Parallel Middle Body Research Articles

Algebraic Surfaces with Three Super Ellipses for Formation of Submarine Hull Surfaces

_ Definite stereotype for the outward look of submarines was worked out in the process of evolution. It is very difficult to take into account all inner and outside factors having an influence on the choice of submarine hull shape. Choosing either factor, designers’ model a great variety of outside lines. A light hull of a submarine is the outer nonwatertight hull which provides a hydrodynamically efficient shape. The pressure hull is the inner hull of a submarine; this holds the difference between outside and inside pressure. Closed algebraic surfaces with the main cross-sections in the form of three superellipses lying in three coordinate planes can help to select a submarine form during early-stage design. Having used a parallel middle body, one can extend considerably the choice of suitable shapes. In this paper, a method of modeling smooth compound closed algebraic surfaces that approximates the outside lines of a submarine is presented. The authors offer to form an outside submarine hull from six fragments of algebraic surfaces. The whole hull surface and its fragments are given by the same parametric equations. A method is illustrated in three examples, and it is realized easily in the form of a computer program. The initial data contain large quantities of constants, and it gives an opportunity to consider an infinitely large quantity of variants of submarine hull surfaces. Keywords submarine hull surface; superellipse; compound algebraic surface; buttock line; waterline; midship section

Design parameter sensitivity analysis for SWATH with minimum resistance at design and service speeds

Parametric hull form is efficient in geometric modification, and can help to obtain new hull forms with excellent hydrodynamic performance. Achieving parametric hull modeling depends on the reasonable definition of design parameters. Currently, in parametric hull modeling and optimization, the lack of an effective parameter selection method usually results in blindness and inefficiency in the hull design. This paper provides an automatic calculation framework for SWATH (Small Water-plane Area Twin Hull) resistance at different speeds. A fully parametric SWATH model is established to realize automatic geometric transformation. SOBOL (Sobol’ quasi-random sequence) algorithm is used for space sampling. The sensitivity analysis of all the parameters of SWATH for resistance is carried out. The correlation study between design variables and resistance is performed and the correlation coefficients of all design parameters are given and discussed. Among the parameters of SWATH, 4 design parameters, those control the longitudinal deformation of the bow of the underwater hull, the transverse deformation of the stern, the position of the parallel middle body of the strut, and the inclination of the strut, respectively, are more sensitive to the resistance. The suggestions for the parametric design of SWATH are given based on the sensitivity analysis and optimization results.

A high-order fractional step finite volume solver towards prediction of longitudinal distribution of cross-sectional ship roll hydrodynamics

A high-order fractional step finite volume solver is developed with a fractional step method along with an explicit fourth-order Runge–Kutta scheme in solving Navier–Stokes equations. And then the solver is applied to the prediction of the longitudinal distribution of cross-sectional ship roll hydrodynamics. The present development ameliorates the previous high-order finite volume solver [Ocean Eng 180:119–129] in solving the pressure–velocity coupled equation to further enhance its robustness on roll simulation. Firstly, accuracy of the solver is validated by shear-driven cavity flows and a series of roll motions with the available published numerical or experimental results. And its convergency is verified with a grid- and time step-dependence study. Then, a roll simulation on the mid-section of a KVLCC2 is performed; it embodies that the present solver can suppress the force oscillation than the previous one [Ocean Eng 180:119–129]. Finally, harmonic excited roll motions for several cross sections of a KVLCC2 are systematically investigated for cases of different roll amplitudes and frequencies. And longitudinal distributions of roll hydrodynamics and flow structures near the ship hull are analyzed. In results, the present solver enhances the robustness on roll simulation compared with the previous one [Ocean Eng 180:119–129]. Roll hydrodynamic coefficients culminate at sections of the parallel middle body, and decrease gradually towards fore and aft, and then they increase at the bow and stern.

Ship Loading Influence on the Slamming Impact of Typical Sections of an S-175 Container Ship

This paper investigates the influence of ship-loading condition on slamming during water entry. Three typical sections of the S-175 container ship, namely the bow, parallel middle body and stern, under three different loading conditions are studied. Full-sized models are established and simulated by commercial software LS-DYNA based on the explicit finite element method (FEM) using the arbitrary Lagrangian–Eulerian (ALE) algorithm. At first, validation is carried out by simulating the Wave Induced Loads on Ships Joint Industry Project II (WILS JIP-II) ship section entering the water and by verifying that the response is in good agreement with published experimental data. Then, nine different cases with three typical sections of the container ship and three different loadings, including the no-load (lightship weight), half-load and full-load weights of the ship, are investigated. Finally, the influence of the ship loading and sectional shape on the water impacts is analyzed and discussed. The present study is useful for the analysis of loading effects on ship slamming at the early stage of ship design.

A Computer Simulation Model for Thermal Forming of Ship and Offshore Structures

This paper presents a study on the line heating simulation process with an efficient "finite element analysis (FEA)" simulation model. The simulation model is conceived using concepts from three dimensional (3D) FEA of heat and mass transfer, plate theory and geometry, and implemented with commercially available software (Ansys*™ Mechanical APDL). The source of thermal energy is assumed to be "Gaussian" distributed heat flux, and we consider the temperature dependency of the material properties. The computer simulation model (CSM) is validated using the published experimental results. We study the discretization requirements for thick plates (>14 mm) that are commonly used in the shipbuilding processes and suggest guidelines for referential use in the industry. Also, we investigate the minimum time step size requirement during the cooling phase of the simulation process and based on the experimental numerical simulations, few efficient simulation practices have been coined, and we show that if they are followed then a noticeable gain in reduction of computational cost and time can be attained. We report extensive simulations of the estimated lines and then compare them with the target shape, and show a close agreement. Finally, our presented results are utilized to derive techniques for the improvement in existing FEA simulation models, and we show that the presented CSM is efficient for the application in ships and offshore structures for high bending of thick plates. 1. Introduction In ship and offshore building industries, geometric shapes are generated by forming of metal plates or sheets into simple or complex curvatures as demanded by the design requirements. Although, the doubly curved structures are used in offshore structures (e.g., spherical tanks and facades), in general, the offshore structures have planar, low curvature formations and developable surfaces, and the ships have a combination of developable and nondevelopable surfaces, low and high curvatures, and planar and nonplanar formations. In engineering sciences, a surface can either be "single curved (developable surface)" or "doubly curved (nondevelopable)" or a combination of them in various regions, e.g., doubly curved—bulbous bow and stern bulb, single curved—parallel middle body, combination—in the zones of transitions. In metal based industries, a single-curved surface can be manufactured with simple mechanical processes—bending, rolling, pressing, and/or a combination of them. For doubly curved surface, after the process of rolling and/or pressing, complex mechanical processes are needed:either the plate is shrunk along its longer edges using line/curve/pattern heating,or the plate is pressed against a base shape restricting its movement and then applying the high forces by pressing.

A multi-objective optimization design framework integrated with CFD for the design of AUVs

This paper presents a multi-objective optimization design framework that is integrated with the Computer Aided Design (CAD) for geometric variation and Computational Fluid Dynamics (CFD) software for hydrodynamic computations for the design of Autonomous Underwater Vehicles (AUVs). The optimization model utilizes the ‘Non-dominated Sorting Genetic Algorithm (NSGA-II)’. In the present model hull geometric parameters (i.e. length of nose (Ln), length of the parallel middle body (Lm), length of the tail (Lt), maximum diameter (Dmax), and two shape variation coefficients of nose (nn) and tail (nt)) are considered as the design parameters and minimization of viscous drag, and maximization of nominal wake fraction and total volume are considered as the objective functions for the integrated design approach. CFD software (Shipflow∗™) is used to evaluate the viscous drag and it is integrated with the CAD definition. The optimization framework NSGA-II is implemented in MATLAB∗∗™. Finally, we present a design example of an existing AUV Cormoran and show that the integration of NSGA-II with CFD and CAD is effective for AUV hull form design. Our reported results show that for the given bounds on the design parameters, the optimization design framework is able to produce more efficient hull forms than the existing design.

Hydrodynamic performance of distributed pump-jet propulsion system for underwater vehicle

A type of distributed pump-jet propulsion system (DPJP) is developed with two or four specially designed pump-jet pods located around the axisymmetric underwater vehicle body symmetrically. The flow field is numerically simulated by solving the RANS equations with the finite volume method. The computational method is validated by comparing the calculated hull resistances of the SUBOFF AFF-3 model and the open water performance of a ducted propeller with experimental data. The hydrodynamic performances of the DPJP with different axial or radial positions and numbers of pump-jet pods are obtained to analyze the interactions between the hull and the pump-jet pods. It is shown in the calculated results that the decrease of the distance between the pods and the hull leads to an increase both in the efficiency of the pods and the thrust deduction factor due to the effect of the stern wake. And, a negative thrust deduction factor can be obtained by locating the DPJP at the parallel middle body near the aftbody of the vehicle to improve the hydrodynamic performance of the DPJP. Besides, the increase of the number of pods will cause a remarkable decrease of the total propulsive efficiency of the DPJP with the pods mounted on the stern planes, while a small decline of the total propulsive efficiency of the DPJP is observed with the pods mounted on the parallel middle body.

축대칭체 주위 고 레이놀즈수 유동에 대한 수치해석

In this paper, numerical analysis based on the RANS equation and the Realizable turbulence model is carried out for flows around an axisymmetric body at three Reynolds numbers(, , ) and the numerical results are compared with experiments data. Computed velocity distributions agree well with experiments as the Reynolds number increases. Pressure distributions agree well with the results of the potential flow except the tail region but differ from experiments for the parallel middle body as well as tail region. Pressure gradients show a good agreement with those of potential flow and experiment except the tail region. Friction coefficients show that the numerical results generally are lower than the experimental results estimated from the measured velocity. The difference of friction coefficients between the calculation and the experiment increases with growing of a boundary layer.

Resistance Reduction by Increased Beam for Displacement-Type Ships

The resistance of a conventional hull with a parallel middlebody was compared with its modified version having no parallel middlebody. The modified hull was obtained by parabolizing the waterlines, that is, by extending the waterlines continuously about the middlebody, which results in an increased beam and elimination of shoulders. Numerical and experimental results suggest that there could be a significant reduction in the ship's EHP by parabolizing the waterlines at modest Froude numbers. Also, a theoretical justification based on Michell's integral is presented.

An Approach to Knowledge Acquisition for the Hull Form Design of Fishing Crafts

The problem of acquiring procedural knowledge for hull form design and construction of a knowledge base for hull form selection is addressed in this paper. An object oriented methodology involving creating classes, state diagrams and data flows for parametric hull form design was undertaken. An interactive graphical tool for the production of hull designs from a parent design was developed based on knowledge acquired from domain experts and the technical literature. Hull variation was accomplished by changing common design parameters including CB, CP, LCB and parallel middle body. Dependent and indendent variation of design parameters was allowed and the tool produced variants of the parent hull rapidly with a high degree of flexibility. The resulting forms then serve as input to a selection tool for constructing the knowledge base. The tool was based on rating grids and involved the elicitation of decision elements, traits and ratings from users to build a set of rules for selection. Sample selection sessions illustrate the applicability of the system.

Near-field behavior of a tip vortex

The near-field behavior of a tip vortex trailing behind a low aspect ratio wing, attached to an axisymmetric body, is investigated in this paper. This study was performed in a tow tank and involved the use of particle displacement velocimetry. Evolution of the tip vortex was studied by mapping its instantaneous lateral velocity at several consecutive axial locations. The axial velocity distribution was also measured. Experiments were repeated at various Reynolds numbers and incidence angles. Repeatability was also examined at the same conditions. The results indicate that roll-up is almost complete at the trailing edge and that less than 66% of the root circulation is entrained into the vortex. At Rec = 2.2 x 10s, the results are steady, and the spatially averaged tangential velocity agrees well with the existing models. At Rec<W5 the entire flow stucture, including the overall circulation, fluctuates from one experiment to the next. The tangential velocity profiles seem to be dominated by secondary vortices located primarily outside of the vortex core. Axial variations in the flow structure along the parallel middlebody, during the same run, are limited to the location of these secondary vortices. The vortex is observed to expand in the afterbody region, without a change in its total strength. For all but one case (Rec = 2.2 x 10s and a = 10 deg), there is a substantial axial velocity deficit within the vortex core near the trailing edge of the wing. At Rec <105, the axial velocity deficit increases with incidence angle and decreasing Rec.

Diffraction by a slender ship: uniform theory for head and oblique seas

The diffraction problem for a slender ship held fixed in short regular incident waves is solved by a matched-asymptotic-expansion method which is uniform with respect to all incident wave directions including head seas. Special inner solutions are employed which satisfy the Helmholtz equation in cross-sectional planes of the ship and are non-singular in head seas. The inner expansion of the outer solution is derived directly for all wave directions rather than as a composite. The case of a ship with a long parallel middle body is studied by means of a mixed numerical and analytical solution which explicitly exhibits the transition between the distinctive behaviours of head and oblique seas and distinguishes effects generated at the bow from those of the parallel middle body. Calculations of the pressure distributions and wave elevations along a ship are reported and compared with experimental measurements. The agreement between theory and experiment is generally good, especially at the upwave end of the ship and along the upwave side.

Geometrical characteristics of noses and tails for parallel middle bodies

Abstract : Two-parameter geometric systems are developed for noses and tails attached to parallel middle bodies in terms of independent polynomials. A new parameter is introduced--the rate of change of curvature with arc length at the juncture with the parallel middle body. Quadratic polynomials are considered for bodies of revolution and square root polynomials for symmetric two- dimensional bodies. Permissible ranges of the two adjustable parameters are obtained for selected geometrical constraints such as the presence of inflection points.

Geometrical characteristics of flat-faced bodies of revolution

Transition curves between flat faces and parallel middle bodies are developed as families of special polynomials termed cubic polynomials. The curves start and end with zero curvature to provide no discontinuities in curvature at the junction with the flat faces and the parallel middle bodies. Each cubic polynomial is a linear combination of independent polynomials controlled by adjustable parameters. Permissible ranges of the adjustable parameters are examined with respect to selected geometrical constraints such as inflection points. Nomenclature = polynomial coefficients = constant of integration = diameter of parallel middle body = diameter of flat face = integral defined in Eq. (31) — cubic polynomial ] = polynomial corresponding to k^ ] = polynomial corresponding to ki ] = polynomial corresponding to ko = curvature = rate of change of curvature with arc length = rate of change of curvature with arc length at x = I = rate of change of curvature with arc length at x = 0 = polynomial for restraining conditions = arc length = axial coordinate = axial length of forebody - normalized axial coordinate = radius = normalized radius = unspecified constant = adjustable conditions = unspecified constant = restraining conditions = unspecified constant = single differentiation with x = double differentiation with x = triple differentiation with x

A Study on the Bilge Keels

The eddy-making resistance due to the bilge keels was investigated in the previous papers. The effect of the ship form on the eddy-making resistance to the rolling of a ship hull is discussed in the present paper from the results of the systematic two dimensional model experiments. It is found that the eddy-making resistance to the rolling of a ship hull is large in the case of a rectangular section as much as the resistance due to the bilge keels and decreases rapidly as a radius of bilge circle increases, and that the resistance to a parallel middle body of a usual ship becomes negligibly small but its resistance to a fore or after section of a ship becomes a considerable amount.Next, the eddy-making resistance to the rolling of a ship hull is found to follow approximately the law of comparison by Froude from the results of the similar rhombic mod el experiment, and a method of approximate estimation of the resistance to the rolling of an actual ship is obtained.

A Simple Approach to Wind Tunnel Constriction Effect

THE paper reviews the problem of the influence of the walls of a closed tunnel in increasing the velocity in the neighbourhood of a model under test. It is shown that, for a perfect fluid, considerations of continuity suffice to establish an exact value of the mean interference velocity for any cross‐section of the tunnel. This mean interference velocity is expressed in terms of the perturbation velocity which would be caused by the same model in the absence of the walls. The linearized theory of subsonic compressible flow is applied and it is shown that the interference velocity for a small two or three dimensional model is increased in proportion to l/β3, where β=√(l—M2) and M is the Mach number. Interference caused by a body with a long parallel middle body, the influence of the wake from a model and of the boundary layer on the tunnel walls are briefly considered.

Systematic Model Experiments on the Cargo Ship Forms

To study the effects of fore-body form, longitudinal distribution of parallel middle body and breadth of cargo ships upon the resistance and mean annular wakes at the position of screw propeller, seventeen models are tested at Teishinsho Experiment Tank, and the results obtained are compared.

Studies in wave resistance: the effect of parallel middle body

1. If a ship is altered by inserting different lengths of parallel middle body between the same bow and stern, the main features of the variation in the wave resistance may be inferred from the principle of wave interference, and may be expressed in terms of a certain length, sometimes called the wave­-making length of the ship. The problem proposed for examination is the alteration in this length with varying length of parallel middle body at the same speed, and, further, its variation for a given ship at different speeds. Recent discussions have attracted renewed attention to this problem. It may be said that there are two approximations based on experimental results of various kinds obtained from ship models. On the one hand the wave-making length is supposed to be approximately independent of speed for a given ship, and to increase directly with the increase of parallel middle body; on the other hand, an empirical formula which agrees with experimental results over a certain range makes the length increase with velocity, the increase being one-quarter of the increase in the wave-length of regular transverse waves. The following contribution to the solution of this problem is mathematical, and necessarily deals with a simplified form of ship. It is true that one cannot compare absolute values of the wave resistance with those of actual ship models; but it has been shown in former studies of the dependence of wave resistance on ship form that one obtains a rather remarkable agreement, at least in the character of the results and in the positions at which changes occur. Leaving detailed discussion of the present extension till later, it may be stated that as regards the two approximate formulæ mentioned above the results are intermediate; after an initial decrease the wave-making length increases until velocity, but not so rapidly as in the quarter wave-length formula.

Societies and Academies

Societies and Academies

The wave-making resistance of ships: a study of certain series of model experiments

1. In a previous communication I proposed a formula for the wave making resistance of ships, and showed that it expressed certain general qualities of experimental results; further, notwithstanding the limitations of theory and the difficulty of interpretation of experimental data, a good numerical agreement was found in several cases with the published results of tank experiments on models when suitable numerical values were given to the coefficients in the formula. This paper records the results of a more systematic study of the numerical values of some of the coefficients, the data being taken from certain recent series of experiments; for the present the discussion is limited to those types of model whose resistance-speed curves show clearly the humps and hollows which are attributed to interference of wave-systems originating at the bow and stern. It has been remarked that although the mode of disturbance is different, the action of the bows of a ship may be roughly compared to that of a travelling pressure-point, and further, that the stern may he regarded in the same way as a negative pressure-point. This point of view originated in the well-known paper of W. Froude on the effect of the length of parallel middle body, and the theory was developed in a later paper by R. E. Froude; from an inspection of experimental results it was seen that the variations in magnitude and position of the oscillations were in directions which agreed with the above interpretation. On account of the lack of an adequate formula, the available data have not yet been examined numerically in any detail; the present investigation aims at supplying this in some measure. Section 2 is theoretical, with some necessary repetition of previous work; Sections 3 and 4 contain a numerical analysis of some available experimental curves. In Section 5 an attempt is made to estimate the effective horse-power of the "Turbinia," in order to illustrate certain points; while in Section 6 the limitations of the interference theory, in the conventional use of the term, are discussed in connection with the residuary resistance curves of finer-ended models.