A generalized hydrodynamic interaction force module and its use in simulation of ship interactions in shallow channels

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A GENERALIZED HYDRODYNA}!IC INTERACTION FORCE MODULE AND ITS USE

IN SIN1JIATÏON OF SHIP INTERACTIONS IN SHALLOW CHANNELS

Paul Kaplan, Virginia Polytechnic Institute and State University, Aerospace and Ocean Engineering Department, Blacksburg, Virginia, USA

ABSTRACT

Hydrodynamic interaction forces between 2 ships in a shallow channel are represented With the effects of differént

relative headings of each vessel,, as well as their respective

motion variables (sway and yaw velocities) included. These forces are then provided in continuous time history form for direct use in simulation studies, which contrasts with prior hydrodynamic force model, obtained from either model test

results or theoretical analysis for constrained conditions such as parallel paths, fixed lateral separation, etc. The

relationship of a computational module (providing such forces) to the simulator equations of motion; the computational

interfaces; and the incorporation of such a module into the total simulator mathematical model are discussed in terms of more realistic modeling and enhancing simulation fidelity and

accuracy.

INTRODUCTION

There have been a number of theoretical studies concerned with the hydrodynamic forces on ships in shallow canals

including interactions between 2 passing ships. The analyses have ranged from simple twodimensional approximations to more complex analysis involving integral, equations, where the ships

have been considered as moving in parallel paths as well as

parallel to the canal walls. While the degree of agreement between theory and model test data varies widely, the form of

the results as well as the effort required for- the computations

precluded utility for simulator studies. This vas a major motivation for carrying out model test studies of forces on passing ships, as was carried out for the recent Panama Canal

simulation studyr at CAORF (see Eda et al. (1986)).

A recent theoretical study by Kaplan and Sankaranarayanan (1987) considered the case of passing ships in an aSyetric canal, with the ships constrained to move parallel to each other

and to the canal walls. The method of analysis used the Lagally theorem for unsteady flow, as Well as a slender body theory lift force model, with the results determined in the form of triple

Moody (1964), also showed fairly good agreement.

All of the. work referred to ¡boye did not consider arbitrary motions of the ships, which would properly reflect their behavior in realistic cases, but only the constraint of parallel motion at fixed lateral separation distances. The most useful tool for. a simulation study would be a mathematical model that would remove that constraint and also include the inter-action effects due to the ship dynamic motions. The present paper describes the development of such a model, and how it is incorporated into a ship simulation model.

HYDRODYNA}IIC ANáLYSIS METhODS

The hydrodynamic analysis methods used potential theory techniques, similar to those used by Kaplan and Saukaranarayanan

(1987). _{The techniques included basic body modeling by a source} distr-ibution along the centerplane; effects of images dùe to the bottom and the channel walls; induced lateral dipole distri-butions; lateral lift forces arising from slender-body theory

analysis; cross-flow drag forces; and the application of the extended unsteady form of the Lagally theorem for determining

the forces. _{An illustration of the general geometry of the}

ships, in the casé of the constrained motion treated by Kaplan and Sankaranarayanau (1987), is given in Figure 1.

In the present case the ships are assumed to have _any geometric orientation relative to each other, as well as

relative to the canal walls. The canal can have asynmietric

depth conditions, which allows export-oriented ports to consider deeper dredged regions for outgoing cargo-laden ships. The hydrodynamic analysis calculates the generalized _hydrodynamic forces acting on each ship due to the effects of _{the other ship,}

including the inflüence of the dynamic motions _{of each ship} (i.e. sway and yaw), as well as the influence of the channel walls, when the ships operate in shallow water. The case of a single ship is also included, so the bank suction problem is

covered as well.

As an approach to reduce the computation time, the initial source distribution representing each Ship is taken as a

one-dimeflsjonal centerline distribution in place of the

previously used two-dimensional centerplane distribution. The mathematical model also includes dipole distributions for both

WZ

L

'J

w

Fig. 1. Definition Diagram with Co-ordinate systems.

allows an arbitrary orientation of each ship relative to the canal walls1 and all of the necessary images to account for the bottom1 walls and free surface area also established for each

ship (both sources and dipoles). The correcting dipole

distributions in each ship are then determined, recognizing the effects of varying orientation and changing positions that are possible due to the motions of each ship when they are

maneuvering.

This mathematical model is presently under development, with completion expected by Fall 1987.

Since representative results obtaifled from the theory by

Kaplan and Saukaranarayanan (1987) are shown in Figures 2-5, which illustrate the generally good predictive capability of the theory when applied to the constrained motion cases considered

there. In view of the degree of correlation obtained between theory and experiment in these conètrained motion cases, it can be expected that similarly good results will be found for the present case of generalized motion.

-90

LE.0

Fig. 2. Lateral Force Comparison with SSPA Case 1: Water depth = 1.15T, Separation 1.125B.

-600 0

S?6TI

CLTEC

Fig. 3. Yaw moment ..- Comparison with SSPA Case 1:

250

u -2SD s

LECE3 CLC.TED 5xP

Fig. 4. Lateral Force Comparisoù with NS Case 1:

Water depth = 1.15T, Separation = 30m.

o o n ISO loo. S0 o a LE CE NC -GCO a ECO 1200 5EPETIOti FI) -600 0 600

5ZPEC

- CLCULT!O

Fig. 5. Yaw Moment - Comparison with NS Case 1:

Water depth = 1.15T, Separation = 30m. j

//

of ship horizontal plane dynamic motion effects on the resulting

hydrodynamic forces.

The detailed determination of such effects

coinputationally is only to be considered as involved due to the

great care required to represent geometric changes in a proper

manner.

Other computational aspects applied to this work include

the effects of use of a one-dimensional centerline source

distribution in place of the earlier two-dimensional centerplane

source distribution

representing the basic hulls, as well as

the method of determining time derivate term!

the force

expressions.

The source distribution used has its strength

proportional to the longitudinal rate of change of

cross-sectional area, While the previous source strength vas

propor-tional to the longitudinal rate of change of the lateral section

offset.

The net result of this change is to eliminate one of

the integration operations (in the vertical direction for each

term appearing in final expressions for forces), thereby

reducing the computation time.

The time derivative operation in the earlier effort by

Kaplan and Sankaranarayanan (1987) vas carried out analytically

in terms of the theoretical expressions developed there.

However, for the generalized case there would be too

quantities in the geometric representations of distances between

the ships that Would be changing with time; viz, longitudinal

and lateral separations, angular orientations

other motion

variables, etc. to consider an analytic evaluation, from both

the analytic formulation effort point of view as veil

as

computationaily.

The time derivative operations are then

represented by first order changes in the values of desired

quantities, i.e. integral and summation terms, at different time

values, which is a sufficiently accurate method for the

present

application.

In order to check the effects of such changes on calculated

results, some cases seen previously for the constrained

condition were evaluated using the above changes.

The

conditions considered vere 2 Panamax bulk carriers of 257

length, passing each other with a speed of 7 kt. for each

vessel.

_{The calculated results vere within 10% of each Other,}

which is mainly due to the change in the form of the

source

distribution, but that is sufficiently good

accuracy for

A major benefit obtained by these procedures is in regard

to computation time.

The computation time corresponding to the

passing case described above, for determining the lateral force

and yaw moment due to interaction from the instant of bow-to-bow

meeting to that of stern-to-stern passing, was 20 sec. for the

original method used by Kaplan and Saukaranarayanan 91987).

in

the present case.the same computation was carried out in about i

sec.

While the real time for this ship passing case was about

70 sec., it must be mentioned that the computation times given

above vere for a large mainframe IBM 3090 computer which is not

the type of maàhine used in ship simulators.

However there are

some relatively fast minicomputers presently in use, or planned

for use, in some simulators that have sufficient computational

speed and capacity that can incorporate the generalized

hydrodynamic interaction force calculation within their

operation when considering fast ti.me simulation.

It is apparent.

that the computation requirements for use in the real time

simulation mode would allow direct utility of this force

calculation.

In establishing the computation of these interaction forces

within a complete ship simulation procedure, it is recognized

that the mathematical model includes all of the motion and

orientation effects of each ship, i.e. it reflects the influence

of the maneuvering of each ship.

The determination of these

interaction forces can be considered to be a separate module

that provides the time histories of the interaction forces

acting on each ship during the time when the ships are

maneuvering (on. the simulator).

This generalized hydrodynamic

interaction force module is structured so that it is linked to

the equations of motion of each ship in order to allow the

simulation model to feed the ship dynamic motions, orientation,

etc. to this force module.

The changing interaction forces will

then also be transmitted to and included in the total dynamic

models of ship motion, so that they will

turn influence the

subsequent responses.

Thus a coupling will exist which is

considered to be a realistic modeling of ship interaction in a

purely dynamic sense, which is not present in existing simulator

models.

A simplified block diagram representation of this

com-bined computation and simulation procedure is shown in Figure 6.

CONCLUDING R(ARKS

The discussion above describes the basic analysis being

used, as well as the concepts for inclusion of a calculation

procedure for determining the generalized hydrodynainic forces

acting on a ship due to another ship as weIl as physical

boundaries in the waterway region.

These forces are not

included when modeling the conventional hydrodynamic forces

acting on a single ship (alone) when it is in either deep or

shallow water.

The inclusion of these forces, when also

accounting for the effects of the dynamic motLons of the ships

on the forces, allows a full modeling of ship interactions which

Channel. geometry

etc.

Hydrodynamic Force computation - for

each ship

Yaw orientatiOn, position and motion responses Ship i

Fig. 6. Simplified block diagram of computation - simulation

procedure.

studies. Aside from caSes of ship passing an4/or overtaking, the influence of ship orientation, "crabbing" motion, etc. for

the case of 2 ships, as well as for a .single ship near a canal wall, can be directly analyzed and plaçed in a form readily

adaptable for usein a simulator.

The calculation procedure for determining these generalized hydrodynamic interaction forces is structured as a separate

modùle that can be integrated into an overall simulation

procedure for the case of 2 ships. The input requirements will only be ship geometry; speed; canal geometry; etc. without any

need for additional special experimental or empirical data. In

this way the force module will be similar to the major elements that are used in predicting ship motions in waves (e.g see Raf f

(1972) for description of t-he SCORES ship motion and load program). _{Only similar type input data is necessary to apply}

this theoretical model, which is a definite improvement in the

field of maneuverability analysis that has relied largely on

experimental data to establish hydrodynamic force models. The prospect of more realistic force modeling of ship interaction forces, and their use in simulator studies, provides an

opportunity for enhancing the simulation fidelity and accuracy for many problems of interest in simulator applications for restricted waterway design and analysis studies.

Equation of motion Ship 1

Yaw orientation, position and motion responses - Ship 2

RERENCES

Eda, H.; Shizume, P.K.; Case, 1.5.; and Puglisi, J.J. (1986). A Study of Shiphandling Performance in Restricted Water;

Development and Validation of Computer Simulation Model3 Trans. SNANE.

Kaplan, P. and Sankaranarayanan (1987). Hydrodynamic

Interaction of Ships in Shallow Channels, Including Effects of Asymmetry. Proc. RINA mt. Conf. on Ship Maneuverability.

MoOdy, C.G. (1964). The Handling of Ships Through on Widened and Asymmetrically Deepened Section of Gaillard Cut in the Panama Canal. David Taylor Model Basin Rpt. 1705.

Raf f, A.I. (1.972), Program SCORES -- Ship Structural Response in Waves. Ship Structure Comm. Rpt. No. SSC-230.

Remery, G.F.M..(1974). Mooring Forces Induced by Passing Ships. Proc. Offshore Tech. Conf., Paper OTC-2066.