Hydrodynamic characteristics of multiple-rudder configurations

Figures & data

Figure 1. Rudder force conventions.

Figure 2. Conventions of twin-rudder and quadruple-rudder configurations.

Figure 3. Applied rudder profiles for multiple-rudder interaction study.

Table 1. Test configurations to analyse the impacts of the spacing and the profile on multiple-rudder configurations.

Section	Profile	yTR (CR)	yTU (CR)
Section 4	NACA 0018	0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0	–
Section 5	NACA 0015, NACA 0020, NACA 0025	0.5, 0.6, 0.7, 0.8, 0.9, 1.0	–
	IFS58 TR15, IFS61 TR25, IFS62 TR25
	Wedge-tail 0015, Wedge-tail 0020, Wedge-tail 0025
Section 6	NACA 0018	0.5, 0.75, 1.0	0.5, 1.0, 1.5

Figure 4. Applied mesh topology and boundary conditions. Adapted from Liu et al. (2016).

Figure 5. Applied unstructured meshes with structured inflation layers.

Figure 6. Streamline contraction along the propeller disc.

Figure 7. Pressure distributions and stream traces of twin NACA 0018 rudders at an angle of attack of 10° with various y_TR, (a) y_TR/C_R = 0.4., (b) y_TR/C_R = 0.5., (c) y_TR/C_R = 0.6., (d) y_TR/C_R = 0.7., (e) y_TR/C_R = 0.8., (f) y_TR/C_R = 0.9., (g) y_TR/C_R = 1.0., (h) y_TR/C_R = ∞. This figure is available in colour online.

Figure 8. Lift and drag coefficients of a single NACA 0018 rudder and either side of twin NACA 0018 rudders with various y_TR. This figure is available in colour online.

Figure 9. Total hydrodynamic coefficients of a single NACA 0018 rudder and twin NACA 0018 rudders with various y_TR. This figure is available in colour online.

Figure 10. Pressure distributions and stream traces of twin-rudder configurations with different profiles at an angle of attack of 10° with y_TR = 0.5 C_R. (a) NACA 0015., (b) NACA 0020., (c) NACA 0025., (d) IFS58 TR15., (e) IFS58 TR25., (f) IFS62 TR15., (g) Wedge-tail 0015., (h) Wedge-tail 0020., (i) Wedge-tail 0025. This figure is available in colour online.

Figure 11. Pressure distributions and stream traces of twin-rudder configurations with different profiles at an angle of attack of 10° with y_TR = 1.0 C_R. (a) NACA 0015., (b) NACA 0020., (c) NACA 0025., (d) IFS58 TR15., (e) IFS58 TR25., (f) IFS62 TR15., (g) Wedge-tail 0015., (h) Wedge-tail 0020., (i) Wedge-tail 0025. This figure is available in colour online.

Figure 12. Total hydrodynamic coefficients of various twin rudders with y_TR = 0.5 C_R. This figure is available in colour online.

Figure 13. Total hydrodynamic coefficients of various twin rudders with y_TR = 1.0 C_R. This figure is available in colour online.

Figure 14. Pressure distribution and stream traces of quadruple-rudder configurations at angle of attack of 10° with different y_TR and y_TU. (a) y_TR = 0.50 C_R and y_TU = 0.5 C_R., (b) y_TR = 0.50 C_R and y_TU = 1.0 C_R., (c) y_TR = 0.50 C_R and y_TU = 1.5 C_R., (d) y_TR = 0.75 C_R and y_TU = 0.5 C_R., (e) y_TR = 0.75 C_R and y_TU = 1.0 C_R., (f) y_TR = 0.75 C_R and y_TU = 1.5 C_R., (g) y_TR = 1.50 C_R and y_TU = 0.5 C_R., (h) y_TR = 1.50 C_R and y_TU = 1.0 C_R., (i) y_TR = 1.50 C_R and y_TU = 1.5 C_R. This figure is available in colour online.

Figure 15. Lift coefficients of each rudder in a quadruple-rudder configuration compared to the lift coefficient of a single rudder. (a) y_TR = 0.50 C_R and y_TU = 0.5 C_R., (b) y_TR = 0.50 C_R and y_TU = 1.0 C_R., (c) y_TR = 0.50 C_R and y_TU = 1.5 C_R., (d) y_TR = 0.75 C_R and y_TU = 0.5 C_R., (e) y_TR = 0.75 C_R and y_TU = 1.0 C_R., (f) y_TR = 0.75 C_R and y_TU = 1.5 C_R., (g) y_TR = 1.50 C_R and y_TU = 0.5 C_R., (h) y_TR = 1.50 C_R and y_TU = 1.0 C_R., (i) y_TR = 1.50 C_R and y_TU = 1.5 C_R. This figure is available in colour online.

Figure 16. Drag coefficients of each rudder in a quadruple-rudder configuration compared to the drag coefficient of a single rudder. (a) y_TR = 0.50 C_R and y_TU = 0.5 C_R., (b) y_TR = 0.50 C_R and y_TU = 1.0 C_R., (c) y_TR = 0.50 C_R and y_TU = 1.5 C_R., (d) y_TR = 0.75 C_R and y_TU = 0.5 C_R., (e) y_TR = 0.75 C_R and y_TU = 1.0 C_R., (f) y_TR = 0.75 C_R and y_TU = 1.5 C_R., (g) y_TR = 1.50 C_R and y_TU = 0.5 C_R., (h) y_TR = 1.50 C_R and y_TU = 1.0 C_R., (i) y_TR = 1.50 C_R and y_TU = 1.5 C_R. This figure is available in colour online.

Figure 17. Total hydrodynamic coefficients of quadruple NACA 0018 rudders with various y_TR and y_TU. This figure is available in colour online.

Table 2. Regression coefficients of the lift coefficients of each rudder in the twin-rudder configurations.

Rudder profile			k^CL1	k^CL2	k^CL3	k^CL4	k^CL5
NACA 0015	6.175	0.000	0.109	−0.493	−0.069	0.378	0.079	0.999	0.001
NACA 0018	6.014	0.000	−0.078	0.387	0.118	−0.514	0.067	0.999	0.010
NACA 0020	5.845	0.000	−0.064	0.372	0.098	−0.475	0.083	0.999	0.012
NACA 0025	5.260	0.000	−0.073	0.437	0.056	−0.401	0.064	0.993	0.024
IFS58 TR15	6.852	0.000	0.140	−0.572	−0.095	0.427	0.071	0.999	0.012
IFS61 TR25	7.265	0.000	0.176	−0.642	−0.076	0.389	0.169	0.999	0.017
IFS62 TR25	7.096	0.000	−0.729	1.101	0.710	−1.235	0.182	0.969	0.080
Wedge-tail 0015	7.159	0.000	0.156	−0.620	−0.092	0.437	0.003	0.998	0.015
Wedge-tail 0020	7.569	0.000	−0.084	0.415	0.167	−0.642	0.065	0.997	0.019
Wedge-tail 0025	8.004	0.000	−0.068	0.377	0.206	−0.713	0.168	0.996	0.030

Table 3. Regression coefficients of the drag coefficients of each rudder in the twin-rudder configurations.

Rudder profile			k^CD1	k^CD2	k^CD3	k^CD4	k^CD5
NACA 0015	0.032	0.008	3.580	−1.524	−0.012	0.045	0.000	0.999	0.001
NACA 0018	0.031	0.009	2.729	−1.145	−0.002	0.019	0.000	0.999	0.001
NACA 0020	0.032	0.01	4.221	−1.562	−0.009	0.046	0.000	0.998	0.001
NACA 0025	0.036	0.011	4.506	−0.990	0.001	0.053	−0.001	0.996	0.002
IFS58 TR15	0.033	0.014	2.210	−1.360	−0.006	0.026	0.001	0.998	0.001
IFS61 TR25	0.051	0.019	3.444	−2.630	0.014	0.031	0.002	0.994	0.002
IFS62 TR25	0.078	0.011	1.749	−1.327	0.265	−0.400	0.003	0.993	0.002
Wedge-tail 0015	−0.005	0.065	−7.663	−7.268	−0.208	0.512	0.001	0.979	0.002
Wedge-tail 0020	0.003	0.055	38.646	−5.670	−0.161	0.376	0.001	0.947	0.006
Wedge-tail 0025	0.014	0.045	17.057	−9.379	−0.113	0.274	0.001	0.993	0.003

Figure 18. Surface fitting of the lift and drag coefficients of the NACA 0018 profile with different spacing. (a) Surface fitting of the lift coefficient., (b) residuals of the lift coefficient fitting., (c) surface fitting of the drag coefficient. and (d) residuals of the drag coefficient fitting. This figure is available in colour online.

Figure 19. Comparison of predicted and tested lift coefficients of different profiles in the twin-rudder configuration with y_TR = 0.5 C_R. This figure is available in colour online.

Figure 20. Comparison of predicted and tested drag coefficients of different profiles in the twin-rudder configuration with y_TR = 0.5 C_R. This figure is available in colour online.

Figure 21. Comparison of predicted and tested lift coefficients of different profiles in the twin-rudder configuration with y_TR = 1.0 C_R.  This figure is available in colour online.

Figure 22. Comparison of predicted and tested drag coefficients of different profiles in the twin-rudder configuration with y_TR = 1.0 C_R. This figure is available in colour online.

Liu J, Quadvlieg F, Hekkenberg R. 2016. Impacts of the rudder profile on manoeuvring performance of ships. Ocean Eng. 124:226–240.

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