Hull hydrodynamic optimization of autonomous underwater vehicles operating at snorkeling depth

Traditionally autonomous underwater vehicles (AUVs) have been built with a torpedo-like shape. This common shaping is hydrodynamically suboptimal for those AUVs required to operate at snorkeling condition near the free surface. In this case, the wave resistance associated to the wavy deformation of the sea surface induced by the motion of the platform is an important component of the drag. This work has investigated the optimum hull shape of an underwater vehicle moving near the free surface. Specifically a first-order Rankine panel method has been implemented to compute the wave resistance on a body of revolution moving close to the free surface. A simulated annealing algorithm was then employed to search those set of parameters defining the hull shape that minimize the wave resistance. The optimization was constrained to keep constant the total volume of the vehicle. The total drag of scaled models of the torpedo-like and resulting optimum shapes was measured in the naval tank of the University of Trieste. Measurements showed a smaller resistance of the optimized shape in the range of the considered Froude numbers.     

Design of ship's bow form by potential-based panel method

A surface panel method treating a boundary-value problem of the Dirichlet type with the free surface is presented to design a three-dimensional body corresponding to a prescribed pressure distribution. The free surface boundary condition is linearized with respect to the oncoming flow, and computed by four-point finite difference scheme. Sample designs for submerged spheroids and Wigley hull are carried out to demonstrate the stable convergence, the effectiveness and the robustness of the method. The design of a 5500TEU container carrier is performed with respect to reduction of the wave resistance. To reduce the wave resistance, calculated pressure on the hull surface is modified to have the lower fluctuation, and is applied as a Dirichlet type dynamic boundary condition on the hull surface. The designed hull form is verified to have the lower wave resistance than the initial one not only by computation but also by experiment.     

有航速浮体时域分析的混合边界元法

给出了一种联合瞬态格林函数和Rankine源进行有航速浮体时域水动力分析的混合——边界元方法。在三维混合边界元方法中,通过一个匹配面将流体域划分为内域和外域,在内域中使用Rankine源以模拟直壁或非直壁船体及线性或非线性自由面条件,在外域中使用瞬态格林函数以满足自由面条件和远方辐射条件。使用该方法计算了一个有航速潜没圆球的波浪力,和解析结果的比较证明了该方法的正确性。进一步给出了一个有航速Wigley船的水动力结果,计算结果稳定,没有外传波向内反射的现象发生。     

Simulation of free surface flow around a VLCC hull using viscous and potential flow methods

Numerical simulations have been carried out to determine the incompressible free surface flow around a VLCC hull form for which experimental results are available. A commercial viscous flow finite volume code using the two-phase Eulerian–Eulerian fluid approach and a potential flow code based on the Rankine source method have been used in this study. The simulation conditions are the ones for which experimental results exist. The shear stress transport (SST) turbulence model has been used in the viscous flow code. A tetrahedral unstructured grid was used with the viscous flow code for meshing the computational domain, while quadrilateral structural patches were used with the potential flow code for meshing the VLCC hull surface and the water surface around it. The results compare well with the available experimental data and they allow an understanding of the differences that can be expected from viscous and potential flow methods as a result of their different mathematical formulations, which make their complementary application useful for determining the total ship resistance.     

The effect of appendages on the hydrodynamic characteristics of an underwater vehicle near the free surface

An underwater vehicle typically has various appendages such as sail, rudders and hydroplanes. These appendages affect the hull hydrodynamic characteristics, including the resistance components and the form of the generated wave due to the motion of the vehicle near the free surface. The effect of the appendages on the hydrodynamic characteristics of an underwater vehicle near the free surface is studied. Initially the DARPPA SUBOFF submarine without the appendages is selected and hydrodynamic characteristics, including the friction resistance, viscous pressure resistance, wave resistance and shape of the created wave on the free surface are calculated for Froude numbers in the range of 0.128–0.84 and non-dimensional submergence depths 1.3, 2.2, 3.3 & 4.4. Then, by adding the appendages and comparing these two conditions, the effect of appendages is obtained. The results of computations indicate that the appendages cause a mean increase of about 16% in the total resistance. This increment is due to viscosity of fluid and also the interaction of the main hull with the appendages. There are no significant changes in the wave pattern and wave making resistance due to the presence of appendages.     

Simulation of Fully Nonlinear 3-D Numerical Wave Tank

A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order bouodary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.     

Hydrodynamic shape optimization by high fidelity CFD solver and Gaussian process based response surface method

A computational framework for hydrodynamic shape optimization of complex ship hull form is proposed and applied to improve the calm water performance of the KRISO Container Ship (KCS). The framework relies on three key features: a novel shape morphing method based on a combination of subdivision surfaces and free form deformations, a robust three dimensional viscous computational fluid dynamic solver based on the openFOAM open-source libraries and a Gaussian process-response surface method (GP-RSM) based on ordinary Kriging model which has been created to speed-up the evaluation of the quantity of interest (QoI) of the design process.The accuracy of the hydrodynamic solver is proven by comparing the obtained results against available experimental measurements. A preliminary sensitivity analysis on the mesh size has been carried out aiming at reducing the computational burden required by the CFD predictions. Three GP-RSMs have been trained relying on increasing number of hull designs. Each surrogate model has been cross-validated by both leave-one-out and k-fold techniques. The behaviours of these multi-dimensional surfaces have been analyzed in details by sampling the investigated design space with 10⁷ points according to a Full-Factorial algorithm, highlighting the regions of maximum deviation with respect to the resistance of the reference hull. The three optimum designs provided by the corresponding GP-RSM models have been verified by using high-fidelity CFD simulations with a refined mesh configuration. Calm water resistance, wave patterns and pressure distributions over the selected hull surfaces have been discussed in the light of the generated shape variations.     

A combined method for the hydrodynamic characteristics of planing crafts

The prediction of the total resistance of planing crafts at high speeds is very important. In this paper, a combined method is investigated for determining the hydrodynamic characteristics of planing crafts in the calm water. The study consists of a potential-based boundary element method (BEM) for the induced pressure resistance, the boundary layer theory for the frictional resistance and practical method for the spray resistance. The planing surface is represented by a number of elements with constant velocity potential at each element. The unknown-induced pressure is obtained by using the free surface elevation condition and the Kutta condition at the transom stern. Hydrodynamic-induced resistance and lift are determined by the calculated dynamic pressure distributions. The boundary layer analysis method is based on calculations of the momentum integral equation applied to obtain the frictional resistance. A particular practical approach is introduced to present the region of the upwash geometry for the spray. A numerical program has been developed for the present research and applied to the hull form of the craft. Four different hull forms of Series 62 model 4666 planing craft are presented. It is shown that the present combined method is efficient and the results are in good agreement with the experimental measurements over a wide range of volumetric Froude numbers.     

A numerical modeling of hydrodynamic characteristics of various planing hull forms

A numerical algorithm based on the boundary element method (BEM) is presented for predicting the hydrodynamic characteristics of the various planing hull forms. The boundary integral equation is derived using Green's theorem on the wetted body surface and the free surface. The ventilation function at the transom is estimated with Doctor's empirical formula. This function is defined as the transom zone free surface boundary condition. The combined boundary integral equation and modified free surface boundary condition are simultaneously solved to determine the dipole on the wetted hull surface and the source on the free surface. The method is applied to investigate three examples of planing hulls, which include flat-plates, as well as wedge-shaped and variable deadrise planing hulls. Their hydrodynamic characteristics are calculated for different speeds. Computational results are presented and compared with existing theories and experiments. On the whole, the agreement between the present method and the selected experimental and numerical data is satisfactory.     

An inverse hull design approach in minimizing the ship wave

The Levenberg–Marquardt Method (LMM) and a panel code for solving the wave-making problem are utilized in an inverse hull design problem for minimizing the wave of ships. A typical catamaran is selected as the example ship for the present study. The hull form of the catamaran is described by the B-spline surface method so that the shape of the hull can be completely specified using only a small number of parameters (i.e. control points). The technique of parameter estimation for the inverse design problem is thus chosen. The LMM of parameter estimation, which is the combination of steepest descent and Newton’s methods, has been proven to be a powerful tool for the inverse shape design problem. For this reason it is adopted in the present study.In the present studies, the inverse hull design method can not only be applied to estimate the hull form based on the known wave data of the target ship but can also be applied to estimate the unknown hull form based on the reduced wave height. The optimal hull forms of minimizing wave for a typical catamaran in deep water at service speed and at the critical speed of shallow water are estimated, respectively. Moreover, a new hull form with the combining feature of the optimal hull forms for deep water and shallow water is performing well under both conditions. The numerical simulation indicates that the hull form designed by inverse hull design method can reduce the ship wave significantly in comparison with the original hull form.     

Time-domain simulation of wave–structure interaction based on multi-transmitting formula coupled with damping zone method for radiation boundary condition

Based on the Rankine source, this paper proposed a time-domain method for analyzing the three-dimensional wave–structure interaction problem in irregular wave. A stable integral form of the free-surface boundary condition (IFBC) is employed to update the velocity potential on the free surface. A multi-transmitting formula, with an artificial wave speed, is used to eliminate the wave reflection for radiation condition on the artificial boundary. An effective multi-transmitting formula, coupled with damping zone method, is further used to analyze the irregular wave diffraction at the artificial boundary. We investigate hydrodynamic forces on floating structure and compare our solution to the frequency-domain solution. It is shown that long time simulation can be done with high stability and the numerical results agree well with the solution obtained under the frequency domain. The efficiency of the proposed multi-transmitting formula and the coupled methods for radiation boundary make them promising candidates in studying the irregular water wave problem in time domain.     

Prediction of added resistance of ships in waves

The prediction of the added resistance of ships in waves is a demanding, quasi-second-order seakeeping problem of high practical interest. In the present paper, a well established frequency domain 3D panel method and a new hybrid time domain Rankine source-Green function method of NTUA-SDL are used to solve the basic seakeeping problem and to calculate first order velocity potentials and the Kochin functions, as necessary for the calculation of the added resistance by Maruo's far-field method. A wide range of case studies for different hull forms (slender and bulky) was used to validate the applicability and accuracy of the implemented methods in practice and important conclusions regarding the efficiency of the investigated methods are drawn.     

Revisiting artificial air cavity concept for high speed craft

Artificial air cavity ship concept has received some interest due to its potential on viscous resistance reduction for high speed craft. Although a small number of ships were designed and built by using this concept, further research on resistance components is required to improve the understanding of artificial air cavity forms. A method based on tank testing with wave pattern measurements to identify resistance components was adopted in the current work. Resistance tests were conducted with two forms; first of which was conventional prismatic planing hull form with a deadrise angle of 10°, and second one was an alternative form with an artificially cavity which was tested both without any air injection, and with two different air injection rates.Total resistance, running trim, sinkage, supply airflow to artificial cavity, air pressure in the cavity and wave pattern generated by the hulls were measured. Frictional resistance was calculated from wetted surface area and compared with resistance component obtained by subtracting wave pattern resistance from the total resistance. Wave pattern spectrums with air cavity configurations were compared across the speed range.     

Linear and nonlinear interactions of surface waves with bodies by a three-dimensional Rankine panel method

Linear and second-order surface wave interactions with floating and bottom-mounted bodies of realistic geometry are simulated in the time domain by a three-dimensional Rankine panel method. The fundamental stability analysis governing the propagation of transient wave disturbances on a panel mesh distributed on the free surface is carried out from first principles. The radiation condition is enforced by a dissipative beach selected to coincide with an outer annulus of panels. The fundamental physics governing the wave energy absorption is presented and the beach attributes are selected and validated for the linear and second-order problems. Computations are presented of the linear and sum-frequency second-order forces on a single and multiple truncated circular cylinders, and very good agreement is found with benchmark computations. The accuracy and efficiency of this method render it a promising candidate for the study of complex nonlinear wave induced phenomena upon offshore platforms, like springing and ringing.     

Response Characteristics of Load on Vessels in Waves

Considering the requirement of direct design and fatigue test for ships and floating structures byuse of FEM technique,a computational procedure of spectral analysis for wave load on the hull surface is de-veloped in this paper.The response of hydrodynamic pressure on the body surface to a designated sea state forships and floating structures is calculated by use of the revised strip method with the hull bound perturbationflow concept.The spectral function of wave load for the defined point on the body surface can be determinedfrom the Wiener-Khinhin theorem and the characteristic load value can be also obtained from spectral mo-ment analysis.A container ship is taken as a computational example and the sample of wave load with a cer-tain probability and corresponding encountered frequency is provided.     

Neumann-Michell theory-based multi-objective optimization of hull form for a naval surface combatant

A numerical multi-objective optimization procedure is proposed here to describe the development and application of a practical hydrodynamic optimization tool, OPTShip-SJTU. Three components including hull form modification module, hydrodynamic performance evaluation module and optimization module consist of this tool. The free-form deformation (FFD) method and shifting method are utilized as parametric hull surface modification techniques to generate a series of realistic hull forms subjected to geometric constraints, and the Neumann-Michell (NM) theory is implemented to predict the wave drag. Moreover, NSGA-II, a muti-objective genetic algorithm, is adopted to produce pareto-optimal front, and kriging model is used for predicting the total resistance during the optimization process to reduce the computational cost. Additionally, the analysis of variance (ANOVA) method is introduced to represent the influence of each design variable on the objective functions. In present work, a surface combatant DTMB Model 5415 is used as the initial design, and optimal solutions with obvious drag reductions at specific speeds are obtained. Eventually, three of optimal hulls are analyzed by NM theory and a RANS-based CFD solver naoe-FOAM-SJTU respectively. Numerical results confirm the availability and reliability of this multi-objective optimization tool.     

Computation of wave-making resistance of a catamaran in deep water using a potential-based panel method

This paper presents a potential-based boundary element method for solving a nonlinear free-surface flow problem for a Wigley catamaran moving with a uniform speed in deep water. Since the interior flow of each monohull of the catamaran is different from the exterior flow, both monohulls must be considered as lifting bodies. The pressure Kutta condition is imposed at the trailing-edge of the lifting body by determining the dipole distribution, which generates required circulation on the lifting part. The effects of wave interference and hull separation on the hydrodynamic characteristics of the catamaran hull are analyzed and the validity of the computer scheme is examined by comparing the wave resistance with the numerical results of others. The present method could be a useful design tool for screening the suitable combinations of hull parameters and hull spacing at the preliminary design stage of catamaran hull.     

Numerical and experimental study on seakeeping performance of ship in finite water depth

Vessels operating in shallow waters require careful observation of the finite-depth effect. In present study, a Rankine source method that includes the shallow water effect and double body steady flow effect is developed in frequency domain. In order to verify present numerical methods, two experiments were carried out respectively to measure the wave loads and free motions for ship advancing with forward speed in head regular waves. Numerical results are systematically compared with experiments and other solutions using the double body basis flow approach, the Neumann-Kelvin approach with simplified m-terms, and linearized free surface boundary conditions with double-body m-terms. Furthermore, the influence of water depths on added mass and damping coefficients, wave excitation forces, motions and unsteady wave patterns are deeply investigated. It is found that finite-depth effect is important and unsteady wave pattern in shallow water is dependent on both of the Brard number τ and depth Froude number F_h.     

Wall effect of underwater explosion load based on wave motion theories

Owing to the existence of the flow field boundary, the shock wave load near the boundary is different from the freefield shock wave load. In the present paper, the hull plate load subjected to underwater shock wave is investigated based onwave motion theories; in addition, the experimental study of the hull plate load is carried out. According to the theoreticalanalysis of the hull plate pressure, we find that the hull plate pressure oscillates repeatedly and decays rapidly with timepassing, the maximum hull plate pressure is 2/（1＋n） times the maximum free field pressure, where n is the ratio ofimpedance, and the impulse is much smaller than the free field impulse. Compared with the experimental study, thetheoretical results agree well with the experimental data.     

Hydrodynamic optimization of ship hull forms

An extremely simple CFD tool is used to compare the calm-water drags of a series of hull forms and to define ‘optimized’ monohull ships for which the total (friction+wave) calm-water drag is minimized. The friction drag is estimated using the classical ITTC formula. The wave drag is predicted using the zeroth-order slender-ship approximation. Comparisons of theoretical predictions and experimental measurements for a series of eight hull forms show that—despite the extreme simplicity of the method that is used here to estimate the friction drag and the wave drag—the method is able to rank the drags of a series of hull forms roughly in accordance with experimental measurements. Thus, the method may be used, with appropriate caution, as a practical hull form design and optimization tool. For purposes of illustration, optimized hull forms that have the same displacement and waterplane transverse moment of inertia as the classical Wigley hull, taken as initial hull in the optimization process, are determined for three speeds and for a speed range.