Ship Self Propulsion with different CFD methods: from actuator disk to viscous inviscid unsteady coupled solvers

10th International Conference on Hydrodynamics

October 1-4, 2012 St. Petersburg, Russia

Ship Self Propulsion with different CFD methods: from actuator disk to viscous

inviscid unsteady coupled solvers

Diego Villa, Stefano Gaggero and Stefano Brizzolara

Department of Naval Architecture and Marine Engineering

University of Genova

Italy

ABSTRACT

The paper deals with self-propulsion problem, i.e. the solution

of the flow around a hull that advances at uniform speed due to

the action of the propeller. Two different approaches are

presented and compared in the paper: an approximated

approach, using the classical actuator disk theory to represent

the time averaged fluid dynamic action of the propeller through

body forces in the RANSE solver; a viscous-inviscid coupled

solution, in which the hull viscous flow is solved through

RANSE, the propeller hydrodynamics in the wake of the hull

through an unsteady panel method and the two solutions are

matched via unsteady body forces. Main differences between

the two approaches are presented also in quantitative sense.

The very good results obtained with the proposed V.I. coupled

method make it an ideally fast and robust tool to be used for

ship self-propulsion characteristics evaluation in ship routine

design activities.

KEY WORDS: CFD; RANSE; Panel Method; Self-propulsion.

INTRODUCTION

The ultimate goal for computational hydrodynamic

methods applied to ship hydrodynamics in calm water

is the simulation of the free surface viscous turbulent

flow in self-propulsion condition. In this general

problem, different sub problems can be addressed,

each one with different levels of approximations and

solving strategies. The most interesting aspects, in

fact, range from the prediction of the self-propulsion

coefficients for preliminary power estimation and

selection of main propeller parameters to the

determination of the nominal/effective wake for the

design of a wake adapted propeller, and eventually to

the analysis of the unsteady hydrodynamics of

rudder/appendages working in the propeller wake.

From an engineering point of view RANSE solvers

represent the state of the art among numerical

approaches to solve all hydrodynamic aspects related

to the self-propulsion problem. Unfortunately this

kind of approach is very onerous in terms of

calculation time and computational resources, since

both the space and the time scales of the propeller and

of the hull flows are of quite different order of

magnitude and, so, the number of cells and the time

step required to accurately solve the whole problem

results normally prohibitive for design purposes.

Hence the opportunity to study some more

approximate and faster CFD solver that can remain

anyhow adequate for obtaining valid results in the

preliminary design phase. If the propeller unsteady

hydrodynamic performance are not specifically under

investigation, its main fluid dynamic influence on the

flowfield around the hull and the nearby appendages

can be approximated with an idealized actuator disk

model, based on the classical impulse theory of R.E.

Froude [1]. This approach has been tested by several

researchers (Stern et al. [2], for instance) and included

into RANSE solvers as a first step toward the solution

of the most general problem.

If, instead, the propeller unsteady hydrodynamic

behavior is searched for as a part of the solution to the

problem, in this paper a novel approach, based on the

representation of the unsteady propeller blade forces

through time-dependent equivalent body forces,

whose intensity is found from an unsteady propeller

potential flow model (Gaggero and Brizzolara [3] and

Gaggero et al. [4]) is proposed .

The work presented in this paper, then, is primarily

focused to address the equivalences and the

differences between the two above mentioned models,

in terms of global predicted forces and flow field

results. The case study taken to validate the two

models is the well-known MOERI KCS hull, designed

at KRISO and tested at SRI (Fujisawa et al. [5]) with

the relative experimental data for validation from the

International Workshop on CFD in Ship

Hydrodynamic, Gothenburg 2010. The ship model

was built at a scale 1:31.5994 and the Froude Number

adopted for the validation is equal to 0.26. The stock

propeller used in the self-propulsion towing tank tests

is the KRISO KP505, a five blade right handed

propeller, with an expanded area ratio of about 0.8 and

a maximum skew at tip of 24°.

After a brief introduction about the potential flow

method and the RANSE solver, the results from the

two approximate models for the evaluation of the self-

propulsion operational point are compared. The

technical focus, here, is the coupling algorithm

between the potential and the RANSE solver. The

actuator disk and the unsteady body forces approaches

imply, in general, different level of approximations,

which result in differences in prediction of the hull

performance, of the propeller unsteady characteristics



and of their mutual hydrodynamic interaction, that are

presented and discussed in the paper.

CFD SOLVERS

Panel method can be successfully applied for the

prediction of unsteady propeller forces (Gaggero et al.

[4]) but they contain too crude approximations in the

estimation of viscous forces to be extended to the

computation of hull frictional drag and wake on the

propeller plane. On the other hand a complete viscous

solution of the hull plus the rotating propeller poses

significant problems in terms of computational

efficiency, due to the completely different spatial and

temporal scales that govern the hydrodynamic

behavior of the propeller and of the hull, respectively.

A coupled viscous/potential solution (RANSE for hull

forces and wake, panel method for unsteady propeller

forces, matched via body forces and effective wake)

represents a straightforward way to obtain, at least, a

preliminary estimation of the effects of the mutual

interaction between propeller and hull.

Panel Method for Propeller

Potential solvers are based on the solution of the

Laplace equation for the perturbation potential , as

in Morino [6], which is the counterpart of the

continuity equation if the hypotheses of irrotationality,

incompressibility and absence of viscosity are

assumed for the flow:

(1)

Green’s second identity allows to solve the three

dimensional problem of Eq.1 as a simpler integral

problem requiring to solve only on the boundary

surfaces of the computational domain. The solution is

found as the scalar field that describes the variation of

the intensity of a series of mathematical singularities

(sources and dipoles) whose simultaneous influence

produces the inviscid, unsteady, flow field on and

around the body. Boundary conditions (kinematic on

the solid boundaries, Kutta condition at the trailing

edge and Kelvin theorem) close the solution of the

linearized system of equations obtained from the

discretization of the differential problem represented

by Eq.1 on a set of hyperboloidal panels representing

the boundary surfaces. An inner iterative scheme

solves the nonlinearities connected with the Kutta

condition while an outer iterative cycle is used to

integrate over the time in order to obtain a periodic

solution, after the virtual numerical transient due to

the key blade approach (as in Hsin [7]). Once solved,

Eq.1 gives the value of the perturbation potential

whose derivatives, with respect to an appropriate

reference system and time, together with the

application of the unsteady Bernoulli’s theorems,

allow to compute time dependent pressure and forces.

RANSE Solver for the Hull

The hull flow is computed using Reynolds Averaged

Navier Stokes Equations. Continuity and momentum

equations, for an incompressible flow, are expressed

by:

(2)

in which is the averaged velocity vector, is the

averaged pressure field, is the dynamic viscosity,

is the momentum sources vector and is the

tensor of Reynolds stresses, computed in agreement

with the two layers Realizable turbolence

model.

Free surface is captured using the Volume of Fluid

approach that requires the solution of another

transport equation for the variable , representing the

percentage of fluid for each cell:

(3)

The Finite Volume commercial code StarCCM+ (CD-

Adapco [8]) has been adopted for the solution of the

RANSE equations, that are solved in accordance to

the segregated flow approach. Main solver and mesh

settings have been tuned in accordance with those

proposed by Brizzolara and Villa [9] for the

International Workshop on CFD in Ship

Hydrodynamics.

VALIDATION

The panel method has been applied for the evaluation

of the open water characteristics of the stock propeller

used for the self-propelled model. For the validation

of the RANSE solver, instead, wave elevation and

velocity component in the wake of the hull have been

considered. Being the evaluation of the effective

velocity field a necessary step for the coupling

strategy, induced velocities in front of the propeller,

computed by the panel method and by the RANSE

solver, have been finally compared with the velocity

field computed, on the same axial plane, by the

RANSE solver in which the propeller is modeled

through equivalent body forces.

The prediction of the propeller hydrodynamic

characteristics in open water is reported in figure 1. A

mesh of 1200 hyperboloidal panels per blade has been

adopted for both the steady (open water) and the



Fig. 1: KP505 Propeller open water characteristics prediction

with panel method.

unsteady computations, in this last using an equivalent

time step of 4.5° and a total of six complete propeller

revolutions in order to reach a periodic solution.

The comparison presented in figure 1 highlights the

generally good agreement of the predicted thrust and

torque with experimental measurements for advance

ratio up to J=0.75. Numerical predictions, in fact,

show a slight difference in curves slope, with a

tendency to underestimate both thrust and torque,

especially close to the zero thrust point, corresponding

to J1.0.

Fig. 2: Mesh arrangements around the hull and the free surface.

The solution of the viscous free surface turbulent flow

around the hull have been achieved by a finite volume

RANSE solver on the unstructured trimmed mesh of

figure 2, consisting of about 2 Millions cells.

Anisotropic refinements have been adopted near the

free surface to better capture wave elevation and prism

layers have been adopted near the hull to adequately

solve the boundary layer flow, ensuring a maximum

value around 100. Both starboard and port hull

sides have been modeled for being able to assign the

asymmetric (with respect to the longitudinal plane) set

of body forces representing the rotating propeller

blades. Numerical predictions of wave pattern and

nominal wake on the propeller plane (0.0175LPP

upstream the aft perpendicular) are quite accurate.

Wave elevation (figure 3) is well predicted. At the

Fig. 3: Comparison of wave patterns at the design speed.

RANSE results (top) and experiments(bottom).

bow, in particular, the agreement is excellent, both in

terms of wave elevation and the shape of the divergent

wave trains. In the stern region the wave elevation

predicted by the RANSE model is a bit overestimated.

However the position of the hump and troughs of the

longitudinal and transversal wave components is very

well captured. Also the usual numerical dissipation

and wave damping downstream the hull, caused by the

locally reduced mesh resolution, is within tolerable

limits.

Fig. 4: Nominal wake in the propeller disk. RANSE (right) and

experimental measurements (left).

The analysis of the predicted nominal wake on the

propeller plane shows some marked differences.

Figure 4 demonstrates that the RANSE solver predicts,

with a reasonably good agreement, the flowfield in the

stern region of the hull, where the effect of boundary

layer growth and separation is evident. At the same

time some differences can be highlighted. Tangential

and radial velocity components measured in the

experiments are higher than those calculated. Close to

the 0° position, in the experiments the velocity vectors

have a stronger counter-clockwise rotation than in the

numerical flow field. The experimental wake is, as a

consequence, more “flat” under the stern and

vertically thicker in correspondence of the

J

KT,1

0K

Q,

o

0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Exp.

Panel Method



longitudinal plane of symmetry. Same kind of

discrepancies has been noted also by other research

groups as for instance by Kim et al. [10], for whom

the numerical nominal wake has a vertical shift with

respect to the experimental measures. Anyhow, if

considered as the input inflow for the panel method,

these results can be considered qualitatively

acceptable.

Finally the axial velocity fields upstream (0.15D) the

propeller, induced by the propeller itself operating in

uniform inflow are shown in figure 5. Results from

the panel method, the fully RANSE approach and the

coupled RANSE/panel method through body forces

show the excellent agreement between the potential

and the fully RANSE computations, with only a

slightly overestimation of the accelerated regions for

the panel method. Coupled solution, instead, shows a

smoothed region of accelerated flow, with the “shape”

of the blade no more visible.

(a) RANSE (b) Panel Method

(c) RANSE with Body Forces

Fig. 5: Comparison between induced propeller axial velocity

0.15D upstream the propeller plane.

The mean value of the induced velocity fields, that

will be adopted for the evaluation of the effective

wake, are, however, very close one each other,

allowing for an overall satisfactory estimation of the

flowfield in which the propeller is operating by both

methods.

COUPLING STRATEGY

When the propeller operates behind a hull, the flow on

the propeller plane is not simply the sum of the

viscous wake calculated in the absence of the

propeller (the so called nominal wake) and the

propeller self-induced velocities due to the propeller

working in this nominal wake. A rather complicated

interaction takes place, that involves boundary layer

modifications due to the suction effect caused by the

propeller that, in its turn, modifies the inflow to the

propeller and eventually the propeller performances.

The total velocity of the wake field, from a classical

idealized approach (see for instance Carlton [11]), can

be seen as the sum of the nominal wake plus the

propeller/hull interaction velocities (these two

contributions are called effective wake) plus the

propeller induced velocities. From the propeller point

of view, it is the effective wake (that is the input flow

generally used in design and analysis codes) that is

important in defining the right working condition of

the propeller behind the hull:

(4)

The effective wake and the body forces are the

concepts on which the iterative coupled procedure,

adopted in this study to compute the propeller/hull

interaction, has been build. The RANSE solver

estimates the total, viscous dependent, velocity, just

ahead the propeller plane, taking into account the

effect of the propeller by equivalent body forces,

computed in turn by the unsteady panel method, and

placed on appropriate cells into the RANSE domain.

The propeller induced velocities, computed at each

iteration by the unsteady panel method with RANSE

wake field as input, let to define, according to Eq. 4,

the effective wake and, as a consequence, the new

resulting body forces at the current iteration to be

included in the next RANSE computation. The

iterative procedure proposed to simulate self-

propulsion tests, in conclusion, requires:

1. To compute, by the RANSE solver, the viscous

flow around the ship hull and the hull total

resistance without the propeller;

2. To extract the spatial non uniform velocity field

in the propeller plane from the RANSE

computation and assign it, as the inflow for the

unsteady computation, to the propeller panel

method;

3. With the input inflow, to define the self-

propulsion point of the propeller adjusting the

rate of revolution in a way such that the mean

unsteady delivered propeller thrust equals the

hull total resistance computed at step 1;



4. Once self-propulsion point is defined, to

calculate the induced velocities (on a plane ahead

the propeller) and the unsteady body forces;

5. To include body forces of step 4 into the RANSE

computation and recomputed hull viscous flow

and ship total resistance;

6. To extract total velocities on the plane ahead the

propeller (the same of step 4) and calculate,

through Eq. 9, the effective wake by subtracting

the propeller induced velocities calculated at step

4 from the actual total velocities;

7. To recompute, as at step 3, the self-propulsion

point with the new effective inflow wake;

8. To iterate step 4-7 until convergence of the hull

resistance and the mean effective wake is

reached.

The total and induced velocity field on a plane ahead

the propeller, as required in steps 4 and 6 of the

iterative self-propulsion test, have obviously, an

unsteady nature. The first is spatially non

homogeneous (due to the hull boundary layer), the

latter changes with time as a consequence of the

propeller operating in a spatial non uniform inflow:

the interaction between hull and the rotating propeller

produces, moreover, a further time dependent

influence on the total velocity field. Panel methods

based on the key blade approach can deal only with

spatial non uniform inflow and require, consequently,

a time averaging of the input velocity fields.

Fig. 6: Propeller shaped mesh used in RANSE solver for the

imposition of body forces.

At each time step, induced velocities are calculated by

the panel method: the effective wake is a “steady”

spatial non uniform velocity field obtained, in a plane

in front of the propeller, as the difference between the

total velocity, calculated from the RANSE at the

current time step, and the time averaged induced

velocity computed by the panel method with the given

inflow.

In order to include the propeller influence in the

RANSE computation via body forces, an accurate

geometrical representation of the propeller needs to be

adopted. Instead of applying the thrust of each blade

to an equivalent propeller disk (Stern et al. [2]) on

which 3D body forces are projected and matched by a

nearest neighbor algorithm to the disk mesh itself, a

new mesh region (figure 6), specifically created in

accordance with the real blade shape, has been

adopted. This “propeller adapted” mesh is generated

by subsequent rotations around the propeller axis of

the cambered mean surface of the blades, with an

angular steps corresponding to the time step adopted

for the simulation. When the propeller is solved with

the effective wake as inflow, unsteady forces are

computed, transformed in forces distributed on the

mean blade surface and, at each time step, assigned to

the “time” corresponding cells of the “propeller

adapted” mesh (figure 7).

Fig. 7: Qualitative comparison between unsteady pressure

coefficient distribution (-CPN) on blades suction side (left) and

corresponding body forces magnitude (right).

RESULTS

Computation of the self-propulsion point with the

coupled algorithm (body forces) has been compared

with the results obtained by the simpler actuator disk

model: with a similar approach to that adopted in

modeling the body forces mesh on the RANSE

computational domain, a disk of finite thickness has

been included in the RANSE domain. Exploiting

StarCCM+ Java scripting capabilities, a momentum

source has been coded inside the disk region,

assigning its value as function of the time dependent

hull total resistance calculated at each time step. For

both the methodologies the total hull resistance

computed by the RANSE has been corrected,

accordingly to the ITTC 1978 procedure for thrust



identity, by the difference ( ) between the model and

the full scale frictional resistance:

(5)

As expected, the inclusion of both the actuator disk

and the body forces alter substantially the flow field in

the stern region of the hull. As presented in figures 8

and 9, the flow is strongly accelerated, by both the

idealized models, with respect to the bare hull case.

By comparison of the two figures, main differences

between the two approaches are also clear. The

inclusion of the actuator disk produces a more

uniform flow, because it models the propeller in an

averaged sense since the momentum source,

proportional to the thrust, needed at each time step to

balance the hull drag, is uniformly distributed over the

entire disk. At 0°/90°/180° position, for instance, the

actuator disk model is not able to take into account the

extra blade loading due to the axial deceleration and

the tangential component of the velocity field visible

in the nominal wake of figure 4.

Fig. 8: Wake fraction on longitudinal and transversal (0.6D

downstream the propeller) planes. Actuator Disk approach.

Fig. 9: Wake fraction on longitudinal and transversal (0.6D

downstream the propeller) planes.Body Forces approach.

These differences are more evident when the velocity

distribution on a plane downstream the propeller is

analyzed. The actuator disk approach produces a wake

field almost symmetrical because of its intrinsic axial-

symmetric action: only the axial component of the

velocity field is affected by the presence of the

actuator disk (that, in fact, takes into account only

axial momentum sources) while tangential and radial

velocity components are practically the same of the

bare hull case. The unsteady body force approach,

instead, is more consistent with the real propeller

hydrodynamic influence on the inflow (as shown in

figure 14) and produces a flow very different from the

actuator disk case The main difference again comes

from modeling of the propeller through a series of

momentum sources, acting not only in the axial

directions but also in tangential and radial directions:

these body forces are applied in the cells

corresponding to the actual time dependent blades

position and their intensity changes as a function of

the local inflow conditions through the unsteady panel

method calculations. Downstream the propeller (figure

9) it is possible to identify a strong asymmetry of the

flow. At 0° position the high load of the blade

combines with the local decelerated wake, producing a

higher acceleration on the flow than in the case of the

actuator disk. A similar combination of flow and

loading happens at 90°/270° positions. Local inflow

tangential velocity components tend to load (90°) and

to unload (270°) blade thrust, with a resulting race

flow accelerated on starboard side and decelerated on

port side. Rotational body forces are, finally,

responsible of the distribution of tangential velocity

on the downstream plane, completely neglected by the

simpler axial actuator disk approach.

Fig. 10: Wake fraction on a transversal (0.2D upstream the

propeller) plane. Actuator disk (left) and body forces (right).

From a quantitative point of view, the two approaches

have been compared in terms of total hull drag. The

coupling procedure has been validated comparing the

predicted propeller rate of revolution and the velocity

field downstream the propeller plane with the

experimental measures reported in Van et al. [12] and



Kim et al. [13]. The idealization of the propeller with

the actuator disk model, being not directly related to

the propeller open water curves, can only give an

estimation of the total hull resistance. However, the

total wakes computed on a plane upstream of the

propeller with the actuator disk or with the body

forces model are very close, as presented in figure 10.

Axial actuator disk effect, as usual is symmetric, while

for the body force approach it is possible to identify a

slight difference in the starboard and port distribution

of the axial velocity. Pressure fields, consequently,

will be close themselves and the effect of the two

approaches on the hull drag is expected to be very

similar.

Table 1: Self-Propulsion convergence during iterations

Iteration Propeller rps

0 (no propeller) 82.15 9.0053

1 90.70 9.3033

2 91.88 9.3790

3 92.01 9.3895

Actuator Disk 89.60 //

Exp. 92.39 9.5000

Table 1 presents a comparison between the results

obtained from the iterative coupled solution, those

obtained from the actuator disk approach and the

experimental measurements. The convergence of the

propeller rate of revolution and of the hull resistance

is fast, and only three iterations (each consisting of

100 complete propeller revolutions) are required to

obtain converged results.

Fig. 11: Total hull drag and effect of body forces inclusion.

Starting from the hull towed at the given speed

without propeller, iteratively, the application of the

panel method is used to calculate the effective wake

(subtracting the induced velocities computed with the

propeller operating in the inflow and at the rate of

revolution of the previous iteration from the actual

total wake) and the new required propeller rate of

revolution (with the propeller operating in this

effective wake) that balances the hull resistance of the

previous iteration.

Fig. 12: Unsteady propeller performances. Single blade thrust

and torque coefficients.

The predicted self-propelled hull resistance converges

to a value of about 92 N with a propeller estimated

rate of revolution of 9.39 rps, very close to the

experimental values of 92.39 N and 9.5 rps (Kim et al.

[13]). The total hull drag calculated by the actuator

disk approach is only slightly lower (89.6 N) but, of

course, no direct information about the propeller

operational point (rpm) is offered by this simplified

approach, nor unsteady effects in the propeller wake.

The effect of the unsteady body forces (calculated

from the unsteady blade operating in the ship effective

wake, as in figure 12) on the hull total drag is

presented in figure 11. The typical oscillatory and

slowly converging value of the resistance, also present

in towing conditions, is visible. As reported during the

2010 Workshop on CFD Hydrodynamics by many

authors (see, for instance Brizzolara et al. [9]), this

oscillatory behavior of the RANSE is a well-known

drawback of the StarCCM+ solver, that appears when

free surface is included in the computation.If for the

actuator disk the balance between momentum

intensity and hull drag is satisfied at each time step, in

case of the unsteady body forces approach a time

average of the drag/required-thrust (which

convergence, instead, is fast enough as highlighted in

figure 11) has been considered and, at each iteration,

(except for the first, for which mean bare hull

resistance has been adopted) the self-propulsion point

has been identified on the basis of unsteady panel

method calculations, using the mean resistance

computed by RANSE at the previous iteration.

A similar convergence trend can be recognized, in

terms of flow field, analyzing the different effective

wakes, shown in figure 13, computed at each iteration.

Propeller induced velocities (0.2D upstream the

propeller plane) are averaged in time and subtracted

from the total RANSE velocities collected, at the same

t [s]

R[N

]

0 50 100 150 2000

20

40

60

80

100

120

Hull Total Drag

Mean Hull Total Drag

Body Forces activated

t

R

190 195 200 205 210 215 220

90

92

94Iter. 3Iter. 1 Iter. 2

KT,

10K

Q

0 60 120 180 240 300 3600

0.02

0.04

0.06

0.08

0.1

KT

10KQ



(a) Nominal wake (0thiter.) (b) 1st iteration

(c) 2nd iteration (d) 3rd iteration

Fig. 13: Nominal wake (bare hull) and effective wakes as a

function of the iteration at 0.2D upstream the propeller plane.

position, each time a new iteration is started.

Propeller suction effect, on a plane 0.2D upstream the

propeller, makes the effective wake narrower with

respect to the 0th

iteration wake (the nominal wake

computed for the bare hull on the same plane),

resulting in a decelerated region closer to the 0°

position and higher radial velocity components due to

the converging streamlines. Downward flow at 0° is

pronounced and no more symmetrical. Unsteady

induced velocities depend, in fact, by the shape of the

blade and by the inflow wake: their time averaged

value, asymmetric in shape, interacts with the total

velocity field that, being computed with the unsteady

rotating body forces, results asymmetric in turn.

Fig. 14: Comparison between measured (left) and computed

(right) wake field 0.25D downstream the propeller.

Differences, however, are significant mostly between

the 0th

and the 1st

iteration while in the subsequent

iterations they are in the order of one percentage point.

Figure 14 presents the validation of the wake field

downstream the propeller computed with the body

forces approach with the experimental measures of

Van et al. [12] and Kim et al. [13]. The overall

agreement is good. Both the accelerated flow on the

starboard side of the wake and the rotating velocity

components in clockwise direction are clearly

observed and well compare with the measured fields:

only at 0° position computed results show an

increased of axial velocity value that is not

experimentally matched.

CONCLUSIONS

A viscous inviscid coupled algorithm has been

formulated and applied to the analysis of ships

advancing in self-propulsion. The method is based on

a panel method to solve for the unsteady forces

produced by the propeller blades working in the hull

wake and a RANSE solver for the calculation of hull

drag with the action of the propeller. The two solvers

are coupled through effective wake (in the panel

method) and unsteady body forces (in the RANSE

solver).

Results obtained with the novel method in case of the

KRYSO KSC test case have been compared with a

simpler unsteady axial actuator disk approach, usually

adopted to simplify the self-propulsion computational

model, and with the experimental measurements in

terms of total hull drag, propeller rate of revolutions

and downstream wake.

Both the methodologies seem adequate to estimate the

thrust deduction factor resulting in a predicted hull

total resistance error within the 3% on the

experimental measurement. The novel approach

based on unsteady body forces shows its advantage in

the prediction of the propeller race flow field. With

the same number of cells and similar computational

time (body forces approach requires, in addition to the

actuator disk method, the calculation of unsteady

propeller characteristics, that takes only 10-15 minutes

every time needs to be updated) the coupled

potential/RANSE solution is able to capture the

asymmetries in the velocities distribution (specially

radial and tangential components) downstream the

propeller plane, that are of primary importance if also

rudder characteristics need to be included in the

numerical model.

Additionally the novel approach has the advantage to

solve for the propeller operational point in terms of

advance coefficient and propeller rpm.

The convergence characteristics of the coupled

Panel/RANSE solvers are good in spite of the

oscillatory behavior of the RANSE solution which is

Vx/V: 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 V

x/V: 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90

Vx/V: 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 V

x/V: 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90



typical every time free surface is included,. Hence the

novel coupled model represents an accurate and

inexpensive (with respect to the standard actuator

disk) approach, particularly worth to address even

more complex problems, such as self-propulsion with

nonlinear effects of sinkage and trim or the prediction

of the evolution capabilities of a maneuvering ship.

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Ship Self Propulsion with different CFD methods: from actuator disk to viscous inviscid unsteady coupled solvers

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