Wave Resistance Coefficient Research Articles

Study on resistance performance of hexagonal hull form with variation of angle of attack, deadrise, and stern for flat-sided catamaran vessel

Abstract The flat-sided hull vessel was designed with the purpose of simplifying hull production by eliminating the requirement for fairing, bending, and assembly of curved panel lines. Nevertheless, implementing the flat hull concept may marginally increase the hull resistance. The objective of the study is to investigate the impact of the hexagonal hull concept on resistance characteristics when altering the deadrise angle, angle of attack, and stern angle. Additionally, the resistance performances of the proposed hexagonal hulls were compared to evaluate the influence of the hull design geometry parameter. The contribution of this work is to identify the configuration of the design parameters to achieve an ideal level of resistance in a hexagonal catamaran hull design. The findings indicate that a greater angle of attack could potentially enhance wave generation and increase the resistance. Despite the increase in the wave resistance coefficient caused by the increment in deadrise angle, the overall resistance was reduced due to the significant reduction in wetted surface area resulting from the greater deadrise angle. As a result, the decrease in friction resistance was more pronounced than the increase in wave resistance. At last, the stern angle can cause a substantial oscillation in the curved line, resulting in a large increase in wave generation and overall resistance, particularly at high speeds.

Ship Forebody Optimization Based on Rankine Source Method

Abstract The shape of the ship’s forebody has a greater impact on the ship’s resistance, and a reasonable optimization of the forebody can play a role in reducing the propulsion power and optimizing the resistance performance. Under the premise of Rankine source method of potential flow wave theory as the theoretical basis, SHIPFLOW software is used as the calculation tool, and CAESES software is used as the optimization tool to study the optimal design of the ship with minimum wave resistance. In the optimization process, a real ship is taken as the object, and the optimal solution of the rising wave resistance coefficient is calculated with the rising wave resistance coefficient as the objective function and the ship speed and displacement as the constraints. The real ship is selected as the mother ship, the parameters of the hull shape are taken as the design variables, and the shape of the forebody is optimized by the Lackenby shift method, so as to obtain a ship shape with less wave resistance at the same speed and within the displacement limit. The results show that the improved ship shape has obvious effect of reducing the wave resistance, which verifies the effectiveness and feasibility of this method for ship shape optimization

Geometric Moment-Dependent Global Sensitivity Analysis without Simulation Data: Application to Ship Hull Form Optimisation

In this work, we propose and test a method to expedite Global Sensitivity Analysis (GSA) in the context of shape optimisation of free-form shapes. To leverage the computational burden that is likely to occur in engineering problems, we construct a Shape-Signature-Vector (SSV) and propose to use it as a substitute for physics. SSV is composed of shapes’ integral properties, in our case geometric moments and their invariants of varying order, and is used as quantity-of-interest (QoI) for prior estimation of parametric sensitivities. Opting for geometric moments is motivated by the fact that they are intrinsic properties of shapes’ underlying geometry, and their evaluation is essential in many physical computations as they act as a medium for interoperability between geometry and physics. The proposed approach has been validated in the area of computer-aided ship design with regard to the capability of global- and composite-SSV to reveal parametric sensitivities of different ship hulls for the wave-making resistance coefficient ( C w ), which is a critical QoI towards improving ship’s efficiency and thus decreasing emissions. More importantly, the longitudinal distribution of the volume below the ship’s floating waterline, which is measurable via geometric moments, has an impact on C w . Through extensive experimentation, we show a strong correlation between the sensitive parameters obtained with respect to SSV and those based on C w . Consequently, we can estimate parameters’ sensitivity with considerably reduced computational cost compared to when sensitivity analysis is performed with respect to C w . Finally, two design spaces are constructed with sensitive parameters evaluated from SSV and C w , and spaces’ quality and richness are analysed in terms of their capability to provide an optimised solution. • Geometric moments in Shape-Signature-Vector (SSV) are invariant to the translation and scaling. • The covariance decomposition approach is utilised to estimate the parameters’ sensitivity. • Geometry is segmented into different parts to construct a composite SSV. • A stronger correlation exists between wave-resistance coefficient ( C w ) and 4th-order SSV. • Designs optimised with parameters sensitive to C w and SSV have similar performance.

An improved radial basis function for marine vehicle hull form representation and optimization

The marine vehicle is one of the most important platforms in oceanic research and development. During the evolution of marine vehicle design, hull optimization is a key topic consisting of various steps such as hull deformation analysis, optimization algorithm selection and hydrodynamic performance evaluation. For hull deformation analysis, radial based function interpolation technique is usually applied with Wendland’s ψ3,1 function, which requires a great number of fixed points. To improve the optimization effect, this paper proposes a novel radial basis function for better support radius condition. According to the support radius condition, the effect of different deformation functions acting on hull form is studied. To verify the effectiveness of the improved radial basis function in marine vehicle hull optimization, a Series 60 hull is taken as the initial hull, and the Rankine source method is utilized as the solver to calculate the wave resistance coefficient. The Non-dominated Sorting Genetic Algorithm (NSGA) is applied to determine the optimal hull form at given speeds. By comparing the optimization results, the benefits and drawbacks of the improved radial basis function are analyzed. The results show that the number of fixed control points can be reduced by applying the improved radial basis function. When different deformation functions are acting on the marine vehicle hull, the improved radial basis function makes the gradient transition smoother. In the process of hull optimization, the wave resistance coefficient obtained by utilizing the improved function to deform the hull is smaller than that of using Wendland’s ψ3,1 function under different support radii.

Investigation of ship responses in regular head waves through a Fully Nonlinear Potential Flow approach

In this study, the hydrodynamic performance of a ship in terms of motions and resistance responses in calm water and in regular head waves is investigated for two loading conditions using a Fully Nonlinear Potential Flow (FNPF) panel method. The main focus is understanding the ship responses in a broad range of operational conditions. Comprehensive analyses of the motions and their correlation with the wave making resistance including their harmonics in waves are presented and compared against experimental data. The predicted motions compare well with experimental data but the resistance prediction is not quite as good. The natural frequencies for heave and pitch are estimated from a set of free decay motion simulations in calm water to provide a better insight into the ship behavior near resonance conditions in waves. Interestingly, in addition to the well known peak in the added wave resistance coefficient around wave lengths close to one ship length, a secondary peak is detected in the vicinity of wave lengths with half the ship length.

Two-Analytical Comparison on Force Measurements and The Wave Pattern

This work presents a comparison of two analytical methods on the components of resistance, transverse and divergent waves, and the profile and contour of the waves. Michell’s thin linearization theory is applied to estimate the wave resistance and analysis of the method compared to the solution of the wave resistance coefficient based on the Rankine source method. The hull of series 60 is utilized as the initial hull, and varying the shape of the bow to the mid-ship with the hull offset variable. Computation of the wave resistance coefficient at low Froude number (Fr<0.3) shows the results of the wave resistance from the thin ship theory are higher, but it gives a graphical agreement with the Rankine source method. The wave profile provides a very similar profile line for both of them. However, the thin ship theory does not establish a significant difference in the wave profile from the initial hull of the improved hull variation. Comparison of contour displays is presented in different versions of the wave contour. Still, it affords a good contour match on the initial hull and the results of hull variations from both methods. At high Froude number (Fr>0.7), the initial hull and variations in the hull have minimal effects with small differences in wave resistance, profile and contour.

Assessing the Interplay of Shape and Physical Parameters by Unsupervised Nonlinear Dimensionality Reduction Methods

The article presents an exploratory study on the application to ship hydrodynamics of unsupervised nonlinear design-space dimensionality reduction methods, assessing the interaction of shape and physical parameters. Nonlinear extensions of the principal component analysis (PCA) are applied, namely local PCA (LPCA) and kernel PCA (KPCA). An artificial neural network approach, specifically a deep autoencoder (DAE) method, is also applied and compared with PCA-based approaches. The data set under investigation is formed by the results of 9000 potential flow simulations coming from an extensive exploration of a 27-dimensional design space, associated with a shape optimization problem of the DTMB 5415 model in calm water at 18 kn (Froude number, Fr = 25). Data include three heterogeneous distributed and suitably discretized parameters (shape modification vector, pressure distribution on the hull, and wave elevation pattern) and one lumped parameter (wave resistance coefficient), for a total of 9000 x 5101 elements. The reduced-dimensionality representation of shape and physical parameters is set to provide a normalized mean squared error smaller than 5%. The standard PCA meets the requirement using 19 principal components/parameters. LPCA and KPCA provide the most promising compression capability with 14 parameters required by the reduced-dimensionality parametrizations, indicating significant nonlinear interactions in the data structure of shape and physical parameters. The DAE achieves the same error with 17 components. Although the focus of the current work is on design-space dimensionality reduction, the formulation goes beyond shape optimization and can be applied to large sets of heterogeneous physical data from simulations, experiments, and real operation measurements.

A 3D direct coupling method for steady ship hydroelastic analysis

Asides from the influence of incoming waves, ships can experience steady motions, such as rigid-body sinkage and trim motions, and flexible-body vertical bending motions, due to a constant forward speed even under calm water conditions. In this paper, a novel approach to analyze steady-ship hydroelasticity, particularly for the steady-ship motions and surrounding steady-wave disturbances, is proposed using a three-dimensional (3D) direct coupling method, based on a higher-order boundary element method (HOBEM) and a higher-order shell finite element method (FEM). Within the linearized framework, a solution method is proposed based on a two-step procedure, using two types of Neumann–Kelvin (NK) linear flow models for the fluid part and a virtual work equilibrium equation for the structural part. The first step is to compute a mean position wave-resistance problem using the modified NK equation, the second step is to solve a perturbed position wave-resistance problem, by employing a classical NK model and a virtual work equation based on the first step’s solution. Detailed mathematical formulation and numerical procedures are described, and a few numerical results are illustrated. These include both rigid and flexible steady-ship motions, Von-Mises stress distributions, and wave-resistance coefficients for Froude numbers ranging from 0.15 to 0.5. Furthermore, the numerical results obtained using the present direct coupling method and a modal-based one are compared.

Numerical Simulation of the Resistance and Self-Propulsion Model Tests1

Abstract The paper proposes a series of numerical investigations performed to test and demonstrate the capabilities of a Reynolds-averaged Navier–Stokes equation (RANSE) solver in the area of complex ship flow simulations. The focus is on a complete numerical model for hull, propeller, and rudder that can account for the mutual interaction between these components. The paper presents the results of a complex investigation of the flow computations around the hull model of the 3600 TEU MOERI containership (KCS hereafter). The resistance for the hull equipped with a rudder, the propeller open-water (POW hereafter) computations, as well as the self-propulsion simulation are presented. Comparisons with the experimental data provided at the Tokyo 2015 Workshop on Computational Fluid Dynamics (CFD) in Ship Hydrodynamics are given to validate the numerical approach in terms of the total and wave resistance coefficients, sinkage and trim, thrust and torque coefficients, propeller efficiency, and local flow features. Verification and validation based on the grid convergence tests are performed for each computational case. Discussions on the efficiency of the turbulence models used in the computations as well as on the main flow features are provided aimed at clarifying the complex structure of the flow around the ship stern.

Validation of potential flow method for ship resistance prediction

Considering the extensive use of numerical methods in naval design, a question about the accuracy numerical tools that could estimate the flow around the ship and which are the limitations of these tools for practical design applications. In this context, experimental test on scaled models play an important role in validation of numerical simulations. This work is dedicated to validation of the method used to calculate the non-linear potential free-surface flow around the ship. Global quantities, as total resistance, wave resistance coefficient, residual resistance coefficient are flow characteristics concentrated in a single value, and their validation provides a criterion for choosing the optimum hull. Validation of physical phenomena is done using the wave profile, the pressure distribution on the body or the free surface topology. Validations were developed by comparing experimental data published for benchmark test cases, results of the resistance test performed in ICEPRONAV towing tank, against the results of numerical calculation performed by the author. Numerical simulations were performed using the XPAN module of the SHIPFLOW program, dedicated to the calculation of non-linear potential free-surface flow. Therefore, in order that the validation to be consistent and not influenced by scale effects, all calculations have been performed for the model scale. For this purpose, numerical studies have been considered for three ship models with different complex geometries. Two of the three hulls, the 60 Series and the DTMB 5415, are benchmark tests, chosen due to a wide range of detailed experimental and numerical results. The other one is case study for which experimental measurements were carried out in the frame of research projects.

Minimum resistance ship hull uncertainty optimization design based on simulation-based design method

In the ship hull optimization design based on simulation-based design (SBD) technology, low precision of the approximate model leads to an uncertainty form of optimization model. In order to enable the approximate model with finite precision to maximize the effectiveness, uncertainty optimization method is introduced here. Wave resistance coefficient approximation model, built by back propagation (BP) neural network, is represented as a form of interval. Afterwards, a minimum resistance optimization model is established with the design space constituted by principal dimensions and ship form coefficients. Double-level nested optimization architecture is proposed: for outer layer, improved particle swarm optimization (IPSO) algorithm with learning factor improvement strategy is used to generate design variables, and for inner layer, modified very fast simulated annealing (MVFSA) algorithm is used to solve the objective function interval with uncertainty region. Cases calculation proves the effectiveness and superiority of uncertainty optimization method for ship hull SBD optimization design, thus providing a good way for finding optimal designs.

Study for the Development of an Optimum Hull Form using One Minus Prismatic

This study investigates the analysis algorithm for developing an optimum hull form with minimum wave resistance by using the practical application of one minus prismatic. In this algorithm the potential- based panel method was adopted to get the wave resistance coefficient as the objective function and SQP method was applied as an optimizer to get the optimum hull form. As an target ship, the series 60(CB=0.6) was taken into account and LBP(length between perpendiculars) of the ship was changed in the direction including a central parallel portion. To verity the validity of this study, the results of the numerical analyses were compared with experimental data.

Wave resistance defect in a planar flow over periodic reliefs

The dependence of the wave resistance coefficients for planar periodic reliefs on the similarity parameters is investigated. It is proved that the wave resistance coefficients of the infinite reliefs and their finite analogs in the case of the whole wave numbers coincide, whereas in the case of the fractional wave numbers they differ.

Hydraulic resistance to overland flow on surfaces with partially submerged vegetation

This study investigates numerically the characteristics of upscaling the Manning resistance coefficient (nt) for areas covered by partially submerged vegetation elements, such as shrub or tree stems. A number of high‐resolution hydrodynamic simulations were carried out corresponding to scenarios with different domain slopes (S), inflow rates (Q), bed roughness (nb), and vegetation cover fractions (Vf). Using simulations performed at fine space‐time scales, two methods were developed for computing the upscaled Manning coefficient, termed “Equivalent Roughness Surface (ERS)” and “Equivalent Friction Slope (EFS).” Results obtained with these two methods indicate that both yield highly correlated estimates of nt. The effects of four independent variables (Vf, S, Q, and nb) on nt were further investigated. First, as Vf increases, nt also grows. Second, two distinct modes of the relationship between S and nt for a fixed Vf and Q emerge: a positive dependence at low‐flow rates and a negative dependence at high‐flow rates. For a fixed Vf and S, two distinct modes of the relationship between Q and nt are also identified: a positive dependence at mild domain slopes and a negative dependence at steep slopes. A regression analysis shows that the two conflicting trends can occur depending on whether the variability of flow depth with respect to S (or Q) is greater than the ratio of h and S (or Q). Third, a rougher soil bed (i.e., larger values of nb) implies a higher resistance due to vegetation. Last, the study argues that nt increases as h increases and decreases as V increases. A generic regression relation that includes all four of the above variables and the difference nt − nb (i.e., the additional resistance due to partially submerged vegetation representing the sum of the form and wave resistances) was developed. The range of applicability of this relation is given by the following conditions: Vf ≤ 0.5, 0.1 ≤ S ≤ 1.1, and 0.0001 ≤ Q ≤ 0.01. The difference nt − nb computed from the developed regression relation was compared with estimates reported by five different studies. Furthermore, the simulated wave resistance coefficients were compared with those predicted from an equation in a previous study; the estimates were consistent in the range of experimental conditions for which the latter equation was developed. The relationship is sufficiently general and applicable to other flow conditions with partially submerged roughness elements.

자유수면을 관통하는 거위목 벌브를 가진 선박 주위의 포텐셜 유동해석

The Ranking source panel method was used to predict the flow phenomenon of a ship with a goose-neck type bulbous bow penetrating the free surface. The non-linearity of the free surface boundary condition was fully satisfied using an iterative calculation method, and the raised panel method was adopted to obtain a more stable solution at each iteration step. The panel cutting method was applied to generate a hull calculation grid at each iteration step, including the first step. At that time, the nose of the goose-neck type bulbous bow was divided by the free surface and the free surface panel was modified at each iteration step using the variable free surface panel method. Numerical calculations were performed to investigate the validity and efficiency of the applied numerical algorithm using the 3600 TEU container carrier. The computed wave resistance coefficients were compared with the experimentally achieved residual resistance coefficients.

선미부에 유동제어판을 부착한 선박에 대한 포텐셜 유동해석

In the paper the effect of a stern-plate attached to a ship was taken into account. The relationship between the trim angle of a ship and the wave-resistance coefficient induced by the a stern-plate was studied using the potential flow analysis method. Numerical algorithm was described using the panel method and the vortex lattice method(VLM) to simulate the flow phenomena around a ship. The non-linearity of the free surface boundary conditions were considered using the iterative method and the IGE-GMRES(Incomplete Gaussian Elimination-The Generalized Minimal RESidual) algorithm was adopted to solve the linear equation at each iterative step. Numerical calculations were carried out to investigate the validity of the adopted algorithm using KCS(KRISO 3600 TEU Container) hull. Possible cases for attachment of the plate were checked. The results showed that the numerical algorithm could be physically appropriate.

패널절단법 선체표면 패널생성을 위한 새로운 시도

In this paper a new hull-panel generation algorithm named 'Panel Cutting Method' was developed to solve the flow phenomena around a ship advancing on the free surface with a constant speed. In this algorithm the non-linearity of the free surface boundary conditions was taken into account using the iterative method and the raised panel was used at each iteration step. Numerical calculations were performed to investigate the validity of the developed algorithm using the series <TEX>$60(C_B=0.60)$</TEX> hull The wave resistance coefficients, the wave patterns and the wave heights were compared between the computed and the experimental results at Fn=0.25 and 0.316. The comparison showed good agreement between computation and experiment.

An Inverse Design Approach in Determining the Optimal Shape of Bulbous Bow With Experimental Verification

An inverse design algorithm in determining the optimal shape of the bulbous bow was developed by utilizing the Levenberg-Marquardt method (LMM) and B-spline surface control technique and basing it on a given design target, such as the desired wave height or wave resistance coefficient. A Wu-Chiang ferry used for domestic traffic in Taiwan was selected as the example ship for this study. Two different design objects, the bow wave profile and wave-making resistance, were considered the target functions. To verify the inverse design algorithm, towing tests were performed for two ship models: the original hull and the hull with optimal bulbous bow. Test results showed that the optimal bulbous bow designed by inverse algorithm improves the ship performance as expected.

Applied hydrodynamic wave-resistance computation by Fourier transform

An applied Fourier transform computation for the hydrodynamic wave-resistance coefficient is shown, oriented to potential flows with a free surface and infinity depth. The presence of a ship-like body is simulated by its equivalent pressure disturbance imposed on the un-perturbed free surface, where a linearized free surface condition is used. The wave-resistance coefficient is obtained from the wave-height downstream. Two examples with closed solutions are considered: a submerged dipole, as a test-case, and a parabolic pressure distribution of compact support. In the three dimensional case, a dispersion relation is included which is a key resource for an inexpensive computation of the wave pattern far downstream like fifteen ship-lengths.

Generation of solitary waves by forward- and backward-step bottom forcing

A finite difference method based on the Euler equations is developed for computing waves and wave resistance due to different bottom topographies moving steadily at the critical velocity in shallow water. A two-dimensional symmetric and slowly varying bottom topography, as a forcing for wave generation, can be viewed as a combination of fore and aft parts. For a positive topography (a bump), the fore part is a forward-step forcing, which contributes to the generation of upstream-advancing solitary waves, whereas the aft part is a backward-step forcing to which a depressed water surface region and a trailing wavetrain are attributed. These two wave systems respectively radiate upstream and downstream without mutual interaction.For a negative topography (a hollow), the fore part is a backward step and the aft part is a forward step. The downstream-radiating waves generated by the backward-step forcing at the fore part will interact with the upstream-running waves generated by the forward-step forcing at the aft. Therefore, the wave system generated by a negative topography is quite different from that by a positive topography. The generation period of solitary waves is slightly longer and the instantaneous drag fluctuation is skewed for a negative topography. When the length of the negative topography increases, the oscillation of the wave-resistance coefficient with time does not coincide with the period of solitary wave emission.