Abstract
Unsteady Reynolds averaged Navier–Stokes (URANS) computations of standard maneuvers are performed for a surface combatant at model and full scale. The computations are performed using CFDShip-Iowa v4, a free surface solver designed for 6DOF motions in free and semi-captive problems. Overset grids and a hierarchy of bodies allow the deflection of the rudders while the ship undergoes 6DOF motions. Two types of maneuvers are simulated: steady turn and zigzag. Simulations of steady turn at 35° rudder deflection and zigzag 20/20 maneuvers for Fr = 0.25 and 0.41 using constant RPM propulsion are benchmarked against experimental time histories of yaw, yaw rate and roll, and trajectories, and also compared against available integral variables. Differences between CFD and experiments are mostly within 10 % for both maneuvers, highly satisfactory given the degree of complexity of these computations. Simulations are performed also with waves, and with propulsion at either constant RPM or torque. 20/20 zigzag maneuvers are simulated at model and full scale for Fr = 0.41. The full scale case produces a thinner boundary layer profile compared to the model scale with different reaction times and handling needed for maneuvering. Results indicate that URANS computations of maneuvers are feasible, though issues regarding adequate modeling of propellers remain to be solved.
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Abbreviations
- a ij :
-
Wave amplitude
- a e :
-
Surface area of solid surface
- A :
-
Bretschneider coefficient which depends on wave period and wave height
- A θ :
-
Coefficient for axial body force
- A x :
-
Coefficient for azimuthal body force
- B :
-
Bretschneider coefficient which depends on wave period
- C 1, C 2, C 3 :
-
Constants defining order of accuracy of 6DoF solver
- D p :
-
Propeller diameter
- f bx :
-
Axisymmetric body force in axial direction
- f bθ :
-
Axisymmetric body force in azimuthal direction
- F e :
-
Fluid forces in the earth reference system
- F prop :
-
Propeller forces in the ship reference system
- F ship :
-
Fluid forces in the ship reference system
- H 1/3 :
-
Significant wave height
- I x :
-
Moment of inertia about x-axis
- I y :
-
Moment of inertia about y-axis
- I z :
-
Moment of inertia about z-axis
- J :
-
Advance coefficient
- J :
-
Transformation matrix from \(\dot{{\varvec {\eta }}}\) to \( {\mathbf{v}} \)
- K i :
-
Wave number
- K Q :
-
Torque coefficient
- K T :
-
Thrust coefficient
- (K, M, N):
-
Moments in x, y, z direction
- L e :
-
Fluid moments in the earth reference system
- L ship :
-
Fluid moments in the ship reference system
- M :
-
Mass
- M(α i ):
-
Directional spectrum
- N :
-
Angular velocity of propeller
- p:
-
Pressure
- p :
-
Roll velocity
- \( \dot{p} \) :
-
Roll acceleration
- p 1 :
-
Upstream point of propeller volume
- p 2 :
-
Downstream point of propeller volume
- q :
-
Pitch velocity
- \( \dot{q} \) :
-
Pitch acceleration
- r :
-
Yaw velocity
- \( \dot{r} \) :
-
Yaw acceleration
- r :
-
Distance vector
- r h :
-
Propeller hub radius
- r p :
-
Propeller radius
- S(ω i ):
-
Frequency spectrum
- T m :
-
Modal wave period
- u :
-
Surge velocity
- \( \dot{u} \) :
-
Surge acceleration
- U :
-
Wave velocity in x-direction
- U ship :
-
Ship forward velocity
- v :
-
Sway velocity
- \( \dot{v} \) :
-
Sway acceleration
- V :
-
Wave velocity in y-direction
- w :
-
Heave velocity
- \( \dot{w} \) :
-
Heave acceleration
- W :
-
Wave velocity in z-direction
- x G, y G, z G :
-
Distance from the center of rotation to the center of gravity of the ship
- x CG, y CG, z CG :
-
Center of gravity
- x rot, y rot, z rot :
-
Center of rotation of ship
- (X, Y, Z):
-
Forces in x, y, z direction
- α:
-
Angle of incidence
- α 0 :
-
Heading angle
- α j :
-
Dispersion angle
- η(x 1, x 2, x 3, ϕ, θ, ψ):
-
Position and Euler angles
- \( \dot{\varvec{{\eta }}} \) :
-
Rate of change of position and Euler angles
- v :
-
Linear and angular velocity vector
- ξ:
-
Wave elevation
- µ j :
-
Angle of incidence
- ϕ ij :
-
Random phase
- φ :
-
Generic degree of freedom on 6DoF solver
- ω i :
-
Wave frequency
- Δt :
-
Time step
- ∇u :
-
Velocity gradient
- Δx :
-
Thickness of propeller disk
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Acknowledgments
This research was sponsored by Office of Naval Research grant N00014-01-1-0073 under the administration of Dr. Patrick Purtell. Computations were performed on the IBM Power 5 at the Department of Defense NAVO Major Shared Resource Center and on the SGI Altix 4700 at the NASA Advanced Supercomputing Division.
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Carrica, P.M., Ismail, F., Hyman, M. et al. Turn and zigzag maneuvers of a surface combatant using a URANS approach with dynamic overset grids. J Mar Sci Technol 18, 166–181 (2013). https://doi.org/10.1007/s00773-012-0196-8
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DOI: https://doi.org/10.1007/s00773-012-0196-8