Hydrodynamic Forces and Dynamic Response of Circular Cylinders in Wave Zones

GANG MIAO

NT

UNIVERSITETET I TRONDHEIM -9!_vrotAt)Y NORGES TEKNISKE HOGSKOLE

TECHNISCHE UNIVERSITEIT

Scheepshydromechanica

Archie(

Mekelwf.g. 2, 2628 CD Delft

Tel:015-2786873/Fax:2781836

HYDRODYNAMIC FORCES AND

DYNAMIC RESPONSES OF CIRCULAR

CYLINDERS IN WAVE ZONES

DOKTOR INGENIORAVHANDLING 1989:3

INSTITUTT FOR MARIN HYDRODYNAMIKK

_FL

TRONDHEIM

HYDRODYNAM-O\

HYDRODYNAMIC FORCES AND DYNAMIC RESPONSES

OF CIRCULAR CYLINDERS IN WAVE ZONES

by

Gang Mao

Trondheim, October 1988

Division of Marine Hydrodynamics The Norwegian Institute of Technology The University of Trondheim

Horizontal cylinders are subjected to impact loads when suddenly immersed. On offshore oil platforms and semi-submersibles these forces can contribute to eventual failure unless allowed for in the initial design calculations. The phenomenon of water impact is particularly complex because it involves both the rapid sweep of the water surface across the structures and the dynamic interaction between fluid and structure motion.

This report describes and discusses a series of experiments conducted to measure pressure distributions, slam force time histories and dynamic responses on a horizontal cylinder slammed into calm water. A test rig was designed and built on which cylinders of 0 = 0.5 m, 0.125 m and 0.05 m were forced at constant velocities of between 0.3 and 2.66 m/s through a still water surface. The motion of the test cylinder was controlled by a

hydraulic system. The time-varying pressure distribution around the circum-ference, at angles between 00 and 300 to the vertical, was measured and the slamming forces acting on the body have been calculated from it. Slamming forces were also measured directly and the hydrodynamic load histories were determined. The test rig and instrumentation have proved to be reliable and to produce repeatable results with little scatter.

Dynamic response of three-dimensional elastic models of horizontal trusses of semisubmersibles and jackets were studied. The mathematical modeling of water impact of a horizontal flexible cylinder was developed. Numerical results were compared with results obtained from dynamic response measure-ments. It has been shown that this dynamic simulation model can be used to provide good estimates of the elastic horizontal cylinders to slam loading. Analysis of the characteristics of the dynamic response suggested that dynamic magnification could be neglected.

The predominant marine fouling species encountered on North Sea structures in the water depth range of 0 - 30 in are mussels and kelp, whilst sea ane-mones and/or barnacles dominate the 30 - 80 in depth range. In the present

study an attempt was made to simulate rigid marine growths such as mussels and barnacles, and soft fouling of long flapping seaweeds such as kelp, by attaching simulator materials to the surface of a cylinder. The forces it experienced in harmonically oscillating flow were then compared with those of the same smooth cylinder. The experiments cover the Reynolds number

range from about 4 x 104 to 3 x 105 at Keulegan-Carpenter number K = 15, and the results for nominally smooth cylinders compare well with results obtained elsewhere. The effect of roughness density was also investigated. Three kinds of roughness density (12.5%, 25%, 100%) were used in the experiments. It was found that the drag force was increased significantly and a simple analysis using the Morison equation indicated that the drag coefficent had been increased by around 200%. The transverse force may be significantly larger than the in-line force. This may have implications for

the design procedure for risers. The results indicate that marine fouling may cause a greater increase in fluid loading than is generally assumed.

ACKNOWLEDGEMENTS

The author acknowledges the supervision provided by professor Harald

Walderhaug. The author also wishes to thank Arne Nervik, Trygve Moe, Sverre Arntsberg and Terje Sotberg for their help and assistance with the

-5-CONTENTS Page

NOMENCLATURE 8

INTRODUCTION 1.1

THEORETICAL ANALYSIS 2.1

2.1 Von Karman's Expanding Plate Analogy 2.2 2.2 Wagner's Flat Plate Fitting with Wetting Correction 2.4

2.3 Fabula's Ellipse-Fitting and Growing Circular 2.5

Arc Approximation

2.4 Added Mass Calculation by Faltinsen 2.7 2.5 Numerical and Experimental Results of Hydrodynamic 2.9

Impact Analysis by EPRI Report

EXPERIMENTAL SURVEY 3.1

DESCRIPTION OF MODELS, INSTRUMENTATION AND EXPERIMENTS

Test Cylinders 4.1

4.2 Test Equipment and Instrumentation 4.9

4.2.1 Water Tank and Equipment 4.9

4.2.2 Test Facility 4.9

4.2.3 Measuring Instruments

4.15

4.2.4 Calibration 4.20

4.3 Description of Tests 4.27

4.3.1 Test Procedure 4.27

4.3.2 Slam Velocity Measurements 4.28

4.3.3 Circumferential Pressure Measurements 4.29

4.3.4 Pressure Phase Measurements 4.29

4.3.5 Force and Moment Measurements 4.29

4.3.6 High-Speed Photography 4.29

TEST RESULTS AND DISCUSSION 5.1

5.1 Velocity Measurements 5.1 5.2 Pressure Measurements 5.1 5.3 Piled-up Water and Spray Root Measurements 5.14 5.4 Impact Circumferential Pressure Distribution 5.24 5.5 Slamming Coefficients Derived from Pressure Data 5.31 5.6 Slamming Force Measurements 5.39

2.,

3.

4.,

-6-5.7 Proposed Slamming Load History 5.44 5.8 Slam Test for a Fouled Cylinder 5.45

5.9 Out of Water Tests 5.46

5.10 Dynamic Strain Response Measurements 5.48

DYNAMIC RESPONSE OF A HORIZONTAL CIRCULAR CYLINDER 6.1 PENETRATING AN INITIALLY CALM FREE SURFACE

6.1 Mathematical Modeling of Dynamic Equations 6.1

6.2 Solution of Dynamic Equations 6.5

6.2.1 Solution for Both Ends Simply Supported 6.8

Uniform Beams

6.2.2 Solution for Both Ends Fixed Uniform Beams 6.11

6.2.3 Numerical Methods for Solution of Second-Order 6.16

Dynamic Differntial Equations

6.2.4 Added Mass Calculation 6.18

6.2.5 Drag Coefficient 6.23

6.2.6 Buoyant Force 6.23

6.2.7 Damping Coefficient 6.26

6.2.7.1 Structural Damping 6.27

6.2.7.2 Hydrodynamic Damping 6.29 6.3 Comparison between Theory and Experiments 6.29 6.4 Stresses Due to Slamming in Offshore Structures 6.37

6.4.1 Quasi-Static Method 6.37

6.4.2 Comparison between Quasi-Static Stresses and 6.40

Dynamic Stresses of Numerical Calculations

THE EFFECTS OF MARINE FOULING ON OFFSHORE STRUCTURES 7.1

7.1 Introduction 7.1

7.2 Description of Marine Growth in the North Sea Area 7.4

7.2.1 Types of Marine Growth 7.4

7.2.2 Sectors of Fouling in the North Sea 7.7

7.2.3 Factors Affecting Growth 7.8

7.2.4 Fouling Communities on North Sea Platforms 7.9

7.2.4.1 Southern North Sea 7.9

7.2.4.2 Central North Sea 7.13

7.2.4.3 Northern North Sea 7.16 7.3 The Effects of Fouling on Hydrodynamic Loading 7.18

7.3.1 Circular Cylinder in Uniform Incident Flow,

Harmonically Oscillating (Bodies) Flows 7.26

6.

8.

-7-7.4 Experimental Investigation 7.34

7.4.1 Experimental Technique and Equipment 7.36

7.4.2 Test Cylinder 7.38

7.4.3 Simulation of Marine Growth 7.39

7.4.4 Data Acquisition 7.41

7.4.5 Results and Discussion 7.41

7.4.5.1 Analysis Method 7.41 7.4.5.2 In-Line Forces 7.43 7.4.5.3 Transverse Forces 7.54 CONCLUSIONS. REFERENCES 8.4 APPENDIX A 8.8

NOMENCLATURE

A Amplitude of oscillations

A33 Added mass Half plate width Ca Added mass coefficient

Cb Buoyancy contribution to slamming coefficient

Cd Drag coefficient

Cdc Drag coefficient at constant velocity

Cdt Total drag force coefficient Cf Frictional force coefficient

CHO Hydrodynamic viscous damping coefficient

C1 Lift coefficient

Cm Inertia coefficient Cs Slamming coefficient

C50 Structural damping coefficient

Cylinder diameter

Or Effective diameter of the rough cylinder Young's modulus

Force

F3 Vertical force per unit length

Fa Added mass force

Fb Buoyant force

Fd Drag force

Fdt Total drag force

Ff Frictional force Fi Inertia force

F1 Lift force

Fm Inertia force of the model itself in motion

Fn Froude number Fs Slamming force Fx Horizontal force Fz Vertical force Frequency parameter Wave height Submergence

Area moment of inertia of cross-section with respect to neutral axis

Keulegan-Caroenter number 0

Roughness height

ki0 Relative roughness Cylinder length

Length of rubber strip Actual mass of the model

rn Mass per unit length Pressure

Displacement in normal coordinates Cylinder radius

Re Reynolds number

Sf Surface area of the end plates contact with water SkiS Roughness density

Wave period or period of oscillations Time from start of slam

tr Rise time

Constant velocity

Um Maximum velocity in a cycle Velocity

Section modulus

x,y,z Rectangular cartesian coordinate

Logarithmic decrement Relative submergence h/R

Kinematic viscosity of water Damping ratio Density of water Stress Normal modes MY 6

Offshore stuctures often have appreciable numbers of main structural and bracing members near the still water level. Slamming loads occur when a moving body strikes and enters a water surface or conversely when a moving surface strikes and submerges a body. They are thus an important element of the wave forces in the splash zone of offshore installasions. If a structural member presents a large face parallel to, or nearly parallel to, the wave surface and if the relative velocity of impact is high, slamming forces are both impulsive and large - usually much larger than the other forces (due to buoyancy, drag and inertia) experienced in fully immersed

flow of the same velocity.

On offshore structures there are several situations in which slamming loads

are significant.

<I> Horizontal bracing members on fixed offshore structures in the splash zone are slammed by waves passing through the structure. Both fati-gue problem and the extreme load case are important.

<2> Bracing members on damaged semisubmersible rigs may be slammed by combination of wave action and vessel motion during severe sea con-ditions (survival draft).

<3> During towing and launch of jacket structures, members, which will spend their design life well away from the surface, are slammed again by a combination of wave action and vessel/rig motion.

<4> Vertical members may be hit by breaking waves, particularly in shallow-water conditions.

Several cases of damage on offshore structures in the North Sea due to slamming loads are reported in the last few years. The intense wave action and persistent hammering of the waves has caused actual loss of horizontal members after years of overstressing.

The original motivation for studies of hydrodynamic impact was the need to estimate the impact loads felt in seaplane landings. During World War II, the use of airborne torpedoes further stimulated interest in water impact problems. The desire to operate ships at higher speeds and in rougher seas

has introduced the ship-slamming problem to hydrodynamicists, while the advent of offshore technology has made the problem of water impact on hori-zontal cylindrical members of equal interest.

Kaplan and Silbert (1976

NI

developed a solution for the forces acting on a cylinder from the instant of impact to full immersion. Miller (1977 [2]) presented the results of a series of wave-tank experiments to establish the

magnitude of the wave-force slamming coefficient for a horizontal, circular

cylinder. He found an average slamming coefficient of Cs = 3.6, where Cs

is defined by

Fs C

-s

1 ,u2DL

2

Fs = the slamming force

p = water density

D = cylinder diameter

L = cylinder length

U = vertical velocity of water surface at impact

Faltinsen et al. (1977 [3]) investigated the load acting on rigid

horizon-tal circular cylinders (with end plates and length-to-diameter ratios of

about 1) that were forced with constant velocity through an initially calm

free surface. They found that the slamming coefficient ranged from 4.1 to

6.4. They also conducted experiments with flexible horizontal cylinders, and found that the analytically predicted values were always lower to SO per cent) than those found experimentally.

Sarpkaya (1978 [41) conducted slamming experiments with harmonically oscillating flow impacting a horizontal cylinder and found that:

the dynamic response of the system is as important as the

impact force. One cannot be determined without accounting

the other.

the initial value of the slamming coefficient is essentially equal to its theoretical value of n.

2

the system response may be amplified or attenuated depending on its dynamic charecteristics.

the buoyancy-corrected normalized force in the drag-dominated region reaches a maximum at a relative fluid displacement of

about 1.75. (See Fig. 1-1)

roughness increase the rise time of the force and tends to decrease the amplification factor.

THEORETICAL EXPERIMENTAL

BUOYANCY

Fig. 1-1 Comparison of theoretical and experimental slamming

coefficients (Sarpkaya 1978)

Campbell and Waynberg (1980 151) analysed the pressure and force measure-ments from horizontal and inclined impacts and proposed a time history of slam load coefficient Cs by the empirical eauation:

Cs = 5.157(1+19 Ut/D) + 0.55

)(tin

where U is the slamming velocity; t the time; and ID the diameter of the

cylinder. This equation is independent of Froude number over the range

tested (Ut/D < 1).

Slamming is impulsive in character and may consequently excite significant

dynamic response.

2 3

(c)

4

The design of offshore structures that must survive in a wave environment depends on a knowledge of the forces that occur at impact as well as on the dynamic response of the system. The horizontal cylindrical members of offshore platforms situated near the sea surface are long and slender, slamming loadings may generate very important and destructive vibrations. The realization that the impact forces is of an impulsive nature requires consideration of the fact that this force does not act on a perfectly rigid body, but rather on a cylinder which is elastic. The response of a long cylinder to an impulsive force is heavily dependent on the exact nature of the force itself as well as on the nature of hydroelastic oscillations of

the cylinder. The objective of my work is to determine basic slamming load

on smooth two-dimensional cylinders and to study the fluid structure interaction problem, dynamic response in time domain, and the effect of

2 THEORETICAL ANALYSIS

The general case of hydrodynamic impact usually is described by using incompressible potential flow theory. The compressibility of water and air and the cushioning effect of air (air boundary layer, depression of the water surface just before impact, etc.) and surface tension are ignored. When a body enters the free surface of a fluid, it causes the fluid to

move, ie. to accelerate. In imparting these (spatially varying)

accelera-tions it increases the momentum of the fluid and consequently experiences al resisting force in accordance with Newtons second law.

F = (fluid momentum)

The problem in estimating slamming forces on a theoretical basis is to satisfactorily describe the motion of the fluid. As in all problems

involving a free surface, a major obstacle is the necessity for satisfying nonlinear conditions on a boundary whose location is unknown a priori, while the fact that the flow is basically unsteady is a further

complica-tion. The primary source of difficulty is the mathematical singularities encountered at the spray root. No exact solutions of the problem exist. Thus, all existing analyses of water impact problem either are numerical or

are based on an approximate version of the free surface boundary

condi-tions. There is no exact mathematical solutions to this problem and the

essential differences between the various theoretical models proposed lie in the degree and type of approximations used in them.

Unfortunately, the results obtained are extremely sensitive to the

aporoxi-mations. There are extensive papers on the liquid/solid impact theories,

but only those dealing specifically with cylinder/water broadside impact

will

be considered here.

It is clear that the common approach for circular cylinders consists of two

parts:

<1> Relating the free surface profile, the wetted width and the added mass of the impacting body to the instantaneous depth of its lowest point below the original still water surface (ie. the draught).

<2> Applying values from <1> to the general equations of motion for the cylinder and its added mass to find the loads and motions during the

Investigators tend to agree that the slam loading has a timewise triangular distribution of very short duration (of the order of milliseconds) and that its magnitude may be related to the velocity at the instant of impact by

the expression:

F

=C 1 pU2

A

S

s2

s s

where

Fs is the slam load per unit length of the body

Cs is a dimensionless slam coefficient

p is the mass density of the fluid

As is a representative impact area (for a circular cylinder, As = diameter 0)

2.1 Von Karman's Expanding Plate Analogy

Numerous theoretical treatises of a body impacting a flat water surface have appeared in the literature during recent years. For the most part

these theories are based on the earlier work of Von Karman, (1929 [6]) later extended by Wagner (1931 [7]). The basic idea of Von Karman was that during impact, the momentum of the dropping body is imparted to the

momen-tum of an appearent mass of water, assumed to be that associated with a flat plate having the dimensions of the body at the intersection of the

water surface. Von Karman, in his twodimensional analysis of seaplane

-float impact, chose to neglect the spray and assumed that the flow field within the water was identical to that around a two-dimensional flat plate,

having the instantaneous beam width (AB in Fig. 2-1) of the float at its intersection with the undisturbed free surface. Now in accelerating flows

Fig. 2-1 Definition Sketch for Expanding Plate Model

it is convenient to treat the momentum of the fluid as effectively that possesed by an indentifiable mass, A33, of fluid moving at a representative velocity, in this case the penetration or slamming velocity U. The mass,

A33, is referred to as the 'added mass'.

For a two-dimensional flat plate in an infinite stream we find:

A33 = pirb2

where

= fluid density = half plate width

Von Karman argued that, because in this free surface problem there is no fluid above the plate and since the invicid flow around a flat plate normal to the stream possesses fore and aft symetry, the appropriate added mass is half that given above

i.e. _{A33 =} pnb2

2

Clearly the half-width b, the width of the half waterline at z = 0 of the submerging body, increase with penetration h.

b2 = R2 - (R-h)2

= h (2R-h)

where R is cylinder's radius.

We now assume constant velocity impact V = U = constant

but So dv thus -- = 0 dt

dA33dV

dA33 F =

1 (A33V)- V

dt + A33 dt - U dt dA33 dh 2 dA33

-u

--

U dh dt dh dA33 1 d(b2) dh

- 2 " dh

pit (R-h) F pnU2 (R-h)

Defining a slamming ciefficient Cs

C

_{s1 2}

--2pU D

We find Cs = it (1-h/R) as shown in Fig. 2-5. According to Von Kaman's theory, for the cylinders Cs is thus a maximum at the instant of impact and

equal to n. In Fig. 2-5 we see that the width of the plate is too small

when compared with the experimental results of Campbell and Weyberg (1980 [5]). This arises because we have neglected the free surface rise up the cylinder surface during penetration. The following methods try to account

for this.

2.2 Wagner's Flat Plate Fitting with Wetting Correction

Wagner (1931 [7]) paid attention to the water which is "piled up" along the sides of an entering body. He used similar arguments to Von Karman, but assumed that the equivalent flat plate extended between the spray roots as

shown in Fig. 2-2. As one might expect, this has a dramatic effect on the

slamming forces. Using Wagner's model Wellicome (1977 [8]) has shown that

2n

Cs

-(1+35)

where D is the cylinder's diameter.

les is a maximum at the instant of impact and equal to 2n, see Fig. 2-5. These results are obtained by integration of the pressure distribution over

the flate plate.

!EQUIVALENT

FLAT PLATE

ASSUMED

ACTUAL S.W.L.

Fig, 2-2 Wagner'Fs Flat Plate Model of Impact

2.3

Fabula's Ellipse, - Fitting and Growing Circular Arc Approximation

fabulla and Ruggles C1955 1[14])1 adapted the theory of Shiffman and Spencer

(1945) for the three dimensional vertical impact of spheres on, calm water to the two dimensional case of vertical broadside water impact of a cir-cular cylinder. Using the resulting velocity potential during impact, they deduced an approximate added mass from which they calculated a time

variation of impact coefficient. Their Cs, value was, maximum at the instant

of cylinder/water contact with a value of about 4-19 and decreased with increasing cylinder draught.

Fabula (1957 i1l51111 amended the ellipsoid fitting technique employed by

Shiffman and Spencer (1951) and applied it to the present case (among

others), See Fig. 2-3 and Fig,. 2-4. He fitted an, ellipse to the submerged

portion of the cylinder to match its wetted width, and draught. Applying the momentum equation to the vertical impact and using the ellipse fitting

technique to defind the upwash velocity at the sides of the cylinder, together with the added mass of the wetted portion of the exact cylinder

shape as given by Taylor (1930 [1])'. This method was developed to avoid

the singularity which appears in the Tinearized problem when flat

plate-fitting is used. Tabula solved for the impact force and impact coefficient

by using an infinite power series expansion. His value for 0s was a maxi-Mum of 6.28 at the instant of cyTinder/water contact and decreased rapidly

as the cylinder draught increased, see Fig. 2-5. It is interesting to see

SPRAY ROOT

S.W.L.

-ti=o

V

Fig. 2-3

7-ig. 2-4

C

that the ellipse fitting technique Fabula predicts the same Co (2n) as Wagner's model, but the force decays much more rapidly with increasing

penetration. C , t 19 s H

V

2

\y..,,WATANABE (EXPERIMENT)

VON K AMMAN THEORY)

WMCU ( EXPERIMENT) CAMPBELL

005 01 015 0-2

d

Fig. 2-5 Circular Cylinder Slamming Coefficients

Comparison of Theory and Experiment

2.4 Added Mass Calculation by Faltinsen

The added mass calculations of Von Karman, Wagner and Fabula were only able to perform calculations up to the point that the circular cylinder bottom has proceeded a distance approximately a radius down in the fluid.

Faltin-sen et al (1977 [3]) has shown a method which is applicable for any

cylinder submergence. He considered an infinitely long horizontal circular rigid cylinder that is forced through a water surface. The water is infi-nite in extent, and has infiinfi-nite water depth. Initially the cylinder is above the free surface and the water is calm. The fluid is incompressible, the flow irrotational and neglect the influence of air flow and spray. Faltinsen used the boundary condition 0 = 0 on the mean free surface, where

is

the velocity potential. The vertical water induced force per unit length is written as

F3 dt I 33

(20) d fA (20) vi pgAd

(1)

where t is the timevariable, V the vertical velocity of the cylinder and

A33(2D) is the two-dimensional vertical infinite frequency added mass

A.

coefficient as a function of submergence. pgAd is the buoyancy force per unit length as a function of submergence. Result of A33 (2D) non-dimension-lized by pR2 is shown in Figure 2-6 as a function of h/R. R is the

cylinder radius and, Ih is the submergence as defined in the figure. The

asymptotic value of A33 (20)/pR2 for large h/R is n. A33(2D) is calculated distributing sources and dipoles over the average wetted' Surface_ The two'

force terms in equation (1) are also shown in Figure 2-6 in, the case the forced velocity is constant. We can then write

dA

d 14(20)1 33 v2

At 3 33 n dh

and define a Cs Value by equating

dA(20)

33 2 1

V - C pV - 2.11'

dh 2 s

Some of the conclusions in Faltiqsen et all were

The force coefficient Cs is numerically estimated. to be 3.1 for a circular cylinder at the moment of contact between cylinder and

water. Experimental values of the same coefficient range 4.1 to

The force coefficient Cs is a function of cylinder submergence.. Buoyancy forces are' important.

Experiments indicate that the force lsh a 'function of Froude,

number. Reynolds number is not thought to have influence for the.

smaller submergences (ie. h/R < 2).

U),

011

3.0 2.0 1.0

Fig. 2-6

(FABULA) Nte.'C S

.. 2.9 ..

-a A33(

7

9.42

z

2.5 Numerical and Experimental Results of Hydrodynamic Impact Analysis by EPRI Report

Both numerical and experimental results concerning the water impact of a circular cylinder were given in an EPRI report (1978, 1161, 117]) concerned

with boiling water reactors. The relevent physical problem is to determine the loads imposed upon a circular cylinder when it is impacted by a mass of fluid. The purpose of this investigation was to approximate the fluid-solid interaction system and to predict the time variation of impact force between the fluid and the rigid circular cylinder. The four numerical models presented in this report are:

an explicit Lagrangian method (Gross, _[16]) a boundary integral method (Geers, _[16]) a finite element

method (Marcel,

[16])

an incompressible Eulerian fluid method (Nicols and Hirt, [16])

Boundary-element results and Finite-difference results for the impact cylinder moving at constant velocity are compared in Fig. 2-7 with two

ana-CF

1 0 2.0

lytical solutions of Fabula and with experimental data [16]. The boundary-element results that included the surge effect, as well as the

finite-difference results, agree well with the experimental data.

7.0 6.0 5.0 4 3.0 2 0 1.0 V. 5.15 m/s R - 0.216 is ) 2.3) m/a R 0.105 m o

B-E Results with Surge

S-E Results without

Surge VD Results of Ref. 16 --- Exp. Results of Ref. 17 Solution of Ref. IS 11,0

= 7.36 mi. Solution of Ref. 14

R 0.105 m

Lower Sounds

Upper Sounds

- 2.10

-%vie

Fig. 2-7 Force per Unit Length on a Rigid Circular Cylinder

Moving at Constant Velocity

EXPERIMENTAL SURVEY

There have been many experimental investigations of slamming over the past decade, which addressed the problem of the circular cylinder. Slamming

forces, calculated from the initial peak in the response curve of the cylinder, showed a wide degree of scatter. The peak slamming coefficient could range from 1.0 up to 6.8. The values of CZ determined experimen-tally from the measured reaction forces at the supports of a cylinder may show wide scatter, depending on the dynamic response of the cylinder and the dynamic characteristics of the test rig and the 'rise time', associated with inclined impact. Additionally, if the surface is not perfectly plane, rise time may vary from experiment to experiment, resulting in an apparent non-repeatibility. In the offshore industry a value of CZ 3.0 [DnV] is

widely used. The more plausible theoretical models suggest that a value of

Co ) 6.0 (27T) is likely.

The experiments can initially be classified according to the way in which slamming is generated. Basically, either (1) The model is propelled at the water surface (DROP TESTS) or (2) The water surface is propelled at the model usually by wave action (WAVE TESTS). In Table 3-1, 13 experimental investigations are summarised. The first 6 (Arhan, Campbell, Schnitzer, Sollid, Watanabe and Souter) are drop tests, the next 6 (Sergren, Canhan, Dalton, Holmes, Miller and Webb) are tests in waves and 1 (Sarpkaya) is a rather special test more analogous with drop tests where the water surface of an oscillating water column impacts the model.

Slam load histories derived from measurements at inclinations up to 8 = 8° are given in Fig. 3-1 and 3-2 [5]. The results were obtained principally at a Froude number of Fn = 2.58, with some checks at F, = 3.56. It can be

seen that the rise in slam load was not linear and that the peak load decreased with inclination. If the cylinder and wave are not exactly

parallel at the moment of impact, the time history of total slamming force changes markedly, introducing a rise time during which the maximum slamming

force is developed, and reducing the value of the maximum force. In controlled drop tests it is relatively easy to control the angle at which

the cylinder impacts the water surface whereas in waves, although the impacts were intended to be parallel, small angles of inclination between

TABLE 3-1 Experimental Investigations of Circular Cylinder Slamming

Investigator Test LID Fn _Cs

Arhan and Delevil[10] Drop test 1.0 1.0 2.4-6.9

Campbell and Weynberg [5] Drop test 6-16 1.9-5.7 3.5-6.5 Schnitzer and Hathaway [9] Drop test 3.6 1.7 3.5

Sollid [13] Drop test 1.1-1.5 4.1-6.4

Watanabe [9] Drop test 0.5 14-21 6.2

Souter, Mahale

and Krachman [17]

Drop test 3.62

4.63

1.62-5.14 5.2-6.8

Bergren [12] Regular waves 40-100 1-3.1

Canham [9] Regular waves 15 0.35-0.6

Dalton [11] Regular waves 20 0.5-1.1 1-4.5

Homes, Chaplin

and Flood [9]

Regular and irregular waves

24-108 0.8-34 0.7-2.9

Miller [2] Irregular wave

packet

15 0.3-1.5 ave.3.5

Webb [9] Irregular waves

full scale

30 3-4

wave and cylinder could not be avoided in practice. Changes in vertical and horizontal asymmetry of the waves generated, and variations in the alignment and curvature of the wave front, reduce the likelihood of a

simultaneous slam along the whole length of the cylinder. Experimental

work [5] demonstrated that the magnitude of the load on the cylinder during impact was very sensitive to the angle of inclination between cylinder and

wave crest. This factor was probably responsible for much of the scatter

since skew angle were inevitably more than 10 for most of the tests. It is

therefore unlikely that wave tests can supply information on true

2-dimensional impact. The rise time due to inclination depends upon the

aspect ratio of the cylinder LID as well as the angle of impact.

Con-sequently one would expect that more reliable measurements of 2-0 impact forces would be obtained for small LID measuring sections. This assumes that the measuring section is well sealed and that 3-dimensional flows are minimized by suitable end extensions. Table 3-1 clearly shows that the highest slam coefficients are given by the more controllable drop test

experiments. On the basis of the above evidence it appears that peak 2-0

5 Cs A Cser 6 4 3 2 1 4 9 4 15 0.2 04

Fitted load histories

6F 2.6,

37

Peaks from strip theory

1.0 1.2

Vt/O.

Fig. 3-2

Inclined Impact Loads from Force Measurements on, a

Smooth Cylinder

=

1 4.0 Fitted load histories

1 Mean inc. OSFLAG data

Nes 1.9

--r 5.6

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--Strip theory of inclined impact

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3-1

Horizontal Impact Loads from, Measurements

on Smooth

Cylinders with Inclined Impact Loads from Strip Theory

Csa

-0

Integrated assure data

Fig.

DESCRIPTION OF MODELS, INSTRUMENTATION AND EXPERIMENTS

4.1 Test Cylinders

The horizontal brace members of both fixed and floating platforms are suf-ficiently long so that it is reasonable to regard the flow around them as two-dimensional. In order to achieve two-dimentional flow conditions the model was driven between two walls, which extended to the full tank depth. The walls were parallel and rigidly connected to the tank floor and at the

sides. They were separated by a distance equal to the model length plus a

small clearance to permit free movement of the model between the walls. This gap was kept to a minimum and filled by felt glued to the end o the test cylinder to insure two-dimensional flow. The inner wall was made of wood but the outer one was made of plexiglass for photographic purpose. The parallel walls have open ends to permit free flow of the surface wave generated during the slam test.

The model for loressure measurements was 0.2 m long with an outer diameter of 0.5 m, and it was made of 8 mm thick aluminium. The instrumented test cylinder is shown in Pictures 4-1, 4-2 and the details in Fig. 4-1.

The actual diameters of horizontal trusses of semisubmersibles and jackets are about 0.4 - 2.0 m. The small dimension corresponds to fixed platform, the large one corresponds to floating platform. With model diameter as large as D = 0.5 m, the scale effect could be considered negligible.

A test cylinder of diameter 0.125 m and length 0.25 m was used in measuring

the impact forces. In order to achieve two-dimensional condition, the

model was equipped with two rectangular end plates with 0.4 m length and

0.3 m width. The profile of the small circular cylinder model with end

plates is shown in Fig. 4-2 and picture 4-3. The test cylinder was made from a standard PVC pipe. The pipe thickness was 3.7 mm. The end plates were made of plexiglass suitable for taking photographs during the impact phase of the experiment.

The arrangement of the model structure with elastic horizontal circular cylinder is shown in Fig. 4-3, and consisted of a supporting frame made of

aluminium and a 0.05 m diameter horizontal PVC tube, 1.52 m long, fitted at each end with aluminium tubes of 0.05 m inner-diameter. The frame was made to satisfy clamped-end condition. The material of the test cylinder has to

guarantee that the strains are measurable dung the test. Steel or alumi-nium bars were considered to be too stiff so that PVC-tube was used, which

has a E-value of 3.0 x 103 N/mm2. The model is representative enough to provide data for comparison with analyses and to assess the effect of

4.3

-Picture 4-1

1

-t.

Picture 4-2

V.

4.5

II

1

Fig. 4-1

-=1"

300

4.7

-Es

Fig. 4-2 A. 0375 25 3o75

4.8

Ogo.L1520 e S Fig. 4-3 Moo 152o ---.0 37. 5 Cr.

4.2 Test Equipment and Instrumentation

4.2.1 Water Tank and Equipment

The experiments were performed in the No. 2 tank at the Ship Model Basin in

Trondheim (SMT). This basin is 28 m long, 2.5 m wide and has a water depth

of 1.0 m. An electro-hydraulic wave generator was at one end of the tank

and an inclined wave absorbing beach at the other end. Glass viewing ports are located in the operating side of the tank for video or motion picture

camera use.

4.2.2 Test Facility

A hydraulic system was designed and constructed to be able to drive the models vertically downward into water at speeds ranging from 0 to about 2.66 meters per second. The hydraulic cylinder was positioned above the

water surface. A rigid frame consisting of two 1-beams spanning the basin

was constructed to serve as a support. The hydraulic setup utilized the wave-maker as a power source which has a working pressure of 100 bar (1400 psi). This assembly is shown in detail in Picture 4-4; it consisted of:

1501 Oiltank

10 HK Electrical Motor, Type ASEA MBL 132 M38-4 Compressor, Type DENISON

Filter, Type PALL

Accumulator

Power was transmitted from the aggregate to the hydraulic cylinder by pressuring oil through flexible tubes. The stroke was regulated by electronically operated valve of type DENSION SA 010, which control the

speed of the cylinder. A linear potmeter used to monitor the stroke was parallelly mounted along the hydraulic cylinder. The reference excitation signal was a command for position, not for velocity or acceleration.

Velocity or acceleration must be converted from the indicated reference

position signal. A filter (see Picture 4-5) was installed in front of the

regulating valve. The vertically mounted hydraulic cylinder specially made

for the present experiments can exert up to 350 kg force to the test model. 0:

The jet pipe valve can supply up to 95 liter (effective range 0-80 liter)

oil per minute. This could yield a model velocity up to 2.66 meters per

second. The hydraulic cylinder have a stroke length about 60 cm. This

hydraulic set up consists of the following elements:

Hydraulic Cylinder, CD-AG-32/22/700/700 HT, 1/2" R Linear Potmeter, NOVOTECHNIK Type LWH 750 (0.A. Nordby) Servovalve, Abex Jet Pipe Type 425

Filter, Type PALL Directions valve Valve block

Regulator Card, Abex Denison S10-19620 0 110 v Trafo, PFM 15 (AFU)

The control unit (Picture 4-6) is composed of a MODEL 9015 VOLT/OHM METER, a FEEDBACK EXCITATION GAIN POTMETER, a D1GTAL STORAGE OSCILLOSCOPE 0S4000 and a MODEL 126 VCF/SWEEP GENERATOR. This unit commands a control signal governing a constant speed of the model during the submergence. It can also command oscillatory motion with varying frequencies. The control

signal as well as the motion signal are displayed on the oscilloscope for monitoring purposes from which the slamming velocity could be estimated.

F:

I,

eD

=--- 1111/41/41

c

tt

assisSoir

Plicture P4-6 Pr vq,

-Linear potmeter

Model 7. 4014

Fig. 4-4

Hydraulic cylinder Excitation

Block

Val ve Filter

4.2.3 Measuring Instruments

Pressures were measured by means of pressure transducers. They were EPX

Series Miniature Threaded Pressure Transducers manufactured by Entran

Devi-ces, Inc.. The transducers are flexible in application and also easy to

install. Five transducers were used. They were mounted flush with the

cylinder face at 2.5° interval radially as shown in Fig. 4-1. They were mounted only on one side of the cylinder since the flow for a vertical

impact is expected to be symmetrical. To avoid disturbance of flow induced

by one transducer to interfere with the others, these transducers were not mounted in line with each other in the longitudinal direction. Rather,

they were zigzagly placed as illustrated in Fig. 4-1.

The EPX Miniature Threaded Pressure Transducer has a circular sensing

sur-face of 3.56 mm diameter. The sensing surface is stainless steel diaphragm

which does not have the cracking and shattering problems normally

associ-ated with silicon diaphragm transducers. The EPX utilizes a semiconductor

strain gage device combined with a fully active wheatstone bridge. The semiconductor elements are bounded directly to the stainless steel

diaphragm thereby providing extremely high frequency response (120 kHz is Used) coupled with extremely low sensitivity to extraneous accelerations,

vibrations and shocks. The semiconductor circuitry is fully compensated

for temperature changes in the environment. The high output enables it to drive most recorders and data monitoring systems directly without

amplifi-cation.

The natural frequency, pressure range, sensitivity and so on are

repre-sented in Table 4-1. The high resonance frequency permits correct

measure-ments of sudden rises of pressure at the transducer face faithfully.

Signal outputs of the transducers were connected directly to a PHILIPS PM3311 Oscilloscope, with a frequency range of 0-60 MHz. This oscilloscope

continuously digitalize and record the signal in al shift register memory,

dropping the oldest recording as the new one enters. Any part of the signal of special interest can be seized in the memory, by a threshold-type triggering either internally or externally. This process also makes possible the recording of that part of the signal which precedes the

trigging. The oscilloscope have three memories and two recording channels.

causes simultaneous triggering of both channels. The sampling rate ranges between 0.1 gs and 0.5 s.

In order to measure small pressures at small impact velocity and large angle 8, four pressure transducers: P7, P8, P9 and P10 were installed as shown in Fig. 4-1. These transducers (Endevco Model 8510) featured a four-active arm strain gage bridge diffused into a sculptured silicon diaphragm for maximum sensitivity and wideband frequency response. The thermal zero shift was found sensitive to temperature changes. This problem was solved by adjusting zero offset before each stroke with the help of a RECKMAN Digital Multimeter. These transducers also exhibited the necessary attri-butes of small sensing-face diameter, high sensitivity, light weight and

high natural frequency (100 kHz).

The outputs of the flush-mounted transducers P7 - P10 were fed through a DC Amplifier and recorded on PHILIPS PM3311 Oscilloscope. The DC Amplifier was KWS 30208 DC-Measuring Amplifier capable of picking up the 10 kHz

signal without noticeable error.

The signals registered on oscilloscope were photographically recorded by a

polaroid camera: TEKTRONIX C-5C Oscilloscope Camera.

It

is realized that the response of the recording system was sufficient to record the entire peaks of the impact pressures. The instrumentation per-formed entirely satisfactorily, yielding excellent data on the time histories of pressure, phase and displacement.

A three-comoonent force transducer of the type shown in Fig. 4-5 with a maximum load capacity of 1 kN was connected to the support steel bar by the force transducer attached to the bottom of the inside surface of the

cylinder (see Fig. 4-5). The gap between the steel bar and the cylinder was closed by very thin sheet rubber to seal the cylinder. The force transducer chosen has a very high stiffness because we want to measure extremely impulsive slamming load. However, even with a gain of 10 k through the processing amplifier, the signals had a low noise content and yielded good resolution.

The long, elastic cylinder was strain gauged in the middle span, and as near to the fixed ends as possible, as this is where the strain is expected to be the largest.

Four strain gauges which is specially suitable for PVC were cemented longi-tudinally at 2.5% (0.035 m) and 50% (0.7 m) of the tube span, vertically at upper and lower sides. When the gauges on the long cylinder had been checked, they were covered by a layer of waterproofing solution. Signals

were recorded from the top and bottom strain gauges wired in half bridge form to give the bending strain at each position along the tube.

The force and strain signal excitation and amplification were provided by a DC Amplifier KWS 3020 B. The data were recorded by a IBM Portable Personal Computer, which has the highest sampling rate about 3500 samples/second. The other instruments include a <hp> HEWLETT PACKARD Think Jet printer and a TEKTRONIX Type 434 storage oscilloscope.

4.18

-Picture 4-8

4.19

-Fig. 4-5

0

0

0

A

4.2.4 Calibration

The calibration of the pressure transducers was carried out by applying air pressure whose value is accurately known. A water manometer of simple U tube with vertical limb was used to measure the applied pressure. Typical

values of transducer output calibration constants are listed in Table 4-1

and 4-2.

The series 8510 pressure transducers were found to exhibit a shift in zero pressure output due to temperature changes. Corrections were applied for this zero shift by adjusting zero offset before each run with the help of a RECKMAN Digital Multimeter.

At the start of each set of runs, the displacement output from the position measuring potmeter was carefully calibrated.

The force transducer was calibrated at the start of the tests in the ver-tical and horizontal directions by hanging known loads from the center of

the cylinder. A linear relationship was found between the strain gauge

output and the applied load. The calibration data were presented in Table 4-3. Curvefit results by least-squares-linear regression is shown in Fig.

4-6 and Fig. 4-7.

The transducers SG1 and S02 that measured the moments were calibrated in place before the experiments were conducted. Known weights were suspended at the 0.4 m-span point between the two strain gauges. Linear relationships were found between the strain gauge outputs and the applied point load from which the relationship between strain gauge outputs and the moments were

determined. The calibration data were presented in Table 4-4 and

Table 4-1 Pressure transducers EPX used during the test

Transducer P1 P2 P3 P4 PS

Model No. EPX-M5-EAP-U-15G

EPX-M5-EAP-U-7G

EPX-M5-EAP-U-3.5G

Serial No. 16R6B359 16R6BJ52 8T6BJ19 15R6B324 15S6B35

Type Miniature

Range 15 bar 15 bar 15 bar 7 bar 3.5 bar

Overrange 30 bar 30 bar 30 bar 14 bar 7 bar

Operating Temperature Range -40°C - +120°C Compensated Temperature Range 00C - +60°C Sensitivity at 20°C 342.66 mV/bar 347.1 mV/bar 321.85 mV/bar 717.49 mV/bar 143.0 mV/bar Thermal Zero Shift + 1.5% FS

_{_}

+ 2% FS Combined Non-Linearity and Hysteresis + 0 5% FS. _{+ 0.759 FS} Installation Torque 0.05 m - daN Resonance Frequency 120 kHz 120 kHz 120 kHz 80 kHz 75 kHz

Table 4-2 Pressure transducers of series 8510

* Calibration data after fed through DC Amplifier

G = 1 (x1000) 5V excitation Transducer P7 P8 P9 P10 Model No. 43 EE 22 EE 27 BN 31 EE Range 1 bar Overrange 3 bar Type Miniature Operating Temperature Range -18°C - +93°C Linearity t0.25% FS0 Hysteresis ±0.1% FS0 Combined Linearity and Hysteresis FS0 Zero Shift at 3 x Overrange +0.3% 3 x F50 Resonance Frequency 100 kHz Sensitivity* 103.5 mV/bar 101.6 mV/bar 138 mV/bar 107 mV/bar

Table 4-3 Calibration data for force transducer F2

For measurements concern: I. 5v excitation voltage

2. G 1, 0.1 mV/v, 10000* amplification

Amplifier KWS 3020 8 SN.74489

Weight Output Voltage of F2

kg Newton Fr (v) Fx (v) 0.0 0.000 0.000 0.000 0.5 4.9033 0.143 0.615

LA

9.8067 0.285 1.228 1.5 14.7100 0.427 1.84 2.0 19.6133 0.570 2.46 2.5 24.5166 0.714 3.07 3.0 29.4200 0.858 3.69 3.5 34.3233 1.000 4.30 3.9 38.2459 1.117 4.78 0.0 0.000 0.000 0.00 =

Table 4-4 Calibration data

for

transducers Sol and 5G2

Fore measurements concern:. 1., lv excitation voltage 2. 0 = 1, 1.0 mV/v, 1000* amplification Amplifier KWS 3020 B SN.74489' Weight 1

61

1 _ 1 112 Output Output (kg) (Nm)j (FV-m> Kv) I 1 Kv) 0.0 0.0 0.0 0.0 i 0.0 I 0.3307 0.068 1 . 0.019 1-0 i 1.972 0.)6614 0.136 0.038 1.5 2.958 0.19921 0.203 1 0.057 2.0 3.944 1 1.3228 I 0.271 0.076 2.5 I 4.930 i 1.0535. 1 0.336 0.097 3.0 5.916 g 1.9842 0-404 I 0.116 1 3.5, 6,902 2.3149 01.470 1 01.136 3.9 7.691 2.5795 0.520 0.153 0.0 0.0 9.0. i 0.0 1 0.0 0.5 0.986

35 30 5 20 0 40 .35 30 25 20 15 10 5 0

Fig. 4-6;

_{CURVE FIT RESULTS}

CALIBRATION DATA FOR 12

0 0.2 0.4 0.6 .12

0 mecartanrd3 OUTPUT

00

maw At

Fr) N ).34 .26*0u tpu t(

4-7'

_{CURVE FIT RESULTS}

CALIBRATION DATA FOR Fe

0' 4

maastnet OUTPUT

40

curve fit Ex ( N).7. 99'Ou tput (v ))

4.25

-Fig.

0.8

2. el 2.6 2.4! 2.2 2 l.8 5 1.6 1. 0.8 0.8 0. 0.2 0 a 5 3 2 4.26,

rig. 44,

_{CURVE FIT RESULTS}

CALIBRATION*DATA FOR 5C.2'

0.07 0:04 0.06 0.06 0.7 4.72 01

lyaaatervel

OUTPUT (W.

curve fit m20.0.16.89.0utputIvfi

Fig. 44

_{CURVE FIT RESULTS}

CALIBRATIONDATAFOR SC!

Oc 0.2 0.4 06 0 'Ineciassrect oUTPUT fit MINnY.14.71.Output(01 0 0.16 (...) 1 7 4 0

4.3 Description of Tests

4.3.1 Test Procedure

The test consisted essentially of driving the model vertically downward into a flat pool of water and the time histories of pressure, displace-ments, pressure phase differences and impact forces or moments were

recorded. Since the superposition of a constant velocity on a mechanical

system does not alter any forces within the system, the loading of the models is the same as if they were held fixed and impact by a body of water moving toward the models at a uniform velocity.

Before any measurements were taken, all electronic equipment was switched on for at least one hour, and the test model was raised and lowered many

times.

The test cylinder was aligned to be parallel with the water surface along its length, both by measurement from an inclinometer on two end walls or end plates and visually by checking the path on contact with water through

the viewing ports in the side of the tank when the cylinder bottom just touch the calm water surface.

When testing commenced, it was found that the characteristic shape of the impact pressure trace could be greatly influenced by the presence of water droplets on the face of the tranceducers. The effect of these droplets was to both attenuate and prolong the initial impact pulse. To avoid errors from this cause, the test cylinder was wiped dry before each run.

Simi-larly, water surface disturbances also affected pressure measurements, so tests were always made on a quiet free surface. Two wave qampel were used on both sides of the experimental setup to attenuate the induced surface wave quickly between runs.

All data of a run were recorded simultaneously in the memories of PHILIPS PM 3311 Oscilloscope for pressure measurements, or on IBM PC and LABTEC NOTEBOOK in the case of force and moment measurements, together with simultaneous motion displacement signal recordings on a DIGITAL STORAGE OSCILLOSCOPE OS 4000. The exceedance of the threshold on a reference chan-nel (pressure transducer or stroke triggering signal) caused the simulta-neous triggering of all the recording channels.

4.3.2 Slam Velocity Measurements

With the help of a position potmeter which follows the motion of the hydraulic cylinder, the displacement of the model was recorded from the beginning of the stroke to the end. This was accomplished by feeding the position potmeter output to a DIGITAL STORAGE OSCILLOSCOPE OS 4000 for

direct check. The displacement signal was also logged by an IBM PC and

stored on floppy disks. Information from the displacement potmeter was used to analyse the motion of the test cylinder during slamming tests. Velocities were estimated from an average slope of the displacement signal

record.

4.3.3 Circumferential Pressure Measurements

In order to measure the impact pressures, the model was driven into still water at speeds from about 0.874 to 2.66 meters per second, so as to

simu-late the actual impact conditions at sea. The test facility and the complete recording system were tested and evaluated many times before any actual recording were taken. Measurements were made of model displacement

and pressure at twelve positions around the circumference from 0° to 300 to

the vertical. Because of limitations in the number of data channels and

tranducers, pressures had

to be

measured in sets of four, and the model was turned at the interval of ten degrees after each set of tests. Tests were repeated to obtain more reliable information. Pressure signals were recorded in the memories of an oscilloscope (PHILIPS PM 3311) for

com-parison. The scatter in the peak pressure was found to be small. The

repeatability of pressure trances was also good. Accurate timely

triggering was required in order to capture data from the slam over one to ten milliseconds, depending on the impact velocity, and this was achieved by using a threshold triggering of pressure signal itself. The experiments

performed entirely satisfactorily, yielding good quality time historiesof

4.3.4 Pressure Phase Measurements

Accurate measurements of the rise of the spray root were possible from the phase of the rise in the pressure transducer response. Since one pressure transducer from each set was used as a reference for the phase and only two recording channel was available, results were obtained at the 00-2.50, 2.50-5°, 2.5°-7.50 and 2.50-100 positions from more than one set of runs. In case of phase measurements at 100 4 4 20° and 20° 4 0 4 30°, the model was turned 10 or 20 degrees and the same test procedure was carried out.

4.3.5 Force and Moment Measurements

The test models were forced through the still water surface by a hydraulic cylinder positioned above the water surface, and held by a rigid frame. With the test rig set up as in Picture 4-3, the cylinders to be tested were

mounted horizontally, parallel to the still water surface at a distance of

about 0.25 im above the water surface. Outputs from the force transducer F2

or from moment transducers SG1. 502 were fed through the amplifier and recorded by an IBM PC and stored on floppy disks. Time series of five slam force measurements (sampling rate 3500/sec.), two cylinder out of water runs (sampling rate 1000/sec.), one slam force measurement with cylinder covered with macroroughness elements (k/O 0.0472, sampling rate

3500/sec.) and eight dynamic strain responses (sampling rate 500/sec.) were

recorded.

4.3.6 High-Speed Photography

The insight of the physical process is always improved if the flow pattern can be visually observed.

A flow pattern visualized with some techniques can be observed by eye or recorded by photographic means. In the latter case one may either expose single photographic pictures, or one can record the visualized flow with a movie camera if the flow pattern changes with time. All the visualizing methods have one feature in common: They visualize the spatial pattern of the flow under study. If the flow pattern changes with time, one may distinguish between two types of such variations. In the first case, the

variations are so slow that they can be recognized, and eventually measured, by visual inspection. An ordinary movie camera is then

appropriate to record such time-dependent events. The human eye, however, has a certain limit to resolving rapidly changing patterns. If the

variation of the flow pattern is faster than a value associated with this limiting resolution, or if the total flow time is shorter than the reaction time of the eye, the flow will remain "invisible" to an observer. The key to visualizing such rapidly changing flow fields is the high speed photo-graphic technique. High-speed photography can therefore be regarded as a method which visualizes the dependence on the fourth coordinate of an unsteady flow field - its dependence on time.

A high-speed movie film consists of a certain number of single exposures separated by the time interval, tw. The inverse value, fw = l/tw, is the associated image frequency or framing rate. The value of fw must be so chosen that it is high enough to allow for a unique and Precise determi-nation of the moving object. On the other hand, fw must not be greater than a certain value beyond which the position of the moving object in suc-ceeding frames can no longer be differentiated.

The high-speed photographic system must fulfil the following requirements:

Short exposure time of each single image

in

order to avoid blurring in the image of the moving object.

Intense illumination System because of the short exposure times.

Image frequency high enough to resolve the fast motion of the object

under study.

Synchronization of the exposure with the high-speed event.

A high speed movie camera (ACTION MASTER 500) was used for viewing the flow of slamming phase. Movies were taken at 300 frames per second, using a wide angle zoom lens. Sufficient time was allowed for the camera to get up to speed before the test was initiated. Standard 16 mm film was used.

Lighting consisted of two photo bulbs, located one in front of the model

TEST RESULTS AND DISCUSSION

5.1 Velocity Measurements

Slam velocity was determined with the help of a position potmeter which followed the motion of the hydraulic cylinder. Fig. 5-1 showed three displacement plots overlaid with their related triggering signals until it reached its maximum submergence, from which it could be seen that the linearity of displacement-time output was good. Velocities (0.51 m/s -2.66 mis) were estimated from an average slope computed from the displace-ment data (see Fig. 5-2 to Fig. 5-6). The smooth displacement traces indi-cated that there was little variation in model's motion. The velocity

could be considered constant in short impact duration.

5.2 Pressure Measurements

Typical examples of the impact pressures measured and recorded at dif-ferrent points along the bottom of the model are shown in Figures 5-7, 5-8,

..., 5-12. It can be seen from these figures that the impact pressure at

each measuring point rises rapidly to form an initial pressure spike of extremely short duration, followed by a low pressure, gradually decaying tail lasting several milliseconds. A typical pressure history versus time at Plot 6 in Fig. 5-7 reveals that the time for the impact presure to reach its maximum is of the order of 50 us and the duration is about 0.1 ms. From such records, the magnitudes as well as the time-dependence of the pressure could be determined.

The sharp pressure rise time seems to increase with a) decreasing slamming

velocity, b) increasing 0 except 0 00. On Fig. 5-15 are plotted the

impact pressures recorded at 0 = 00 and 0 = 2.5° (Plot 39). The pressures from transducer measurement at the bottom of a cylinder, 0 = 00, were characterized by a slight initial rise followed by a rapid rise to the peak

(see also Plot 4 in Fig. 5-7, Plot 50 in Fig. 5-9 and Plot 16 in Fig. 5-13). By comparison, the impact pressure recorded at impact point 0 = 2.5° with the same slamming velocity U = 1.52 m/s has a shorter rise time (20

_us).

start of slamming Fig.. 5-2 start

_{of slamming}

5:,21H o' siar.fn: PLOT 1

U=0.674 m/s

X=50

_ms/div

= 7 cm/divi

PLOT 2' U=1.52 m/s X=20

ms/div

.Y.67 cm/div

PLOT 3 U=2.66 m/s

X=20 ms/div

7=7 "idly

-0 14 0 12 0.1 0.08 006 0.04 0.02 0 0.02 0.04 0.06 008

0.1

0.72 0.14 0.14 0.12 0.1 0.08 0. OH 0.04 0.02 ov 1.4 4

0.02

0.04

0.06

0.08

0.1

0.12

0.14

5.3

TIME (s) 0 0.2 0.4 0.6 TIME (s)

Fig. 5-3

VELOCITY MEASUREMENT

Mo 2

Fig. 5-2

VELOCITY MEASUREMENT

.Vo

a 14 0.12 0. 1 0.08 0.06 0.04 0.02 lei 0

0.02

-0.04 006

0.08

0.1 0.12

0.14

0.14 0. 12 0.1

anti

0 06 0 04 0.02 0

0.02

0.04

0. 06 0. 08 0,1

0.12

0.14

-

5.4

-Fig. 54

VELOCITY MEASUREMENT

TIME (5)

0 0.1

02

0.

Fig. 5-5

_{VELOCITY MEASUREMENT}

WO. J 0.28 n O. 24 0.76 0. 08

012

0.04 0 (s). 4

5 . 5

-Fig. 5-6

_{VELOCITY MEASUREMENT}

0 0.04 0,08 0.12 0.16 0.2 0 24 TIME ( ) (1.14 0.12 0 1 0.06

ace

0.04 0.02 0 0.02 0.04 0.06 -0.08 -0.1 0.12 -0.14

This phenomenon can be attributed to the existence of an air cushion at the

impact point. The transducer situated at that point is warned of the

arri-val of water by the air compression. At points 0 = 2.5° and more, the air is blown out by water and a more sudden pressure rise occurs when the water encounters the transducer diaphragm.

Measurements from transducers further around the cylinder at 0 = 5° - 27.5°

showed no air-cushion phenomenon but exhibited increasing rise times, due to the passage of the spray root across the transducer diaphragm, then died

out slowly.

The highest pressure measured over the bottom of the cylinder was found to occur at location 0 = 2.50 with slamming velocity U = 2.66 m/s. That

pressure history was represented in Plot 51 of Fig. 5-10. It has the shortest rise time around 15 ps and highest peak pressure about 9.1 bar, which is of the order of one kilogram per square centimeter.

It appears on Plot 17 in Fig. 4-8 that the pressure peak at point 0 = 2.5° has ended when the peak in 0 = 5° occurs (see also Plot 16 in Fig. 5-13,

Plot 20 in Fig. 5-14. Plot 43 in Fig. 5-16 and Plot 64 in Fig. 5-17). One

can deduce that the high pressure region was concentrated highly in or near the place where the spray is formed, the arc width instantaneously subject to the high pressure impact does not exceed 1.5 degrees, and that arc moves

along the cylinder circumference as the structure penetrates in the water.

The zero pressure signal prior to impact was generally noise free although often the transduces responded to the impact before the spray root reached

them. In the case of the transducers at 0 r 0° this was probably due to air cushioning, whilst at other position it was more likely to be the response of the diaphragm to jetting water droplets. After the sharp rise

the pressure decayed with a superimposed oscillation of the order of 5kHz. The effect of oscillation was more noticeable at the locations 0 10°, see Fig. 5-7, Fig. 5-10 and Fig. 5-11. Whilst these oscillations were not simple harmonic, for a particular location different runs at the same con-dition produced very similar set of responses and by overlaying traces from the data store on an oscilloscope (PHILIPS PM 3311) it was observed that not only were these responses in phase, but also they were of similar

The added mass effect was thought to be responsible. The natural frequency of the pressure transducers (120 kHz in air) was lower in water due to added mass increase. Maybe some dynamic amplifications were involved for those measurements near the cylinder bottom center line where the pressure was the highest. The repeatability of pressure measurements was found to be good. Some scatter, however, appeared at very early immersions, someti-mes amounting to as much as 10 percent. Several reasons might be invoked for that scattering: the instability of the air-cushion phenomenon, the perturbations of the basin surface that sometimes had not died down

= d, Fig. 5-7 5 PLOT d = T70 Phil ii = 0.874 m/s X = 0.2 ms/div = 0.292 bar/div Peak pressure: L08 bar

PLOT 5

0 = 2.5° ch.2 U = 0.874 m/s X = 0.1 ms/div Y = 0.2881 bar/div

peak pressure: 1.47

bar

PLOT 6

0 = 50 ch.3

U = 0.874 m/s X = 0.1 ms/div Y1= 0.3107 bar/div peak pressure: 0.79 bar 0

111011111

nig

tiummmt-1-hiarelleallr

I

monnoll

swim

.1

;peak pressure:: 0.14 bar

1 = 0.5 ms/div Y = 0.098425 bar/dlv peak pressure: 0.29 bar

PLOT 1I 0 = 17.50 ch.I0 U = 0.874 m/s X = 0.5 m/s Y = 0%04375 bar/div ;PLOT 30 0 = 7.500 ch.4 "U = Ii.. 52 m/s X = 0.1 ms/div = 0.279 bar/div Fig. 5-8.

_L-.

a.

PLOT 9 0 = 12.5° ch.8

aU

U = 0.874 m/s

1111a111111

1,9 bar peak pressure:, 5.9 -Y

Fig. 5-9

111111111111T=

Mid=

PLOT 31 0 = 10° ch.1 U = 1.52 m/s X = 0.2 ms/div Y 0.292 bar/div peak pressure: 1.4 bar

PLOT 37

= 25° ch.9 U = 1.52 m/s X 1 ms/div Y = 0.0725 bar/div

peak pressure: 0.225 bar

PLOT 50 0 = 00 ch.1

U = 2.66 m/s X = 0.05 ms/div Y = 1.1673 bar/div peak pressure: 7.47 bar

-=

Fig. 5-10

1,..

litlitosiJEI

EIMMEME

EIHMEEME

MEEME

SEEM

:WE

PLOT 51 0 = LS° ch,2 Ul = 2.66 m/s X = 0:05 ms/div Y = 1.1524 bar/div

peak pressure: 9.1

bar-PLOT 53

sQ = 7.50' ch.4

ti = 2.66 m/s,

= 0.05 ms/diu Y = 1.394 bar/div

peak pressure.: 5-02 bar

.PLOT 54

= 10,0 ch.1 U = 2.66 m/s X = 0.1 ms/div

= 1.1673 bar/div peak pressure: 3.62 bar

Fig. 5-11 PLOT 55 0 = 12.5° ch.2 U = 2.66 m/s X = 0.2 ms/div Y = 1.1524 bar/div peak pressure: 2.3 bar

PLOT 56 0 = 15° ch.4 U = 2.66 m/s X = 0.2 ms/div Y = 0.5575 bar/div peak pressure: 1.65 bar

PLOT 57

0 = 17.5° ch.4 U = 2.66 m/s X = 0.2 ms/div Y = 0.5575 bar/div peak pressure: 1.12 bar

11 Fig.

1111IPPE271.7

-7L-1211FtIZIC

:TM;

_11111.

2. PLOT 72 8 = 10° ch.1 = 1.52 m/s X = 0.5

ms/div

= 0.298'

bar/div

PLOT 73 = 12.50 ch.2 U = 1.52 m/s X = 0.2

_ms/div

= 0.29

bar/div

PLOT 71 20° --- 27.5P' chc7. ch.10 U = 2.66 m/s

X = 1 ms/div!

= 2

v/div

5-12 U 9

5.3 Piled-up Water and Spray Root Measurements

The shape cf the free-water surface was obtained from the high speed movies and shown for several times during the critical impact period in Fig. 5-18. Indicated also is the still waterline for these times. The point at which the water surface meets the cylinder section is called the spray root. The

film showed that at very early stages of impact sizeable spray was generated, but the earliest time at which any piled-up water could be clearly identified was at the relative immersion h/R = 0.0507. We see that the splash can be considered in two parts: The top portion is thin and may detach itself from the body as happens in Fig. 5-18. Part of the water is jetted away from the spray root. In any case it has little effect since the pressure over this part of the body is atmospheric. Below this thin

sheath occurs a thick base which has a marked effect on the force. In fact

the peak pressure occurs in this part of the flow near the point where the cylinder base joins the thin sheath.

Accurate measurements of the rise of the spray root were possible from the phase of the rise in the pressure transducer response. The double trace records shown in Figures 5-13, ..., 5-17 are the time-history curves of the impact pressure measured at the same run. Both traces indicate the instant of time when the transducer start to respond and when the maximum impact pressure occurs. One can determine the phase differences of start rising points and maximum pressure points. For a particular record, Plot 20 in

Fig. 5-24 for instance, the spray root reached the transducer at 0 = 12.50 about 1 ms later than the transducer at 0 = 10°. The maximum pressure of the 0 = 12.5° transducer occured about 1.1 ms after the transducer at 0 = 100 reached its maximum.

Tables 5-1, 5-2 and 5-3 list the spray root location estimation where

es arc cos (1 - Ut/R). The ratio of Op/Os associated with the wetted width to width at still waterline is plotted in Fig. 5-19 as a function of

relative submergence. The ratio remained constant for Ut/R > 0.02 at a value of 1.4 - 1.5. The scatter at very early immersions may be attribut-able to small initial disturbances in the water surface or to a depression

from air cushion. The air may deform the water surface and be forced into

the water. The fact that Op/Os is less than unity shows that the air

pressure under the middle of the model bottom forces the water surface

there down. Therefore it appears that some air remains trapped between the

water and the model's bottom. In any event, this causes the impact pressure there to be reduced.