Initial Roll Angle Research Articles

Study on numerical simulation and mitigation of parametric rolling in a container ship under head waves

To investigate the parametric rolling motion of container ships navigating in head seas, this study utilizes the unsteady RANS approach combined with dynamic overlapping grid technology to simulate parametric roll in a container ship under the coupled motions of roll, pitch, and heave. Initially, the model was validated against experimental results, demonstrating good agreement and thus confirming the reliability of the computational method. Furthermore, the paper investigates the impacts of the initial roll angle, encounter frequency, and the addition of bilge keels on parametric rolling. The research findings indicate that the initial angles of rolling impact the duration needed to attain a steady roll condition, yet they have minimal effect on the amplitude post-stabilization. The likelihood of parametric rolling arises when the frequency of encounters doubles that of the ship's inherent roll frequency. Furthermore, the likelihood of parametric rolling escalates when the wavelengths approach the length of the ship. Installing bilge keels markedly reduces the parametric rolling movement in vessels, and the occurrence of parametric rolling is also delayed.

Experimental investigation and intelligent control of the magnus anti-rolling device for ship stability at zero speed

Under zero-speed conditions, ships are particularly susceptible to the effects of waves, which directly impact the safety of the vessel. A ship anti-rolling device based on the Magnus effect is designed to mitigate rolling motions across a full range of speeds, thereby enhancing the vessel's stability. This study presents an experimental investigation and intelligent control of Magnus anti-rolling devices aimed at enhancing ship stability at zero speed. The test setup, intelligent control algorithm, and experimental procedures specifically tailored for evaluating the Magnus anti-rolling device were designed. Following this, a comprehensive analysis was conducted to assess the effects of different cylinder geometries, swinging speeds, initial roll angles, and control methods on the anti-rolling characteristics of the device. Results demonstrate that the intelligent control method achieves an average anti-rolling efficiency of 89%. Additionally, the optimised geometric model of the Magnus anti-rolling device exhibits improved anti-rolling efficiency relative to the original model. The study confirms the stability and robustness of the intelligent Magnus anti-rolling device and suggests future research directions for practical applications aboard full-scale vessels in complex marine environments.

Numerical simulation of wedges slamming non-Newtonian fluids based on SPH method

Current research on non-Newtonian fluids using Smoothed Particle Hydrodynamics (SPH) has primarily focused on dynamic behavior, with limited exploration into interactions between rigid bodies and non-Newtonian fluids. Leveraging the SPH method's effectiveness in addressing free surface flow challenges, a two-dimensional numerical model of a rigid body impacting non-Newtonian fluids based on the Herschel-Bulkley-Papanastasiou (HBP) constitutive model is developed within the SPH framework. The study integrates experimental and numerical findings from non-Newtonian dam break scenarios, comparing particle distribution and the evolution of the waterfront over time to ensure accurate representation of non-Newtonian fluid behavior. While ensuring the convergence of SPH results, the research simulates the impact of a wedge on the surface of non-Newtonian fluids. This comparison of the slamming load exerted by non-Newtonian fluids on the wedge serves to validate the accuracy of the numerical method. Furthermore, the study explores the effects of varying initial velocities and roll angles of wedges slamming into specific non-Newtonian fluids. It analyzes fluid jet phenomena and changes in slamming loads.

Stability and roll angles of the ship at its small finite tilts from different starting positions

The article, within the framework of the acceptability of the metacentric formula, presents a solution to the problem of comparing the stability of the ship, the angles of rotation and the roll angles that it takes while in different starting positions: in a straight state (with the center of gravity (CG) unbiased from the diametrical plane) and with the initial roll angle (with the displaced CG). This comparison is carried out when the following factors affect the ship: the same heeling moment; the rotation of the ship at the same roll angle; the transfer of the same cargo parallel to the deck at the same distance; the inclination of the ship to the same position. The purpose of this comparison is to clearly show that a ship with a displaced CG exhibits better stability within the specified framework than in a straight state. It is shown that the transfer of cargo in any direction from side to side will turn the ship with the initial angle by a smaller angle in the direction of transfer than the same ship in the initial straight state. The exception will be the same transfer, in which the initially cloned ship will restore a straight state or take a roll opposite to the original one. In the first case, the rotation of the ship (relative to the initial roll) will occur at exactly the same angle as when the ship is tilted with an initially straight state, and in the second case - by a larger angle. The materials of the article can be useful in analyzing the behavior of a ship at small roll angles.

Analysis of Roll Decay for Surface-Ship Model Experiments With Uncertainty Estimates

Abstract Roll decay of David Taylor model basin (DTMB) Model 5720, a 23rd-scale free-running model of the research vessel (R/V) Melville, is evaluated with uncertainty estimates. Experimental roll-decay time series was accurately modeled as an exponentially decaying cosine function, which is the solution of a second-order ordinary differential equation for damping coefficient of less than one (N < 1). The curve-fit provides damping coefficient (N), period (T), and offset. Roll period in calm water was dependent on Froude number (Fr) and initial roll angle (a). Roll decay data are from 76 runs for three nominal Froude numbers, Fr = 0, 0.15, and 0.22. The initial roll angle variation was 3 deg–25 deg. The natural roll period was 2.139 ± 0.041 s (±1.9%). The decay coefficient data were approximated by a plane in three dimensions with Fr and initial roll amplitudes (a) as the independent variables. Curve-fit results are compared to decay coefficient by log decrement and period from time between zero crossings. Examples demonstrate average values for a single roll decay event from log decrement are the same as values by the curve-fitting method within uncertainty estimates. The uncertainty estimate for the decay coefficient is significantly less by curve-fit method in comparison to log-decrement method. By log decrement, the relative uncertainty increases with decreasing roll amplitude peak; consequently, focus should be on the damping coefficient at the largest peaks, where the uncertainty is the smallest.

Effect of initial roll or pitch angles on the vortex-induced motions (VIM) of floating circular cylinders with a low aspect ratio

The vortex-induced motions (VIM) is a phenomenon that can promote large oscillatory amplitudes on circular platforms in the horizontal plane, such as spar or monocolumn production, storage, and offloading system (MPSO). Floating offshore wind turbines (FOWT) can use a spar-type platform to support the turbine, and due to the wind incidence, roll or pitch angles can occur. The main goal of this work was to experimentally investigate the effect of the initial roll or pitch angles on the VIM amplitudes of a floating circular cylinder with a low aspect ratio. Four different initial angle conditions were carried out, namely vertical, roll angle, positive pitch angle, and negative pitch angle. The Reynolds number range performed was 12,000<R<100,000. The results of VIM amplitudes showed that the yaw motion was affected by the initial pitch angle. The initial pitch angles proved to be responsible for creating a geometric asymmetry of the body and promoted more significant yaw motions than the case without initial angle conditions. The yaw motions started to be substantial after the mean pitch angle of the cylinder reached 3°. The yaw motion increased as the reduced velocity was increased and showed to be essential to be correctly modeled and analyzed in the case of VIM on FOWT.

Aerodynamic Performance of the InSight Mars Lander

The Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) mission touched down in Elysium Planitia on 26 November 2018, becoming NASA’s eighth successful entry, descent, and landing (EDL) at Mars. InSight inherited the successful 2008 Phoenix (PHX) EDL system, flying a nonspinning, ballistic trajectory with a 70 deg sphere–cone aeroshell (2.65 m diameter), a disk–gap–band parachute, and pulsed terminal descent and landing engines. InSight and Phoenix exhibited similar behavior, primarily in terms of trim attitude and an uninitiated roll reversal correlated with dynamic pressure, although the behaviors observed for InSight were more severe. For InSight, the initial clockwise roll and nonzero trim angle of attack were significant contributors to a short timeline, larger-than-predicted deceleration loads, and cross-track and up-track errors in landing location. The InSight and Phoenix reconstructions together indicate behavior more characteristic of a single, continuous instability region, suggesting that errors in the trim behavior from hypersonic nonequilibrium aerodynamics predictions along the dynamic pressure pulse may have a more substantial impact on nonspinning, ballistic entry vehicle performance.

URANSE-Based Numerical Prediction for the Free Roll Decay of the DTMB Ship Model

In the present study, Computational Fluid Dynamics (CFD) is used to investigate the roll decay of the benchmark surface combatant DTMB-5512 ship model appended with bilge keels, sailing in calm water at different speeds (Fr = 0.0, 0.138, 0.2, 0.28 and 0.41) and with different initial roll angles. The numerical simulations are carried out using the viscous flow solver ISIS-CFD of the FINETM/Marine software provided by NUMECA. The solver uses the finite volume method to build the spatial discretization of the transport equation to solve the unsteady Reynolds-Averaged Navier–Stokes equations. Two-phase flow approach is applied to model the air–water interface, where the free surface is captured using the volume of fluid method. The closure to turbulence is achieved by making use of the blended Menter shear stress transport and the explicit algebraic Reynolds stress models. First, a systematic validation against the experimental data at medium speed and initial roll angle of 10° are performed; then, the effect of the initial roll angle and ship speed is later studied. Numerical errors and uncertainties are assessed using grid and time step convergence study based on Richardson Extrapolation method. A special focus on the flow in the vicinity of the bilge keels during the simulation is also investigated and presented in the form of velocity contours and vortical structure formations. The resemblance between the CFD results and experimental data for roll motion and flow characteristics are within a satisfactory congruence; however, some discrepancies are recorded for the over predicted roll amplitudes in the second and, sometimes, the third roll cycle, which appeared mostly in the cases with high initial roll angles.

Semi-Active Control for a Helicopter with Multiple Landing Gears Equipped with Magnetorheological Dampers

Due to their extensive use in various applications, helicopters need to be able to land in a variety of conditions. Typically, a helicopter landing gear system with skids or passive wheel-dampers is designed based on only one critical touchdown condition. Thus, this helicopter landing gear system may not perform well in different landing conditions. A landing gear system with magnetorheological (MR) dampers would be a promising candidate to solve this problem. However, a semi-active controller must be designed to determine the electrical current applied to the MR damper to directly manage the damping force. This paper presents a new skyhook controller, called the skyhook extended controller, for a helicopter with multiple landing gears equipped with MR dampers to reduce the helicopter’s acceleration at the center of gravity in off-normal landing attitude conditions. A 9-DOF simulation model of a helicopter with multiple MR landing gears was built using RECURDYN. To verify the effectiveness of the proposed controller, co-simulations were executed with RECURDYN and MATLAB in different initial pitch and roll angles at touchdown. The main simulation results show that the proposed controller can greatly decrease the peak and rms acceleration of the helicopter’s center of gravity compared to a traditional skyhook controller and passive damper.

A mobile stereo vision system with variable baseline distance for three-dimensional coordinate measurement in large FOV

A novel mobile stereo vision system (MSVS) with variable baseline distance for three-dimensional (3D) coordinate measurement in large field of view (FOV) is established herein. Each independent mobile camera can rotate in the horizontal and vertical directions, and the position of the cameras are obtained by differential GPS in real time. In order to achieve rapid camera calibration in large FOV, a simplified model of MSVS based on differential GPS is constructed in this paper. A six-point method is proposed to quickly estimate the camera’s initial parameters (i.e. focal length, initial roll, pitch, and yaw angles) in the situation that the approximate value of the initial yaw angle is unknown. Moreover, the camera’s roll angle is equivalent to its approximate value measured by a high-precision inclinometer during the movement, and the unknown extrinsic parameters of each camera are reduced to the pitch and yaw angles after the camera moves. The refined pitch and yaw angles are eventually estimated by only using a single control point, which makes it possible that the 3D coordinate can be measured online after the camera moves. The computer simulation verifies the effectiveness of the extrinsic parameters calibration method using a single control point. The quantitative results demonstrate that the standard deviation of the focal length of the camera does not exceed 0.028 mm, and the mobile camera’s pitch angle and yaw angle estimated by a single control point is extremely close to the reference values. In addition, the average error of the 3D coordinate on each axis after the camera moves is smaller than 0.08 m in the measuring distance of 100 m, and that on X-axis and Z-axis is comparable and does not exceed 0.35 m. The proposed methods are suitable for the occasions that high accuracy is not required in the field of 3D coordinate measurement in large FOV.

MLCA-A Machine Learning Framework for INS Coarse Alignment.

Inertial navigation systems provides the platform’s position, velocity, and attitude during its operation. As a dead-reckoning system, it requires initial conditions to calculate the navigation solution. While initial position and velocity vectors are provided by external means, the initial attitude can be determined using the system’s inertial sensors in a process known as coarse alignment. When considering low-cost inertial sensors, only the initial roll and pitch angles can be determined using the accelerometers measurements. The accuracy, as well as time required for the for the coarse alignment process are critical for the navigation solution accuracy, particularly for pure-inertial scenarios, because of the navigation solution drift. In this paper, a machine learning framework for the stationary coarse alignment stage is proposed. To that end, classical machine learning approaches are used in a two-stage approach to regress the roll and pitch angles. Alignment results obtained both in simulations and field experiments, using a smartphone, shows the benefits of using the proposed approach instead of the commonly used analytical coarse alignment procedure.

CFD Simulation on Workability of a Seaweed Harvesting Boat Due to Wake-Wash

In the present study, a 2-ton class seaweed harvesting boat was optimized by employing a W-shape hull form to reduce roll motion due to wake-wash from passing boats. A series of numerical simulations were conducted using Star-CCM+, a commercial CFD (computational fluid dynamics) software, to improve workability by optimizing the hull form from the conventional design (original hull form). The 2-dimensional roll decay motion of various hull forms with W-shape midsection were simulated and the hull form with the best performance in free roll decay test was selected. To evaluate stability of each hull in wake-wash, the original or optimized hull was alternately located at the middle of a computational domain as a target ship while an advancing ship (original hull) moved forward generating Kelvin waves which impact the original or optimized boat. Two kinds of working conditions, i.e., ballast and full loading conditions, of the target ship were considered with and without initial roll angle. It was observed through the comparison of motion between the original and optimized hulls a decrement of roll motion for the optimized ship demonstrating the effectiveness of the W-shape hull. Decrement of roll motion was observed for both working conditions. Additionally, the optimized W-shape hull showed an extraordinary performance under the ballast condition without initial roll angle.

A Numerical Study of the Roll Damping for Double-Symmetric Bodies

Roll damping is essential for describing properly the motions of a ship, particularly when operating in rough sea conditions, being determinant for parametric or synchronous roll phenomena. Roll damping is a complex process of energy transfer from the hull to the water, which affects the amplitude of motion. Roll damping is dominated by viscous effects as well as by the interaction of the ship with the free surface. Numerical simulations of the free roll decay are carried out in this paper for a double-symmetric floating hull with one or two bilge keels based on an unsteady viscous flow solver. The numerical solutions reported in here are computed with the ISIS-CFD viscous flow solver, part of the Numeca FineTM/Marine suite. Turbulent flow is simulated by solving the unsteady equations of flow. Closure to the turbulence is achieved through the Shear Stress Transport (SST hereafter) based Detached Eddy Simulation (DES), which provides the accuracy of LES for highly separated flow regions and a computational efficiency of RANS in the near-wall region. Free roll decay is studied for various initial roll angles at a given advancing speed of the main hull. The influences of the bilge keel surface and initial roll angle on the roll damping coefficient are discussed.

Research on the Rolling Motion Mode of a SWATH-USV

This paper takes a SWATH-USV as the research object, and carries out a series of static water roll attenuation tests under different drafts and different initial roll angles. In order to study the roll motion mode of the SWATH-USV, we have established three mathematical models of the roll motion mode, and written the system identification software in C# language, based on the system identification theory and the genetic programming algorithm. Firstly, by calculating the predicted values of angular velocity under different drafts and different initial roll angles, the error between the test value and the fitted value was analyzed, and the consistency between the predicted value and the test result was found to be good, which proves the reliability of the system identification software. Secondly, through the further processing of the test data, the variation law of the torque coefficient affecting the rolling motion with the draft and the initial roll angle is preliminarily analyzed. Finally, the polynomial response surface method is applied to fit the equation containing the rolling hydrodynamic torque coefficient and the recovery moment coefficient, and the equation is found to be applicability. The analysis results and methods can provide reference for the study of the wave resistance of such USV, and provide important technical support for the subsequent optimization of the boat type.

Dynamic response of a wedge through asymmetric free fall in 2 degrees of freedom

In this article, a mathematical model is presented for simulation of the coupled roll and heave motions of the asymmetric impact of a two-dimensional wedge body. This model is developed based on the added mass theory and momentum variation. To this end, new formulations are introduced which are related to the added mass caused by heave and roll motions of the wedge. These relations are developed by including the asymmetrical effects and roll speed. In addition, by considering the roll speed, a particular method is presented for the time derivative of half-wetted beam of an asymmetric wedge. Furthermore, two equations are derived for the roll and heave motions in which damping terms appear. Validity of the proposed method is verified by comparing the predicted results against available experimental data in two conditions of roll motion and no roll motion. Favorable agreement is observed between the predicted results and experimental data. The pressure and hydrodynamic load are computed, and the differences between the results associated with the considered conditions are explored. Subsequently, the effects of different physical parameters including deadrise angle, initial roll angle, and initial velocity on the dynamic response of a two-dimensional wedge section are investigated. Ultimately, time histories of hydrodynamic coefficients are determined in order to provide a better understanding of the derived equations.

An analytical procedure for time domain simulation of roll motion of the warped planing hulls

Prediction of the roll motion is considered as an important problem in planing hull motion, since safety of the craft highly depends on it at high speeds. Accordingly, the main aim of the present study is to analyze this motion in time domain and estimate its amplitude at various frequencies. In many of the earlier works performed for predicting the motion of planing hulls, the 2d + t theory has been used. However, in all of these studies, water entry phenomenon was modeled without considering the asymmetric condition. In order to overcome this problem, a mathematical model is hereby proposed for prediction of the roll motion which is derived by applying an analytical model of the water entry in which asymmetric condition is taken into account. The suggested method may be used for the warped planing boats. Validity of the model is examined by comparing the obtained results against different experimental results. Another objective of the present study is to examine the effects of deadrise angle, longitudinal center of the gravity and the hullform on the amplitude of motion and hull response. The response is investigated at different conditions: (1) sinusoidal exciting moment, (2) a fixed existing moment and (3) an initial roll angle without any exciting moment. The proposed model is also used to evaluate the horizontal forces and moments acting on the hull during the roll motion.

Inertial migration of a 3D elastic capsule in a plane Poiseuille flow

The inertial migration of a three-dimensional (3D) elastic capsule in a plane Poiseuille flow has been simulated by using the penalty immersed boundary method. An improved front-tracking method was developed to take into account the difference between the viscosities of the interior and exterior fluids. The calculation domain was confined to the capsule boundary by employing the ray casting algorithm. The dynamic motions and the lateral equilibrium positions of the elastic capsules in moderate Reynolds number (Re) flows were examined as functions of the initial lateral position (y0), Re, the aspect ratio (ε), the viscosity ratio (λ), the membrane stretching coefficient (ϕ), the bending coefficient (γ) and the initial roll angle (θx). Three dynamical motions were observed: tank-treading, swinging and tumbling. The initial behavior of the capsule is influenced by the initial lateral position (y0), but the equilibrium position of the capsule is not affected by variation in y0. The equilibrium position is determined by the balance between the wall effect and the shear gradient effect.

Another look at the static stability factor (SSF) in predicting vehicle rollover

We consider once again how the static stability factor (SSF) may be a predictor of vehicle rollover propensity. The SSF is known as a vehicle's track width (t) divided by twice the height (h) of the mass centre above the ground (t/2h), while the vehicle is empty and at rest. We define ‘rollover’ as a 1/4 axial rotation, or equivalently at the point where the mass centre reaches its highest position above the ground. Although some have questioned the efficacy of the SSF in predicting rollover we present another approach providing additional insight via a dynamic analysis of a ‘barrel-roll’, and via the introduction of a new parameter called the ‘dynamic stability factor’, defined in the same way as the SSF, but for the dynamic case. The analysis shows that the SSF is a prominent term in the governing equations of motion. But then in examining the stability of a critical solution of these equations we show that we can predict rollover in terms of the SSF, the tire/roadway friction, and the initial roll angle.

Forward Speed Calm Water Roll Decay for Surface Combatant 5415: Global and Local Flow Measurements

Global and local flow measurements for forward speed calm water roll decay are performed in a towing tank for surface combatant model 5415 for both bare hull (BH) and bilge keel (BK) conditions. Roll motion is oscillatory with underdamped exponential decay and linear with respect to initial roll angles less than the average initial roll angle (9°). For larger mean roll angles (&amp;gt; 3°), damped natural frequency is a few percent below the hydrostatic natural roll frequency with larger values for BH than BK condition and increasing Froude number (Fr), whereas for smaller mean roll angles, it sharply increases toward the hydrostatic natural roll frequency. For larger mean roll angles, logarithmic decrement and linear damping linear increase with larger values for BK than BH condition and increasing Fr, whereas for smaller mean roll angles, they sharply increase. For increasing Fr, mean and initial roll angle averaged mean roll angle decreases by 50%; damped natural frequency increases by 6% with larger values for BH than BK condition; and logarithmic decrement/linear damping coefficient increase by a factor of three/four with larger values for BK than the BH condition. Logarithmic decrement and Himeno method linear damping coefficients are qualitatively similar. Nonlinear damping coefficient is two orders of magnitude smaller than linear damping coefficient. Roll reconstruction errors are smallest for Himeno with linear and nonlinear damping. The phase-averaged wave pattern and velocity and axial vorticity fields at x/L = 0.675 initially show larger amplitudes followed by oscillatory exponential decay. Alternating vortex pairs are shed from the bilge keel tip with damped magnitudes for decreasing mean roll angles. The local flow indicates lower frequencies and larger damping than the roll motion.

Forward Speed Calm Water Roll Decay for Surface Combatant 5415: Global and Local Flow Measurements

Global and local flow measurements for forward speed calm water roll decay are performed in a towing tank for surface combatant model 5415 for both bare hull (BH) and bilge keel (BK) conditions. Roll motion is oscillatory with underdamped exponential decay and linear with respect to initial roll angles less than the average initial roll angle (9°). For larger mean roll angles (> 3°), damped natural frequency is a few percent below the hydrostatic natural roll frequency with larger values for BH than BK condition and increasing Froude number (Fr), whereas for smaller mean roll angles, it sharply increases toward the hydrostatic natural roll frequency. For larger mean roll angles, logarithmic decrement and linear damping linear increase with larger values for BK than BH condition and increasing Fr, whereas for smaller mean roll angles, they sharply increase. For increasing Fr, mean and initial roll angle averaged mean roll angle decreases by 50%; damped natural frequency increases by 6% with larger values for BH than BK condition; and logarithmic decrement/linear damping coefficient increase by a factor of three/four with larger values for BK than the BH condition. Logarithmic decrement and Himeno method linear damping coefficients are qualitatively similar. Nonlinear damping coefficient is two orders of magnitude smaller than linear damping coefficient. Roll reconstruction errors are smallest for Himeno with linear and nonlinear damping. The phase-averaged wave pattern and velocity and axial vorticity fields at x/L = 0.675 initially show larger amplitudes followed by oscillatory exponential decay. Alternating vortex pairs are shed from the bilge keel tip with damped magnitudes for decreasing mean roll angles. The local flow indicates lower frequencies and larger damping than the roll motion.