Practical Ship Hydrodynamics

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60 Practical Ship Hydrodynamics form and even, as a last resort, diameter). However, the previous steps are not repeated and this step can be treated as a self-contained module. 7. Check against classification society rules Known at this stage: all of the above (updated) A finite-element analysis is used to calculate the strength of the propeller under the pressure loading. The von-Mises stress criterion is plotted and inspected. As the analysis is still limited to a radially averaged inflow, a safety margin is added to account for the real inflow. In most cases, there is no problem. But if the stress is too high in some region (usually the trailing edge), the geometry is adjusted and Step 6 is repeated. The possible geometry modifications at this stage are minor and local; they have no strong influence on the hydrodynamics and therefore one or two iterations usually suffice to satisfy the strength requirements. 2.7 Propeller-induced pressures Due to the finite number of blades the pressure field of the propeller is unsteady if taken at a fixed point on the hull. The associated forces induce vibrations and noise. An upper limit for the maximum pressure amplitude that arises on the stern (usually directly above the propeller) is often part of the contract between shipyard and owner. For many classes of ships the dominant source for unsteady hull pressures is the cavitation on the propeller-blades. The effect of cavitation in computations of propeller-induced pressures is usually modelled by a stationary point source positioned in the propeller plane. To assure similarity with the propeller cavitation, the source must be given an appropriate volume amplitude, a frequency of oscillation, and a suitable position in the propeller plane specified by a radius and an angle. As the propeller frequency is rather high, the dominant term in the Bernoulli equation is the time-derivative term. If mainly fluctuating forces from propeller-induced hull pressures are of interest, the pressure is therefore usually sufficiently well approximated by the term t, where denotes the potential on the hull due to the perturbations from the propeller. If pressures and forces induced by a fluctuating source on solid boundaries are to be considered, the point source may be positioned underneath a flat plate to arrive at the simplest problem of that kind. The kinematic boundary condition on the plate is ensured via an image source of the same sign at the opposite side of the plate. For the pressure field on a real ship, this model is too coarse, as a real ship aftbody does not look like a flat plate and the influence of the free surface is neglected. Potential theory is still sufficient to solve the problem of a source near a hull of arbitrary shape with the free surface present. A panel method (BEM) easily represents the hull, but the free surface requires special treatment. The high frequency of propeller rpm again allows a simplification of the treatment of the free surface. It is sufficient to specify then: ⊲x, y, z D , t⊳ D 0 at the free surface z D . If the free surface is considered plane ( D 0), D 0 can be achieved by creating a hull image above the free surface and changing the sign for the singularities on the image panels. An image for the source that
Propellers 61 represents the cavity (again of opposite sign in strength) has to be introduced as well. The free surface can be considered in good approximation as a plane for low Froude numbers, such as typically encountered for tankers and bulkers, but it is questionable for moderate and high Froude numbers. A pronounced stern wave will have a significant effect on the wetted areas at the stern. The main problem of the above procedure is the reliability of calculated cavity volumes.
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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
Page 19 and 20: Introduction 9 margin may make a di
Page 21 and 22: Introduction 11 solution either. Ev
Page 23 and 24: Introduction 13 in naval architectu
Page 25 and 26: Introduction 15 ž Finite differenc
Page 27 and 28: Introduction 17 makes seakeeping pr
Page 29 and 30: Introduction 19 ship. Inner flow co
Page 31 and 32: Introduction 21 performed on workst
Page 33 and 34: Introduction 23 experts, while boun
Page 35 and 36: Introduction 25 two more decades be
Page 37 and 38: Introduction 27 Figure 1.3 A cylind
Page 39 and 40: Introduction 29 resolved by conside
Page 41 and 42: Introduction 31 ž LSOR (line succe
Page 43 and 44: Introduction 33 flow direction. CDS
Page 45 and 46: Introduction 35 equation, i.e. the
Page 47 and 48: 2 Propellers 2.1 Introduction Ships
Page 49 and 50: Propellers 39 ž rake iG The face o
Page 51 and 52: KT KQ h 10 . K Q K T Figure 2.3 Pro
Page 53 and 54: Propellers 43 methods or panel meth
Page 55 and 56: Propellers 45 This formula can be i
Page 57 and 58: Propellers 47 power. The earliest l
Page 59 and 60: Propellers 49 corrected subsequentl
Page 61 and 62: Propellers 51 flow computations are
Page 63 and 64: Propellers 53 occurs earlier, as ca
Page 65 and 66: Propellers 55 2.5.2 Open-water test
Page 67 and 68: Propellers 57 the traditional prope
Page 69: Propellers 59 (model/full-scale shi
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 and 114: Ship seakeeping 103 Re denotes the
Page 115 and 116: Ship seakeeping 105 the ship axis x
Page 117 and 118: Ship seakeeping 107 The procedure t
Page 119 and 120: Ship seakeeping 109 If several ω r
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a 0.015 0.010 0.005 0 1 2 3 4 5 Uc/
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Ship seakeeping 113 The (only stati
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Ship seakeeping 115 height H1/3 for
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Ship seakeeping 117 using data of B
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Ship seakeeping 119 for each strip
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Ship seakeeping 121 between near fi
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Ship seakeeping 123 wave length of
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Ship seakeeping 125 The elements of
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Ship seakeeping 127 4.4.3 Rankine s
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Ship seakeeping 129 to zero. Then t
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Ship seakeeping 131 for commercial
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Ship seakeeping 133 Since the spect
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Ship seakeeping 135 ž The ωj are
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Ship seakeeping 137 changing sea sp
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Ship seakeeping 139 The wave impact
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Ship seakeeping 141 pressure gauges
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v(t) h(x,t) y u(x,t) Figure 4.23 On
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Ship seakeeping 145 computations wi
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Ship seakeeping 147 4. Derive the p
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Ship seakeeping 149 The free consta
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5 Ship manoeuvring 5.1 Introduction
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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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