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RANS study of Strouhal number effects on the stability derivatives of an autonomous underwater vehicle

  • M. H. Shojaeefard
  • A. Khorampanahi
  • M. Mirzaei
Technical Paper

Abstract

This paper presents a numerical procedure to calculate the stability derivatives of an Autonomous Underwater Vehicle (AUV). In addition, the effects of Strouhal number on the stability derivatives are investigated. The stability derivatives are obtained by finding the body hydrodynamic responses to some specified time variant motions. Here, three distinct oscillating maneuvers: surge, pure-heave, and pure-pitch are proposed based on the linearized equations of motion. A Computational Fluid Dynamics (CFD) method based on Reynolds Averaged Navier–Stokes (RANS) equations with dynamic mesh technique is used to simulate the specified maneuvers. To verify the numerical scheme, computational results for simulation of the flow field are then validated by comparison with experimental data. In addition, a comparison between quasi-steady (Theodorsen’s theory) and RANS approaches is taken into account, which shows that the quasi-steady methods do not guarantee the solution accuracy for the purpose of stability derivative calculation. Finally, the effects of Strouhal number variations on these coefficients are investigated which shows that the dimensionless damping coefficients (except longitudinal damping coefficient) are evidently dependent on the Strouhal number, specially at high frequencies. However, the Strouhal number variation effects on the added-mass coefficients are small.

Keywords

Stability derivatives Theodorsen’s theory Strouhal number Dynamic mesh 

List of symbols

A

Wake width, approximated as 2z0

CT

Mean thrust force coefficient

Iyy

Moment of inertia in pitch

F

Thrust force

H0H1

Hankel functions of the first kind and the second kind

Re

Reynolds number

St

Strouhal number

T

Period of oscillations (s)

XZM

Surge and heave forces and pitch moment

X′, Z′, M

Dimensionless surge, heave forces, and pitch moment

c

Hydrofoil chord

f

Frequency of oscillation (1/s)

x0z0θ0

Amplitude of surge, heave, and pitch motions

lref

Reference length

m

Mass of the body

t

Time variable

uwq

Surge, heave, and pitch velocities

\(\bar{u},\bar{w},\bar{q}\)

Steady velocities in surge, heave, and pitch directions

u′, w′, q

Fluctuating velocities in surge, heave, and pitch directions

u*w*q*

Dimensionless velocities in surge, heave, and pitch directions

xz

Surge and heave positions

xCGzCG

Position of center of gravity in xz plane

θ

Pitch angle

ρ

Density

ω

Frequency of oscillation (rad/s)

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • M. H. Shojaeefard
    • 1
  • A. Khorampanahi
    • 1
  • M. Mirzaei
    • 2
  1. 1.School of Mechanical EngineeringIran University of Science and TechnologyTehranIran
  2. 2.Hydro-Aeronautical Research Center, Shiraz UniversityShirazIran

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