Estimation of hull form effects on wake with CFD-tools

ESTIMATION OF HULL FORM EFFECTS ON WAKE WITH CFD-TOOLS

M. Hoekstra

Maritime Research Institute Netherlands,

Raagsteeg 2, P.O. Box 28, 6700 AA Wageningen, The Netherlands

ABSTRACT

Numerical predictions are presented of the viscous flOw around a ship, neglecting wave formation The results for two tanker hulls with different. aftbody shapes are compared. After a potential flow analysis, the viscous flow behaviour at the stern is examined. Limiting streamline patterns and velocity distributions are com-pared.. One of the hulls shows flow reversal ahead of the propel-1er, which the propéller action does not remove completely, as additional computations indicate This is sufficient reason to disqualify the design. Neither is the other hull form fülly satis-factory. Suggestions are given for the design of a third variant.

1. INTRODUCTION

Ship designing has a Strong bias towards traditionalism, i.e. it relies heavily on sùccessful hull designs of the past. But even if this often means that only small deviations from earlier hull forms are acceptable, a designer will Once in a while be facing the question: how does this conceived modification affec.t the wake of my ship? Of course, it is not so much the flow field itself that he is

worried about,. but rather the

cnse-quences for propulsive performance, rpm, risk of cavitation, vibration level, etc. However, wake field information is the basic requirement for an estimation of. these consequences.

The usual way of verifying the influence of design variations is by model

test-ing, but not until an advanced phase of the design process has been reached. Ai awkward situation may arise when the

tests show the deslÉn to be unsatisfac-tory: the later the .need for additional modifications comes up, the more costly

is their implementation.

Numerical flow simulations can help to reduce the risk of the designer's choices in an earlier design stage.

-1-Along with the impressive hardware

de-velopments of the last years, the dis-cipline of Computational Fluid Dynamics (CFD) has expanded and continues to pro-duce new or improved tools which can play a useful role, complementary to that of experimental investigation, in a design process. Prediction methods for ship stern flows form one class of tools which has matured considerably. If not yet quantitatively, in full agreement with experimental data, the results Of present-day wake prediction sóftvare can at least indicate the main trends añd the sensitivity of the flow to the hull form _{change.. The cost at which they are} obtained is still appreciable, but there is a safe prospect of réduction In the future. Numerical stern flow prediction. will then be highly suited for

explora-tory work within the margins set by de-sign constraints and within the limited budgets availáble.

This paper gives an example of wake pre-diction by CFD. The flow around two tankers, differing only in aftbody shape,. is predicted and the results are discussed. Our aim is twofold: to show

the _{present capabilities of CFD in wake}

prediction and to indicate how it can fruitfully be sed in designing via com-parative qualification.

2. OUTLINE OF COMPUTATIONAL APPROACH Since not all readers will be familiar vith the current methodology in numeri-cal wake prediction., a concise introduc-.

t.ion to our approach of the problem may be appropriate.

The _{numerical simulation of the viscous} flow around a ship, even under the sim-plest operating conditions of steady mo tion through still water, is undoubtedly an intricate matter. Although there is a. sound màthematical model (the Navier-Stokes equations for incompressible

flow), the solution for a given set of boundary conditions cannot be obtained without, restrictions. For instance, present-day computers do not allow dis-cretizations fine enough to resolve the small scale motions inherent in

turbu-lence, a phenomenon that always occurs in _{some parts of the flow field.} Conse-quently, the high-frequency motions have to be removed and an estimate of their time-mean _{effect on the flow as a whole} is to be made via a 'turbulence model'. Also the presence of the free surface is a _{complication, the characteristic} dif-ficulty being the imposition of boundary conditions on a surface of which shape and location are to be obtained as a

part of the solution. Under the assump-tion that free surface disturbances have

'a negligible influence on the wake

dis-ttibution, we omit this problem by

treating the undisturbed free surface as

a symmetry plane (no waves; see ref. [1]

for examples how to deal with f

ree-surface problems under. inviscid flow assumptions).

Simplifications of the above kind imply more or less serious shortcomings in the physical representation of the flow.

They are distinct from 'another aspect: accuracy versus cost. It will be clear that any numerical discretization of the mathematical model implies a bound on the quantitative accuracy. With

increas-ing refinement of the discretization, the calculations become more accurate as wll as more. expensive. The cost of the. computations in relation to the quality

of the result is a critical factor for

acceptance.. Any means to reduce the

costs without deteriorating the result is _therefore welcome. For the flow

around a ship, characterized by _{a high} Reynolds number, a considerable

reduc-tion of, the computational effort is ob-tained by dividing the flow domainl into regions with different degree of flow complexity and by solving simpler qua-tions in the regions of 'simple' 'flow.

If the regions are properly chosen, _this

d'oes no real harm to the quality of the physical flOw representation. In the

method _{to be used here, three zones are} distinguished (Fig. 1):

zone I, the external flow region, .where the flow is assumed to be

invis-cid and irrotational;

- zone II, the boundary-layer region, covering the forward part of the hull, where boundary-layer theory

issup-posed to give añ adequate description of the flow;

- zone III., the stern-flow-and-wake region, where the Reynolds-averaged Navier-Stokes equations are. solved..

loe

Figure 1:

Division of flow field into three zOnes.

The _{solutions in the three zones cän be} linked, by schemes of varying degree of interaction; here, the link has been assumed non-interactive., which is not completely correct but good enough for practical purposes. Solution Of the

ensuing reduced problem is feasible at present.

Thus, in order to predict the nominal wake of a ship, _{we calculate the} f low

around a double model of its submerged part by a combination of three computa-tional _{elements: a potential flow code,} a boundary-layer method and a stern-flow solver. The potential flow code is based on a boundary-integral method, employing

,a Rankine source _{distribution on the}

hull _{surface. it supplies boundary} con-ditions for the boundary-layer method and the stern-flow solver. The latter

are both finite-difference methods, and require the generation of a grid in the space chosen for the calculation (zónés II and III respectively). To each grid node discrete values of the variables (velocity components ánd pressure) are assigned which are the unknovn tó be solved iteratively. The viscous flow methods are described in some detail in [2,3,4].

3. HULL GEOMETRIES

Results vilI be presented för two tank-ers which differ only in. the aftbödy shape. The main dimensions of both hulls are the same and are listed below:

Length between perpendiculars L = 253.0 m Breadth B

38.33m

Dra ugh t T = 14.20 ni Displacement volume V = 117000 rn Wetted surface S = 14755 in Block coefficient Cb = 0.85 Even the lengthwise position of the cen-tre of buoyancy has

been fixed at 32

pér cent of the ship's length ahead of midship for both hUlls. Most statistical drag _{prediction methods., based on módel}

-3-test resúlts of the. past and describing

the hull gèóinetry in terms of global fotm parameters such as L/B, Cb, etc., would therefore not be able to indicate a preference.

The differences betveèn the two hull

forms are apparent in the frame shapes. The body plans and stern contours are compared in Fig. 2. Tanker 2 has pro-nounced U-type frame lines in the region directly_f ahead of the propeller. Those tanker 1 tend to b moré V-shaped. Moreover, the frame lines show a com-pletely different character in the upper stern region. The curves of sectional areas are only marginally different,

though.

Insiders will recognize the two hull

forms as the test cases for a workshop

on stern flow prediction, held recently in Sweden.

For later reference, a coordinate x is introduced here - pôinting from bow to

stern, and with the origin at the bow -by which a lengthwise pOsition along the hull can be indicated. Thus, x/L = O corresponds with the position of the fOrward perpendicular, x/L = i with the áf t perpendicular.

4. POTENTIAL FLOW

In _{this section the results of the} Po-tential flow calculations will be consi-dered _{separately. It may seem}

paradoxi-cal to do so because the main Interest is in the wake, the _{structure of which} is _{primarily determined by viscous} ef-fects. _{However, it is to emphasize that} the potential flow results - which are obtained at relatively low cost - give us a meaningful global impression of the flow around the hull. Moreover, they usually allow some qualitative

specula-tion on the _{behaviour of the viscous} f low.

As mentioned earlier, the potential flow calculations have been carried out with a _{Rankine source panel method.} Approxi-mately 2000 panels were distributed _over the _{submerged part of the hull, with a}

concentration of panels on the aftbody.

Fig. 3 shows the calculated streamlines on _{the hull surface, while the pressure} distributions are given in Fig.

_4.

These results indicate some small but

important differences.

In the lower stern area, the streamlines are more bent for tanker 2; in the upper stern area an _{opposite effect can be} observed. The pressure _{distributions} confirm that tanker 2 has a more pro-nounced _{aft shoulder: at the end of the} parallel _{midbody, the pressure is lower} near the waterline. For both hulls, a depression is found in the bilge region just ahead of the stern, but it is stronger for.tanker 2. This is relevant

(a) Tanker i

for _{the wake distribution because these} depressions are related to the _formation of longitudinal vortices.

The above, results _{have been obtained} under _{the assumption of the fluid being} inviscid. _{What can be said in}

anticipa-tion about the _{behaviour of the real}

(viscous) _{flow, merely on the basis of} these potential flow data?

Let us first recall some basic facts about _{boundary-layer development, by} considering four classes of flpv in

order of increasing complexity:

a. The thickness of a two-dimensional boundary layer on a flat surfacé _will slowly grow in the streamwise

direc-tion. That is because momentum is needed to overcome the

fricjonal

forces.

b If _{the flat surface is replaced by a}

two-dimensional displacement body, an additional _{effect occurs: there is a} pressure _{variation over the body. A} favourable pressure gradient (from high to lw pressure) tends _tó sup-press the rate of thickening _{of the} boundary-layer, an adverse _pressure gradient to enhance it.

c. Another feature enters when

aisym-metric bodies are considered, viz.

convergence _{or divergence.of}

stream-lines. Diverging streamlines - as over the front part of the body - act to reduce the growth rate., convrging streamlines to increase it.

(b) Tanker 2 Figure 3: Streamlines along the hull in potentiàl flow.

(a) Tanker i

(b) Tanker 2

d. We _{finally make the step to a} three-dimensional body like a ship. All above effects are present, but in ad-dïtion there are lateral _pressure gradients. They imply streamline cur-vature _{in planes locally tangent to}

the _{hull, but also cross-flow in the}

boundary _{layer. This can be made} un-derstandable as follows. To first approximation the pressure is uniform in _{the boundary layer along a normal} to the hull, and hence the lateral pressure gradient too. At the outer edge of the boundary layer the veloc-ity is high and only a slight stream-line _{curvature is sufficient to} bal-ance _{the pressure gradient by a} cen-trifugal _{force. Inside the boundary} layer the speed is lower and more streamline curvature is required for

- a balance (near the surface, shear

forces _{assist the centrifugal förce} to balance the pressure force, pre-venting the streamline curvature from becoming infinite). It follows that the direction of the flow near the hull surface can differ significantly from _{.the direction of the outer-flow} streamlines (Fig. 5).

STREAMWISE VOCrTY. pço

W4LL CROSS . ANOLE

Figute 5:

Cross-flow in a boundary layer.

When _{these simple rules are applied to}

the present potential flow data, some features of the viscous flow can readily be predicted. The _{pressure rises towards}

\ VLcITY PROFILE

CROSS - WISE

the stern, particularly _{ovér the last} ten per cent of the length, so _{that a} rapidly growing boundary _{layer can be} expected _{there. But the streamlinés are} seen _{to diverge strongly from thè keel,} whence the boundary layer _{growth along} the keel line will be suppressed. _{Qn the} other _{hand, they converge along a line} along the hull just above the conavity in the frame lines. Accordingly, the

boundary layer is expected to be

rela-tively thick there..

Appreciable streamline curvature (in

planes _{tangential to the hull surface)} has been observed also, notably _{over the} foot of the stern frames, _{and at} the

stern close to the waterline _{where the} streamlines bend upwards. The flOw in-side the boundary layer can be predicted to bend in the same direction but more than _{the potential flow streamlines do.} As cross-flow develops, the near-surface

flow _{streamlines will converge at quite} another place as the outer-bounary-layer flow does.

Thus, by potential flow calculations alone, a qualitative picture of the global _{boundary-layer behaviour can be} established. _{I.n order to go beyondthis} qualitative guess., we have to enter the domain of the viscous flow calculations.

5. VISCOUS FLOW

Where _{an ideal fluid can slide over the} hull surface, a real fluid adheres to it, _{causing the formation of a boun4ary} layer. _{The development of this boundary}

layer over the forward portion of the hull has been simulated, assuming _{fiFst_} order boundary-layer theory to apply.

Aft _{of station 7 (at 65 per cent of' the} ship's length), we adopted a slightly reduced form of the Reynolds-averaged Navier-Stokes equations as the mathema-tical _{model. The calculations have been} carried out at a. Reynolds number Rn = 5*10 , which is typical for the

experi-mental situatiOn in a towing tañk.

Let us concentrate immediately on the

results in the stern region.. Consider

first _{Fig. 6(a)., displaying the}

disttri-bution of the longitudinal (axial) ve-locity component for tanker 1 at xII. =

varïa-tion of the _{boundary layer} thickness along the girth. In accordance with the speculations in the previous section, .a bulge appears just above mid-girth, while the boundary layer is very thin at the keel. It is also thin at the water-line, which is a transverse curvatúre effect: the angle betveen..vaterline and frame line increases tovads the stern, implying that more space

becomesgrad-uaily available for the fluid near the waterline, which has a thinning effect on the boundary layer.

The corresponding results of tanker 2 in Fig. _{6(b) indicate similar tendencies,} but _{there are already small differences} in the flow structure (e.g. the boundary layer at the keel is thicker, and lower near-hull _{velocities are found near the} concavity in the frame line).

To get an overall impression of the be-haviour of the flow close to the hull sürface, visualization of the hull shear stress direction (limiting streamlines) is helpful. The experimental equivalent is the 'paint test'. The computational results _{are presented for the two hulls}

in _{Figs. 7 and 8. tn Fig. 7 'tufts' are}

used _{to indicate the direction (not the} magnitude!) of the local skin frictIon

1.0

vector in a side view; Fig. 8 shows _the limiting streamlines as derived from such a tuft plot, but now in a rear

vi ev.

A comparison with the potential flow streamliñes - which are _{representative} for the flow direction in the outer part of the böundary layer - reveals appreci-able _{differences, indicating the strong} three-dimensionality of the flow. Both hulls show a confluence of limiting streamlines in the lower stern region which marks the origin of a longitudinal vortex, On tanker 2 there is in addition a congestion of limiting streamlines in the upper stern region, along an almost horizontal line. But the flow behaviour in its neighbourhood is quite different since it is a line of flow attachment (limiting _{streamlines are pointing away} from it, not towards it).

The most significant difference is of course the flow reversal at the stern of tanker 1, which has been avoided on tanker 2 by moving the stern post aft. Notice, _{however, that there is a region}

on tanker 2 as far upstream as x/L =

0.9, where the flow is close to

rever-sal. Recovery from this near-calamity occurs further downstreäm by lateral momentum supply.

Figure 6: Axial velocity distribution at stationx/L _{= 0.908.}

(a) Tanker i

(a) Tanker ]r

x/L = 1.0

.966 .937 .908 - .878

(b) Tanker 2

Figure 7: Direction of shear stress _{vector on the hull surface.}

:-_--- -

--

,

i i

--

,

/

i___.

.-

--.

_-

-

/ /

_-

-

/

, ; ,__

-

--S-.-..

,,_.

-- ---

S--

-

--

-

-

_-.

.-- .-- ____.--.--.--__ S.--

-.

The occurrence of flow separation on tanker 1 has been _confirmed experimen-tally by an oil-flow test in a wind tunnel (5J.

The _{wake fields in the propeller}

planes - visualized as usual by a contour plot of the lines of equal axial _{velocity and} a vector plot of the transverse velocity components = are shown in Figs 9 and 10. Notice that the location of _thq pro-peller plane of the two ships is differ-ent; _{for tanker 1 it is at x/L = 0.976,} and for tanker 2 at x/L = 0.991.

In both wakes a longitudinal _{vortex is} present but it is more _{developed and} stronger for tanker 2. _{This correlates} with the more pronounced _{depression in,}

the _{bilge region that we saw in the}

po-tential _{flow results, although}

the ef-fects _{are enhanced by the more rearward} propeller _{plane position. We would try} to avoid these _{vortices but for their} favourable equalizing effect on the

axial _{velocity distribution. The}

inten-tional creation of _{vortices is therefore} justified in a lot of cases.

Disappointingly, the calculated axial velocity _{distribütions are rather}

unre-(a) Tanker i (x/L 0.976)

Figure 9: Axial velocity distribution in propeller _plane.

alistic in the propeller disk _{area, an} observation that is _{confirmed by the} comparison with experimental data _{[6J in} Fig. 9(a). Somehow the _{computations fail} to produce the retardation of _{the axial} velocity near the corè _{of the vortex.} The _{narrowness of the predicted wake is}

the _{more surprisingin view of the flow} reversal further ahead fr _{tanker 1. The} reasons for this anomaly _{have not yet} been _{resolved completely, but it is of} course a serious shortcoming that has to

be carefully studied and _{as soon as} pos-sible removed. In _{other respects the}

axial flow is _{fairly well predicted.}

Moreover, the results _{give clear} evi-dence of the wake peak in the longitudi-nal _{centreplane being more pronounced}

for _{tanker 1, although the distance}

be-tween _{propeller plane and stern is} al-most equal for both hulls. The _{effect of}

the _{difference in stern contour}

is

no-ticeable in the lower part of the wakes. So far, we have only pointed _{out certain} differences in the flow around the two

hulls. The _{necessary next step is to} talk _{about their possible}

implications,

in _{order to allow a decision On a}

pref-erence. of the one hull _{over the Other,} or a suggestion for design adaptations.

(a) Tanker i (xi!.. = 0.976)

N

N

N

\\\\\\

N

_N

N

N

\\\

\

\

N

fffl\\\\\

_\\

'11''' \'

\ \

\

\

\

\ \

\

-N

N

N

N

N

\

(b) Tanker 2 (x/L = 0.991)

Figure _{10: Transverse components in propeller plane.}

N

N

_N

N

\

N

N

\

n

\ \

x/L = 1.0 .966 .937.

Tanker i has flow reversal in the. lover stern region which causes the _hull re-sistance to be greater. The _calculations have identified thé _{increase as extra} pressure _{resistance; the tvo hulls have} practically equal _{frictional drag. In} addition, _{the wake peak above the shaft}

in _{the respective Propeller planes is} more pronounced for tanker 1. This tends to increase the. variation of the propel-1er blade loading _{during a revolution} and hence the risk of vibrations.

Superficially, therefore, it is tempting to _{choose tanker 2 as the best of the} two. But it should be borne in mind _that

the _{interaction with the propeller may} change a lot. Could it be, for _instance, that _{the flow reversal at the stern of}

tanker _{i disappears. when the propeller} is _{operating? Because this can be} veri-fied _{computationally, we have repeated}

the calculations for tanker i with

addi-tion of a propeller, represented _{by an} actuator disk. For convenience, _{we have} applied thrust forces only; forces in

radial and _{circumferential direction} have been omitted (N.B. inclusion _{of the} latter would imply the loss _of port-starboard _{symmetry of the flow and thus} considerably more computational _work). The _{propeller loading - with a radially} varying but _{circumferentially uniform} distribution - was chosen approximately in accordancé with the _{self-propulsion} condition. _{Further, we omitted the hub} in _{order to avoid an}

adaptation of the computational grid.

As a result, the hull _{shear stress} di-rection as modified by the propeller action _{is presented in Fig. li. Indeed,}

the _{flow reversal has disappeared}

below the _{propeller shaft, but not}

above it. Ve expect that it wOuld not, disappear even if we _{more realistically}

-had concentrated a greater part of the pro-peller _{loading in the top sector of the} disk. Therefore it _{seems that the design} of _{tanker i requires some modification.} Since _{we do not liké either 'the} almost-flow-reversal on tanker 2 near x/L = 0.9 - which is unlikely to _{be affected by} the propeller -, and ve prefer the milder aft shoulder of tanker _{1, a third} variant _{is considered as the best} op-tion. We would copy the design _{of tanker}

i somewhere up to x/L = 0.9, move the propeller slightly aft, which allows the waterlines to be stretched, _sufficient to _{avoid flow reversal in the propelled} mode. The design of the lover stern area (frame foot) would _{depend on the} in-stalled power and the risk for

vibra-tions. _{We would try to create a strong}

vortex (as on tanker 2) in case of a

serious risk, .but _{a weaker vortex (as on}

tanker 1) in the opposite _{circumstances.}

6. CONCLUDING REMARKS

The _{results of the numerical simulation} of _{the flow around two slightly}

differ-ent _{hull forms have been presented. We}

hope to have shown that such results yield _{useful information for a ship} de-signer. Admittedly, the prediction of

the _{axial velocity distribution}

in the propeller plane. has turned out to be defective _{for the subject hulls.}

Never-theless, _{the amount of detail and} real-ism _{of the overall result is sufficient} to allow preferential choices _{to be made}

.908

, __

--_

__

---.----.

Figure 11:

Direction of shear stress direction on the hull with operating propeller _{(Tanker 1).}

or certain design _{improvements to be} suggested. Anyway, _{the information is} better than what the _{best-informed}

guess, _{derived from}

experience or sta-tistical/empirical _{methods, could} pro-vide This will be _{reason enough for a} more _{frequent application of}

numerical vàke _{prediction to design}

problems. Further _{improvements and extensions}

of the code, and the

expected reduction Of

the _{expenditure, involved}

in is use,

will _{have a favourable}

and stimulating influence on this development.

REFERENCES

Eli

Van _{den Berg, W. et al.,} "Free-sur-face potential flàw _{calculations for} merchant _{vessels", paper}

presented at this Symposium.

[2] Hoekstra, M., _"Applicatij

of a high_order fini te-différence _method

to the _{solution of the}

boundary_ layer _{equations", MARIN Report}

No.

44519-2-SR, Nov. 1981.

[31

Hoekstra, M., "Computation _{f Steady}

visCOuS

flow near a _{ship's stern"} Notes on Numerical Flüid _Mechanics Vol. 17, ed. _{P. Wesseling,!}

Vieweg Verlag, 1987.

[4]. Hoekstra, _{M., "Recent}

deveopments

in a ship stern flow _prediction

code", _{5th Conf. on}

Numerical Ship Hydrodynamics, Hiroshima, _1989. [5] Kux,

_{j, "Berechnungsverfh}

der Schiffshydrodynamjk _{- Vergleich der} Ergebnisse _{mit Messungen",}

Jahrbuch STG, 83 Band, 1989.

[61 Wieghardt, _{K. and Kux, J.,}

"Nomi-neller Nachstrom auf Grund von Wind-kanalvrsuchen", Jahrbuch STG 74, pp. 303-318, 1980.: