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A study on dynamic response of a semi-submersible floating wind turbine considering combined wave and current loads Yuliang Liu, Takeshi Ishihara E-mail: Department of Civil Engineering, School of Engineering, The University of Tokyo The current loads on floating structures and mooring lines are known to be essential and are recommended to be included in the design as required by international standards. In modeling hydrodynamic loads, the drag force in the Morison’s equation is widely used to account for the viscous effect. Many experiments showed that the drag coefficient ( ) for a circular cylinder in the oscillating flow is different from that in a steady flow. It is crucial to select appropriate drag coefficients for the prediction of hydrodynamic loads on floating structures and mooring lines. Liu and Ishihara [1] proposed a method to determine the hydrodynamic coefficients of a FOWT based on the forced oscillation tests. However, this method was validated by the wave-only water tank tests, and its performance in the combined wave and current condition was not examined. In this study, the responses of a FOWT in the combined wave and current condition is investigated using a 1:50 scale semi-submersible model, which was used in the Fukushima FORWARD project. Firstly, a water tank test is carried out to investigate the influence of current on the responses of the FOWT. A hydrodynamic force model is then proposed to predict drag force in the combined wave and current condition. Finally, the proposed model is validated by the water tank tests for several load cases. Introduction The motions and mooring tensions of a 1:50 scale semisubmersible FOWT for the Fukushima FORWARD project are investigated by the water tank tests. The model is positioned by 4 catenary mooring lines of 10.3 m anchored on the bottom of the water tank at the depth of 2.5 m as shown in Fig.1. The origin of coordinate locates at the centerline of center column of the floater on the water surface and the reference point of motions is defined at the gravity center of the floater . Both wave and current are generated from the left side. The current velocity is measured at the location 7.3m away from the floater. (a) Overview of 1:50 scale model of the platform (b) Arrangement of the mooring lines Figure 1 Configuration of the water tank test Water tank tests Drag coefficient for a circular cylinder Fig. 2 shows the drag coefficient of a circular cylinder in steady and oscillatory flows in the water tunnel and forced oscillation tests. It changes with the increase of Reynolds number and shows different values in the steady and oscillatory flows. Figure 2 of a circular cylinder in the steady and oscillatory flows A combined hydrodynamic force model In this study, the obtained from the forced oscillation test is assumed to be appropriate for predicting the floater motions in the wave only case. Since of a cylinder in the oscillating flow is different from that in the steady flow, a combined hydrodynamic force model is proposed to calculate the drag force contributed from the wave and current based on the Morison’s equation as: = 1 2 + + + 1 2 where is the drag coefficient of cylinder obtained from the forced oscillation test and is a function of KC number, frequency and interaction effect between the cylinders [1]. means the drag coefficient of the cylinder measured in the steady flow and is a function of Reynolds number. and denote the current velocity and the relative velocity without the current component, respectively. In the wave-only and current-only cases, the drag forces by the proposed formula are the same as those by the conventional Morison’s equation. In the combined wave and current condition, the current-induced forces are calculated using from the steady flow, while the wave and motion induced forces are predicted using from the forced oscillation test. Hydrodynamic force model (a) Mean surge (b) RAO in the wave only in the current only case case (H=0.06m, T=2.5s) Figure 3 Comparison of predicted responses by the proposed and conventional models in the wave-only and current-only cases Combined wave and current condition Fig. 4 presents the predicted mean and dynamic responses by the two models in the combined current and wave case. The conventional model overestimates the mean surge, which is consistent with the conclusion in the current-only case. The predicted RAO of mooring tension is overestimated due to the overestimation of the mean surge and the predicted RAO of pitch is underestimated by the conventional model. The predicted responses by the proposed model match well with the experimental data. (a) Mean response (b) RAOs Figure 4 Comparison of predicted responses by the proposed and conventional models in the wave and current case (H=0.06m, T=2.5s, v=0.2m/s) Validation In this study, a combined hydrodynamic force model is proposed to estimate the drag force on the floating platform in the combined wave and current condition. 1. A combined hydrodynamic force model to predict the drag force of the floater is proposed to consider the difference of drag coefficients for a cylinder in the wave only and current only conditions. 2. The predicted mean and dynamic responses of floater motion and mooring tension by the proposed model show good agreement with the experimental data, while those by the conventional model are overestimated or underestimated when the current is existing. This research is carried out as a part of the Fukushima floating offshore wind farm demonstration project funded by the Ministry of Economy, Trade and Industry. Conclusion [1] Liu, Y., Ishihara, T. , 2019. Prediction of dynamic response of semi-submersible floating offshore wind turbines by a novel hydrodynamic coefficient model. Journal of Physics: Conference Series, 1356, 12035 Reference 0 1 2 3 10 3 10 4 10 5 10 6 10 7 10 8 10 9 Steady flow Oscillatory flow Cd Re 0 10 20 30 0 0.05 0.1 0.15 0.2 Exp. Cal. proposed model Cal. conventional model Mean motion Surge (m) Heave (m) Pitch (rad) Tension (N) Mean tension 0 1 2 3 Exp. Cal. proposed model Cal. conventional model 0 1 2 3 RAO of motion Surge (m/m) Heave (m/m) Pitch (rad/m) Tension (N/m) 0 10 20 30 RAO of tension The proposed model is validated through a comparison between predicted and measured motions of the platform and tensions of the mooring lines in the current-only, wave-only and combined wave and current conditions. The result by the conventional model using by the forced oscillation tests is also investigated. Current only and wave only condition The simulations are conducted using Orcaflex. Fig.3 shows the comparison of predicted responses by the proposed and conventional models. In the current-only case as shown in Fig.3 (a), the conventional model overestimates the surge motions due to the large value of from the forced oscillation tests, while the predicted responses by the proposed model show good agreement with the experiment. In the wave-only case, both models predict RAOs well as shown in Fig.3 (b) since the same obtained in the oscillatory flow is applied in the two models. 0 1 2 3 Exp. Cal. proposed model Cal. conventional model RAO of motion Surge (m/m) Heave (m/m) Pitch (rad/m) Tension (N/m) 0 10 20 30 RAO of tension 0 0.05 0.1 0.15 0.2 Exp. Cal. proposed model Cal. conventional model 0.05 0.1 0.15 0.2 Surge (m) Velocity of current (m/s)

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A study on dynamic response of a semi-submersible floating wind turbine considering combined wave and current loads

Yuliang Liu, Takeshi IshiharaE-mail: [email protected]

Department of Civil Engineering, School of Engineering, The University of Tokyo

The current loads on floating structures and mooringlines are known to be essential and are recommended tobe included in the design as required by internationalstandards. In modeling hydrodynamic loads, the dragforce in the Morison’s equation is widely used to accountfor the viscous effect. Many experiments showed that thedrag coefficient ( 𝐶 ) for a circular cylinder in theoscillating flow is different from that in a steady flow. Itis crucial to select appropriate drag coefficients for theprediction of hydrodynamic loads on floating structuresand mooring lines. Liu and Ishihara [1] proposed amethod to determine the hydrodynamic coefficients of aFOWT based on the forced oscillation tests. However, thismethod was validated by the wave-only water tank tests,and its performance in the combined wave and currentcondition was not examined.

In this study, the responses of a FOWT in the combinedwave and current condition is investigated using a 1:50scale semi-submersible model, which was used in theFukushima FORWARD project. Firstly, a water tank testis carried out to investigate the influence of current on theresponses of the FOWT. A hydrodynamic force model isthen proposed to predict drag force in the combined waveand current condition. Finally, the proposed model isvalidated by the water tank tests for several load cases.

Introduction

The motions and mooring tensions of a 1:50 scalesemisubmersible FOWT for the Fukushima FORWARDproject are investigated by the water tank tests. The modelis positioned by 4 catenary mooring lines of 10.3 manchored on the bottom of the water tank at the depth of2.5 m as shown in Fig.1. The origin of coordinate locatesat the centerline of center column of the floater on thewater surface and the reference point of motions isdefined at the gravity center of the floater . Both wave andcurrent are generated from the left side. The currentvelocity is measured at the location 7.3m away from thefloater.

(a) Overview of 1:50 scale model of the platform

(b) Arrangement of the mooring linesFigure 1 Configuration of the water tank test

Water tank tests

Drag coefficient 𝑪𝒅 for a circular cylinder

Fig. 2 shows the drag coefficient 𝐶 of a circular cylinder insteady and oscillatory flows in the water tunnel and forcedoscillation tests. It changes with the increase of Reynolds numberand shows different values in the steady and oscillatory flows.

Figure 2 𝐶 of a circular cylinder in the steady and oscillatory flows

A combined hydrodynamic force model

In this study, the 𝐶 obtained from the forced oscillation test isassumed to be appropriate for predicting the floater motions inthe wave only case.

Since 𝐶 of a cylinder in the oscillating flow is different fromthat in the steady flow, a combined hydrodynamic force model isproposed to calculate the drag force contributed from the waveand current based on the Morison’s equation as:

𝐹 =1

2𝜌𝐴𝐶 𝑣 + 𝑣 𝑣 + 𝑣 +

1

2𝜌𝐴 𝐶 − 𝐶 𝑣 𝑣

where 𝐶 is the drag coefficient of cylinder obtained from theforced oscillation test and is a function of KC number, frequencyand interaction effect between the cylinders [1]. 𝐶 means thedrag coefficient of the cylinder measured in the steady flow andis a function of Reynolds number. 𝑣 and 𝑣 denote the currentvelocity and the relative velocity without the current component,respectively. In the wave-only and current-only cases, the dragforces by the proposed formula are the same as those by theconventional Morison’s equation. In the combined wave andcurrent condition, the current-induced forces are calculated using𝐶 from the steady flow, while the wave and motion inducedforces are predicted using 𝐶 from the forced oscillation test.

Hydrodynamic force model

(a) Mean surge (b) RAO in the wave onlyin the current only case case (H=0.06m, T=2.5s)

Figure 3 Comparison of predicted responses by the proposed and conventional models in the wave-only and

current-only cases

Combined wave and current condition

Fig. 4 presents the predicted mean and dynamicresponses by the two models in the combined current andwave case. The conventional model overestimates the meansurge, which is consistent with the conclusion in thecurrent-only case. The predicted RAO of mooring tensionis overestimated due to the overestimation of the meansurge and the predicted RAO of pitch is underestimated bythe conventional model. The predicted responses by theproposed model match well with the experimental data.

(a) Mean response (b) RAOsFigure 4 Comparison of predicted responses by the

proposed and conventional models in the wave and current case (H=0.06m, T=2.5s, v=0.2m/s)

Validation

In this study, a combined hydrodynamic force model isproposed to estimate the drag force on the floating platformin the combined wave and current condition.

1. A combined hydrodynamic force model to predict thedrag force of the floater is proposed to consider thedifference of drag coefficients for a cylinder in the waveonly and current only conditions.

2. The predicted mean and dynamic responses of floatermotion and mooring tension by the proposed modelshow good agreement with the experimental data, whilethose by the conventional model are overestimated orunderestimated when the current is existing.

This research is carried out as a part of the Fukushimafloating offshore wind farm demonstration project fundedby the Ministry of Economy, Trade and Industry.

Conclusion

[1] Liu, Y., Ishihara, T. , 2019. Prediction of dynamicresponse of semi-submersible floating offshore windturbines by a novel hydrodynamic coefficient model.Journal of Physics: Conference Series, 1356, 12035

Reference

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The proposed model is validated through a comparisonbetween predicted and measured motions of the platform andtensions of the mooring lines in the current-only, wave-only andcombined wave and current conditions. The result by theconventional model using 𝐶 by the forced oscillation tests isalso investigated.

Current only and wave only condition

The simulations are conducted using Orcaflex. Fig.3 shows thecomparison of predicted responses by the proposed andconventional models. In the current-only case as shown in Fig.3(a), the conventional model overestimates the surge motions dueto the large value of 𝐶 from the forced oscillation tests, whilethe predicted responses by the proposed model show goodagreement with the experiment. In the wave-only case, bothmodels predict RAOs well as shown in Fig.3 (b) since the same𝐶 obtained in the oscillatory flow is applied in the two models.

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