists a validation work of (BIEM) numerical implementation. Excellent agreement between analytical and numerical results is observed. Porosity influence on wave exciting forces, added mass and damping is also investigated.

Cutaneous Receptive Field Organization in the Ventral Posterior Nucleus of the Thalamus in the Common Marmoset

1999 ◽  
Vol 82 (4) ◽  
pp. 1865-1875 ◽  
Author(s):  
P. Wilson ◽  
P. D. Kitchener ◽  
P. J. Snow
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Receptive Fields ◽  
Common Marmoset ◽  
The Body ◽  
Common Marmosets ◽  
Body Regions ◽  
Low Threshold ◽  
The Common ◽  
Receptive Field Organization

The organization of cutaneous receptive fields in the ventroposterior (VP) thalamus of the common marmosets ( Callithrix jacchus) was determined from single-unit recordings, and these data were correlated with the cytochrome oxidase (CO) histochemistry of the thalamus in the same animals. Under continuously maintained ketamine anesthesia, the receptive fields of a total of 192 single units were recorded from the right VP thalamus using 2 MΩ glass microelectrodes. After the receptive fields were mapped, the brains were reacted for CO histochemistry on 50-μm coronal frozen sections through the entire VP thalamus. The majority of units were localized to the CO-reactive regions that define the medial and lateral divisions of VP (VPm and VPl). Apart from the expected finding of the face being represented in VPm and the body in VPl, reconstructing the electrode tracks and unit locations in the histological sections revealed a general association between discrete regions of CO reactivity and the representation of specific body regions. Some low-threshold cutaneous units were apparently localized to VPi (the CO weak regions dorsal, ventral, and interdigitating with, the CO regions of VP). These VPi units were clearly part of the same representational map as the VPl and VPm units. We conclude that the low-threshold cutaneous receptive fields of the marmoset are organized in a single continuous representation of the contralateral body surface, and that this representation can most simply be interpreted as being folded or crumpled into the three-dimensional space of VP thalamus. The folded nature of the body map in VP may be related to the folded nature of VP as revealed by CO histochemistry.

Aeroacoustic noise generated by flow around circular cyinder with permeable boundary

2020 ◽  
Vol 34 (14n16) ◽  
pp. 2040086
Author(s):  
Fang Wang ◽  
Qiuhong Liu
Keyword(s):  
Three Dimensional ◽  
The Body ◽  
Circular Cylinders ◽  
Pressure Amplitude ◽  
Step Method ◽  
Integral Boundary ◽  
Low Mach Number ◽  
Vortex Sound ◽  
Aeroacoustic Noise ◽  
Sound Theory

A new integral computational formulation is presented to evaluate the noncompact noise induced by low Mach number flows. Based on Howe’s Vortex Sound Theory and wave equation of Green’s function in free space, we obtain a new integral equation by choosing a permeable boundary as the integral boundary. The flow calculation is developed with second-order CFD solvers, and noise calculation is executed with a two-step method to solve scattered sources and far field pressure. Two- and three-dimensional circular cylinders are chosen as test examples. The pressure amplitude obtained with permeable boundary agrees well with that obtained with body-fitted high-order method. Numerical results indicate that the present method is valid and efficient to calculate noncompact noise, and the permeable boundary can replace the body surface as the integral boundary.

scholarly journals On finding a cavity in a thermoelastic body using a single displacement measurement over a finite time interval on the surface of the body

2018 ◽  
Vol 26 (3) ◽  
pp. 369-394 ◽  
Author(s):  
Masaru Ikehata
Keyword(s):  
Time Domain ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Coupled System ◽  
The Body ◽  
Time Interval ◽  
Heat Equations ◽  
Time Domain Data ◽  
Thermoelastic Body ◽  
The Time Domain

AbstractA mathematical formulation of an estimation problem of a cavity inside a three-dimensional thermoelastic body by using time domain data is considered. The governing equation of the problem is given by a system of equations in the linear theory of thermoelasticity which is a coupled system of the elastic wave and heat equations. A new version of the enclosure method in the time domain which is originally developed for the classical wave equation is established. For a comparison, the results in the decoupled case are also given.

Oblique interaction between water waves and a partially submerged rectangular breakwater

2019 ◽  
Vol 234 (1) ◽  
pp. 154-169 ◽  
Author(s):  
R. B. Kaligatla ◽  
N. M. Prasad ◽  
S. Tabssum
Keyword(s):  
Water Waves ◽  
Eigenfunction Expansion ◽  
Wave Scattering ◽  
Wave Reflection ◽  
Expansion Method ◽  
Algebraic Equations ◽  
Eigenfunction Expansion Method ◽  
Balance Relation ◽  
Orthogonal Property ◽  
The One

A problem of oblique wave scattering by a rectangular breakwater floating in water of uneven depth is solved by applying matched eigenfunction expansion method. Three positions of breakwater are considered. The width and draft of breakwater are assumed to be finite, whereas its length is infinite. Breakwater is studied in the settings of without backwall and with a backwall. By using matching conditions at interface boundaries and making use of orthogonal property of eigenfunctions, the problem is converted to a system of algebraic equations. Breakwater’s position is proposed for which wave reflection, transmission, and force on wall are optimized. The breakwater with certain width and draft reflects more wave energy than the one with zero-draft. In the case of absence of wall, breakwater at lee side to the step induces least transmission of waves. In the case of presence of wall, suitable position of breakwater is suggested based on a range of wave frequency to mitigate force on wall. Optimum distances between wall and breakwater are found to attain less force on wall. Using Green’s identity, energy balance relation is derived to check accuracy in results. The findings are likely to be useful to assess the performance of a breakwater in different positions in water of uneven depth.

THREE-DIMENSIONAL PERISTALTIC FLOW OF A WILLIAMSON FLUID IN A RECTANGULAR CHANNEL HAVING COMPLIANT WALLS

2014 ◽  
Vol 14 (01) ◽  
pp. 1450002 ◽  
Author(s):  
R. ELLAHI ◽  
ARSHAD RIAZ ◽  
S. NADEEM
Keyword(s):  
Fluid Model ◽  
Rectangular Channel ◽  
Three Dimensional ◽  
Expansion Method ◽  
Peristaltic Flow ◽  
Three Dimensions ◽  
Physical Parameters ◽  
Williamson Fluid ◽  
Eigenfunction Expansion Method ◽  
Compliant Walls

In this study, the mathematical observations for the peristaltic flow of a Williamson fluid model (e.g., chyme) in a cross-section of a rectangular duct having compliant walls were considered. The flow was assumed incompressible and unsteady. The constitutive equations were reduced under the assumptions of low Reynolds number and long wavelength approximations. The resulting dimensionless governing equations were solved using the homotopy perturbation method (HPM) and eigenfunction expansion method. The results obtained were explained graphically. The velocity distribution was plotted for physical parameters both in two and three dimensions. The streamline graphs are presented in the end, which explain the trapping bolus phenomenon. All theoretical and graphical results are then discussed simultaneously.

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