Maritime University of Szczecin
Akademia Morska w Szczecinie
2013, 35(107) pp. 144–148 2013, 35(107) s. 144–148
ISSN 1733-8670
The influence of propeller emergence on the load of a marine
engine of a ship sailing on irregular wave
Tadeusz Szelangiewicz, Katarzyna Żelazny
West Pomeranian University of Technology in Szczecin, Faculty of Maritime Technology and Transport 71-065 Szczecin, al. Piastów 41, e-mail: tadeusz.szelangiewicz@zut.edu.pl
Key words: ship motions on irregular wave, propeller emergence, decrease in torque value of a propeller Abstract
When a ship is saling on waves the relative motions occur which result in propeller emergence, and as a consequence – propeller thrust reduction which results in a decrease in the ship’s speed. Propeller emergence is also accompanied by the decrease in torque values, with which the propeller affects the marine engine. The article presents both calculation results and the algorithm for calculating the decrease in torque of the propeller during ship motions on irregular wave.
Introduction
During ship sailing on irregular wave irregular ship motions and relative motions appear, which result in a propeller emergence. These phenomena are similar to those observed on regular wave, how-ever they will occur randomly also at random val-ues of – among others propeller emergence.
The decrease in thrust and torque value at a pro-peller will be random too. The article presents both calculation results and the algorithm for calculating the decrease in torque of the propeller during ship motion on irregular wave. Both instantaneous and average decrease in random torque value have been calculated. Taking into account the work of a pro-pulsion system, mainly the engine, such instantane-ous decrease in torque is very significant, as it leads to load changes affecting the engine.
Propeller emergence on irregular wave During ship sailing on irregular wave relative motions and propeller emergence must be calculat-ed using stochastic equations which describe ship motions [5]. In such equations all values are ran-dom, while there are also present phase shifts be-tween the irregular wave ordinate ξ(t) and irregular ship motion ordinate u(l)(t), as well as phase shifts
between individual ship motions which constitute the relative motion.
In order to determine ship motion on irregular wave, impulse response function [1] is used.
Then potential dampening [b(k,l)(t)] of a ship
mo-tion on irregular wave equals:
0 ) ( ) , ( ) ( ) , ( (t) u (t) K () u (t ) d bkl l kl l k, l = 1, 2, ...6 (1)and hydrodynamic masses [m(k,l)(t)] take then the
following form:
0 ) , ( ) , ( ) , ( ) d ~ sin( ) ( ~ 1 ) ~ ( ) (t m K t t t mkl kl kl k, l = 1, 2, ...6 (2) where:[K(k,l)] – matrix of impulse response function;
[m(k,l)(~)] – matrix of generalised hydrodynamic
masses related to a regular wave of the ~ frequency;
~ – regular wave frequency arbitrary chosen;
τ – time interval.
The form of a function K(k,l)(t) for floating
vessels has been given in [3]:
0 ) , ( ) , ( ( )cos( )d 2 ) (t b t Kkl kl π k, l = 1, 2, ...6 (3)where [b(k,l)(ω)] is the matrix of generalised
coeffi-cients of potential dampening of ship motions on irregular wave.
Taking into account (1), ship motions on irregu-lar wave can be described by the following pair of equations:
C t
u
t
F
t
t u K t t u t m M k l l k H l l k l l k l k
, 0 , , , d ) ( ) ( ) ( k, l = 1, 2, ...6 (4) where:[m(k,l)(t)] and [K(k,l)(τ)] are given accordingly by (2)
and (3);
[CH(k,l)] – matrix of generalised hydrostatic
coeffi-cients of restoring forces;
u(l) – vector of generalised accelerations fromship motions on irregular wave;
u(l) – vector of generalised velocities from shipmotions on irregular wave;
u(l) – vector of generalised displacement fromship motions on irregular wave;
{F(k)(t)} – vector of generalised wave forces
excit-ing ship motions on irregular wave. In order to determine ship motions on irregular wave using (4) equations, the function of general-ised irregular wave exciting ship motion must be known {F(k)(t)}.
In the case of a linear regular wave, the force exciting ship motions takes the form of:
F(k)(t)
FA(k)cos(EtF)
, k = 1,2,...,6 (5) where:{FA(k)(t)} – generalised amplitude of a wave force
exciting ship motions for the direction k;
εF – angle phase shift between a regular wave
ordinate and an ordinate of a generalized force exciting ship motion:
) ( ) (k A F E A Y F (6)
YFζ(ωE) – amplitude characteristics of a regular
wave force (exciting ship motions):
*
2 ) ( 2 ) ( A E S k A E C k A E F F F Y (7) A A * for k = 1, 2, 3 A A K * for k = 4, 5, 6 C k A S k A k F F F ) ( ) ( ) ( arctan (8) S k AF ( ) – sinusoidal part of the complex amplitude of the exciting force FA(k);
C k A
F ( ) – cosinusoidal part of the complex ampli-tude of the exciting force FA(k).
From irregular wave described in the form of sum components of harmonic waves:
) cos( ) ( 1 i i N i Ai t t
(9)generalised irregular wave force exciting ship mo-tions takes the form of:
) cos( ) ( 1 ) ( ) ( Ei i Fi N i i k A k t F t F
(10) where:for individual components “i” FA(k) (6) is given,
and εF (8);
εi – angle phase shift between components of
harmonic waves;
ζAi – amplitude of a harmonic wave component
calculated for ωi in the function of
spec-tral density of wave energy / wave energy spectral density function Sζζ(ω):
Ai 2S( i)Δ (11)
Propeller emergence on irregular wave – an example
Calculations of ship relative motion have been performed for irregular wave described by the spec-tral density function of wave energy according to ITTC: 5 exp 4 ) ( B A S (12) where: 4 1 2 173 T H A S , 4 1 691 T B ;
HS – significant wave height;
T1 – average characteristic period.
Vertical motion relative to irregular wave pre-sents as follows: ) ( ) ( ) (t S t t Rz z (13)
where ζ(t) is the ordinate of irregular wave (9), and
) ( ) ( ) ( ) (t Z t y t x t Sz p p (14)
where Z(t), (t), (t) are the ordinates of ship motions on irregular waves at time t calculated from the pair of equations (7).
Methods of computer simulations of ship motion on irregular wave have been presented among others in [3].
The results of computer simulations have been presented in figures 1–4. 0 50 100 150 200 250 300 350 400 450 500 550 600 6 4 2 0 2 4 6
Fig. 1. The course of an ordinate of a random irregular wave at 8 B (HS = 5.25 m, T1 = 8.5 s) and w = 0
0 50 100 150 200 250 300 350 400 450 500 550 600 4 2 0 2 4 600 0 t
Fig. 2. The course of the ordinate of the absolute motion of the top end of a propeller blade on irregular wave at 8 B (HS = 5.25 m,
T1 = 8.5 s) and w = 0
0 50 100 150 200 250 300 350 400 450 500 550 600
10 0
Fig. 3. Vertical relative motion of the top end of a propeller blade on irregular wave at 8B (HS = 5.25 m, T1 = 8.5 s) and w = 0
0 50 100 150 200 250 300 350 400 450 500 550 600
0 2 4
Fig. 4. The emergence of the top end of a propeller blade on irregular wave at 8 B (HS = 5.25 m, T1 = 8.5 s) and w = 0, hws(av) =
0.03 m Sz(t) [m] ζ(t) [m] t [s] t [s] t [s] t [s] Rz(t) [m] hws(t) [m] hws(av)
240 245 250 255 260 265 270 5
0 5
Fig. 5. The movement of the top end of a propeller blade during emergence on irregular wave in the time course at 8B (HS = 5.25 m,
T1 = 8.5 s) and w = 0 0 0 50 100 150 200 250 300 350 400 450 500 550 600 0 200 400 600
Q = 519.14 kNm – with the propeller fully sumberged, Qav = 519.079 kNm, ΔQav = 0.061 kNm, ΔQmax = 391 kNm
Fig. 6. Changes in propeller torque on irregular wave 8 B in course of time (HS = 5.25 m, T1 = 8.5 s) and w = 0
On the basis of the ordinate describing the emergence of the top end of a propeller blade in the course of time hws(t) (Fig. 4), the average value of
propeller emergence height in 3 hours has been calculated (T = 10800 s):
T ws ws h t t T h 0 ) ( ( )d 1 av (15) where: case opposite in the for 0 0 ) ( ) ( ) (t R t R t hws zP zPThe duration of a single emergence of a propel-ler on irregular wave (Fig. 4) is so long, as to allow the propeller to fully rotate several times (Fig. 5).
With the help of a specialist computer pro-gramme based on an algorithm [4], calculations have been performed of an instantaneous decrease in propeller torque during propeller emergence in case of a ship sailing on irregular waves (Fig. 6). The same figure shows also the average value of torque calculated in a similar fashion to that of an average propeller emergence (15).
Average decrease in propeller torque value on irregular wave in different sea conditions and dif-ferent wave direction in relation to the ship have been presented in figure 7.
Fig. 7. Torque changes during propeller emergence on irregular wave at different sea conditions and wave directions w relative
to ship (V = 6 m/s)
Results obtained here on the decrease in propel-ler thrust during ship motion have been compared against results in [2]. The article does not give ship and propeller parameters, but exclusively the de-crease in thrust value in the propeller emergence function.It can be assumed, that the results given in
450 470 490 510 530 550 8 9 10 11 12 0 30 60 90 120 150 180 w [] Qav [kNm] [ B] t [s] hws (t) [m] t1 t2 t3 t4 5 s 6 s
Propeller emergence course The movement of the top end of a propeller blade in time course
t [s] Q(t)
[kNm]
Average torque value Q(av)
[2] are the average values for various types of ships and propellers, while our own algorithm presented here allows to calculate the decrease in thrust values for any given geometrical characteristics of both the ship and its propeller.
Since, as it follows from figure 8, great con-formity between our own calculations and the measurement results in [2] for thrust decrease has been attained, hence also a great deal of accuracy in torque decrease can also be expected.
Case 1 – decrease in thrust only as a result of propeller emergence;
Case 2 – decrease in thrust as a result of propeller emer-gence, generating wave system at the stern, changeable lift force at a propeller blade;
KTw – thrust coefficient for an emerging propeller;
KT – thrust coefficient for a fully submerged propeller. Fig. 8. Comparing own calculation results with the results contained in [2]
Conclusions
The algorithm presented here and calculation results account exclusively for the influence of propeller emergence on decrease in torque values. The air content in water while the propeller emerg-es and submergemerg-es in water has not been accounted for, nor have the changes in the velocity of follow-ing wake due to wave action and ship motion.
There is a great deal of conformity between results in [2] (Fig. 8) and our own calculation results.
Presented algorithm allows calculation of torque values during propeller emergence of a ship sailing at changing velocity on irregular waves of various parameters and different wave direction relative to the ship.
Calculation results of the decrease in torque val-ue can be used to predict the working of a ship pro-pulsion system on any sailing route.
The algorithm presented here, will be further expanded in following articles, as to include other factors related to wave action and ship motion which affect propeller torque values.
References
1. CUMMINS W.E.: The impulse response fluction and ship
motions. Shiffs-technik, Vol. 47, No. 9, January 1962, 101–109.
2. FALTINSEN O.M.: Sea Loads on Ships and Offshore
Struc-tures. Cambridge University Press, Cambridge 1990. 3. OGILVIE T.F.: Recent progress towards the understanding
and prediction of ship motions. Fifth Symposium of Naval Hydrodynamics, Bergen 1964.
4. SZANTYR J.A.: Method for Analysis of Cavitating Marine Propellers in Non-uniform Flow. Intern. Shipbuilding Pro-gress, Vol. 41, No. 427, 1994.
5. SZELANGIEWICZ T.: Podstawy teorii projektowania
ko-twicznych systemów utrzymywania pozycji jednostek pły-wających. Okrętownictwo i Żegluga, Gdańsk 2005.
0 0.2 0.4 0.6 0.8 1 1.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 own calculations P ws D h 1 [–] T Tw K K [–] acc [2] – Case 1 acc [2] – Case 2
