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OCR for page 744
Scale Effects on Ducted Propellers
M. AbJel-Maksoud, H.-~. Heinke
(Potsdam Mode} Basin, SVA)
ABSTRACT
For certain applications, ducted propellers have
advantages in comparison to free running propellers,
especially in case of high loading coefficients or
strong in-homogeneity of the inflow. In both cases,
there is a strong effect of the viscosity on the
propeller performance. An accurate estimation of
the Reynolds number effect on the performance of
propellers is very important for extrapolation of the
model results to full-scale.
Results of numerical calculations for a ducted
propeller are presented for model and full-scale. The
numerical full-scale results show that the flow
velocity in the nozzle is comparatively higher than
in model scale. This fact leads to an increase of the
nozzle thrust and to a reduction of the thrust and of
the torque of the propeller. The influence of the
Reynolds number on the torque of a ducted
propeller is consequently higher than on a free
running propeller. That may be an explanation for
often observed too light loaded propellers in full-
scale which were designed on the basis of test
results in model scale.
INTRODUCTION
In fact, long experience and well established
methods are available for considering the scale
effect on the characteristic of free running
propellers, e.g. the ITTC 1978 method. Increasing
the Reynolds number leads to an increase of the
thrust coefficient and to a decrease of the torque
coefficient. The effect of the Reynolds number on
the torque coefficient is much higher than on the
thrust coefficient. The reason is that friction forces
have more influence on the torque than on the
thrust. The estimation of the scale effects for ducted
propellers is not a straightforward subject. The
nozzle is a part of the propulsion system, which may
produce more thrust than the propeller at bollard
pull condition. The strong interaction between the
nozzle and the propeller is dependent on the
Reynolds number. The inflow of the propeller is
directly effected by the form of the nozzle and vice
versa.
The report of the specialist committee for
unconventional propulsors of the 22n~ ITTC focused
the problem of the extrapolation of powering
performance of ducted propellers, ITTC (1999~. The
three methods presented by Stierman (1984) were
discussed. In the first one the nozzle is considered as
an appendage of the hull, in the second one as a part
of the propulsion system. The last method considers
the interaction between three objects: ship, nozzle
and propeller.
The investigation of a hull fitted with a nozzle alone
(without propeller) as the case in the first and the
third method, will lead to limited informative
results. The flow around the propeller or the nozzle
alone differs totally from the flow around the ducted
propeller system. Therefore the drawback in the first
and the third method is the weak consideration of
the interaction between the nozzle and the propeller.
In the second method of Stierman (1984) the
thrust of the nozzle and of the propeller are scaled
separately. The extrapolation of the propeller
characteristics is carried out using the ITTC 1978
method. The resistance of the nozzle is corrected by
employing a flat plate friction line or a formula
according to Hoerner. The resistance of the nozzle
can be measured at zero thrust of the propeller. The
drawback of this method is that the flow around the
nozzle is strongly dependent on the thrust loading
coefficient of the propeller. The consideration of the
information on the flow around the nozzle at a very
low propeller loading coefficient in order to correct
the nozzle thrust at a high loading condition will
lead to more inaccuracies in the results. At high
loading conditions the ratio of the friction resistance
of the nozzle to the nozzle thrust is very small. This
means that this correction will have nearly no
influence on the nozzle thrust.
It is known in the practice that in some cases
full-scale ducted propellers are not able to absorb
the available torque at the given number of
revolutions. This means that full-scale propellers are
loaded lightly than expected according to model test
results. The variation of the thrust-torque ratio
between model and full-scale shows a certain
influence of the Reynolds number on the
performance of the ducted propeller, which cannot
be covered or explained by the available
extrapolation methods. The weak consideration of
the scale effect on the nozzle performance and the
interaction parameter between nozzle and propeller
may be responsible for the discrepancies between
model and full-scale results.
The aim of the presented study is the
investigation of the flow at different Reynolds
numbers and loading conditions. This is helpful to
have a better understanding of the flow behaviour
on ducted propellers and to improve the accuracy of
the extrapolation methods.
The experimental and numerical investigations
for improving the performance of ducted propellers
have been intensified during the recent years. The
main aim of this research work was the optimisation
of the nozzle and the propeller. Achieving a high
OCR for page 745
total thrust coefficient under the bollard pull
condition is often an important criterion for the
operation of ducted propellers. In model scale, the
results of the open water tests are adequate to
compare different designs. The extrapolation of the
measured results from model to full-scale is not a
straightforward task, because the results are directly
effected by the employed assumptions of the
Reynolds number effects.
Viscous flow methods can be applied to
overcome this drawback and to have more detailed
information on the viscous flow through and around
ducted propellers in model and full-scale. The
comparison of the numerical results for model and
full-scale is very helpful for the analysis of scale
effects.
The examination of scale effects requires a high
quality of the numerical results. Therefore many
investigations have been carried out to study the
effect of different boundary conditions, the size of
the calculation domain and the topology of the
numerical grid on the numerical results.
NUMERICAL CALCULATION
The calculation of the viscous flow on a ducted
propeller is more complicated than that on a free
running propeller. Convergence problems may take
place at high thrust loading coefficients. The
convergence problems are raised due to the extreme
ratio between the inflow velocity and the
circumferential speed as well as the high difference
between the velocity at the inlet of the calculation
domain and the inflow velocity of the propeller.
While the first one is independent on the simulation
time tS the inflow velocity to the propeller is
simulation time dependent. The ratio between the
nozzle and propeller thrust and thus the amount of
the total thrust of the ducted propeller system and
the torque of the propeller changes significantly at
the beginning of the simulation, see Figure 1. The
high circumferential speed of the propeller and the
flow in the gap between the blade tip and nozzle are
also problematic for the convergence behaviour of
the calculation.
In case of a ducted propeller working in a
homogeneous flow, the calculation domain is
periodic in space and the calculation may be
restricted to one propeller blade. The interaction
with other blades can be considered by a periodic
boundary condition. In this case, the calculation
domain is divided into a stationary part and a
rotating part. The last one contains the propeller
region of the numerical grid. A Cartesian co-ordinate
system is applied to the stationary part. The flow
around the propeller is calculated in a rotating co-
ordinate system. A sliding interface is defined
between the rotating and the fixed numerical grid.
The RAN S equations in a rotating co-ordinate
system involve additional terms for the centrifugal
and coriolis forces (Abdel-Maksoud, Menter and
Wuttke 1998~. The velocity vector in the inertial
system Ci can be divided into a velocity vector in
the rotating system Wi and the velocity vector due to
the rotation of the system Ui as follows:
Ci = Wi + Ui
(1)
Capital letters refer to time averaged variables. The
speed of rotation is defined as:
Ui = eijkojxk
(2)
In this equation the permutation tensor eikk is used
i+ 1 for ijk cyclic,
eijk = ~ - 1 for ijk anticyclic,
~ 0 for ijk all other combinations.
The equation for the conservation of mass reads:
P+~j)=o
at dXj
The momentum equations in a rotating system are:
8(tij + pwjwj )
_ .
0(P~) 8(PWjCi)
+ _
at dXj Hi AXE
Pe;jk ~ j Ck
(3)
(4)
(5)
This form of the equations is optimal for the
numerical simulation of flows with strong relative
rotation between the co-ordinate system and the
fluid. The overbar refers to time averages of the
turbulent variables. The viscous stress tensor is:
[ij=_~0Wi +0Wj]
(6)
The standard k-e model in combination with wall
function or the SST model can be applied to
consider the effects of turbulence on the flow. The
SST model combines the k-e and k-m models. For
the free stream region the k-e model is used and for
the near wall flow region the k-co model is applied,
(Menter 1994~. The strong variation of the local
velocity distribution on the duct and on the propeller
leads to strong fluctuations of velocity near the wall
region. The treatment of the boundary conditions
near the wall must be able to handle this problem
without losses of robustness or accuracy of the
numerical solution. The local tangential velocity
component UT at the first node of the numerical grid
and the distance of the first node from the wall An
are used to define the dimensionless distance from
the wall y + as follows:
2
OCR for page 746
p ton UT
y =-
For the application of the logarithmic wall function
the y+ value should be higher than 11. Due to the
strong variation of the velocity near the wall the
applied numerical method must be able to handle
small y+values. This problem can be solved by
applying the scalable wall fi~nctinn technolo~v
(Grobans and Menter, 1998~. Another way to
overcome the problem is to switch between the k-m
model at small y+ values and the wall function at
high values of it.
The CFX-TASCflow solution method is applied
at the Potsdam Model Basin SVA, (Abdel-Maksoud
and Heinke, 2000~. The numerical solution is based
on the conservative finite volume method, (Raw,
1995~. The code has been optimised and intensively
tested for different applications such as a propeller
in uniform flow and a ship with rotating propeller
flow, (Abdel-Maksoud, Rieck and Menter, 2000~.
This work was part of long-term co-operative
research activities between the Potsdam Model
Basin and AEA Technology Otterfing GmbH. The
German Ministry for Education and Research kindly
sponsored the research projects.
The numerical method includes fully
conservative stage capabilities to simulate the
interaction of the propeller and the Droculsion
system, (Menter, Abdel-Maksoud and Galpin,
1998~. The discretisation in space is based on a
block-structured finite volume grid around the duct
and the blade of the propeller. The faces of the
control volumes at the interface between the rotating
and the stationary frame can be non-matching. The
applied code is able to handle non-overlapping non-
matching grid interfaces.
EXAMINATION OF THE BOUNDARY
CONDITIONS
turbulence models and/or dimensions of the
calculation domain for the thrust loading coefficient
CTh = 1 COO of the ducted propeller system are shown
in Table 1. The evaluation of the numerical results
of the different cases is given in Abdel-Maksoud
(2000~. The results of the study show that for CTh =
1000 a certain dimension of the calculation domain
should be maintained to avoid any influence on the
numerical results. The dimensions are given as a
ratio of the propeller diameter D. The position of the
inflow plane should be located at 87 D, the outflow
plane at 130.5 D. The diameter of the calculation
domain should be at least 70 D.
The comparison between the k-£ and SST
turbulence model shows that better results can be
achieved by employing the SST model in particular
for a separated flow. which is the case at a high
thrust loading coefficient. The numerical grid of the
fifth case was optimised to achieve the requirements
of the SST model. The numerical results of the fifth
case show a good agreement with the measured
coefficients of the ducted propeller system, see
Table 1.
NUMERICAL INVESTIGATIONS
The numerical investigations were carried out for
one propeller geometry and one nozzle form. The
geometry of the Wageningen 1 9A nozzle and
Wageningen KA 5-75 propeller were selected for
the investigations. The computations were carried
out for four propeller diameters (D = DM= 0.201 m
and D = DS= 1.005, 2.01, 4.02 m) and four different
thrust loading coefficients (CTh~ 4.25, 8.5, 85 and
850~. The data of the propeller and nozzle are given
in the Tables 2 and 3 for the diameter DM= 0.201 m.
In all numerical calculations the SST turbulence
model was applied. The numerical grid in the near
wall region was modified for each Reynolds number
in order to improve the distribution of grid points in
the boundary layer. The number of grid nodes and
topology of the grid were kept constant during the
computation. The number of nodes of the applied
grid for one propeller blade was 821,718. The
multiblock grid consisted of 26 blocks. Figure 2
shows the numerical grid on the nozzle and the
geometry of the investigated configuration.
The impact of boundary and initial conditions and
the local optimization of the numerical grid on the
results of the calculation have been studied on a
ducted propeller system, (Abdel-Maksoud 2000~. A
3D CAD model was applied to generate the
numerical grid. The CAD model contained the
nozzle and propeller geometry without
simplification. The gap between the blade tip and
the cylindrical part of the nozzle was considered.
The numerical calculation was executed with two
numerical grids. Each consisted of 25 blocks. The
first one contained 320,000 nodes for one propeller
blade and the second one twice as much. Not only
the resolution of the numerical grid was varied but
also its topology. A simulation period of approx. 30
seconds was applied to all calculations.
The boundary conditions of the calculation have
been studied for various thrust loading coefficients.
The results of five calculations with different
OPEN WATER CHARACTERISTICS
Figure 3 shows a comparison of the coefficients of
the propeller KA 5-75 working in the nozzle Wag.
l9A, calculated with CFX-TASCflow and with the
polynomial coefficients of Wageningen PSP version
1.02, (Kuiper, 1992~.
The agreement between the coefficients of the
numerical calculations and the polynomial
coefficients from MARIN is good. The numerical
results confirm that CFD calculations with ducted
propellers are possible for high thrust loading
coefficients (CTh < 1000) and also for reversed
3
OCR for page 747
direction of rotation of the propeller (the ducted
propeller is working backwards).
The knowledge acquired in the systematic
investigations of the boundary conditions, the
optimization of the numerical grid, the analyses of
calculated and measured characteristics of ducted
propellers and the study of local velocity fields was
very important to achieve accurate results for the
calculation of ducted propellers.
FLOW DETAILS
The velocity vectors for each thrust loading
coefficient and scale ratio are shown in Figures 4 to
19. The velocity vectors are presented on different
selected regions on the ducted propeller such as: on
the outside wall of the nozzle profile, near the
leading and trailing edges of the nozzle and in the
region of the gap between the propeller blade and
nozzle.
The results for CTh= 4.25 are shown in Figures 4
to 7. The velocity distribution on the outside wall of
the nozzle is presented in Figure 4. In model scale
(JAM= 0.201 m) the velocity vectors have the
expected character of low Reynolds number velocity
profiles with a thick boundary layer in comparison
to scale ratios 2= 4, 2 and 1. Figure 5 shows the
velocity vectors near the leading edge of the nozzle,
as it is expected, a separation may take place near
the leading edge of the nozzle of the model at a low
thrust coefficient. This separation region disappears
with increasing the Reynolds number of the
investigated ducted propeller see Figure 5.
Figure 6 shows the velocity vectors near the
trailing edge of the nozzle. It can be seen that the
thickness of the boundary layer and the size of the
separation region behind the nozzle decrease at high
Reynolds numbers. The velocity vectors in the tip
region of the blade are shown in Figure 7. The tip
vortex is directly effected by the thickness of the
boundary layer on the inside wall of the nozzle. The
relatively low velocity in the boundary layer in
model scale increases the thrust loading of the
propeller blade near the tip. Therefore, it should be
expected that the influence of the Reynolds number
on the behaviour of the tip vortex of a ducted
propeller and of a free running one is completely
different.
The results for CTh= 8.5 are presented in Figures
8 to 11. The comparison between velocity vectors
on the outside wall of the nozzle at different
Reynolds numbers shows the relatively higher
thickness of the boundary layer in model scale,
Figure 8. It can be seen that the acceleration of the
flow on the leading edge of the nozzle increases
with increasing the Reynolds number. Due to the
increase in the thrust loading the axial velocity
component outside the nozzle at CTh= 8.5 (Figures 8
and 9) is smaller than at CTh= 4.25 (Figures 4 and
51.
Figure 10 shows the velocity vectors near the
trailing edge of the nozzle at CTh = 8.5. The
separation point moves to the trailing edge and the
size of the separation region behind the nozzle
decreases with increasing the Reynolds number. The
influence of the Reynolds number on the behaviour
of the tip vortex can be seen in Figure 11. The
difference in the tip vortex between model and full-
scale will be smaller with increasing the thrust
loading. The reason is that with increasing the thrust
loading the thickness of the boundary layer on the
inside wall of the nozzle decreases due to the higher
acceleration of the flow through the nozzle. This
effect reduces the thrust loading of the tip of the
propeller blades.
The results for CTh= 85 and 850 are shown in
Figures 12 to 19. With increasing the thrust loading
coefficient the location of the stagnation point
moves on the outside wall of the nozzle in the
direction of the trailing edge. The acceleration of the
flow on the nozzle also increases at high Reynolds
numbers, which means that more pressure reduction
on the nozzle and more nozzle thrust should be
expected. Figures 14 and 18 show that the
separation region behind the nozzle is reduced by
increasing the thrust loading, compare the
corresponding results at CTh= 4.25 and 8.5.
REYNOLDS NUMBER EFFECTS
The differences of the flow behaviour around the
ducted propeller at the different scales have a strong
influence on the performance characteristic of the
propeller and nozzle.
Figure 20 shows the calculated changes of the
propeller and nozzle coefficients due to the
Reynolds number effect. The coefficients KTPS, KQS
and KTNS for the propeller diameters DS= 1.005,
2.01 and 4.02 m are given in relation to the
coefficients KTPM, KQM and KTNM for the propeller
diameters DM= 0.201 m.
The thrust of the nozzle is increasing with the rising
of the Reynolds number (~KTNS/KTNM= 1.03 - 1.10)
for the investigated thrust loading coefficients. The
change in the nozzle thrust coefficients depends on
the difference in Reynolds number and the flow
around the nozzle, characterized by the thrust
loading coefficient. The Reynolds number effect on
the nozzle thrust is stronger for low thrust loading
coefficients.
The thrust coefficients of the propeller are
decreasing due to the Reynolds number effect
(KTPS/KTPM= 0.95 - 0.995~. The torque coefficients
of the propeller are decreasing distinctively with the
increasing of the Reynolds number (KQVKQM= 0.93
- 0.981. The influence of the thrust loading
coefficients on the propeller torque and thrust
coefficients is limited in the range of 4.25 < CTh <
850.
The- decrease of the propeller thrust and torque
coefficients is effected by the increase of the flow
velocity through the nozzle due to the higher
efficiency of the nozzle at full-scale Reynolds
numbers. The torque of the propeller is additionally
4
OCR for page 748
reduced due to the lower friction on the blades at
higher Reynolds numbers. Therefore, the effect of
the Reynolds number on the torque of the ducted
propeller is stronger in comparison with a free
running one. The tendency of a reduction of the
propeller thrust at higher Reynolds numbers should
also be taken into account.
The changing of the characteristic of the ducted
propeller due to the Reynolds number depends on
the propeller geometry (blade line, pitch and camber
distribution) and the nozzle profile. The results in
the Figure 20 can only demonstrate the trend and the
magnitude of the Reynolds number effects for the
ducted propeller DP 215- 1345.
CONCLUSION
The scale effect on a ducted propeller is a
complicated subject due to the interaction between
the nozzle and the propeller. The numerical results
confirm that CFD methods are very helpful tools for
support the extrapolation of the model test results to
full-scale ones.
The Reynolds number effect on the characteristic of
ducted propellers can be sumrnarised as follows:
- high reduction of the propeller torque
coefficient,
reduction of the propeller thrust coefficient,
increase of the nozzle thrust coefficient,
nearly unchanged total thrust coefficient.
Although the calculated results for full-scale agree
with the observed tendencies in full-scale tests,
more research work is needed to validate it.
ACKNOWLEDGEMENTS
The authors thank the German Ministry for
Education and Research for sponsoring their
research work on application of CFD methods on
ducted propellers. The authors also thank Mr.
Pierzynski and Mr. Lubke for their help by carrying
out the numerical computations.
REFERENCES
Abdel-Maksoud, M.,
Menter, F. R., Wuttke, H.,
"Viscous Flow Simulations for Conventional and
High Skew Marine Propellers", Ship Technology
Research, Vol. 45, No. 2, 1998.
Abdel-Maksoud, M., "Convergence Study of
Viscous Flow Computations Around a High Loaded
Nozzle Propeller", Numerical Towing Tank
Symposium NuTTS 2000, Tjarno, Sweden, 2000.
Abdel-Maksoud, M., Heinke, H.-J., "Investigation
of Viscous flow on modern Propulsion Systems",
95. Annual General Meeting, Schiffbautechnische
Gesellschaft, Hamburg,, 2000 (in German).
AbJel-Maksoud, M., Rieck, K., Menter, F. R.,
"Unsteady Numerical Investigation of the Turbulent
Flow Around The Container Ship Model (KCS)
with and without Propeller", Gothenburg 2000, A
Workshop on Numerical Ship Hydrodynamics,
Gothenburg, Sweden, 2000.
Grotjans,H., Menter,F. R., "Wall Functions for
General Application CFD codes", ECCOMAS 98,
Fourth European Computational Fluid Dynamics
Conference, Athens, 1998.
ITTC "22 International Towing Tank
Conference", Proceedings volume II, Seoul, Korea
& Shanghai, China, 1999.
Kuiper, G., "The Wageningen Propeller Series",
MARIN Publication 92-001, May 1992
Menter, F. R., "Two-equation Eddy-Viscosity
Turbulence Models for Engineering Applications",
AIAA-Journal, Vol. 32, 1994.
Menter, F. R., Abdel-Maksoud, M., Galpin, P.,
"Numerical and Modelling Aspects of Flow
Simulations in Rotating Machines", Proceeding of
FED'98, FED SM 98-5002, ASME,, 1998.
Raw,M. J., "A Coupled Algebraic Multigrid
Method for the 3D Navier-Stokes Equations in Fast
Solvers for the Flow Problems", ed. W.
Hackebusch, G. Wittum, Notes on Numerical Fluid
Mechanics, Vol. 49, 1995.
Stierman, E.J., "Extrapolation Methods for Ships
with Ducted Propeller", International Shipbuilding
Progress, Vol. 31, No. 356, 1984.
5
OCR for page 749
Nomenclature
Ci [ms~ l
CTh
CTP
D [mJ
LD [ml
eijk
i
i
k
velocity vector in the inertial
system
thrust loading coefficient
thrust loading coefficient of the
propeller
propeller diameter
diameter of calculation domain
permutation tensor
index refer to the Cartesian
co-ordinate direction (i)
index refer to the Cartesian
co-ordinate direction G;
index refer to the Cartesian
co-ordinate direction (if
torque coefficient
thrust coefficient of the nozzle
propeller thrust coefficient
total thrust coefficient
number of revolutions
[_]
I]
I]
I]
[s I]
[Pa] pressure
[Nm] torque of the propeller
[s] time
[N] thrust of the propeller
Table 1: Influence of the applied boundary conditions on the
.
Test case
Propeller thrust coefficient KTP
Torque coefficient 10KQ
Nozzle thrust coefficient ~ TV
Totalthrust coefficient Ken
Ratio KTP/KQ
Ratio K~KQ
Ratio KTN/KTP
Thrust loading coefficient C77,
Diameter of the grid Dca/c/D
Location of inflow plane x/D .
Location of outflow plane x/D
Turbulence model
Table 2: Data of the propeller P 1345 (\ = 20)
Type
Diameter
Pitch ratio
Blade area ratio
Hub diameter ratio
Number of blades
Direction of rotation
TN
Is
TT
UT
Ui
[N]
[s]
[N]
[ms~l]
[ms~l]
thrust of the nozzle
simulation time
total thrust
tangential velocity at the first node
of the wall
velocity vector due to the rotation
of the co-ordinate system
[ms~l] inflow velocity
[ms~i] velocity vector in the
rotating system
[m] spatial co-ordinates
[-] dimensionless distance from the
wall
[ - ] scale
,u [kqm~~s~~] molecular viscosity of the fluid
p [kqm~3] density
~ [Nm~2] viscous stress sensor
Hi [rads~i]
vector of system rotation
model
S full-scale
calculated coefficients of a ducted propeller
1 1 2
0.186 0.229
0.363 0.387
0.084 0.208
0.271 0.437
5.127 5.925
7.450 11.289
0.453 0.905
621 1004
4
3.5 3.5
6.5 22
k-e k-£
Wageningen KA 5-75
D [m]: 0.201
P/D [- ]: 1.1867
AE/Ao [ - ]: 0.750
d~D [- ]: 0.1813
Z [-]: 5
right handed
6
.
3 4
0.243 0.238
0.372 0.365
0.214 0.211
0.457 0.449
6.539 6.537
12.304 12.323
0.882 0.885
1050 1032
. 90 90
87 87
130.5 130.5
_ k-£ SST
5
0.225
0.381
0.216
0.441
5.896
11.545
0.958
1012
70
87
130.5
SST
Table 3: Data of the nozzle D 215 (X = 20)
Type Wageningen 19A
Nozzle length LD [m]:
Diameter at propeller location Di [m]:
Diameter at the entrance
cross-section
Diameter at the leaving
cross-section
Radius at the entrance edge
Radius at the leaving edge
Propeller position
Experiment |
0.222 i
0.373
0.215
0.437
5.960
.718
0.966
002
0.10036
0.203
De [m]
Da [m]
re [m]
ra [m]
xp/LD [ ~ ]
0.2395
0.2118
2.8
1.9
0.5
OCR for page 750
0.50
0.40
0.30
0.20
0.10
0.00
-0.10
-0.20
0.0
0.70 · -
0.60- -A
1`
t ~ K"
^_~
~ KTN
Proneller
0.5 1.0 1.5
~ IS
Figure 1: Variation of thrust coefficients during
the simulation time ts
0.60
0.50
0.40
0.30
0.20
0.10
o.oo
OCFD calculation
l~lpolynomial coeffidents
_ PSP Version 1.02
DP 215-1345
J = 0.60, CTh = 2.2, PJD = 1.1867
10KQ
0.80 ·
0.70
0.60
o.so
EICFD calculation
E3 polynomial coeffiaents
PSP Version 1.02
0.40-
0.20
0.10
0.00
DP 215-1345
J = 0.05, CTh = 670, P/D = 1.1867
0.30 ~; ~]
KTP 10KQ KTN KTT
_
2.0 2.5 3.
0.80
0.70
0.60
o.so
0.40
0.30
0.20
0.10
0.00
0.00
-0.10
-0.20
-0.30
-0.40
-0.50
-0.60
-0.70
-0.80
Figure 2: Numerical grid
. OCFDcalculabon
I E I polynomial coefficients
1 PSP Version 1.02
O CFD calculation
propeller KA 5-75
Q polynorial coefficients
PSP Version 1.02
propeller KA 4-70
DP 215-1345
J = 0.2242, C7N = 27, PID = 1.1867
10KQ KTN
10KQ
DP 215-1345
J = 0.05, C7N = -420 (baCkWard), P/D = 1.1867
Figure 3: Comparison of the coefficients for the ducted propeller DP 215-1345 (propeller KA 5-75,
nozzle Wag. 1 9A), numerical results and polynomial coefficients
7
OCR for page 751
[~ Dot = 0.201 m
N Rn = 3.95X105
;~9 ~~ Ds = ·.005 m
Rn = 4~42X106
:~1 m
R-= 1.25X107
Figure 4: Velocity vectors outside the nozzle, CTh= 4.25
44~ ~—
Rn = 3.53X107
DM=O.201 m
Rn = 3.95X105
· ~~~ ,,- gem N- ~
Ds = LOOS m
Rn = 442X106
ant' ''
it. :;'' k ~ ~ ~
I' ~ ~ ~ id
~ ,/ , ~
~ \; , 1,
=~A'// ~ ;/ ~
Ds = 2.01 m
Rn = 1.25X107
~ ~~ i! A, '. i.
.4 ., ~ ~ ~
:,,~,
^.~W I , ~ ~ ~ ~
//~, ,, ~
~ hi'
Figure 5: Velocity vectors on the nozzle leading edge, CTh = 4.25
8
Ds= 4.02 m
Rn = 3.53X107
OCR for page 752
Figure 6: Velocity vectors on the nozzle trailing edge, CTh= 4.25
I~ ~ 1
~ _
II If DM = O.201 m
_ ~ Rn = 3.95x105
I,
~ ~~ —
2) l Ds=1.005m
Rn = 4.42x106
1 ~ — _.
1~_
1 1 — -
~I j D5=2.01 m ~ ~ I ~ I l DS=4.02 m
_~ Rn = l 25x107 ~ ~ !— ~ Rn = 353x107
Figure 7: Velocity vectors on the propeller blade tip, CTh= 4.25
9
OCR for page 753
~ LY
~ }
D5= 1.005 m
Rn= 4.37x106
Do = 2.01 m
R.-= 1.24x107
Figure 8: Velocity vectors outside the nozzle, CTh= 8.5
; ~~ ;~ ~ 1; 0 4 07 m
Rn = 3.50x107
. ~ ._~._.~____ _ _. __~ ~.
~ ~ ~ .
r ~ I_
DM= 0.201 m
Rn = 3.91x105
,_. - t
,=l,/y,lf ~ ~ i / a:
~~ I I{/ ~ ~ ~
Life ~ ~ .
~ Z it, a N
,,, _ ~ I'- LIN ,.
~~,~w ~ <1 ~ ~ ,
~~ ~~/ ', ~
Figure 9: Velocity vectors on the nozzle leading edge, CTh= 8.5
10
D5= 1.005 m
Rn = 4.37x106
Ds=4.02 m
R-= 3.50xlO'
OCR for page 754
figure 10: Velocity vectors on the nozzle ~aiDng edge, ^= 8.5
^=~1 m
R" = 3.91~105
1 -- _
. _.
1
~=2~1 m ~
ad= 1.24~107 ;
_
.
1 - :
, it -
. _ ... . ___ _ _ ___._.__ _ _
Figure 11: Velocity vectors on the propeller blade hp. ^= 8.3
11
M
= 4.02 m
ad= 3.50~107
_ ~ ~
1 t -- ~
. . . ... .. _ ; !: ... .. ... ..... ..... ~=
OCR for page 755
~-~ ~ (~:~ = ~ -~
I ~ I] ~ ',~1 ~ ~ ,,; ~
~ I , , , , ~ ~ ~ ~ I/i S I I l ) lil//i ~ 1 , ~ ~ ~ ~ I f ~ 1{1 S ~ i i t il;;I'~]
4'it:~ :,~d':, ,::_,,: ~
I ~x Rn = 3.87x105 ~g ~ L~ Rn = 4.32x106 _
~=— ~ _
''1' ' ' ' ' ' ~ , , , , ,, ,, ,~?~. I
OCR for page 756
~ ~ -
DM= 0.201 m
Rn = 3.87xlOs
4~
Figure 14 Velocity vectors on the nozzle trailing edge, CTh = 85
DS = 1.005 m
Rn = 4~32X106
Figure 15: Velocity vectors on the propeller blade tip, CTh= 85
13
i
Ds=4.02m
I l Rn = 346x107
~ _
I _ ~
~ . . ... .
OCR for page 757
at: iCLL~
~ ll ~""'x'""~1 it j " ""'~'"";f
1 , ,,,.1. . . ' ' ' "I"' >1 1 . - ' ' ' ""' -I
·j , ,'''''''""' jar 1 - -'"2 ""'of
. *, ~ ~ _. ~ ~ No , ~ ~ ~~ \<
,~ = ~1,+~
Ds=2.01m Hi— Ds=4.02 m
l Rn= 122x107 ~ 1 Rn= 345x107
Figure 16: Velocity vectors outside the nozzle, CTh= 850
~ : ~ i', I"'''',' ~ ~,~ ~N ~
DM = 0.201 m ~/ fi~f`if i' /~' ~ Ds = 1.005 m I ~' I' f
R" = 3 ~ ~ / ~ Rn = 4~:
~ ~ ~ ~ ~ =~~; ~
Ds= 2.01 m ~,y,/~//',t,f ~ ,( ~ ~ Ds= 4.02 m `,b:~7j! if;
Rn=~' ~ Rn=3~-~ ~ <~'
Figure 17: Velocity vectors on the nozzle leading edge, CTh= 850
14
OCR for page 758
DM= 0.201 m
Rn = 3.86x105
., , · , ~ :~
,, ~ ;: Ds=2.01m
Rn = 1.22x107
~ ,
, .
I~ /~/,,,~ D5= 1.005 m
l A Rn= 431X106
D5= 4.02 m
Rn = 3.45x107
Figure 18: Velocity vectors on the nozzle trailing edge, CTh = 850
I_ DM=O.201 m
It Rn = 3.86xlO
_ ~
~ __
\ ~
~ ~ _.
! 1 Ds=leoo5m
_ ~ R ~ = 4.31~106
l
Figure 19: Velocity vectors on the propeller blade tip, CTh= 850
15
i_ ~ _
_ ~ _
t . _ ~
.1 ~ ~
— Ds=4.02 m
Rn = 3.45x107
OCR for page 759
1.10
1.09
1.08
1.07
1.06
1.05
1.04
1.03
1
0.99
0.97
0.99
0.98
0.97
0.96
0.95
0.94
1 .00 ~ _ _ I ~ T , I I I ~
-098 ~ ~
' ' 1 ~1 ~ 11
0 96 L ~L UT
1.00
Propeller thrust coefficients
DP 215-1345
1
1
10
CTh [-]
10
100
CTh [ ]
. _ _ , . . . . . . . .
Propeller torque coefficients
DP 215-1345
~ ·~ ~
1 12
1.11 ur z~-~o I I
~ ,~..
1~1~
Propeller torque coefficients
DP 215-1345
r-
1
100
1000
· 1 1 1 1
Nozzle thrust coefficients
DP 215-1345
1 ~
1000
Nozzle thrust coefficients
DP 215-1345
10
Ds/D`~r -- ~
]t nS —4.31 - 4.41 1 i)6
It.:l = 3~S - 3.gS 10.
Ds/DM = 10
R ,~s = 1.21 - 1.25 107
RnM =3.85-3.95 10
D s/D .,~ = 20
R,,.s = 3.44 - 3.52 107
R n.~l 3.85 - 3.95 105
CTh I I
100
Figure 20: Influence of the Reynolds number and the thrust loading coefficient on the propeller and nozzle
coefficients of the DP 215-1345 (nozzle Wag. 1 9A, propeller Wag. KA 5-75)
16
Representative terms from entire chapter:
ducted propeller
