Scien fic Journals
Zeszyty Naukowe
Mari me University of Szczecin
Akademia Morska w Szczecinie
2010, 21(93) pp. 83 87 2010, 21(93) s. 83 87
Prediction of the influence of propeller emergence on its thrust
reduction during ship navigation on waves
na
West Pomeranian University of Technology, Faculty of Maritime Technology
71-e-mail: tadeusz.szelangiewicz@zut.edu.pl, katarzyna.zelazny@zut.edu.pl
Key words: ship motions on waves, vertical relative motion Abstract
consequence reduces the propeller thrust. The article presents an algorithm for calculating the propeller thrust reduction as a result of ship motions on waves. The algorithm has preset parameters: significant wave height HS, period T1 and geographical direction.
Abstrakt
HS, okres T1 i kierunek
geogra-ficzny. Introduction
Ship motions are the direct effect of sailing on waves. These motions, like waves inducing them, occur continuously. Some dangerous phenomena are associated with ship motions, such as e.g. acce-lerations or relative motions, which also occur con-stantly, as well as phenomena occurring sporadi-cally, for example deck wetness, slamming or the emergence of the propeller. The latter phenomena
result, inter alia relative motions
and in this case the frequency of their occurrence within one hour or per 100 waves is investigated. The propeller emergence is a dangerous phenome-non for the whole propulsion system. Besides, it also causes the propeller thrust reduction which
(such speed reduction is also caused by other fac-tors). When determining the value of the propeller thrust reduction and a consequent ship speed
reduc-tion that will occur we have to know the frequency of propeller emergence, e.g. per hour, as well as the value of repeated emergence along a given ocean route. On the basis of knowledge of the size [value] of emergences, it will be possible to determine va-lues of the propeller thrust reduction, and then of
route. In the first part the method of predicting propeller emergence and propeller thrust reduction will be presented, whereas in the second part the
due to emergence of merchant ship propeller on a given ocean route.
Relative movement of the ship and propeller emergence
In the commonly applied linear theory of ship motions [1], regular waves are described by this equation:
t kx
t Acos (1)
and ship motions on these waves are expressed in the following form:
u E A t u t u() cos (2)
where: (t) ordinate of regular wave, A
ampli-tude of regular wave, frequency of regular wave, t time, k wave number:
g k
2
(3)
g acceleration due to gravity, x coordinate on direction of wave propagation, u(t) ordinate of
uA u
E frequency of ship motions:
w
E kV cos (4)
V ship speed, w wave angle (Fig. 1), w = 0
following waves (from aft), w = 90 , beam wave:
180
w (5)
direction of waves in geographical direction ( = 0 northern wave, ( w = 90 eastern wave),
ship course in geographic co-ordinates ( = 0 northern course, ( = 90 eastern course).
Fig. 1. The wave angle and Rys. 1. Kierunek fali i kurs statku
Instead of the solution described by the equation -racteristics of ship motions related to frequency are more often used, defined as:
) ( ) ( , / t t u V i Hu E w for u(t) X,Y,Z (6a) or ) ( ) ( , / t t u V i Hu E w for u(t) , , (6b)
where: X, Y, Z linear ship motions along the axes x, y, z; , , angular ship motions around axes x, y, z; (t) wave slope angle.
The real part (module) of characteristics related to frequency: A A w E u w E u u V Y V i H / , / , or A A u (7)
is the amplitude transfer function of ship motions, and the argument:
V V
i
Hu E/ w, u E/ w,
Arg (8)
is phase characteristics, A is the amplitude of the
wave slope angle.
Random motions of the ship on irregular waves can be simply determined from data on the ampli-tude characteristics of the ship motions on linear regular waves when the function of random ship motions energy spectral density is known. Then the variance of ship motions is equal to:
0 2 d , / , u E W E E W uu V Y V S D (9)
where: Duu variance of ship motions u,
u = 1, 2 ... 6; yu amplitude transfer functions of
ship motions u on regular waves; S ( E) function
of the random wave energy spectral density, the value of which depends mainly on the significant wave height HS and on period T1.
During ship motions on waves, its movement (displacement) can be determined, related to wavy water surface. The occurring relative movement (relative displacement) has a decisive influence on the propeller emergence (Fig. 2).
The vertical, absolute displacement of the ship resulting from the ship motions is equal to:
x y Z
SzP G P P (10)
whereas the relative motion of the ship: t S
RzP zP (11)
where: (t) is the wave profile described by equa-tion (1).
As in the case of ship motions, the relative movement of the ship can be written in the form of characteristics expressed in equation (10), relating to frequency. Because in equation (10) three kinds of ship motions (Z, , ) occur, with phase displacements between them, the amplitude
y0 00 0 y x V x0 xo wave W
Prediction of the influence of propeller emergence on its thrust reduction during ship navigation on waves
characteristics [frequency transfer functions] of relative movement of the ship is presented in real form (R) and in imaginary form (I):
w w p p z z R RZ y x k kY x kY y Y Y sin cos cos cos cos cos 1 1 (12a) w w p p z z I RZ y x k kY x kY y Y Y sin cos sin sin sin sin 1 1 (12b) where: I RZ R RZ Y
Y , real part (R) and imaginary part (I) of amplitude transfer functions of vertical rela-tive motion of the ship on waves; Yz, Y , Y
ampli-tude transfer functions of ship motions (Z heav-ing, swayheav-ing, pitchheav-ing, respectively); z, ,
angles of phase displacements for ship motions Z, , ; xp, yp coordinates of the point for which
relative movement is calculated, in this case the point on the propeller blade in its upper position, hence yp = 0; x1, y1 coordinates of the point (cor-responding to point xp, yp) for which the ordinate of
wave (t) is calculated.
The amplitude functions of relative motion of the ship is as follows:
2 2 I RZ R RZ RZ Y Y Y (13)
However, the value of relative motion of the ship on irregular waves is calculated from the variance described by this equation:
E E w E RZ w RZ V Y V S d D 2 0 , / , (14) RZ AZ D R 1/3 2 (15)
where: RAZ1/3 is the significant amplitude of the
relative motion of the ship on irregular waves.
The propeller thrust during ship motions on waves
The separated propeller thrust can be calculated from the formula:
2 4 p p w T D n K T (16)
where: Dp propeller diameter, np propeller r.p.m.; KT thrust coefficient for the propeller of
the following parameters: (P / D) propeller pitch ratio; (AE / A0) expanded blade area ratio; Z number of blades, is approximated by the expres-sion: 3 3 2 2 1 0 A J A J A J A KT (17)
where: A0, A1, A2, A3 coefficients of polynomial describing thrust characteristics, dependent on (P / D), (AE / A0), Z [2]; J advance coefficient: p p T n D V w V J 1 (18)
wT (V) wake coefficient, dependent on ship speed
V.
The presented expressions for propeller thrust (16) and (17) are correct for the ship sailing in calm water or on waves where the motions and relative motions are so small that the propeller does not emerge. During ship navigation on waves at high ship motions and the relative motions the propeller works in rather air-locked water or it emerges from water. This causes thrust fluctuation and reduction of the mean effective thrust in relation to that in
Instantaneous ship position resulting from ship motions Average ship position
(t) Po T TP x 0 DP z
Fig. 2. The influence of relative movement of the ship on propeller emergence Rys. 2.
speed and the propel-ler r.p.m. are constant).
The thrust is reduced, among others, due to the effect of water particles velocities in the wave motion on the wake (coefficient wT), and due to
propeller emergence as a result of the ship substantial relative motions on waves. The thrust reduction during ship navigation on waves is presented in various publications in which approximated formulae are included for assessing influence of water relative movements on the propeller parameters.
In the study [3] the formulae are presented for correcting the speed of water reaching the propeller in a situation when it is not fully immersed (Fig. 3).
Fig. 3. The propeller emergence on waves [3] Rys. 3.
The corrected advance coefficient Jw is as
fol-lows:
G J
Jw (19)
where: J advance coefficient according to [3]; G correction factor, dependent on the propeller parameters and its load, which according to [3] has the following form:
2 2 2 1 3 1 V w D T U G T p w (20) p n Aw p p D w T h D U 0 (21) 21 6 . 0 c B c wn B (22) 3 . 0 if 09 . 0 3 . 0 if 21 2 21 n n n F c F F c (23)
where: T thrust of fully immersed propeller; TAw
stern immersion on waves, resulting from relative
movements (Fig. 3); hp0 vertical distance from PP
to blade tip of the propeller in its lower position
(Fig. 3); cB b Fn Froude number, w n gL V F .
The propeller emergence leads to a reduction of thrust and torque, which might result in an increase of engine speed if it were not for engine speed regulator.
The thrust reduction coefficient was introduced in the following form [4]:
T p Tw T K R h K (24)
where: KTw (hp / R) thrust coefficient for the
emerging propeller (the quantities hp and R) are
shown in figure 4); KT thrust coefficient for fully
immersed propeller.
Fig. 4. The propeller immersion depth hp in equation [3]
Rys. 4. hp [3]
Changes [variations] of the T coefficient value
depending on (hp / R) are shown in figure 5 [3].
The thrust coefficient KTw (hp / R) occurring in
equation (24) can be calculated making the ex-panded blade area ratio (AE / A0) dependent on rela-tive propeller immersion depth (hp / R) and taking
into account the corrected advance coefficient Jw,
equation (19). The instantaneous propeller immer-sion depth [draught] hp(t), or TAw(t) occurring in
equation (21) will be calculated on the basis of the ship motions on waves and the associated propeller emergences.
The emergence of propeller occurs when the relative movement (significant amplitude RAZ1/3 of
the relative movement from equation (15) exceeds the immersion depth TPw (Figs 3 and 4) of the blade
tip of the propeller in its upper position:
Pw AZ T R 1/3 (25) Tpw Tp Tp0 R hp(t) Tp0 Tp Tpw PP Dp hp0 TA w
Prediction of the influence of propeller emergence on its thrust reduction during ship navigation on waves
Fig. 5. The thrust reduction (coefficient) during emergence of propeller [4]
Rys. 5.
hence the size [value] of emergence Tp is:
Pw AZ
p R T
T 1/3 (26)
and the propeller immersion depth [draught] hp(t) in
equation (24) will be:
P P p t D T h 2 1 ) ( (27)
Calculating, for different ocean wave parame-ters: HS, T and and ship courses and speeds V, 1
we will be able to calculate the value of the emer-gence of propeller Tp or propeller immersion
draught hp(t) as well as the probability of
occur-rence of these values. Then the thrust reduction coefficient T can be calculated, equation (24) and
the ship speed reduction on a given ocean route. Calculations of the ship thrust reduction as a re-sult of the propeller emergence on a given ocean route are presented in [5].
References
1. DUDZIAK J. . Wydawnictwo Morskie, 2. OOSTERVELD M.W.C., VAN OOSSANEN P.: Futher Computer Analyzed Data for the Wageningen B-Screw Series. In-ternational Shipbuilding Progress, 1975, 22, 251.
3. HOLTROP J.: A Statistical Re-analysis of Resistance and Propulsion Data. International Shipbuilding Progress, 1984, 363, 272 276.
4. MINSAAS K.J., THON H.J., K W.: Influence of Ocean Environment on Thruster Performance. Proc. of Int. Symp. Propeller and Cavitation, Supplementary volume, Shanghai 1986, 124 142,
5. SZELANGIEWICZ T., ELAZNY K -atku w wyniku wy
na danej linii
Naukowo-Techniczna Explo-Ship 2010.
The scientific work financed from resources allocated for research and science in the years
2007 2009 as a research and development project no. R10 003 02.
Recenzent: Akademia Morska w Szczecinie
R hp 1.0
thrust reduction resulting from propeller emergence
thrust reduction resulting from: propeller emergence
generation of aft wave pattern variable dynamic lift on propeller
blade 0.5
