Servan Camas et al 2018a - Revision history

Julio: Julio moved page Draft Garcia-Espinosa 291836717 to Servan Camas et al 2018a

2019-11-04T19:49:11Z

Julio moved page Draft Garcia-Espinosa 291836717 to Servan Camas et al 2018a

Julio at 19:42, 4 November 2019

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Julio at 19:39, 4 November 2019

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Julio at 19:25, 4 November 2019

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Julio at 19:23, 4 November 2019

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Julio at 19:21, 4 November 2019

2019-11-04T19:21:13Z

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 A number of tests were carried out with bichromatic waves in order to analyse the second-order response of the platform. The incident wave periods range between 5.5 and 21 seconds. The wave frequency difference ranges from 0.0128 Hz to 0.0167 Hz. The latter frequency is intentionally close to the surge resonant frequency as the focus of the analysis will be on the surge response to the slow drift.
-<span id='cite-_Ref465934909'></span>[[#_Ref465934909|Table 12]] provides the experimental test matrix, including incident wave height ( <math display="inline">H</math>), frequency <math display="inline">(f)</math>, and the frequency difference and sum. All these cases have been simulated in the time-domain using the FEM model proposed in this work for the diffraction-radiation problem. The different cases have been analysed using the quasi-static elastic catenary and the non-linear FEM dynamic cable models. Once the simulations were carried out, the time series were transformed via FFT to the frequency domain in order to enable the comparison of results with the experimental data. No filtering was undertaken on the experimental and numerical data.
+<span id='cite-_Ref465934909'></span>[[#_Ref465934909|Table 12]] provides the experimental test matrix, including incident wave height (<math display="inline">H</math>), frequency (<math display="inline">f</math>), and the frequency difference and sum. All these cases have been simulated in the time-domain using the FEM model proposed in this work for the diffraction-radiation problem. The different cases have been analysed using the quasi-static elastic catenary and the non-linear FEM dynamic cable models. Once the simulations were carried out, the time series were transformed via FFT to the frequency domain in order to enable the comparison of results with the experimental data. No filtering was undertaken on the experimental and numerical data.
 When analysing the wave elevation in the experiments, it was found that the wave energy spectrum was not bichromatic, showing energy spread around the frequency pair under analysis. In order to better reproduce the experiment, a set of waves reproducing the free surface elevation of the experiment was used, instead of a pure bichromatic wave.

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-====6.5 Validation test 2: bichromatic waves====
+====6.5. Validation test 2: bichromatic waves====
 A number of tests were carried out with bichromatic waves in order to analyse the second-order response of the platform. The incident wave periods range between 5.5 and 21 seconds. The wave frequency difference ranges from 0.0128 Hz to 0.0167 Hz. The latter frequency is intentionally close to the surge resonant frequency as the focus of the analysis will be on the surge response to the slow drift.
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 {| style="width: 100%;border-collapse: collapse;"
 |-
-|  style="vertical-align: top;width: 50%;"|[[Image:Draft_Garcia-Espinosa_291836717-image20.png|288px]]
+|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_Garcia-Espinosa_291836717-image20.png|288px]]
 <span style="text-align: center; font-size: 75%;">(a): Case 1</span>
-|  style="vertical-align: top;width: 50%;"|[[Image:Draft_Garcia-Espinosa_291836717-image21.png|288px]]
+|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_Garcia-Espinosa_291836717-image21.png|288px]]
 <span style="text-align: center; font-size: 75%;">(b): Case 2</span>
 |-
-|  style="vertical-align: top;width: 50%;"|[[Image:Draft_Garcia-Espinosa_291836717-image22.png|288px]]
+|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_Garcia-Espinosa_291836717-image22.png|288px]]
 <span style="text-align: center; font-size: 75%;">(c): Case 3</span>
-|  style="vertical-align: top;width: 50%;"|[[Image:Draft_Garcia-Espinosa_291836717-image23.png|288px]]
+|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_Garcia-Espinosa_291836717-image23.png|288px]]
 <span style="text-align: center; font-size: 75%;">(d): Case 4</span>
 |-
-|  style="vertical-align: top;width: 50%;"|[[Image:Draft_Garcia-Espinosa_291836717-image24.png|288px]]
+|  style="text-align: center;vertical-align: top;width: 50%;"|[[Image:Draft_Garcia-Espinosa_291836717-image24.png|288px]]
 <span style="text-align: center; font-size: 75%;">(e): Case 5</span>
-|  style="vertical-align: top;width: 50%;"|[[Image:Draft_Garcia-Espinosa_291836717-image25.png|288px]]
+|  style="text-align: center;ertical-align: top;width: 50%;"|[[Image:Draft_Garcia-Espinosa_291836717-image25.png|288px]]
 <span style="text-align: center; font-size: 75%;">(f): Case 6</span>
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 |}
 {| style="width: 100%;border-collapse: collapse;"
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 |  colspan='2'  style="text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Figure 13: (continued)</span>
 |}
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 |  style="border-top: 1pt solid black;border-bottom: 1pt solid black;border-right: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">30.89</span>
 |}
 ====6.3 Validation test 3: irregular waves====

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 <span id='_Toc435436133'></span>
-===1.7.1 Problem description===
+=====5.2.1 Problem description=====
 <span id='_Ref426107620'></span>This test case deals with the solution to the diffraction problem of second-order monochromatic surface waves by a semisubmerged horizontal cylinder of rectangular cross section. The boundary-value problem is resolved and the results are compared with the analytical solution obtained by the method of matched Eigen function expansions presented in [<span id='cite-24'></span>[[#24|24]]]. Horizontal and vertical forces and the moment about the heel of the prismatic cylinder are analysed for different monochromatic waves. An illustration of this problem is shown in figure 4. Relevant geometric parameters are: depth (h = 1 m), half beam (b = 1 m), and draught (d = 0.2 m).

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 ====5.1 Verification case 1: mean drift forces on a hemisphere====
 This case consists of estimating the mean drift forces on a hemisphere. In this work, mean drift forces are obtained by averaging the time series of the corresponding second-order force. The analytical solution for the fixed hemisphere was obtained by Fernandes and Levy [<span id='cite-21'></span>[[#21|21]]], and for the freely floating hemisphere was obtained by Kudou [<span id='cite-22'></span>[[#22|22]]] and reported by Pinkster [<span id='cite-23'></span>[[#23|23]]]. In this section, the numerical results are compared with the analytical solution. The details of the hemisphere particulars are given in <span id='cite-_Ref426102176'></span>[[#_Ref426102176|Table 1]]. Both fixed and free floating cases were analysed. Figure 2 (left) shows the mesh used for the calculations. It can be observed that mesh refinement is required in the area of the waterline in order to obtain accurate results of mean drift forces. Figure 2 (right) shows a snapshot of the wave elevation around the hemisphere in one of the cases run. Finally, figure 3 (above) compares the analytical results with the numerical results in the case of the fixed hemisphere, while figure 3 (below) compares the results in the free floating case. Good correlation is observed for the whole range of waves analysed.
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 <span style="text-align: center; font-size: 75%;">Figure 3: Mean drift forces on Hemisphere.</span>
 |}
 ====5.2 Verification case 2: diffraction of second-order monochromatic waves by semisubmerged horizontal rectangular cylinder====

← Older revision		Revision as of 19:23, 4 November 2019
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−	=====5.1.2 Verification case 2: diffraction of second-order monochromatic waves by semisubmerged horizontal rectangular cylinder=====	+	====5.2 Verification case 2: diffraction of second-order monochromatic waves by semisubmerged horizontal rectangular cylinder====

	<span id='_Toc435436133'></span>		<span id='_Toc435436133'></span>

← Older revision	Revision as of 19:49, 4 November 2019
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 ====5.1 Verification case 1: mean drift forces on a hemisphere====
-===1.6.1 Problem description===
+=====5.1.1 Problem description=====
 This case consists of estimating the mean drift forces on a hemisphere. In this work, mean drift forces are obtained by averaging the time series of the corresponding second-order force. The analytical solution for the fixed hemisphere was obtained by Fernandes and Levy [<span id='cite-21'></span>[[#21|21]]], and for the freely floating hemisphere was obtained by Kudou [<span id='cite-22'></span>[[#22|22]]] and reported by Pinkster [<span id='cite-23'></span>[[#23|23]]]. In this section, the numerical results are compared with the analytical solution. The details of the hemisphere particulars are given in <span id='cite-_Ref426102176'></span>[[#_Ref426102176|Table 1]]. Both fixed and free floating cases were analysed. Figure 2 (left) shows the mesh used for the calculations. It can be observed that mesh refinement is required in the area of the waterline in order to obtain accurate results of mean drift forces. Figure 2 (right) shows a snapshot of the wave elevation around the hemisphere in one of the cases run. Finally, figure 3 (above) compares the analytical results with the numerical results in the case of the fixed hemisphere, while figure 3 (below) compares the results in the free floating case. Good correlation is observed for the whole range of waves analysed.
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-====1.7 Verification case 2: diffraction of second-order monochromatic waves by semisubmerged horizontal rectangular cylinder====
+=====5.1.2 Verification case 2: diffraction of second-order monochromatic waves by semisubmerged horizontal rectangular cylinder=====
 <span id='_Toc435436133'></span>

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 ===5. Numerical model verification===
-====1.6 Verification case 1: mean drift forces on a hemisphere====
+====5.1 Verification case 1: mean drift forces on a hemisphere====
 ===1.6.1 Problem description===