Escort tug, hull and fin, Force coefficients against yaw angle
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
-0.1 0
0 5 10 15 20 25 30 35 40 45 50 55 60 Yaw angle, deg.
Figure 7, Comparison of CFD predictions for force coefficients with experiment values, hull and fin
The predicted normal force (pressure) and tangential force (viscous) components acting on the tug hull (fitted with the fin) from the hexahedral mesh are given in Table 6. These data show that as the yaw angle was increased, the proportion of viscous force to total force decreased. At zero yaw, the viscous force
5. CFD PREDICTIONS OF FLOW PATTERNS AT 45 DEGREES YAW
was
approximately 25% of the total force, whereas at 10 degrees yaw, this had dropped to 9%, and at 30 degrees yaw it had dropped to 2%. At high yaw angles very little error in the forces at the hull would be expected by ignoring the viscous forces completely. One important element of including the viscosity forces within the fluid is to ensure the formation of vortices within the flow. It is important to check the predicted fluid flow patterns as well as the resulting forces.
Table 6, Comparison of pressure and viscous forces acting on tug and fin (hexahedral mesh)
Yaw Pressure Angle Force 0
10 20 30 40 50
6.07
22.11 46.08 72.16 94.05
102.91 Viscous Degrees N N Total
Force Force N
2.06 1.93 1.71 1.45 1.14 0.88
8.13
22.73 46.32 72.27 94.16
103.11
Viscousl /Tota
0.254 0.085 0.037 0.020 0.012 0.008
Particle Image Velocimetry experiments were carried out to measure the flow around the same tug model at speeds of 0.5 and 1.0 m/s, with a yaw angle of 45 degrees (Molyneux & Bose, 2007). Measurements were made within a plane, normal to the direction of the incoming flow, at two locations on the hull. One location was a plane that intersected with the midship section on the upstream side of the hull, and the second location was a plane that intersected the midship section on the downstream side of the hull. These planes are shown in relation to the CFD grid (for the hexahedral mesh) and the flow direction in Figure 8. The PIV experiments were carried out on the upstream side of the hull for the hull without the fin, and on the downstream side of the hull, with and without the fin.
As the grid for the CFD simulations had been created using ship-based coordinates, it was necessary to use the transformations given below, to convert the coordinates and vectors within the CFD simulations to the same flow based coordinate system as the PIV experiments.
xx y yx y
fs s fs s
(Cos Sin ) (Sin Cos
)
where; xf and yf are in the flow based coordinates xs and ys are in the ship based coordinates
Cq, estimated from experiments
Cl, estimated from experiments
Cq, Tetrahedral mesh Cl, Tetrahedral mesh Cq, Hexahedral mesh Cl, Hexahedral mesh
B-48
©2008: Royal Institution of Naval Architects
Cl, Cq
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