Strip Theory Research Articles

Application of Arbitrary Lagrangian–Eulerian strips with fully nonlinear wave kinematics for force estimation

The initial design of offshore constructions generally uses a combination of model tests and second-order wave theory to reconstruct the wave kinematics to determine wave forces using the Morison equation. This routine becomes difficult to apply to steep waves without model test data where the second-order theory is not valid. In this article, a novel approach combining a fully nonlinear numerical wave tank (NWT) using the σ-grid with strip theory and the Morison equation in an Arbitrary Lagrangian–Eulerian (ALE) framework is presented. This provides improved wave kinematics from the nonlinear numerical wave tank, an improved representation of the instantaneous velocity field associated with the instantaneous location of the free surface, making an accurate estimation of the wave hydrodynamics of highly nonlinear and breaking waves possible at a reasonable computational cost.The method is verified by comparing the calculated wave kinematics for a fifth-order Stokes wave with the analytical solution. The procedure for the estimation of the hydrodynamic loads on a cylinder is validated using comparisons with model test data for wave forces on a cylinder due to regular, irregular and focussed waves. A good agreement is seen for the estimated wave forces, including for the breaking waves in the irregular wave train. Some overestimation of the wave forces due to irregular waves is seen due to the frequency-independent force coefficient used in the Morison equation. The results demonstrate the potential of the ALE method combined with a nonlinear NWT to evaluate a three-hour irregular sea state simulation and generate wave loading statistics for the initial stochastic design of offshore structures without model test data.

Turbine tonal noise prediction using an improved quasi-3D linear model

This study presented a fast tonal noise prediction method for the turbine. The improved quasi-3D linear model was developed based on Hanson's coupled 2D cascade theory of blade row and Goldstein's duct aeroacoustics equation. The improved model can take into the influence of the radial modes account by applying the strip theory. Furthermore, a two-flat-plates assumption was used for the first time to account for the large turning angle of the turbine blade, and different wake velocity defect models with coefficient correction have been developed for each of the two-flat-plates. Briefly, firstly applying extended Hanson's theory to predict the unsteady load on blade surface and then using Goldstein equation to calculate cut-on modes and sound power level of interested frequencies. The present model was validated by URANS/Goldstein hybrid model by comparing the tonal noise radiation generated by the final stage of the GE E3 low pressure turbine at different rotational speeds and various stator-rotor spacings. The results showed that the present model generally agreed well with the hybrid model and can correctly capture the variations of the sound power level with the operating conditions, which indicated that the present model might be applied as an effective tool for turbine tonal noise prediction with less cost in early design phase of turbine blade.

Application of smoothed particle hydrodynamics method for simulating the flooding process of a damaged ship cabin in full-time domain

The flooding process of a damaged ship is very complicated and it closely relates to the ship survivability and life security. Therefore, it is very necessary to master the process of water flooding and its influencing factors. There are many approaches for the studies, such as the static one, the quasi-static one, and the full-time domain one, etc. In this paper, the Smoothed Particle Hydrodynamics (SPH) method combined with the strip theory is used to study the flooding process of a damaged ship cabin in full-time domain and three kinds of cabins are studied. The displacement, velocity, and rolling angle of the cabin during the process are compared and analyzed. Firstly, the flooding processes of damaged cabins with different opening positions, and opening sizes are simulated and the responses of the damaged cabins to the flooding hydrodynamics are obtained. Then, the effects of the barriers in the cabin on the flooding process are studied. Some reasonable suggestions are put forward to provide references for the anti-sinking design of ships.

A nonlinear aerothermoelastic model for slender composite beam-like wings with embedded shape memory alloys

This paper reports the formulation of an aerothermoelastic tool developed to investigate the behavior of flexible beam-like wings made of a hybrid adaptive material. Here, hybrid materials are defined as laminated composites additionally reinforced with embedded shape memory alloy wires. As main novelties, the proposed model couples geometrical, material, and aerodynamic nonlinearities to the thermal dynamics of SMA wires undergoing Joule’s effects, thereby establishing a multi-physical nonlinear problem. Geometrical nonlinearities were taken into account via an FE model of a 2D Timoshenko’s beam experiencing large deformations. Material nonlinearities were incorporated by a semi-empirical micro-mechanical model that computes the properties of hybrid laminates. To complement, nonlinear aerodynamic effects were introduced via an unsteady strip theory method in the time-domain, along with a nonlinear stall model and an assumption of follower aerodynamic forces. A set of numerical aerothermoelastic cases was performed by assuming various layups and SMA temperatures, with the objective of tailoring the aeroelastic response of hybrid wings. These cases were shown to lead to a considerable reduction in both post-flutter oscillations and post-divergence amplitudes as the SMA temperature increases. The outcomes have indicated compelling evidences on the applicability of embedded SMAs for structural, shape or aeroelastic control of flexible wings.

Willmore function on curvatures of the curve-surface pair under mobius transformation

We find a geometric invariant of the curve-surface pairs on Willmore functions with the mean and Gauss curvatures. Similar to the work in [5,19], in this work, we define Willmore functions on curve--surface pair and give new characterizations about Willmore functions with necessary and sufficient condition with strip theory in Euclidean 3-space for the first time. In this paper Willmore function on curvatures of the curve-surface pair under Möbiüs transformation is provided invariant.

High-Frequency Vibration Control of Rotating Beam Based on Trailing-edge Flap

This study is to investigate an active control method, based on trailing-edge flap, in high-frequency vibration control of rotating blade beam. The structure is modeled as composite blade beam with circumferentially asymmetric stiffness configuration, which is based on analysis of the elastic flap-wise/twist displacements and incorporates the angle control of trailing-edge flap driven by a stepping motor. Aerodynamic expressions are based on a novel quasi-steady model suitable for trailing-edge flap. Based on a strip theory, the multi-body dynamic aeroelastic system is analyzed and solved. The active control is realized by Hœ algorithm using linear matrix inequality (LMI) design. This study is to investigate time-domain stability analysis and robust control method, realize displacement response analysis and robust performance analysis, and input signal display of trailing-edge flap angle. The optimization mechanism of LMI is to optimize uncertain robust performance parameters based on the selection of robust control parameters, so that the controlled displacement and control input are kept within reasonable ranges. The reliability and robustness of H» control algorithm based on LMI are verified by comparisons of the results of high-frequency vibration control using different robust performance parameters.

The Effect of Trim on Stability and Seakeeping of Tanker, Container, and Bulk Carrier

Stability and seakeeping are important factor that must be owned by a ship because it related to the safety of the ship, meanwhile the trim also affecting the ship operation. The study has a purpose to find out the impact of the trim to the stability and seaworthiness of the ship. The analysis is carried out on 3 types of ships, namely tankers, containers, and bulk carriers. A.N. Krylov method is using to calculate the stability, whereas the seakeeping is analysed by strip theory. Both of the results for stability and seakeeping are calculated by Maxsurf Software. Stability and seakeeping analysis was carried out when the ship is in even keel condition, trim by bow, and trim by stern in maximum and extreme condition. The results shows that the trim by stern of the ship can increased the ship stability rate by 0.5~5.4%. While the effect of trim on ship motions varies due to the differences characteristics of each ship. The results shows due to the trim impact by values of RAO’s, which some of ship motions have increased meanwhile for some ship motion have decreased of ship motion condition.

Formulations of Hydrodynamic Force in the Transition Stage of the Water Entry of Linear Wedges with Constant and Varying Speeds

There is an increasing need to develop a two-dimensional (2D) water entry model including the slamming and transition stages for the 2.5-dimensional (2.5D) method being used on the take-off and water landing of seaplanes, and for the strip theory or 2D+t theory being used on the hull slamming. Motivated by that, this paper numerically studies the transition stage of the water entry of a linear wedge with constant and varying speeds, with assumptions that the fluid is incompressible, inviscid and with negligible effects of gravity and surface tension, and the flow is irrotational. For the constant speed impact, the similitude of the declining forces of different deadrise angles in the transition stage are found by scaling the difference between the maximum values in the slamming stage and the results of steady supercavitating flow. The formulation of the hydrodynamic force is conducted based on the similitude of the declining forces in the transition stage together with the linear increasing results in the slamming stage. For the varying speed impact, the hydrodynamic force caused by the acceleration effect in the transition stage is formulated by an added mass coefficient with an averaged increase of 27.13% compared with that of slamming stage. Finally, a general expression of the hydrodynamic forces in both the slamming and transition stages is thus proposed and has good predictions in the ranges of deadrise angles from 5 deg to 70 deg for both the constant and varying speed impacts.

Unsteady Aerodynamic Modeling and Analysis of Load Distribution for Helicopter Rotor Blades

The complexity of the kinematics and aerodynamics of rotors is a challenging problem for achieving accurate modeling for prediction of rotor loads. The present paper describes an unsteady aerodynamic model based on strip theory for the prediction of local aerodynamic loads on helicopter blades in translational flights. The proposed model accounts aerodynamically for unsteady behavior, poststall, leading-edge suction, and, structurally, local elastic torsion. Also, the local pitching moment coefficient is calculated according to the local parameters of both aerodynamic characteristics and unsteady angle of attack. A case study with published experimental data is selected to validate the model for the same operating conditions. The case is the 7A rotor high-speed test (point 312) performed in the French Space Lab’s (ONERA) S1MA wind tunnel in Modane-Avrieux, France. The proposed model is capable of predicting, qualitatively, the variation in both local normal force and pitching moment coefficients. Computational solver results are compared with experimental results to qualitatively clarify the physical differences between them. The main conclusion is that the proposed model calculations generally reflect the same trends as the test data, providing confidence in the ability to increase the model’s fidelity in calculating the aerodynamic behavior of rotors.

Influence of skew angle on the random vibration response of propeller-shafting system induced by turbulent inflow

The influence of skew angle on the random vibration response of propeller induced by turbulent inflow is investigated. A three-step method is applied to compute the broadband force loaded on the propeller face and its random vibration response. Firstly, the broadband force spectrum induced by the turbulent inflow is calculated based on the strip theory. Then the transfer frequency response function matrix between face nodes and the transmitted forces are formed based on the finite element model. Finally, the transmitted forces to the bearings are computed by multiplying the broadband forces matrix to the transfer functions matrix. The random response of David Taylor Model Basin (DTMB) propellers 4381–4384 are calculated and compared. The influences of skew angle on the vibration response are discussed. It is shown that the influence of skew angle on the random response of propeller lies in two aspects. On the one hand, the increase of skew angle will slightly increase the broadband force near the blade passing frequency when the turbulence integral length is greater than blade spacing. On the other hand, the propeller rigidity is decreased with the increase of skew angle. Thus the force transmitted to bearings and blade vibration intensity is enhanced, which has the potential to increase structural noise radiated by the propeller and hull.

NUMERICAL PREDICTION OF VERTICAL SHIP MOTIONS AND ADDED RESISTANCE

Along with the development of computer technology, the capability of Computational Fluid Dynamics (CFD) to conduct ‘virtual computer experiments’ has increased. CFD tools have become the most important tools for researchers to deal with several complex problems. In this study, the viscous approach called URANS (Unsteady Reynolds Averaged Navier-Stokes) which has a fully non-linear base has been used to solve the vertical ship motions and added resistance problems in head waves. In the solution strategy, the FVM (Finite Volume Method) is used that enables numerical discretization. The ship model DTMB 5512 has been chosen for a series of computational studies at Fn=0.41 representing a high speed case. Firstly, by using CFD tools the TF (Transfer Function) graphs for the coupled heave- pitch motions in deep water have been generated and then comparisons have been made with IIHR (Iowa Institute of Hydraulic Research) experimental results and ordinary strip theory outputs. In the latter step, TF graphs of added resistance for deep water have been generated by using CFD and comparisons have been made only with strip theory.

CFD SIMULATION OF MOTION RESPONSES OF A TRIMARAN IN REGULAR HEAD WAVES

CFD has proved to be an effective method in solving unsteady Reynolds–Averaged Navier-Stokes (RANS) equations for analysing ships in free surface viscous flow. The research reported in this paper is intended to develop a better understanding of the parameters influencing high-speed trimaran motions responses. Variations of gridding system and time step have been investigated and reliability analysis was performed in solving the RANS equations. Different turbulence models were investigated, and the SST Menter K Omega turbulence model proved a more accurate model than Realizable K-epsilon model. In order to validate the CFD method, the results of the motions response of a high- speed trimaran are compared against a set of experimental and numerical results from a 1.6 m trimaran model tested in various head seas conditions. The results suggest that CFD offers a reliable method for predicting pitch and heave motions of trimarans in regular head waves when compared to traditional low speed strip theory methods. Unlike strip theory, the effect of breaking waves, hull shape above waterline and green seas are considered in CFD application. A wave resonance phenomenon was observed and wave deformation as a result of wave-current-wind interaction in CFD was identified as the main source of discrepancy. The results from this work form the basis for future analysis of trimaran motions in oblique seas for developing a better understanding of the parameters influencing the seakeeping response, as well as passenger comfort.

OPERATIONAL BEHAVIOUR OF AN OFFSHORE MULTIPURPOSE SUPPORT VESSEL IN THE EASTERN MEDITERRANEAN SEA

The objective of this work is to analyse the operational behaviour of an offshore multipurpose support vessel designed to operate in the Eastern Mediterranean Sea. First, the seakeeping analysis is performed in a regular wave condition for different heading angles estimating heave and pitch motions through the strip theory. After that, the effects of the vertical acceleration on the bow, occurrence of slamming or hydrodynamic impact of the hull on the surface of the water; wetted deck, occurrence or invasion of water on the deck of the vessel and propeller emersion, motion sickness and wave-induced additional resistance are analysed. The present analysis is extended in an irregular sea condition, and the estimated seakeeping criteria are compared to the acceptable levels. In defining the most suitable operational mode of the offshore support vessels, multi-criteria decision techniques and probabilistic approach are employed to perform an adequate evaluation of the seakeeping performance accounting for different hazardous events through the service life.

NON LINEAR ANALYSIS OF SHIP MOTIONS AND LOADS IN LARGE AMPLITUDE WAVES

A non linear time domain formulation for ship motions and wave loads is presented and applied to the S175 containership. The paper describes the mathematical formulations and assumptions, with particular attention to the calculation of the hydrodynamic force in the time domain. In this formulation all the forces involved are non linear and time dependent. Hydrodynamic forces are calculated in the frequency domain and related to the time domain solution for each time step. Restoring and exciting forces are evaluated directly in time domain in a way of the hull wetted surface. The results are compared with linear strip theory and linear three dimensional Green function frequency domain seakeeping methodologies with the intent of validation. The comparison shows a satisfactory agreement in the range of small amplitude motions. A first approach to large amplitude motion analysis displays the importance of incorporating the non linear behaviour of motions and loads in the solution of the seakeeping problem.

FULL-SCALE MOTIONS OF A LARGE HIGH-SPEED CATAMARAN: THE INFLUENCE OF WAVE ENVIRONMENT, SPEED AND RIDE CONTROL SYSTEM

To assess the behaviour of large high-speed catamarans in severe seas, extensive full-scale trials were conducted by the U.S. Navy on an INCAT Tasmania built vessel in the North Sea and North Atlantic region. Systematic testing was done for different speeds, sea states and ride control settings at different headings. Collected data has been used to characterise the ship’s motions and seakeeping performance with respect to wave environment, vessel speed and ride control system. Motion response amplitude operators were derived and compared with results from a two-dimensional Green function time-domain strip theory seakeeping prediction method. An increase of motion response with increasing vessel speed and a decrease with the vessel moving from head to beam seas was found. In higher sea states and headings ahead of beam seas an increasing influence of the centre bow on pitch motion damping was found. Significant motion RAO reduction was also found when the ride control system was active. Its effectiveness increased at higher speeds and contributed to heave and pitch motion RAO reduction. Predicted motion magnitudes with the time domain seakeeping code were consistent with the measured motion responses, but maximum heave was predicted at a rather higher frequency than was evident in the trials.

NUMERICAL AND EXPERIMENTAL STUDY OF THE PARAMETRIC ROLLING OF A FISHING VESSEL IN REGULAR HEAD WAVES


 
 
 The dynamic behaviour of a fishing vessel in waves is studied in order to reveal its parametric rolling characteristics. This paper presents experimental and numerical results in longitudinal regular waves. The experimental results are compared against the results of a time-domain non-linear strip theory model of ship motions in six degrees-of-freedom. These results contribute to the validation of the parametric rolling prediction method, so that it can be used as an assessment tool to evaluate both the susceptibility and severity of occurrence of parametric rolling at the early design stage of these types of vessels.
 
 

VISCOSITY IN SEAKEEPING

Application of strip theory for the prediction of ship motions in waves relies on sectional hydrodynamic coefficients; i.e. the added mass and damping coefficients. These coefficients apply to linearised problems and are normally computed for inviscid fluids. It is possible to account for viscosity but this cannot be done by the RANS equations, as in linear problems there is no room for turbulence. The hydrodynamic coefficients can include the effect of viscosity but this can be done rightly through the classic Navier–Stokes equations for laminar (non-turbulent) flows. For solving these equations commercial RANS software can be used, assuming no Reynolds stresses.

Applying Frequency-Domain Unsteady Lifting-Line Theory to Time-Domain Problems

Frequency-domain unsteady lifting-line theory is better developed than its time-domain counterpart. To take advantage of this, this paper proposes a method to transform time-domain kinematics to the frequency domain, perform a convolution, and then return the results back to the time domain. This paper demonstrates how well-developed frequency-domain methods can be easily applied to time-domain problems, enabling prediction of forces and moments on finite wings undergoing arbitrary kinematics. Results are presented for rectangular wings of various aspect ratios, undergoing pitch and heave kinematics. Computational fluid dynamics is used to test the effectiveness of the method in the Euler and low-Reynolds-number () regimes. Overall, the proposed method provides fast and reasonably accurate predictions of lift and moment coefficients, particularly in comparison to strip theory, which is commonly used for problems involving arbitrary kinematics.

On seakeeping capabilities evaluation of a large off-shore barge

Usual specially designed barges are involved in the off-shore operations that have to be evaluated by several criteria, inclusive of the seakeeping capabilities. The paper includes a comparative seakeeping study of two constructive versions for a large off-shore barge with a length of 189 m, having different breadths 40 m and 50 m. Both constructive versions are on the full cargo 23000 t condition. The seakeeping analyses are done with our own software DYN-OSC, developed by linear potential Lewis’s strip theory. The seakeeping studies are done in oblique irregular waves with a maximum height of 12 m and for the off-shore barge maximum operation speed of 7 knots. The results of this comparative study reveal the differences in the seakeeping operation capabilities for the two off-shore barge constructive versions.

Comparison of computational methods for hydrodynamic performance prediction of oscillating marine propulsors

The biomimicry of fish fins has been suggested as an efficient and low-noise approach to propulsion for remotely operated and autonomous underwater vehicles. Propulsion of this type is achieved through the use of fin-like propulsors that undergo oscillatory motions. Two computational approaches of differing fidelity and computational space/time requirements have been used to calculate thrust and efficiency of oscillating marine propulsors in order to determine the region where each method is most appropriate for design applications. The higher fidelity and computational cost method is an unsteady Navier–Stokes approach. The lower fidelity and computational cost method is a lifting-surface potential flow method supplemented with strip theory to account for viscous effects. In comparison with two-dimensional experimental results, both methods were able to accurately capture magnitudes and trends in light to moderate thrust conditions (CT<0.7) assuming no dynamic stall occurs. Under these operating conditions, computational savings for three-dimensional analysis on the order of 5,000 processor-hours are achieved by using the lower fidelity method, making it the more appropriate choice for design applications. At high thrust conditions (CT>0.7) and in conditions where dynamic stall effects are prevalent (αmax>20∘, low Strouhal numbers), the higher fidelity method is required to achieve sufficient predictive accuracy.