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Slow Drift Eddy Making Damping of a Ship
Abstract
This paper discusses how to obtain eddymaking damping coefficients for slow drift oscillations of a moored ship in irregular waves. By deriving a simple expression for the standard deviations of the motions it is shown that it is not necessary to have great accuracy in predicting the damping coefficients. A single vortex method has been derived and used together with experimental U-tube results to discuss the hull parameter dependence of eddymaking damping. The single vortex method is shown to agree well with experimental results for midship sections without bilge keels. The effect of a bilge keel is strong at small KC-numbers and cannot be predicted theoretically by a simple single vortex model.
... This viscous damping contribution has been the subject of many investigations, beginning with that of Froude [12]. Important contributions in more recent times include the work of [22], who demonstrated that the eddy-making damping is nearly independent of Froude number, and [6,11], who applied a vortex tracking method to the problem. For the conventional application, the bilge keel is subject to an oscillating flow induced by the roll motion of the ship. ...
... For the conventional application, the bilge keel is subject to an oscillating flow induced by the roll motion of the ship. This unsteady process is normally investigated in U-shaped water tunnels, as in [11,38], among others, or with an oscillating cylinder as in [45]. ...
... It is understood that the bilge keel should act to promote flow separation along the leading bilge, contributing to the non-linear sideforce term. In Fig. 12 for the non-linear sideforce coefficient, the response in the neighborhood of the nominal bilge keel height for the experiment (H3)-corresponding to h∕r b =0.375-is nearly linear with keel height, a result also reported by [11], whereas the behaviour at small values of h∕r b appears to approach the bare hull value asymptotically. Bilge keel H1 ( h∕r b =0.11) is a geometric scaling for a representative full-scale bilge keel (h = 0.5 m at full scale). ...
Wind propulsion for commercial ships has been identified as a key component in the energy transition for the maritime industry. The sailing hybrid ship will operate with leeway (drift) angles to produce a lateral force known as sideforce, for steady operation under sail. In this paper, experimental results for the sailing performance of ships fitted with bilge keel appendages are presented. Systematic variations in appendage height, length, and position were tested, including several special cases (multiple bilge keels). The appendage typology is shown to mitigate the strong ‘destabilizing’ yaw moment that is characteristic of wind-assisted commercial vessels and to promote the non-linear sideforce component. The working principal for bilge keels—promotion of flow separation—can be employed to specify the separation location for components of the vessel vortex wake to improve the sailing performance of the ship.
... This viscous damping contribution has been the subject of many 90 investigations, beginning with that of Froude in 1865 [32]. Important contributions in more recent times include the work of Ikeda 91 [33], who demonstrated that the eddy-making damping is nearly independent of Froude number, and Braathaen [34] and Faltinsen 92 [35], who applied a vortex tracking method to the problem. For the conventional application, the bilge keel is subject to an 93 oscillating flow induced by the roll motion of the ship. ...
... For the conventional application, the bilge keel is subject to an 93 oscillating flow induced by the roll motion of the ship. This unsteady process is normally investigated in U-shaped water tunnels, 94 as in Sarpkaya [36] and Faltinsen [35], among others, or with an oscillating cylinder as in van 't Veer [37]. The present study for 95 bilge keels in steady (oblique) flow corresponds to a special case of the unsteady process considered by previous researchers. ...
... It is understood that the bilge keel should 409 act to promote flow separation along the leading bilge, contributing to the non-linear sideforce term. In Figure 13 for the non-410 linear sideforce coefficient, the response in the neighborhood of the nominal bilge keel height for the experiment (H3)-411 corresponding to ℎ/ =0.375-is nearly linear with keel height, a result also reported by Faltinsen [35], whereas the behaviour at 412 small values of ℎ/ apears to approach the bare hull value asymptotically. Bilge keel H1 (ℎ/ =0.11) is a geometric scaling for a 413 representative full-scale bilge keel (ℎ=0.5 m at full scale). ...
... For sections with bilge keels (sections 7-13), the above introduced procedure cannot be applied, as the drag coefficient depends strongly on the breadth of the bilge keels. Instead, we estimate the drag coefficient based on the experimental data from Faltinsen and Sortland (1987). In these experiments, B/(2D) = 1.35, r/D = 0.22 and three bilgekeel breadth-to-draft ratio b/D = 0, 0.03 and 0.06 were examined. ...
... The drag coefficient is expected to be mainly determined by the parameter b/D, so its value can be obtained through interpolating the experimental data in terms of b/D, see Figure 5.16. There are differences of B/(2D) and r/D between the well-boat sections with bilge keels and the sections studied experimentally and Faltinsen and Sortland (1987). Solid curve: interpolated value for the cross-section of the well boat equipped with bilge keels. ...
... We deduct the in-line drag coefficient associated with the frictional force in phase with the ambient velocity and get C D = 2.92. The fact that the width to height ratio 8/6 for the pontoons is higher than for a square section is likely to cause a higher drag coefficient [6]. They used a single vortex method which suggests a C D -value of 3.10 for the rectangular cross-section of the pontoons at KC= 1.5. ...
... Furthermore, we must notice the effect of different width-to-height ratios of the cross-sections at one pillar radius from the end of the pontoons. This has a small effect according to [6]. Then comes 3D effects which is pronounced at the ends. ...
Motion predictions of floating bodies in extreme waves represents a challenging problem in naval hydrodynamics. The solution of the seakeeping problem involves the study of complex non-linear wave-body interactions that require large computational costs. For this reason, over the years many seakeeping models have been formulated in order to predict ship motions using simplified flow theories, usually based on potential flow theories. Neglecting viscous effects in the wave-induced forces might largely underestimate the energy dissipated by the system. This problem is particularly relevant for unconventional floating bodies at resonance. In these operating conditions the linear assumption is no longer valid and conventional Boundary Element Methods, based on potential flow, might predict unrealistic large responses if not corrected with empirical viscous damping coefficients. The application considered in this study is an offshore platform to be operated in a wind farm requiring operability even in extreme meteorological conditions. In this paper, we compare heave and pitch Response Amplitude Operators, predicted for an offshore platform using three different seakeeping models of increasing complexity; namely a frequency-domain BEM, a partly nonlinear time domain BEM and a non-linear fully viscous model based on the solution of the Unsteady Reynolds Averaged Navier-Stokes equations (URANS). Results are critically compared in terms of accuracy, applicability and computational costs.
... The mathematical model of the Dynasim and validation results are presented in Refs. [9][10][11][12][13]. ...
... The simulator is able to import the hydrodynamic coefficients from different commercial codes, such as Wamit, Wadam, Hydrostar, or AQWA. A detailed explanation on how wave forces and motions are computed in the Dynasim simulator can be found in Ref. [12,13]. ...
In drilling vessels, the dynamic positioning (DP) system has great importance for the operation, since it ensures the station keeping ability for the drilling operation. However, an emergency situation involves ungoverned drift due to problems associated with the DP system failures, such as thrusters, generators, powerbus or control system. During this situation, the vessel drift is subjected to the influence of environmental conditions and the drift can lead to collisions with floating obstacles or submerged systems, wellhead emergency disconnection, damage to equipment and potentially causing major environmental disasters. It is then necessary to define a safety region for the drilling ship operation and to determine the limiting operation offset that the drilling vessel can disconnect from the wellhead without damage to any equipment. This limit offset is obtained through a riser analysis and drift-off study, important inputs for the WSOG (Well Specific Operating Guidelines). A validated time domain simulator is required, able to predict the vessel drift trajectory after the DP failure under several environmental conditions. The aim of this work is to present a large set of model and full scale drift tests and the validation of a time-domain numerical simulator (Dynasim), based on the main parameters of the drift tests: drift distance, heading variation and trajectory. The comparisons between the numerical simulation results with full and model scale data demonstrated the accuracy of the numerical model, confirming that the simulator is a reliable tool to predict the motion of a drilling vessel after a blackout.
... For sections with bilge keels (sections 7-13), the above introduced procedure cannot be applied, as the drag coefficient depends strongly on the breadth of the bilge keels. Instead, we estimate the drag coefficient based on the experimental data from Faltinsen and Sortland (1987). In these experiments, B/(2D) = 1.35, r/D = 0.22 and three bilge-keel breadth-to-draft ratio b/D = 0, 0.03 and 0.06 were examined. ...
... The effect of bilge keels on the drag coefficient C D at small KC numbers. Symbols: experimental data from Faltinsen and Sortland (1987). Solid curve: interpolated value for the cross-section of the well boat equipped with bilge keels. ...
... Some smoothing of the kernels representing the vortices has been applied in this respect. Continuous representation of the free shear layer used e.g. in [9,10] and more recently in [11,12] has the advantage relative to discrete methods that the actual vortex shedding is well defined, and the fine structures of the free shear layer is represented in a more rigorous way. The disadvantage, however, is the requirement that the whole free shear layer be connected at all times leading to increasingly complicated structures during time evolution in unsteady flow. ...
... Analytically-based approaches were adopted e.g. in [10,13] where local solutions of the vortex shedding matched to outer solutions provided means of investigating slow drift and roll damping. ...
Near resonance the piston mode amplitude in semi-entrained volumes of fluid such as in moonpools or in between a ship and a terminal may become large relative to the level of excitation. Linear theory is known to over-predict the fluid response in these types of systems significantly, suffering from the lack of damping whose only manifestation is radiated waves. In reality, however, viscous effects may act as damping and nonlinear effects associated with the free surface conditions may cause transfer of energy between the different modes. In the present work, which is within the framework of potential theory, a fully nonlinear numerical wavetank based on Green’s 2nd identity coupled with an inviscid vortex tracking method is applied to the moonpool problem. The paper presents a methodology for perpetual simplification of the free shear layer as the system undergoes near sinusoidal motion in order to reach steady state. This is practically impossible without such simplifications due to the otherwise exceedingly complex wake structures evolving only after the first one or two periods. Also the in- and out-flow of the boundary layers are modelled. The results are compared to experiments. In the investigated cases models of rectangular shape with sharp corners provide well-defined separation points, and such sharp corners are in practice introduced e.g. by bilge keels. It is found that: (1) The damping effect associated with the nonlinear free surface conditions are of minor importance, (2) the effect of the in- and out-flow of the boundary layer is negligible to all practical purposes, whereas (3) the flow separation explains the major part of the discrepancy between the measured response and that estimated by linear theory.
... The different dc-motor control strategies are obtained by choosing and according to Table II in Appendix A. Experimental verifications of the one-state and two-state models are found in Whitcomb and Yoerger [28]. A more general model is the three-state propeller shaft speed model of Blanke et al. [3]: (11) where damping in surge is modeled as the sum of linear laminar skin friction (see [8]) and nonlinear quadratic drag (see [7]). Similarly, linear damping is included in the axial flow model since quadratic damping alone would give an unrealistic response at low speeds (zero quadratic damping at zero speed). ...
... where and (see [3]). The vessel dynamics in surge (28) is modeled according to Fossen [9], where is the mass of the vessel including hydrodynamic added mass, is damping due to linear skin friction (see [8]) and quadratic drag (see [15]), and is the thrust deduction number (typically 0.05-0.2) due to propeller-hull interactions. Notice that linear damping is added in addition to the quadratic term . ...
Accurate propeller shaft speed controllers can be designed by using nonlinear control theory and feedback from the axial water velocity in the propeller disc. In this paper, an output feedback controller is derived, reconstructing the axial flow velocity from vehicle speed measurements, using a three-state model of propeller shaft speed, forward (surge) speed of the vehicle, and the axial flow velocity. Lyapunov stability theory is used to prove that a nonlinear observer combined with an output feedback integral controller provide exponential stability. The output feedback controller compensates for variations in thrust due to time variations in advance speed. This is a major problem when applying conventional vehicle-propeller control systems. The proposed controller is simulated for an underwater vehicle equipped with a single propeller. The simulations demonstrate that the axial water velocity can be estimated with good accuracy. In addition, the output feedback integral controller ...
... For low frequency motion of sea surface vehicles linear skin friction due to laminar boundary theory is essential [36]. For high frequency motion in addition to linear skin friction, a nonlinear or quadratic skin friction due to turbulent boundary layer will exists. ...
In this thesis, control and guidance algorithms for unmanned sea surface vehicles are
studied. To design control algorithms of different complexity, first a mathematical model for an unmanned sea surface vehicle is derived. The dynamical and kinematical equations for a sea surface vehicle are obtained, and they are adapted to real life conditions with necessary additions and simplifications. The forces and torques effecting on the vehicle are investigated in detail. Control algorithms for under-actuated six degrees-of-freedom model are designed. PID and LQR controllers are implemented to attain desired surge speed and yaw position. The autopilots are designed and their performances are compared. Based on the autopilots, a guidance algorithm is implemented to achieve desired motions of the
vehicle. An obstacle avoidance algorithm is proposed for safe motion among the obstacles. A next-point generation algorithm is designed to direct the vehicle to next possible waypoint if one ahead is missed. The effects of disturbances on the motion of the vehicle are studied thoroughly on simulation results. PID controller for unmanned sea surface vehicle is implemented on ArduPilot Mega v1.4 controlling Traxxas Spartan model boat. The performance of the controller is validated. Simulations and experimental results are provided.
... where denotes the linear damping due to potential damping and linear skin friction (Faltinsen and Sortland, 1987), whereas the quadratic damping is given as ( ) based on cross-flow drag principle (Faltinsen, 1990). This gives: ...
This paper focuses on obstacle avoidance for the environmentally-driven unmanned surface vehicles (USVs) in large-scale and uncertain environments. A novel speed adaptive robust obstacle avoidance (SAROA) approach is proposed with the deep reinforcement learning (DRL). A feature enhanced dynamic training method for the DRL is proposed, which significantly improves the sampling efficiency and accelerates convergence. The sensory cues, the executed action and the reward feedback function are properly designed for reinforcement learning to realize robust obstacle avoidance in uncertain environment. Moreover, the obstacle perception domain and the line-of-sight (LOS) based target tracking method are proposed to enable the USVs to avoid collision as well as to follow the path in large-scale environment. In addition, regarding that the environmentally-driven USV is normally super under-actuated and its speed is uncontrollable, a speed adaptive zone is proposed to adapt the obstacle avoidance policies to various navigation speeds, which significantly improves the adaptability and robustness of the proposed obstacle avoidance strategy. Extensive obstacle avoidance tests for the environmentally-driven USV with different navigation speed are conducted, which demonstrates that the DRL based SAROA approach shows excellent practicability and robustness for the environmentally-driven USVs in large-scale and uncertain environments.
... • Traditionally a number of analytical methods have been developed in an attempt to derive the viscous damping effects, for example the single vortex method (Faltinsen and Sortland, 1987) and the matched isolated edge (Bearman et al., 1985). • For simple shapes such as cylinders or for previously studied hull geometries, values may be taken from existing literature or recommended practices (Veritas, 2010). ...
In order to economically, efficiently and reliably deploy offshore moored structures, the calculation of slow drift motions is crucial. Although there has been a great deal of research into this topic in recent years, the predicted accuracy of simulations is still poor. In parallel, the deployments of novel structures such as floating wind turbines on a diverse range of platform types and designs is increasing rapidly, necessitating the greater understanding of these motions.
The viscous damping effects are crucial to the slow drift motion predictions, but are also one of the most difficult parameters in a model to quantify. In this work, a novel experimental numerical method for calculating nonconstant drag coefficients is introduced and applied to a moored advanced spar. The method involving a combined potential flow and Morison’s equation model is used to calculate the drag coefficients and added mass from decay tests in still water, monochromatic sinusoidal waves and in current flows. An inverse KC number drag coefficient relationship was observed for both still water and wave cases. With increasing current flow velocity the KC number drag coefficient tendency decays to a constant value equal to the steady state drag coefficient. A similar inverse KC number drag coefficient relationship is shown from the full scale Fukushima FORWARD’s floating substation. Discussions on the flow behaviour and recommendations on simulation techniques are given.
... A robot dynamics model based on a combination of theory and simulation data and verification by experimental data would provide an efficient control system development platform and an alternative to the typical trialand-error control system tuning method. Fjellstad and Fossen (1994) [1,2] presented research on underwater robots' attitude and position control in six degrees of freedom using an adaptive control strategy [3]. The adaptive integral control technique was used for controlling ODIN [4]. ...
Underwater robots are to be extensively used in various submerged missions. A few research works have been conducted to investigate the nonlinear dynamical behavior of such systems in ocean flows. In this paper, dynamics modeling and parameters estimation for these complicated systems are developed for using model-based predictive control. It is begun by presenting the nonlinear equations governing the dynamics of an underwater robot in an ocean open flow. Additionally, the movement of the diving and depth motion of the robot in such cases is analyzed. A method to estimate hydrodynamic and other parameters of an underwater robot is presented and compared with experimental data. This method consists of close-to-reality simulation using a CFD subsystem of the ANSYS software. Finally, these parameters are used to design a model-based controller. Numerical simulations are carried out to evaluate the performance of the controllers. Among all the model-based controllers, nonlinear Model Predictive Control (nonlinear-MPC) with constraints will be able to follow the setpoints within less time and less control effort. The experimental data confirm the simulation results, proving the underwater robot's capability for path-following in an ocean open flow.
... Experiments by Mercier and Huijs (2005) indicate that the drag coefficient, in steady flow, increases with at least 50% due to bilge keels. On the other hand, experiments by Faltinsen and Sortland (1987) show that the effect of bilge keel decrease with increasing Keulegan-Carpenter number = , where is the amplitude of the oscillatory flow, is the period of oscillation, and is the characteristic size of the body, e.g the draft of a ship section. They tested a ship section without bilge keels and with bilge keels, for two different bilge keel dimensions. ...
The importance of the transverse viscous loads, in a modular maneuvering model, is investigated. A method to estimate steady sectional drag coefficients is first presented. A 2D+t approach, which accounts for forward-speed effects, is also presented. The time-varying drag coefficients, in the 2D+t method, are estimated with three methods: two simplified methods using results from the literature directly, and one more sophisticated method which uses time-derivatives, from time-dependent drag coefficients for hull forms in the literature, and integrates the drag coefficients along the hull. Turning circles with 25∘ and 35∘ rudder angle are simulated in calm water and regular waves for a range of wavelengths between λ∕Lpp=0.281 and 1.120, with wave steepness H∕λ=1∕40, and initial head sea. The Duisburg Test Case (DTC) is used as a test ship. The numerical simulations are compared with free-running model tests. Overall, the 2D+t method, with integrated drag coefficients, shows a better match with the experiments compared to the cross-flow approach. However, both methods capture the main trends considering tactical diameter and advance for the tested wave conditions. Furthermore, using scaled time-varying drag coefficients for a circular cylinder can be a good starting point in a 2D+t approach.
... For this reason, over the years many seakeeping models have been formulated in order to predict ship motions using simplified flow theories [10][11][12][13][14], usually based on potential flow theories solved within the linear assumption, which limits their range of applicability in cases of practical interest. Furthermore, second-order potential-flow solvers [15][16][17][18][19][20][21][22][23][24][25] represent the state-of-the-art numerical methods for wave-induced response of vessels and other large-volume marine structures. Important viscous damping effects such required in modeling the rolling of ships and slow-drift motions of moored structures are accounted for by empirical formulas. ...
Predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. It involves computing complex nonlinear wave-body interactions, hence taxing heavily computational resources. Here, we put forward a new simulation paradigm by training recurrent type neural networks (RNNs) that take as input the stochastic wave elevation at a certain sea state and output the main vessel motions, e.g. pitch, heave and roll. We first compare the performance of standard RNNs versus GRU and LSTM neural networks (NNs) and show that LSTM NNs lead to the best performance. We then examine the testing error of two representative vessels, a catamaran in sea state 1 and a battleship in sea state 8. We demonstrate that good accuracy is achieved for both cases in predicting the vessel motions for unseen wave elevations. We train the NNs with expensive CFD simulations offline , but upon training, the prediction of the vessel dynamics online can be obtained at a fraction of a second. This work is motivated by the universal approximation theorem for functionals (Chen & Chen, 1993. IEEE Trans. Neural Netw. 4 , 910–918 ( doi:10.1109/72.286886 )), and it is the first implementation of such theory to realistic engineering problems.
... These numerical methods are usually based on potential flow theories solved within the linear assumption, which limits their range of applicability and are inaccurate in severe sea states. Furthermore, second-order potential-flow solvers [7][8][9][10][11][12][13][14][15][16][17] represent the state-of-the-art numerical methods for wave-induced response of vessels and other large-volume marine structures. Nevertheless, important viscous damping effects, such as those required in modeling of rolling of ships and slow-drift motions of moored structures, are not numerically resolved and are accounted for by empirical formulas. ...
Predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. It involves computing complex nonlinear wave-body interactions, hence taxing heavily computational resources. Here, we put forward a new simulation paradigm by training recurrent type neural networks (RNNs) that take as input the stochastic wave elevation at a certain sea state and output the main vessel motions, e.g., pitch, heave and roll. We first compare the performance of standard RNNs versus GRU and LSTM neural networks (NNs) and show that LSTM NNs lead to the best performance. We then examine the testing error of two representative vessels, a catamaran in sea state 1 and a battleship in sea state 8. We demonstrate that good accuracy is achieved for both cases in predicting the vessel motions for unseen wave elevations. We train the NNs with expensive CFD simulations offline, but upon training, the prediction of the vessel dynamics online can be obtained at a fraction of a second. This work is motivated by the universal approximation theorem for functionals [1], and it is the first implementation of such theory to realistic engineering problems.
... Towards this, 6-DOF simulations are carried out on Model 2 (scaled full length model) and Model 3 (prototype model), both with bilge keel length of 0.3L. Although, the scale effects on roll decay motion for model with bilge keel are insignificant (Faltinsen, 1990;Faltinsen and Sortland, 1987), here the authors would like to present results of 0.3L long bilge keel on prototype scale. The bilge keel thickness used in model experiments was 3 mm, which, when scaled up to full scale (1:100) becomes 300 mm but the simulations in full scale were carried out for 30 mm thick bilge keel. ...
Estimation of roll damping of ships from free roll decay experiments or using appropriate semi-empirical formulae is a common practice. The total roll damping of a ship or a barge can be strongly nonlinear consisting of linear and nonlinear components; especially when bilge keel is fitted to the hull as a damping device and also when angles of roll are large. CFD simulations of nonlinear roll motion with experimental validation is gaining acceptance in the recent past.
The present work reports three dimensional simulations of roll decay of a ship model, both with and without bilge keel, with experimental validation. A good comparisons of roll damping, natural period and added mass with experiments are obtained. The use of large eddy simulation on this class of problems is explored and commented upon. Ikeda's semi-empirical method over-predicts roll damping at larger roll angles. The pressure aft of bilge keel is found to be deviating whereas the pressure in front of bilge keel showed a close resemblance with semi-empirical calculations. Effect of bilge keel thickness, degrees of freedom and scaling on roll motion and damping is found to be insignificant for a barge-like ship model chosen in this study.
... A possible cause for this difference could be a linear damping in longitudinal motion, that was not considered in the mathematical model. Faltinsen and Sortland (1987) state that this linear damping can play an important role in the longitudinal motion at low speed, caused by potential damping and linear skin friction. As a future improvement of this research, the authors are going to test the influence of this linear damping term in the longitudinal motion. ...
In drilling vessels, the dynamic positioning (DP) system has great importance for the operation, since it ensures the station keeping ability for carrying out the drilling operation. However, an emergency situation involves ungoverned drift due to problems associated with the DP system failures, such as thrusters, generators, powerbus or control system. During this emergency situation, the vessel drift is subjected to the influence of environmental conditions and the drift can lead to collisions with floating obstacles or submerged systems, wellhead emergency disconnection, damage to equipments and potentially causing major environmental disasters. Due to the possible occurrence of this emergency condition, it is necessary to define a safety region for the drilling ship operation and to determine the limiting operation offset that the drilling vessel can disconnect from the wellhead without damage to any equipment. This limit offset is obtained through a riser analysis and drift-off study, being an important input for WSOG (Well Specific Operating Guidelines). The study will provide vessel drift trajectory after the DP failure under several environmental conditions. A validated time domain simulator must be used for obtaining such data. In the present work, the Dynasim software, developed from the partnership between Petrobras and Brazilian universities, is applied. Thus, the aim of this work is to validate the Dynasim numerical model using drift data from full scale tests performed on vessels operated by Petrobras and under several environmental conditions. For the validation and calibration of the numerical model, three main parameters were compared: distance time-series, heading variation and trajectory during the drift of the vessel. The comparisons between full scale data and numerical simulation results demonstrated the accuracy of the numerical model. Therefore, the application of this tool provides a valuable contribution to the reliability of WSOG analysis, planning of the operations, allowing the determination of the drift path in relation to the wind, current and waves, and the definition of drift maps and establishing safety zones for the drilling vessel operation, minimizing the risk of collisions.
... where D υ r denotes the linear damping due to potential damping and linear skin friction [36] , while the quadratic damping is given as d( υ r ) based on cross-flow drag principle [37] . This gives: ...
Wave glider is a new wave-powered autonomous marine vehicle, which is composed of a submerged glider connected to a surface floater via a tether. Such an advanced vessel is designed to harvest energy in ocean surface waves to generate forward thrust. Equipped with solar panel and battery as well as some dedicated sensors, the wave glider is able to achieve long duration missions via sea-side control. In this paper, a 4-DOF (degree-of-freedom) mathematical model of the wave glider is established using Newton–Euler approach. The second-order wave drift force on the horizontal plane and the first order wave force on the vertical direction are considered. The hydrodynamic parameters were calculated using the potential flow theory and empirical formula. Furthermore, motion simulation of the wave glider with respect to the sensitivity analysis to some key environmental factors and the heading control ability is conducted. The simulation results are presented and discussed in detail, which provides theoretical guidance and reference for wave glider design.
... The ship resistance provides the damping in surge and it is modeled as the sum of linear laminar skin friction X u u (see [12]) and of nonlinear quadratic drag X |u|u |u| u (see [13]) ...
The aim of this work is to analyze the influence of a non-constant ship speed on the onset and development of the parametric roll resonance. A 2-DOF nonlinear surge-roll model is set up and analyzed. Perturbation methods are also applied to evaluate the influence of dynamic variations of surge velocity on the onset of parametric roll. The theoretical results are illustrated and validated using a 4-DOF hydrodynamic and control theory model.
... The scale effects are prominent when the flow pattern and flow separation points in the model and prototype scale are not similar due to switching between laminar and turbulent flow regimes. As explained in Faltinsen [21] and Faltinsen and Sortland [24], when the flow separation points are sharp edges like bilge keel or sharp corners of the barge, the scale effects are minimal. The flow separation phenomenon for a rounded bilge may show some difference between the model and prototype scales. ...
The most common method of reducing roll motion of ship-shaped floating systems is the use of bilge keel which act as damping elements. The estimation of the damping introduced by bilge keel is still largely based on empirical methods. The present work adopts the CFD approach to the estimation of roll damping, both without and with bilge keel and validates the results with experiments conducted in a wave flume. Specifically, free oscillation tests are conducted at model scale to obtain roll damping, both by experiments and CFD simulation and reasonably good comparisons are obtained. The experiments also include PIV study of the flow field and attempt has been made to correlate the measured flow field with that obtained by CFD. The CFD methodology has the potential to determine rationally the size and orientation of bilge keels in design with reasonably accurate estimate of the additional roll damping that it provides to ship's roll motion.
... Some of the past work done on the subject of roll motions includes an investigation into the eddy-making damping in slow-drift motions performed by Faltinsen and Sortland [1987]. The authors showed the importance of bilge-keel depth, especially for low Keulegan-Carpenter numbers. ...
... where D is a linear damping matrix from linear skin friction (Faltinsen and Sortland, 1987), D n (v) is a nonlinear damping matrix from potential and wave drift damping, and damping from vortex shedding (Fossen, 1994;Newman, 1980), fX u ; Y v ; Z w ; K p ; M q ; N r g is for linear coefficients which can be derived by hydrodynamic derivatives, and fX u j ju ; Y v j jv ; Z w j jw ; K p j jp ; M q j jq ; N r j jr g is for nonlinear cross flow coefficients that can be estimated by calculating the hull drag similar to strip theory (Prestero, 2001). The G(η) vector can be defined as a combination of the effects of the vehicle's weight and buoyancy. ...
This work considers a general fully coupled autonomous underwater vehicle (AUV) for applying nonlinear suboptimal control. In most cases, AUV models are nonlinear and affine in control, especially without modeling rudders and fins. The aim of this work is to address the challenges of nonlinear non-affine AUVs for implementing the controllers, as this aspect of control design has received little attention in this field of research. The NPS II is a well-known AUV that is often mentioned in research on nonlinear, non-affine modeling. This model is considered for applying the state-dependent Riccati equation (SDRE) controller with a non-affine structure for point-to-point motion that generates a suboptimal path. Furthermore, the control, design and simulation results are provided without any simplification or decoupling of the entire system. The design approach of this paper is implemented on NPS II; nonetheless, this point of view can be actualized on any AUV using the same technique.
... The usual result from momentum theory [3] gives ...
This paper describes mathematical models of propeller thrust and torque. The models are traditionally based on steady state thrust and torque characteristics. These characteristics usually are obtained in model towing tanks. Often experimental results are showed that these quasi steady state models do not accurately describe the transient phenomena in a thruster of the marine mechatronic system. Nowadays papers published in conference proceedings includes dynamic models usually was based on the experimental observations. Describing zero advance speed conditions accurately, this model however does not work for a marine vehicle at nonzero relative water speed. This paper derives a dynamic model of propeller that includes the effects of transients in the flow over a wide range of sea operation. The results of this trials are essential for accurate thrust control in precise control of marine vehicle.
This treatise, based on a thorough literature search, examines mean and low-frequency second-order wave forces and related interests like viscous effects, low-frequency hydrodynamic coefficients, wave directionality and grouping, mooring parameters, and statistical estimates for moored offshore structures like semi-submersibles. It has been noticed that the present state-of-the-art method of predicting the second-order mean and low-frequency wave force has achieved more or less success, though new problems are still being addressed to find an exact solution to such a complex problem.
It will not be too much to say that almost all the numerical solutions were accomplished using linear potential theory (either 2-D or 3-D) with some approximations in their formulations to ease the solution technique. Initially, experimental procedures were also adopted to understand the root of the second-order force. With time, more and more related interests are being initiated by the researchers in this field. Some of them, like viscous effects, low-frequency hydrodynamic coefficients like added mass, and potential and viscous (linear and nonlinear) damping factors, need profound knowledge to treat the problems further. For a moored structure, the linear wave radiation damping is small; therefore, non-linear potential and viscous effects are significant. Great uncertainty lies in choosing the appropriate values of drag coefficients. The environment, like wave-current interactions, low-frequency turbulent wind spectra, and the dynamic effects of the mooring system, including their damping contributions, also significantly affect the low-frequency response amplitude of a moored structure like semisubmersibles.
Especially the modification of the current and wave velocity fields and forces resulting from the interaction of the velocity fields. 4
For greater accuracy, it is often suggested that the effect of wave directionality be accounted for while predicting the motion characteristics of a moored structure. This is similar to the case with wave grouping, which is important for moored structures where the second-order wave force produced by grouping may excite large resonant motions.
This chapter applies to bodies that are small compared to the wave lengths, of dimensions similar or smaller than the wave amplitude. As a result separation cannot be neglected and semi-empirical methods are usually applied to formulate the wave and current loading. The Reynolds number is introduced and the different flow regimes, for a circular cylinder in current, are illustrated. The Morison equation is introduced and applied to the wave loading upon cylinders. Experimental values of the inertia and drag coefficients, vs the Reynolds and Keulegan-Carpenter numbers, are presented. The deficiencies of the Morison equations, in complex flows, are emphasized. Alternatives such as the independent flow-field formulation, or wake models, are introduced. The oscillatory lift force, in steady current, is introduced and the Strouhal number and reduced velocity are defined.
In this study, the weathervane performance of Floating Offshore Wind Turbines (FOWTs) moored by Single-Point-Mooring (SPM) system is assessed through a series of experiments and numerically simulating time-series history. Two types of scaled FOWT models, a semi-submersible and a spar are designed and manufactured, based on Froude's scaling law. The 1/200 scaled models are experimented in a circulating water tank at Osaka Prefecture University, Osaka, Japan under only-wind and wind-current conditions. A time-series numerical simulation technique modeling wind, current and mooring loads is developed. Damping coefficients are determined from the experiments and used in the simulation. The equation of motion is set up and solved numerically using Runge-Kutta-Gill method. A good agreement was found between experimental and numerical simulation results. Further, the influence of slow-drift motion of FOWT resulting from the weathervane is clarified by comparing the numerical simulation results with and without damping force. It was found that accurate predictions were possible by considering the slow-drift damping of FOWT than the numerical simulation without damping, although the effect of damping is found to be nominal. It can be concluded that estimation of slow-drift damping is needed for accurate prediction of weathervane phenomenon.
Research in autonomous underwater vehicles (AUVs) has reached a level of maturity where robotic systems can be expected to efficiently perform complex missions involving intelligent agents in unstructured underwater environments without teleoperation. As the AUVs becomes more independent, the requirements for robust and reliability software increases to ensure safe operations, particularly for those missions that are expensive or
risk-intensive.
The research of this thesis is motivated by the desire to design and create an open-sourced software architecture for AUVs that could support coordinated mission execution for many scenarios. First an review of the current state-of-the-art software architectures and explanation of design principles was conducted. After that, a software flow diagram of the Manta v1 was developed, showing the necessary components, their interdependence and the communication backbone. The implementation of each of the components in the architecture was done in a bottom-up fashion starting of with a mathematical formulation of the Manta AUV. Next, a high-fidelity testbed for 3-D simulation of the vehicle with actuators and sensors was created. Next, the necessary low-level navigation, guidance and motion control systems was designed, implemented and tested using the 3-D simulation testbed. Once all the low-level components was developed and thoroughly tested, a high-level mission control was develop to ensure a coordination and execution of mission.
Through comparison of results from testing the nonlinear PID controller and the nonlinear
backstepping controller in simulation and in physical experiments, it can be concluded that the derived mathematical model of the Manta AUV is accurate. From physical experiments it can also be concluded that the implemented extended Kalman filter for localization, as well the nonlinear PID controller and nonlinear backstepping controller all achieves high performance much similar to what was seen in simulations. A lesser appealing result came from the computer vision object detection. It performance well in a simulated environment, however in physical experiments the object detection is more brittle and sensitive to noise. As recommendations for further work, it should be invested time in creating particle filters for mapping of the environment, once that is done it is possible to start investigating path planning and path generation. When it comes to object detection, it is suggested to shift from traditional computer vision techniques to using convolutional neural networks.
To this end, the Manta v1 software architecture has been developed as seen by Figure 1. It
is an extensive software stack consisting of about 25.000 lines of code. Manta v1 supports the efficient execution of real-world missions involving multiple concurrent goals. The largest component of Manta v1 is its mission control, which continuously optimizes the execution of a mission as information about the world is acquired. The architecture is rich in functionality, distributes its computation, and performs efficient re-planning in an unknown, unstructured, and changing environment. This system has been demonstrated on the Manta AUV in an indoor experimental pool and extensively verified in simulation.
This work presents an Autonomous Surface Vehicle (ASV) with tracking capability. The ASV is able to follow after an Autonomous Underwater Vehicle (AUV) without prior knowledge of the AUV’s actual position. Tracking an AUV can significantly increase the communication range and bandwidth of the transferred data, which means that the AUV can operate without nearby operators. Mathematical models to represent ASV’s kinematics and kinetics were developed as well as a controller that takes into account sea wave effects. Simulations of the ASV with a ranger interrogator system was developed to test the tracking algorithm. The proposed method allows computing the possible location of the AUV, which can be used to reduce the navigation error of the AUV. This method was tested both in a simulation environment and at sea trials in the Red Sea. In both cases, the algorithm performed well and precise tracking was achieved.
Ships are prone to large roll motions in beam and oblique seas at encounter frequencies near the design frequency of the vessel. The nonlinearity of roll damping and roll motion has been investigated in the past by various researchers. The prediction of roll damping and roll motion of ships becomes difficult by simplified approaches. Ship roll motion is highly influenced by viscous flow around the hull. Vortex formation and its shedding from the hull and appendages have larger contribution to roll damping. Therefore, the popular approach for prediction of roll damping and roll motion of ships is with the help of model experiments and more recently URANS (Unsteady Reynolds-averaged Navier–Stokes)-based simulations. Free roll decay experiments in calm water conditions give a good estimate of roll damping of ships at natural frequency. The flow characteristics around the hull may not be the same when the ship is moving at a forward speed. Hence, it is important to take into consideration the effect of forward speed on roll damping obtained from free roll decay of the ships. This paper addresses the effect of forward speed on roll damping of a 1:100 (Froude) scaled container ship model. The model is 2.88m in length, 0.345m in beam and was loaded to a draft of 0.12m; free roll decay experiments at zero forward speed were carried out in a wave flume at Department of Ocean Engineering, IIT Madras. The wave flume is 4m wide, 90m long and has water depth of 2.5m. The held-over free roll decay tests were carried out by subjecting the model to known initial heel and releasing it. The roll angle was measured using inclinometer via data acquisition CPU. The URANS-based simulations of the free roll decay experiments at zero forward speed were carried out in a commercial computational fluid dynamics (CFD) software and validated. The CFD model was then used to carry out the free roll decay simulations at two forward speeds of the ship model. The effect of forward speed on roll damping of the ship model was assessed from the results of CFD simulations.
A dynamic positioning (DP) system includes different control functions for automatic positioning and guidance of marine vessels by means of thruster and propeller actions. This paper describes the control functions which provide station-keeping and tracking. The DP controller is designed using model-based control, where a new modified LQG feedback controller and a model reference feedforward controller are applied. A reference model calculates appropriate reference trajectories. Since it is not desirable nor even possible to counteract the wave-frequency movement caused by first-order wave loads, the control action of the propulsion system should be produced by the low-frequency part of the vessel movement caused by current, wind and second-order mean and slowly varying wave loads. A Kalman filter based state estimator and a Luenberger observer are used to compute the low-frequency feedback and feedforward control signals. Full-scale experiments with a supply vessel demonstrate the performance of the proposed controller.
This thesis presents the design of a novel type of miniature floating offshore platforms with a heave plate attached at the keel, suitable for developing deep-water marginal fields. This design features a small displacement, easy fabrication, reduced cost and a favourable motion performance in waves. The design process includes the preliminary estimation, hydrodynamic analysis and hull optimization. A self-developed model "Discrete Vortex Ring Model" (DVRM) to efficiently estimate the viscous drag due to the vortex shedding of the oscillatory heave plate is presented in details. This new model DVRM combined with the standard radiation/diffraction code WAMIT is used to analyse the effect of different geometric parameters on the motion behaviour of the platform. Finally, these two models are integrated into a genetic optimization algorithm to obtain a final optimal design.
Nowadays the study of parametric resonance has great importance in the
analysis of ship stability in waves,since it is a phenomenon in which the
ship can reach large roll amplitudes in few cycles. Parametric rolling
induced by internal excitement associatedwith periodic variations of certain
parameters of the oscillatory system, as the roll restoring moment, is a
function of the ship vertical motions and incident wave characteristics.
In the present work a mathematicalalgorithm aimed at solving the nonlinear equations of motion in time domain with consideration of memory
effects is introduced, capable of simulating the heave, roll and pitch motions
in regular waves in situations in which parametric rolling are contemplated.
Hydrodynamic reactions are expressed in terms of convolution integrals.
Fluid memory effects are modeled by impulse response functions derived
from frequency domain hydrodynamic forcesand moments. The aim of this
thesis is the assessment of the relevance of memory effect on the occurrence
of non-linear instabilities associated with parametric rolling.
source: http://www.oceanica.ufrj.br/intranet/modules/PDdownloads/viewcat.php?cid=16
A numerical model has been used to study separated flow around two-dimensional bodies in harmonically oscillating incoming flow. The work is based on a thin free shear layer method which assumes that the vorticity is concentrated in thin boundary layers around the body and in thin free shear layers. A flat plate and a midship cross section with bilge keels have been used. The separation points are assumed to be fixed at the sharp edge of the plate or bilge keel. The inline force has been calculated, and the drag and inertia coefficients have been found.
Wave drift damping and low-frequency oscillations of a moored elliptic cylinder is examined. The cylinder is restricted to move along a horizontal frictionless constraint. The moorings are simulated by slack linear springs. The fluid layer is infinitely deep and the motion is two-dimensional. The fluid flow around the body and the forces acting upon it are computed in the frame of reference following the low-frequency position of the body. The slowly varying force is calculated by the approximation due to Marthinsen1. One part of the resulting slowly varying force is a damping force being proportional to the low-frequency velocity of the body. This force is closely related to wave drift force damping. For long incoming waves, we obtain positive damping. For short incoming waves, however, the damping force becomes negative. Also slowly varying frequency of encounter of the incoming waves is introduced due to the slowly varying velocity of the body. The equation of motion for the low-frequency oscillations is solved by numerical integration. Results for several sea states are examined. The impact of the damping force obtained here is compared with the impact of wave drift force damping and viscous damping.
Handbook of Marine Craft Hydrodynamics and Motion Control is an extensive study of the latest research in hydrodynamics, guidance, navigation, and control systems for marine craft. The text establishes how the implementation of mathematical models and modern control theory can be used for simulation and verification of control systems, decision-support systems, and situational awareness systems. Coverage includes hydrodynamic models for marine craft, models for wind, waves and ocean currents, dynamics and stability of marine craft, advanced guidance principles, sensor fusion, and inertial navigation.
This important book includes the latest tools for analysis and design of advanced GNC systems and presents new material on unmanned underwater vehicles, surface craft, and autonomous vehicles. References and examples are included to enable engineers to analyze existing projects before making their own designs, as well as MATLAB scripts for hands-on software development and testing. Highlights of this Second Edition include:
- Topical case studies and worked examples demonstrating how you can apply modeling and control design techniques to your own designs
- A Github repository with MATLAB scripts (MSS toolbox) compatible with the latest software releases from Mathworks
- New content on mathematical modeling, including models for ships and underwater vehicles, hydrostatics, and control forces and moments
- New methods for guidance and navigation, including line-of-sight (LOS) guidance laws for path following, sensory systems, model-based navigation systems, and inertial navigation systems
This fully revised Second Edition includes innovative research in hydrodynamics and GNC systems for marine craft, from ships to autonomous vehicles operating on the surface and under water. Handbook of Marine Craft Hydrodynamics and Motion Control is a must-have for students and engineers working with unmanned systems, field robots, autonomous vehicles, and ships.
Nonlinear ship control systems can be designed by exploiting system properties like passivity and dissipativeness in nonlinear system. The nonlinear ship model is written in a vectorial setting with emphasis placed on matrix properties like positiveness, symmetry and skew-symmetry. As a result of energy conservation the ship dynamics can be considered as two interconnected systems. The first system describes the dissipative motion of the rigid-body (ship) while the second system represents the forces due to potential theory generated by the ambient water particles. It is shown that for a stable ship, both subsystems are passive as well as the interconnected system. For an unstable ship, the ambient water system is input feedforward passive with shortage of passivity and therefore the ship must be stabilized by positive feedback. The structural properties of the nonlinear equations of motion are exploited in the Lyapunov analysis when designing ship control systems.
Hydrodynamic damping of floating bodies is due mainly to wave radiation and viscous damping. The latter is particularly important in controlling those responses of the body for which the wave damping is small. The roll response of ship hulls near resonance in beam seas is an example of this. The present paper applies a discrete vortex method as a local solution to model vortex shedding from the bilges of a barge hull of rectangular cross-section and hence provides an analytic method for predicting its coupled motions in three degrees of freedom, including the effects of the main component of viscous damping. The method provides a frequency-domain solution satisfying the full linearized boundary conditions on the free surface.
A dynamic positioning (DP) system includes different control functions for the automatic positioning and guidance of marine vessels by means of thruster and propeller actions. This paper describes the control functions which provide station-keeping and tracking. The DP controller is a model-based control design, where a new modified LQG feedback controller and a model reference feedforward controller are applied. A reference model calculates appropriate reference trajectories. Since it is not desirable, nor even possible, to counteract the wave-frequency movement caused by first-order wave loads, the control action of the propulsion system should be produced by the low-frequency part of the vessel movement caused by current, wind and second-order mean and slowly varying wave loads. A Kalman-filter-based state estimator and a Luenberger observer are used to compute the low-frequency feedback and feedforward control signals. Full-scale experiments with a multipurpose supply ship demonstrate the performance of the proposed controller.
Self-propelled artificial objects are at the current forefront of research. We demonstrate here that the motion directionality of millimetre sized self-propelled objects is highly dependent on the Reynolds numbers (Re) of the systems, with emphasis on the "intermediate" Re region (1-600). Our findings have strong implication on the motion controllability and predictability of these independent self-propelled systems.
There is a great interest in reducing the toxicity of the fuel used to self-propel artificial nanomachines. Therefore, a method to increase the efficiency of the conversion of chemicals into mechanical energy is desired. Here, we employed temperature control to increase the efficiency of microjet engines while simultaneously reducing the amount of peroxide fuel needed. At physiological temperatures, i.e. 37 °C, only 0.25% H(2)O(2) is needed to propel the microjets at 140 μm s(-1), which corresponds to three body lengths per second. In addition, at 5% H(2)O(2), the microjets acquire superfast speeds, reaching 10 mm s(-1). The dynamics of motion is altered when the speed is increased; i.e., the motion deviates from linear to curvilinear trajectories. The observations are modeled empirically.
: Mathematical models of propeller thrust and torque are traditionally based on steady state thrust and torque characteristics obtained in model basin or cavitation tunnel tests. Experimental results showed that these quasi steady state models do not accurately describe the transient phenomena in a thruster. A recently published dynamic model was based on the experimental observations. Describing zero advance speed conditions accurately, this model, however, does not work for a vessel at nonzero relative water speed. This paper derives a large signal dynamic model of propeller that includes the eects of transients in the ow over a wide range of operation. The results are essential for accurate thrust control in dynamic positioning and in underwater robotics. Keywords: propellers, thrusters, dynamic positioning, underwater robotics, thrust control 1. INTRODUCTION Underwater vehicle (UUV) speed and position control systems are subject to an increased focus with respect to ...
A coordinate generation method for use in computational fluid dynamics problems is developed which is much simpler, more accurate, and more flexible than currently existing methods. This approach is based on numerical integration of Schwarz-Christoffel transformations for general curved surfaces. It is shown to be second-order accurate in mesh size with extensions to higher-order accuracy levels identified. In addition, this method directly provides the two dimensional incompressible potential flow solution for flow past complex body shapes including flows with free streamlines. Example symmetric cases are given for flow past a hexagon, a six point cross, a NACA airfoil, and free streamline flow past a circular cylinder. Finally, the method is extended to more general cases and, in particular, to flows with circulation and channel flows.
The influence of the low-frequency-wave-drifting force on the motions of moored vessels and the loads in the mooring system is demonstrated from results of model tests in irregular waves. The origin of the wave drifting force is discussed and methods for calculating the mean drifting force are reviewed. To facilitate calculation of the low-frequency-wave drifting force on an object in irregular waves, an existing method using the mean drifting force in regular waves is generalized. The results of calculations using the method introduced in this paper are compared with previously published test results. Finally, some remarks are added concerning effects that have not been accounted for in existing calculation methods.
Introduction
A vessel moored at sea in stationary conditions with regard to waves, wind, and current is subjected to forces that tend to shift it from the desired position. For a given vessel and position in the position. For a given vessel and position in the horizontal plane, the motions depend on both the mooring system and the external forces acting on the vessel. In steady conditions, the forces caused by a constant wind and current are constant quantities for a given heading angle of the vessel. The forces caused by a stationary irregular sea are of an irregular nature and may be split into two parts: first-order oscillatory forces with wave parts: first-order oscillatory forces with wave frequency, and second-order, slowly varying forces with frequencies much lower than the wave frequency.The first-order oscillatory wave forces on a vessel cause the well known ship motions whose frequencies equal the frequencies present in the spectrum of the irregular waves. These are the linear motions of surge, sway, and heave and the three angular motions of roll, pitch, and yaw. In general, the first-order wave forces are proportional to the wave height, as are the ensuing motions. The magnitude of the linear oscillatory motions is in the order of the height of the waves.The second-order wave forces, perhaps better known as the wave drifting forces, have been shown to be proportional to the square of the wave height. These forces, though small in magnitude, are the cause of the low-frequency, large-amplitude, horizontal motions sometimes observed in large vessels moored in irregular waves. Tests run in irregular waves in wave tanks of the Netherlands Ship Model Basin revealed a number of properties and effects of the low-frequency-wave properties and effects of the low-frequency-wave drifting force that are discussed here using the results of two test programs.The first of these programs concerns tests run with the model of a 125,000-cu m LNG carrier moored in head seas with an ideal linear mooring system. The second program deals with a 300,000-DWT VLCC moored with a realistic nonlinear bow hawser to a single-buoy mooring in waves, wind, and current coming from different directions.The results of the tests with the LNG carrier are shown in Figs. 1 through 3, while the results of the tests with the 300,000-DWT VLCC are shown in Fig. 4. All results are given in full-scale values. Fig. 1 shows the wave trace and the surge motion of the LNG carrier to a base of time.
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This paper presents a comparison between theory and experiment for the in-line forces on cylinders of general cross-section in planar oscillatory flows of small amplitude. The theoretical analysis evaluates corrections to the standard inviscid inertial force at low Keulegan-Carpenter numbers which arise from the presence of viscous laminar boundary layers and from the development of vortex shedding. The boundary-layer contribution due to both skin friction and displacement effects is calculated to first order in the Stokes parameter β −½ . The contribution to the in-line force from separation and vortex shedding, for which the results presented only apply to sharp-edged bodies, is taken from previous work on vortex shedding from isolated edges using the discrete vortex modelling technique. The resulting force has components both in phase with the fluid acceleration (inertia) and in phase with the velocity (drag).
The theoretical results are compared to measurements taken in a [xcup ]-tube water channel on a number of cylinders of different cross-section including circular cylinders and sharp-edged sections. The comparisons suggest that the theory is valid for Keulegan–Carpenter numbers below about 3 and for moderately high values of the β parameter.
This paper describes an analysis of the forces induced by separation and vortex shedding from sharp-edged bodies in oscillatory flow at high Reynolds number. The analysis which is valid for the case of small oscillations of the fluid is compared with experimental data obtained at fairly low Keulegan–Carpenter numbers. 1
Hydrodynamic viscous force acting on oscillating cylinders with various shapes The Society of Naval Archi-tects of Japan The forces on sharp-edged cylinders in oscil-latory flow at low Keulegan-Carpenter numbers Low-speed drag of cylin-ders of various shapes
- N Tanaka
- Y Ikeda
- K Nishino
- N K Delaney
- N E Sorensen
Slow drift eddymaking damping of a ship.. O. M. Faltinsen and B. Sortland 9 Tanaka, N., Ikeda, Y. and Nishino, K. Hydrodynamic viscous force acting on oscillating cylinders with various shapes, Proc. 6th Syrup. of Marine Technology, The Society of Naval Archi-tects of Japan, December 1982 10 Graham, J. M. R. The forces on sharp-edged cylinders in oscil-latory flow at low Keulegan-Carpenter numbers, J. HuM Mech. 1980, 97,331 11 Delaney, N. K. and Sorensen, N. E. Low-speed drag of cylin-ders of various shapes, NACA Technical Note 3038, 1953 12 Brown, C. E. and Michael, W. H. Nat. Adv. Comm. Aero Teeh. Note 3430, 1955
Numerical methods for coordinate generation based on a mapping technique, VKI LS 81-5, Comp. Fhdd Dynamics Vortex shedding from sharp edges, LC. Aero Report 77-06, Department of Aeronautics, Imperial College of Science and Technology
- R T Davis
- J M R Graham
Davis, R. T. Numerical methods for coordinate generation based on a mapping technique, VKI LS 81-5, Comp. Fhdd Dynamics, 1981 14 Graham, J. M. R. Vortex shedding from sharp edges, LC. Aero Report 77-06, Department of Aeronautics, Imperial College of Science and Technology, London, November 1977 15 Graham, J. M. R. Forces on cylindrical bodies in oscillatory flow at low Keulegan-Carpenter numbers, in Mechanics of Wave-induced Forces on Cylinders, Shaw, T. L., ed., Pitman Publishing Ltd, 1979 16 Schlicting, H. Boundary Layer Theory, McGraw-Hill Book Co., 7th Edn, 1979 17 Landau, L. D. and Lifschitz, E. M. Fluid Mechanics, Pergamon Press, 1959
Current forces on ships
- Aarsnes
Vortex shedding around two-dimensional bodies at high Reynolds number
- Faltinsen
Hydrodynamic viscous force acting on oscillating cylinders with various shapes
- Tanaka
Low-speed drag of cylinders of various shapes
- Delaney
Slowdrift damping and response of a moored ship in irregular waves
- Faltinsen
Application of a vortex tracking method to current forces on ships
- Aarsnes
Vortex shedding from sharp edges
- Graham
Forces on cylindrical bodies in oscillatory flow at ow Keulegan-Carpenter numbers
- Graham