A maneuvering simulation model for large angles of attack and backing propellers

effect of separated vortex. The difference between the two methods varies with the yawing angle. The calculated results which include the separated vortex proved to be more consistent with the experimental values. This verifies that the model and the numerical methods are feasible.

References

[1] Chapman R.B., "Free Surface Effect for Yawed Surface-Piercing Plates". J.S.R. Vol. 20, 30.

[2] Keiichi Yamasaki, Masataka Fujino el al., "Hydrodynamic Forces Acting on the Three Dimensional Body Advancing on the Free Surface". J.S.N.A.J. (1st Report, Vol. 154, 1983); (2nd Report, Vol. 156, 1984); (3rd Report, Vol. 157, 1985).

PS-4.7

M.A. A B K O W I T Z

Massachusetts Institute of Technology, U.S.A.

A MANEUVERING SIMULATION M O D E L FOR LARGE ANGLES OF A T T A C K AND BACKING PROPELLERS

I ,

Part of the special maneuvering trials carried out on the ESSO OSAKA (300.000 tons) consisted of 10710° zigzag, 20720° zigzag and 35° hard rudder maneuvers. The data obtained from these maneuvers were to be used in the system identification computer programs developed at M.I.T. specifically for ship motion analysis. Simulated ship data had been generated

beforehand and was used to test and tune up the system identification techniques being developed.

The usual form of the equations of motion had been used in the simulation model consisting of linear and non linear terms resulting from a Taylor expansion of the motion variables. When the trial data was received, it showed that in a hard rudder turn, the ship slowed from 12 feet per second to 3 feet per second, with the propeller maintaining ils original RPS(n). This meant that the flow into the rudder was coming mainly from the propeller race with only a small amount coming from the ship's forward velocity. It became necessary to alter the form of the equations to account for the actual hydrodynamics acting on the ship during realistic operational maneuvers. The equations of inotion were reformulated so that;

(1) the propeller thrust is expressed as a continuous function of propeller rotational speed (n) and the ship's forward speed (u).

(2) the inflow velocity (c) to the rudder includes the velocity in the propeller race which is a function of u and the propeller thrust loading represented by the coefficient K,.

(3) the rudder forces (lift and drag) are a non-linear function of thc angle of attack on the rudder (e) and not specifically the rudder deflection (6).

Figures 1, 2 and 3 show the equations of motion in the form which includes the features described above. A more detailed description of the realism of the equations and the successful identification of a valid maneuvering simulation model for the ESSO OSAKA are described in Reference 1.

• D e f i n i t i o n o f Terms; • • u - surge speed r e l a t i v e to w a t e r . V • sway speed r e l a t i v e to w a t e r , r • yaw a n g u l a r v e l o c i t y . t • s h i p ' s heading a n g l e . rudder d e f l e c t i o n angle

c • weighted average flow speed i n t o r u d d e r ( a x i a l ) e • e f f e c t i v e a n g l e of a t t a c k on r u d d e r . e - 6 - t a n - ' - f | ) L • l e n g t h o f s h i p . p • mass d e n s i t y o f the w a t e r . n ^ , a r e p r o p e l l e r t h r u s t c o e f f i c i e n t s Cjj • r e s i s t a n c e c o e f f i c i e n t n ' • mass o f s h i p ; m' - — - — k 1/2 PL-^ n • p r o p e l l e r speed i n r e v o l u t i o n s per s e c o n d . Xg - l o c a t i o n o f c e n t e r of g r a v i t y from o r i g i n ; - X g / L I j , • moment o f i n e r t i a of s h i p i n yaw. • l i n e a r v e l o c i t y of s h i p r e l a t i v e to w a t e r , U

Fig. 1. Derived form of the simulation equations

. - I' - S ' f t f L ' u- ' ] r ^ 4 r ; 3[ f

* K t^ - S> f ' • ' r) 4 N ; [ | L ^ ^ ] 6 * Ï; 7 ^ ( | i V ' l r ' y . . / j l f c ^ ] e '

The f^, f^, and e q u a t i o n s a r e the X ( l o n g i t u d i n a l force"), Y ( t r a n s v e r s e

f o r c e ) , and N (yaw moment) e q u a t i o n s as f u n c t i o n s o f u , v , r 6, and n. The f o r c e s and moments as f u n c t i o n s o f ii , v and r a r e accounted f o r i n the f^ e q u a t i o n . S o l u t i o n s o f the e q u a t i o n s o f motion a r e : 1 u y • k ( i , - H . ) f 2 . ( m x g - y . ) f 3 ] '4

O . S u ^ . + (1.w)u

V

:A

:is

Vi'^'W''

• ''°rr>:''

Geometrical r e l a t i o n s h i p between the p r o p e l l e r and the rudder. ' projected area of rudder

Ap • projected area of rudder In race 1.0 0.8 "A OJ 0.2 0.0

/

- 2 . 0 - 1 . 0 0.0 1.0 2,0 X/0.5D

[(1-w)u + k u ^ j 2 • ^ (l-wT^U^

c I s the e q u i l i b r i u m c o n d i t i o n of c for the speed u , when the p r o p e l l e r

° 0 u

"r 0

t h r u s t c o e f f i c i e n t to produce an equMlbrium with drag a t forward speed u . ( ^ ' ^ ) u ^ ^ - . ( l . w ) u + \ / { l- w) V + ^ . ( n D ) ' ^

T { l - t ) - pn^D*K^(l-t) - n i u ^ n g n u + n 3 n ^ where t - t h r u s t deduction f a c t o r , K • wake f r a c t i o n , T - p r o p e l l e r t h r u s t and K j - p r o p e l l e r t h r u s t c o e f f i c i e n t .

Fig. 3. Derived form of thc simulation equation

A few examples of the realism of this form of thc equations are described below.

When a ship executes a hard rudder tum, say of 35° rudder, initially the angle of attack on the rudder is 35° and therefore the rudder forces are in the non-linear range. In the steady tum, the angle of attack reduces to about 23° which indicates thc forces are essentially in the linear range (rudder still at 35°). It requires about six additional non-linear coefficients (which arc usually not included in the previous form of the equations) if the non-linear term in the rudder deflection is included in the equations.

In the equations shown in Figure 2, there arc terms involving (C-CQ) which represent the difference between the longitudinal inflow velocity to the rudder (c) and thc inflow velocity that would occur i f the propeller were operating at an RPM which would produce an equilibrium speed of u. The rodder in the undeflected position acts as a stabilizer and the flow over the rodder (c) at a croising speed includes thc race velocity of the propeller at the equilibrium RPM for that speed. So at equilibrium speed c = Cg, the term disappears and the stabilizing effect of the rodder appears in the Yy, Ny, Y, and N, terms. Any change in the propeller RPM from this equilibrium condition changes the flow over the rodder and thereby either increases or reduces the stabilizing effect of the rodder. Any slowing and especially reversing of the propeller (c<Co) may reduce the stabilizing effect of the rodder enough to render the ship unstable in straight line motion causing the ship to tum without rodder deflection. This condition would increase the probability of collision when two ships were heading toward one another.

A very common ship maneuver is thc pulling away from the dock by applying a significant propeller RPM with the rudder hard over. Since the ship has no forward velocity, the flow over the rodder is coming solely from the propeller race. In this case u = o and c is very large thereby producing a large rodder force resulting in a yaw moment which causes the ship to turn away from the dock. The equations of motion are in a form which can readily predict this maneuver.

Thc propeller thrust expressed as a general quadratic in u and n provides a continuous prediction of propeller throsl as both u and n vary during a maneuver. The coefficients r|i, r\2 and r\j depend on propeller geometry. Usually one set of r|'s holds through the range 0, n>0, and two other sets cover the range of ua 0 and n<0. Figure 4 shows curves of throst coefficient (K^) vs. speed coefficient (J = u/nd) for typical propellers over these ranges.

\

\\^

4

\

w

i

Fig. 4. Representative Kt vs J, for forward speed, + - rpm

In the simulation of any maneuver, the instantaneous values of u and n are being computed and the propeller set of fi's can be automatically introduced into the computation of the velocity induced by the propeller and thereby the velocity over the rudder. From these values of thrust, the velocities induced by the propeller, both positive and negative, can be calculated. In the case of a stopped or backing propeller (negative induced velocities), the flow over the rudder is reduced, thereby reducing thc stabilizing effect of the rudder as was indicated earlier. However, in the case of a submersible with the stabilizing fins and control surfaces forward of thc propeller, the negative induced velocity of a backing propeller reduces the flow over the stabilizing fins, rendering them much less effective than expected from the

design. As a result, the submersible may become unstable in straight line motion during a crash-stop propeller backing maneuver.

A crash slop backing maneuver, with zero rudder deflection, was simulated for an unmanned underwater vehicle (UUV) and the results of this simulation are shown in Figure 5 and 6. Notice that the vehicle became unstable towards the end of the run as indicated in Figure 5 by the significant values of yaw rate (R), heading angle, and adverse displacement (Y) which are reached in the absence of any rudder deflection and in Figure 6 by the significant value of transverse velocity (V). The other plots shown in the figures were trom a simulation of the same maneuver that did not include the effect of propeller induced velocities over the stabilizing and control surfaces.

The usual forms of the equations of motion pertain to those maneuvei's which ships perform while operating

at sea, where even in very light turns the angle of attack (drift angle) on the hull is moderate in magnitude, usually not exceeding 30°. In this case, the lift forces and moments on the hull result from the hydrodynamics associated with the phenomenon of "circulation". Therefore, the linear coefficients which are predominant at small angles of attack and the non linear coefficients which become effective at moderate angles of attack result from circulation hydrodynamics. At very large angles of attack, specially at 90°, the hydrodynamic phenomenon is not circulation but rather predominantly "cross flow-drag" where thc nature of the flow is quite different from lhat of circulation, Any valid simulation model must take into account the basic hydrodynamics involved.

Since the range of operational maneuvers for the unmanned underwater vehicle (UUV) covered both normal cruising and hovering,the simulation equations were altered to comply wilh the change in the hydrodynamics that occur at large angles of attack. The equations were consistent with circulation hydrodynamics from 0° lo 30° angles of attack and were consistent with cross flow hydrodynamics from 60° to 90° angles of attack, with a smooth transition between the two in the region 30° to 60°. The UUV is a small vehicle of mostly circular cross section with rounded nose, tapered tail, propeller at the extreme stem with stabilizer fins and control surfaces forward of the propeller. At relatively low transverse velocity, cross flow over the circular sections can result in laminar separation where the cross flow drag coefficient is significantly greater than the drag coefficient when the separafion is turbulent at a slightly higher flow velocity. Since in most maneuvers, there is a combination of transverse

O ÜD tn LD CD CO (—1 Li_ CM O X O O O O E— — O r g 1 O O CD L J m O m UD 1—. ₆ JZ n 1 Q_ n 1 O c i - 9 CD Lü Q Q t r tn m • r g cb N . ó O c n CD L J Q 0.0 9 --O O z 1 r ' c

\

\

T I M E

SECONDS

Fig. 5. _{Trajectories of crashback, runs made on RIHSIM: • = augmented EOM} O = revised standard EOM

velocity and angular velocity on the body, there can be significant differences in the cross flow velocity between bow and stern sections. This can produce, for example, laminar separation on some stem sections while some bow sections have turbulent separation resulting in significant differences in sectional forces even though most bow and stern sections are identical. Cross flow drag on the stabilizing surfaces are essentially that for a flat plate of the proper aspect ratio.

The hydrodynamic aspects discussed above were incorporated into the simulation model for the UUV and a buoyant rise was simulated. The buoyant rise maneuver was effected by removing a weight (small percentage of the displacement) from the UUV at the center of gravity location at a time when the vehicle was in neutral buoyancy, at zero pitch angle, and at zero forward speed. Figures 7 and 8 show the resulting trajectory. In Figure 7, it can be seen that the UUV quickly assumes a vertical velocity (W) but also picks up a significant pitch moment (M), a significant forward velocity (U) and a large steady angle of attack (alpha) i.e. a steady glide angle. This pitch moment forward velocity and angle of attack do not occur in an alternate simulation which excludes some of the basic hydrodynamics. In Figure 8, it can be seen that the pitch angle (theta) is small at the end of the maneuver although the glide angle is large. The figure also indicates a build up of RPM as the vehicle picks up forward speed. This is the windmilling of the propeller generated by the vehicle's forward velocity on an unlocked propeller. Details of the UUV maneuvering simulation are given in Reference 2.

A form of the equations of motion have been presented which we believe represents valid hydrodynamics for use in maneuvers with backing propellers and large angles of attack.

References

[1] Abkowitz, M . A . , "Measurements of Hydrodynamic Characteristics from Ship Maneuvering Trials by System Identification". Transactions of the Society of Naval Architects and Marine Engineers, November, 1980.

[2] Hickey, R.J., "Submarine Motion Simulation Including Zero Forward Speed and Propeller Race Effects". S.M. Thesis Department of Ocean Engineering, M.I.T., February 1990.

PS-4.8

M . HIRANO, J. TAKASHINA and M . FUKUSHIMA

Akishima Laboratories (Mitsui Zosen) Inc., Japan

TURNING TRAJECTORIES OF A SWATH PASSENGER SHIP

In general, due to changes in trim and sinkage and due to wave-making phenomenon, ship maneuvering motion of high speed vehicles is greatly affected by their advance speed. The authors had a chance to study maneuverability of a high-speed SWATH passenger ship (Lpp = 31.5m). Extensive investigations were carried out from both experimental