Practical Ship Hydrodynamics

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104 Practical Ship Hydrodynamics i.e. with a speed slower than celerity c, namely with group velocity cgr: c for deep water � 1 cgr D c 2 C � kH sinh⊲2kH⊳ for finite depth The linearized Bernoulli equation p C ∂ ∂t gz D p0 cgr D 1 2 and the wave potential give the difference pressure to atmospheric pressure at a point below the water surface (for deep water): p p0 D gz g Re⊲Ohe kz e i⊲ωt kx⊳ ⊳ p0 is the atmospheric pressure, the water density, z the depth of the point below the calm-water surface. The first term represents the hydrostatic pressure in calm water. The second term represents the pressure change due to the wave. As with all wave effects, it decays exponentially with depth. The pressure gradient ∂p/∂z is for the hydrostatic case equal to the specific weight of the fluid and causes a buoyant lifting force on the immersed body that equals the weight of the displaced water. This lifting force changes in a wave! The lifting force is lower in a wave crest, higher in a wave trough. This is called the Smith effect. The mechanical energy E per area of the water surface is composed of potential and kinetic energy. Let be the momentary elevation of the free surface. Then the potential energy (per area) is: Epot D g⊲ ⊳ D 2 1 2 g 2 The potential energy is positive both in wave troughs and wave crests and oscillates in time and space between 0 and gjOhj 2 . The time average is Epot D 1 4 gjOhj 2 The kinetic energy per area is: Ekin D � 1 1 2 ⊲v2x C v2z ⊳ dz D � 1 1 2 ω2 jOhj 2 e 2kz dz ³ � 1 0 ... dz D 1 4 gjOhj 2 Here the formulae for vx and vz have been used and in a linearization the wave elevation was substituted by 0. The kinetic energy is constant in time and space. The time-averaged total energy per area for a deep-water wave is then: E D 1 2 The average energy travels with cgr in the same direction as the wave. For finite-depth water the average energy remains the same but the kinetic energy oscillates also in time and space. The elementary wave was so far described in an earth-fixed coordinate system. In a reference system moving with ship speed V in the direction of gjOhj 2
Ship seakeeping 105 the ship axis xs under an angle of encounter (Fig. 4.3), the wave seems to change its frequency. The (circular) frequency experienced by the ship is denoted encounter frequency: y � � � ωe Djω kV cos jD� � ω m y s v c x s ω 2 V g cos x � � � � � Figure 4.3 Definition of angle of encounter Figure 4.4 illustrates this phenomenon. For course against the sea ( >90°) the encounter frequency is higher than the incident wave frequency ω. For course with the sea (
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Practical Ship Hydrodynamics
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Butterworth-Heinemann Linacre House
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3 Resistance and propulsion .......
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5.4.5 Interaction of rudder and shi
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Preface The first five chapters giv
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1 Introduction Models now in tanks
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Introduction 3 certain investigatio
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Introduction 5 there have been prop
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Introduction 7 is a material consta
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Introduction 9 margin may make a di
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Introduction 11 solution either. Ev
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Introduction 13 in naval architectu
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Introduction 15 ž Finite differenc
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Introduction 17 makes seakeeping pr
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Introduction 19 ship. Inner flow co
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Introduction 21 performed on workst
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Introduction 23 experts, while boun
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Introduction 25 two more decades be
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Introduction 27 Figure 1.3 A cylind
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Introduction 29 resolved by conside
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Introduction 31 ž LSOR (line succe
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Introduction 33 flow direction. CDS
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Introduction 35 equation, i.e. the
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2 Propellers 2.1 Introduction Ships
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Propellers 39 ž rake iG The face o
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KT KQ h 10 . K Q K T Figure 2.3 Pro
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Propellers 43 methods or panel meth
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Propellers 45 This formula can be i
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Propellers 47 power. The earliest l
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Propellers 49 corrected subsequentl
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Propellers 51 flow computations are
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Page 65 and 66: Propellers 55 2.5.2 Open-water test
Page 67 and 68: Propellers 57 the traditional prope
Page 69 and 70: Propellers 59 (model/full-scale shi
Page 71 and 72: Propellers 61 represents the cavity
Page 73 and 74: Resistance and propulsion 63 1. The
Page 75 and 76: Resistance and propulsion 65 3.1.2
Page 77 and 78: Figure 3.3 Double-body flow y Wave
Page 79 and 80: Resistance and propulsion 69 course
Page 81 and 82: Resistance and propulsion 71 limite
Page 83 and 84: Table 3.1 Recommended values for CA
Page 85 and 86: Resistance and propulsion 75 3.2.6
Page 87 and 88: P B ⋅ 10 3 (kW) 40 30 20 10 0 n P
Page 89 and 90: Resistance and propulsion 79 t is t
Page 91 and 92: Resistance and propulsion 81 are no
Page 93 and 94: 3.4 Simple design approaches Resist
Page 95 and 96: Resistance and propulsion 85 of the
Page 97 and 98: Resistance and propulsion 87 non-li
Page 99 and 100: Resistance and propulsion 89 resist
Page 101 and 102: Resistance and propulsion 91 (doubl
Page 103 and 104: Resistance and propulsion 93 only b
Page 105 and 106: Resistance and propulsion 95 resist
Page 107 and 108: Resistance and propulsion 97 1°. S
Page 109 and 110: Ship seakeeping 99 3. Addition of t
Page 111 and 112: Ship seakeeping 101 1. No recording
Page 113: Ship seakeeping 103 Re denotes the
Page 117 and 118: Ship seakeeping 107 The procedure t
Page 119 and 120: Ship seakeeping 109 If several ω r
Page 121 and 122: a 0.015 0.010 0.005 0 1 2 3 4 5 Uc/
Page 123 and 124: Ship seakeeping 113 The (only stati
Page 125 and 126: Ship seakeeping 115 height H1/3 for
Page 127 and 128: Ship seakeeping 117 using data of B
Page 129 and 130: Ship seakeeping 119 for each strip
Page 131 and 132: Ship seakeeping 121 between near fi
Page 133 and 134: Ship seakeeping 123 wave length of
Page 135 and 136: Ship seakeeping 125 The elements of
Page 137 and 138: Ship seakeeping 127 4.4.3 Rankine s
Page 139 and 140: Ship seakeeping 129 to zero. Then t
Page 141 and 142: Ship seakeeping 131 for commercial
Page 143 and 144: Ship seakeeping 133 Since the spect
Page 145 and 146: Ship seakeeping 135 ž The ωj are
Page 147 and 148: Ship seakeeping 137 changing sea sp
Page 149 and 150: Ship seakeeping 139 The wave impact
Page 151 and 152: Ship seakeeping 141 pressure gauges
Page 153 and 154: v(t) h(x,t) y u(x,t) Figure 4.23 On
Page 155 and 156: Ship seakeeping 145 computations wi
Page 157 and 158: Ship seakeeping 147 4. Derive the p
Page 159 and 160: Ship seakeeping 149 The free consta
Page 161 and 162: 5 Ship manoeuvring 5.1 Introduction
Page 163 and 164: Ship manoeuvring 153 ž yaw rate (r
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Ship manoeuvring 155 Table 5.2 Non-
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Ship manoeuvring 157 but also the i
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C y 1.50 1.25 1.00 1.75 0.85 0.80 0
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Ship manoeuvring 161 section. The l
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Ship manoeuvring 163 methods have b
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esistance R is proportional to spee
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Ship manoeuvring 167 accuracy, but
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Ship manoeuvring 169 the difference
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Ship manoeuvring 171 it is importan
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d, y 20° 10° 0° −10° −20°
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Distance Lateral deviation Length o
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Ship manoeuvring 177 also performed
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Ship manoeuvring 179 ž Rudders out
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ehind the leading edge (nose) is: c
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Ship manoeuvring 183 the rudder. In
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Ship manoeuvring 185 attack ˛ of n
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V a /V 0.4 0.3 0.2 0.1 V a /V 2.0 1
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Ship manoeuvring 189 ž Rudder with
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average between VA and V1: � �
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C L (V corr ≠ V A ) C L (V corr =
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Ship manoeuvring 195 hull influence
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Ship manoeuvring 197 - Estimate the
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Ship manoeuvring 199 rudder tip vor
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Ship manoeuvring 201 (1993) uses de
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Ship manoeuvring 203 ž Profiles wi
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Ship manoeuvring 205 The ship perfo
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6 Boundary element methods 6.1 Intr
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C ⊲t1n3 C n1t3⊳⊲t3 xxz C s3 x
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xx D ⊲ 3 x⊲x xq⊳ ⊳/r 2 xy D
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The velocity in the x direction is:
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∂ ∂z Boundary element methods 2
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Boundary element methods 217 2. Thr
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and ⊲ , ⊳ is: r D � ⊲x ⊳
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⊲1⊳ y D � d 2 y d r 2 f ⊲c
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Boundary element methods 223 the so
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2 0 8xz D 2 2 0 8xxz D 2 2 0 8xzz D
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Figure 6.9 Velocities induced by po
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It is convenient to write ϕ as:
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Boundary element methods 231 usuall
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Boundary element methods 233 From t
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with: Boundary element methods 235
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Numerical example for BEM 237 S is
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Numerical example for BEM 239 In ea
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Numerical example for BEM 241 Once
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Numerical example for BEM 243 ž Tr
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Numerical example for BEM 245 that
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Numerical example for BEM 247 is ch
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Table 7.1 Sign for derivatives of p
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z y Figure 7.5 Coordinate system us
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the contour (Fig. 7.5): n� iD1 i
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Numerical example for BEM 255 Let E
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Numerical example for BEM 257 At th
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Numerical example for BEM 259 This
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Numerical example for BEM 261 The i
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Numerical example for BEM 263 The e
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References Abbott, I. and Doenhoff,
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References 267 Morgan, W. B. and Li
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Index Actuator disk, 44 Added mass,
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Practical Ship Hydrodynamics

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