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Study on the cavitation characteristics of cupped foils

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Abstract

The effects of cupping on a 0.7 radius foil section with a maximum thickness ratio of 3.5% of the Gawn-Burrill propeller series were studied both numerically and experimentally. A cupped foil increases its lift as a result of the induced camber by the cup, as the numerical results demonstrate. Also, the minimum pressure location of cupped foil moves from midchord to the cupped position near the trailing edge when the foil is in shock-free entrance. The calculated results and the tests confirm that cupped foil increases lift and may improve the cavitation performance of an underpitched propeller.

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Abbreviations

A + :

constant for the Baldwin-Lomax turbulence model, value 26

C :

chord length of foil

C cp :

constant for the Baldwin-Lomax turbulence model, value 1.2

C du :

uncorrected measured drag coefficient

C kleb :

constant for the Baldwin-Lomax turbulence model, value 0.65

C L, Cl :

lift coefficient

C lu :

uncorrected measured lift coefficient

C m1/4u :

uncorrected moment coefficient about a quarter chord

C p :

pressure coefficient on the foil surface

C pm :

measured pressure coefficient after blockage correction

C pmin :

minimum pressure coefficient

C pmu :

uncorrected measured pressure coefficient

C τ :

calculated local skin friction coefficient

D :

drag of foil

F :

flux vector

F max :

maximum value ofF(y)

F wake :

parameter of the Baldwin-Lomax model which is equal toF maxymax

F(y) :

moment of vorticity

F kleb(y):

Klebanoff function

G :

flux vector

H :

height of the test section of the cavitation tunnel

K :

Clauser constant for the Baldwin-Lomax turbulence model, value 0.0168

k :

constant for the turbulence model, value 0.4

L :

lift of foil

l :

mixing length

N :

total number of grid points

p :

pressure of flow field

p * :

pressure normalized by\(\rho ,P* = \frac{P}{\rho }\)

q :

flow variable vector includingp *,u, ν

R n :

Reynolds number based on the chord length of the foil

t :

time coordinate

T :

maximum thickness of foil

U ∞ :

reference velocity

u :

velocity vector

u :

velocity inx-direction

u i :

velocity components (u 1, u2)=(u, ν)

u τ :

shear velocity

ν:

velocity in they-direction

x :

x coordinate along the flat face side of the foil

x b :

x location of the pressure hole on the back of the foil

x cup :

length of cup in thex direction

x f :

x location of the pressure hole on the face side of the foil

x i :

components of Cartesian coordinates (x 1, x2)=(x, y)

y :

y coordinate upward and perpendicular tox coordinate

y c :

intersection of the outer layer and inner layer of the boundary layer

y cup :

drop of the trailing edge in they direction

y max :

location ofF max

y + :

yu τ/ν

y +1 :

y + value of first grid point

α:

angle of attack, which is the angle between the inflow direction and thex coordinate (the flat face side of the foil)

α 0 :

zero angle of attack

α sc :

induced angle of attack of streamline curvature

σ:

density of fluid

τ ij :

turbulent shear stress,i, j,=x, y

σ:

boundary thickness

ν:

kinematic viscosity plus turbulent eddy viscosity

V ∞ :

kinematic viscosity

V t :

turbulent eddy viscosity

\(v_{t_{outer} } \) :

turbulent eddy viscosity of the outer layer

\(v_{t_{inner} } \) :

turbulent eddy viscosity of the inner layer

\(v_{t_{wake} } \) :

turbulent eddy viscosity of the wake

ε:

pressure correction coefficient

ω:

vorticity

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Authors and Affiliations

  1. Department of Naval Architecture and Ocean Engineering, National Taiwan University, 73 Chou-Shan Road, Taipei, Taiwan

    Jing-Fa Tsai

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Tsai, JF. Study on the cavitation characteristics of cupped foils. J Mar Sci Technol 2, 123–134 (1997). https://doi.org/10.1007/BF02489804

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  • DOI: https://doi.org/10.1007/BF02489804

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