scholarly journals Ultra Low Frequency Wave Produced by Underwater Oscillating Sphere and Its Measurement

2021 ◽  
Vol 9 (12) ◽  
pp. 1317
Author(s):  
Huan Wang ◽  
Erzheng Fang ◽  
Mingze Wu ◽  
Lianjin Hong ◽  
Zongru Li
Keyword(s):  
Free Surface ◽  
Lower Layer ◽  
Low Frequency ◽  
Single Layer ◽  
Multipole Expansion ◽  
Linear Potential ◽  
Surface Gravity Wave ◽  
Frequency Wave ◽  
Periodic Movement ◽  
Oscillating Sphere

When an underwater target moves in viscous fluid, it may cause the periodic movement of the surrounding fluid and generate ultra-low-frequency (ULF) gravity waves. The initial domain of the gravitational surface wave propagating above the moving target is named circular wave. This article studies the ULF circular wave generated by underwater oscillating sphere, which will provide basis for underwater long-range target detection. Firstly, the circular wave caused by the sphere oscillation in a finite deep fluid is studied based on the theory of linear potential flow. Meanwhile, the multipole expansion theory is established to solve the circular wave field. Secondly, the interface wave generated by the target oscillation in a two-layer fluid are numerically analyzed by comparison with the free surface fluctuation of a single-layer fluid. The results show that the amplitude of the internal interface displacement (AIID) is smaller than that of the free surface (AFSD). When the sphere is in the lower layer, the layering effect of the fluid has significant influences on the AFSD. Finally, the results of the pool experiment verified that the wave generated by the oscillating sphere is the surface gravity wave. Furthermore, the change trend of the test result is consistent with the simulation result.

Hysteresis and nonlinear detuning in a spatial-resonance phenomenon

1973 ◽  
Vol 61 (2) ◽  
pp. 401-413
Author(s):  
Ian Huntley ◽  
Ronald Smith
Keyword(s):  
Free Surface ◽  
Experimental Work ◽  
Alternative Model ◽  
Pressure Field ◽  
Low Frequency ◽  
Theoretical Description ◽  
Resonance Phenomenon ◽  
Theoretical Problem ◽  
Frequency Wave ◽  
Spatial Resonance

The experimental work of Franklin, Price & Williams (1973) shows that for moderately large driving amplitudes there are features of spatial resonance that are not predicted by the model representation of Mahony & Smith (1972). We here derive an alternative model, which remains valid for moderately large driving amplitudes, and we are able to obtain a theoretical description of both hysteresis and nonlinear detuning of the low frequency wave response. An experiment in which surface waves were generated by a sinusoidal pressure field at the free surface (and which corresponds almost exactly to the theoretical problem) was conducted in order to test these predictions.

Experimental Studies of Hydrodynamic Interaction of Two Bodies in Waves

2015 ◽  
Author(s):  
Quan Zhou ◽  
Ming Liu ◽  
Heather Peng ◽  
Wei Qiu
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Potential Flow ◽  
Numerical Solutions ◽  
Experimental Studies ◽  
Low Frequency ◽  
Surface Elevation ◽  
Linear Potential ◽  
Free Surface Elevation ◽  
Two Bodies

There are challenges in the prediction of low-frequency load and especially the resonant free surface elevation between two bodies in close proximity. Most of the linear potential-flow based seakeeping programs currently used by the industry over-predict the free surface elevation between the vessels/bodies and hence the low-frequency loadings on the hulls. Various methods, such as the lid technique, have been developed to suppress the unrealistic values of low-frequency forces by introducing artificial damping coefficients. However, without the experimental data, it is challenging to specify the coefficients. This paper presents the experimental studies of motions of two bodies with various gaps and the wave elevations between bodies. Model tests were performed at the towing tank of Memorial University. The objective was to provide benchmark data for further numerical studies of the viscous effect on the free surface predictions. The experimental data were compared with numerical solutions based on potential flow methods. The effect of tank walls were examined. Preliminary uncertainty analysis was also carried out.

Accuracy Effects of Low Frequency Wave Loads on Ships Offshore to LNG Marine Terminal Design

2004 ◽  
Author(s):  
Monica J. Holboke ◽  
Robert G. Grant
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Low Frequency ◽  
Second Order ◽  
Surface Boundary ◽  
Wave Loads ◽  
Wave Load ◽  
Frequency Wave ◽  
First Order ◽  
Terminal Design

This paper presents the results of a two-body analysis for a moored ship sheltered by a breakwater in shallow water with and without free surface forcing in the low frequency wave load calculation. The low frequency wave loads are determined by second order interactions from the first order. The free surface forcing term arises from the free surface boundary condition, which is trivial to first order but is not at second order. We demonstrate in the frequency domain the importance of this term in a two-body analysis. Additionally, we show how inaccurate calculations of the off-diagonal terms of the Quadratic Transfer Function can translate to over or under prediction of low frequency wave loads on moored ships sheltered by breakwaters in shallow water. Low frequency wave load accuracy has direct consequence for LNG marine terminal design. Generally, LNG marine terminals are sited in sheltered harbors, however increasingly they are being proposed in offshore locations where they will require protection from persistent waves and swells. Since breakwaters typically cost twice as much as the rest of the marine facilities, it is important to optimize their size, orientation and location. In a previous paper we described this optimization process [1], which identified a key step to be the transforming of waves just offshore the breakwater into wave loads on the moored ships. The ability to do this step accurately is of critical importance because if the loads are too large, the breakwater will be larger and more expensive than necessary and if the loads are too small, the terminal will experience excessive downtime and loss of revenue.

A Practical O(Δω) Approximation of Low Frequency Wave Loads

2013 ◽  
Author(s):  
Charles Monroy ◽  
Guillaume de Hauteclocque ◽  
Xiao-Bo Chen
Keyword(s):  
Free Surface ◽  
Order Term ◽  
Low Frequency ◽  
Radial Distance ◽  
Second Order ◽  
Radial Coordinate ◽  
Wave Loads ◽  
Surface Integral ◽  
Frequency Wave ◽  
The Difference

The low-frequency quadratic transfer function (QTF) is defined as the second-order wave loads occurring at the frequency equal to the difference frequency (ω1 − ω2) of two wave frequencies (ω1, ω2) in bi-chromatic waves of unit amplitude. The exact formulation of the QTF which is recalled here is difficult to implement due to numerical convergence problems mainly related to the evaluation of an arduous free surface integral. This is why several approximations have been used for practical engineering studies. They have been the subject of a detailed review in [5]. Following this work, two closely-related formulations are investigated in this paper. In [2], the classical formulations of QTF are examined by an analysis based on the Taylor development with respect to Δω for Δω ≪ 1 and an expansion of QTF in power of Δω is then obtained. It is shown that the zeroth-order term is a pure real function equal to the drift loads and that the term of order O(Δω) is a pure imaginary function. The second-order low-frequency wave loading of order O(Δω) contains a free-surface integral representing the second-order corrective forcing on the free surface. Since the integrand is of order O(1/R4) with R as the radial coordinate, the free-surface integral converges rapidly with the radial distance. Unlike what has been assumed in previous studies of particular cases, this free-surface contribution is, in general, not negligible for high Δω compared to other components and the complete QTF. Depending whether we use the O(Δω) approximation for the whole QTF or only for this free surface integral, it leads to two different approximations. The first one is called original O(Δω) approximation, because it is on this form that the O(Δω) approximation was first described in [2]. If we use the O(Δω) approximation only for the free surface integral, we call this approximation the practical O(Δω) approximation. It is shown in this paper that the original formulation fails to predict the behaviour of the QTF even for small O(Δω). Comparison for the O(Δω) approximation of the free surface integral is performed against the analytical solution and the exact numerical formulation. The results are improved compared to when we neglect this free surface integral for the range of Δω of interest, but still the agreement with the exact solution is not ideal. A path for further improvement is finally proposed.

Supercritical withdrawal from a two-layer fluid through a line sink

1995 ◽  
Vol 297 ◽  
pp. 37-47 ◽  
Author(s):  
G. C. Hocking
Keyword(s):  
Free Surface ◽  
Solution Method ◽  
Numerical Solutions ◽  
Lower Layer ◽  
Single Layer ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Line Sink ◽  
Supercritical Flows ◽  
Good Agreement

Accurate numerical solutions to the problem of finding the location of the interface between two unconfined regions of fluid of different density during the withdrawal process are presented. Supercritical flows are considered, in which the interface is drawn directly into the sink. As the flow rate is reduced, the interface enters the sink more steeply, until the solution method breaks down just before the interface enters the sink vertically from above, and becomes flow from the lower layer only. This lower bound on supercritical flow is compared with the upper bound on single-layer (free surface) flow with good agreement.

Boundaries Influence on the Flow Field Around an Oscillating Sphere

2013 ◽  
Author(s):  
Domenica Mirauda ◽  
Antonio Volpe Plantamura ◽  
Stefano Malavasi
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Boundary Conditions ◽  
Damping Ratio ◽  
Water Channel ◽  
Open Water ◽  
Free Surface Flows ◽  
The Body ◽  
Sphere Diameter ◽  
Oscillating Sphere

This work analyzes the effects of the interaction between an oscillating sphere and free surface flows through the reconstruction of the flow field around the body and the analysis of the displacements. The experiments were performed in an open water channel, where the sphere had three different boundary conditions in respect to the flow, defined as h* (the ratio between the distance of the sphere upper surface from the free surface and the sphere diameter). A quasi-symmetric condition at h* = 2, with the sphere equally distant from the free surface and the channel bottom, and two conditions of asymmetric bounded flow, one with the sphere located at a distance of 0.003m from the bottom at h* = 3.97 and the other with the sphere close to the free surface at h* = 0, were considered. The sphere was free to move in two directions, streamwise (x) and transverse to the flow (y), and was characterized by values of mass ratio, m* = 1.34 (ratio between the system mass and the displaced fluid mass), and damping ratio, ζ = 0.004. The comparison between the results of the analyzed boundary conditions has shown the strong influence of the free surface on the evolution of the vortex structures downstream the obstacle.

The hydraulics of two flowing layers with different densities

1986 ◽  
Vol 163 ◽  
pp. 27-58 ◽  
Author(s):  
Laurence Armi
Keyword(s):  
Lower Layer ◽  
Single Layer ◽  
Critical Conditions ◽  
Hydraulic Jumps ◽  
Flow Configurations ◽  
Pass Through ◽  
Bottom Depth ◽  
Downstream Flow ◽  
Energy Equations ◽  
Simple Flow

This is a theoretical and experimental study of the basic hydraulics of two flowing layers. Unlike single-layer flows, two-layer flows respond quite differently to bottom depth as opposed to width variations. Bottom-depth changes affect the lower layer directly and the upper layer only indirectly. Changes in width can affect both layers. In fact for flows through a contraction control two distinct flow configurations are possible; which one actually occurs depends on the requirements of matching a downstream flow. Two-layer flows can pass through internally critical conditions at other than the narrowest section. When the two layers are flowing in the same direction, the result is a strong coupling between the two layers in the neighbourhood of the control. For contractions a particularly simple flow then exists upstream in which there is no longer any significant interfacial dynamics; downstream in the divergent section the flow remains internally supercritical, causing one of the layers to be rapidly accelerated with a resulting instability at the interface. A brief discussion of internal hydraulic jumps based upon the energy equations as opposed to the more traditional momentum equations is included. Previous uniqueness problems are thereby avoided.

Linear and non-linear potential-flow calculations of free-surface waves with lift and induced drag

2000 ◽  
Vol 214 (6) ◽  
pp. 801-812
Author(s):  
C-E Janson
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Lift Force ◽  
Radiation Condition ◽  
Linear Potential ◽  
Surface Boundary ◽  
Model Approximation ◽  
Non Linear ◽  
Lifting Surfaces ◽  
The Waves

A potential-flow panel method is used to compute the waves and the lift force from surface-piercing and submerged bodies. In particular the interaction between the waves and the lift produced close to the free surface is studied. Both linear and non-linear free-surface boundary conditions are considered. The potential-flow method is of Rankine-source type using raised source panels on the free surface and a four-point upwind operator to compute the velocity derivatives and to enforce the radiation condition. The lift force is introduced as a dipole distribution on the lifting surfaces and on the trailing wake, together with a flow tangency condition at the trailing edge of the lifting surface. Different approximations for the spanwise circulation distribution at the free surface were tested for a surface-piercing wing and it was concluded that a double-model approximation should be used for low speeds while a single-model, which allows for a vortex at the free surface, was preferred at higher speeds. The lift force and waves from three surface-piercing wings, a hydrofoil and a sailing yacht were computed and compared with measurements and good agreement was obtained.

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