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: K T, K Q, C TH, η o, J A, and R n0.75. Plot K T -10K Q -η o -J A curves for the propeller. Note that c 0.75 is 0.093m at model scale. Solution D 0.21 m temp 16.4 Deg C n 10 rps visc 1.1E-06 M^2/s ρ 998.7 kg/m^3 measured measured measured V T Q J K T 10K Q η o C TH R n (0.75R) [m/s] [N] [Nm] [-] [-] [-] [-] [-] [-] 0.617 49.418 1.332 0.294 0.254 0.327 0.364 7.503 4.222E+05 0.774 43.661 1.205 0.369 0.225 0.295 0.446 4.212 4.241E+05 0.865 40.358 1.135 0.412 0.208 0.278 0.489 3.119 4.253E+05 0.960 36.909 1.059 0.457 0.190 0.260 0.532 2.316 4.268E+05 0.967 36.010 1.043 0.460 0.185 0.256 0.531 2.227 4.269E+05 1.061 33.040 0.974 0.505 0.170 0.239 0.573 1.698 4.285E+05 1.166 29.214 0.888 0.555 0.150 0.218 0.611 1.243 4.305E+05 1.268 23.557 0.754 0.604 0.121 0.185 0.630 0.847 4.325E+05 1.273 24.989 0.792 0.606 0.129 0.194 0.639 0.892 4.326E+05 1.371 19.705 0.662 0.653 0.101 0.162 0.650 0.606 4.348E+05 1.468 15.969 0.576 0.699 0.082 0.141 0.648 0.429 4.370E+05 1.566 12.194 0.489 0.746 0.063 0.120 0.622 0.288 4.395E+05 1.577 12.377 0.492 0.751 0.064 0.121 0.632 0.288 4.398E+05 1.689 7.546 0.372 0.804 0.039 0.091 0.546 0.153 4.427E+05 1.788 2.154 0.234 0.851 0.011 0.057 0.262 0.039 4.455E+05 1.888-2.596 0.114 0.899-0.013 0.028-0.683-0.042 4.485E+05 1.908-2.334 0.118 0.909-0.012 0.029-0.600-0.037 4.491E+05 0.700 0.600 0.500 K T-10K Q- η o 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 [-]
1b. Using the K T -10K Q -η o -J A 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 K T -10K Q -η o -J A chart in question 1a, the maximum open water efficiency occurs at about J=0.65 where K T = 0.101 & K Q =0.0162. Assume standard temperature of 15 C so (seawater) density is 1025.9 kg m -3 and viscosity is 1.1883 10-6 m 2 s -1. 2 2 4 105 4 T = KT ρn D = ( 0. 101)( 1025. 9) 6. 2 = 468. 9kN 60 2 2 5 105 5 Q = KQ ρn D = ( 0. 0162)( 1025. 9) 6. 2 = 466. 3kN.m 60 Speed of advance is 105 V A = JnD = 0. 65 6. 4 = 7. 05m/s 60 Question 2. Define and illustrate the following terms. propeller disk area projected blade area pitch angle rake contra-rotating propeller skewback skew skew induced rake sheet cavitation hub radius chord camber leading edge & trailing edge face & back pitch pressure & suction sides radius fraction fixed pitch propeller Solution (the definitions below are very brief the figures are clearer) PROPELLER DISK AREA: The disk area A 0 is the area of the circle swept out by the tips of the blades of a propeller diameter D: A o =π D 2 / 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 A D 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)
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)
(HARVALD)
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.