Analog anti-roll tank facility. Surf Simulation

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ARCHIEF

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E. E. Zarnick

Naval Ship Research and Development Center

Washington, D.C.

To be presented at the

16th American Towing Tank Conference

Sao Paulo, Brazil 9 August 197L

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_{ScheepsouwkunkIe}

Technische Hogeschoot

ANALOG ANTI-ROLL TANK FACILITY

In the past decade a number of ships have been equipped with free-surface type anti-roll tanks. They are very simple and economical to build, and they are superior Lo roll fins at low speeds (when properly

designed). Unfortunately, not all tank installations have proven to be satisfactory and this bas motivated the Center to develop a new technique for evaluating anti-roll tank designs.

The design of specific tank installations have been based primarily upon the adaptation of the work of Chadwick and Kiotter for "U" type tanks which the designers force to fit the free-surface type tank. In

many cases tests were conducted which consisted of harmonically oscillating a tank model filled to the prescribed depth with water and measuring the resulting tank moments. A tank design was judged satisfactory if it provided sufficient stabilizing moment at the ships natural roll period. in some instances the tank test results were used to estimate the stabilized roll motion by assuming the tank system to be linear (contrary to the

evidence).

when reports of the inadequacy of certain tank designs became known it was evident that a more quantitative evaluation of a tank design was

needed. This required that tank non-linearities (which were previously neglected) be accounted for adequately. Subsequent attempts to develop a non-linear mathematical model for the tank system using lump-parameters was not successful so this approach was abandoned. We are currently developing a technique which we believe will provide for the quantitative evaluation of specific tank design and also lead to a better understanding

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of ship-tank system. _{A mechanism or oscillator table has been constructed}

which will enable us to oscillate a tank model in roll and sway with arbitrary motions. It is planned to use this equipment in conjunction with an analog computer to model specific ship-tank _{systems. The}

analog computer will be used to model the ship system while a tank model on the oscillator table will physically model the tank _{system. Figure 1} shows a simple schematic of this approach.

Figure 2 is a photograph of the oscillator table. _{The table can} accommodate tank models 4 to 6 feet wide weighing up to 300 pounds. The

maximum roll amplitude is ± 15 degrees and the maximum sway amplitude is

± 1½ feet. The roll center can be adjusted _{± 2 feet. The frequency range}

is approximately O - 1.0 Hz.

The ship tank system can be represented by an integro-differential system of equations coupled in roll, sway and yaw. _{For the sake of} this illustration and for the initial studies, _{a system of differential} equations with constant coefficient and with coupling in roll and sway only will be used, i e

AO + B10 +

ee + CB + dY+ eY

=

aB +bB+DY

_+EY=FW+FT

where O = roll amplitude Y = sway amplitude

A, B, C, D, E, a, b, d, are coefficients

roll exciting moment due to waves roll moment developed by tank

-Fw = sway exciting force due to waves

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FT = sway force developed by tank

and the dots denote differentiation with respect to time.

It should be noted that non-linear terms such as quadratic damping in roll present no additional difficulties since the equations will be solved in the time domain.

The coefficients in the equations of motion as well as the

exciting forces and moments can be obtained either experimentally _or

analytically. The experiments would consist of forced oscillation tests in calm water to determine the coefficients in the equations of motion and restrained model tests in regular waves to determine the exciting forces and moments at the speed and heading conditions to be studied. _{Using the} regular wave force and moment data, transfer functions _{or filters can be} determined which will enable the synthesis of roll exciting moment and sway exciting force power spectra by passing a white noise 'source through the appropriate filter. This will be done for a variety of sea states.

The left-hand side of the equations of motion is readily synthesized on an analog computer using standard techniques. _{The only terms left in the} equations of motion of the tank-stabilized ship is the tank moments and

forces. _{These will be determine experimentally by oscillating a model of}

the roll tank with the corresponding roll and sway motions and measuring the forces and moments directly. This is illustrated with more detail in

Figure 3. On the left-hand side of the figure, a white noise source is passed through appropriate filters to obtain random signals representing the roll exciting moment and sway exciting force. _{This time varying}

signal is then fed trito an analog simulation of the ship system

which in this case represents the equation previously presented. On the

right-hand side of the figure, we have the output of the analog computer which represents, of course, the roll and sway motion of the ship.

These signals provide the control signals for driving the roll tank oscillator shown in the lower center portion of the figure. Feed ahead compensation is required to account for phase lag and attenuation in the oscillator motions. Force gages located under the roll tank model provide direct measurement of tank moment and sway force which are fed back to the analog computer thus closing the ioop.

It is hoped that with this system a more rational approach can be made to the study of anti-roll tank performance and design.

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ANALOG COMPUTER

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ROLL OSCILLATOR

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EXCITATION Çl FILTER

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FEED AHEAD OSCILLATOR; COMPENSATION

a+b+D+E=F +F

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SURF S! IJLAT ON

Davidson Laboratory

Stevens 1nstitute oF Technology

lioboken, N.J., USA

To be presented at the

16th American Towing Tank Conference Sao Paulo, Brazil

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i NTROD!JCT ON

Mr. John F. Daizell of Davidson Laboratory undertook a literature search leading to the design of a surf beach which was installed ¡n DL Tank 3 (313' x 12' x 5.57) ¡n August 1970. The initial requirements were for a 2 percent beach slope which wouÌd give a maximum plunging surf height

of 6 inches.

The literature search revealed a reasonable amount of observations of significant height of breakers, average apparent period, and water depth at breaking point. Analytical approaches to the mechanism of surf generation were not available.

Much of the terminology and most of the practically useful results have corne directly or indirectly from experiments in wave tanks. This

type of experiment involves the generatîon and propagation of simple (usually periodic) waves onto beaches of various slopes. _{Qualitatively} and sometimes quantitatively the results have been related to full scale.

What happens in the "surf zone" on a laboratory beach under the influence of incident periodic waves from deep water depends upon

combi-nations of the following parameters:

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a, Period or deep water wave length (T, L0) b. Deep water wave height.

_(H0)

C. Beach steepness (m)

Calvin classifies surf characteristics as follows:

Spilling - Bubbles and turbulent water spill doiin front face of wave. The upper 25 of the front face may become vertical before breaking.

Plunging - Crest curls over a large air pocket. _Smooth

Collapsing - Breaking occurs over lower half of wave, minimal air pocket and usually no splash-up.

Bubbles arid foam present.

Surging - Wave slides up beach with little or no bubble

production. t'ater surface remains almost plane.

The types of breakers grade continuously into one-another. Relatively small variations ¡n period and in some cases the reflections from previous waves can alter the type. !n the field successive combinations of adjacent types are ordinarily observed on the same beach at about the same time due to wave variability.

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The question of the definition of breaker height for each classi-fication arises. Generally, breaker height ¡s defined as the difference between maximum water surface elevation at the position on the beach where breaking starts and the minimum water elevation when the preceding trough passed that point.

BEACH CONFIGURATiON

From preliminary tests with a ₅ percent beach and correlation with outside sources of data, it was deduced that the specified 6-inch plunging

suri would not be achieved on a 2 percent beach running straight to the bottom of the

_5.5

ft depth of water. Galvin at the Coastal Engineering Research Center had overcome a similar problem by constructing a beach with stepped slopes. He found that by placing a slope transition just. offshore of

th

breaking depth of water, a larjer breaker would result and would propagate further than if the slope were constant.

deep water wave height, H , was also measured.

The measured breaker heights, FI8 , and corresponding values of d3

were charted as d8/H5 and the breaker height index H8/H on a base of the parameter /ymT2, wiiere g is acceleration of gravity, ni is beach slope,

and T is wave period.

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Accordingly, the final beach configuration, shown ¡n Figure 1, has

a transition from a 5 percent slope to a 2 percent slope at about

6.6

inches

water depth.

EVALUATION EXPERHENTS

Motion pictures were taken of the first wave runs. Ho electronic instrumentation was used but a Ttyridt? consisting of 12 rods was mounted on center line.

Three wave probes, two of which could be moved along the tank, were utilized ¡n the actual measurement program following the motion pictures. All three measurements were recorded on a visicorder.

By definition, a breaking wve is changing in height as ¡t travels. The quantity most desired was the breaker height which is the difference

between trough and crest at the position on the beach where the crest first becomes near vertical and before curl-over or actual breaking.

The test technique involved locating probes along the center line of the tank at the breaker point previously determined by visual

obser-

t-vation. While records were taken, note was made of the type of breaker and the condition of the crest line (bent, etc.). The depth of water at which the records were taken was noted as ?d8T _{the breaker depth. The}

Galvin ¡ndicates values of' d6/H to bc 0.9 For plunging waves and 1.7 for spilling; DL data compare well with these values. However, the breaker height index HB/HO is lower than design predictions and data from other experimenters. However, breaker heights of 6 inches in the region

of a 2 second period were obtained for use in landing craft model tests.

RE F E RE N CES

CALVIN, C.J., "Breaker Type ClassiFication on Three Laboratory Beaches," Journal Geophysical Research

_73,

No. 12, June _1968.

WEIGEL, R.L., Oceanographical Engineering, Prentice Hall Inc., 1968. IVERSON, H.W., "Laboratory Study of Breakers," NBS Circular 521,

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FIGURE

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ELEVATION DIAGRAM OF SURF BEACH

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Slope

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