Splashing a ship with collision-generated spray

Cold Regions Science and Technology, 14 (1987) 65-83 Elsevier Science Publishers B.V., Amsterdam -- Printed in the Netherlands

SPLASHING

A SHIP WITH

COLLISION-GENERATED

65

SPRAY

W . Paul Z a k r z e w s k i * Department of Geography, Division of Meteoro/ogy, University of Alberta, Edmonton, Alberta T6G 2/-/4 (Canada)

ReceivedJanuary 8, 1986; accepted in revisedform October 10, 1986)

ABSTRACT

The collision-generated spray flux was defined using formulas derived for the vertical distribution of the liquid water content and time of ship exposure to spray originating from the spray cloud induced by ship-wave collision. These formulas were derived using published data on a Russian field experiment in the Sea of Japan. The time-averaged water flux to an object (cylinder and vertical plate) can be computed for any given wind speed, fetch, ship speed and heading angle. The runoff of seawater from vertically oriented objects located on a ship has been investigated. The ratio between the duration of moving water film residence on the object's surface to the time interval between two successive splashings of a ship with spray has been computed for several values of wind speed, ship speed, and heading. This ratio has been used to correct the time-integrated ice growth rates on elevated objects, The results are applicable for calculating the ice loads on a ship.

1. I N T R O D U C T I O N Icing has caused the loss of many small and medium fishing vessels (Shellard, 1974; Aksjutin, 1979) and it has been known to affect adversely the seaworthiness of small cargo vessels (Lundquist and Udin, 1977; Aksjutin, 1979). Analysis of all known cases of ship icing proved that (1) spray icing is the most common type of icing on ships, and (2) the *Formerly with the Polish Academy of Science, Institute of Oceanology in Sopot, Poland.

0165-232X/87/$03.50

largest icing rates have been predominantly reported when the ships were affected by spray (Table 1 ). Recently Zakrzewski (1986d) has proved that windgenerated spray does not splash a medium-sized fishing vessel (MFV), even in high seas. Therefore, collision-generated spray is thought to be the one and only source of water delivery to the ship if water flux due to snow, fog, rain, drizzle, and the flooding of the ship's deck by waves is neglected. Although numerous studies have been conducted on ship icing, those most important in terms of ship operations involved the analysis of ice growth rates on the ship superstructure. To date, the most important research on this subject includes the work of Overland et al. (1986), Zakrzewski (1986c), Stallabrass (1980), Wise and Comiskey (1980), Borisenkov and Pchelko (1975), Kachurin et al. (1974), Borisenkov (1969), Mertins (1968). The thermodynamics of icing seems to be well understood, yet there is a lack of accurate models relating the splashing o f a ship with spray to the icing phenomenon. This may, in part, be due to the scarcity of field data by which to test proposed models. However, some theory has been developed by Panov et al. (1975) and some data on spraying an MFV have been collected (among others, Borisenkov et al. (1975) and Kultashev et al. (1972)). An effort to describe the water delivery to a ship has recently been given by Zakrzewski (1986d). The emphasis was placed on modelling the splashing of a ship with the sea spray whipped off the wave crests by a wind, and spray originating from a ship-wave interaction (collision-generated spray). The MFVs of the Soviet type only were considered in these analyses because the published data sets from field experiments are available only for this type of ship

© 1987 Elsevier Science Publishers B.V.

66 TABLE 1 Causes of icing of ships Region

Total number of observations

Sea

spray All seas North Pacific North Atlantic Arctic Gulf of St. Lawrence Scotian Shelf Grand Banks NE Newfoundland Shelf Labrador Sea and Davis Strait

Reference

Cause of icing (%) Spray and fog or rain or snow

4(2)'

Shehtman (1968)

2.7

Aksjutin (1979)

400 3000~

89 (82) ~ 89.8

Unknown 100 536 100 233

50.0 81.0 94.2 97.0 95.9

41.0 2.0 3.0 2.0 1.4

9.0 17.0 2.8 1.0 2.8

Aksjutin (1979) Brown and Roebber (1985) Brown and Roebber (1985) Brown and Roebber (1985) Brown and Roebber (1985)

86.9

11.1

1.7

Brown and Roebber (1985)

72

7 ( 16) ' 7.5

Other types

tReported cases of fast growth of ice are given in parenthesis, if known. 2Makkonen (1984) and Shellard (1974) mentioned more than 2000 cases of icing. (Fig. 1). Computations were given for two bodies (cylinder and vertical plate) of unit area (1 mZ), located on an MFV within a given range of elevation above the ship's deck. This paper presents an updated version of the model described above. Water delivery due to splashing a ship only with collision-generated spray is presented below. An MFV moving into the waves ( a > 90 ° )* is considered. Some spray originates from the crests o f interference waves generated by ship motion, but this mechanism of water delivery will be neglected here. Two different objects are considered in our analyses: a cylinder located on the main deck of an MFV exactly at the place of the ship's foremast (see Fig. 1 ), and a plate which is assumed to be located very close to the central part of the front side of the ship's superstructure. These objects ("foremast" and front side of the ship's superstructure) are located at distances equal to about 10 and 21 m from the ship's bow, respectively. To simplify any computations it is assumed that for any ship heading, ship speed and wind speed, the surface of these objects is perpendicular to the spray droplet trajectories. To calculate the time-averaged water flux to an *Ship heading (a) is defined as equal to the angle between the ship heading and the direction normal to the wave crest. o¢= 0 for the ship passing the waves, and t~= 180° for the ship going precisely into the waves.

object located on the deck of a ship near her windward side we have to: (1) examine the water delivery to a ship resulting from a single splashing on the ship with spray, and (2) find the frequency of generation of the spray cloud.

2. EFFECT OF A SINGLE SPLASHING ON A SHIP WITH COLLISION-GENERATED SPRAY The cloud of spray induced by the ship-wave interaction is wind-driven. Spray generated in front of the bow and on the windward side of the ship splashes here on its way to the sea surface. The mass of water delivered to an object during a single splashing event is given per unit area by the formula (Zakrzewski, 19 86b) m = Ec Urs w LJt~s

kg m - 2,

( 1)

where Ec is the collection efficiency, Urs is the spray speed relative to the object located on a ship (in m s - l ) , w is the liquid content (in kg m - 3 ) , and 3tds is the time of exposure of an object to spray (in s).

2.1. Collection efficiency A simple approximation of the collection efficiency was proposed by Stallabrass (1980) for cyl-

67

Fig. 1. A Soviet MFV generating a cloud of spray in moderate seas (Panov, 1976). A ship of this type usually has an overall length of 39.5 m, breadth 7.3 m, a displacement of 418-462 tonnes, and a maximum speed of 8-9 knots (Aksjutin, 1979). inders and vertical plates. He found that - 3200 f ~+27000

Ur=x/U~h+Vz+2Uh V c o s ( 1 8 0 - a )

(2)

L

- 2800 ~+ 11700

for vertical plates

where the dimensionless parameter ~ is given by

UO.6dl.6 ~-~,

l

(4)

for cylinders

Ec =

ms

(3)

Ur is the relative wind speed in the vicinity of an object (m s l), dis the water drop diameter (#m), and L is the characteristic length of an object ( m ) . If the vertical component o f the wind speed is neglected, the relative wind speed, Ur, for an object located on an MFV may be found by the formula

where Uh is the wind speed (m s - l ) in the vicinity of an object, Vis the ship speed (m s - l ) , and a is the ship heading (degrees). For Ur--3-60 m s-~, d = 20-1000 /tm, and L = 0 . 0 3 - 1 m (cylinder), and L = 0 . 0 3 - 3 m (vertical plate), Stallabrass (1980) obtained a satisfactory correlation. These values of Ur and L correspond quite well with wind speeds over the ocean and with typical dimensions of ship equipment and superstructure, respectively. However, for spray droplet diameter much larger than 1 mm, as reported by Panov (1976), the trajectories to an object are deflected very little. Therefore, the collection efficiency may be assumed to be equal to 1.0 (see also Stallabrass, 1980).

68

2.2. Spray speed relative to the object

parallel to the y direction, one has Vx=0, Vy= - V, and Vz= O. To determine the components of the resultant spray speed vector in the horizontal plane, let us assume that in the horizontal plane the spray moves with the speed equal to the wind speed over the ocean, Uh. Since the horizontally-oriented components of the spray speed vector, Ux and Uy, may be defined in the heading angle and the wind speed Uh, one has: U x = - Uh sin a, and, Uy=- Uh COS a. Consequently, for the component of the spray speed vector in the vertical direction equal to Uz, eqn. (7) can be rewritten as

The spray speed relative to the object located on an MFV is given by

Urs=x/U2+V2-2UVcos7

ms -l ,

(5)

where U is the spray speed ( m s - l ) , V is the ship speed ( m s~ ~), and ~, is the angle between the vectors U and V (Fig. 2). Since the vector of the spray speed at the moment of hitting the object consists of two components: (1) the speed in the horizontal plane ~ Uh) and (2) the speed in the vertical direction (U~), the spray speed, U, is given by U=x/~h+U~z

ms -l .

(6)

y = arccos For the assumed three-dimensional system of reference (x,y,z), the value o f the angle between two vectors U and V is given by the formula

Vx/U 2 sin 2 a + U 2 cos 2 a + U~ Oh COS O/

= arccos ~

UxVx + UyVy + U2V2 y = arccos x~ U2 + Uy2.+ Uz2 x/V2 + V2y_-4--2V2'

VUh COS O/

•%

Ship heading

%

/ Z

'/;/

o,

x

Y

Fig. 2. The spray flight in the air above a ship.

(8)

Equations ( 5 ) - ( 7 ) may be used to approximate the spray speed relative to the object located on an MFV moving into the waves with the known speed V and ship heading a, if the spray speed in the horizontal plane, Uh, and in the vertical direction Uz, were

( 7)

where subscripts x,y, and z for vectors ~J and ~'refer to their components in the x,y, and z directions, respectively. If the vector o f the ship speed, V, is

/

+ U~"

69 known. Since we have already assumed that the spray speed in the horizontal plane is equal ,to the wind speed, let us discuss the wind speed over the ocean in the vicinity of a ship. This parameter is poorly investigated and not easy to estimate due to both the ship's effect on the air stream and the air flow over the wavy boundary. Let us ignore the effect of a ship on the air stream. The local wind speed over a wavy boundary follows the logarithmic law. Based on Brooke Benjamin's (1959) study it can be approximated by the formula U(t/) = U , In q, /¢

(9)

z0

1.2

f o r 4 ~ < U ~ o < l l m s -~

0.49+0.065Uio

forll~
103 CI0=

(13)

11=z-aexp(-kz) cos(kx) m,

(10)

where a is the wave amplitude, k is the wavenumber (k=2n/2; 2 is the wavelength), and x (measured from the wave crest) and z (measured from the mean water level) are the coordinates in x and z directions, respectively. For a fully-developed open sea, the wave amplitude a may be replaced by the significant wave height, H~/3. The significant wave height may be defined for the mean wind speed at a height of 10 m above the mean water level. Based on the tabulated relationship between the significant wave height, the wind speed and the fetch given in the Handbook of Oceanographic Tables (1966), it has been found (Zakrzewski, 1986d) that a fifthdegree polynomial regression fitted this relationship fairly well:

HI/3 =Bo +Bi Ulo +B2 U~o + B 3 U30 +B4U410+BsUSI 0 m ,

(11)

where the constants, Bo, B~, B2, B3, B4, and B5 are listed in Table 2 for a given fetch. This polynomial is valid for wind speeds up to 32.4 m s-~ because the field data dealt only with this range of wind speed. The shear velocity, U,, is given by the formula ms -l,

(12)

~.

The roughness length, Zo, is given by the formula Z o = 1 0 e x p ( - / ¢ c l o ½) m.

where q, the curvilinear coordinate perpendicular to the free surface, is the variable describing the distance from the free surface (m), U. is the shear velocity (m), x is von Karman's constant (0.4), and Zo is the roughness coefficient. The variable q is given by the formula

U,=Ulox~lo

where Ul0 is the mean wind speed at a level of 10 m above the mean water level (MWL) and clo is the drag coefficient. The drag coefficient reduced to a height of 10 m and for neutral conditions is independent of stability and fetch and is equal to (Large and Poind, 1981 )

(14)

If the ship motion relative to the free surface is ignored, the distance between the free surface and an object elevated at h' above the deck of an MFV of freeboard h, will be

tl=h+h' m.

(15)

Substituting the term of t/in eqn. (9) by the righthand side of eqn. (15), eqn. (9) may be rewritten as:

U(~)=U*In h+h' m s -~.

(16)

Zo Consequently, one gets a very convenient formula to compute the local wind speed for a given height above the free surface. However, eqn. (16) may not be recommended for any further computations until one checks to see if it applies to the open sea conditions. Brooke Benjamin (1959) assumed that the wave amplitude in eqn. (10) is small compared to the wavelength, and the term of (ka) 2 is negligibly small (k is the wavenumber, a is the amplitude of a wave). Let us compare the significant wave height, H~/3, and the wavelength for a fully arisen sea which may be approximated by the empirical formula (Pierson et al., 1955 ) 2= 1.5616P 2 m,

(17)

where P is the period of significant wave. Based on data listed in the Handbook of Oceanographic Tables (1966), Zakrzewski (1986d) has found that the period of significant waves may be defined in a wind speed Ulo by

70 TABLE 2 Constants of the fifth-degree polynomial in wind speed to compute significant wave height Fetch (n.m.) Bo

B~

B2

B3

B4

B5

100 200 300 400 500

-4.41178o10 -1 2.71899,10 I 5.96961-10 -I --3.41913-10 -I --3.78443o10 -1

1.16227,10 -I 1.07151,10-2 -1.71261-10 3 1.14635,10 -I 1.11329o10 -I

-7.87593,10 -3 _8.30642o10-4 -1.75507,10 3 -8.51850,10 -3 -7.55389,10 -3

2.62150-10 4 5.99481o10-5 1.32954,10-4 3.24417-10 4 2.75507,10 4

-3.34401,10 6 _1.20460o10-6 _2.40288,10-6 -4.49695,10 6 -3.75483,10 6

8.68869-10 -I -7.71688,10 I -2.31314 4.86322,10 -I 6.55261,10 -]

P = Co + Ci UI 0 + C2 U20 "q-C3 UI30

+C4U4o+CsU~o s

(18)

where c o n s t a n t s Co, CL, C2, C3, C4 a n d C5 o f t h e fifth-degree p o l y n o m i a l regression in w i n d speed are listed for a given fetch in T a b l e 3. C o m p u t e d v a l u e s o f the significant w a v e height, H1/3, a n d w a v e l e n g t h 2, are c o m p a r e d in T a b l e 4 for w i n d s p e e d 1 0 - 3 0 m s -~. Since the significant w a v e height is only slightly s m a l l e r b y one o r d e r o f magn i t u d e t h a n the wavelength, B r o o k e B e n j a m i n ' s (1959) a s s u m p t i o n on the negligible v a l u e o f ( k a ) 2 ( w h e r e k is the w a v e n u m b e r a n d a is the a m p l i t u d e o f a w a v e ) , d o e s n o t h o l d especially for high seas. Therefore, it is p r o b a b l y b e t t e r to use the m e a n w i n d speed at a height o f 10 m a b o v e the m e a n w a t e r level, U~o, a n d a s s u m e t h a t t h e s p e e d o f the a i r flow in the h o r i z o n t a l p l a n e in t h e v i c i n i t y o f a ship m a y be roughly a p p r o x i m a t e d b y this p a r a m e t e r . T h e v e r t i c a l c o m p o n e n t o f the s p r a y speed, Uz, is n o t k n o w n b u t s o m e effort to r o u g h l y a p p r o x i m a t e this p a r a m e t e r is m a d e below. Since the z o n e o f

splashing a ship with s p r a y s e e m s to d e p e n d o n the ship heading, let us distinguish the following objects l o c a t e d on an M F V with r e g a r d to the ship heading: (1)windward side o f s h i p ' s s u p e r s t r u c t u r e (90 °
TABLE3 C~nstants~fthefi~h-degreep~yn~mia~inwindspeedt~c~mputethepen~d~fsignificantwave Fetch (n.m.) Co

CI

C2

C3

C4

C5

100 200 300 400 500

-6.29590-10 I 1.64186 6.97189,10 -j 1.58956 4.02249-10 -I

1.47148,10-1 -1.67453,10 -I -3.75184-10 2 -1.20539,10 J 6.62677o10 -4

_ 1.06925,10-2 9.40820,10 3 1.36520,10-3 5.08323,10 3 -5.85091,10 -4

3.39925,10-4 -2.52521-10 4 _1.85457,10-5 _9.81111,10-s 2.55276,10 -s

-3.96520-10 6 2.56951,10 -6 1.45308,10 -8 6.44218,10 -7 -3.66318,10 -7

4.68269 -2.41866-10 i 2.92959 -8.14976,10 -2 4.68527

-

71 TABLE 4 Selected parameters of significant waves for various wind speeds at 10 m reference level W i n d speed ( m s I)

10

15

20

25

30

(m) (s) (m)

2.67 6.57 67.4 0.04

5.03 7.63 90.9 0.05

8.04 8.70 118.2 0.07

11.40 9.60 143.9 0.08

13.89 10.22 163.2 0.08

Parameter

Ht/3 P 2

Hl/3/.~

component of spray droplet speed, Uz, may be approximated by the formula ( Zakrzewski, 1986b)

U_~=hs- -h'-ht, - -

ms-

l

(19)

where hs is the elevation of the object's surface above the top of the windward bulwark of height hb, and z is the duration of spray flight to the object. If the spray speed in the horizontal plane is assumed to be equal to the wind speed at a height of 10 m above the mean sea level, U~o, the duration of spray flight to an object located on an MFV may be approximated by the formula (Zakrzewski, 1986a) =

X 2 x/Ulo + ~ o - 2UIoVcos a

s

(20)

where o~ and V are the ship heading and speed (m s-*), respectively, and X (m) is the distance of spray travel downwind (relative to a moving ship) in the air to a given object. For given wind speed U~o and ship speed V, such a distance of the spray flight to a given object vary with the ship heading (Fig. 3). For the cases when spray splashes several parts of an MFV, listed in items ( 2 ) - ( 6 ) , the spray trajectories are much more difficult to estimate. Some theory has been given by Panov et al. (1975), but they have investigated only complicated processes of launching the spray cloud due to ship-wave collision. However, based on several observations of launching a cloud of collision-generated spray conducted by us during a number o f ship cruises, it has been found that spray is generated in the form of water jets/fountains which move upwards and simultaneously are wind-driven. The forehead of the spray cloud reaches its maximum height and then starts to fall down being wind-rafted at the same

time. The objects located on a ship are hit by the spray which travels along the curvature. Since there are no field data on the vertical component of the air stream flowing around a ship, it is very difficult to estimate the spray speed in a vertical direction relative to the air. Therefore, it is probably better to neglect at this stage the effect of the vertical component of the air flow around a ship on the spray movement. In our model, we assume that the water in the jet/fountain of just-generated spray moves upwards and is partly dissipated by the wind. To neglect initial conditions of launching a water jet, let us also assume that the movement of a given water droplet upwards is stopped almost immediately after leaving the main core of a water jet by such a spray droplet. Consequently, a spray droplet flies with wind and gradually lowers its height due to the gravity force until it impinges onto an object's surface. The equation of the vertical component of the spray droplet trajectory is given by the formula

z=hst-gz2/2

m,

(21)

where hst is the height (with respect to the ship's deck) on which the spray droplet starts to be winddriven and leaves the water jet, g is the aceleration due to gravity, and r is the time. A given point on the object's surface may be directly hit by a spray droplet originating only from a certain part of a water jet (Fig. 4). Thus, the height on which such a spray droplet leaves the water jet may be defined in the coordinates of a given point on the icing surface if the frame of reference is chosen as it is shown in Fig. 4. For an object elevated h' (m) above the ship's deck and located X (m) downwind (relative to a

72

has been already approximated, one can determine the height above the ship's deck on which a spray droplet has to leave a water jet to hit a given point on the object's surface:

windI heading

2

~)

crest

+~

U~lo+ V2_2Ujo cos a

m

(23)

where the terms of X, a, U~o, and Vare the same as in eqn. (20). Based on the analyses of a few photographs showing an MFV in moderate and high seas for which the basic air-sea and ship motion parameters were known, the maximum extent of the spray flight in the vertical direction, hmax (in metres with respect to the top of the ship's bulwark) was roughly approximated by the simple empirical formula (Zakrzewski, 1986b) hmax~0.7 gr

m,

(24)

where Vr is the ship speed relative to the surface of an oncoming wave. For a ship speed of Vand heading a, the ship speed relative to the waves, Vr, may be approximated by the formula (Zakrzewski, 1986d)

Vr=Cw-Vcosa m s - l ,

(25)

where Cw is the speed of wave propagation in the sea. For a deep sea (sea depth not smaller than a half of the wavelength, 2), the speed of wave propagation may be approximated by the empirical formula (Pierson et al., 1955) .............. 1

m 2

i

i 3

Cw=l.559P Fig. 3. Potential distances of spray flight over an MFV for various heading angles. 1. area of wave impact; 2. bulwarks and sides of ship's superstructure exposed to spray impingement; 3. bulwarks and sides of ship's superstructure not exposed to spray impingement. moving ship) from the core of the water jet, one has that the spray droplet lowers its height from hst to h'. Therefore, eqn. (21 ) for the moment of spray droplet impact onto the object's surface may be rewritten as

h'=hst-gr2/2 m,

(22)

where r is the duration o f spray flight over a ship. Since the duration of spray flight to a given object

ms

~,

(26)

where P is the period of the significant wave. The maximal extent of the spray splash zone in the horizontal direction may be approximated using the maximum height o f the spray cloud, h . . . . For a given wind speed (U~o) and ship speed (V) and heading ( a ) , the maximal distance travelled by spray prior to lowering its height above the ship's deck to h', can be determined using the formula Xmax ~ N/~IIO -4- l/~lo--2UIo VCOS 0¢

~/2(hmax +hb g

~ h ~)

m,

(27)

where ( hmax+ hb) is the maximum range in the ver-

73

WIND hmax

hst

- -

i

ax (h')

X

-~

main deck

}eve~]~_ ~ ~ .

Fig. 4. Generation of spray cloud by ship-wave collision.

tical direction of spray cloud above the ship's deck (hb is the height of the ship's bulwark). The spray speed in the vertical direction at a moment of hitting an object is given by

U~=gr

(28)

X = g x/U~,o+ V2- 2UloVcos a

ms

i.

One can easily note that U= is defined only in the ship motion parameters and wind speed and potential distance of the spray travel (relative to a moving ship) in the horizontal plane.

2.3. Liquid w a t e r content The simplest presentation of the LWC distribution above the sea surface after wave impact on a ship is that of Kachurin et al. (1974). They assumed that the LWC is a function of wave height only:

w=~.H kgm -3,

(29)

where H is the wave height and ~ is a constant. No methodology is given in this reference except a note that the constant ~ for an MFV moving into the waves (a>~ 140 °) with the speed of 6-8 knots ( 3.09-4.12 m s- ) was assumed to be equal to 10- 3 kg m -4. A more sophisticated equation has been proposed by Borisenkov (1972), who argued that the 1

LWC is a function of the modal diameter of water drops (dm) and the modal value of the probability density (fm) of water droplets of such a diameter: w=

20Zcpwe2 2~fmd4m

gcm -3,

(30)

where Pw is in g cm -3, dm is in cm, fm is in cm -4, and e is equal to 2.7183. It is commonly believed that there are no published measurements of the vertical distribution of the LWC in the collision-generated spray. However, going through Soviet publications on icing, one such report has been found. Based on a field experiment conducted in the Sea of Japan, Borisenkov et al. (1975 ) approximated the vertical distribution of the LWC by the formula w=2.36X 10-s exp (_0.55 h,) cm3 cm 3,

(31)

where h' is the elevation (m) above the deck of the MFV. The dimension of w is cm 3 cm 3, as this value gives the volume of water in a unit volume of air. In other words, w is dimensionless. Assumingpw = 1025 kg m-3 and converting the dimensions of w to kg m -3, eqn. (25) becomes w = 2 . 4 2 X 1 0 - 2 e x p ( - 0 . 5 5 h ') kgm -3.

(32)

Aksjutin (1979) and Panov (1976) recommended this formula for use in any air-sea condition. However, eqns. (31) and (32) were derived experimentally for the Russian MFV "Narva"

74 moving into the waves at an angle of a = 110-90 ° with a speed of 5-6 knots ( 2.57-3.09 m s - ~), while the wind speed was equal to 10-12 m s - L. This data set indicates that eqn. (32) cannot be used for the approximation of vertical distribution of the LWC above any ship under any air-sea condition because the ship-wave interaction under certain conditions during this experiment resulted in generation of spray cloud, the parameters o f which ( a m o n g others, the LWC) have been measured. Therefore, if eqn. (32) reflects the LWC distribution above the ship deck in a cloud of collision-generated spray, it should be proportional to the wave height and to the square of the ship speed relative to the surface of an oncoming wave. The first assumption is in agreement with Kachurin et al. (1974). Thus, the distribution of the LWC under any condition may be presented for the same type of ship by the formula

W= Wo \-~o ] \'-Voo] exp ( -0.55h')

k g m -3,

(33)

where H and Vr are the wave height and ship speed relative to the waves, respectively. H0 and Vo are the wave height and ship speed relative to the waves during the Russian experiment, and Wois a constant equal to 2.42X 10 -z kg m -3 obtained from eqn. (32). If values of Ho and Vo are determined, the vertical distribution of the LWC can be easily found for any given wave height H and ship speed relative to waves (Vr). Unfortunately, Borisenkov et al. (1975) have not listed these parameters. We shall try to approximate the values of rio and Vo based on other parameters reported by them. First, we shall find the wave height Ho during the experiment. The value of wind speed (U~o= 10-12 m s - l ) , provided by Borisenkov et al. (1975), is sufficient for this purpose if the fetch is known. The experiment was carried on in the Sea of Japan and a fetch equal to 200 nautical miles seems to be appropriate. For this fetch and a wind speed of U~o = 11 m s - i, the significant wave height is equal to Ho = 3.09 m. Second, the ship speed relative to the waves is given in eqn. (25). For a fetch equal to 200 nautical miles, wind speed U t o = l l m s -L, ship speed V=2.83 m s -~ (5.5 knots), and ship heading of

0.2-

? E v Fz uJ tz

1:3 CD 0.1

u.l

[] (3l.

<

0 ...i

o

1'o M E A N W I N D S P E E D ( m s -1)

Shipspeed Ship speed

437ms -1A180 ° .1500 m120 °Q91 o 2 8 3 m s -1 A 1 8 0 ° ¢r150 ° [ ] 1 2 0 ° O 9 1 0

Fig. 5. The liquid water content in the cloud of collision-generated spray at a height of 1 m above the ship's deck as a function of wind speed, ship speed and heading. a = 100 °, the ship speed relative to the waves is equal to 11.01 m s i. Then, eqn. (33) becomes w = 6 . 4 6 × 10 -5

Hi/3 V~ exp ( -0.55h')

k g m -3,

(34)

where Vr ( m s - L) and oz are the ship speed relative to the waves and heading, respectively, H~/3 is the significant wave height ( m ) , and h' is the height above the deck of an MFV. The LWC has been computed for an M F V moving into the waves (o~ = 180, 150, 120 and 91 ° ) with the speeds 2.83 and 4.37 m s-1. The calculations have been done for the height h' = 1 m above the ship's deck and wind speeds at 10 m reference level equal to 10, 20, and 30 m s -~. The results are given in Fig. 5. The LWC increases significantly with the wind speed. The LWC is largest for a ship moving precisely into the waves ( a = 180 ° ) and it decreases with decreasing ship heading, being smallest for an MFV moving almost parallel to the wave crest ( a = 91 ° ). The LWC increases with ship speed for any ship heading but that of a = 91 °. The effects of ship speed and heading on the LWC are significant in high seas. For the vertical distribution of the LWC in the cloud of collision-generated spray, one can easily note that it decreases abruptly with the height above

75 the ship's deck. At the heights of h' = 5 m and 10 m above the ship's deck, the LWC is 9 and 141 times smaller than at a height of 1 m above the ship's deck, respectively.

2.4. Duration of direct spraying of an object For a single spraying event, the duration of direct spraying of an object located on an MFV, Atds, may be given by the formula

Atds=At-z

s,

(35)

where At is the total duration of the spray cloud residence above the vessel (m) and z is the time of spray flight to the object's surface (s). The time of spray flight to a given object, z, can be readily approximated by eqn. (20) if the wind speed, ship speed and heading are known. However, the formula for total duration of the cloud of collision-generated spray above the ship, At, has to be derived. When the morphology of the spray cloud is unknown due to the lack of field observations, we can make a rough approximation of this parameter only. For a given ship, the time o f ship exposure to a spray should depend on the ship speed relative to the wave at the moment of wave impact, the height of the wave, and the wind speed. The first two factors affect the extent o f the spray cloud and its morphology. Since the wind speed in the horizontal plane affects the duration of spray flight over a ship, the third term determines the residence time of the spray cloud. Thus formally, A t = f ( H , U~o, Vr).

(36)

If the g-theorem from dimensional analysis is used, we get [H][ V~]

[At]- U ([ , o ] ) ~

(37)

and then, eqn. (36) can be rewritten as

A HV~ t=c-~-o s,

(38)

where c is an empirical constant that depends first of all on the shape and size of the ship hull. Hence, for a given type of ship, we can find the value o f the

constant c if the values of other terms in eqn. (38) are known. Fortunately, some data have been found in the Soviet literature. First, Borisenkov and Panov (1972) mentioned Gashin's unpublished data from the Atlantic cruise of MFV "Iceberg" in August-November of 1969, when the ship was affected by swell, and some measurements of spray cloud residence were made. The duration of the spray cloud was given (At= 2 s) but the ship speed, wind speed, and wave height were not. On the other hand, the ship was affected by swell rather than wind waves, and the swell height is not related to the wind speed encountered by the ship during the measurements. As a result, this report is useless for our purposes. Fortunately, however, Borisenkov et al. (1975) said more about the air-sea conditions under which spray cloud duration was measured on the MFV "Narva" in the Sea of Japan in February 1973. For a ship speed 2.83-3.09 m s-~ (5-6 knots), wind speed U~o=10-12 m s-~ and ship heading of a = 90-110 °, the measured time of ship exposure to spray was equal to At= 5.8 s. If the significant wave height (Hi/3-- 3.09 m for a fetch of 200 miles) and the mean wind speed at a height of 10 m above the mean water level ( Ut o = 11 m s- ~) are used, one can find that for a given ship speed of V=2.83 m s -L and heading of a = 100 °, the constant c in eqn. (38) is 20.62. Hence, eqn. (38) becomes At=20.62

H1/3 Vr s. U~lo

(39)

The times of direct spraying of the foremast and the front side of the superstructure of an MFV have been computed for various ship speeds and headings, and wind speeds. Since there is only a very slight difference between the duration of direct spraying of the foremast and the superstructure, caused by somewhat longer duration of spray flight to the superstructure rather than to a foremast, the results are shown in Fig. 6 for the foremast only. Basically, the duration of spraying decreases with wind speed. It increases with the ship speed for any ship heading but that when a ship moves almost parallel to the wave crests ( a = 91 ° ). The duration of spraying is largest for a ship heading of a = 180 and 150 °, and it decreases as ship heading decreases.

76 FRONT SIDE OF SHIP'S SUPERSTRUCTURE

FOREMAST

fE

8~ 7

40 ~r

z

35

>,< rr

5 O.

CO W 30

n

0

•

_z o: <

121

u_ O z

25-

O

_o

,,= 2 0 -

n

CI)

z

n.-

I~c z

a5

15A

or

i

O

MEAN

WIND SPEED

10-

i

(ms -1) U-

Ship s p e e d Ship s p e e d

4 3 7 r n s -1 • 1 8 0 0

~r150 ° II2O

5-

°@91 °

2 8 3 m s -1 Z~180 ° # 1 5 Q ° D 1 2 Q ° O

91 o

[]

[]

CO

CI

II a. o

Fig. 6. Duration of directly spraying the foremast of an MFV as a function of wind speed, ship speed, and heading. It should be noted that for such various air-sea and ship m o t i o n parameters as those which were considered (wind speed U~o= 10-30 m s-~, ship speed V = 2.83-4.37 m s - l , and ship heading a = 9 1 - 1 8 0 ° ) , the duration o f direct spraying a ship seems to be in fact very steady, varying from only about 5 s to a little more than 7 s. If all terms on the right-hand side o f eqn. (1) are approximated as above, one can compute the spray flux to an object as a function o f wind speed, ship speed, and heading. For a fetch of 200 miles, the results are presented in Fig. 7. The objects are elevated h' = 1 m above the ship's deck. In general, the spray fluxes to the foremast and the front side o f the ship's superstructure are very similar. However, the spray flux to the foremast is s o m e w h a t larger than that to the ship's superstructure. One can also note that in low seas (wind speed 10 m s - t ) there is no spray flux to the superstructure o f an MFV moving into the waves ( a = 180 ° ) with the speed o f 2.83 m s - 1. That is, the spray travelling downwind splashes, under such conditions, objects in the range o f up to 17 m (with respect to the ship's bow), while the front side o f a superstructure is just beyond this range.

,o

20

3o

MEAN WINDSPEED(ms Shipspeed Shipspeed

lo -1)

2'o

MEANWINDSPEED(ms

3'0 -1)

4 3 7 m s -1 • 1 8 0 0 ~'150 ° I 1 2 0 ° 0 9 1 ° 2 8 3 m s -1 z~180 ° ~ ' 1 5 0 ° 1 3 1 2 0 0 0 9 1 0

Fig. 7. Spray flux originating from a single splash as a function of wind speed, ship speed and heading. The spray flux depends on the wind speed, ship speed, and heading. This increases with wind speed and it is largest for ships moving precisely into the waves ( a = 180 ° ) and diminishes as the ship heading decreases. As the ship speed increases, the spray flux increases for any heading but that when ship travels almost parallel to the wave crests (o~ = 91 ° ). Since the LWC decreases abruptly with the height above the ship's deck, the spray flux shows the same tendency. Let us approximate the total mass of spray impinging onto the entire M F V during a single spraying event. The only field data is given by Bori s e n k o v et al. (1975). They approximated that the total v o l u m e o f the LWC in the cloud o f collisiongenerated spray was equal to 300 litres when the Soviet MFV "Narva" was moving into the waves ( a ~ 1 0 0 ° ) , with speed V ~ 2 . 8 3 m s ~. Since they reported wind speeds o f U~0~ 11 m s - ], the significant wave height was equal to H~/3 = 3.09 m for an assumed fetch o f 200 miles. For these air-sea conditions and the ship moving almost parallel to the

77 wave crests, we assume that the spray was flying over a ship through a 'window' whose height is equal to about hma×= 7.7 m above the top of the ship's bulwark. This window spreads from the ship's bow to the front side of the superstructure, and its length is equal to about 21 m. Integrating eqn. (1) from a height of the ship's deck to a height on which the wind-driven spray droplets splash a ship (they do not fly over a deck impinging onto the sea surface yet), one can find, using our model, that about 40 litres of water should impinge onto the entire MFV during a single spraying event. This value is in quite good agreement with the approximation made by Borisenkov et al. (1975) for a whole spray cloud; only a part of the spray splashes a ship, while the rest of the water returns directly to the sea.

3. T I M E - A V E R A G E D F L U X OF C O L L I S I O N GENERATED SPRAY

The time-averaged spray flux (TASF) to an object located on a ship is

M=mn=EcUrsWAtdsn k g m - 2 m i n -~,

(40)

where n is the frequency of splashing a ship with collision-generated spray (min i) and the other terms are the same as in eqn. (1). The TASF is then a function of spray flux originating from a single spraying event and the frequency of spraying. This frequency may be roughly approximated based on the assumption that any ship-wave collision generates a spray cloud. Since the time interval, P~, between two successive ship-wave collisions is (Aksjutin, 1979) P~

-

2 s, 1.25 x ~ - / , ' c o s ot

(41)

where 2 is the wavelength (m), and 1I (m s-~) and ot are the ship speed and heading, respectively, the frequency of such collision bein_g n--

60(1.25 x/-2- l/costx) 2

min_ ~ "

(42)

To check the accuracy of eqn. (42) Zakrzewski (1986d) used the data set of Panov (1976) on the frequency of spraying an MFV. It has been found

T .E E

16-

°oo Z

14

r co ~_

12-

A

~

-

0

lO-

•%

-

4-

[]

/

Q

/

WAVE LENGTH O1Om A20m • 30m •40m [] 50m

/

z~@//

_ 0

F

/

-

Q U.I

/

/

6-

LL

•

/

z.~ 8D'~

ZX /

zx Aft,/

S . -

~z n"

A

i// I I I I I I I

I

I

I

I

I

I

I

I

I

8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 OBSERVED F R E Q U E N C Y OF S P L A S H I N G (min -1)

Fig. 8. Observed, and computed by Panov's ( 1971 ) formula, frequencies of splashing a Soviet type MFV with collisiongenerated spray. that a spray cloud is generated, on the average, every other ship-wave collision. The frequency of spraying seemed to be strongly dependent on the wavelength. Therefore, eqn. (42) should.not be used for computing the frequency of spraying a ship, even when an empirical factor is chosen for a given wavelength (Zakrzewski, 1986d). Fortunately, the frequency of spraying an MFV was approximated by the empirical formula of Panov (1971): "

n=15.78-18.04exp(-4.26/Pr) min -~ ,

(43)

where Pr is the frequency of ship-wave collision (min-~). To verify this formula, the field data set of Panov (1976) has been used (Zakrzewski, 1986d) and the results are shown in Fig. 8. The computed frequencies of spraying an MFV, no, fit rather well the measured frequencies, nm. The scatter is significant. However, in general, eqn. (43) does not underestimate the frequency of spraying. Based on some statistical analyses, Zakrzewski (1986d) has proven that the nm/nc ratio does not depend on the wavelength and it is close to 1.0. Therefore, Panov's (1971) empirical formula is recommended for MFV's of Soviet type for 15~>Pr>~3.5 s.

78 FOREMAST

FRONT SIDE OF S H I P ' S SUPERSTRUCTURE

220 200 7 .E

E 180-

height

Hi/3= 6.16 m are generated by wind speeds

equal to Ulo= 17 m s -] if the fetch is equal to 200 miles. For this wind speed and the same ship motion parameters, the TASF to the entire MFV is equal to about M = 960 kg m-1. This value shows that our model output is in reasonable agreement with the results of Soviet measurements.

E _~ 160-

X

A ¢t

140-

U-

~120O

CO 100uJ < n- 8 0 w

OD z~

>60-

A

i []

~-- 4 0 I---

aD

O CI

20-

1~

Jo

M E A N WIND S P E E D ( ms -1)

MEAN W ND S P E E D ( m s -1)

Shipspeed 4 3 7 m s -1 • 1 8 0 ° " 1 5 0 0 I 1 2 0 ° O 9 1 0 ShiDsl3eed 2 8 3 m s -1 A180 o ~-150 o 0 1 2 0 0 O910

Fig. 9. Time-averaged spray flux as a function of wind speed, ship speed, and heading. The TASF to the foremast and the front side of the ship's superstructure as a function of wind speed, and ship speed, and heading is given in Fig. 9. The height of objects was chosen to be equal to h' = 1 m above the ship's deck. The spray fluxes show tendencies similar to those on Fig. 7. The TASF is considerably large, especially in high seas. That is, this exceeds 100 kg m -2 rain-] if the object is elevated up to 2 m above the ship's deck and the wind speed is high. It is worthwhile to compare the results given by our model with experimental data. Panov (1976, Fig. 4.6) presented the relationship between the total water delivery to an MFV with the collision-generated spray and the height of the ship's bow. Panov (1976) has given that approximately 1-1.1 m 3 of water is delivered to the entire MFV per minute for the bow height equal to 3.7 m, ship speed V= 6 knots (3.34 m s- ] ) and ship heading a = 125 °, and a wave height of 6 m. In our model, the waves of significant

4. APPLICATION OF THE SPLASHING MODEL TO CORRECT THE ICE GROWTH RATES OF AN MFV Since ice can grow only when the icing surface is covered with a film of supercooled spray for calculating the time-integrated icing rates on any object exposed to the spray flux, one has to know the ratio of the time period during which the water film resides on the icing surface to the period of time between two successive generations of spray cloud. The assumption that a water film resides on the icing surface permanently during the icing event can result in overestimating the time-integrated icing rates if the period of water film residence on the icing surface is somewhat shorter than the time interval between two successive generations of the spray cloud. For a single spraying event, the period of water film residence on the icing surface (Ats) is given by

Ats=At-z+3tr

s

(44)

where At is the total duration of the spray cloud above the vessel, 3tr is the duration of water runoff after the direct spraying is stopped, and z is the time of spray flight to the object's surface. Let us estimate the period of time during which the moving water film resides on the icing surface of an object located on an MFV and compare it to the period of time between two successive generations of the spray cloud. Based on the analyses of a number of photographs of MFV's available from fishing companies and my cruise on the fishing vessel "Jan Turlejski", it was found that an MFV moving into the waves for a heading angle of o~> 90 ° generates a cloud of spray due to the ship-wave collisions if the wind force is not lower than force 3 on the Beaufort scale (wind speed 3.4-5.4 m s -~). Splashing the entire MFV (main deck, foredeck,

79 V=2.83

m s -1

V = 4 . 3 7 m s -1

14131209 ~ 110 0 IOLU if) 9 Z W 8-

~

7'-

~

•

J

Let us assume that the structure in the spray cloud is temporarily uniform. The mass of spray delivered due to direct impingement to unit area of a vertical plate during the last second of a spraying event is

m=UrsWEc k g m -2.

R

i

@

8

z~

6-

g

5i

MEAN

WIND SPEED

I

U l o ( m S -1 )

Time interval b e t w e e n s p l a s h i n g s @~=180 o • a=lS0 o me=120 o D u r a t i o n of d i r e c t s p r a y i n g O~ =180 ° Z~=150 o 1:3e = 1 2 0 °

Fig. 10. Duration of directly spraying an MFV and time intervals between two successive splashings for various wind speeds, ship speeds, and headings. rigging, bulwarks, superstructure) takes place for winds force 7 on the Beaufort scale and stronger. Thus, the wind speed in order to result in splashing the entire MFV by spray is equal to about 14 m s - ' (minimum wind speed for Beaufort number 7). In Fig. 10 the period of time between two successive generations of the spray cloud and the period of direct spraying of the central part o f the front side of the ship's superstructure are plotted for wind speeds of 15, 20, 25, and 30 m s - t. An MFV moving with speed V=2.83 m s - t and V=4.37 m s -1 into the waves has been considered for heading angles a = 120, 150, and 180 °. For a wind speed of Uto= 15 m s -t, the time of direct spraying the superstructure (~lt- r) is very close to the period of time between two successive splashings (60/n, where n is the frequency of splashing an MFV per minute). For a wind speed of U~oI> 20 m s - ' , the spray impinges onto the superstructure during about one half of the period between two successive splashings. Thus, for these high wind speeds, from eqn. (44) one can find that the moving water film on the icing surface resides a priori during at least one-half of the duration of the icing event.

(45)

For a vertical plate of height 5 m (the superstructure of an MFV) the mass of spray delivered during the last second of the spraying event is quite large for a ship travelling into the waves with a speed of only 2.83 m s-~ as one can find from eqn. (45). At the end of the direct splashing, the icing surface is covered with a moving water film, the thickness of which increases downwards. To determine the period of time during which the water film flows down the vertical plate, a simple experiment has been conducted. A vertical metal plate 1 m in width was painted white with an oil paint, and on this several black horizontal lines were drawn. This plate was flooded from the top with fresh water supplied through a horizontal pipe with several small holes. The speed of water film flowing down the plate was measured by recording on a VCR the movement of colored water delivered occasionally to the pipe. For a water film thickness of up to 2 ram, the speed of water runoffdid not exceed 0.86 m s ', being equal, on the average, (for 19 runs) to 0.51 m s - t (standard deviation 0.17 m s- ~). Since the height of the vertical plate was equal to only 2.1 m, it was difficult to investigate the character of water flow: no significant increase in the speed of the water film with decreasing height has been found. The assumption of the steady-stable movement of the water film will cause no large error in estimating the speed of water runoff from the low vertical plates. However, for high objects from which the runoff water can flow down with increasing speed, this not fully tested assumption can result in overestimation of the time of moving water film residence on the icing surface. Employing the mean value of the speed of water rundown from our sample tests (0.5 m s- ~), one can find how long, after stopping the direct spraying, the water film resides on the wall of the ship's superstructure (Table 5). To simplify calculations, the ship's superstructure was divided into five sections, each 1 m high and their centres were elevated 0.5, 1.5 . . . . 4.5 m above the ship's deck.

80 TABLE 5

1.0-

Duration of water runoff from a 5 m high vertical plate after the moment when the direct spraying is stopped Elevation above the ship's deck (m)

4.5

3.7

2.5

1.5

0.5

0.9

\

rr 0.8 O I.O

\

<

,~ 0.7it

~0.6-

o-----o...~ "m

-"i

Time (s)

1

3

5

7

9

<

0 Q50.4

It is worth noting that in the field the speed of water rundown from the vertical plate, covered with ice, will be somewhat smaller because of the surface tension. Thus, the duration of water film residence on the icing surface Seems to be longer than listed in Table 5. To calculate the icing rates, a knowledge of the ratio of the time of moving water film residence on the icing surface to the period of time between two successive splashings is most important. This ratio is given by the formula At + Atr - r A=n

60

(46)

where n is the frequency of splashing an M F V with collision-generated spray per minute. A value of A >/1.0 means that the icing surface is covered permanently with a moving water film and there is no need to correct the calculated icing rate I (kg m -2 h ~). For A < 1.0 one has to correct the icing rate using the formula Icor=AI

kgm

2

h-'

(47)

where I is the time-integrated icing rate, Icor is the corrected icing rate, and A is the scaling factor. Values of the scaling factor A are plotted in Fig. 11 for a wind speed of 30 m s - ~; it seems to decrease with decreasing ship speed and increases with decreasing heading angle being greatest for a heading angle of o~= 150 ° and further significantly decreases for c~= 120 ° . In high seas the ship roll and wind drag force result in removing seawater delivered by spray and temporarily accumulated on the top side of the bulwarks. This water flows down irrespective to the runoff of spray hitting the vertical sides of the bulwarks and this process affects the regular water runoff from their vertical sides. The seawater delivered

ij... ~

I

-e--- ~

'XO

"o

I

I

180" 150" 120" SHIP HEADING (degrees)

Fig. 11. Scaling factor A as a function of ship heading and elevation above the ship's deck (dots 4.5 m, squares 3.5 m, triangles 2.5 m) for a ship speed of 2.83 m s -~ (black) and 4.37 m s ~ (white). by a wave which flooded the main deck and/or foredeck also affects the water film on the bulwarks making them wet as the MFV responds to the waves. Therefore, the method described above may not be used to calculate the time of water film residence on the bulwarks. However, taking into consideration the results listed in Zakrzewski (1986d) and the effects of the direct flooding on the ship's deck by the waves and the runoff water from the top sides of the bulwarks on the time of moving water film residence on the vertical sides of the bulwarks, one may conclude that in high seas the bulwarks of an M F V moving into the waves are covered with a moving water film at all times. On the other hand, it is worth noting that it is not possible to calibrate the time-integrated ice growth rates on the bulwarks, because there are no available field data on the duration of water film resistance on them.

5. CONCLUSIONS The flux of collision-generated spray to an object located on an MFV, originating from a single splashing, is a function of collision efficiency, spray speed relative to the object, liquid water content ( L W C ) and duration of direct spraying. The spray speed relative to the object and liquid water content are the least known parameters involved in the spray flux. Since there are no data on the wind speed in the vicinity of a ship, one has

81 to assume that spray travels through the air in the horizontal plane with the speed equal to the mean wind speed at a height of 10 m above the mean water level. The vertical component of the spray speed at the moment of hitting an object may be roughly approximated using the relative wind speed and a distance travelled (relative to a moving ship) in the horizontal plane by a spray droplet. There are very few field data available that present the vertical distribution of the LWC in the c l o u d of collision-generated spray. This is a function of the height above the ship's deck, wave height and ship speed relative to the waves. The empirical formula of Borisenkov et al. (1975) for the vertical distribution of the LWC above the ship's deck has been improved for use in any air-sea conditions. Using Russian field data from the Sea o f Japan, an empirical relationship between the total duration of spray cloud residence over an MFV, the wave height, ship speed relative to the waves, and mean wind speed has been derived. The duration of direct spraying of an object located on an MFV is equal to the total duration o f spray cloud residence over a ship less the duration of spray flight. Time-averaged spray flux to an object is a function of mass flux from a single splashing of a ship with spray and the frequency of splashing. The latter parameter is fairly well approximated by Panov's (1971) empirical formula, while the simple relationship between the frequency of ship-wave collisions, the wavelength, ship speed, and heading is less accurate even when a scaling factor for various wavelengths is applied. Spray flux to a cylinder is smaller than to a large vertical plate. Since the spray flux increases with wind speed, ship speed, and heading, the spray flux is largest for a ship moving into the waves with high speed in heavy seas. Under most severe weather conditions, spray flux to an object elevated 1 m above the ship deck exceeds 200 kg m -2 m i n - l . Spray flux does not depend on ship speed if the ship moves parallel to the wave crests ( a = 90 ° ). The proposed ship spraying model will soon have to be improved by taking into account: ( 1 ) turbulence of the airflow and the shadow effects caused by the bulwarks, hatches and superstructure of the ship; (2) the air drag force effects on the spray droplet velocities in horizontal and vertical direc-

tions; and (3) the object's orientation with respect to the spray droplet trajectories. For an MFV travelling into the waves in high seas, the front and windward sides of the ship's superstructure, bulwarks, mast and rigging, and probably also the deck equipment, are covered with water at all times. Only the upper parts of elevated objects located on an MFV within the zone of direct spraying, are water film-free during a short period of time when compared to the period of time between two successive splashings. Since the runoff water flows down, the time of moving water film residence on such objects increases as the height above the ship's deck decreases. The ratio of the time of the moving water film residence on the icing surface to the period of time between two successive splashings of an MFV decreases as ship speed decreases. For investigated values of the ship heading ( a = 180, 150, and 120 ° ) this ratio was greatest for a = 150 ° and smallest for a - - 1 2 0 °. Thus, the time-integrated local icing rates on upper parts of elevated vertical objects located on an MFV should also decrease if the ship speed decreases. These icing rates should vary with the ship heading showing a similar tendency as the above mentioned ratio. There is an urgent need to launch a comprehensive field experiment to investigate the zones affected by collision-generated spray for several types of ships, and the duration of water film residence on several parts of a ship under conditions of icing. The spray cloud morphology and structure, as well as the spray cloud movement over a ship and the wind speed in the vicinity of several parts of a ship, should be also investigated. It will help to improve the accuracy of time-integrated icing rates. Since the total ice growth rates on a ship depend on the area surface exposed to wetting by direct spraying and/or moving water film, ships intended for navigation in regions prone to icing should have a minimal surface of all objects exposed to wetting, especially in the bow, main deck and foredeck areas. The bow and freeboard should be reasonably high, and the hull of such ships should generate a minimal amount of spray during a ship-wave collision and impacts due to pitch and heave. The bow and board shapes, which reject spray from a hull in the horizontal plane, are recommended.

82

ACKNOWLEDGEMENTS T h i s p a p e r has b e e n p r e p a r e d d u r i n g b o t h the a u t h o r ' s stay as V i s i t i n g Scientist at C - C O R E , M e m o r i a l U n i v e r s i t y o f N e w f o u n d l a n d , St. J o h n ' s , C a n a d a , a n d at the D i v i s i o n o f M e t e o r o l o g y , U n i versity o f A l b e r t a , E d m o n t o n , C a n a d a . F i n a n c i a l s u p p o r t f r o m a n N S E R C Strategic G r a n t d u r i n g his stay in E d m o n t o n is k i n d l y a c k n o w l e d g e d . T h e a u t h o r is grateful to P r o f e s s o r E d w a r d P. L o z o w s k i for his v a l u a b l e c o m m e n t s . T h e careful t y p i n g b y Ms. L. S m i t h a n d h e r c o n t r i b u t i o n to editorial w o r k are also k i n d l y a c k n o w l e d g e d . Special t h a n k s to Mr. G. L e s t e r a n d his s t a f f for g r a p h i c a l w o r k on figures.

REFERENCES Aksjutin, L.R. (1979). Icing of Ships. Sudostroeyne Publishing House, Leningrad, 126 pp. (in Russian). Borisenkov, Ye.P. (1969). Physical examination of hydrometeorological complex favourable for icing of ships. In: Hydrometeorological Conditions of Icing of Ships. Published by the Arkticheskii i Antarkticheskii NauchnoIssledovatelskiiInstitut. Leningrad, pp. 7-20 (in Russian). Borisenkov, Ye.P. (1972). On the theory of spray icing of ships. In: Arkticheskii i Antarkticheskii Nauchno-Issledovatelskii Institut. Trudy 298, Gidrometeoizdat, Leningrad, pp. 34-43 (in Russian). Borisenkov, Ye.P. and Panov, V.V. (1972). Primary results and prospects for investigating hydrometeorological conditions favourable for icing on ships. In: Arkticheskii i Antarkticheskii Nauchno-Issledovatelskii Institut. Trudy 298. Gidrometeoizdat, Leningrad, pp. 5-33 (in Russian). Borisenkov, Ye.P. and Pchelko, I.G. (1975). Indicators for forecasting ship icing. United States Army Cold Regions Research Engineering Laboratory, Draft Translation No. 481, Hanover. Borisenkov, Ye.P., Zablockiy, G.A,, Makshtas, A.P,, Migulin, A.I. and Panov, V.V. ( 1975 ). On the approximation of the spray cloud dimensions. In: Arkticheskii i Antarkticheskii Nauchno-lssledovatelskii Institut. Trudy 317. Gidrometeoizdat, Leningrad, pp. 121-126 (In Russian). Brooke Benjamin, T. (1959). Shearing flow over a wavy boundary. J. Fluid Mech., 6: 161-205. Brown, R.D. and Roebber, P. (1985). The ice accretion problem in Canadian waters related to offshore energy and transportation. Canadian Climate Centre. Report No. 85.13, Downsview, Ont., 295 pp. Grochowalski, S. (1982). The prediction of deck wetting in beam seas in the light of results of model tests. Proceedings of the 2nd International Conference on Stability of Ships and Ocean Vehicles. Tokyo, Japan, Oct. 1982, pp. 125-139.

Handbook of Oceanographic Tables (1966). U.S. Naval Oceanographic Office, Washington, D.C. 20390. Kachurin, L.G., Gashin, L.I. and Smirnov, I.A. (1974). Icing rate of small displacement fishing vessels under various hydrometeorological conditions. Meteorologiya i Gidrologiya, 3:50-60 (in Russian). Kultashev, E.N., Malakhov, N.F., Panov, V.V. and Schmidt, M.V. ( 1972). Spray icing of SRT and SRTM fishing vessels. United States Army Cold Regions Research Engineering Laboratory, Draft Translation 411, Hanover. Large, W.G. and Pond, S. (1981 ). Open ocean momentum flux measurements in moderate to strong winds. J. Phys. Oceanogr., 11 (3): 324-336. Lundquist, J.E. and Udin, I. (1977). Ice accretion on ships with special emphasis on Baltic conditions. Winter Navigation Research Board, Norrkj~iping, Res. Rep. 23, 34 pp. Makkonen, L. (1984). Atmospheric icing. United States Army Cold Regions Research Engineering Laboratory, Hanover, Monograph 84-2, 92 pp. Mertins, H.O. (1968). Icing of fishing vessels due to spray. Marine Observer, 38(221 ): 128-130. Overland, J.E., Pease, C.H., Preisendorfer, R.W. and Comiskey, A.L. (1986). Prediction of vessel icing. J. Climate Appl. Meteor. (in press). Panov, V.V. (1971 ). On the frequency of splashing a mediumsized fishing vessel with sea spray. In: Theoretical and Experimental Investigations of the Conditions of Icing of Ships. Gidrometeoizdat, Leningrad, pp. 87-90 (in Russian). Panov, V.V. (1976). Icing of ships. Arkticheskii i Antarkticheskii Nauchno-Issledovatelskii Institut. Trudy 334. Gidrometeoizdat, Leningrad, 263 pp. (in Russian). Panov, V.V., Panyushkiin, A.V. and Shvayshteyn, Z.I. (1975). Physical processes during splashing a ship with spray. In: Arkticheskii i Antarkticheskii Nauchno-lssledovatelskii Institut. Trudy 317. Gidrometeoizdat, Leningrad, pp. 13-31 (in Russian). Pierson, W.J., Neumann, G. and James, R.W. (1955). Practical methods for observing and forecasting ocean waves by means of wave spectra and statistics. U.S. Navy Hydrographic Office, H.O. Publ. 603, Washington, 284 pp. Shehtman, A.N. (1968). Frequency and intensity of icing on sea-going ships. Trudy NIIA (Research Institute of AirClimatology, U.S.S.R.), 50:55-65 (in Russian). Shellard, H.C. (1974). The meteorological aspects of ice accretion on ships. World Meteorological Organization. Marine Science Affairs Report No. 10 (WMO-0No. 397 ), 34 pp. Stallabrass, J.R. (1980). Trawler icing. A compilation work done at NRC. National Research Council Canada, Mechanical Engineering Report ND-56, NRC No. 19372, Ottawa, 103 pp. Wise, J.A. and Comiskey, A.L. (1980). Superstructure icing in Alaskan waters. Pacific Marine Environment Laboratory, Seattle, Washington, NOAA Special Report, 30 pp. Zakrzewski, W.P. (1986a). Ice growth rates on sea-going ships.

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Ice growth rates and simulation of icing. Proceedings of the 8th Int. IAHR Symposium on Ice, Iowa City, August 18-22, 1986, Vol. 2, pp. 195-207. Zakrzewski, W.P. (1986d). Icing of ships. Part I: Splashing a ship with spray. NOAA Technical Memorandum, ERL PMEL-66, Seattle, 74 pp.