Application of an alternative mesh morphing method on the numerical modeling of oscillating wave surge converters

Vargas, Guilherme Fuhrmeister; Schettini, Edith Beatriz Camaño

doi:10.1590/2318-0331.241920180102

Guilherme Fuhrmeister Vargas

Instituto de Pesquisas Hidráulicas, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brasil

http://orcid.org/0000-0002-6923-6842

Edith Beatriz Camaño Schettini

Instituto de Pesquisas Hidráulicas, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brasil

E-mails: guilherme.fuhrmeister@ufrgs.br (GFV), bcamano@iph.ufrgs.br (EBCS)

Authors contributions Guilherme Fuhrmeister Vargas: Performed the research, the numerical simulations and worked on the manuscript writing.

Edith Beatriz Camaño Schettini: Assisted the manuscript structuring and revision.

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Figure 1
Scheme of operation and power generation of an OWSC (adapted from OpenEI, 2018OPEN ENERGY INFORMATION – OPENEI. Marine and hydrokinetic technology glossary. Department of Energy, 2018. Available from: <https://openei.org/wiki/Marine_and_Hydrokinetic_Technology_Glossary>. Access on: 07 feb. 2019.
https://openei.org/wiki/Marine_and_Hydro... ).

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Figure 2
Detail of the mesh elements being deformed to represent the rigid body dynamics.

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Figure 3
Dimensions of the computational domain used in the numerical verification stage.

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Figure 4
Dimensions of the flap used in the first domain simulations.

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Figure 5
Dimensions of the computational domain used in the comparative studies between the moving and the fixed bottom.

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Figure 6
Dimensions of the flap used in the numerical simulations of the second domain.

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Figure 7
Representation of the boundaries used in the numerical simulations.

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Figure 8
Location of water level probes and pressure sensors used in numerical validations.

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Figure 9
Comparison of velocity magnitudes according to the applied boundary conditions.

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Figure 10
Comparison of the results obtained by applying different velocity boundary conditions, (a) considering the angular amplitude reached by the flap and (b) the pressure measured on the pressure sensor 2.

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Figure 11
Comparison between the results obtained by the fixed bottom and moving bottom methods with the experimental and numerical studies presented in the literature.

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Figure 12
Distances to the bottom of the domain applied in the verification of the moving bottom method.

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Figure 13
Comparison of the velocity fields, presenting the movement of the flap of an OWSC, during the passage of a wave crest, considering the fixed bottom and moving bottom methodologies.

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Figure 14
Comparison between time histories of angular amplitude (θ), angular velocity (ω) and horizontal force (F_x), for fixed bottom and moving bottom cases, considering openings of 0.025 m (above) and 0.3 m (below).

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Figure 15
Relative differences of the calculation statistical parameters, considering the fixed bottom and moving bottom methodologies, along five adimensional openings.

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Table 1
Velocity and pressure boundary conditions applied on the OpenFOAM code.

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Table 2
Coordinates of water level probes and pressure sensors.

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Table 3
Relative errors for the analysis of the angular amplitude.

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Table 4
Relative errors for the analysis of the pressure sensor 2.

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Table 5
Relative errors for the S1, S2, S3, S4 and S5 series, considering the numerical results obtained by Rafiee et al. (2013)RAFIEE, A.; ELSAESSER, B.; DIAS, F. Numerical simulation of wave interaction with an oscillating wave surge converter. In: XXXII INTERNATIONAL CONFERENCE ON OCEAN, OFFSHORE AND ARCTIC ENGINEERING, 32., 2013, Nantes, France. Proceedings... ASME, 2013. p. 1-9. http://dx.doi.org/10.1115/OMAE2013-10195.
http://dx.doi.org/10.1115/OMAE2013-10195... and Wei et al. (2015)WEI, Y.; RAFIEE, A.; HENRY, A.; DIAS, F. Wave interaction with an oscillating wave surge converter, part I: viscous effects. Ocean Engineering, v. 104, p. 185-203, 2015., the moving bottom methodology and the fixed bottom method.

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(2)

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Contorno	Velocidade	Pressão
flap	Variable¹ 1 The velocity boundary condition changes according to the considered case, the considerations are detailed in the section “Important considerations”.	fixedFluxPressure
“a” type bottom	noSlip	fixedFluxPressure
“b” type bottom	noSlip	fixedFluxPressure
inlet	waveVelocity	fixedFluxPressure
outlet	waveAbsorbtion2DVelocity	zeroGradient
top	pressureInletOutletVelocity	totalPressure
Domain sides	Empty	Empty

	X (m)	Y (m)	Z (m)
Water level probe 1	3.99	0.52	0.71
Water level probe 2	8.92	0.52	0.71
Pressure sensor 1	9.76	0.52	0.50
Pressure sensor 2	9.76	0.52	0.70

Boundary condition	RMS	$A_{m}$	$D_{p}$	$D_{m}$	Mean
Boundary condition	(%)
noSlip	0.16	5.88	0.44	5.31	2.95
slip	5.03	3.98	4.63	4.27	4.47
movingWallVelocity	60.41	62.57	60.86	62.28	61.53

Boundary condition	RMS	$A_{m}$	$D_{p}$	$D_{m}$	Mean
Boundary condition	(%)
noSlip	17.28	28.72	4.29	7.69	14.50
slip	10.60	20.92	9.34	1.23	10.52
movingWallVelocity	58.74	59.71	56.87	57.53	58.22

Series	Applied Method	RMS	$A_{m}$	$D_{p}$	$D_{m}$	Mean
Series	Applied Method	(%)
S₁	Moving bottom	5.60	6.17	2.24	4.23	4.56
	Fixed bottom	0.16	5.88	0.44	5.31	2.95
	Numerical (authors)	10.53	12.11	10.71	12.46	11.45
S₂	Moving bottom	9.90	8.72	12.03	10.56	10.30
	Fixed bottom	3.98	5.82	12.97	12.15	8.73
	Numerical (authors)	10.25	6.18	7.86	5.49	7.44
S₃	Moving bottom	20.09	24.62	27.86	28.61	25.30
	Fixed bottom	17.13	21.99	29.14	26.91	23.79
	Numerical (authors)	4.29	0.81	3.84	0.67	2.40
S₄	Moving bottom	1.71	3.76	34.83	27.78	17.02
	Fixed bottom	2.73	0.62	40.94	41.51	21.45
	Numerical (authors)	0.73	2.80	36.14	32.64	18.08
S₅	Moving bottom	15.07	16.70	7.34	16.65	13.94
	Fixed bottom	17.28	28.72	4.29	7.69	14.50
	Numerical (authors)	42.09	37.90	53.63	54.42	47.01

\frac{\partial \bar{u_{i}}}{\partial t} + \bar{u_{j}} \frac{\partial \bar{u_{i}}}{\partial x_{j}} = g_{i} - \frac{1}{ρ} \frac{\partial \bar{p}}{\partial x_{i}} + \frac{\partial}{\partial x_{j}} (ν \frac{\partial \bar{u_{i}}}{\partial x_{j}} - \bar{u_{i}^{'} u_{j}^{'}})

[1] E-mails: guilherme.fuhrmeister@ufrgs.br (GFV), bcamano@iph.ufrgs.br (EBCS)

Brasil

Brasil

Application of an alternative mesh morphing method on the numerical modeling of oscillating wave surge converters

Aplicação de uma metodologia alternativa de deformação de malhas na modelagem numérica de conversores oscilantes por translação de ondas

ABSTRACT