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Offshore Hydromechanics Intro, Hydrostatics, Stability

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Offshore Hydromechanics Intro, Hydrostatics, Stability Offshore Hydromechanics Module 1 Dr. ir. Pepijn de Jong 1. Intro, Hydrostatics and Stability Introduction OE4630d1 Offshore Hydromechanics Module 1 • dr.ir. Pepijn de Jong Assistant Prof. at Ship Hydromechanics & Structures, 3mE • Book: Offshore Hydromechanics by Journée and Massie • At Marysa Dunant (secretary), or download at www.shipmotions.nl 2 Introduction OE4630d1 Offshore Hydromechanics Module 1 • Communication via Blackboard • Exam (date&place may be subject of change!) • Formula sheet comes with exam, however... • Closed book • Don't forget to subscribe! 3 Introduction Overview Tutorial Lecture Online Assignments Week date time location topic date time location topic deadline topic 8:45- Intro, Hydrostatics, 2 11-Sep 3mE-CZ B 10:30 Stability 8:45- DW-Room Hydrostatics, 3 18-Sep 10:30 2 Stability 8:45- TN- Hydrostatics, 8:45- Hydrostatics, 4 23-Sep 25-Sep 3mE-CZ B Potential Flows 27-Sep 10:30 TZ4.25 Stability 10:30 Stability 8:45- 5 02-Oct 3mE-CZ B Potential Flows 10:30 8:45- TN- 8:45- 6 07-Oct Potential Flows 09-Oct 3mE-CZ B Real Flows 11-Oct Potential Flows 10:30 TZ4.25 10:30 8:45- TN- 8:45- 7 14-Oct Real Flows 16-Oct 3mE-CZ B Real Flows, Waves 18-Oct Real Flows 10:30 TZ4.25 10:30 8:45- 8 23-Oct 3mE-CZ B Waves 25-Oct Waves 10:30 9:00- TN- Exam 30-Oct Exam 12:00 TZ4.25 4 Introduction Assignments • Online on Blackboard • Automatic • Feedback included • 4 series with deadlines: • Hydrostatics & Stability • Potential Flow • Real Flows • Waves • First series and details follow later this week • Regular exercises and old exams on Blackboard 5 Introduction Topics of Module 1 • Problems of interest Chapter 1 • Hydrostatics Chapter 2 • Floating stability Chapter 2 • Constant potential flows Chapter 3 • Constant real flows Chapter 4 • Waves Chapter 5 6 Contents Lecture 1 • Introduction Module 1 done • Problems of interest (Chapter 1) next up • Hydrostatics (Chapter 2) • Floating stability (Chapter 2) 7 Learning Objectives Chapter 1 • Describe the field of application for hydromechanics in the offshore industry • Know the definition of ship motions 8 Chapter 1 Coordinate system and ship motions heave yaw sway pitch O,G surge roll 9 Contents Lecture 1 • Introduction Module 1 done • Problems of interest (Chapter 1) done • Hydrostatics (Chapter 2) next up • Floating stability (Chapter 2) 10 Learning Objectives Chapter 2 • To carry out and analyse hydrostatic and floating stability computations at a superior knowledge level, including the effect of shifting loads and fluids in partially filled tanks 11 Hydrostatics Naming Conventions Ship Dimensions L Length B Beam/width 푇 D Depth T Draft 퐷 퐿 퐵 12 Hydrostatics Hydrostatic pressure 푝0푑푥푑푦 푑푥 푑푦 푝0푑푥푑푦 + ρ푔푧푑푥푑푦 = 푝푑푥푑푦 푊 = ρ푔푧푑푥푑푦 푧 푝 = 푝0 + ρ푔푧 푝푑푥푑푦 13 Hydrostatics Hydrostatic pressure 푧 푝 = ρ푔푧 14 Hydrostatics Hydrostatic pressure Which one has the largest pressure on its bottom? 15 Hydrostatics Hydrostatic paradox 16 Hydrostatics Hydrostatic paradox 17 Hydrostatics Hydrostatic paradox 18 Hydrostatics Archimedes Law and Buoyancy • The weight of an floating body is equal to the weight of the fluid it displaces • Displacement of a floating body: The amount of fluid the body displaces often expressed in terms of mass or volume: g • Weight of displacement [N] • g Gravity accel. [m/s2] 9.81 • Density [kg/m3] 1025 • Volume of displacement [m3] 19 Hydrostatics Archimedes Law 'proof' 푧 • Replace volume by solid body: 푦 푥 푑푥 푑푦 Horizontal forces cancel 푧 푝 = ρ푔푧 → 퐹 = ρ푔푧푑푥푑푦 → 퐹 = ρ푔훻 20 Hydrostatics Archimedes Law and Buoyancy • The weight of an floating body is equal to the weight of the fluid it displaces • Displacement of a floating body: The amount of fluid the body displaces often expressed in terms of mass or volume: g • Weight of displacement [N] • g Gravity accel. [m/s2] 9.81 • Density [kg/m3] 1025 • Volume of displacement [m3] 21 Hydrostatics Archimedes Law and Buoyancy • Two ways of looking at buoyancy: 1. As distributed force Δ = ρ푔훻 2. The result of external (hydrostatic) pressure on the interfaces • Illustration: drill string suspended in a well with mud 22 Hydrostatics Example: drill string in mud Steel drilling pipe ρ푠 Sea bed Drill hole filled with drilling mud 퐿 ρ푚 Drilling mud 23 Hydrostatics 2 Consider buoyancy result of pressures 푧 퐿 24 Hydrostatics 1 Consider distributed buoyant force 퐿 푧 푇푒 = ρ푠푔퐴 퐿 − 푧 − ρ푚푔퐴 퐿 − 푧 Steel drilling pipe ρ푠 푇푒 = ρ푠 − ρ푚 푔퐴 퐿 − 푧 Drilling mud ρ푚 25 Hydrostatics 1 Consider distributed buoyant force 퐹표푟푐푒 0 ∧ 푝푟푒푠푠푢푟푒 푧 푇푒푚푢푑 퐿 푧 푇푒푎푖푟 푇푒푚푢푑 = ρ푠 − ρ푚 푔퐴 퐿 − 푧 Do you agree with this situation?? 푇푒푎푖푟 = ρ푠푔퐴 퐿 − 푧 26 Hydrostatics 2 Consider buoyancy result of pressures 푧 퐿 27 Hydrostatics 2 Consider buoyancy result of pressures 푧 퐿 푇 = ρ푠푔퐴 퐿 − 푧 − ρ푚푔퐴퐿 퐹 = ρ푚푔퐴퐿 28 푇푟푒푎푙푚푢푑 = ρ푠푔퐴 퐿 − 푧 − ρ푚푔퐴퐿 Hydrostatics 푇푒푚푢푑 = ρ푠 − ρ푚 푔퐴 퐿 − 푧 Comparison 푇푒푎푖푟 = ρ푠푔퐴 퐿 − 푧 퐹표푟푐푒 0 ∧ 푝푟푒푠푠푢푟푒 푇푟푒푎푙푚푢푑 푇푒푚푢푑 퐿 푧 푇푒푎푖푟 29 Contents Lecture 1 • Introduction Module 1 done • Problems of interest (Chapter 1) done • Hydrostatics (Chapter 2) done • Floating stability (Chapter 2) next up 30 Floating stability Definition • All properties that floating structures exhibit when perturbed from their equilibrium state • A ‘stable’ ship quickly restores its equilibrium when perturbation is removed • Often we wish for: • A stable working platform, i.e. a platform that does not move too much in waves • Is this the same property? • Do we always desire maximum stability? 31 Floating stability Example [1] 32 Floating stability Example [2] 33 Floating stability Example [3] 34 Floating stability Equilibrium states unstable indifferent stable negative neutral positive 35 Floating stability Equilibrium for floating structures vertical horizontal rotational 36 Floating stability Center of buoyancy and center of gravity B point about which first moment of submerged volume = 0 G point about which first moment of mass or weight = 0 37 Floating stability First moment of area/volume/mass/... 푦 푑푢 푢 푥1 푥2 푑푥 푥 38 Floating stability First moment of area/volume/mass/... Area: 푑퐴 = 푦푑푥 푥2 퐴 = 푦 푑푥 푑푢 푦 푥1 푢 푥1 푥2 푑푥 푥 39 Floating stability First moment of area/volume/mass/... Static moment: 푑푠푥 = 푢푑푢푑푥 푦 2 푑푆푥 = 푢 푑푢푑푥 = 1 2 푦 푑푥 푑푢 푦 표 푥2 푢 2 푆푥 = 1 2 푦 푑푥 푥 푥2 1 푥1 푑푥 푥 40 Floating stability First moment of area/volume/mass/... Static moment: 푑푆푦 = 푥푦푑푥 푥2 푆푦 = 푥 푦푑푥 푑푢 푦 푥1 푢 푥1 푥2 푑푥 푥 41 Floating stability First moment of area/volume/mass/... Center of area 푆 푦 = 푥 퐴 퐴 푆푦 푦 푑푢 푥 = 퐴 퐴 푢 푥1 푥2 푑푥 푥 42 Floating stability Center of buoyancy and center of gravity 퐺 퐷 퐵 푇 퐾퐵 =? 퐾퐺 =? 퐾 43 Floating stability Center of buoyancy and center of gravity Length: 퐵푑푒푐푘 퐻 푑푒푐푘 퐿 퐺 퐵푙푒푔 퐻푙푒푔 퐷 퐵 푇 퐵푓푙표푎푡 퐻푓푙표푎푡 퐾퐵 =? 퐾 퐾퐺 =? 44 Floating stability Stability moment φ 퐺 퐵 퐾 45 Floating stability Stability moment φ Emerged wedge 퐺 Immersed wedge 퐵 퐾 46 Floating stab. Stability moment φ 퐺 퐵 퐵φ 퐵φ′ 퐾 47 Floating stab. 푀, 푁φ Metacenter φ 푊 퐺 퐵 퐵φ ρ푔훻 퐾 48 Floating stab. 푀, 푁φ Metacenter Stability moment φ 푊 퐺 푍φ 퐵 퐵φ ρ푔훻 퐾 49 Floating stab. 푀, 푁φ Stability moment φ 푀푠 = 퐺푍φρ푔훻 푊 퐺푍φ = 퐺푁φsinφ 퐺 푍φ 퐵 퐵φ ρ푔훻 퐾 50 Floating stab. 푀, 푁φ Stability moment φ 푀푠 = 퐺푍φρ푔훻 푊 퐺푍φ = 퐺푁φsinφ 퐺 푍φ 퐵 퐵φ We need to find: ρ푔훻 퐾 퐺푀, 퐺푁φ Metacenter height 51 Floating stab. 푀, 푁φ Metacenter height 퐺 푍φ 퐵 퐵φ 퐾 GM = KB + BM - KG 52 Floating stability Metacenter height • KB en KG straightforward GM = KB + BM - KG • BM more complicated: • Determined by shift of B sideways and up • Three 'methods': • Initial stability: wall sided ship and sideways shift of B • Scribanti: wall sided ship and B shifts sideways and up • 'Real ship': determine GZ curve for actual shape 53 Floating stability Shift of mass or volume center 푦 Total mass: 푚 푝 퐺푝0 퐺0 퐺푚−푝 푥 54 Floating stability Shift of mass or volume center 푦 푝 푑 푝 퐺푝1 푝 ⋅ 푑 퐺 퐺 = 퐺푝0 0 1 푚 푏 푑 ∥ 퐺 퐺 퐺1 0 1 퐺0 푎 퐺푚−푝 푥 55 푁φ Floating stab. 푀 푀푁 = 퐵′ 퐵 BM, BN φ φ φ φ 퐵퐵φ′ 퐵푀 = tanφ 퐺 푧푒 푧푖 퐵 퐵φ 푧′푖 퐵φ′ 퐾 56 푁φ Floating stab. 푀 Working out on blackboard... 푀푁 = 퐵′ 퐵 BM, BN φ φ φ 푦 φ 퐵퐵φ′ 푦 퐵푀 = tanφ 퐺 푦 ∙ tanφ 푧푒 푧푖 푦 ∙ tanφ 퐵 퐵φ 푧′푖 퐵φ′ 퐾 57 Floating stability BM, BN 퐼푡 퐿 퐿 2 1 3 푦3푑푥 1 2 1 3 푦3푑푥 퐵퐵′ = 0 tanφ 퐵′ 퐵 = 0 tan2φ φ 훻 φ φ 2 훻 퐵퐵φ′ 퐼 1 퐼푡 퐵푀 = = 푡 푀푁 = tan2φ tanφ 훻 φ 2 훻 58 Floating stability Metacenter height • For small heeling angles (<5 to 10 degrees): Initial stability 퐼 퐺푀 = 퐾퐵 + 퐵푀 − 퐾퐺 = 퐾퐵 + 푡 − 퐾퐺 훻 • For slightly larger heeling angles (5 to 15 degrees): Scribanti 퐼 퐺푀 = 퐾퐵 + 퐵푁 − 퐾퐺 = 퐾퐵 + 푡 1 + 1 2 tan2φ − 퐾퐺 φ 훻 • Exact? • For large heeling angles (> 10 to 15 degrees) • Need of more accurate description: GZ curve 59 Floating stability Second moment of area: moment of inertia of area 푦 2 3 푑퐼푥푥 = 푢 푑푢푑푥 = 1 3 푦 푑푥 0 푥2 퐼 = 1 푦3푑푥 푦 푑푢 푥푥 3 푥1 푢 푥1 푥2 푑푥 푥 60 Floating stability Moment of inertia of water plane area 푦 퐿 3 퐼푡 = 1 3 푦 푑푥 0 0 퐿 푥 61 Floating stability Moment of inertia of water plane area 푦 퐿 3 0 퐼푡 = 2 1 3 푦 푑푥 퐿 푥 0 62 Floating stability Moment of inertia of water plane area 푦 퐵 2 0 퐿 푥 퐵 2 퐿퐵3 퐼 = 푡 12 63 Floating stability Moment of inertia of water plane area 푦 2b 0 푥 2a π 퐼 = 푎푏3 푡 6 64 Floating stability Moment of inertia of water plane area 푦 퐷 = 2R 푅 0 푥 π π 퐼 = 푅4 = 퐷4 푡 4 64 65 Floating stability Moment of inertia of waterplane area 푦 퐵 푑 퐿퐵3 Steiner's 퐼 = 2 + 2퐿퐵푑2 푡 12 theorem! 0 퐿 푥 퐵 −푑 66 Floating stability Moment of inertia of water plane area 푦 퐵 푑 Etcetera 0 퐿 푥 퐵 −푑 67 Floating stability Questions • How do submerged bodies remain stable? • How to increase stability? • Why shape semi-submersibles? [5] [4] 68 Sources images [1] Topside is skidded onto the HYSY229 launch barge, source: Dockwise Ltd.
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