Modern container ship has large flare on the bow flare region for the purpose of accommodating more containers and their safe handling. This flare region on the forward part of the ship's hull surface experiences hydrodynamic load in actual operating conditions in waves. Traditionally, strength requirements in the bow flare region is evaluated based on the empirical formula proposed by various classification societies. Study reveals that a sizeable difference occurs in evaluated strength requirements by using classification society's empirical formula. Therefore, a direct calculation method is needed for evaluating the strength in the flare region in the design stage of hull surface. Inviscid potential-flow based numerical methods are used widely for evaluating wave resistance because of its' robustness and less computational time requirements. However, flow separation, generation of vortex and non-linear wake field occurs in real conditions, which are due to viscous effects. Therefore, improvement is necessary in numerical calculation methods. The possible candidate is the Reynolds averaged Navier-Stokes (RaNS) based computational fluid dynamics method (CFD).

The hydrodynamic load experienced by flare region on the forward part of the hull surface due to ship motions and wave action is termed as bow flare slamming in naval hydrodynamics. In actual operating conditions, bow part of the hull surface lifts completely out of water and hits the free surface. It implies the necessity of studying water entry of 2D sections before proceeding to 3D ship models. Also, the velocity of hull is not constant when it hits the free surface. Therefore, water entry of 2D sections of a 30 deg. wedge and ship is carried out with commercial numerical method called FLUENT(R) at variable velocity. Water entries of these two sections are carried out because of the availability of their drop test results. Incorporation of velocity variation is carried out by fitting 4th order polynomial as a function of impact time in the experimental velocity profile of the sections and take it as an input velocity in the numerical method. During numerical simulation, velocity profile is updated as each time step. In the simulation domain, the body is held stationary and flow past it is achieved by having a velocity inlet at the bottom of the domain. At the top of the domain, there is a pressure boundary set at atmospheric pressure to allow outflow of excess air. The sectional geometry is defined as wall boundary condition with no-slip and the far end of the domain is defined as wall boundary conditions with free slip. Geometrical symmetry about the centerline allowed the flow to be simulated in half of the domain. To avoid high skewness of the mesh, multi-block domain is used. Slam loads and local pressure at the measuring points of the experiments along the sectional surface for wedge and ship section at different instances are evaluated and compared with experiment and RaNS based method at constant entry velocity. It is observed that by incorporating velocity variation, well agreement with experiments for local pressure predictions both of wedge and ship sections are achieved than other RaNS based method. Also, comparison of slam loads with experiments for wedge and ship section show that effect of velocity variation for ship section is significant.

For analysis of 3D ship models, in-house RaNS based CFD code named WISDAM-X is used. Improvement and modification of WISDAM-X is carried out to overcome the limitations and applicability of the method in present analysis. As experimental results of slamming for the ship models KCS and SR108 are not available, numerical method is first validated with available experimental results. Validations are made for regular head and oblique waves with heave and pitch free conditions. Reasonably well agreement of computed results with experiments for ship motions motions in both oblique and head waves is achieved. Total drag does not compare well with experiments in head wave conditions. The possible reason is the difference in flexibility of towing the model during experiments and numerical method. Other researchers also compare their numerical methods for regular head wave cases with the same experimental results. Comparison for resistance data show similar manner like present numerical predictions.

Analysis of slamming on the bow flare region is carried out by visualization of flow field. Visualization of numerical results of WISDAM-X for slamming conditions is used. Simulation conditions for slamming events are achieved for a particular ship speed with ratio of wave length to ship length and wave amplitude to ship length in regular head waves for containership model named KCS. The instances for slamming are found. Contour of wave elevation and contour of pressure on hull surface during slamming events are analyzed to find the region on the flare part of the hull surface where slamming occurs with high pressure load. Fig. 1 shows the contour of pressure and its close-up view on the bow flare region during slamming events. Non-dimensional pressure (integrated pressure on the hull surface) value of 2.2 exists in the flare region during slamming events. Pressure is non-dimensionalized based on density of water, square of ship's speed. Flare region of KCS exposed to slamming is in between forward part (F.P.) and station no.9. This region is further divided into sections at an equal interval. Selected particular region and shape of different sections of that region is shown in Fig. 2. In present study, these sections are named as BF1, BF2, BF3, BF4, BF5 and BF6; here BF can be abbreviated as Bow Flare. Convex shaped bulb on the bottom part with low angled concave shape flare exists for section BF1 whereas high angle concave shaped flare angle with no bulb in the bottom part is for section BF6. Other sections in between BF1 and BF6, the proportion of bulb and flare angle is changing in such a way to form a continuous smooth surface.

Water entry of sections named BF1, BF2 and BF6 are carried out at variable velocity by using commercial finite volume based CFD code FLUENT(R). The reason for choosing these three sections is for their sectional shapes as bulb with lower flare, bulb with higher flare and flare without bulb. Numerical results are presented with position of free surface colored by volume of fluid function and velocity vector colored by velocity magnitude at instances. The instances are chosen based on BF1 to analyze the effects of bulb on water entry. The instances are counted initially after the section touching the free surface. The instances are when the flow past the bulb section and its immediate after, when flow is at the flare section and when the section completely goes into water. Fig. 3 shows the location of free surface colored by volume of fluid (VOF) function, contour of velocity magnitude for sections BF1, BF2 and BF6 at time instances 0.025sec.Visualization of numerical results of water entry of sections shows that two times more than that of initial entry velocity (2.453 m/s) is concentrated on bulb and flare for the section with bulb in all the instances considered. Due to presence of bulb in the bottom of the section, the contact surface area with water increases with time after initial impact of surface in the free surface. This increased area displaces additional mass of water, which is called added mass in naval architecture term. Added mass increases the momentum of the flow. Visualization of velocity magnitude contours of the sections at instances for WISDAM-X's computed results in slamming conditions made and shown in Fig. 4 for instance 0.675Te, here Te is one wave period. In this case, 10% more velocity magnitude than that of uniform flow is concentrated on the flare part.

Three dimensional shape effects on slamming are discussed between container ship models SR108 and KCS. The basic shape difference between SR108 and KCS is that SR108 has large flare (compare to KCS) with small bulb on the lower bottom of forward part of the hull surface and round shaped stern whereas KCS has bulbous bow on the forward part with transom stern. Numerical simulation for SR108 is conducted with the same slamming condition for KCS. Visualization of computed results shows that although SR108 experiences around 45% more pitch motions than that of KCS, no slamming occurs on the flare part of SR108. Amplitude of heave motions for both SR108 and KCS is almost equal.

Three important aspects as mentioned below are noticed in present study;

1.Slamming can happen in regular head waves for hull surface that has the bulbous bow on the forward part

2.Flare region does not experience high pressure in the highest wave elevation

3.Location of high pressure region in the flare part is under the free surface which cannot be visualized in towing tank experiments

Present analysis shows that numerical method WISDAM-X can be used as an effective tool for hull form improvement and numerical results can be used in structural strength analysis procedure especially for the bow flare region on the forward part of the hull surface.

Figure 1: Contour of pressure and its close-up view on the bow flare region during slamming instance for KCS

Figure 2: Selected particular region and shape of different sections of that region

Figure 3: Position of free surface and contour of velocity for sections BF1, BF2 & BF6 from 2D simulations at instance 0.025 sec.

Figure 4: Contour of velocity magnitude for sections BF1, BF2, BF3, BF4, BF5 & BF6 from 3D simulations at instance 0.675Te

大型コンテナ船では、荒天を航海中に船首フレア部の外板に想定以上の荷重を受け、損傷する事故が報告されている。これは船体動揺と波浪によってフレア部が海面に打ち付けられる、バウフレアスラミングによるものである。この荷重を予測する方法は確立されておらず、国際的な船級協会の間でも構造強度の規則に差が生じている。これまでの経験から、船首底部の強度は、十分なレベルに達している。一方、荒天時にのみ大荷重がかかるフレア部の強度を決める事は難しく、なんらかの手法でスラミング荷重を推定する事が必要とされている。本研究では、2次元の船体断面モデルの水面上落下試験を模擬する流体数値シミュレーションを行い、従来の解析の問題点を明らかにした。さらにピッチ、ヒーブ連成運動を伴う3次元船体の流体シミュレーションを行い、2次元解析の対比および3次元的なスラミングの特徴を調べた。

まず、2次元の楔型モデルおよび船首部断面モデルの落下試験は、スラミング現象解明の基礎実験として従来から行われている。流体数値解析による現象解明は、ストリップ法、境界要素法、有限体積法などが使われているが、計測結果を十分に再現する事が困難であった。これについて多くの研究者が、計測と数値解析の乖離を、実験で排除できなかった流場の3次元性によるものとしている。著者はこれに疑問を持ち、これまでの研究で仮定されていた等速度落下に代えて、実験から得られている加減速のプロファイルを流体シミュレーションに取り入れる検討を行った。本検討には、市販の汎用流体シミュレーションソフトウェアであるFLUENTを用い、得られた数値解析結果は、実験結果を良く再現する事となった。水面上落下問題では、多くの場合、大質量の落下模型を使用し、水面インパクト後も等速運動である事を仮定している。本研究の結果は、模型の加減速の効果を適切に考慮する事が必要である事を明らかにした。また後で検討するコンテナ船形状のバルブ付き船首部についても、選択した複数の断面について水面突入の数値解析を行った。この検討では、突入するバルブがバルブ側方の流体の上昇速度を加速する結果を得た。 周囲の流体よりも2倍程度に加速された流体塊は、バルブから剥離し、上方のフレア部に衝突するなど、3次元問題の理解につながる知見が得られた。

バウフレアスラミングの3次元問題では、研究室内で開発してきたReynolds averaged Navier-Stokes (RaNS)ソルバーであるwisdamコードを改良して用いた。本コードは、波浪中の非定常船体運動を任意の運動自由度で評価し、密度関数法による自由表面処理を特徴とする。解析対象とした船体形状は、SR108とKCSの2種類のコンテナ船型である。KCS船型の波浪中ピッチ&ヒーブ連成運動の推定精度については、Gothenburg 2010 Workshop on CFD in Ship Hydrodynamics(2010, Sweden)において、曳航水槽実験との比較検討が行われ、ピッチおよびヒーブの運動時刻歴の再現性が十分に高い事が確認された。

バウフレアスラミングの機構を見るため、特に船体運動と波浪外力の周期が同調する条件でのシミュレーションを実施し、流場の詳細検討を行った。水槽における波浪中運動試験では、流場の広範囲な情報を得る事は非常に困難である。このため、バウフレアスラミングが発生する状況での流場情報は貴重である。

本手法は、斜波条件、ロール条件でも解析が可能であるが、正面向かい波においてもフレア部の荷重集中が観測できた事から、この条件に絞った検討を行った。KCS船型は、大型化した船首バルブと船首フレアを併せ持つ現在の標準的なコンテナ船型の特徴を備えている。フレアスラミングが起きる状況の流場解析からは、バルブが下降する際に、バルブ左右の側面で流体が加速され、加速された流体塊は、周囲の水面よりも高速でフレア部に衝突する。また船体の前進に伴い、衝突箇所はバルブよりも後方の広がったフレア部となるため、流体塊の速度ベクトルと船体表面のなす角が大きく、荷重を強めている事が明らかになった。このような機構は、2次元断面を取り出した実験や数値解析には現れないものであり、より現実に近い3次元流体数値計算を適用した事で、はじめて明らかになったものである。また、観察された流体現象は、今後のバウフレア部強度の実験式や、認証ルール作りに重要な示唆を与えるものである。

本研究は、バウフレアスラミングにおける2次元、3次元の流体現象を解析し、その発生機構を説明したものである。これは学術的にも、実用的にも重要な知見を提供している。

よって本論文は博士(工学)の学位請求論文として合格と認められる。