Bingham, Harry B.

Newman, J. N.

Read, Robert

In the field of water waves, there has been recent interest in a process known as cloaking. Accordingto this concept, the waves scattered by a fixed body are manipulated in the region immediately surrounding the object to eliminate scattering at large distances from the body. Cloaking of a bottom-mounted vertical monopile was first proposed by Porter (2011), who manipulated the bathymetry in the surrounding region to minimise the scattered energy to values approaching zero. Newman (2013) investigated cloaking of a surface-piercing cylinder of finite draft by introducing an array of bodies or an axisymmetric structure around the central object. In this case, a multivariate optimiser was successfully coupled with the boundary-integral equation software WAMIT to identify geometric arrangements resulting in minimal far-field wave scattering at a specified wavelength. The existence of arrays of bodies capable of cloaking has more recently been confirmed numerically by Kashiwagi et al.(2015) using the theory of Kagemoto and Yue (1986) in conjunction with a higher-order, boundary-element method. Kashiwagi et al have furthermore presented experimental results supporting the numerical findings for array-type cloaking. From a practical perspective, the elimination of the meandrift force on a surface-piercing structure associated with the cloaking process may find application in the reduction of second-order mooring loads in large offshore structures.This paper describes a further experimental investigation into the cloaking of a circular cylinder of finite draft using a circumferential array of eight surrounding cylinders. The aims of the work were:to identify a cloaking geometry suitable for investigation in the facilities available at DTUto design and build an apparatus to investigate wave scattering by this and other geometries,to confirm cloaking at one wavelength by measuring the mean drift force and far-field scattering

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N.Published in:Proceedings of the 31th International Workshop on Water Waves and Floating Bodies (IWWWFB 2016)Publication date:2016Document VersionPeer reviewed versionLink back to DTU OrbitCitation (APA):Read, R., Bingham, H. B., & Newman, J. N. (2016). Measurements of Cloaking Produced by an Array of CircularCylinders. In Proceedings of the 31th International Workshop on Water Waves and Floating Bodies (IWWWFB2016)Measurements of Cloaking Produced by an Array of Circular Cylinders1R. W. Read, 1H. B. Bingham, and 2J. N. Newman1Dept. of Mechanical Engineering, Technical University of Denmark (DTU).rrea@mek.dtu.dk, hbb@mek.dtu.dk2jnn@mit.edu1 IntroductionIn the field of water waves, there has been recent interest in a process known as cloaking. Accordingto this concept, the waves scattered by a fixed body are manipulated in the region immediatelysurrounding the object to eliminate scattering at large distances from the body. Cloaking of a bottom-mounted vertical monopile was first proposed by Porter (2011), who manipulated the bathymetryin the surrounding region to minimise the scattered energy to values approaching zero. Newman(2013) investigated cloaking of a surface-piercing cylinder of finite draft by introducing an array ofbodies or an axisymmetric structure around the central object. In this case, a multivariate optimiserwas successfully coupled with the boundary-integral equation software WAMIT to identify geometricarrangements resulting in minimal far-field wave scattering at a specified wavelength. The existence ofarrays of bodies capable of cloaking has more recently been confirmed numerically by Kashiwagi et al.(2015) using the theory of Kagemoto and Yue (1986) in conjunction with a higher-order, boundary-element method. Kashiwagi et al have furthermore presented experimental results supporting thenumerical findings for array-type cloaking. From a practical perspective, the elimination of the meandrift force on a surface-piercing structure associated with the cloaking process may find application inthe reduction of second-order mooring loads in large offshore structures.This paper describes a further experimental investigation into the cloaking of a circular cylinderof finite draft using a circumferential array of eight surrounding cylinders. The aims of the work were:• to identify a cloaking geometry suitable for investigation in the facilities available at DTU,• to design and build an apparatus to investigate wave scattering by this and other geometries,• to confirm cloaking at one wavelength by measuring the mean drift force and far-field scattering.2 Experimental SetupThe experiment described here has proved challenging for several reasons. Firstly, the surge meandrift force is small in comparison to the surge excitation force (1.5% here), and therefore difficultto extract accurately from the total force signal. An additional problem in this regard is that thesurge force sensor may register so-called cross-talk signals associated with the considerable heaveexcitation force and pitch moment acting on the apparatus. A second challenge is presented by thesmall differences between the mean drift forces and the scattered wave amplitudes at the uncloakedand cloaked conditions. For example, the maximum far-field scattered wave amplitude generatedby the uncloaked cylinder is only 3.6 mm, compared to an incident wave amplitude of 18.8 mm. Athird difficulty is the requirement that the generated incident waves should be spatially uniform andrepeatable, with higher harmonics reduced to a minimum. Whilst the wave-generator used here wasnot ideal in this respect, attempts have been made to correct for the non-uniformities encountered.The cloaking configuration investigated in this paper consisted of an inner cylinder surroundedby eight smaller outer cylinders. A variety of inner-cylinder diameters and drafts were considered,with the aim of maximising the ratio of the surge drift force to the surge excitation force at thecloaking frequency whilst limiting the size of the complete apparatus. Having selected a potentialinner-cylinder radius and draft, computations using WAMIT coupled to a multivariate optimiser wereperformed by J. N. Newman to identify the radius, draft and mounting radius of the outer cylinders tominimise scattering. The finite depth of the tank was specified during this process. Having identifiedthe optimised geometry, the forces on the inner and outer cylinder assemblies and the wave elevationat points around the structure, were independently confirmed by the authors using WAMIT. The final,xy927.1200112.7F1xz6081.6(a) (b)Dimensions in millimetres.Figure 1: The configuration of the cloaking apparatus: (a) plan view, (b) side view.selected configuration is illustrated in Figure 1. A hemispherical base was included on all cylinders tominimise viscous effects.Having selected the geometry, an apparatus was constructed to support the cylinder assembliesfrom above. This structure was designed to be as stiff as possible, whilst allowing a degree of adaptationfor future investigations of other cloaking geometries. The support structure incorporated a load cell tomeasure the surge force on the inner cylinder alone, the outer cylinders alone, or the entire structure.As the measurement uncertainties are typically specified as a percentage of the full-scale reading, therange of the load cell was carefully selected to only slightly exceed the maximum predicted surgeexcitation force. Furthermore, a sensor with a particularly low cross-talk was specified to minimisethe effects of the wave-generated heave forces and pitch moments. To further minimise measurementuncertainties, the inner and outer cylinder assemblies were ballasted to achieve neutral buoyancy.00.20.40.81.423412345678910111213140 2.1 5.38 13 15 17 28.45 310.90 1.33 2 2.67 4(a)(b) (c)Lengths in metres.T = 0.90 s,λ = 1.26 m,A = 18.8 mm, = 3%.Figure 2: The experimental configuration (a) plan view; (b) end view; (c) side view.The entire cylinder assembly was installed in a wave tank 31 m long by 4 mwide by 0.9 m deep,located at DTU. This arrangement is illustrated in Figure 2. Waves with a period of 0.90 s and asteepness of 3%, were generated by a piston-type wavemaker. Resistive wave gauges were installedat a variety of locations to measure the free-surface elevation. Among these were two lines of gaugesdeployed two metres up- and downwave of the cloaking apparatus (numbered 3-7 and 9-13 respect-ively). These wave gauges were installed at transverse intervals designed to coincide with points ofsmall and large scattering amplitude for the uncloaked case. Ten test runs were conducted for each ofthree cylinder configurations: no cylinders, the inner cylinder installed alone, and the inner and outercylinders both installed. Data corresponding to ten complete wave periods were extracted from eachtime series. A sinusoidal least squares fit was made to the data, and the amplitude of the mean andthe fundamental was extracted from the force and the surface-elevation data for comparison with thenumerical results.3 ResultsThe numerical and experimental results for the excitation and mean drift forces are presented inFigure 3. Whilst the original intention was to measure the force on the entire structure with thecloaking cylinders installed, unexpected compliance of the load cell led to a small pitching motionof the structure in waves. Having observed this, the cloaking structure, consisting of the eight outercylinders, was locked in position, and the surge force on the inner cylinder alone recorded. At thecloaking wavelength, the mean drift force on the inner cylinder alone should also be zero. Furthermore,the numerical results suggest that the excitation force on the outer cylinder assembly should be zeroas well, suggesting that there should be no difference between the excitation force measured on thetotal structure and that measured on the inner cylinder alone.0 1.25 2.5 3.75 5 6.25 7.5 8.75 1000.040.080.120.160.200.240.280.32(a)k (m−1)Fm,1(N)N = 1 num. N = 1 exp.N = 9 num. N = 9 exp.0 1.25 2.5 3.75 5 6.25 7.5 8.75 1001.252.53.7556.257.58.7510(b)k (m−1)Fe,1(N)N = 1 num. N = 1 exp.N = 9 num. N = 9 exp.Figure 3: Surge forces with N cylinders installed: (a) mean drift forces, (b) excitation forces.The numerical results for the force on the total structure are presented for a range of wave numbers,where k = 5 corresponds to the cloaking value. In accordance with plans for future experiments atother wavelengths, for wavenumbers less than the critical value, the amplitude has been limited tothat at the critical value, whereas a constant steepness is maintained for larger wavenumbers. Theexperimental results for the excitation force show reasonable agreement with the numerical results,but all forces are larger than predicted by theory. This is especially evident for the mean drift forces.Here, the error bars represent solely the variability in results between tests. Whilst these values aresmall, a full error analysis will be presented at the Workshop. It is suspected that the primary sourceof error in these results is cross-talk contributions to the surge signal from the heave force and pitchmoment also being applied to the structure. Compensation for these effects should be achievable andis being investigated.0 0.25 0.5 0.75 1 1.25 1.5 1.75 2151617181920212223(a)|y| (m)|Ad|(mm)N = 0 num. N = 0 exp.N = 1 num. N = 1 exp.N = 9 num. N = 9 exp.0 0.25 0.5 0.75 1 1.25 1.5 1.75 2151617181920212223(b)|y| (m)|Ad|(mm)N = 0 num. N = 0 exp.N = 1 num. N = 1 exp.N = 9 num. N = 9 exp.Figure 4: Diffraction wave amplitude with N cylinders installed: (a) 2 m upwave (gauges 3-7), (b)2 m downwave (gauges 9-13).The numerical and experimental results for the wave amplitude upwave and downwave of theassembly are presented in Figure 4. Due to irregularities in the wave generation, the spatial variationof the wave amplitude was significant without any structure in place. The results have thereforebeen corrected for the variations in the amplitude of the incident wave by dividing the uncloakedand cloaked structure wave amplitudes by the true incident amplitude and multiplying by the targetamplitude. The experimental results are then seen to be in general agreement with the numericalpredictions. The error bars presented here again correspond to the test-to-test variation alone. Theuncertainty associated with the elevation itself is likely to be less than 1 mm, but the specific value isalso presently being identified for the particular design of wave gauge used here.AcknowledgementsThe authors wish to thank COWIfonden for their generous financial support.H. Kagemoto and D. K. P. Yue. Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method.Journal of Fluid Mechanics, 166:189–209, 1986.M. Kashiwagi, T. Iida, and M. Miki. Wave drift force on floating bodies of cloaking configuration and associated wave patterns. In30th International Workshop on Water Waves and Floating Bodies, Bristol, UK, 2015.J. N. Newman. Cloaking a circular cylinder in deep water. In 28th International Workshop on Water Waves and Floating Bodies,L’Isle-sur-la-Sorgue, France, 2013.R. Porter. Cloaking of a cylinder in waves. In 26th International Workshop on Water Waves and Floating Bodies, Athens, Greece,2011.

Measurements of Cloaking Produced by an Array of Circular Cylinders

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Measurements of Cloaking Produced by an Array of Circular Cylinders

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