Ship Project A ASSIGNMENT ONE RAN XIAO & THEIR TOMAS

Transcription

1 2014 Ship Project A ASSIGNMENT ONE RAN XIAO & THEIR TOMAS

2 Resistance estimation Methodology brief As our ship concept is in form of catamaran, it is not proper to simply introduce the method and diagrams of monohull ship series. For catamarans, the interaction of waves generated by twin hulls cannot be ignored and thus affects the friction resistance as well as wave pattern resistance. Different from the methodology used in the previous report where Delft Series (98 ) and John Winter s empirical resistance diagram are introduced, here we apply the method and diagrams deduced in <Resistance Experiments on a Systematic Series of High Speed Displacement Catamaran Forms: Variation of Length-Displacement Ratio and Breadth-Draught Ratio>. By this method, resistance coefficient is defined as follow: C tcatamaran = (1 + k) σ C f + τ C W Where is related to the pressure field change and τ is about wave resistance intereface factor. For simplification, the formula is transformed into: C tcatamaran = (1 + β k) C f + τ C W Based on this equation, the practical resistance expression is deduced as: C tcatamaran = C Fship + C Rmodel β k (C FModel C Fship ) According to our design, parameters are summarized as: 3 C B C P C w L/ S/L B/T Then we can select the corresponding diagram and mother ship from <Resistance Experiments on a Systematic Series of High Speed Displacement Catamaran Forms: Variation of Length- Displacement Ratio and Breadth-Draught Ratio>. Here model are classified as: We choose 3b* since it is the most similar one. Relevant parameters of 3b* are: Here are some apparent differences in terms of C P, which may lead to some unexpected estimation

3 result. As C P stands for how full the underwater part of hull is, a relatively larger value can make the predicted resistance larger than it should be. But since it is a rough estimation, the estimation error is acceptable. Determination of coefficients Source: <Resistance experiments on a systematic series of high speed displacement catamaran forms: variation of length-displacement ratio and breadth-draught ratio> As mentioned previously, we know C tcatamaran = (1 + β k) C f + τ C W and in this figure, the curves of C tcatamaran and (C tcatamaran C W ) have been given, together there are also curves of C f and (1.65) C f. Apparently, illustrated in the figure, the curve of (C tcatamaran C W ) matches very well with that of (1.65) C f outside the Froude Number zone of [0.2, 0.65]. Unfortunately the resistance we are studying is in this zone, so we have to estimate the value of 1 + β k one by one according to the graph above, and we yield following graph:

4 1+beta*k 1+beta*k 1+beta*k beta*k speed (knots) And from the graph below we can also conclude all the C Rmodel = C Rship = C R at corresponding speed.. Source: <Resistance experiments on a systematic series of high speed displacement catamaran forms: variation of length-displacement ratio and breadth-draught ratio>

5 Resistamce coefficient Resistance prediction Now we have all the values needed for resistance calculation. According to the resistance expression C tcatamaran = C Fship + C Rmodel β k (C FModel C Fship ) as well as formulas C Fmodel = following graph: [log 10 (Fn ) 2} 2 and ITTC 57 Correlation line: C F = [log 10 Rn 2] 2, we have the Resistacne Coefficient prediction Ct Speed (knots) The coefficient climbs greatly after the speed exceeds 12 knots due to the drastic increase of C R at the corresponding speed. Now lastly, we assume our wet surface is 75 m 2. We are able to calculate the drag according to the previous formula and draw the curve in the figure below:

6 resistance (N) Resistance prediction speed (knots) Rotation Speed & Propeller Design Parameters & assumptions According to the report and previous calculation, we can find out the following information: Engine type: Type: Standard azimuth thrusters - type US 55P4 Max input power: 330 KW Propeller diameter: 1050 mm Vessel design speed: 15 knots Resistance at 15 knots: N Now as we are going to design the propeller initially, we have to make some assumption for further calculation and we ll go back to check if our assumptions are reasonable. So here we assume: t = 0,125 Ap = 0,55 w = 0,45 η H = 1 t = 1,591 and η = 0,98 (taken from empirical statistics from vessels whose 1 w s engines are located at the rear part), η G = 0,96 for gear box efficiency

7 Propeller design Based on the resources we have at hand, we choose Wageningen B4-55 as our propeller type. As we already have the thrust deduction and wake factor, the table below can be work out for application of the B-series diagram and data interpolation. Speed (knot)/(m/s) D(m) N(round/s) J K T V A(m/s) ᵹ 15 7, ,05 3 1, , , , , ,05 3,5 1, , , , , ,05 4 1, , , , , ,05 4,5 1, , , , , ,05 5 1, , , , , ,05 5,5 0, , , , , ,05 6 0, , , , , ,05 6,5 0, , , , , ,05 7 0, , , , We can interpolate the ᵹ values that we have into the diagram Fig. 1 to find out the corresponding values of η 0, pitch ratio and B P with which we can calculate the deliver power and effective power. Fig. 1 B4-55 diagram N(round/s) ᵹ P/D η 0 Bp 4 0, ,17 0,734 0,41 4,5 1, ,07 0,729 0,43 5 1, ,99 0,712 0,45 According to the formula given in figure 1: B P2 = P D 0,5 D V A 1,5, here comes the deliver power. Using the efficiency we have assumed and η 0 we get, the corresponding effective power and engine power

8 power (KW) are able to be listed out. N(round/s) Bp P D P s P E 4 0,41 77, ,52 90,65 4,5 0,43 85, ,77 99,04 5 0,45 93, ,40 105,93 Since in previous calculation we have known that the needed power for our design at 15 knots is about 101,8 KW for each propeller, now we can make a graph to see where the needed power and effective power meet so that we can determine the optimal pitch ratio and RPM for our propeller. RPM against Power engine power effective power needed power engine power effective power needed power propeller speed (round/s) Apparently, the optimal configuration for our design is RPM = 278 with P/D = 1,05 Assumption Examination Previously we assume w = 0,45. Now we know our pitch ratio and K T is available, we can check if it makes sense. As T = in total, K T = T/(2*1025*ρ*N 2 *D 4 )=0,56 corresponds to the J 0=0,65. Therefore, w = 1- J 0/J = 0,41 which is quite close to our estimated value.

9 Propeller coefficient η 0 η H η S η G Reference 1. Molland, A.F., Wellicome, J.F. and Couser, P.R. (1994) Resistance experiments on a systematic series of high speed displacement catamaran forms: variation of length-displacement ratio and breadth-draught ratio. Southampton, UK, University of Southampton, 84pp. 2. Sverre Steen and Knut Minsaas, Ship Resistance, Department of Marine Technology, NTNU, Zhengbang Sheng, Zhongying Liu, Shanghai Transportation University, <Ship Principal>, 2003.