Numerical Modelling of the Potential Flow Around Ducted Propellers

CMNE/CILAMCE 2007CMNE/CILAMCE 2007 11
NUMERICAL MODELLING OF THE POTENTIALNUMERICAL MODELLING OF THE POTENTIAL
FLOW AROUND DUCTED PROPELLERSFLOW AROUND DUCTED PROPELLERS
J. BaltazarJ. Baltazar1*1*
and J.A.C. Falcão de Camposand J.A.C. Falcão de Campos11
11
MARETEC/ISTMARETEC/IST
Departamento de Engenharia Mecânica,Departamento de Engenharia Mecânica,
Instituto Superior TInstituto Superior Téécnico, Lisboa, Portugalcnico, Lisboa, Portugal
Congresso de MCongresso de Méétodos Numtodos Numééricos em Engenhariaricos em Engenharia
FEUP, Porto, 13 a 15 JunhoFEUP, Porto, 13 a 15 Junho
Portugal, 2007Portugal, 2007

Ducted propellers can be commonly seen in tugs,Ducted propellers can be commonly seen in tugs,
trawlers, tankers and bulk carriers.trawlers, tankers and bulk carriers.
Prediction of pressure distributions and integratedPrediction of pressure distributions and integrated
forces are important for the design of such systems.forces are important for the design of such systems.
The pressure field is important for cavitation analysisThe pressure field is important for cavitation analysis
and pressure fluctuations.and pressure fluctuations.
Pressure distribution and forces may be predicted byPressure distribution and forces may be predicted by
BEM potential flow models.BEM potential flow models.
MotivationsMotivations

Evaluation of BEM potential flow model requirementsEvaluation of BEM potential flow model requirements
for calculation of steady wetted flow around ductedfor calculation of steady wetted flow around ducted
propellers:propellers:
–– Potential bladePotential blade--duct gap model.duct gap model.
–– Potential model for duct wake from round trailing edges.Potential model for duct wake from round trailing edges.
–– Duct and blade grids for numerical accuracy inDuct and blade grids for numerical accuracy in
prediction of pressure distributions.prediction of pressure distributions.
Extension of BEM code PROPAN (Falcão de Campos,Extension of BEM code PROPAN (Falcão de Campos,
2000) for ducted propellers.2000) for ducted propellers.
ObjectivesObjectives

BEM FormulationBEM Formulation
Mathematical Model (1)Mathematical Model (1)
02
=∇ φ
V U φ∞= + ∇
on
, on
0, if r or
B D H
W
n U S S S
n
n U p p S
n n
x
φ
φ φ
φ
∞
+ −
∞ + −
∂
= − ⋅ ∪ ∪
∂
∂ ∂
= = − ⋅ =
∂ ∂
∇ → → ∞ → −∞
Laplace Equation:Laplace Equation:
Boundary Conditions:Boundary Conditions:
Velocity Field:Velocity Field:
y
z
x
r
U
θ
Ω

Mathematical Model (2)Mathematical Model (2)
Fredholm Integral Equation for Morino Formulation:Fredholm Integral Equation for Morino Formulation:
Kutta Condition:Kutta Condition: ∞<∇φ
( ) ( ) ( ) ( )2 ,
B D H Wq q qS S S S
G G
p G p q q dS q dS
n n n
φ
πφ φ φ
∪ ∪
⎡ ⎤∂ ∂ ∂
= − − ∆⎢ ⎥
∂ ∂ ∂⎢ ⎥⎣ ⎦
∫∫ ∫∫
GreenGreen’’s Function:s Function: ( , ) 1/ ( , )G p q R p q= −

Numerical ImplementationNumerical Implementation
Surface Discretization:Surface Discretization:
BiBi--linear quadrilateral panels.linear quadrilateral panels.
Propeller blades: cosine stretching along radius and blade sectiPropeller blades: cosine stretching along radius and blade sections.ons.
Propeller hub: elliptical grid generator, EPropeller hub: elliptical grid generator, Eçça (1994).a (1994).
Duct: equidistant stretching along the circumferential directionDuct: equidistant stretching along the circumferential direction, Vinokur, Vinokur
(1983) stretching function and the same stretching of the blade(1983) stretching function and the same stretching of the blade tip sectiontip section
along the streamwise direction.along the streamwise direction.
BEM Method:BEM Method:
Integral equation solved by the collocation method.Integral equation solved by the collocation method.
BiBi--linear elements with constant source and dipole distributions.linear elements with constant source and dipole distributions.
Influence coefficients calculated using the formulations of MoriInfluence coefficients calculated using the formulations of Morino and Kuono and Kuo
(1974).(1974).
LU direct solver. SecondLU direct solver. Second--order differentiation scheme.order differentiation scheme.
Rigid wake model with iterative pressure Kutta condition.Rigid wake model with iterative pressure Kutta condition.

Duct NSMB 19ADuct NSMB 19A
Duct and Wake GridsDuct and Wake Grids
Cylindrical PanellingCylindrical Panelling Helical PanellingHelical Panelling
X
Y
Z
X
Y
Z

Comparison BetweenComparison Between
Cylindrical and Helical PanellingCylindrical and Helical Panelling
s/c
-Cp
0.0 0.2 0.4 0.6 0.8 1.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Cylindrical Panelling
Helical Panelling
θ
∆φ/(ΩR2
)
0.0 30.0 60.0 90.0
-0.24
-0.16
-0.08
0.00
Cylindrical Panelling
Helical Panelling

Pressure DistributionPressure Distribution -- ComparisonComparison
s/c
-Cp
0.0 0.2 0.4 0.6 0.8 1.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Present Method - Helical Panelling
Falcão de Campos (1983)
Experimental - Outer Side
Experimental - Inner Side

Position of the Stagnation PointPosition of the Stagnation Point
1
2
3
s/c
-Cp
0.0 0.2 0.4 0.6 0.8 1.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
99.7% - Outer Side
100%
99.7% - Inner Side
1
2
3
Stagnation Point Location % of Chord

KKaa44--70 inside NSMB 19A70 inside NSMB 19A
Ducted Propeller and Wake GridsDucted Propeller and Wake Grids
X
Y
Z
X
Y
Z

Convergence with Grid Refinement, J=0.7Convergence with Grid Refinement, J=0.7
s/c
0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.5
0.0
0.5
1.0
20×11 Blade Grid - 60×10 Duct Grid
r/R=0.75
-Cp
s/c
0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.5
0.0
0.5
1.0
r/R=0.99
-Cp
s/c
-Cp
0.0 0.2 0.4 0.6 0.8 1.0
-0.2
0.0
0.2
0.4
0.6
0.8
θ=0º
s/c
-Cp
0.0 0.2 0.4 0.6 0.8 1.0
-0.2
0.0
0.2
0.4
0.6
0.8
θ=40º
r/R
∆φ/(ΩR2
)
0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.06
0.09
Position between blades [º]
∆φ/(ΩR2
)
0.0 30.0 60.0 90.0
0.00
0.03
0.06
0.09

Influence of the GapInfluence of the Gap
r/R
∆φ/(ΩR2
)
0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.06
0.09
0.4% Gap
0.0% Gap
s/c
0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.5
0.0
0.5
1.0
0.4% Gap
0.0% Gap
r/R=0.99
-Cp
s/c
-Cp
0.0 0.2 0.4 0.6 0.8 1.0
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.4% Gap
0.0% Gap
θ=40º
∆φ/(ΩR2
)
0.0 30.0 60.0 90.0
0.00
0.06
0.12
0.18
0.4% Gap
0.0% Gap

Influence of the Shedding Line LocationInfluence of the Shedding Line Location
s/c
0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.5
0.0
0.5
1.0
99.9% - Outer Side
100%
99.9% - Inner Side
r/R=0.75
-Cp
s/c
-Cp
0.0 0.2 0.4 0.6 0.8 1.0
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
99.9% - Outer Side
100%
99.9% - Inner Side
θ=40º
r/R
∆φ/(ΩR2
)
0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.06
0.09
99.9% - Outer Side
100%
99.9% - Inner Side
∆φ/(ΩR2
)
0.0 30.0 60.0 90.0
0.00
0.04
0.08
0.12
99.9% - Outer Side
100%
99.9% - Inner Side

Comparison with Experimental DataComparison with Experimental Data
J
KT,10KQ
0.4 0.5 0.6 0.7 0.8
-0.2
0.0
0.2
0.4
0.6
0.8
Experimental
Present Method
KTD
KTT
10KQ

ConclusionsConclusions
Duct NSMB 19A:Duct NSMB 19A:
Small differences between the panel method and the surfaceSmall differences between the panel method and the surface
vorticity method, Falcão de Campos (1983). Poor comparison withvorticity method, Falcão de Campos (1983). Poor comparison with
experiment due to leadingexperiment due to leading--edge separation.edge separation.
Location of the stagnation point is of primary importance in theLocation of the stagnation point is of primary importance in the
determination of the solution.determination of the solution.
KKaa44--70 inside NSMB 19A:70 inside NSMB 19A:
Convergence of the numerical results with grid refinement. LargeConvergence of the numerical results with grid refinement. Large
grid discretizations to describe the solution near the propellergrid discretizations to describe the solution near the propeller tiptip
vortex.vortex.
Strong influence of the gap in the potential solution.Strong influence of the gap in the potential solution.
Large variations in the potential solution with the location ofLarge variations in the potential solution with the location of thethe
wake vorticity shedding line.wake vorticity shedding line.
Significant differences in the thrust and torque coefficients beSignificant differences in the thrust and torque coefficients betweentween
the numerical results and experimental data; suggesting a morethe numerical results and experimental data; suggesting a more
complex interaction between propeller and duct.complex interaction between propeller and duct.

Numerical Modelling of the Potential Flow Around Ducted Propellers

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Numerical Modelling of the Potential Flow Around Ducted Propellers