Journal of Marine Science and Technology

, Volume 18, Issue 2, pp 166–181 | Cite as

Turn and zigzag maneuvers of a surface combatant using a URANS approach with dynamic overset grids

  • Pablo M. CarricaEmail author
  • Farzad Ismail
  • Mark Hyman
  • Shanti Bhushan
  • Frederick Stern
Original article


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.


Ship maneuvers 6DOF URANS Surface combatant Dynamic overset grids 



Wave amplitude


Surface area of solid surface


Bretschneider coefficient which depends on wave period and wave height


Coefficient for axial body force


Coefficient for azimuthal body force


Bretschneider coefficient which depends on wave period


Constants defining order of accuracy of 6DoF solver


Propeller diameter


Axisymmetric body force in axial direction


Axisymmetric body force in azimuthal direction


Fluid forces in the earth reference system


Propeller forces in the ship reference system


Fluid forces in the ship reference system


Significant wave height


Moment of inertia about x-axis


Moment of inertia about y-axis


Moment of inertia about z-axis


Advance coefficient


Transformation matrix from \(\dot{{\varvec {\eta }}}\) to \( {\mathbf{v}} \)


Wave number


Torque coefficient


Thrust coefficient

(K, M, N)

Moments in x, y, z direction


Fluid moments in the earth reference system


Fluid moments in the ship reference system




Directional spectrum


Angular velocity of propeller




Roll velocity

\( \dot{p} \)

Roll acceleration


Upstream point of propeller volume


Downstream point of propeller volume


Pitch velocity

\( \dot{q} \)

Pitch acceleration


Yaw velocity

\( \dot{r} \)

Yaw acceleration


Distance vector


Propeller hub radius


Propeller radius


Frequency spectrum


Modal wave period


Surge velocity

\( \dot{u} \)

Surge acceleration


Wave velocity in x-direction


Ship forward velocity


Sway velocity

\( \dot{v} \)

Sway acceleration


Wave velocity in y-direction


Heave velocity

\( \dot{w} \)

Heave acceleration


Wave velocity in z-direction

xG, yG, zG

Distance from the center of rotation to the center of gravity of the ship


Center of gravity


Center of rotation of ship

(X, Y, Z)

Forces in x, y, z direction



Angle of incidence


Heading angle


Dispersion angle

η(x1, x2, x3, ϕ, θ, ψ)

Position and Euler angles

\( \dot{\varvec{{\eta }}} \)

Rate of change of position and Euler angles


Linear and angular velocity vector


Wave elevation


Angle of incidence


Random phase


Generic degree of freedom on 6DoF solver


Wave frequency


Time step


Velocity gradient


Thickness of propeller disk



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.

Supplementary material

Supplementary material 1 (MPG 6084 kb)

Supplementary material 2 (MPG 7954 kb)

Supplementary material 3 (MPG 4372 kb)

Supplementary material 4 (MPG 8062 kb)


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Copyright information

© JASNAOE 2012

Authors and Affiliations

  • Pablo M. Carrica
    • 1
    Email author
  • Farzad Ismail
    • 2
  • Mark Hyman
    • 3
  • Shanti Bhushan
    • 4
  • Frederick Stern
    • 1
  1. 1.IIHR Hydroscience and EngineeringThe University of IowaIowa CityUSA
  2. 2.School of Aerospace EngineeringUniversiti Sains MalaysiaPenangMalaysia
  3. 3.Naval Surface Warfare Center Panama CityPanama CityUSA
  4. 4.Center for Advanced Vehicular SystemsMississippi State UniversityStarkvilleUSA

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