Steady Forward Speed Research Articles

On the Calculation of Propulsive Characteristics of a Bulk-Carrier Moving in Head Seas

The present work describes a simplified Computational Fluid Dynamics (CFD) approach in order to calculate the propulsive performance of a ship moving at steady forward speed in head seas. The proposed method combines experimental data concerning the added resistance at model scale with full scale Reynolds Averages Navier–Stokes (RANS) computations, using an in-house solver. In order to simulate the propeller performance, the actuator disk concept is employed. The propeller thrust is calculated in the time domain, assuming that the total resistance of the ship is the sum of the still water resistance and the added component derived by the towing tank data. The unsteady RANS equations are solved until self-propulsion is achieved at a given time step. Then, the computed values of both the flow rate through the propeller and the thrust are stored and, after the end of the examined time period, they are processed for calculating the variation of Shaft Horsepower (SHP) and RPM of the ship’s engine. The method is applied for a bulk carrier which has been tested in model scale at the towing tank of the Laboratory for Ship and Marine Hydrodynamics (LSMH) of the National Technical University of Athens (NTUA).

Green function of steady forward speed with ice cover

The Green function representing the potential flow generated by a source with unit strength advancing beneath an ice cover along a straight path at a constant speed is studied in the paper. The ice is modelled as elastic plate. The Green function satisfying the linearized covered-surface condition is derived and expressed in the form of a double Fourier integral with respect to wavenumber k and polar angle θ on the Fourier plane. The computing method of Green function is then proposed, the polar integral is first performed by using the theorem of residues, the resultant wavenumber integral is reformulated by removing the weak singularities and evaluated numerically. The Green function is shown to be suitable for the prediction of ice plate deflection. The given solution is analysed as a function of speed and ice thickness.

Stability analysis of high-order finite-difference discretizations of the linearized forward-speed seakeeping problem

A high-order finite-difference method solution of the linearized, potential flow, seakeeping problem for a ship at steady forward speed was recently presented by Amini-Afshar et al. [1,2]. In this paper, we provide a detailed matrix-based eigenvalue stability analysis of this model, highlighting the sources of instability and the effects of possible remedies. In particular, we illustrate how both boundary treatment and grid stretching are important factors which are not typically captured by a von Neumann-type analysis. The new analysis shows that when grid stretching is used together with centered finite difference schemes, the method is generally unstable. The source of the instability can in some cases be traced to an effective downwinding of the convective terms. Stable solutions can be obtained either by introducing upwind-biased schemes for computing the convective derivatives on the free-surface, or by application of a mild filter at each time-step. A second source of instability is associated with the treatment of the convective derivatives of the free-surface elevation at points close to the domain boundaries. Here it is necessary to consider whether the surrounding fluid points lie in an upwind or a downwind direction. For upwinded points, ordinary one-sided differencing can be used, but for downwinded points we instead impose a Neumann-type boundary condition derived from the body and free-surface boundary conditions. As an example application to complement those already given in [1,2], the method is applied to solve the steady wave resistance problem and comparison is made to reference solutions for a two-dimensional floating cylinder and a submerged sphere. Estimates of the wave resistance of the Wigley hull are also compared with experimental measurements.

Study on weakly nonlinear motions of ship advancing in waves and influences of steady ship wave

Time domain Rankine source method incorporated with HOBEM is developed and applied to solve motion of ship advancing with steady forward speed in waves. Steady ship wave (SW) potential is solved beforehand and is applied in both boundary conditions of free surface and ship hull for solving time domain ship motion. mj-terms in body boundary condition are computed with ship wave potential, time domain free surface conditions of radiation and diffraction problems are derived by use of ship wave potential. Since steady incoming flow has significant influences on ship motions, the two simplified steady flow models of uniform stream (US) and double body flow (DB) are also applied in time domain simulations for the comparative studies. In addition, nonlinear Froude-Krylov and restoring forces are used in ship motions equation.A numerical program is originally coded by Fortran and is used to solve motions of four types of hulls, which are Series60 ship, Wigley-1, S-175 container ship and a full formed tanker, at various speeds. The results of added mass, damping coefficients, wave exciting forces and ship motions are in generally good agreement with related model tests data. It shows that both hydrodynamic coefficients and ship motions obtained by SW and DB are apparently more accurate than by US. The accuracy of motions is improved for ships with complex and full formed hulls by the present method, which takes SW as steady flow. Numerical results of ship motions are affected by both the different free surface conditions due to different steady flow models and mj-terms, while added mass and damping coefficients are mainly influenced by mj-terms. More physical phenomenon are detailedly investigated and discussed.

Estimation of hydrodynamic forces and motion of ships with steady forward speed

The growing number of large ships demands predicting their optimum performance with respect to travel time, fuel efficiency and the safety of cargo and personnel in specified shipping routes. This can be achieved using efficient and easy to use numerical tools capable of predicting hydrodynamic loads on floating vessels with steady forward speed and solving their motion response in various wave conditions. A three-dimensional potential theory based code using the Green function method is developed with consideration of forward speed effects. The generalized coordinate system is used to allow motion response calculations with respect to any desired body coordinate system and a common quadrilateral meshing format. The formulation and calculation of added mass and damping coefficients at zero and infinite frequency in forward speed case has been also provided. A number of structures including simple geometries and full ship hull forms have been analyzed and validated against published theoretical, numerical and experimental results. The comparison results are found to be in excellent agreement. The theoretical formulation, numerical implementation and result comparisons are presented here.

Experiments with actively pitch-controlled and spring-loaded oscillating foils

Experiments with a horizontal foil undergoing harmonic heave motion while traveling at a steady forward speed were performed. The objective was to study different pitch strategies for maximizing the forward thrust. An oscillating foil can replace the rotating propeller as ship propulsor, or the foil can be mounted to the ship in order to create auxiliary thrust in waves. The latter was the motivation behind the experiments presented in this paper. An actively pitch-controlled foil was tested, where two vanes measured the inflow angle to the foil and a motor pitched the foil based on a specified control algorithm. The effect of varying the parameters in the pitch-control algorithm was tested in practice and is discussed here. A spring-loaded foil was also tested. The pitch motion of the spring-loaded foil is shown to produce higher thrust than that of the actively pitch-controlled foil tested. It was also found that the efficiency with spring-loaded pitch motion was higher than the efficiency with forced harmonic pitch motion leading the heave motion with a 90° phase angle.

Hydrodynamics of a submerged hydrofoil advancing in waves

The hydrodynamic problem of a hydrofoil travelling at constant speed in water waves has been investigated through velocity potential theory. The boundary conditions on the free surface have been linearized, and the effects are accounted for through the Green function. The overall problem is decomposed into the steady forward speed problem and periodic wave radiation and diffraction problems. Each of these problems is solved using the boundary integral equation over the hydrofoil surface together with a vortex sheet behind the trailing edge. The body surface boundary condition is imposed on its mean position. As a result the steady potential will contribute a well-known mj term to the body surface boundary condition on the radiation problem. The numerical difficulty in dealing with this term is effectively resolved through a difference method. The effects of the thickness on the wave radiation and diffraction are investigated. The applicability of various reciprocity relationships in this problem is discussed.

Increase of push-off propulsion to compensate heel strike loss during step-to-step transition is limited at faster gait speeds

The role of push-off propulsion as a major source of energy generation to compensate for heel strike collisions has been emphasized analytically and experimentally. The predicted increase of push-off forces with gait speeds, however, may be physiologically limited by intrinsic muscle mechanics. In this study, we examined whether the contribution of push-off propulsion to step-to-step transition is restricted with gait speed. Seven healthy young subjects participated in over the ground walking experiments. Ground reaction forces (GRFs) were measured at four different gait speeds ranging from self-selected to the maximum gait speed. The results showed that the vertical push-off force showed saturation, whereas the horizontal push-off forces proportionally increased with speed. The configuration of the trailing leg showed greater forward leaning during faster gait trials, which increases the horizontal push-off force without a significant increase in the total push-off forces. In contrast, both vertical and horizontal heel strike forces increased with speed. The lack of energy supplied by push-off to counter the heel strike collision loss during the double support phase was followed by an increase in the GRF work during the single support phase. These results imply that the intrinsic muscle mechanics limit the compensatory increase in the push-off force against the heel strike collision loss at faster gait speeds, which then leads to changes in the leg configuration to guarantee horizontal propulsion so as to maintain a steady forward gait speed.

Global wave load combinations by cross-spectral methods

This paper presents a cross spectral stochastic analysis methodology for the determination of the combination of global wave-induced dynamic loads by taking into account uncertainties associated with the wave heading, the joint probabilities of the wave environment and the correlations between different global wave-induced dynamic loads. The methodology considers the use of bivariate probability density functions (the cross-spectral probabilistic approach) or the co-variances of two random variables with their associated derivatives (the cross-spectral Hamilton's method) and assumes only rigid body hydrodynamic actions under steady forward speed conditions. The design extreme values of principal global wave-induced load components and their combinations for a container ship progressing in irregular seaways are predicted using these two cross-spectral methods together with the short-term and long-term statistical formulations. It is shown that in general terms both cross-spectral analysis methods can be employed to assess the effects of loads in ship design and reliability analysis. However, the cross-spectral Hamilton's method predicts slightly higher load combinations than the cross-spectral probabilistic approach.

Time domain three-dimensional fully nonlinear computations of steady body–wave interaction problem

Three-dimensional fully nonlinear waves generated by moving disturbances with steady forward speed without motions are solved using a mixed Eulerian–Lagrangian method in terms of an indirect boundary integral method and a Runge–Kutta time marching approach which integrates the fully nonlinear free surface boundary conditions with respect to time. A moving computational window is used in the computations by truncating the fluid domain (the free surface) into a computational domain. The computational window maintains the computational domain and tracks the free surface profile by a node-shifting scheme applied within it. An implicit implement of far field condition is enforced automatically at the truncation boundary of the computational window. Numerical computations are applied to free surface waves generated by Wigley and Series 60 hulls for the steady problem. The present numerical results are presented and compared with existing linear theory, experimental measurements, and other numerical nonlinear computations. The comparisons show satisfactory agreements for these hydrodynamic problems.

Experimental investigation of a fast monohull in forced harmonic motions

The paper presents the results of an experimental investigation of added masses and damping coefficients of a model of a fast monohull. A model of 4.5 m length between perpendiculars was constructed of fiber glass reinforced plastic (FRP) with four segments connected by a backbone. The backbone was instrumented with load cells at the positions of the cuts. This configuration, combined with load cells measuring the force exerted by the forced motion actuators, made it possible to obtain the hydrodynamic coefficients for each of the four hull segments. The investigation focused on the vertical motions. Thus, the experimental program included forced harmonic heave and pitch motions in calm water (no incident waves). Subtracting inertial and restoring forces from total measured forces, one obtained the hydrodynamic component, which then resulted in the hydrodynamic coefficients. The effects of steady forward speed on the radiation forces were investigated by conducting model tests at four forward speeds. Finally, nonlinear effects were assessed by conducting model tests for three amplitudes of forced heave and forced pitch motions.

Forces, moment and wave pattern for surface combatant in regular head waves

Unsteady resistance, heave force, pitch moment and free-surface elevations for DTMB 5512 at steady forward speed and in regular head waves are investigated with different measurement systems for a fairly wide range of test conditions in the IIHR towing tank. Test data are procured for validation of Reynolds-averaged Navier–Stokes computational fluid dynamics codes and for understanding the physics of unsteady ship hydrodynamics. The second part of the paper presents the measurement results and discussions.

Forces, moment, and wave pattern for surface combatant in regular head waves

A model-scale naval surface combatant, DTMB 5512, is studied experimentally in steady forward speed and regular head waves with the Iowa Institute of Hydraulic Research towing-tank facilities. Unsteady resistance, heave force, pitch moment and free-surface elevations are investigated with different measurement systems for a fairly wide range of test conditions. Test data is procured for validation of RANS computational fluid dynamics codes and for understanding the physics of unsteady ship hydrodynamics. In the first part of the two-part paper, details of data reductions, measurement systems and uncertainty assessment procedures are provided.

TIME-DOMAIN MOTION COMPUTATIONS OF TWIN- AND MONO­ HULL SHIPS IN HEAD SEAS

Wave exciting forces on a restrained body with steady forward speed in the time-domain were computed by the authors (1995). As one step further, radiation forces and ship motions in regular waves are computed in the present paper. With impulse response functions, the integral-differential equations of motions are solved in the time-domain. The same method is also applied to compute the radiation forces of a catamaran with forward speed. The results show that the time-domain computation for ship motions is particularly meaningful in the cases where the forward speed effect is considered. Added mass and damping coefficient of a catamaran with the Lewis-form demi-hull are computed for Froude numbers 0.15 and 0.30. Good agreements with experimental results for heave and pitch motions are obtained. A Wigley hull and a Series 60, C B = 0. hull are also adopted for the motion computation. The computed results for Froude number 0.20 are compared with experimental results.

The Forward Speed Diffraction Problem

This paper examines the theory and computational methods behind predicting the linear unsteady motion of a ship with steady forward speed in waves. The focus is on the wave exciting force impulse-response function as computed via the transient free-surface Green function. The linear equation of motion for a ship in waves was first written in a rational form, using the concept of the impulse-response function, by Cummins (1962). Some years later King et al (1988) added the corresponding wave exciting force in its appropriate convolution form. We extend this work by clarifying the definition of the impulsive incident wave in following seas, and show it to be easily computable. Continuing truncated calculations towards infinite time becomes especially important in following waves, and the method suggested by Bingham et al (1994) is employed here. A novel filtering scheme is also introduced to prevent short wave contamination of the solution. These developments allow calculations in following waves to be presented for the first time using this approach. The integral equation formulation of the linear seakeeping problem is reviewed in some detail, and the relevant equations derived. Transient Haskind relations for bodies with forward speed are also derived although, like their frequency-domain counterparts, these are only approximate. Computed, first-order exciting forces and response-amplitude operators for real ship geometries, in head and following seas, are presented that demonstrate the usefulness of the transient approach for the diffraction problem.