Question 1a. Values of forward speed, propeller thrust and torque

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ENGR 4011 Resistance & Propulsion of Ships
Assignment 4: 2016
Question
1a. Values of forward speed, propeller thrust and torque measured during a propeller open water
performance test are presented in the table below. The model propeller was 0.21 meters in diameter
and tested at a constant shaft speed of 10 rps. The water temperature was 16.4°C. For each
measurement, calculate the following: KT, KQ, CTH, ηo, JA, and Rn0.75. Plot KT-10KQ-ηo-JA curves for the
propeller. Note that c0.75 is 0.093m at model scale.
Solution
D
0.21
n
10
998.7
ρ
measured measured
V
T
[m/s]
[N]
m
temp
rps
visc
kg/m^3
measured
Q
J
[Nm]
[-]
16.4
Deg C
1.1E-06 M^2/s
KT
[-]
10KQ
[-]
ηo
[-]
CTH
[-]
Rn(0.75R)
[-]
0.617
0.774
49.418
43.661
1.332
1.205
0.294
0.369
0.254
0.225
0.327
0.295
0.364
0.446
7.503
4.212
4.222E+05
4.241E+05
0.865
0.960
0.967
1.061
1.166
1.268
1.273
1.371
1.468
1.566
1.577
1.689
1.788
1.888
1.908
40.358
36.909
36.010
33.040
29.214
23.557
24.989
19.705
15.969
12.194
12.377
7.546
2.154
-2.596
-2.334
1.135
1.059
1.043
0.974
0.888
0.754
0.792
0.662
0.576
0.489
0.492
0.372
0.234
0.114
0.118
0.412
0.457
0.460
0.505
0.555
0.604
0.606
0.653
0.699
0.746
0.751
0.804
0.851
0.899
0.909
0.208
0.190
0.185
0.170
0.150
0.121
0.129
0.101
0.082
0.063
0.064
0.039
0.011
-0.013
-0.012
0.278
0.260
0.256
0.239
0.218
0.185
0.194
0.162
0.141
0.120
0.121
0.091
0.057
0.028
0.029
0.489
0.532
0.531
0.573
0.611
0.630
0.639
0.650
0.648
0.622
0.632
0.546
0.262
-0.683
-0.600
3.119
2.316
2.227
1.698
1.243
0.847
0.892
0.606
0.429
0.288
0.288
0.153
0.039
-0.042
-0.037
4.253E+05
4.268E+05
4.269E+05
4.285E+05
4.305E+05
4.325E+05
4.326E+05
4.348E+05
4.370E+05
4.395E+05
4.398E+05
4.427E+05
4.455E+05
4.485E+05
4.491E+05
0.700
0.600
K T -10K Q - η o
0.500
0.400
0.300
0.200
0.100
0.000
-0.100
0.000
0.200
0.400
0.600
0.800
1.000
J [-]
ass4-a-2016.doc
Brian Veitch, EN2110c, Tel: 864-8970, e-mail: [email protected]
Assignment 4: 2016
1b. Using the KT-10KQ-ηo-JA curves for the propeller above, calculate the thrust and torque developed
by a 6.2 m propeller operating at peak efficiency. If n =105 rpm at this operating condition, what is the
speed of advance?
Solution
From the KT-10KQ-ηo-JA chart in question 1a, the maximum open water efficiency occurs at about
J=0.65 where KT = 0.101 & KQ =0.0162. Assume standard temperature of 15°C so (seawater) density is
1025.9 kg⋅m-3 and viscosity is 1.1883×10-6 m2 ⋅s-1.
2
T = KT ρn D
4
⎛ 105 ⎞
= (0.101)(1025.9)⎜
⎟
⎝ 60 ⎠
2
6.2 4 = 468.9 kN
2
⎛ 105 ⎞
5
Q = K Q ρn D = (0.0162)(1025.9)⎜
⎟ 6.2 = 466.3 kN.m
60
⎝
⎠
2
5
Speed of advance is
V A = JnD = 0.65 ×
105
× 6.4 = 7.05 m/s
60
Question
2. Define and illustrate the following terms.
• propeller disk area
• projected blade area
• rake
• contra-rotating propeller
• skew
• skew induced rake
• hub radius
• chord
• leading edge & trailing edge
• face & back
• pressure & suction sides
• radius fraction
• pitch angle
• skewback
• sheet cavitation
• camber
• pitch
• fixed pitch propeller
Solution (the definitions below are very brief – the figures are clearer)
• PROPELLER DISK AREA: The disk area A0 is the area of the circle swept out by the tips of the
blades of a propeller diameter D: Ao =π D2 / 4
• PROJECTED BLADE AREA: It is the area enclosed by the outline of the propeller blades outside
the hub projected onto a plane normal to the shaft axis. (see Fig. 6.3.2)
• DEVELOPED BLADE AREA: The developed blade area AD is the surface area of the propeller
that approximately equals the area enclosed by an outline of the blade times the number of blades. (see
Fig. 6.3.2)
• RAKE: Rake is the displacement from the propeller plane to the generator line in the direction of the
shaft axis. (see Fig. B3, B4)
• SKEW: Skew is the distance between the generator and the blade reference line as viewed in a
projected blade profile. (see Fig. B3, B4)
• SKEW INDUCED RAKE: The axial displacement between the generator line and the propeller
reference line, in addition to the rake displacement is called skew induced rake. (see Fig. B3)
• PITCH: The axial distance covered per revolution is called the pitch. (see Fig.9)
• CHORD: A section of the propeller blade is called chord. (see Fig. B2)
• LEADING EDGE AND TRAILING EDGE: The edge of the propeller blade which encounters
with sea first is called leading edge and the other edge is called trailing edge. (see Fig. 6.3.2)
ass4-a-2016.doc
Assignment 4: 2016
• FACE AND BACK: The backward faced surface of the propeller blade is called face (high pressure
side). The opposite surface is called back (low pressure side). (see Fig. 6.3.2)
• PRESSURE AND SUCTION SIDES: The side of the propeller blade which faces the sea is called
pressure side and the side which faces the ship hull is called suction side. (see Fig. B2)
• RADIUS FRACTION: The value r/R is called Radius fraction where r is the radius of any section
and R is the propeller radius.
• HUB RADIUS: The radius of the propeller hub is called the hub radius
• CAMBER: The curvature of the propeller blade is called the camber. (see Fig. B2)
• PITCH ANGLE: The angle between the pitch line and the propeller reference line is called pitch
angle. (see Fig. 9)
• SKEW BACK: Skew-Back is the displacement between the generator and the propeller reference
line. (see Fig. B3)
(HARVALD)
ass4-a-2016.doc
Assignment 4: 2016
(HARVALD)
ass4-a-2016.doc
Assignment 4: 2016
ass4-a-2016.doc
Assignment 4: 2016
ass4-a-2016.doc
Assignment 4: 2016
ass4-a-2016.doc
Assignment 4: 2016
ass4-a-2016.doc
Assignment 4: 2016
ass4-a-2016.doc
Assignment 4: 2016
Question
3a. Draw a velocity diagram for a blade section including induced velocities.
Question
3b. Show lift and drag force vectors on a blade section. Resolve the forces into thrust and tangential
force components.
ass4-a-2016.doc
Assignment 4: 2016
ass4-a-2016.doc

Question 1a. Values of forward speed, propeller thrust and torque

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