Journal of Marine Science and Technology

, Volume 14, Issue 3, pp 373–386 | Cite as

Estimation of the hydrodynamic coefficients of the complex-shaped autonomous underwater vehicle TUNA-SAND

  • Sulin Tang
  • Tamaki Ura
  • Takeshi Nakatani
  • Blair Thornton
  • Tao Jiang
Original Article


Hydrodynamic coefficients strongly affect the dynamic performance of autonomous underwater vehicles (AUVs). Thus it is important to have the true values of the coefficients in order to simulate the AUV’s dynamic performance accurately. Although these coefficients can be predicted by many methods, most are only applicable for AUVs with streamlined shapes. Computational fluid dynamics (CFD) can be applied to estimate the hydrodynamic coefficients of AUVs with complex shapes. In this study, CFD was applied to estimate the hydrodynamic coefficients of the AUV TUNA-SAND (which stands for terrain-based underwater navigable AUV for seafloor and natural resources development), which has a complex block-like structure. First, the validity of the CFD simulation was verified by comparison with experimental results. Second, the relationships between hydrodynamic loads and motions for all six degrees of freedom were analyzed using the simulated results. Third, the importance of each hydrodynamic coefficient was investigated based on these relationships. There are 16 key damping coefficients that relate to viscosity and 12 key inertial coefficients that relate to the potential flow around TUNA-SAND. Finally, the values of all the key coefficients were obtained and verified by comparing the solutions of the simulated dynamics with the experimental results.


Autonomous underwater vehicle (AUV) Computational fluid dynamics (CFD) Complex block-like shape Hydrodynamic coefficient 

List of symbols


Body-fixed frame


Earth-fixed frame

X, Y, Z, L, M, N

Surge, sway, and heave hydrodynamic forces, and roll, pitch, and yaw hydrodynamic moments


Surge, sway, and heave force, and roll, pitch and yaw moments provided by the thrusters

u, v, w

Surge, sway, and heave velocity

p, q, r

Roll, pitch and yaw angular velocity

u′, v′, w

Surge, sway and heave acceleration

p′, q′, r

Roll, pitch and yaw angular acceleration


Mass of the vehicle


Density of water

Drain volume of the vehicle


Centre of buoyancy

Ix, Iy and Iz

Moments of inertia

Φ, Θ and Ψ

Euler angles between Earth-fixed frame and the body-fixed frame

Xi, Yi, Zi, Li, Mi, Ni

Hydrodynamic coefficients for surge, sway, heave, roll moment, pitch and yaw moment, e.g. \( X_{u|u|} = \partial X/\partial u|u| \)




Rotational speed of thruster


Diameter of thruster


Inlet flow velocity


Thrust coefficient


Thrust coefficient for J = 0, J = Va/nD


Reynolds number


Length of body


Kinematic viscosity of salt water at 15°C, ν = 1.19 × 10−6


Quality and reliability assurance coefficient of grids, 0 ≤ QRAS ≤ 1


Design speed


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Copyright information

© JASNAOE 2009

Authors and Affiliations

  • Sulin Tang
    • 1
    • 2
  • Tamaki Ura
    • 2
  • Takeshi Nakatani
    • 2
  • Blair Thornton
    • 2
  • Tao Jiang
    • 1
    • 3
  1. 1.Key Laboratory of Tectonics and Petroleum Resources (Ministry of Education)China University of GeosciencesWuhanChina
  2. 2.The Underwater Robotics and Application (URA) LaboratoryThe University of TokyoTokyoJapan
  3. 3.Ocean Research InstituteThe University of TokyoTokyoJapan

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