Three-dimensional unsteady potential flow calculations for marine propellers with a low order BEM are presented. A brief discussion of rigid wake models for the convection of the blade vorticity is given. Consistency numerical studies between the steady and unsteady solutions, and spatial convergence are presented for the propeller DTMB P4119. Comparisons of numerical calculations with other methods and experimental measurements are presented for the propeller DTMB P4679 and the Seiun-Maru propeller.

1. CNMNMFT 2006 1
UNSTEADY POTENTIAL FLOW CALCULATIONS
OF MARINE PROPELLERS USING BEM
J.Baltazar1* and J.A.C.Falcão de Campos1
1MARETEC/IST
Departamento de Engenharia Mecânica,
Instituto Superior Técnico, Lisboa, Portugal
Conferência Nacional de Métodos Numéricos em
Mecânica dos Fluidos e Termodinâmica 2006
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006

2. CNMNMFT 2006 2
Motivations
BEM potential flow calculations have been extensively
used in the analysis of marine propellers.
The unsteady loads are important in the analysis of shaft
vibrations.
The unsteady pressure field is important for cavitation
analysis and pressure fluctuations.
Objectives
Update of the BEM code PROPAN (Falcão de Campos,
2000) to compute the unsteady wetted flow on propeller
blades in non-axisymmetric inflow conditions.
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006

3. CNMNMFT 2006 3
BEM Formulation
Mathematical Model (1)
02
 
V V   
r r
on
, on
0, if
B H
W
V n S S
n
V n V n p p S
r



 
 
 
    
 
   
   
r r
r rr r
r
Undisturbed Inflow Velocity Field:
Laplace Equation:
Boundary Conditions:
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006
Velocity Field:
   , , , , ,eV x r t U x r t x      
r r r r

4. CNMNMFT 2006 4
BEM Formulation
Mathematical Model (2)
Wake Model:
Fredholm Integral Equation for Morino Formulation:
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006
   
 0 , , , TE
r t r t
t
   
  

     
        
   
Kutta Condition: 
       2 , , , ,
B H Wq q qS S S
G G
p t G p q q t dS q t dS
n n n

  

   
    
    
 

5. CNMNMFT 2006 5
BEM Formulation
Numerical Implementation
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006
Time Discretization:
• Time step n=t/t, where t=2/(Nt).
Surface Discretization:
• Bi-linear quadrilateral elements.
• Conventional grids taken from Vaz (2005).
BEM Method:
• Integral equation solved in space by the collocation method for the key blade.
• Bi-linear elements with constant source and dipole distributions. Linear dipole
distribution at the first radial wake strip.
• Influence coefficients calculated using the formulations of Morino and Kuo (1974).
• LU direct solver. Second-order differentiation scheme.
• Rigid wake model with iterative pressure Kutta condition.

6. CNMNMFT 2006 6
Propeller DTMB P4119
Blade and Wake Grid
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006

7. CNMNMFT 2006 7
DTMB P4119
Convergence of Mean Pressure
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006
s/c
-Cp0
0.0 0.2 0.4 0.6 0.8 1.0
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
20x10
30x15
40x20
50x25
60x30
r/R=0.25
s/c
-Cp0
0.0 0.2 0.4 0.6 0.8 1.0
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
20x10
30x15
40x20
50x25
60x30
r/R=0.50
s/c
-Cp0
0.0 0.2 0.4 0.6 0.8 1.0
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
20x10
30x15
40x20
50x25
60x30
r/R=0.75
s/c
-Cp0
0.0 0.2 0.4 0.6 0.8 1.0
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
20x10
30x15
40x20
50x25
60x30
r/R=0.99
J=0.833
Oblique Inflow
Condition
Shaft Angle =7.5º

8. CNMNMFT 2006 8
Propeller DTMB P4119
Time Convergence of Thrust Force
-0
[º]
KT
0 360 720 1080 1440 1800
0.13
0.14
0.15
0.16
Propeller
-0
[º]
0 360 720 1080 1440 1800
0.03
0.04
0.05
0.06
0.07
KT
Blade
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006
J=0.833; Oblique Inflow Condition; Shaft Angle =7.5º

9. CNMNMFT 2006 9
Propeller DTMB P4679
Blade and Wake Grid
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006

10. CNMNMFT 2006 10
Propeller DTMB P4679
Mean Pressure
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006
s/c
-Cp0
0.0 0.2 0.4 0.6 0.8 1.0
-0.2
0.0
0.2
0.4
Present Method
Vaz (2005)
Experimental (upper)
Experimental (lower)
r/R=0.50
s/c
-Cp0
0.0 0.2 0.4 0.6 0.8 1.0
-0.2
0.0
0.2
0.4
Present Method
Vaz (2005)
Experimental (upper)
Experimental (lower)
r/R=0.70
J=1.083; Oblique Inflow Condition; Shaft Angle =7.5º

11. CNMNMFT 2006 11
DTMB P4679
First Harmonic of Pressure
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0
0.05
0.1
0.15
0.2
Present Method
Vaz (2005)
Experimental (upper)
Experimental (lower)
r/R=0.70
Cp1
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0
0.05
0.1
0.15
0.2
Present Method
Vaz (2005)
Experimental (upper)
Experimental (lower)
r/R=0.50
Cp1
s/c
(Cp1
)[º]
0.0 0.2 0.4 0.6 0.8 1.0
0
120
240
360
Present Method
Vaz (2005)
Experimental (upper)
Experimental (lower)
r/R=0.50
s/c
(Cp1
)[º]
0.0 0.2 0.4 0.6 0.8 1.0
0
120
240
360
Present Method
Vaz (2005)
Experimental (upper)
Experimental (lower)
r/R=0.70
J=1.083
Oblique Inflow
Condition
Shaft Angle =7.5º

12. CNMNMFT 2006 12
Seiun-Maru Propeller
Grid and Inflow
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006
z0
-1.0 -0.5 0.0 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0
Vxxxxx: 0.15 0.26 0.37 0.48 0.59 0.70 0.81 0.93
y0
Uey
2
+Uez
2
=VS
2
Uex /VS:
r/R
0.2 0.4 0.6 0.8 1.0 1.2
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Uex
/VS
Uer
/VS
Ue
/VS

13. CNMNMFT 2006 13
Seiun-Maru Propeller
Pressure Distribution
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006
s/c
-Cpn
0.0 0.2 0.4 0.6 0.8 1.0
-2.0
0.0
2.0
4.0
6.0
8.0
Present Method
Vaz (2005)
Experimental (Back)
Experimental (Face)
r/R=0.70, -0=90º
s/c
-Cpn
0.0 0.2 0.4 0.6 0.8 1.0
-2.0
0.0
2.0
4.0
6.0
8.0
Present Method
Vaz (2005)
Experimental (Back)
Experimental (Face)
r/R=0.70, -0=0º
s/c
-Cpn
0.0 0.2 0.4 0.6 0.8 1.0
-2.0
0.0
2.0
4.0
6.0
8.0
Present Method
Vaz (2005)
Experimental (Back)
Experimental (Face)
r/R=0.70, -0=180º
s/c
-Cpn
0.0 0.2 0.4 0.6 0.8 1.0
-2.0
0.0
2.0
4.0
6.0
8.0
Present Method
Vaz (2005)
Experimental (Back)
Experimental (Face)
r/R=0.70, -0=270º
Real Ship Wake
KT=0.172

14. CNMNMFT 2006 14
Seiun-Maru Propeller
Pressure Distribution
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006
s/c
-Cpn
0.0 0.2 0.4 0.6 0.8 1.0
-2.0
0.0
2.0
4.0
6.0
8.0
Present Method
Vaz (2005)
Experimental (Back)
Experimental (Face)
r/R=0.90, -0=0º
s/c
-Cpn
0.0 0.2 0.4 0.6 0.8 1.0
-2.0
0.0
2.0
4.0
6.0
8.0
Present Method
Vaz (2005)
Experimental (Back)
Experimental (Face)
r/R=0.90, -0=90º
s/c
-Cpn
0.0 0.2 0.4 0.6 0.8 1.0
-2.0
0.0
2.0
4.0
6.0
8.0
Present Method
Vaz (2005)
Experimental (Back)
Experimental (Face)
r/R=0.90, -0=180º
s/c
-Cpn
0.0 0.2 0.4 0.6 0.8 1.0
-2.0
0.0
2.0
4.0
6.0
8.0
Present Method
Vaz (2005)
Experimental (Back)
Experimental (Face)
r/R=0.90, -0=270º
Real Ship Wake
KT=0.172

15. CNMNMFT 2006 15
Conclusions
 Numerical studies for the DTMB P4119 at an oblique
inflow condition: spatial convergence and convergence
with time.
 DTMB P4679 at an oblique inflow condition: good
agreement between the present method and the
experimental data for the mean and first harmonic
amplitude pressure distribution; some differences are
observed for the phase angle.
 Seiun-Maru propeller operating behind a ship wake field:
good agreement with experimental data; some
differences are observed on the back side near the
propeller tip.
FCT-UNL, Monte da Caparica, 8 e 9 Junho
©APMTAC,Portugal, 2006