Experimental uncertainty of a physical model of a tanker moored to a terminal in a port

This paper presents the uncertainty modelling of experimental results for a physical model of a tanker moored to a terminal inside a port. The physical model was built for an oil terminal at the port of Leixões in Portugal. The model incorporates the new modified port layout, as well as a future 300 m extension of the port outer north breakwater to enhance operational conditions. The physical model tests were performed on a scale of 1:80 in the Portuguese Civil Engineering Laboratory (LNEC). A generic mooring system of four mooring lines and two fenders is simulated using a nonlinear spring system. Decay tests are carried out to evaluate the natural periods of the moored model. Then, tests are carried out for the moored model in waves. The major aim of the experimental study is to obtain novel results for the wave elevation and direction at various locations inside the port, the ship motions at six degrees of freedom, and loads on mooring lines and fenders including the modified port layout. As the physical model measurements are subjected to different types of uncertainties, a systematic uncertainty analysis is carried out here, following ITTC guidelines and recommendations, to quantify all possible sources of uncertainties. The results are discussed, and several conclusions are reached. Based on the experimental results, the presented physical model study may replicate the results for waves and motions with uncertainties less than 9% of the significant amplitudes. The assessment of the applied nonlinear spring model reveals load predictions on the moorings, with uncertainties less than 4% of the maximum mooring loads.     

Numerical modelling of hydrodynamic responses of Ocean Farm 1 in waves and current and validation against model test measurements

With the continuous growing of the aquaculture industry and increasingly limited fish farming sites at close to shore areas both in Norway and worldwide, there is a need to develop fish farms suitable for aquaculture production in typical offshore environments. For this purpose, SALMAR has developed and deployed the Ocean Farm 1 facility for offshore fish farming.The main purpose of this paper is to develop a reliable numerical model and investigate the motion responses of the Ocean Farm 1 structure in waves and current. The established numerical model consists of the Ocean Farm 1's frame structure (with rigidly-connected circular column components), the net and the mooring system. The hydrodynamic external loads and coefficients of the frame structure are obtained by using potential flow theory. The quadratic drag load on the individual circular columns of the frame structure is formulated by a given drag coefficient. The loads on the net are formulated by using the screen model, where the Reynold number dependent lift and drag forces are formulated as a function of the solidity ratio Sn of the net, relative inflow angle and velocity. The hydrodynamic loads on the mooring lines are formulated using the Morison's equation and the structural responses of the mooring lines are obtained using a nonlinear FE model.With the developed numerical model, time domain simulations are performed. The simulation results are firstly validated against measured data from the decay tests, current tests, and regular wave tests. After the validation, numerical simulations are performed in different irregular wave and current combined weather conditions and the obtained motion response of Ocean Farm 1 are discussed and compared with available measurement data.     

Fatigue analysis of water intake risers: Hydrodynamic damping effect and a hybrid frequency-time domain method

The fatigue performance is key to the design of water intake risers (WIRs), which is a novel concept used to convey cooling water for liquefaction of natural gas at sea. To estimate the fatigue life, it is crucial to accurately predict the response amplitude of the WIRs, which is dominated by hydrodynamic damping. In operational conditions, the motion amplitudes of WIRs are usually smaller than their diameter, and thus leading to a flow regime of KC < 5. It is found in this flow regime; the hydrodynamic damping largely depends on the motion magnitude of the risers. To consider this coupling effect, a hybrid frequency-time domain fatigue analysis method is proposed, where a nonlinear stress transfer function is adopted. The hybrid method accounts for the coupling effect between the hydrodynamic damping and the structural motion. Significantly reducing the computational cost, this method provides results as accurate as that from a time domain analysis based on the relative velocity model with a constant drag coefficient. Furthermore, recommendations for further simplification of the fatigue analysis recognizing the coupling effect are given.     

Refined parameter and uncertainty estimation when both variables are subject to error. Case study: estimation of Si consumption and regeneration rates in a marine environment

The problem of estimating parameters and their uncertainty from experimental measurements in marine ecosystems is a common task and often necessitates solving nonlinear equations. If the measurements are subject to individually varying errors (i.e., heteroscedastic data), the parameters are often estimated using a Weighted Least Squares (WLS) method. For estimating the parameter uncertainties, a linearized expression for the covariance matrix exists. Yet, both methods assume that the errors on the independent variable, also called “input”, is negligible, which is often not true. For instance, in order to determine uptake and regeneration rates of silicic acid by phytoplankton, concentration and isotopic abundance measurements are performed at the beginning (input) and at the end (output) of an incubation experiment. Here, the so-called input and output are measurements of the same quantities, i.e., determined in exactly the same way, only differing by the time at which the measurements were performed. Clearly, there is no reason to assume that the input measurements are subject to less error than the output measurements. We propose a refinement of the two abovementioned estimation methods which enlarges their applicability to cases where input noise is not negligible. The refined methods are evaluated on the uptake and regeneration processes of silicic acid and compared to the original procedures using Monte-Carlo simulations. The results reveal a smaller bias for the refined WLS estimator compared with the original one. An additional advantage of using the refined WLS cost function is that its residual value can be interpreted as a sample from a χ² distribution. This property is especially useful because it enables an internal quality control of the results. In addition, the parameter uncertainty estimation is significantly improved. By neglecting the effect of the input noise, a (potentially) important origin of the parameter variation is simply ignored. Therefore, without the refinement, the parameter uncertainties are systematically underestimated. Using the refined method, this systematic error disappears and on the whole, the parameter standard deviations are accurately estimated.     

基于随机Melnikov方法的甲板上浪船舶混沌运动研究

应用随机Melnikov方法和庞加莱截面研究甲板上浪时船舶的混沌运动。考虑甲板上浪对船舶静稳性的影响,建立随机横浪中船舶横摇运动方程。由随机Melnikov过程结合均方准则确定船舶产生混沌运动的参数域,计算不同参数域中船舶横摇响应的庞加莱截面和时间历程。结果表明,增加船舶阻尼将抑制混沌运动的发生。甲板上浪时船舶横摇响应的庞加莱截面上有两个吸引域,船舶运动过程有两个横摇中心。在非混沌参数域中,船舶只围绕其中的一个横摇中心运动;在混沌参数域中,发生由一个横摇中心到另一个横摇中心的随机跳跃。     

Measurements of hydrodynamic forces, surface pressure, and wake for obliquely towed tanker model and uncertainty analysis for CFD validation

This article presents hydrodynamic forces and moments, surface pressures, estimated side force distributions, and wakes under oblique towing conditions for a practical tanker model (model KVLCC2M), which was designed by the Korea Research Institute of Ships and Ocean Engineering (KRISO). Ship offset data is readily available and can be obtained from the Internet. The model ship has no appendages and no rudder. Trim and sinkage were adjusted to zero in the static condition and the model ship was constrained against any motion. Although the drift angle β was primarily set to 0°, 6°, and 12°, other settings were used in some experiments. All experimental results were processed using uncertainty analysis. The uncertainty analyzing method follows the ANSI/ASME Performance Test Code (PTC19.1-1985) and the AIAA Standard S-071-1995. Only a few error components were considered here and they were empirically chosen because they had a heavy weighting when used in the uncertainty calculation. The results of these towing tank experiments will contribute to the development of computational fluid dynamics (CFD) research in ship hydrodynamics.     

Hydrodynamic damping of a circular cylinder at low KC: Experiments and an associated model

This paper investigates the hydrodynamic damping of a smooth circular cylinder undergoing forced oscillations at Keulegan-Carpenter (KC) numbers smaller than 5 and Reynolds (Re) numbers from 10³–10⁵ with and without background steady currents. A series of experiments are conducted with a circular cylinder oscillating in still water, in-line currents and cross currents. The measured drag coefficients of the smooth cylinder in the still water condition match with the well-published results and the theoretical solution of Stokes and Wang at very small KC numbers. The hydrodynamic damping increases with the in-line steady current whereas it remains almost constant at small transverse velocities and increases notably when the latter becomes large. To predict the hydrodynamic damping in in-line steady currents, the performance of the Morison equation based on relative velocity and independent velocity is explored, respectively. The latter model, by separating the drag into two independent parts, leads to a better fit of the drag force than the former, which is not surprising. However, the former is still a preferable option for engineering design due to its simplicity. The experimental data suggest that the existing design guidelines such as ISO-19902 or DNVGL-RP-C205 should be used with caution for KC < 5.     

浅水湖泊平面二维水质模型研究

磷氮元素在水体中迁移对湖泊富营养化研究具有重要性。采用有限元伽辽金加权余量法建立了简单的二维水质模型,并计算了在风场作用下的苏州市澄湖丰水期和枯水期的氮磷的分布以及输移。计算中引入了可由实测资料率定的可为正负的综合衰减参数,综合考虑了氮磷元素的沉降速率和释放速率,这样减少了水质多参数难确定的困难。计算的结果表明,流态与实际情况吻合较好,氮磷元素的浓度计算值与实测值相差不大。     

PMM tests in a circulating water channel and nonlinear analysis

As a result of frequent marine disasters leading to the loss of human life and pollution of vast areas of the ocean, ship manoeuvrability has become a very important characteristic of ship design. Among several recent experimental techniques to determine ship manoeuvrability, the most popular is captive model testing using a planar motion mechanism (PMM). This article describes some tests, analyses, and results of PMM tests in a circulating water channel (CWC) using a model of a training ship. The hydrodynamic forces and moments acting on a model of the training ship Shioji Maru in pure yawing motion were measured, and hydrodynamic derivatives were obtained using two different methods of analysis: singular value decomposition (a least-squares fit method) and Fourier analysis. Derivatives obtained from the tests were used to simulate the turning trajectory of the actual ship, and these were compared with the results of sea trials. The results indicate that both methods of analysis yield fairly similar derivatives. The simulation results were also found to be a close match with the trial results. Received: February 7, 2002 / Accepted: May 14, 2002 Address correspondence to: K. Shoji (shoji@ipc.tosho-u.ac.jp)     

Assessment of uncertainty in the CFD simulation of the wave-induced loads on a vertical cylinder

The paper addresses different uncertainty analysis methods commonly used for uncertainty quantification in Computational Fluid Dynamics (CFD) studies and compares a constant Courant–Friedrichs–Lewy (CFL) number based approach for uncertainty estimation to the ITTC recommended grid and time-independent procedures. Four different uncertainty estimation procedures are presented and discussed. To compare their performance and better understand CFD related uncertainty quantification in wave load simulations on offshore structures, the methods are applied to a case study of the wave loads on a fixed vertical cylinder. The numerical or CFD wave tank is generated using the open-source CFD toolkit OpenFOAM. Uncertainty is assessed for the case study using four different uncertainty estimation procedures for verification and later, validation is attempted by comparing the CFD results with experiments. The study concludes that a constant CFL number based uncertainty study provides more stable results and is better suited for uncertainty estimation in CFD than the ITTC recommended individual grid and time step uncertainty study.     

Prediction method of hydrodynamic forces acting on the hull of a blunt-body ship in the even keel condition

The mathematical modeling group (MMG) model is well known and is widely used in the field of ship maneuverability. However, the MMG model can be applied only after determination of the hydrodynamic coefficients either from comprehensive captive model tests or from general empirical data. Around the cruising speed, when a ship's drift angle is relatively small, several methods have been developed to predict hydrodynamic coefficients from the ship's principal particulars, e.g., Kijima's method. Kijima's method is efficient in predicting the ship's maneuverability at the initial design stage and is even able to assess the effect of changes in stern design. Similarly, for the low speed range when a ship's drift angle is relatively large, several methods for predicting the ship's hydrodynamic coefficients have been proposed, based on captive model tests, such as those by Kose, Kobayashi, and Yumuro. However, most of the methods developed for low speeds cannot be applied to general ship types without additional experiments being performed. In contrast, Karasuno's method uses theoretical and empirical approaches to predict the hydrodynamic forces, even for large drift motions. Although Karasuno's model utilizes the ship's principal particulars and is applicable to a general vessel, it has not been widely used. This is because the form of Karasuno's model is relatively complicated and its accuracy around the cruising speed is less than that for other methods that have been specifically developed for the cruising speed range. A practical method for predicting hydrodynamic forces for the entire operating speed range of blunt-body ships is proposed in this article. It is based on the MMG model and predicts hydrodynamic coefficients based on a ship's principal particulars. A regression model for the proposed method has also been proposed by analyzing 21 different blunt-body ships. Finally, simulations of a very large 4-m crude carrier (VLCC) model using the proposed method were carried out and the results compared with free-running experiments (both at the cruising speed and at low speeds) to validate the efficacy of the model.     

Three-dimensional numerical analysis of shipping water onto a moving ship using a particle method

The objective of this study was to develop a numerical analysis method based on the moving particle semi-implicit method for simulating shipping water on a moving ship. Towing tests of a very large crude carrier were numerically analyzed for three typical wavelengths. The ship was forced to move in order to express previously measured ship oscillations, and the calculated fluid behavior and the impact pressure on the deck were compared with the experimental results.     

混合湍流模型的参数优化与分析

在以全流场N-S方程为研究对象的空化流动数值计算中,湍流模型在很大程度上影响了对空化流动的精确预测。为了进一步完善针对非定常空化流动数值计算构建的基于密度分域的混合湍流模型（FBDCM）,利用代理模型方法对FBDCM模型参数的整体敏感度进行了分析,评价了相关经验系数的扰动对空化流场及水动力特性预测精确度的影响,建议了针对非定常空化流动计算的模型参数的具体取值。结果表明,经验系数C2通过调节FBDCM中FBM模型和DCM模型的影响比重,成为对模型预测精度影响程度最大的因素;通过代理模型优化分析确定经验系数的混合湍流模型,能更好地调整流场内的湍流粘性,精确计算了反向射流区域大尺度涡团的流动,与实验结果更为接近。     

海上自升式平台动力分析方法研究(英文)

A jack-up platform,with its particular structure,showed obvious dynamic characteristics under complex environmental loads in extreme conditions.In this paper,taking a simplified 3-D finite element dynamic model in extreme storm conditions as research object,a transient dynamic analysis method was proposed,which was under both regular and irregular wave loads.The steps of dynamic analysis under extreme conditions were illustrated with an applied case,and the dynamic amplification factor(DAF) was calculated for each response parameter of base shear,overturning moment and hull sway.Finally,the structural response results of dynamic and static were compared and analyzed.The results indicated that the static strength analysis of the Jack-up Platforms was not enough under the dynamic loads including wave and current,further dynamic response analysis considering both computational efficiency and accuracy was necessary.     

基于显式有限元方法的二维楔形刚体入水砰击载荷并行计算预报

局部砰击载荷是在船舶首部结构设计时重点关注的问题。文章基于显式有限元方法,选用任意拉格朗日—欧拉算法(ALE),针对某30°二维楔形刚体入水砰击问题,开展了数值预报工作。针对模型网格密度开展了收敛性分析。数值预报的加速度、砰击压力等时域结果与已公开发表的模型实验的结果进行了比较,吻合非常好。鉴于在微机上数值计算时间比较长的问题,文中探讨了并行计算技术在模拟中的应用。     

Stochastic wave spectra estimation (SWSE) based on response surface methodology considering uncertainty in transfer functions of a ship

In this paper, a new wave spectra estimation method is proposed in which the frequency domain wave estimation method (FDWE) is extended into a probabilistic analytical framework in order to estimate the encountered sea states involving uncertainty in transfer functions of a ship. The proposed method, named the Stochastic Wave Spectra Estimation (SWSE), makes use of an Hermite polynomial chaos expansion (PCE) to represent the uncertainty in the transfer functions and the response surfaces. The method involves a mathematical formulation where an extension of the deterministic FDWE concept to the space of random variables is made. The proposed method can accurately and easily estimate the encountered wave spectra based on ship response measurements accounting for uncertainty in the transfer functions. In this paper, numerical and experimental investigations of the proposed SWSE are made, where the uncertainties in the transfer functions of heave and pitch motions of a containership are taken into account. The validity of the SWSE is demonstrated by comparison to results of uncertainty analyses through the Monte-Carlo simulations (MCS).     

Using a random displacement model to simulate turbulent particle motion in a baroclinic frontal zone: A new implementation scheme and model performance tests

Numerical artifacts can limit accurate simulation of turbulent particle motion when Lagrangian particle-tracking models are implemented in hydrodynamic models with stratified conditions like fronts. Yet, modeling of individual particle motion in frontal regions is critical for understanding sediment dynamics as well as the transport and retention of planktonic organisms. The objective of this research was to develop a numerical technique to accurately simulate turbulent particle motions in a particle-tracking model embedded within a hydrodynamic model of a frontal zone. A new interpolation scheme, the ‘water column profile’ scheme, was developed and used to implement a random displacement model for turbulent particle motions. A new interpolation scheme was necessary because linear interpolation schemes caused artificial aggregation of particles where abrupt changes in vertical diffusivity occurred. The new ‘water column profile’ scheme was used to fit a continuous function (a tension spline) to a smoothed profile of vertical diffusivities at the x–y particle location. The new implementation scheme was checked for artifacts and compared with a standard random walk model using (1) Well Mixed Condition tests, and (2) dye-release experiments. The Well Mixed Condition tests confirmed that the use of the ‘water column profile’ interpolation scheme for implementing the random displacement model significantly reduced numerical artifacts. In dye-release experiments, high concentrations of Eulerian tracer and Lagrangian particles were released at the same location up-estuary of the salt front and tracked for 4 days. After small differences in initial dispersal rates, tracer and particle distributions remained highly correlated (r = 0.84 to 0.99) when a random displacement model was implemented in the particle-tracking model. In contrast, correlation coefficients were substantially lower (r = 0.07 to 0.58) when a random walk model was implemented. In general, model performance tests indicated that the ‘water column interpolation’ scheme was an effective technique for implementing a random displacement model within a hydrodynamic model, and both could be used to accurately simulate diffusion in a highly baroclinic frontal region. The new implementation scheme has the potential to be a useful tool for investigating the influence of hydrodynamic variability on the transport of sediment particles and planktonic organisms in frontal zones.     

不同湍流模型在螺旋桨敞水性能预报中的应用分析

为研究不同湍流模型在螺旋桨敞水性能预报中适用性,本文采用计算流体动力学(CFD)软件,结合雷诺平均纳威斯托克斯方程(RANS),应用Realizable k-ε模型、SST k-ω模型、雷诺应力方程模型(RSM)3种不同湍流模型对粘性流场中某集装箱船螺旋桨水动力性能进行计算与分析。比较3种不同湍流模型数值模拟结果与敞水试验结果,以分析不同湍流模型数值模拟结果在不同进速系数的特点。结果表明,3种湍流模型均适用于螺旋桨水动力性能计算,仅在不同进速系数区间存在不同特点。