Practical Ship Hydrodynamics

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54 Practical Ship Hydrodynamics VR is the absolute value of the local velocity at 0.7 of the propeller radius. VA is the inflow velocity to the propeller plane. Ap is the projected propeller area. Burill uses as reference pressure the atmospheric pressure plus the hydrostatic pressure at the propeller shaft: p0 D patm C gh The Burill diagram then yields limiting curves (almost straight) to avoid cavitation (Fig. 2.13). The curves have been transformed into algebraic expressions and are also included in propeller design programs. The upper limit for c yields indirectly a minimum Ap which yields (for Wageningen B-series propellers) approximately the expanded blade area: AE ³ Ap 1.067 0.229⊲P/D⊳ 2.5 Experimental approach 2.5.1 Cavitation tunnels Propeller tests (open-water tests, cavitation tests) are usually performed in cavitation tunnels. A cavitation tunnel is a closed channel in the vertical plane recirculating water by means of an impeller in the lower horizontal part. This way the high hydrostatic pressure ensures that even for reduced pressure in the tunnel, the impeller itself will not cavitate. The actual test section is in the upper horizontal part. The test section is provided with observation glass ports. The tunnels are designed to give (almost) uniform flow as inflow to the test section. If just the propeller is tested (with the driving shaft downstream), it is effectively tested in open water. Larger circulation tunnels also include ship models and thus testing the propeller in the ship wake. The ship models are sometimes shortened to obtain a thinner boundary layer in the aftbody (which thus resembles more the boundary layer in a large-scale model). Alternatively, sometimes grids are installed upstream to generate a flow similar to that of a full-scale ship wake. This requires considerable experience and is still at best a good guess at the actual wake field. Vacuum pumps reduce the pressure in the tunnel and usually some devices are installed to reduce the amount of dissolved air and gas in the water. Wire screens may be installed to generate a desired amount of turbulence. Cavitation tunnels are equipped with stroboscopic lights that illuminate the propeller intermittently such that propeller blades are seen always at the same position. The eye then perceives the propeller and cavitation patterns on each blade as stationary. Usual cavitation tunnels have too much background noise to observe or measure the noise making or hydro-acoustic properties of a propeller which are of great interest for certain propellers, especially for submarines or antisubmarine combatants. Several dedicated hydro-acoustic tunnels have been built worldwide to allow acoustical measurements. The HYKAT (hydroacoustic cavitation tunnel) of HSVA is one of these.
Propellers 55 2.5.2 Open-water tests Although in reality the propeller operates in the highly non-uniform ship wake, a standard propeller test is performed in uniform flow yielding the so-called open-water characteristics, namely thrust, torque, and propeller efficiency. The model scale for the model propeller should be the same as for the ship model in the propulsion tests. For many propulsion tests, the ship model scale is determined by the stock propeller, i.e. the closest propeller to the optimum propeller on stock at a model basin. The similarity laws (see section 1.2, Chapter 1) determine for geometrical and Froude similarity: � � � � VA VA D n Ð D s n Ð D m In other words, the advance number J D VA/⊲nD⊳ is the same for model and full scale. J has thus a similar role for the propeller as the Froude number Fn has for the ship. VA is the average inflow speed to the propeller, n the propeller rpm, and D the propeller diameter. Ð n Ð D is the speed of a point at the tip of a propeller blade in circumferential direction. The Reynolds number for a propeller is usually based on the chord length of one blade at 0.7 of the propeller radius and the absolute value of the local velocity VR at this point. VR is the absolute value of the vector sum of inflow velocity VA and circumferential velocity: VR D � V2 A C ⊲0.7 nD⊳2 Propeller model tests are performed for geometrical and Froude similarity. It is not possible to keep Reynolds similarity at the same time. Therefore, as in ship model tests, corrections for viscous effects are necessary in scaling to full scale. ITTC 1978 recommends the following empirical corrections: � c KTs D KTm 0.3 Ð Z Ð KQs D KQm C 0.25 Ð Z Ð D � � c � D rD0.7 rD0.7 Ð P Ð 1CD D Ð 1CD c is the propeller blade chord length at 0.7R, R the propeller radius, 1CD D CDm CDs is a correction for the propeller resistance coefficient with: � CDm D 2 Ð � CDs D 2 Ð 1 C 2 t c 1 C 2 t c � � 0.044 Ð R 1/6 n 5 R 2/3 � n � � Ð 1.89 C 1.62 log � c kp �� 2.5 Here t is the (maximum) propeller blade thickness, Rn is the Reynolds number based on VR, both taken at 0.7R. kp is the propeller surface roughness, taken as 3 Ð 10 5 if not known otherwise.
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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
Page 13 and 14: Introduction 3 certain investigatio
Page 15 and 16: Introduction 5 there have been prop
Page 17 and 18: 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
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Page 67 and 68: Propellers 57 the traditional prope
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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
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Ship seakeeping 105 the ship axis x
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Ship seakeeping 107 The procedure t
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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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