An advanced CFD method for predicting the propulsive performance of traditional fishing vessels

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AN ADVANCED CFD METHOD FOR PREDICTING THE

PROPULSIVE PERFORMANCE OF TRADITIONAL FISHING VESSELS by

G. D. Tzabiras, A. C. Prifti, G. J. Grigoropoulos and T. A. Loukakis LAboratory for Ship and Marine Hydrodynamics

Department of Naval Architecture and Marine Engineering National Technical University of Athens, Greece.

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A viscous flow solver has been applied to calculate the turbulent flow field around a model of a traditional fishing vessel. The propeller is simulated by an actuator disk

while the free surface is considered as a plane. Calculated results for the total

resistance and the required thrust

to

attain a certain speed are compared to

experimental values. Complex flow phenomena, like three-dimensional separation are also studied while the method's capabilities to improve hull forms or to perform liii! scale predictions are examined.

AUTHORS' BIOGRAPHIES

T.A.Loukakis: Professor,

Director of the

Laboratory for

Ship

and Marine

Hydrodynamics. Diploma in Mechanical and Electrical Engineering NTUA (1962), M.Sc. in Naval Architecture and Marine Engineering, Massachusetts Institute of Technology (1966), D.Sc. in Naval Architecture and Marine Engineering, Massachusetts Institute of Technology (1971).

G.D.Tzabiras: Assoc.

Professor, Diploma ¡n Naval Architecture and Marine

Engineering, NTUA (1975), Diploma in Mechanical Engineering, NTUA (1978), Dr.-Eng., Naval Architecture and Marine Engineering, NTUA (1984).

G.I.Grigoropoulos: Asst. Professor, Diploma in Naval Architecture and Marine Engineering, NTUA (1981), Diploma in Mechanical Engineering, NTUA (1986), Dr.-Eng., Naval Architecture and Marine Engineering, NTUA (1989).

A.C.Prifti: Dr. Candidate, Diploma in Naval Architecture and Marine Engineering, NTUA (1991).

I. INTRODUCTION

In several countries, various types of vessels have been built to serve the needs in fishing. In Greece, there are more than 11,000 traditional vessels of the perama,

irechantiri, kara'oskaro, liberty, varka/as, and other types, ranging from 6 m to 25 m in length. Similar forms can be found al! over Eastern Mediterranean and Black Sea while hull shapes that approach the aforementioned types exist in various places in Europe. Most of these vessels were using sails which, later, were replaced by engines and propellers. Although some of them had the proper shapes to be fast sailing ships, the use of propellers resulted in rather high powering demands to attain the same speed.

Obviously, the proper selection of the propulsion plant (engine and propeller) is of crucial importance for the economical operation of fishing vessels. Since there is a lack of systematic series and experimental data to assist the designers to improve hull forms or to make accurate powering estimations, the usual practice has been to install engines with rather excessive horsepower. In order to provide useful information concerning an optimum propeller-engine selection, a research project has been initiated in the Laboratory for Ship and Marine Hydrodynamics of the National Technical University of Athens (N.T.U.A.) since 1980. Systematic towing tank experiments have been carried out to study the resistance and propulsion characteristics of several types of traditional fishing vessels.

From the first experiments [1], it was found that for certain hull forms the thrust deduction factor exhibited very high values in the whole range of the tested Froude numbers. Recent experimental studies with a model of the "perama" hull form revealed that the aforementioned behavior is the result of very complicated flow phenomena that occur around its stern. More specifically flow visualization techniques indicated the existence of an extended separation area as well as a strong interaction between the propeller and the free surface. The use of fins in front of and above the propeller disk improved drastically the propulsive parameters, showing that simple devices may be quite effective for reducing the required horsepower.

In order to study in more detail the stern flow of the particular vessel, an extensive numerical investigation has been carried out. This investigation has been based on the application of a computational method that solves the turbulent flow field around ship hulls. The aim of the present work is to show how such a method can provide a deeper understanding of the relevant flow phenomena, and may be used as a constructive tool for improving designs. Since, theOretically, the application of a CFD (Computational Fluid Dynamics) code does not suffer from scale effects, calculations have also been performed at full scale to study the trends of the solution. It should be kept in mind that 3D viscous flow computations require high performance computers as well as

basic knowledge of fluid mechanics in order to derive useful conclusions of

engineering interest.

2. PRESENTATION OF EXPERIMENTAL RESULTS

Extended resistance and self-propulsion tests have been conducted for the 1:10 model of the "perama" fishing vessel in the towing tank of N.T.U.A. The lines plan of the

model is shown in Fig. i and its principal characteristics are presented in Table I. The overload test procedure has been adopted to calculate the self-propulsion parameters while the main characteristics of the propeller that was used in all experiments are shown in Table 2. In order to analyze various factors affecting the hydrodynamic behavior of the model, systematic tests have been performed:

- with different lengths of propeller axes - with or without rudder

- with different shapes of the aft stem

- without tins or with one fin of a length equal to 0.029 m on each side at the aft part In addition, flow visualizations using paint or tufts were performed in order to attain a

picture of the flow field at the stern region of the model where extended separation was observed. The results presented in Tables 3 and 4 correspond to a standard length of propeller axis and have been obtained using a refined modification of the stern post without rudder. This configuration has also been used in the numerical calculations. The original hull tests without fins are exhibited in Táble 3. The thrust deduction factor t in this Table has been calculated as

_T_Rî

T

where R1

is the total model resistance at the examined speed and T the propeller thrust. Evidently, the values of t are unusually high at all tested speeds. A substantial improvement is observed in Table 4 where corresponding results are presented when a single fin is added on each side of the model near the waterline and just in front of the propeller.

Table 1: Model characteristics

(1)

Leflgth overalJ (rn) 2.06

Length between perpendiculars (m) 1.93

Length of keel (m) 1.60 Beam maximum (rn) 6.50 Height (m) 0.34 Depth mean (m) 0.26 Draft mean (m) 0.22 Model displacement (kg) 102.057 LCB fwd middle frame (m) -0.048

Trim by stern (del)

2.4

Keel section breadth (m) x height (m) O 20x0 25

T,

Table 2 : Propeller characteristics

Table 3: Model "Perama" Resistance and Self-Propulsion Tests

Table 4: Model "Perama with fins" Resistance and Self-Propulsion Tests

Propeller type Wageningen

B-series

Diameter (m) 0.160

Pitch ratio 0.880

Expanded blade area ratio 0.628

Number of bladés 4

Length of hub (m) 0.048

Diameter of hub (m) 0.028

Inclination

of shaft

axis with

respect to keel line (deg)

6.250 Model speed (m/s) Froude Number Resistance (kp) Thrust (kp) Torque (kp x cm) RPS t 0.411 0.094 0.0835 0.166 - 3.654 0.496 0.617 0.142 0.1826 0.309 0.291 4.971 0.409 0.822 0.189 0.3361 0.519 0.618 6.517 0.352 1.029 0.236 0.5708 0.791 1.119 7.942 0,278 1233 0283 08501 1285 2360

9919

0338

I 43i

0 330 1 4q29 2 420 4 780 12 760 0 383 1.643 0.378 2.4511 3.967 8.219 15.810 0.382 1.949 0425 4.6306 6.878 14.830 20.480 0.326 Model speed (m/s) Froude Number Resistance (kp) Thrust (kp) Torque (kp x cm) RPS t 1.029 0.236 0.507 0.584 1.200 7.907 0.132 1.233 0.283 0.848 0.959 2.300 9.882 0.115 1.437 0.330 1.404 1.925 4.100 12h32 0.270 1643

0378

2576

3119

6800

15446 0174 1849 0425 5025 6057 13400 20158

0170

3. ThE COMPUTATIONAL METHOD

A finite volume method developed to calculate the turbulent flow field around ship hulls [2],[3] has been applied to study the resistance and self-propulsion characteristics

of the examined vessel. Modifications in the original code have been made to:

overcome the geometrical irregtlarities near the keel as well as to improve the

convergence procedure in recirculation zones due to the stern flow separation. Since the complete solution of the problem including the free surface and the unsteady propeller operation is still beyond the capabilities of CFD codes, the employed method introduces two simplifications relevant to these aspects. First, the free surface is considered as a plane (double body approximation) and the wavemaking resistance

component is estimated by subtracting the calculated total resistance from the

measured one at the same Froude number. The result is added to the body resistance which is computed in the numerical simulation of the self-propulsion problem. The second approximatiàn concerns the propeller action, which is modeled using the actuator disk concept [4] A more detailed description of the method is presented in the sequel.

3.1 GRID GENERATION

An H-type numerical grid is employed to solve the flow equations around the hull. A perspective view of characteristic grid surfaces is shown in Fig. 2. The 3D mesh

consists of subsequent plane orthogonal curvilinear grids that are generated on

transverse sections by applying a conformal mapping technique. Each section contour is firstly transformed to a unit circle under the mapping fùnction [5]:

ç = (2)

where z represents the complex plane of the unit circle on [O, -it12] and Ç the plane of the examined section. The coefficients a are calculated by an iterative procedure.

Assuming that P points

are specified on the section contour (offsets) and the angles q,p that define the corresponding points on the unit circle are known, the transformation coefficients are calculated by minimizing the sum:

E, ₌ (3)

which results in N equations with unknowns the values of a. Since the obtained coefficients from the solution of the corresponding system depends on the selected angles; a new approximation for p is made by finding the minimum of the distance

-

for each input point. This is obtained by defining a partition on the circle which is successively refined. For a conventional ship the above procedure converges quite fast and normally 6 to 10 coefficients are adequate to represent its sections. On the contrary, when the geometry of a section is complex, the iterative calculation of coefficients may result to quite different shapes, mainly due to the way that angles pp are approximated. In the examined vessel, relevant difficulties have been encountered

near the junction of the keel beam and the hull. With the described method unrealistic shapes, like the one presented in Fig. 3, were obtained even if 60 coefficients were used to represent midship sections. Detailed study of these forms revealed that they were quite sensitive to(p distribution near the keel. To overcome this difficulty, it was assumed that q varies linearly with respect to the length of the section contour close to. the ship centerline. This interpolation was applied only to P-1 point, i.e. between the value of(p on the centerline point P (being equal to -it/2) and its value at point P-2. A

surprising better approximation of the hull geometry was, then, achieved and 60 coefficients were found adequate to represent all sections along the ship.

Once coefficients a have been calculated, an orthogonal curvilinear grid around a section can be easily generated by transforming the corresponding grid on the unit circle. The latter consists of radial lines and concentric circles. In addition, intermediate grids that are needed to obtain accurate numerical results, can be effectively created by calculating the required coefficients using simple cubic interpolation among the input frames. An orthogonal curvilinear grid around a "perama" transverse section is shown in Fig. 4. The grid lines normal to the section contour and circumferentially are

denoted as x2 and x3 , respectively, while the third direction x1 is always parallel to the

ship symmetry axis. The mean velocity components are also defined on this local curvilinear co-ordinate system as (u1, U2, u3) and they are parallel to (xi, x2, x3).

3.2 THE TRANSPORT EQUATIONS

It is assumed that the time-averaged Navier-Stokes (or Reynolds) equations together with the continuity equation describe the turbulent flow field around the hull. In a local orthogonal curvilinear co-ordinate system (x,,x2,x3) corresponding to a particular transverse section, the u Reynolds (momentum) equations reads [2]:

C(u)=-

-+p4K1 +puK1 puuK puu1K11

_+(o

-o)K

+

+(

o11)K +a1(2K1

+K1) +

h ¿

h ¿3

h1 c

(4)

where h1,h,hk are the metrics of the system, p is the pressure, p the fluid density and K the curvature tensor defined as

lai.

K..= '

IJ

h.h

The left hand side of (4) represents the convection terns of a scalar variable 1, i.e.

c(D)

rÛ(hb1CD)

o(h1h1uCD)

û(hhuCD)]

h.hh1[

cc +

'i

j

while the stress tensor components appearing on the right hand side of (4)

are expressed as:

r

= 2/1e[Ç_+

uK + u1Ku

[h

(u'

_{h. û (u}

where Pe is the effective viscosity that is equal to the sum of fluid density p and the isotropic eddy viscosity p,. The latter is calculated according

to the standard k-e

turbulence model [6]:

//1

=p+O.09pk2/e

(8)

where k is the turbulence kinetic energy and e its dissipation rate. Two more equations are introduced in order to calculate the field values of k and e, which complete the system of transport equations that describe the problem [6]. The term fb on the right hand side of(4) shows the external body forces which approximate the propeller action according to the theory of the actuator disk [4].

Ali transport equations are integrated in control volumes that correspond

_{to a}

staggered grid arrangement [7] and their discretized form is written as:

= +S (9)

In eq. (9) CD denotes the value of the variable CD on the centre ofa control volume and

CDI the corresponding values on the six neighboring nodes. Coefficients A represent the

combined convection and diffusion terms and they are calculated according to a hybrid upstream and central differencing scheme [3]. Since the discretized equations

are of

elliptic character, boundary conditions have to be specified on each boundary of the calculation domain, Fig. 2. The free surface W is treatedas a plane and the U3 velocity component, being normal to W, is equal to zero whereas zero-gradient conditions are applied for all other variables. The same treatment is followed on the flow symmetry plane E. Atthe inlet plane U and the external boundary N the velocity components and the pressure are calculated by the potential flow solution around the actual body while the turbulence characteristics are assumed equal to zero. The potential flow field is computed by the classical Hess and Smith method [8]. On the solid surface S the wall function method [6] is employed to model the effect of near wall turbulence on the velocity profiles as well as to calculate the turbulence characteristics. Finally, _{at the} exit plane D the flow is assumed fully developed and zero-gradient (Neumann) conditions are applied for all variables,

except the pressure which

is linearly extrapolated.

(7) (6)

3.3 SOLUTION OF THE RESISTANCE PROBLEM

A marching solution procedure is applied to solve the strongly coupled system of eq. (9). The whole computational domain is divided in two sub-regions corresponding to the bow and stern part, in order to obtain fine grid resolution along the ship as well as to avoid unnecessary computations when the self-propulsion problem is solved. The computations in the bow sub-region follow the steps of Table 5.1. An initial guess for the velocity and pressure field is made by extrapolating potential flow results. Then the. solution proceeds successively on transverse sections until a sweep of the domain is completed. The procedure is repeated for several steps until convergence is achieved. This iterative method follows in general the principles of the partially parabolic algorithm [9] but solves the complete Reynolds equations. The pressure field is

calculated implicitly on each section by solving the continuity equation accordingto a SIMPLE-like scheme [lO],[3].

Unlike the bow field where the dominant velocity component along x permits the parabolic solution of all transport equations, the existence of recirculation regions at the stern part affects unfavorably convergence when marching schemes are followed. Therefore a different solution has been applied in the stern sub-region, that follows the steps shown in Table 5.2. The momemtum as well as the turbulence model equations are still solved in a parabolic way, but the pressure field is calculated at the end of a sweep by solving a 3D fully elliptic system for the continuity equation. Evidently, in this case, three-dimensional storage is required in-core for the coefficients of eq. (9) and the pressure, while two-dimensional storage is used for all other variables. The input boundary conditions in the second sub-region are calculated for all variables by linear interpolation among the computed values of the bow part solution. In anycase, it is assumed that convergence has been achieved when the integrated skin friction R and pressure R forces satisf' for 60 successive steps n the following criteria:

- Rr'

0.0002R

I n n-II

Rp Rp 0.0002jR

where n is the increasing number of sweeps and

(10)

RF=JrW(?.T)ds

RpJp(iJ)dS

(11)

s s

In expressions (11), S is the body surface covered by the domain, r,., the wall shear

stress, Pwthe pressure on the wall, the tangential vector to the body contour, ñ the

normal one and ¡ the unit vector parallel to x1. The wall shear stress is calculated by the wall function method, while the pressure value _{is derived assuming a zero} gradient condition normal to the solid boundary.

Table 5.1

Iterative solution algorithm for the bow region

Table 5.2

Iterative solution algorithm for the stern region

3.4 SOLUTION OF THE SELF-PROPULSION PROBLEM

According to the method of body forces the propeller is considered as an actuator disk of diameter Dp and length Ip with infinite number of blades. Integration of_{terms fb of} eq. (4) in a control volume located within the actuator disk results in:

Epf()

(12)

fT(r)rdr

where f1 is the discretized body force which is included in the source term S1 of the eq. (9), T is the propeller thrust, F(r) a prescribed circulation distribution, Ep the transverse area of the control volume and rh, r1 the propeller hub and tip radius, respectively. In the present investigation it is assumed that r(r) follows _{a sinusoidal} distribution. Evidently, relation (12) shows that, when the value of thrust T is _known,

BOW SLUTION

I Guess initial values for flow variables

2 K=O

3 Section K=K+1

3.1 Solve the momentum equations

3.2

Solve the continuity equation and calculate

the pressure

3.3 Solve the turbulence model equations 4 Repeat step 3 until the last section is reached

5 If convergence is not achieved repeat steps 2-4 If convergence is achieved stop the bow solution

ÏEP

STERN SOLUTION

I Guess initial values for flow variables

K=O

3 Section K=K+1

3.1 Solve the momentum equations 3.2 Solve the turbulence model equations

4 Repeat step 3 until the last section is reached

5 _{Solve the whole field continuity equation and correct}

the pressure

6 If convergence is not achieved repeat steps 2-5 If convergence is achieved stop the procedure

the body forces are explicitly calculated and a solution of the flow field can be

obtained. An iterative algorithm is followed to compute the final value of T, as shown in Table 6.

Table 6

Sólution procedure for the self-propulsion problem

According to Table 6 after the solution of the flow field at a given speed around the ship is completed, the total resistance RT is calculated. Setting 1= R1, the influence of body forces determined after (12) changes the flow field around the stern and a new solution is carried out. This procedure is continued until for five successive steps the

j value ofT changes by less than 0.1%. Evidently self-propulsion calculations have to be performed only in the stern part domain. The solution of the 3D pressure equations was proved quite effective in obtaining satisfactory convergence of the adopted self-propulsion procedure. This behavior has been attributed to the immediate propagation of disturbances through the satisfaction of the overall continuity equation.

It should be mentioned here that the described actuator disk model does not take into account the propeller swirl. Numerical experiments on conventional ship forms have

shown that the circumferential body forces due to the propeller torque do not

significantly influence the field variables upstream. 4. THETEST CASES

Calculations were, at first, performed for the model speed of 0.822m/s corresponding to Froude (Fr) and Reynolds (Re) numbers equal to 0.189 and I .34x 0. Although this case corresponds to a low ship speed with regard to the design point, it has been selected to compare with the results of the viscous code because the wavemaking resistance is expected to be unimportant. The total resistance R1 was calculated equal to 0.360kp while its measured value was about 0.336kp, i.e. computations over-predicted the model resistance by almost 7.5%. Beyond the experimental uncertainties, which may be serious in this range of Froude numbers, this overprediction was expected for two reasons. The first one is related to the flow nature around the bow,

where computations do not take into account the laminar effects which may be

meaningful at the low Reynolds number that is examined. The second, and more

important reason, is the existence of separation at the stern of the model which

becomes more intense as the Reynolds number decreases. It is well known that, in such complex cases two-equation turbulence models as well as wall functions cannot

STEP SELF PROPULSION CALCULATIONS

Solve the simple resistance problem and

calculate R1

2 Set

T=R1 and

calculate body forces through relation (12)

3 Solve the stern flow field and calculate R1

4

_{If TR1 repeat steps 2-3}

If T=R1 for 5 Successive steps stop this procedure

predict accurately the flow parameters and, in general, they tend to overpredict

velocities near the stern. Taking into account the aforementioned shortcomings, the difference of 7.5 % in RTbetween experimental and numerical results may be regarded as a rather satisfactory approximation.

Next, calculations were carried out for the design speed of the vessel corresponding to Fr0.33 and Re=2.34x106, which is the most interesting case. The computational grid. extended from XIL=-O. 1 to XIL=1 .35, where X denotes the distance from the forward perpendicular and L the waterline length. At model scale L=1.855m and the design speed vsl .437m1s. The dependence of the numerical results on the grid density concerning the resistance problem are presented in Table 7. These comparisons are

required to assure that the solution converges within acceptable limits, so that

meanirigftil condusions can be derived. Table 7 is divided in two parts corresponding to the bow and stern calculations. In each case, the first column denotes the grid size, i.e. Nl is the number of transverse sections, N2 the number of points normal to the surface and N3 the number of nodes girthwise. The second column shows the number of iterations IT (domain sweeps) which are required to obtain convergence. A grid refinement technique has been followed [3] to accelerate convergence according to [3]. The method is based on the calculation of the initial flow variables by interpolating among the values of a solution obtained with a coarser grid. A remarkable save in CPU time can be achieved with this procedure, which requires about 1/lo times lower computing effort than applying directly the finer grid. The third column of Table 7

shows the total resistance coefficient C1 at bow and over the whole ship (stern

calculations). A difference less than 3% is observed between the finer grid densities in any case; indicating that the value of CT is practically convergent. It is noticeable that the viscous pressure coefficient Cp was computed equal to 3.6x103 Which is close to the total friction coefficient CF of 4.4x103. This result, being unusual in conventional ships, is related to the steep variation of the stern geometry which causes separation.

Table 7

Grid dependence tests

Towing tank experiments carried out at the design speed have indicated stern flow separation. In photograph 1, black paint was used to detect the direction of flow lines around the stern frames. Obviously there is a strong deceleration of flow at the upper side after frame I where a rapid change of geometry occurs. Although the afore-mentioned experimental technique is not offered for a detailed study, there is a clear indication that the flow separated in this region. It is remarkable that computations also predict separation, as it is shown in Fig. 5 where the mean velocity vector on the adjacent to the body surface points is projected on the longitudinal plane. The local

flow directions are

in agreement with photograph I

while low axial

velocity

BOW STERN

Nl x N2 x N3.

FT _CrX Ni x N2 x N3 IT _{C1 x IO}

Six 12x12

1.99 7.115

51x20x15

700 8.379

96x24x24

115 6.112

101x35x30

110 8.007

116x36x36

116 5661

181x45x45

97

7950

146x45x45

95 5502

cmponents appear after frame I showing a separation line at points S, i.e. after frame 1/2. The limiting streamlines, i.e. the flow lines which are calculated close to the solid surface, demonstrate clearly separation over the same area in Fig. 6. Provided that with the employed turbulence model the mean velocity is overpredicted, a larger separation area should exist near the stern.

At the examined Froude number the wave resistance component Rw is significant and results in a substantially higher total resistance R1 than the predicted one by the viscous code which adopts a plane free surface. To estimate R it has been assumed that the value of the wave resistance coefficient can be approximated by:

Cw=CTECTh (13)

where is the experimental total resistance coefficient and Cm the computed one. The corresponding value of R was then added on the viscous resistance of the body R to calculate the propeller thrust in the self-propulsion computations. In these calculations the actuator disk had an external diameter of 0. 16m and a hub diameter equal to 0.028m to simulate the real propeller geometry (Table 2). An active length lpQ.013m was assumed and the centre of the disk was placed at a distance of 1.5cm

after the last section of the vessel and 0. 13m below waterline according to the

experiments. Since the propeller axis has an inclination of 9 deg with respect to the waterline, the numerical body forces where analyzed in two components. The sum of

axial body forces was set equal to the total resistance while the perpendicular forces, that affect the transverse velocity components, were calculated so that the discretized thrust vectors had the same direction with the propeller axis . About 30 iteration steps

were needed to obtain convergence for the self-propulsion problem. In each step, corresponding to a constant value ofT, 30 domain sweeps were performed.

After convergence has been achieved, the calculated value of thrust was found equal to I .8kp that is significantly lower than the measured one of 2.42kp without using fins (Table 3). The corresponding difference of 25% between calculations and experiments is rather unusual, because it was expected that the. propeller action should reduce separation and, therefore, computations should be more accurate. Consequently, the above discrepancy demonstrated that more complex phenomena occur when the propeller operates close to the free surface. Careful experimental observations revealed that strong flow suction appears upstream and over the propeller disk that interacts with the free surface and reduces locally the wave height. As a consequence, the total resistance is more intensively increased than in the case of a fully submerged body and

results in high values of the thrust deduction factor. The same trends between

calculated and measured values were observed at the low speed of O.822m/s. The computed thrust was found equal to 0.470kp while the corresponding measured one was 0.519kp. The difference between the two values, in this case being 9% due to the lower propeller loading, shows an opposite behavior to the simple resistance problem. The velocity vector plots close to the body surface and on the symmetry plane that are presented in Fig. 7 support the above mentioned considerations. The propeller causes unusual flow patterns that exhibit recirculation zones at the upper half of the disk. This

components in the separation area. A better picture of this interaction is obtained by plotting isowakes, i.e. contours of constant axial velocity values non-dimensionalized by the model speed. In Figs. 8 to IO isowakes are plotted on transverse sections at x1.825, x1.845 and x=1.870m (propeller midplane). At the most upstream of these frames the propeller action causes higher velocity values than in the case without body forces, that is the expected situation for attached flows. On the contrary, at the frames closer to and on the propeller disk contours of negative axial components Show that separation appears stronger when the propeller operates. This behavior is explained by the mass conservation law. Since the fluid is accelerated in the propulsor whereas the mass flow through the whole transverse section should remain constant, the velocities just outside the disk will be reduced. Ifthe propeller is close to a symmetry plane, like the waterplane which represents the free surface, a more drastic reduction of the axial components should occur. The contour

plots of Figs. 9 and 10 reveal two weak

points of the computational method. The first is related to the applied actuator disk model which uses a prescribed circulation distribution to calculate the body forces. According to the theory of hydrofoil sections, circulation depends

on the angle of

attack.

Since at the upper part of the disk the low axial velocity

components

contribute to increased incidence angles, higher values for circulation should be adopted in this region. If the body forces were modified accordingly, then the total resistance should also be increased because lower pressures would be induced on the larger part of the stern surface. The second weak point of the applied viscous code is the treatment offree surface which is unaffected by the propeller operation.

Trying to modify the simple actuator model so that circulation depends on the local hydrodynamic pitch angle, an increase of about 5%

was obtained for the total

resistance. Since this value corresponds still to a low thrust, the difference between calculations and measurements was attributed mostly to the propeller - free surface interaction . The measurements which have been made with the fins (Table 4) seem to

support this aspect, although the observed improvement may be a result of more complicated flow changes. Actually the fins upstream and above the propeller disk impose a local plane boundary condition similar to that of the calculation method. If this assumption is true, it explains the low thrust value of I .925kp obtained with the fins, which is only 5% higher than the calculated. To investigate how the propeller operation close to the free surface may produce increased thrust, a simplified two-dimensional model has been examined. It was assumed that

a 2D actuator disk of

height H equal to the propeller diameter operates beneath a free boundary at the same depth as in the actual model. An equivalent thrust loading per unit width equal to the mean surface distribution of axial forces on the real propeller was imposed and the free stream velocity was taken equal to the speed of the vessel, i.e. 1.43 7m/s. The 2D free surface above the disk was calculated following an iterative procedure so that both the kinematic and the dynamic boundary conditions are satisfied [12]. Resúlts concerning the induced pressure around the disk are plotted in Fig. 1 1. The vertical axis represents

the integrated pressure force non-dimensionalized by the propeller loading

on transverse sections of height H around the disk, while the horizontal axis refers to longitudinal distances. The plotted curves show that when the real free surface is taken into account, the induced pressure force is significantly lower in the region upstream the disk which contributes mostly to thrust deduction than in the case where a plane free boundary is considered. Therefore the pressure integration on the hull surface results to increased resistance in the former case.

The sensitivity of the numerical results with respect to the position of the propeller has also been examined by shifting the propeller centre 1cm towards the free surface as well as 0.5cm closer to the hull. The calculated thrust was then found equal to 2.Olkp, i.e. almost 12% higher. Apparently this trend is due to the lower pressure values that are induced closer to the actuator disk and they are integrated on a larger projected hull surface. A test was also made to study the influence of geometrical changes at the aflermost part of the hull on the resistance components. Increasing the body length only by 2cm ( about 1% of L) a remarkable decrease of 11% was achieved for the total resistance which was a result of the drastic changes of the pressure field near the elongated stern region.

To investigate numerically the Reynolds scale effect on the resistance components, calculations were also carried out for the 10:1 full scale vessel at the same Froude number of the design speed. The full scale Reynolds number was calculated equal to 7x107. An 180x65x45 bow and an 180x65x45 grid was used in this case, i.e. the grid

resolution along the normal to the body surface was increased to approximate

adequately the thinner boundary layer. Assuming that Cw is equal to that of model scale, the calculated total resistance coefficient C1 was found equal to 937x1 0. By extrapolating the experimental value according to the Froude method associated with the ITTC-57 friction line, the full scale C1 is estimated as 9.62xl03 which is very close to the computed one. This result may be explained by the high value of the pressure coefficient which is almost equal for both scales. It

is interesting to notice that

separation still exists at the aftermost part of the full scale ship, as it is shown in Fig. 12. By comparing the plotted results with the corresponding Fig. 8 it is apparent that higher values of axial velocity components exist closer to the hull upstream the aft end of the vessel, which is consistent with the Reynolds number increase. On the contrary, the differences are less pronounced near the propeller plane,

Finally, self-propulsion calculations at full scale were performed and a thrust deduction factor about 0.16 was computed. By comparing this value to the corresponding t 0.2 of model scale, it is evident that numerical predictions are influenced by the Reynolds scaling and show that t tends to decrease as the Reynolds number becomes higher. Although this result may be a consequence of drastic changes in the particular stern flow field, systematic numerical investigation should be carried out to accept or not the aforementioned trend.

CONCLUSIONS

The presented applications have shown that advanced CFD methods are offered for detailed studies of complex flow phenomena like those occurring at the stern of the examined traditional vessel. Therefore, these methods can be effectively used in conjunction with model tests for improving hull forms as well as fOr designing special devices that reduce powering requirements.

ACKNOWLEDGMENTS

The authors wish to acknowledge the contribution of the technicians F. Kasapis,

M. Nounos, D. Synetos to the model tests as well as the support of the High

7. REFERENCES

GANOS, G. C. 'Methodical series of traditional Greek fishing boats" Doctoral dissertation, National Technical University of Athens, 1988.

IZABIRAS, G.D. "A numerical study of the turbulent flow around the stern

of ship models ", ¡ni. Journal for Numerical Methods in Fluids, 1991, 13,

1179-1204

7Z4BIR4S. G.D. "Resistance and self-propulsion numerical experiments on Iwo tankers at model andfull scale ", Ship Technology Research, 1993, 40(1). 20-38.

STERN, F., KIM, H. T, PA TEL, V. C. and CHEN, H C. "Viscous flow computation ofpropeller-hull interaction" Proceedings of ¡6" ONT? Symposium, Berkeley, 1986.

VON KER CZEK, C. and TUCK, E.O. "The representation of ship hulls by conformal mapping techniques ", Journal of Shio Research, 1969, 19, 284-298.

LA UNDER, B. E. and SPA LDJNG, D. B. "The numerical computation of turbulent flows ", comput. Methods in Applied Mechanics and Engineering, ¡974, 3, 269-289.

7Z4BIR.4S, G.D. "Numerical and experimental investigation of the turbulent flow-field around the slerui of double ship hulls ", Ph. D. dissertation (in

Greek), National Technical University of Athens, Greece, 1984.

HESS, J.L and SMITH, A.M. O. "Calculation ofpotential flow about arbitraty bodies", Prog. in Aeronaut. Sci., 1966, 8, 1-138.

PRA TAP, VS. and SPALDING, D.B. "Numerical computations of the flow in curved ducts" Journal ofAeronauiical Sc., 1975, 26, 219-232.

PATANKAR, S. V. and SPALDING D.B. "A calculation procedure for heat, mass and momentum transfer in 3D parabolic flows ", ¡ni. journal of heat and Mass Transfer, 1972, 15,1787-1806.

7ZABIRAS, G.D. and VEWTJKOS, Y. "Calculation of a Wave Pattern Generated by a 2D Submerged Hydrofoil: A Navier-Slokes approach ", Proceedings of the first International Conference oui Mathematical and Numerical aspects of wave propaga/io/i phenomena, Stra.sbouirg, France, April 23-26,1991, .106-414.

-Fig I. Lines pla,i of "perama" vessel

Fig 2. The complilazional grid aroii,id ¡he vessel

peramo

Fig 3. _{Unrealistic representation of transverse section}

Fig 4. The onhogonal curvilinear grid around a transverse

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without propeller

Fig 8. Calculated. isowakes _{ai x=1.825 (mode/scale)}

with propeller

Fig 9. Calculated isowakes at x 1.845 (model scale)

Q 0.6 0.4 0.2 -0.2 -0.4 -0.6 o

Fig 10, Calculated isowakes

_{at x}

_{1.870 (model scale)}

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-with calculated boundary

-free surface line

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X(m)

Fig 11. Induced pressures by a 2D actuator disk operating

under free surface.

0.6 0.8 1

x= 18.25m

18.45 m Fig 12. Calculaged isowakes al two slern frames