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OCR for page 511
Experimental and Numerical Investigation of
the Unsteady Flow around a Propeller
P. G. Esposito, F. Salvatore, F. Di Felice, G. Ingenito
(Istituto Nazionale per Studi ed Esperienze di Architettura Navale, Italy),
G. Caprino (Centro per gli Studi di Tecnica Navale, Italy)
ABSTRACT
In the present paper the analysis of the flow around the
propeller of a twin screw vessel is performed both ex-
perimentally by LDV measurements and numerically
by a potential flow solver. The velocity fields obtained
through the experimental survey have been used to as-
sess the accuracy of the solver for the application to
modern propellers, featuring rather extreme geomet-
ries and large pitch variations. The results show that,
in spite of the approximations introduced, the solver is
able to capture the main features of the flow. The com-
bined use of numerical and experimental tools reveals
itself as a fundamental step for a deep comprehension
of phenomena taking place in modern ship units.
INTRODUCTION
Large fast vessels represent a severe challenge to ship
designer in the quest for outstanding calm-water per-
formance. The hydrodynamic optimization of the pro-
peller being an essential step of this pursue, the need
of reliable and effective tools for the analysis of pro-
peller flow is much felt. The typical configuration is
a twin screw controllable pitch propeller with quite a
long shaft, due to the gradual rise of the keel in the
aftbody, and a set of shaft brackets with a L arrange-
ment so that the vertical bracket is in the shaft wake.
The request of large thrust and the constraint on the
maximum diameter posed by tip clearance naturally
lead to high expanded area ratios; rather extreme skew
distributions are adopted to decrease induced pressure
pulses, while large pitch variations allow to avoid ex-
cessive loading at the propeller tip. Time honored
computer codes based on lifting surface theory are in-
adequate to deal with the new propulsive configura-
tions and are currently in the process to be replaced
by panel methods, which provide a fully three dimen-
sional model of blade geometry. On the other hand,
the complexity of the unsteady phenomena involved
requires a thorough validation of such codes in operat-
ing conditions. To this end, high quality experimental
data of the flow around the propeller are needed.
A joint effort within the framework of the na-
tional research program has been undertaken by IN-
SEAN and CETENA to achieve a better physical un-
derstanding of the unsteady effects on propeller per-
formance through model tests in the circulating water
channel and the application of an unsteady panel code,
described in Esposito and Giordani (20004.
Flow field survey has been performed up-
stream and downstream the propeller by using Laser
Doppler Velocimetry (LDV). LDV is a key technique
for investigating the complex flow around propellers
and many studies are available for uniform inflow, see
e. g., Min (1978), Kobayashi (1982), Cenedese et al.
(1985), Jessup (1989), and for axisymmetric inflow
by Hayun and Patel (19914. However, very few stud-
ies of propellers operating in non uniform inflow are
available, since the experimental analysis is particu-
larly onerous, requiring several days of facility oc-
cupancy and a huge amount of data to be processed.
The experimental technique adopted for the present
measurements allows the reconstruction of the three
dimensional velocity field in phase with the propeller.
The high level of detail reached by these measure-
ments represents a powerful tool for the analysis of
the complex phenomena taking place in propeller-hull-
appendage interaction.
In addition to the experimental investigations,
a theoretical analysis of the flow field around the pro-
peller has been performed by using a Boundary Ele-
OCR for page 512
=~
ment Method (BEM) for the velocity potential. By
comparing the numerical results with the experimental
findings, the capability of a potential flow model to
study the wake past a propeller in the non uniform flow
induced by a ship hull is addressed. In literature, many
works dealing with the prediction of marine propeller
performance by BEM are available. Unsteady flow
analyses are given, e. g., by Kinnas et al. (1990), Koy-
ama (1992), Hoshino (19934. In these formulations
the shape of the wake is prescribed either from blade
pitch distribution or by using semiempirical models.
Such approaches do not allow accurate predictions of
the trailing vorticity path and hence of the flow field
downstream the propeller. In order to overcome these
limitations, the shape of the wake must be determined
as a part of the flow field solution. Theoretical models
in which the propeller wake is aligned with flow velo-
city are proposed by Greeley and Kerwin (1982) and
Pyo and Kinnas (19974.
In the present approach a Langrangian wake-
alignment procedure is used. In order to reduce the
computational effort, a two-step technique is proposed.
The wake shape is assumed to be slightly affected by
the circumferential variations of the incoming flow.
Hence, a steady-flow wake alignment analysis is per-
formed by using as input an axisymmetric inflow ob-
tained by considering the circunferential average of the
hull wake on the propeller disk. Next, the computed
wake surface is used as input of a prescribed wake un-
steady flow computation in which the actual non uni-
form inflow is used.
EXPERIMENTAL ANALYSIS
Experimental setup
Measurements have been carried out at the INSEAN
free surface Circulating Water Channel, having a test
section of 10 m x 3.6 m x 2.25 m; the maximum flow
speed is 5 m/s, and pressure may be reduced to 4 KPa.
Figure 1: Sketch of the hull model.
A.....
Figure 2: View of the model installed in the water
channel.
The hull model is represented by the star-
board half of a twin screw vessel and it is 6.4 m long,
while the propeller has a diameter D p = 275 mm. The
propeller and the aft region between the transom and
the 8/20 station are scaled by factor ~ = 20. The fore
region is shrieked in the longitudinal direction in or-
der to fit into the channel test section while preserving
the sectional area distribution (see Fig. 14. The four-
bladed, adjustable-pitch, highly skewed propeller is in-
stalled on an open shaft supported by two bearings that
are attached to the hull by shaft brackets. Figure 2
shows a view of the model with the propeller installed.
Fig. 3 shows a sketch of the experimental
setup. Flow velocity components are measured by
means of a two component back scatter LDV system,
in which a 5 W Argon laser produces a radiation that
is collimated by an underwater fiber optic probe in
the measurement point. The frequency shift, required
for the velocity versus ambiguity removal, is provided
by a 40 MHz Bragg cell. Real time analysis of the
OCR for page 513
1~ ~~
LDV master processor —~
.¢
essor ~ '
— ~ Modelship
~ ~ Encoder
~ Troversino system
:: : [~ H Bl~ NY~
~ _ : ,,~, -::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::
( ~ --:
Phc~ m'. tier ~ Und r~t~F~prdbe~
Figure 3: Sketch of the experimental setup.
Doppler signal is performed by two TSI IFA 550 pro-
cessors. Only two velocity components can be meas-
ured simultaneously, thus two optical configurations
are adopted for resolving the three dimensional ve-
locity field and measuring respectively the longitud-
inal/vertical and the transversal/vertical velocity com-
ponents. Therefore, particular care is required in the
initial location of the measurement volume to reduce
positioning errors of the two optical configurations.
The initial position of the probe volume is fixed with
an accuracy of about 0.5 mm. The underwater probe
is set up on a computer-controlled traversing system,
which permits to get a displacement accuracy of 0.1
mm in all directions and to achieve a high automation
of the LDV system.
A rotary incremental 3600 pulse per revolu-
tion encoder supplies the actual propeller position with
an angular accuracy of 0.2°. Signals from the encoder
are processed by a synchronizer which provides the
propeller angular position to a two-bytes digital port
available on the LDV master processor.
In order to improve the processor data rate
and to reduce the time acquisition length per point,
the channel water is seeded upstream the ship model
with titanium dioxide (TiO2) particles by using a spe-
cial seeding rake device.
Data acquisition is accomplished by using
a low-end personal computer, whereas the post pro-
cessing analysis requires several GBytes of data stor-
age. First, the hull nominal wake is measured on
the propeller disk. The operating propeller condi-
tion is analyzed on two transverse measurement planes
placed upstream and downstream the propeller. On
each plane, 400 measurement points are distributed
by a Cartesian grid within a circular area of diameter
DM = 316.25 mm = 1.15Dp. A grid spacing of
12 mm in both horizontal and vertical directions is
sufficient to have a good resolution in the tip vor-
tex regions; a higher grid resolution is used in the
wake regions of the brackets. Measured data are post-
processed in order to obtain velocity fields with angu-
lar resolution of 2°.
Phase sampling technique
The application of flow measurement techniques with
operating propeller is complicated by the flow unstead-
iness also in a frame of reference that rotates with the
propeller.
As a consequence, experimental techniques
for open water propellers based only on radial move-
ments of the measurement volume, like those de-
scribed in Min (1978), Kobayashi (1982), Cenedese
et al. (1985), Jessup (1989), are not valid and a differ-
ent approach is required.
In particular, measurements covering all the
investigated disk must be taken at different pro-
peller angular positions. In addition, the acquisition
time must be so long to provide a sufficient num-
ber of samples to make possible statistical data post-
processing.
In the present work, the Tracking Triggering
Technique (TTT) proposed by Stella et al. (1998) is
utilized. Velocity samples are acquired when Dop-
pler signal is detected on the corresponding LDV sys-
tem channel. Next, each LDV sample is tagged with
the angular propeller position at the measurement time
by means of an encoder-synchronizer system and then
stored in the PC memory. This process is repeated in-
dependently for both LDV channels because it is ex-
perienced that Doppler burst are not necessarily detec-
ted simultaneously.
In the post processing phase, data averaging
is performed. A slotting technique is required be-
cause LDV samples are not equally spaced in time
(burst detection in the measurement point is a random
event) and classical ensemble averaging is not pos-
sible. Therefore, each sample is rearranged in angular
slots of constant width. By evaluating averages at each
slot, values of velocity components at any angular po-
sition are obtained.
The choice of the slot width is critical for this
kind of analysis as described by Stella et al. (20004.
In fact, a compromise should be obtained between the
need to increase the angular resolution (to capture ve-
locity fluctuations) and to have an adequate number of
samples (required for statistical consistency). For in-
stance, the standard slotting procedure-N contiguous
slots of constant width from 0° to 360°- provides poor
statistical processing accuracy. Hence, more complex
OCR for page 514
slotting procedures are to be implemented in order to
guarantee statistical requirements and angular resolu-
tion, also in the case of critical data rate conditions.
Three independent slotting procedures are
used in the post-processing phase: overlapping, blade
slotting and weighted slotting. The overlapping pro-
cedure provides partial overlapping, i\e wide, for con-
tiguous slots. Hence, any sample in the overlapping
area increases the two overlapped slots statistical pop-
ulation simultaneously, with statistical processing ad-
vantages.
The blade slotting procedure is based on the
assumption that all the propeller blades are identical
both in mechanical and in geometrical terms. By
this assumption, the velocity field at any measurement
point is a periodic function of time with blade fre-
quency. Thus, the slotting procedure can be limited
inside a circular sector of width 360°/Z, where Z is
the number of blades. A given slot, with center in the
angular position Hi and width 2e (0i—~ ~ ~ ~ Hi + c),
will contain all the velocity samples acquired when the
angular position is ~ = Hi + 2~n/Z, (n = O. 1, ...Z).
Hence, the sample population of each slot is increased
by a factor corresponding to the propeller blade num-
ber.
In the weighted slotting procedure a weighted
average is introduced in the statistical analysis so that
the influence of each sample decreases by a prescribed
law (linear or Gaussian) as the distance from the slot-
ting center increases, with accuracy improvement.
In the present analysis, statistical evaluation
is performed by using a blade slotting technique with
360 overlapped slots of amplitude 2e = 2° and
weighted averaging by Gaussian law. In such way
150 200 samples per slot are collected; in addition,
angular resolution is adequate to describe flow regions
with high gradients.
THEORETICAL ANALYSIS
Governing equations
In the following, a frame of reference (Oxyz) that is
fixed with the propeller (hereafter referred to as the ro-
tating frame of reference), as shown in Fig. 4, is con-
sidered.
The hull-induced wake is prescribed in the
propeller disk as VW = VW (0, r ), where ~ and r are po-
lar coordinates in the propeller disk plane. Hence, the
flow incoming to the propeller in the rotating frame of
~ .
reference 1S
VI (X, t) = VW + Q x x. (1)
where Q = (Q. O. 0) is the angular velocity of the pro-
z!
vw
\\
.) ,Wx
a,:
.~
\
Figure 4: Frame of reference.
pelter.
\
The perturbation induced by the propeller to
the velocity field is assumed to be irrotational, and
hence it can be expressed in terms of a scalar potential.
Denoting by ~ the perturbation velocity potential, the
total velocity field in the rotating frame of reference is
given by
q=vlr +V¢. (2)
Under the assumption of incompressible flow,
the velocity potential ~ satisfies the Laplace equation,
V ~ = 0 on Up, (3)
where (p denotes the unbounded fluid region sur-
rounding the propeller and its trailing wake. As usual
in potential flow analyses of lifting bodies, the wake
is included by assuming that the vorticity generated on
each blade is shed into a zero thickness layer which
is replaced by a discontinuity surface for the velocity
potential.
The pressure field in (p is given by the
Bernoulli equation that, in the rotating frame of ref-
erence, reads
2 + P = I v2 + PO, (4)
where q = A, vat = Aver If, p0 is the undisturbed flow
pressure and p is the fluid density.
In order to solve Eq. (3), boundary conditions
must be imposed on amp. On the propeller surface
Up the impermeability condition yields q n = 0, and
recalling Eq. (2),
I'd' = —vat n on Dip,
OCR for page 515
where n is the outward unit normal to Gyp.
Boundary conditions for ~ on the wake sur-
face )°w are determined by applying mass and mo-
mentum conservation laws across the surface. One ob-
tains
~ ta¢> = 0
yang
Ap = 0
on Low, (6)
where the symbol i\ denotes the jump across upper
and lower sides of the wake.
Applying the Bernoulli equation (4) on the
two sides of the wake and recalling Eqs. (6), yields
D pa ~
Dt ~ (at + qw · VJ i\¢ = O. <7~
where qw denotes the averaged flow velocity on the
two sides of the wake. Equation (7) means that the po-
tential discontinuity is convected along wake stream-
lines with velocity qw. Hence, the potential discon-
tinuity at an arbitrary wake point XW and time t may
be expressed as
4) ( w, t) A\) (XWTE, t TW ) ' (8)
where XWTE is the trailing edge wake point lying on the
same streamline as xw, whereas TW denotes the con-
vection time from XWTE to xw.
A further condition on ~ is required in or-
der to assure that no finite pressure jump may exist
at the blade trailing edge (Kutta condition). Following
Morino et al. (1975), this is equivalent to impose
4) ( WTE, t) 4) (XTE ~ t) 4) (XT E ~ t), (9)
where XT+E and XTE denote, respectively, blade trailing
edge points on suction and pressure sides.
Boundary integral formulation
In the present approach, the Laplace equation for ~ is
solved by means of a boundary integral formulation.
By recalling the first of Eqs. (6), the application of
third Green's identity gives
Et )¢,( ~ J (a¢G BEG) d,5°(
Top an an
J At_ d)°(y) on Lip, (10)
N°w an
where G = - 1/4}T fix—yet is the Green's function of
the Laplacian operator in an unbounded three dimen-
sional domain; in addition, E = O. 1/2, 1 if x is inside,
on, or outside Gyp, respectively.
If x is on Gyp, Eq. (10) represents a Fredholm
integral equation of the second kind for ~ in which
a ¢/en on )°p is known from Eq. (5), and i\¢ on
)°w is expressed in terms of ~ on )°p by combining
Eqs. (8) and (94.
The perturbation velocity Vat may be evalu-
ated by taking the gradient of both sides of Eq. (10),
as
Vat (x, t) = J [ at VxG - ¢, Ox (aaG)] d,5°(y)
J50W ~ Ax ( arl ) d)°(y) (11)
where Vx is the gradient operator acting on x. Once
~ on )°p is known from the solution of Eq. (10), the
equation above provides an explicit representation of
the perturbation velocity field.
Wake analysis
In both Eqs. (10) and (11) the location of the wake
surface is not known a priori and should be either pre-
scribed or determined as a part of the flow field solu-
tion.
In order to determine the location of )°w' the
condition that all the wake points move according to
the local flow velocity is applied. Such procedure is re-
ferred to as wake alignment, and it stems from Eqs. (6)
and (74. In the present work a Lagrangian scheme
is used: the location XW Of an arbitrary wake point
changes with time as
rt+At
XW (t + i\t) = XW (t) + ~ q (XW, T) d T.
t
However, the inclusion of a wake alignment
procedure into a boundary element analysis of un-
steady propeller flows produces time consuming com-
putations. In fact, Eq. (12) requires at each time step
the evaluation of the velocity q at all the wake nodes
(see below).
In order to reduce the computational effort, a
two-step technique is used.
First, a steady flow wake alignment analysis
is performed by using as input an axially symmetric
inflow which is obtained by averaging in circumferen-
tial direction the non uniform hull-induced inflow (cfr.
Eq. (l))
air VW + Q x,
with
vaWv (r ~ = 2 | VW (0, r ~ d 0.
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Representative terms from entire chapter:
velocity components
Next, the computed wake surface )°w is used
as input of an unsteady flow computation with pre-
scribed wake in which the non uniform inflow vlr is
used.
Discretization
A numerical solution of the boundary integral formu-
lation for the velocity potential outlined above is ob-
tained here by using a boundary element method.
The propeller surface and the wake are di-
vided into hyperboloidal quadrilateral elements. The
angular extension of wake elements is constant and is
given by i\0w = Q/\t, where At denotes the time
step.
The distribution of ~ over )°p is evaluated by
enforcing Eq. (10) in discretized form at each centroid
on the propeller surface (collocation points). Flow
quantities are assumed to be constant on each element.
Denoting by Np the number of elements on the pro-
peller surface, and by NW the number of elements on
the wake, one obtains
~ (5ij + Dij) f j = ~ Sij ( ad)
Jvw
—ZDijA¢j (i= 1, Np) (15)
Jo=
where ~ij = 1 if i = j and ~ij = 0 otherwise, and
sij = J G (xi, y) d )°(y)
Wi aG (16)
Dij= J a Hi y~d~°
Figure 5: Computed wake surface.
and or ~ to, 11 is a weight factor (in the present ana-
A
lysis, or = 1/2). The quantity At represents here a
relaxation parameter.
The alignment procedure is applied only in
the wake portion close to the propeller (near wake),
whereas the remaining portion (far wake) is de-
termined as a helical surface with prescribed pitch,
smoothly connected to the near wake. This yields a re-
duction of the computational effort, and enhances the
robustness of the numerical procedure.
Once the wake surface is updated, wake coef-
ficients Dij are re-computed and a new distribution
of ~ on )°p is obtained by Eq. (154. The process is
repeated until convergence of wake node locations is
achieved. As a convergence criterion, the root mean
square of the displacement of all wake nodes between
two subsequent steps must be smaller than a fixed
value (5 10-4 in present calculations). A sample view
of the computed wake surface is shown in Fig. 5.
The unsteady flow solution is obtained by
solving Eq. (15) in which the non uniform inflow vlr
is used in the impermeability condition on Gyp; in ad-
dition, the computed flow-aligned wake geometry is
used.
The pressure distribution on )°p is obtained
by the Bernoulli equation (44. Next, unsteady forces
acting on the propeller are computed by pressure integ-
ration over Gyp. A simple viscosity correction is intro-
duced by evaluating the friction coefficient C f accord-
ing to the Prandtl-Schlichting friction line formula.
FLOW FIELD INVESTIGATIONS
Tests have been carried out with propeller angular ve-
locity of 7.7 rps and channel upstream velocity of 2.4
m/s, corresponding to an advance ratio J = 1.133
and a blade Reynolds number at r = 0.7R, Reo.7 =
3.7. 105.
twofold:
The aim of the experimental investigations is
· the measurement of the nominal wake to be used
as input of the BEM code;
· the study of the velocity field upstream and down-
stream the propeller.
All the measurements are taken for two different ap-
pendage configurations: vertical bracket at an angle of
attack of 0° (configuration A) or 7° (configuration B)
with respect to the x axis. In both cases, the horizontal
bracket is at zero angle of attack with respect to the x
axis.
In the following, all plots show the right in-
ward rotating propeller as seen from the stern.
Hull nominal wake
Figure 6 depicts the velocity field on the propeller disk
by means of contour levels of the axial component
and vector plot of the crossbow for the two different
bracket configurations.
The perturbation induced by the hull and its
appendages is mainly concentrated in the top left por-
tion of the propeller disk area, where the two brackets
are located; in that region, the effect of the hull bound-
ary layer, the wakes of the brackets and of the shaft are
clearly identified. In the other regions of the investig-
ated area the perturbation induced by the hull reduces
to a flow inclination due to the rise of the keel in the
aft region (see Fig. 24.
The low velocity region covering a wide sec-
tor around ~ = 0° is strongly affected by the angle of
attack of the vertical bracket. In fact, in the case of
configuration B. the bracket induces a flow accelera-
tion and improves wake uniformity in the outer region,
whereas a larger flow separation is observed close to
the shaft, compared to configuration A.
Similar considerations arise from the analysis
of the crossbow. In particular, the upward flow inclin-
ation due to the keel shape in the aft region is apparent.
In addition, it may be noted a vortex pair in the shaft
wake region that is more pronounced in the case of
Configuration B (Fig. 6, right).
Flow field around the propeller
The velocity field with operating propeller is stud-
ied in two transverse planes located upstream at x =
—0.245 D p, and downstream at x = 0.37 1 D p . Due
to flow periodicity, results are shown in the range
0° <0 <90°.
Experimental results are compared to theor-
etical predictions. The capability of present numerical
A ~ ~ ~
aim..........
Configuration A
1~
results to agree with measurements is affected by some
basic approximations. First, the measured hull wake is
used as an input in the numerical analysis to compute
the inflow VW (see Eq. (24), and no attempt is made
to determine the correction due to propeller suction ef-
fects (effective wake). In fact, while theoretical models
to infer the effective wake from nominal wake surveys
have been developed for single screw vessels by e. g.
Huang and Groves (1980), similar approaches for twin
screw vessels with appendages are not available to the
authors' knowledge. In addition, the dependence of
the inflow with respect to the axial abscissa x is not
taken into account; thus, values measured at the pro-
peller disk (x = 0) are assumed to be constant at any
x in the computational domain. Furthermore, the ef-
fect of the inclined flow induced by the rise of the keel
in the aft region is neglected in the modeling of the
propeller wake.
The numerical results presented here are ob-
tained by using 48 x 24 elements on each blade surface
and 12 x 88 elements on each hub sector between two
adjacent blades. Wake elements with angular exten-
sion of 6° are used, and two wake turns are considered
in the calculations (with wake alignment limited to one
turn). These values provide results whose dependence
on discretization parameters is negligible.
Downstream plane First flow measurements and
theoretical predictions downstream the propeller are
considered. Here, the flow field is characterized by
the propeller trailing vorticity path. Investigations in
this region are of basic importance due to the close re-
lationships between trailing wake shedding and thrust
generation by the propeller.
~ t I ~ ~ ~ f /
..
1 ~ ~ ~ ~ ..~ ...............
Configuration B
Figure 6: Hull nominal wake.
The trace of the wake in the investigated
plane may be determined from the analysis of the tur-
bulence intensity of the measured axial velocity com-
ponent. Figure 7 shows turbulence levels in the meas-
urement plane at ~ = DO, 30° and 60°, for both config-
urations A and B. Traces of the wake surface predicted
by the BEM code are also drawn in Fig. 7 by dashed
white lines. The agreement in wake locations between
experiments and theoretical predictions is good. In
particular, both shapes and angular locations of the
wake traces are accurately predicted by the present un-
steady flow wake alignment approach.
The locations of the four wake tip vortices are
indicated by high turbulence cores; differences of tur-
bulence intensity among the tip vortices reflects the un-
steadiness of the flow, whereas the wake confinement
inside the propeller disk circle (represented by a black
line) reveals the contraction of the stream tube down-
stream the propeller. The effect of vorticity diffusion
is apparent from the thickness of the measured wake.
In addition, the strong effect of the hub wake with very
high turbulence levels is appreciated.
The results in Fig. 7 show that the present
theoretical model is capable to accurately predict the
trailing wake shedding process. This proves that the
approximated representation of the incoming flow vlr
discussed above has only a minor impact on the solu-
tion.
On the other hand, the numerical evaluation
of the velocity field, based on the hypothesis of neg-
ligible streamwise variations of the nominal wake,
shows some drawbacks. In fact, by comparing experi-
mental and theoretical results, some discrepancies in
terms of velocity intensity predictions are observed.
This is shown in Fig. 8 that depicts the axial velocity
= 0° (Configuration A)
~ = 0° (Configuration B)
Q.~0
a.l~e
O.1:~G
0.14
O.~p
0.1:0
0.~e
O.~6
0.04
0.~2
~ = 30° (Configuration A)
~ = 60° (Configuration A)
~ = 30° (Configuration B)
0:.2
0.1:8
~.1 6~
:~.14
0:.~2
0:.1:D
0.~:e
0 0:~
OnG4
O~.0:2
~ = 60° (Configuration B)
.~0
0.18
:a.1:~6
0.14
0.1~2
.~0
O.~$
0.06
0.04
~0.0~2
Figure 7: Experimental turbulence levels of the axial velocity component and location of the trailing wake by numerical
simulations on the downstream measurement plane.
~ = 0° (experiments)
~ = 30° (experiments)
1.50
1.40
1.30
. . 1.20
1 .1:0
1 .00
0.90
0.80
0.7Q
Q.BO
0.50
0.40
1.50
1.40
1.30
1 .20
1.1:0
1.00
0.90
O.80
0.70
I Q BO
0.40
~ = 60° (experiments)
~ = 0° (numerical)
~ = 30° (numerical)
1.50
1.40
.30
1.20
1.1:0
1.00
0.90
0.80
O.7Q
Q.SO
0.50
0.40
~ = 60° (numerical)
Figure 8: Downstream axial velocity component (Configuration A).
= 0° (experiments)
~ = 0° (numerical)
= 30° (experiments)
~ = 30° (numerical)
= 60° (experiments)
Figure 9: Downstream axial velocity component (Configuration B).
~ = 60° (numerical)
Experimental
Numerical
Figure 10: Upstream axial velocity component at ~ = 0° (Configuration A).
Experimental
Numerical
Figure 11: Upstream axial velocity component at ~ = 0° (Configuration B).
component at angular positions ~ = DO, 30O, 60°, in
the case of configuration A.
Similar considerations arise from velocity
field surveys in the case of bracket configuration B.
In particular, the axial velocity component at angular
positions ~ = GO, 30O, 60°, are presented in Fig. 9. A
comparison between Fig. 8 and Fig. 9 shows that the
velocity field downstream the propeller is slightly af-
fected by the different bracket arrangement used. In
fact, both experimental and numerical results show
that the perturbation induced by the propeller tends to
smooth any difference between the velocity fields in-
coming to the propeller.
Upstream plane Figures 10 and 11 show the axial
velocity component in the upstream plane at the rep-
resentative angular position of ~ = 0° for the two
bracket arrangements. By comparing the experimental
measurements referred to the two configurations, large
differences concentrated in the region where vertical
bracket and shaft wakes merge are observed.
The agreement between measurements and
numerical predictions is not satisfactory. This shows
that the hypothesis of neglecting the streamwise vari-
ation of the hull wake in the computations is not ad-
equate for theoretical analyses of the velocity field up-
stream the propeller. This effect has been already poin-
ted out in the discussion of results in the downstream
plane, but it is more pronounced upstream. If fact, the
measurement plane is extremely close to the trailing
edges of the brackets; thus the velocity defect of the
bracket wakes is stronger and confined in a thinner re-
gion than on the propeller disk plane, where the nom-
inal wake used in the computations is measured. Fur-
ther, this effect is enhanced by the low intensity of the
perturbation induced by the propeller.
Pressure and performance For the sake of com-
pleteness, some additional results obtained by the the-
oretical analysis are presented. Specifically, Fig 12
shows history of thrust coefficient KT and torque coef-
ficient KQ for both configurations A and B. It may be
observed that the stronger shaft wake of configuration
B determines higher fluctuations for both KT and KQ
than in the case configuration A results. For bracket
configuration A, pressure coefficient distributions on
the blade surfaces at angular locations ~ = DO, 30°,
and 60° is given by Fig. 13.
CONCLUDING REMARKS
An experimental and theoretical analysis of the flow
field around a four-bladed propeller installed on a twin
screw vessel has been presented.
Flow field survey upstream and downstream
the propeller has been performed by using LDV. Par-
ticular attention is payed to set up a procedure suit-
able for measurements of unsteady velocity fields as
is the case of propellers in the wake of a hull. Phase
sampling is performed by means of a Tracking Trig-
ger Technique, by which velocity samples are arranged
into angular slots according to the propeller position
at measurement time. The procedure provides a sat-
isfactory compromise between statistical requirements
and angular resolution. The results of the measurement
campaign demonstrate the capability of the present
LDV phase sampling technique to provide an accurate
description of both hull and propeller wakes. The ana-
lysis of measured velocity fields is helpful to highlight
some important features of the interactions among
wakes of the hull appendages and to investigate the
flow field in the propeller wake region.
In addition, experimental results are used to
assess the validity of a theoretical approach based on
a boundary element method for the analysis of pro-
pellers in non uniform flows. Comparisons with meas-
ured velocity fields show that the present theoretical
approach provides reasonable predictions of the most
relevant flow features in the propeller wake region. In
particular, the wake alignment procedure is fully ad-
equate to simulate the trailing vorticity convection pro-
cess, in which viscosity has a minor influence. Better
agreement between theoretical predictions and experi-
mental results could be obtained by taking into account
the streamwise variation of the hull wake used in the
computations.
ACKNOWLEDGMENTS
The present work was supported by the Ministero dei
Trasporti e della Navigazione in the frame of INSEAN
and CETENA Research Programs 1997-99.
REFERENCES
Campbell, R., 1973, Foundations of Fluid Flow
Theory, Addison-Wesley.
Cenedese, A., Accardo, L., and Milone, R., 1985,
"Phase sampling technique in the analysis of a pro-
peller wake," in Proc. of the International Conference
on Laser Anemometry Advances and Application.
Esposito, P. G. and Giordani, A., 2000, "Numerical
analysis of non cavitating propeller in uniform and non
uniform flow conditions," in Proc. of the 9th IMAM
Congress, pp. B21-B28.
Greeley, D. S. and Kerwin, J. E., 1982, "Numerical
methods for propeller design and analysis in steady
flow," SNAME Transactions, vol. 90, pp. 416-453.
Hayun, B. S. and Patel, V. C., 1991, "Measurements
in the flow around a marine propeller at the stern of an
axisymmetric body," Experiments in Fluids, vol. 11,
pp. 105-117.
Hoshino, T., 1993, "Hydrodynamic analysis of pro-
pellers in unsteady flow using a surface panel method,"
Journal of The Sociey of Naval Architects of Japan,
vol.l74,pp.71-87.
Huang, T. T. and Groves, N. C., 1980, "Effective wake:
Theory and experiment," in Proc. of the Thirteenth
Symposium on Naval Hydrodynamics, pp. 651-673.
Jessup, S. D., 1989, An Experimental Investigation
of Viscous Aspects of Propeller Blade Flow, Ph.D.
thesis, The Catholic University of America, Washing-
ton, D.C.
Kinnas, S., Hsin, C., and Keenan, D., 1990, "A poten-
tial based panel method for the unsteady flow around
open and ducted propellers," in Proc. of the Eighteenth
Symposium on Naval Hydrodynamics, pp. 677-685.
Kobayashi, S., 1982, "Propeller wake survey by
laser doppler velocimeter," in Proc. of the 4th
International Symposium on Application of Laser
Doppler Anemometry to Fluid Mechanics.
0.7 r
0.29
0.28
0.27
0.26
0.25
0.24
0.23
0.22
I'd ~ ~-
. . . ~ ~
it'
0 45 90 135 180 225 270 315 360
Thrust coefficient KT
0.69
0.68
0.67
0.66
064
0.63
nap
n 61
.A .A .A ./
0.6 -
0 45 90 135 180 225 270 315 360
Torque coefficient 10KQ
Figure 12: History of propeller loads during a revolution: /\, configuration A; A, configuration B.
Koyama, K., 1992, "Application of a panel method to
the unsteady hydrodynamic analysis of marine pro-
pellers," in Proc. of the Nineteenth Symposium on
Naval Hvdrodvnamics. no. 817-836.
Min. K. S., 1978, Numerical and Experimental
Methods for Prediction of Field Point Velocities
Around Propeller Blades, Tech. Rep. 78-12, MIT De-
partment of Ocean Engineering.
Morino, L., Chen, L.-T., and Suciu, E., 1975, "Steady
and oscillatory subsonic and supersonic aerodynam-
ics around complex configurations," AIAA Journal,
vol. 13, pp. 368-374.
Pyo, S. and Kinnas, S., 1997, "Propeller wake sheet
roll-up modeling in three dimensions," Journal of Ship
Research, vol. 41, pp. 81-92.
Stella, A., Guj, G., Di Felice, F., Elefante, M., and Ma-
tera, F., 1998, "Propeller flow field analysis by means
of LDV phase sampling techniques," in Proc. of the 3th
International Symposium on Cavitation, pp. 171-188.
Stella, A., Guj, G., and F. Di Felice, 2000, "Pro-
peller wake flowfield analysis by means of LDV phase
sampling techniques," Experiments in Fluids, vol. 28,
pp. 1-10.
= 0° (suction side)
= 30° (suction side)
D.6D
~ 0.20
· .... 0~00
-0~.20
-0.40
-0:.60
-0.60
-1 .00
-1 To
-1 .40
-~.60
-1 .80
w -2.DO
~ = 0° (pressure side)
~ = 60° (suction side)
.... .;
~ = 3()° (nressllre side)
D.60
0.20
i'°~0
-2.DO
Figure 13: Pressure coefficient on blade.
A...
~ = 60° (pressure side)
| D.60
0.20
· 0.00
-0.20
-0.40
-0.60
-OHIO
-1 .00
-1 .2Q
-1 .40
-~.60
-~.60
AN -2.00
DISCUSSION
T. Hoshino
Mitsubishi Heavy Industries, Ltd.
Japan
The authors should be congratulated for their efforts
to measure the complicated flow fields around a
propeller operating in non-uniform flow by LDV and
develop a panel method with a flow-aligned wake. I
have the following questions.
(1) Did you compare the calculated flow fields
between with flow-aligned wake and without
flow-alignment procedure?
(2) Where is the remaining wake (far wake) with
prescribed pitch starting from?
(3) How many calculations are needed to obtain a
final convergent solution?
AUTHOR'S REPLY
The authors wish to thank Dr. Hoshino for
submitting his comments and discussion to the paper.
In response to his questions the following remarks
can be made:
1. Some comparisons concerning the effects of
wake alignment have been presented in a
previous paper by Esposito and Giordani
t1], where the Seiun Maru HSP propellers
has been analysed. In Figure 1, the tip
vortex line of the prescribed wake is
compared to the flow aligned wake. Of
course the different position of the wake in
the two cases has a strong impact on the
flow field on downstream planar sections
orthogonal to the axis. Some effects are also
apparent in the loads as shown in Figure 2.
2. In the present computation two wake turns
are used, with wake alignment limited to the
first turn.
Our experience showed that the number of
iterations needed to reach wake alignment
convergence is slightly greater than the
number of streamwise elements of the free
portion.
1.1.REFERENCES
1. Esposito, P.G., Giordani, A. "Numerical
Analysis of Non Cavitating Propeller in
Uniform and Non Uniform Flow
Condition", Proceedings of the IMAM 2000
Conference, Ischia, Italy, Apr. 200O, pp. B-
21:28.
_. HoshinO, T., "Hydrodynamic Analysis of
Propellers in Unsteady Flow Using a
Surface Panel Methos", Journal of the
Society of Naval Architects of Japan, Vol.
174, 1993, pp.7 1:87.
Figure 1: Propeller free wake geometry in
axysimmetric flow.
~ 17
~ ~ . .:.. d.> ~ .~ ~
~ ~ A ~ ~ ~ ~ i~ 8~ Do ~ i ~~.~ ~ ~
mu'
::~
0~ ~ ~ ~ ~ U '
~ CZ ~ ".
~ ~ ~ ~ ~ ~ ~ . D ~ O ~ ~ ~
Figure 2: Single blade contribution to thrust and
torque coefficients along a revolution.
KT~
