Practical Ship Hydrodynamics

More documents

Recommendations

Info

190 Practical Ship Hydrodynamics propeller integrated in the main rudder. Thus besides auxiliary propulsion qualities, a directed thrust is available within the range of the main rudder angles. This increases the manoeuvring qualities of the ship especially at low speeds. ž Steering nozzle with rudder Steering nozzle may be fitted with flapped or unflapped rudders. This highly effective steering device is sometimes fitted to tugs, research or fishery ships. A fixed fin above the rudder improves the yaw checking stability as much as if the area of the fixed fin would be included in the movable rudder. However, for course-changing ability only the movable rudder is decisive. In fact, a fixed fin has a course-stabilizing property and increases, e.g., the turning circle diameter. A gap between the rudder top and the hull increases the rudder resistance at centre position due to the induced resistance of the oblique inflow of the propeller slipstream and the resistance of the rudder. Twin-screw ships may be fitted with spade or semi-balanced rudders, either behind the propellers or as midship rudders. For fast ships with a rudder arrangement on the centreplane cavitation problems are avoided, but this arrangement is less effective than rudders in the propeller slipstream especially on shallow water. 5.4.4 Interaction of rudder and propeller Rudders are normally placed in the propeller slipstream for the following reasons: ž A profiled rudder increases the propulsive efficiency by utilizing a part of the rotational energy contained in the propeller slipstream. ž In steady ahead motion, the rudder forces are typically more than twice those of a rudder outside of the propeller slipstream. ž Even for a stationary or slowly moving ship, substantial rudder forces may be generated by increasing the propeller rpm (especially to provide increased rudder effectiveness during transient manoeuvres). Because the rudder forces are proportional to the flow speed squared at the rudder, an accurate determination of the speed in the propeller slipstream at the rudder position is required to correctly predict rudder forces. According to the momentum theory of the propeller, the mean axial speed of the slipstream far behind the propeller is � V1 D VA 1 C CTh where CTh is the thrust loading coefficient: CTh D 8 Ð KT D 2 J T 2 V2 A AP VA is the mean axial speed of inflow to the propeller, AP the propeller area. The theoretical slipstream radius r1 far behind the propeller flows from the law of continuity, assuming that the mean axial speed at the propeller is the
average between VA and V1: � � 1 r1 D r0 1 C 2 VA � V1 Ship manoeuvring 191 Here r0 is half the propeller diameter D. Normally the rudder is in a position where the slipstream contraction is not yet completed. The slipstream radius and axial velocity may be approximated by (Söding (1982)): rx D r0 Ð 0.14⊲r1/r0⊳ 3 C r1/r0 Ð ⊲x/r0⊳ 1.5 0.14⊲r1/r0⊳ 3 C ⊲x/r0⊳ 1.5 and: Vx D V1 Ð � � r1 2 r Here x is the distance of the respective position behind the propeller plane. To determine rudder force and moment, it is recommended to use the position of the centre of gravity of the rudder area within the propeller slipstream. The above expression for rx is an approximation of a potential-flow calculation. Compared to the potential flow result, the slipstream will increase in diameter with increasing the distance x from the propeller plane due to turbulent mixing with the surrounding fluid. This may be approximated (Söding (1986)) by adding: 1r D 0.15x Ð Vx VA Vx C VA to the potential slipstream radius and correcting the slipstream speed according to the momentum theorem: � �2 r Vcorr D ⊲Vx VA⊳ C VA r C 1r The results of applying this procedure are shown in Fig. 5.19. Vcorr is the mean value of the axial speed component over the slipstream cross-section. The rudder generates a lift force by deflecting the water flow up to considerable lateral distances from the rudder. Therefore the finite lateral extent of the propeller slipstream diminishes the rudder lift compared to a uniform inflow velocity. This is approximated (Söding (1982)) (based on two-dimensional potential flow computations for small angles of attack) by multiplying the rudder lift determined from the velocity within the rudder plane by the correction factor determined from: � �f � �8 VA 2 D with f D 2 Ð 2 C d/c Vcorr Here VA is the speed outside of the propeller slipstream laterally from the rudder. d is the half-width of the slipstream. For practical applications, it is recommended to transform the circular cross-section (radius r C 1r) ofthe
Page 1 and 2:
Practical Ship Hydrodynamics
Page 3 and 4:
Butterworth-Heinemann Linacre House
Page 5 and 6:
3 Resistance and propulsion .......
Page 7 and 8:
5.4.5 Interaction of rudder and shi
Page 9 and 10:
Preface The first five chapters giv
Page 11 and 12:
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
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 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 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
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
Page 165 and 166: Ship manoeuvring 155 Table 5.2 Non-
Page 167 and 168: Ship manoeuvring 157 but also the i
Page 169 and 170: C y 1.50 1.25 1.00 1.75 0.85 0.80 0
Page 171 and 172: Ship manoeuvring 161 section. The l
Page 173 and 174: Ship manoeuvring 163 methods have b
Page 175 and 176: esistance R is proportional to spee
Page 177 and 178: Ship manoeuvring 167 accuracy, but
Page 179 and 180: Ship manoeuvring 169 the difference
Page 181 and 182: Ship manoeuvring 171 it is importan
Page 183 and 184: d, y 20° 10° 0° −10° −20°
Page 185 and 186: Distance Lateral deviation Length o
Page 187 and 188: Ship manoeuvring 177 also performed
Page 189 and 190: Ship manoeuvring 179 ž Rudders out
Page 191 and 192: ehind the leading edge (nose) is: c
Page 193 and 194: Ship manoeuvring 183 the rudder. In
Page 195 and 196: Ship manoeuvring 185 attack ˛ of n
Page 197 and 198: V a /V 0.4 0.3 0.2 0.1 V a /V 2.0 1
Page 199: Ship manoeuvring 189 ž Rudder with
Page 203 and 204: C L (V corr ≠ V A ) C L (V corr =
Page 205 and 206: Ship manoeuvring 195 hull influence
Page 207 and 208: Ship manoeuvring 197 - Estimate the
Page 209 and 210: Ship manoeuvring 199 rudder tip vor
Page 211 and 212: Ship manoeuvring 201 (1993) uses de
Page 213 and 214: Ship manoeuvring 203 ž Profiles wi
Page 215 and 216: Ship manoeuvring 205 The ship perfo
Page 217 and 218: 6 Boundary element methods 6.1 Intr
Page 219 and 220: C ⊲t1n3 C n1t3⊳⊲t3 xxz C s3 x
Page 221 and 222: xx D ⊲ 3 x⊲x xq⊳ ⊳/r 2 xy D
Page 223 and 224: The velocity in the x direction is:
Page 225 and 226: ∂ ∂z Boundary element methods 2
Page 227 and 228: Boundary element methods 217 2. Thr
Page 229 and 230: and ⊲ , ⊳ is: r D � ⊲x ⊳
Page 231 and 232: ⊲1⊳ y D � d 2 y d r 2 f ⊲c
Page 233 and 234: Boundary element methods 223 the so
Page 235 and 236: 2 0 8xz D 2 2 0 8xxz D 2 2 0 8xzz D
Page 237 and 238: Figure 6.9 Velocities induced by po
Page 239 and 240: It is convenient to write ϕ as:
Page 241 and 242: Boundary element methods 231 usuall
Page 243 and 244: Boundary element methods 233 From t
Page 245 and 246: with: Boundary element methods 235
Page 247 and 248: Numerical example for BEM 237 S is
Page 249 and 250: Numerical example for BEM 239 In ea
Page 251 and 252:
Numerical example for BEM 241 Once
Page 253 and 254:
Numerical example for BEM 243 ž Tr
Page 255 and 256:
Numerical example for BEM 245 that
Page 257 and 258:
Numerical example for BEM 247 is ch
Page 259 and 260:
Table 7.1 Sign for derivatives of p
Page 261 and 262:
z y Figure 7.5 Coordinate system us
Page 263 and 264:
the contour (Fig. 7.5): n� iD1 i
Page 265 and 266:
Numerical example for BEM 255 Let E
Page 267 and 268:
Numerical example for BEM 257 At th
Page 269 and 270:
Numerical example for BEM 259 This
Page 271 and 272:
Numerical example for BEM 261 The i
Page 273 and 274:
Numerical example for BEM 263 The e
Page 275 and 276:
References Abbott, I. and Doenhoff,
Page 277 and 278:
References 267 Morgan, W. B. and Li
Page 279 and 280:
Index Actuator disk, 44 Added mass,
show all

Practical Ship Hydrodynamics

Create successful ePaper yourself

Delete template?

Save as template?