Open-Water Thrust and Torque Predictions of a Ducted Propeller System With a Panel Method

Open-Water Thrust and Torque Predictions
of a Ducted Propeller System With a Panel Method
J. Baltazar1, J.A.C. Falc˜ao de Campos1 and J. Bosschers2
1Marine Environment and Technology Center (MARETEC)
Instituto Superior T´ecnico, Technical University of Lisbon, Portugal
2Maritime Research Institute Netherlands (MARIN), the Netherlands
smp’11 Hamburg, Germany 15-17 June 1 / 21

Motivations
Panel Methods (or Boundary Element Method - BEM)
still provide a most useful computational tool for
analysis of marine propulsors.
Advantages of Panel Methods:
Quick analysis of cavitating propellers in prescribed ship
wake ﬁeld.

Motivations
Application of Panel Methods to ducted propellers
involves additional modelling issues:
Complex interaction of propeller blades and duct surface
- Gap flow -
Duct trailing edge where flow separation may ultimately
determine the duct circulation:
May be difficult with a thick round trailing edge
Much easier with a sharp trailing edge
- where a classical Kutta condition applies -

Objectives
Performance predictions of a ducted propeller system with a
low-order Panel Method.
Modelling aspects discussed:
Gap flow;
Alignment of the blade wake;
Influence of the duct boundary layer on the blade wake pitch.
The analysis is carried out for propeller Ka4-70 with P/D=1.0
operating without and inside a modified duct 19A (19Am):
Duct 19A
Duct 19AmStraight
Cylindrical
rounded trailing edge is replaced by a sharp trailing edge.

Numerical Method
Panel Code PROPAN
Surface Discretisation:
Structured surface grid with quadrilateral hyperboloidal
elements.
Panel Method:
Integral equation solved by the collocation method.
Constant source and dipole distributions.
Inﬂuence coeﬃcients calculated using the formulations of
Morino and Kuo (1974).
Iterative pressure Kutta condition.

Gap Flow Models
Gap Flow Model with Transpiration Velocity:
Non zero-gap width: a partial ﬂow is allowed to pass
in the gap region, Hughes (1997).
Transpiration velocity on the gap strip:
Vn = |U∞|CQ ∆Cpn · nc
Blade
Hub
Duct
Gap
Transpiration
Velocity
Closed Gap with Zero Gap Width:
Blade tip is on the duct surface (matching grids)

Vortex Wake Model
Rigid Wake Model:
Propeller Blade Wake
Constant pitch of vortex lines
Geometrical blade pitch is used in the present study
Empirical contraction following Hoshino (1989)
Duct Wake
Constant radius vortex sheet
Shedding line a the duct trailing edge
Wake Alignment Model for Blade Wake:
Euler scheme in (x,r,θ) coordinate system
To control wake alignment stability,
the radial coordinates are kept constant
⇒ Vortex Pitch Wake Alignment.

A Simple Model for the Interaction of the Blade
Wake with the Duct Boundary Layer
Duct Inner Surface
Gap Strip
δG/R = 0.83%
Propeller Blade
δ
Vx
r
Velocity Profile
Power Law Distribution: Vx (Rd −r)
Vx (δ)
= Rd −r
δ
1
n
with δ/R = 4% and n = 7.

Viscous Corrections
Blade section drag coeﬃcient of 0.007;
No viscous drag correction to the duct thrust;
Simple model for suppression of the leading edge suction force:
(Corrections applied between r/R = 0.7 and r/R = 1.0)
Flat Plate
V
α
LFn
Fs
Lift Force Fn after suppression

Test Case
Experimental Data for Ka4-70 Inside Ducts 19A and 19Am
Duct 19A
Duct 19AmStraight
Cylindrical
J
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Ka4-70 in Duct 19A
Ka4-70 in Duct 19Am
KT
10KQ
KTD
P
η

Panel Arrangement
Ka4-70 Inside Duct 19Am
X
Y
Z
Panel Discretisation:
50×25 Blade, 142×160 Duct, 55×80 Hub.

Results
Ka4-70 Without Duct - Comparison With Experimental Data
J
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Experiments: Re=ΩR/ν=1.23×106
Rigid Wake Model, no SF Correction
KT
10KQ
J
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Rigid Wake Model, SF Correction
KT
10KQ

Results
Ka4-70 Without Duct - Comparison With Experimental Data
J
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 Experiments: Re=ΩR/ν=1.23×10
6
Rigid Wake Model, SF Correction
Wake Alignment Model (WAM)
WAM with Contraction
KT
10KQ X
Y
Z

Results
Ka4-70 Inside Duct 19Am - Comparison With Experimental Data
J
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
6
Gap Model with Transpiration Velocity
Closed Gap Model
Rigid Wake Model
KT
10KQ
KTD
P
J
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
6
Closed Gap Model
Wake Alignment Model
KT
10KQ
KTD
P

Results
Ka4-70 Inside Duct 19Am - Comparison With Experimental Data
J
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Rigid Wake Model
WAM with Duct Boundary Layer Correction
Transpiration Velocity Gap Model
KT
10KQ
KTD
P
J
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Rigid Wake Model
Closed Gap Model
KT
10KQ
KTD
P

Results - Ka4-70 Inside Duct 19Am
Vortex Pitch Distributions - J = 0.5
r/R
0.2 0.4 0.6 0.8 1.0
0
20
40
60
80
Gap Model with Transpiration Velocity - Rigid Wake Model
x/R=0.5
βv
[º]
r/R
0.2 0.4 0.6 0.8 1.0
0
20
40
60
80
x/R=2.0
βv[º]

Wake Alignment Model with Duct Boundary Layer Correction - J = 0.5
X
Y
Z
X
Y
Z

Circulation Distributions - J = 0.5
r/R
∆φ/(ΩR
2
)
0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.06
0.09
Closed Gap Model - Rigid Wake Model
Blade
Position between blades [º]
∆φ/(ΩR
2
)
0.0 30.0 60.0 90.0
0.00
0.05
0.10
0.15
Closed Gap Model - Rigid Wake Model
Duct

Pressure Distributions - J = 0.5
s/c
0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.5
0.0
0.5
1.0
Blade - r/R=0.95
-Cp
s/c0.00 0.05 0.10
-0.5
0.0
0.5
1.0
s/c
-Cp
0.0 0.2 0.4 0.6 0.8 1.0
-0.2
-0.1
0.0
0.1
0.2
0.3
Duct - θ=0º

Variation with the Duct Boundary Layer Thickness
δ/R
KTP
−KTP exp
KTP exp
KTP+D
−KTP+D exp
KTP+D exp
KQ −KQexp
KQexp
0.0% 19.8% 17.2% 11.9%
1.0% 8.4% 9.0% 3.2%
2.0% 0.4% 4.0% -3.0%
3.0% -1.5% 2.2% -4.3%
4.0% -3.3% 0.2% -5.9%
5.0% -6.1% -0.8% -8.1%

Conclusions
Ka4-70 Without Duct:
A reasonable to good agreement with experimental data is
obtained when a leading edge suction force correction is applied.
Ka4-70 Inside Duct 19Am:
The gap model has a small inﬂuence on the propeller and
duct loading.
Predictions of duct and propeller loading are critically
dependent on the blade wake pitch, especially at the tip.
Further investigation by comparison with RANS results.

Open-Water Thrust and Torque Predictions of a Ducted Propeller System With a Panel Method

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