analysis of ducted propellers by combining potential flow · pdf file ·...
Post on 20-Mar-2018
221 Views
Preview:
TRANSCRIPT
Fourth International Symposium on Marine Propulsors smp’15, Austin, Texas, USA, June 2015
Analysis of Ducted Propellers by Combining
Potential Flow and RANS Methods
Johan Bosschers1, Chris Willemsen
2, Adam Peddle
3, Douwe Rijpkema
4
1,4 Maritime Research Institute Netherlands, MARIN, Wageningen, The Netherlands 2 University of Twente, Enschede, The Netherlands, presently at MARIN
3 MARIN, presently at University of Exeter, Exeter, Devon UK.
ABSTRACT
An iterative procedure to analyze ducted propellers in open
water conditions using a combination of a RANS solver and
a boundary element method (BEM) has been developed and
tested. The RANS solver analyses the viscous flow over the
duct modeling the propeller through the use of body forces.
These body forces are obtained from the BEM in which
both duct and propeller are analyzed. In the BEM solution
the loading on the duct is prescribed and obtained from the
RANS solution. The results of this procedure are compared
with results obtained from a full RANS and a full BEM
computation and with experimental data.
Keywords
Ducted Propellers, BEM, RANS.
NOMENCLATURE
n Shaft rotation rate [rev/s]
p Pressure [Pa]
p Free-stream pressure [Pa]
D Propeller diameter [m]
Density of fluid [kg/m3]
V Free-stream velocity [m/s]
pnC Pressure coefficient,
2 212pnC p p n D
J Advance ratio, J V nD
RF Radial force coefficient,
2 4RadialForce[N]RF n D
TK Thrust coefficient,
2 4Thrust[ ]TK N n D
QK Torque coefficient,
2 5Torque[Nm]QK n D
Efficiency,
, , ,2T prop T duct Q propJ K K K
pre
1 INTRODUCTION
The analysis and design of propellers using boundary
element methods (BEM) that solve the potential flow
equations is common practice in the marine industry.
However, the analysis of ducted propellers is still
challenging when only boundary element methods are used
as there are a number of features in this flow that cannot be
captured by potential flow. Some of these features are given
in Figure 1. The boundary layer on the inner surface of the
duct influences the loading on the propeller, the flow
through the gap and the convection of the vortices generated
at the tip of the propeller. The gap leads to the generation of
a tip leakage vortex that influences the loading on the
propeller blade. At the blunt trailing edge of the duct flow
separation will occur that can not be captured by potential
flow. The location of the separation point at the blunt
trailing edge is very important as it influences the loading
on the duct. The last item shown in Figure 1 is the presence
of flow separation on the outer surface near the leading
edge of the duct that may occur for high advance ratios.
Baltazar et al. (2012) have shown that a BEM is able to give
a good prediction of the open water characteristics for a
duct with a sharp trailing edge provided the velocity defect
due to the duct boundary layer is used in the iterative wake
alignment procedure. The influence of the velocity through
the gap was shown to be small. At higher advance ratios the
prediction of especially the duct thrust was not so good due
to the occurrence of flow separation on the duct.
The viscous flow features are captured by solving the
Reynolds-Averaged Navier-Stokes (RANS) equations but
the grid generation is more complex and much more
computational resources are required. For that reason there
is still a demand for BEM computations by for instance
propeller designers. A comparison between BEM
computations and RANS computations for a ducted
propeller with a neutral duct is presented by Baltazar et al
(2013).
Figure 1: Typical flow features for a ducted
propeller influenced by viscosity; (1) boundary layer inner
duct surface; (2) gap flow; (3) flow separation at the blunt
trailing edge; (4) flow separation on the outer surface of the
duct for low propeller loading. The colour coding represents
the circumferential component of vorticity computed by a
full RANS solution at high advance ratio.
In the present paper an iterative procedure for the analysis
of ducted propellers in open water conditions using a
combination of a RANS solver and BEM is used to capture
some of the viscous flow features given in Figure 1, being
the flow over the blunt trailing edge, the flow separation
near the leading edge for high advance ratios and the
boundary layer on the inner duct surface.
A coupling between RANS and BEM has already been
developed for the analysis of the propulsive performance of
ships. The viscous flow over the ship hull has been analyzed
with a RANS solver taking the propeller action into account
by using body forces obtained from the BEM (Starke &
Bosschers, 2012 and Rijpkema et al. 2013). We will show
here a somewhat similar approach by analysing the viscous
flow for the duct using RANS in which body forces are
used to represent the propeller action. These body forces are
obtained from the solution computed by BEM in which the
duct is taken into account but the blunt trailing edge has
been made sharp. A procedure has been developed through
which the loading on the duct can be adjusted to a user
prescribed value that can be obtained from for instance the
RANS solution. This leads to an iterative method for the
viscous flow analysis of ducted propellers. The results of
this coupling procedure is compared with experimental data
for a Ka4-70 propeller with pitch P/D= 1.0 operating in a
19A duct. The geometry of this configuration is given by
Kuiper (1992).
The used numerical methods are described first in the next
section followed by a more detailed description of the
coupling procedure. Open water results of the full BEM (i.e.
without coupling to RANS) are first compared to
experiments, followed by the results of the coupled
approach. The loading and pressure distribution are then
compared in more detail with full RANS results. The paper
finishes with the conclusions and recommendations for
further work.
2 NUMERICAL METHODS AND GRIDS
2.1 PROCAL
The boundary element method that is used to solve the
incompressible potential flow is the PROCAL code.
PROCAL has been developed by MARIN within the
Cooperative Research Ships (CRS1) for the unsteady
analysis of cavitating propellers operating in a prescribed
ship wake and is currently in development for the analysis
of ducted propellers. It has been validated for open water
characteristics, shaft forces and moments, sheet cavitation
extents and propeller induced hull-pressure fluctuations.
The code is a low order BEM that solves for the velocity
disturbance potential using the Morino formulation. Initial
validation studies and details on the mathematical and
numerical model can be found in Vaz & Bosschers (2006)
and Bosschers et. al (2008). The geometry of the blade
wake can be determined by an iterative procedure to align
the propeller wake with the flow or by using a prescribed
wake pitch and contraction using empirical formulations to
reduce CPU time.
For the analysis of ducted propellers a similar method as
proposed by Baltazar et al. (2012) has been implemented.
An iterative wake alignment method is used for the wake of
the propeller and duct in which the radial position of the
trailing vortices is prescribed while the pitch is obtained
from the computed induced velocities. The induced
velocities near the duct surface are reduced depending on a
user specified boundary layer thickness. The gap between
propeller blade and duct is modeled as a surface on which
the transpiration velocity can be prescribed according to a
user specified value or using the gap model of Kerwin et al.
(1987). Unless otherwise specified, the transpiration
velocity in the gap is neglected by default and the gap is
modeled as a rigid surface. The duct trailing edge geometry
is modified such that a sharp trailing edge is present and the
location from which the vortices trail from the duct is
clearly defined. An iterative pressure Kutta condition is
applied in which the duct and propeller wake strength is
modified until the pressure difference on the two surfaces at
the trailing edge of blade and duct is smaller than a user
specified value. Results of PROCAL for ducted propellers
are also presented by Moulijn (2015).
The grid on the propeller blade, hub, gap and duct is
generated by the computer code with graphical user
1 www.crships.org
interface PROVISE, developed by DRDC Atlantic within
the CRS. An example of the grid is shown in Figure 2.
2.2 REFRESCO
ReFRESCO is a viscous-flow CFD code that solves
multiphase (unsteady) incompressible flows using the
RANS equations, complemented with turbulence models,
cavitation models and volume-fraction transport equations
for different phases, Vaz et al.(2009). The equations are
discretised using a finite-volume approach with cell-
centered collocated variables, in strong-conservation form,
and a pressure-correction equation based on the SIMPLE
algorithm is used to ensure mass conservation. Time
integration is performed implicitly with first or second-
order backward schemes. At each implicit time step, the
non-linear system for velocity and pressure is linearised
with Picard’s method and either a segregated or coupled
approach is used. In the latter, the coupled linear system is
solved with a matrix-free Krylov subspace method using a
SIMPLE-type preconditioner, Klaij and Vuik (2013). A
segregated approach is always adopted for the solution of
all other transport equations. The implementation is face-
based, which permits grids with elements consisting of an
arbitrary number of faces (hexahedrals, tetrahedrals, prisms,
pyramids, etc.), and if needed h-refinement (hanging
nodes). State-of-the-art CFD features such as moving,
sliding and deforming grids, as well automatic grid
refinement are also available. For turbulence modeling,
RANS/URANS, SAS and DES approaches can be used
(PANS and LES are also being studied). The code is
parallelized using MPI and subdomain decomposition, and
runs on Linux workstations and HPC clusters. Application
of ReFRESCO for different propeller types is treated by
Rijpkema and Vaz (2011).
In the RANS simulations a k-ω SST turbulence model was
used. For the discretization of the convective flux of the
momentum and turbulence equations a QUICK and upwind
scheme were used respectively. For the boundary conditions
a uniform flow at the inlet and constant pressure at the
external boundary was applied. At the outlet, an outflow
boundary condition is prescribed with zero normal gradient
for the flow variables. For the full RANS simulations, a no-
slip boundary condition is set at the propeller blades, duct
and shaft. A rotational velocity is prescribed to the blades
and shaft, while the duct does not rotate. For open water
(steady) computations the equations are solved in the body-
fixed reference frame.
Figure 2: Example of a typical panel distribution on the
ducted propeller (Ka4-70 propeller with duct 19A).
Figure 3: Example of the grid for the full RANS
computations for propeller Ka4-70 and duct 19A.
Figure 4: Example of the RANS grid for the duct 19A
using body forces to represent the propeller action.
x
r
-1-0.500.511.5
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
An example of the grid layout for the full RANS
computations is presented in Figure 3 while the grid for the
RANS computations using body forces is shown in Figure
4. The y+-values for all grids are smaller than one with all
computations made for model scale conditions. The grid
sizes used are presented later.
3 RANS-BEM COUPLING PROCEDURE
3.1 Description
In the coupled approach the flow on propeller blade and
duct is analyzed with the BEM PROCAL. However, due to
the user generated sharp trailing geometry of the duct, an
error in the duct loading is likely to occur which may also
lead to an error in propeller blade loading. For that reason
the flow on the duct with unmodified trailing edge geometry
is analyzed with the RANS solver ReFRESCO. The
influence of the propeller blades is taken into account
through the use of body forces. The force distribution on the
blade camber surface in PROCAL is transferred from the
BEM grid to the RANS grid. In the present approach the 3-
D flow is analyzed but for open water conditions an
axisymmetric RANS solver can be used to reduce CPU
time.
The loading on the duct is likely to be different in viscous
flow simulations than in the potential flow computations.
As the loading on the duct influences the loading on the
propeller blade, the loading on the duct in the BEM needs to
be adjusted such that it is identical to the value obtained in
the RANS solver. This can be accomplished by applying
surface transpiration velocities on the duct which can be
interpreted as adding a boundary layer displacement
thickness to the duct which effectively changes the
thickness and camber of the duct. To simplify the
procedure, the variation of the boundary layer displacement
thickness with distance to the leading edge is prescribed and
is applied on the inner surface of the duct only. The value at
the duct trailing edge is then left as the only unknown. Its
value can either be prescribed by the user or it can be
obtained through an iterative procedure in which its value is
adjusted until an user specified duct force is obtained.
The resulting iterative procedure using a sequence of BEM
and RANS computations is sketched in Figure 5. In the
BEM computation the transpiration velocity on the duct is
modified until the duct force matches the value obtained
from the RANS computation. The resulting propeller force
distribution is then used to update the RANS computation.
The computations are repeated for a number of iterations
which are prescribed in advance at present. The
computational procedure starts with a BEM computation
without transpiration velocity.
Figure 5: The RANS-BEM coupling procedure for the
analysis of a ducted propeller in open water.
3.2 Applying body forces in RANS
Even though the application of body forces in the RANS
computations is rather straight forward, first results showed
a large region with flow separation on the inner surface of
the duct starting at the propeller tip for low advance ratio,
see Figure 6a. The flow separation only occurred for high
propeller loading at low advance ratio and disappeared for
lower propeller loadings. The separation was generated by
the high tip loading of the propeller which generated an
upstream directed velocity in the gap where no body force
was present. In reality a tip leakage vortex is generated in
this region but due to the axisymmetric flow in the RANS
simulations for the RANS-BEM coupling, no tip leakage
vortex can be generated and hence this flow separation is
considered a deficiency of the imposed axisymmetric flow
conditions. The separation could easily be avoided by
applying a body force in the gap region which can be
obtained from the BEM computation because the gap is also
discretized with dipole and monopole panels. The resulting
flow is shown in Figure 6b.
The separation bubble leads to a significant change in duct
loading with the duct thrust changing from , 0.117T ductK
for the situation without body forces in the gap to
, 0.173T ductK for the situation with body forces in the gap.
In the experiments a value of , 0.170T ductK was measured.
For advance ratios J= 0.5 and J= 0.8 the RANS results did
not show any influence of applying body forces in the gap
region because for these advance ratios flow separation did
not occur when no body forces were applied in the gap.
Therefore, all computations have been performed with body
forces in the gap region.
a) No bodyforces in gap
b) With bodyforces in gap
Figure 6: Influence of applying bodyforces in the gap
region for the RANS solution at J= 0.2, Shown is the non-
dimensional vorticity magnitude.
3.3 Transpiration velocity on duct
The influence of the parameter describing the duct surface
transpiration velocity, which can be interpreted as the
boundary layer displacement thickness at the duct trailing
edge, is presented first. The parameter is systematically
varied in the BEM computation and the influence on duct
radial force coefficient and propeller thrust coefficient is
presented in Figure 7. Note that the radial force has a
negative value which implies that it is directed inwards.
An increase in displacement thickness implies that the
camber on the duct is reduced as the surface transpiration is
applied on the inner surface of the duct, hence the trailing
edge is effectively moved inward. As a result, the radial
force on the duct reduces in magnitude and the duct induced
velocities also decrease. This leads to an increase of the
propeller thrust. The variation of the force with
displacement thickness is almost linear and does not change
much with advance ratio. This suggests that the proposed
procedure of prescribing the duct (radial) force through
iterating on the displacement thickness works well. Results
have shown that the approach also works for negative
values of the displacement thickness which has no physical
meaning but which simplifies the computational procedure.
The duct thrust reduces by 10% when the displacement
thickness increases by 8% of the duct length while the
radial force is reduced by 45%. Because the radial force on
the duct is much larger than the thrust force (factor seven
for the computation shown) and shows a larger sensitivity to
the displacement thickness, the radial force is used in the
coupling procedure.
4 RESULTS
4.1 Grid sensitivity and iterative convergence behaviour
For the full RANS simulations a fine mesh of about 30
Mcells has been applied. Comparison with a mesh of 55
Mcells showed differences in the forces and moments less
than 0.6% at J= 0.4. The L2 norm of the iterative
convergence error was smaller than 1.E-6.
For the 3-D RANS solution in RANS-BEM method a
detailed grid verification study has been performed for J=
0.2 and J= 0.5 with six grids varying between 200 kcells
and 11.3 Mcells. The grids with a larger number of cells
than 1M were within the asymptotic range. For the present
study a grid consisting of 2.8 Mcells has been selected
which had an estimated discretisation error of the duct
thrust less than 4%. The L2 norm of the iterative
convergence error was smaller than 1.E-6.
Grid sensitivity studies were also performed for the BEM.
The solution was not so sensitive to the number of panels
with typical variations in thrust of less than 2% if the grid is
varied with a factor of about 2.5 along one direction. For
the present calculations 60x30 panels are used on each
blade and 105x31 panels on each duct segment.
An example of the iterative convergence of the propeller
and duct forces of the RANS-BEM coupling procedure is
X/L
Z/L
-0.500.5
0.6
0.8
1
1.2
1.4w: 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
X/L
Z/L
-0.500.5
0.6
0.8
1
1.2
1.4w: 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Figure 7: Influence of the boundary layer displacement
thickness at duct trailing edge on duct radial force
coefficient Fr and propeller thrust coefficient Kt for
advance ratio J= 0.55.
d*_te/L
Kt
Fr
0 0.02 0.04 0.06 0.080.16
0.18
0.2
0.22
0.24
-0.4
-0.35
-0.3
-0.25
-0.2
Fr
Kt
shown in Figure 8. Our initial procedure is to prescribe the
number of iterations in RANS, 500 for the present test-case,
after which a BEM solution is generated with prescribed
radial force followed by an update of the body forces in
RANS. An oscillatory convergence is observed and 12
RANS-BEM coupling steps have been applied after which
the change in duct forces is smaller than 0.3% and the
change in propeller thrust is even smaller. For higher
advance ratios less number of coupling steps are needed. In
each BEM computation the radial force is prescribed and it
is seen that when the radial (and thrust) force is, in absolute
sense, too high compared to the value at convergence, the
propeller thrust becomes too small and vice versa. The
coupling procedure still needs to be optimized to reduce the
CPU time.
4.2 Full BEM results
To evaluate the applicability of a BEM code for ducted
propellers, duct 19A was modified by changing the outer
surface such that the trailing edge was made sharp. This
duct, designated 19a-mod and shown in figure 9, was tested
at MARIN (Bosschers & van der Veeken, 2009). The
propeller diameter is 240 mm and the shaft rotation rate was
set at 900 RPM.
The open water predictions by PROCAL are compared to
the experimental data in Figure 10. A constant boundary
layer thickness of 1% of the duct length was applied for the
iterative wake alignment procedure for all advance ratios.
The propeller thrust and torque are well predicted for almost
all advance ratios but the duct thrust is significantly
overpredicted for advance ratios larger than J= 0.55. This is
most likely due to the occurrence of flow separation on the
outer surface of the duct. As a result, the unit efficiency is
also overpredicted for these advance ratios.
The PROCAL results are rather similar to the BEM results
by Baltazar et al. (2012) for this configuration.
4.3 Trailing edge flow
An important motivation for the present RANS-BEM
approach for analysis of ducted propellers is the ability to
capture the correct flow at the blunt trailing edge. However,
in the applied RANS analysis the flow is axisymmetric and
the tip leakage vortex is not present. Analysis of the full
RANS results shows that this vortex has an influence on the
flow around the trailing edge as shown in Figure 11. The
tip leakage vortex, indicated by the local increase in
vorticity, induces a change in streamlines when the vortex
passes the trailing edge. As a result, the flow now varies in
circumferential direction close to the trailing edge but
further downstream the variation is small. The
axisymmetric solution for J= 0.2, shown in Figure 12, gives
an acceptable prediction for the mean flow near the trailing
edge when compared to the full RANS results. It also
clearly shows that due to the accelerated flow on the inner
surface, the streamlines coming from inside the duct move
almost without curvature along the trailing edge whereas
the streamlines describing the flow outside the duct show
significant curvature near the trailing edge. The flow around
the trailing edge is rather similar for J= 0.2 and J= 0.5 while
for J= 0.8 a large separation bubble is present on the outer
surface of the duct.
Figure 8: Variation of the propeller and duct thrust with
iteration number as computed by RANS-BEM at J= 0.2.
After every 500 iterations, a BEM computation is made and
the body force in RANS is updated.
Figure 9: Geometry of duct 19A and 19A-mod.
Figure 10: Open water characteristics for Ka4-70, P/D=
1.0 and Duct 19A-mod.
iteration #
Kt
1000 2000 3000 4000 5000 60000.15
0.2
0.25
0.3
Prop (BEM)
Duct (RANS)
19A
19A-mod
J
Kt,
10
Kq
,E
ta
0.2 0.4 0.6 0.8
0
0.2
0.4
0.6
0.8
PROCAL
EXP.ETA
10KQ_PROP
KT_PROP
KT_DUCT
a) Theta = 0 deg.
b) Theta= 20 deg.
c) Theta= 30 deg.
d) Theta= 50 deg.
Figure 11: Streamlines near the duct trailing edge at
various positions for the full RANS results at J= 0.2, the
colour coding shows the non-dimensional vorticity
a) J= 0.2
b) J= 0.5
c) J= 0.8
Figure 12: Streamlines near the trailing edge for the RANS
results using body forces to represent the propeller action.
4.4 Open water characteristics
The open water characteristics of the RANS-BEM method
and the full RANS method for the Ka4-70 with P/D= 1.0
and Duct 19A are compared to the experimental data in
Figure 13. The experimental data is the average of two
independent measurements performed at MARIN in 2000
and 2004. The difference between the two measurements is
less than 1% relative to the value at bollard pull. These
measurement data show some differences with the
polynomial data as published in Oosterveld (1970) which
can be due to for instance the modified test set-up and
location of the dynamometer in use since the 1980’s.
The full RANS results gives a good prediction of the open
water characteristics with a mean difference to experimental
data of 1% for duct thrust (relative to value at J= 0.1), 3.5%
for propeller thrust and 2% for propeller torque. The
RANS-BEM method gives a small overprediction of the
duct thrust (about 5%) but a good prediction of propeller
thrust and torque which is only about 3% too large.
Comparison to full BEM results presented in Figure 10
x
r
-0.8-0.75-0.7-0.65-0.6-0.55-0.5-0.45-0.4-0.35-0.3
1
1.05
1.1
1.15
x
r
-0.8-0.75-0.7-0.65-0.6-0.55-0.5-0.45-0.4-0.35-0.3
1
1.05
1.1
1.15
shows that the RANS-BEM method is capable of predicting
the open water characteristics at high advance ratio where
flow separation on the outer surface occurs. In the RANS-
BEM results the duct thrust is taken from the RANS results
and the propeller thrust from the BEM.
The circumferentially averaged pressure distribution on the
duct for the PROCAL results is compared to the values of
the (axisymmetric) ReFRESCO results in Figure 14. In
general good agreement is observed for J= 0.2 and J= 0.5
(latter not shown here) with the largest differences
occurring on the inner surface downstream of the blade
leading edge. For J= 0.8 flow separation is present on the
outer surface of the duct and therefore large differences in
the pressure distribution on the outer surface are present.
The pressure distribution on the inner surface is still in good
agreement.
In the presented computations the trailing edge geometry
used in PROCAL was made sharp by modifying the aft end
of the duct geometry only. The sensitivity of the RANS-
BEM coupling to different trailing edge geometries still
needs to be investigated. For a full BEM computation this
position has a large influence on the duct loading and
therefore also on the propeller loading, see Moulijn (2015)
for example. For the proper selection of the trailing edge
position for the BEM geometry use can be made of the
streamlines aft of the trailing edge in the RANS solution as
shown in Figure 12.
The contribution of the shear stress to the duct thrust
changes only slightly with advance ratio (a factor two for
the advance ratios computed) and its value is less than 2%
of the total duct thrust at J= 0.2.
4.5 Comparison with full RANS
The results of the RANS-BEM coupling can be compared in
more detail to the results obtained from full RANS. The
variation of the axial loading with radius on the propeller
blade is shown in Figure 15 for three advance ratios.
a) J= 0.2
b) J= 0.8
Figure 14: Pressure distribution on the duct. Shown are the
ReFRESCO results of the RANS-BEM coupling and the
circumferential averaged pressure of the PROCAL results.
Figure 15: Distribution of the sectional thrust force with
radius on the blade as obtained from the full RANS
computations with ReFRESCO and the RANS-BEM
computations with ReFRESCO-PROCAL.
+++++
+
+++++
++++++++++ +++++ +++++ +++++ ++++++++++
++++++
++++++++
+++++++++++++++
+++++++
++
+++
++++
+++++++++++++++
++++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++++++++ ++++++++++++++
+
+
+
+
+
+
+
+
+++++
X/L
CP
N
0 0.2 0.4 0.6 0.8 1
-1
-0.5
0
PROCAL
ReFRESCO+
+++++++++++
+++++ +++++ +++++ +++++ +++++ ++++++++++
++++++++++++++++
+++++
+++++++++++++++
++ +++
++++
+++++
++++++
+
+++
++++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++++++++ ++++
++++++++++
+
+
+
+
+++++
++++
X/L
CP
N
0 0.2 0.4 0.6 0.8 1
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
PROCAL
ReFRESCO+
r/R
Kt
0.2 0.4 0.6 0.8 10
0.02
0.04
0.06
0.08
0.1
0.12
0.14PROCAL
ReFRESCO J= 0.2
J= 0.5
J= 0.8
Figure 13: Open water characteristics for Ka4-70 and
Duct19A.
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Kt,
10
Kq
, eta
J
EXP.
ReFRESCO-PROCAL
ReFRESCO
η
10KQ_PROP
KT_PROP
KT_DUCT
a) J= 0.2
b) J= 0.5
Figure 16: Pressure distribution on the duct at theta= 0 deg.
Shown are the full RANS results obtained with ReFRESCO
and the PROCAL results of the RANS-BEM coupling.
In general an acceptable agreement is observed showing at
most 10% difference in loading between the two methods.
The overall variation is rather well predicted but especially
at J= 0.2 differences are observed in the tip region. This is
due to the presence of the tip leakage vortex in the full
RANS simulations not captured by potential flow.
The PROCAL pressure distribution on the duct for theta= 0
deg. (a cut at the 12 o’clock position through the propeller
reference line) is compared to the pressure distribution of
the full RANS computations in Figure 16. A reasonable
agreement is observed upstream of the blade, but at the
propeller tip and downstream the blade the tip leakage
vortex captured by RANS induces a low pressure region on
the duct. As this vortex is not modeled by BEM, the low
pressure regions are not present in the PROCAL pressure
distribution.
The slightly different location of the jump in pressure at the
blade location is related to the different tip geometries used
in RANS and BEM. In the BEM the blade tip is extended to
a) J= 0.2
b) J= 0.5
c) J= 0.8
Figure 17: Pressure distribution on the blade at 0.7R.
Shown are the full RANS results obtained with ReFRESCO
and the PROCAL results of the RANS-BEM coupling.
the duct with a gap section of finite thickness whereas in the
RANS the blade tip is rounded and the gap is open.
++++
++
+
+++
+++
+
+
+
++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++ +++ ++ ++ ++++++++++++++++++++
+++
++
+++
++
+
+
++
++
++++++++++++++++
++
+++
+
++++
+++ +++++++++++++++++++++++++++++++++++
+++++
+++++++++
+
+
++
+++++++
+
+
+++
+++++
+
+
+
+
++++
+
++
+
++
+
+
+
+
+
+
+
+
+
+
+
X/L
CP
N
0 0.2 0.4 0.6 0.8 1
-2.2
-2
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
PROCAL
ReFRESCO+
++++
++++
+++
+
+
++
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++
+++++
+
+++
++
++
++ +++++++++++++++++
++++
++
+++
++
+
+
++
++
+++++++++++++
+
+
++
+
++++++++
+++ +++++++++++++++++++++++++++++++++++
+++++
+++++
+
+
+
+
+
+++++++
+
+
+
++
+++++
+++
+
++++
+
++
+
++
++
+ +
+
+
+
+
+
+
+
X/L
CP
N
0 0.2 0.4 0.6 0.8 1
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
PROCAL
ReFRESCO+
++++
+++
++
+++++ +++++++++++
+++++++++ ++++ +++++++
++ +++++ +++++++++++++ ++++++ ++++++
+++++++
++
++
++++++++++++++++++++
++++
+++++
+++++++++++
+
+++
+++
++
+++++
++
+
+
+
+
+
++++
+
+++++
+
+++
++
+++
+
+++++++ ++
+
+
++++++++
+++++++++
++++
+++
+++++
+++
+
++ ++ ++ ++ ++++ ++ ++++++++ +++ +++++++ +++++ +++ ++ ++ ++++ ++ ++ + ++ + ++ ++ ++ + +++ ++ ++ ++++++++
+
+
++
++++++++++++
++
+
++
++
++++
++++
+
++++ +
+++
+
++
+
++
++
+
+
++++++
++
+
++
++++++
++
+
+
+
++
+++++++
x/c
Cp
n
0 0.2 0.4 0.6 0.8 1
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
PROCAL
ReFRESCO+
++++
+++
+
+
+++++ +++++++++++
+++++++++
+++++++++
++++ +++++
+++++++++++++ ++++++ ++++++
+++++++
++
++
++++++++++++++++++++
++++
++++
+
+++++++++++
+
+++
+++
++++
+++
++
++
++
+++++
++++++
+
++++
+
+++
++
++++
++
+
+ +
+
++++++++
+++++++++
++++++++++++
++++
++ ++ ++ ++ ++++ ++ ++++++++ +++ +++++++ +++++ +++ ++ ++ ++++ ++ ++ + ++ + ++ ++ ++ + +++ ++ ++ ++++
++++
+ +++++++++++++++
++
+
+
++++
++++ +++
++ +
+
+++ ++
+++ +++ ++
+++
++
+++++++ +++ +++++++++
+
+
+
+++++++
x/c
Cp
n
0 0.2 0.4 0.6 0.8 1
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
PROCAL
ReFRESCO+
+++++++
+
+++++ +++++++++++
++++
+++++
++++
+++++++
++ ++++++++++++
++++++++++++ ++++++
+++++++
++
++
+++++++++++++++++++++++++++++++
+++
+++
++
++
+++
++
+
+
+
+
+
++++
+
+++++
+
+++
++
+++
+
+
+
+++
++
+
+
++
++++
++++
++++
+++++
++++
++
+
++++++++ ++ ++ ++ ++++ ++ ++++++++ +++ +++
++++ +++++ +++ ++ ++ ++++ ++ ++ + ++ + ++ ++ ++ + +++ ++ ++ ++++
+
+++
+
+
++
+++++++++++++++
+
+
++++ +
+
++
+
++
+
++++
++
++
+
++
+
++
++++
+
+
++
+
+
+
+++++++
x/c
Cp
n
0 0.2 0.4 0.6 0.8 1
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
PROCAL
ReFRESCO+
The PROCAL pressure distributions on the blade at 0.7R
are compared to the full RANS results in Figure 17. For J=
0.5 and J= 0.8 good agreement is obtained except near the
trailing edge which is due to a difference in geometry: the
blunt trailing edge used in RANS was made sharp for the
BEM. At J= 0.2 PROCAL predicts a pressure peak at the
leading edge that is not present in the ReFRESCO
calculation suggesting a difference in induction velocities.
In general the pressure distribution at lower radii are in very
good agreement while the pressure distribution at higher
radii show somewhat larger differences than at 0.7R.
5 CONCLUDING REMARKS
An iterative procedure to analyze ducted propellers in open
water conditions using a combination of a RANS solver and
a boundary element method (BEM) has been developed and
tested. The advantage of the approach is that flow
separation occurring at the blunt trailing edge and on the
outer surface of the duct at high advance ratio can be
captured by the RANS solver while the flow on the
propeller can still be predicted by a BEM. The iterative
procedure was shown to converge and to give an acceptable
prediction of the open water characteristics. Aspects to be
further investigated are the influence of alternative sharp
trailing edges for the duct and propeller as used in the BEM
while the method also needs to be tested for other propeller
and duct geometries. Comparison with full RANS results
shows that the radial loading distribution is well predicted
by BEM, but the absence of the tip leakage vortex leads to a
different flow behavior in the tip region.
ACKNOWLEDGMENTS Support for the development of the RANS-BEM coupling
was provided by the Cooperative Research Ships
organization, www.crships.org. The full RANS simulations
were made in the EU FP7-Streamline project. The authors
like to thank Prof. H.W.M. Hoeijmakers of the University
of Twente for the stimulating discussions.
REFERENCES
Baltazar, J., Falcao de Campos, J.A.C., and Bosschers, J.,
“Open-Water Thrust and Torque Predictions of a Ducted
Propeller System With a Panel Method”, International
Journal of Rotating Machinery, Volume 2012
Baltazar, J., Rijpkema, D., Falcao de Campos, J.A.C.,
Bosschers, J., “A Comparison of Panel Method and
RANS Calculations for a Ducted Propeller System in
Open-Water”. Third International Symposium on Marine
Propellers SMP’13, Launceston, Tasmania, Australia,
May 2013.
Bosschers, J., Vaz, G., Starke A.R. and van Wijngaarden,
E., “Computational analysis of propeller sheet cavitation
and propeller-ship interaction”. RINA conference
“MARINE CFD2008”, Southampton, UK, 26-27 March
2008.
Bosschers, J., van der Veeken, R., “Open Water Tests for
Propeller Ka4-70 and Duct 19A with a Sharp Trailing
Edge”. MARIN Report No. 22457-2-VT, 2009
Kerwin, J.E., Kinnas, S.A., Lee, J-T., Shih, W-Z., “A
Surface Panel method for the Hydrodynamic Analysis of
Ducted Propellers”, SNAME Transactions Vol. 95,
1987.
Klaij, C. M., and Vuik, C., “Simple-type Preconditioners for
Cell-centered, Collocated Finite Volume Discretization
of Incompressible Reynolds-averaged Navier-Stokes
Equations”, International Journal for Numerical
Methods in Fluids, 71(7), pp. 830–849. 2013.
Kuiper, G., “The Wageningen Propeller Series”, MARIN
Publication 92-001, 1992.
Moulijn, J. “Application of Various Computational
Methods to Predict the Performance and Cavitation of
Ducted Propellers”, Fourth International Symposium on
Marine Propulsors SMP’15, Austin, Texas, USA, 2015.
Oosterveld, M.W.C., “Wake Adapted Ducted Propellers”,
MARIN publication No. 345, Wageningen, The
Netherlands, 1970.
Rijpkema D., and Vaz G., “Viscous flow computations on
propulsors: verification, validation and scale effects”, In
Proceedings of RINA conference MARIN CFD2011,
2011.
Rijpkema, D., Starke, B., and Bosschers, J., “Numerical
simulation of propeller-hull interaction and
determination of the effective wake field using a hybrid
RANS-BEM approach”. Third International Symposium
on Marine Propulsors, SMP’13, Launceston, Tasmania,
Australia, 2013
Starke, B., and Bosschers, J., “Analysis of scale effects in
ship powering performance using a hybrid RANS-BEM
approach”. 29th Symposium on Naval Hydrodynamics,
Gothenburg, Sweden, August 2012.
Vaz, G. and Bosschers, J., “Modelling three dimensional
sheet cavitation on marine propellers using a boundary
element method”. Sixth International Symposium on
Cavitation CAV2006, Wageningen, The Netherlands.
Vaz, G., Jaouen, F., and Hoekstra, M., “Free-surface viscous
flow computations. Validation of URANS code
FRESCO”, In Proceedings of OMAE2009, May 31–
June 5, Hawaii, USA. 2009.
DISCUSSION
Question from Anirban Bhattacharyya
Is there a difference in the nature and extent of separation
zone outside the duct near the leading edge using fully
RANS and RANS-BEM coupling methods (typically for
high advance coefficients)?
Authors’ closure
Thank you for your question. There is indeed a difference in
the separation zone for the two solutions as illustrated in
Figure I: In the RANS-BEM coupling method the
separation zone is axisymmetric and a single vortex is
present while in the full RANS solution the separation zone
is varying in azimuthal direction and consists of multiple
vortices. The corresponding pressure distributions on the
duct is presented in Figure II. Despite these differences the
loading on the duct is in close agreement.
Question from Ye Tian
It would be worthwhile to run a fully 3D Euler simulation
for a ducted propeller system to see if the boundary layer of
the inner surface of the duct has so significant effects shown
in the paper. A k-ϵ model may reduce the undesired flow
separation.
Author’s closure
Thank you for your comments. The paper shows how a
prescribed boundary layer displacement thickness near the
duct trailing edge in the BEM influences the duct loading
and thereby the propeller loading. In the RANS-BEM
coupling procedure it is used as a mechanism to prescribe
the duct loading in BEM which is obtained from the RANS
solution. This is necessary as the duct trailing edge has been
modified for the BEM and the flow separation at the round
duct trailing edge is not captured by BEM. An Euler
solution does also not capture this flow separation and we
therefore expect that it does not provide any additional
information in this respect. To study the propeller tip
loading and tip leakage vortex in absence of a boundary
layer on the inner surface of the duct we would prefer to
apply a slip boundary condition on the duct surface in our
RANS method. For our calculations we used the k-ω SST
turbulence model as we expect it to be more accurate in
predicting duct forces and in capturing flow separation at
the duct trailing edge and for low advance ratio at the outer
surface of the duct. A sensitivity study on the influence of
the turbulence model on the various separation regions has
not been performed but may be topic of future studies.
a) Axisymmetric RANS
b) Full RANS, slice at theta= 0
Figure I: Comparison of streamline patterns on the duct for
J= 0.8 between axisymmetric RANS and full RANS. Colour
indicates the vorticity magnitude.
Figure II: Comparison of pressure distributions on the duct
for J= 0.8 between axisymmetric RANS and full RANS
++++++
++++++++++
+++++ +++++ +++++ +++++ ++++++++++
+++++++++++++++++
+++++++++++++++++++
+++++
++++
+++++
+++++
+
+
+++
++++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++ +++++++++++ ++++
++++++++++
+
+
+
+
+
++++
++++
X/L
CP
N
0 0.2 0.4 0.6 0.8 1
-1.5
-1
-0.5
0
0.5
1
RANS, axisymmetric
RANS, Theta= 0 deg+
top related