2.6 Forces Imposed by Fluid Flow
a
leading
edge
. ------------------angle -0/ attack -Fig. 2.27: A typical shape of hydrofoils
61
trailing edge
This ratio varies considerably for marine organisms and no general rule exists.
We will discuss this problem in more detail in Chap. 11. Here, we only give
some basic results and provide the terminology and some theoretical results.
For our purpose, a symmetric streamlined body is assumed. The angle between the free stream and the chord line is called the angle of attack. In some
hydrofoils, as in aerofoils, the chord line between leading and trailing edges is
not a line of symmetry, and such hydrofoils are known as 'cambered'.
How does a hydrofoil produce lift? The theory of aero foils and hydrofoils was
developed by Russian hydrodynamicist Zhukovskii (or Joukowsky) early in the
present century. Rather than proceed with the derivation of the governing
theoretical equations, we provide a physical explanation of lift creation by
the hydrofoils. When a slightly inclined (0: > 0) hydrofoil starts to move it
splits the flow into two streams: flow over the upper surface and flow under
the lower surface. The velocities in these streams are not equal due to the
inclination of the hydrofoil. When these two streams meet at the trailing
edge, a separation appears and a starting vortex forms. This vortex is shed
downstream and a smooth streamline develops over the hydrofoil and Mt is
fully developed. However, within the boundary layer the flow is viscous and
due to the velocity gradient, vorticity exists (for definition of vorticity see
Appendix C.t). Physically, the existence of vorticity means that the vortices
in the fluid are generated in a boundary layer and their strength depends on
the velocity gradient.
Because the velocity gradients on the top and bottom surfaces are of opposite
sign, the vorticities also have opposite signs. When these vorticities are equal in
strength, the resultant circulation around the hydrofoil is zero. This is a case of
symmetrical hydrofoil with zero angle of attack. If the vorticity (also velocity
gradients) over the top surface exceeds that over the bottom, the resultant
circulation is a non-zero quantity. Velocities over the upper surface are higher
than under the lower surface. According to the Bernoulli equation, such a
a
leading
edge
. ------------------angle -0/ attack -Fig. 2.27: A typical shape of hydrofoils
61
trailing edge
This ratio varies considerably for marine organisms and no general rule exists.
We will discuss this problem in more detail in Chap. 11. Here, we only give
some basic results and provide the terminology and some theoretical results.
For our purpose, a symmetric streamlined body is assumed. The angle between the free stream and the chord line is called the angle of attack. In some
hydrofoils, as in aerofoils, the chord line between leading and trailing edges is
not a line of symmetry, and such hydrofoils are known as 'cambered'.
How does a hydrofoil produce lift? The theory of aero foils and hydrofoils was
developed by Russian hydrodynamicist Zhukovskii (or Joukowsky) early in the
present century. Rather than proceed with the derivation of the governing
theoretical equations, we provide a physical explanation of lift creation by
the hydrofoils. When a slightly inclined (0: > 0) hydrofoil starts to move it
splits the flow into two streams: flow over the upper surface and flow under
the lower surface. The velocities in these streams are not equal due to the
inclination of the hydrofoil. When these two streams meet at the trailing
edge, a separation appears and a starting vortex forms. This vortex is shed
downstream and a smooth streamline develops over the hydrofoil and Mt is
fully developed. However, within the boundary layer the flow is viscous and
due to the velocity gradient, vorticity exists (for definition of vorticity see
Appendix C.t). Physically, the existence of vorticity means that the vortices
in the fluid are generated in a boundary layer and their strength depends on
the velocity gradient.
Because the velocity gradients on the top and bottom surfaces are of opposite
sign, the vorticities also have opposite signs. When these vorticities are equal in
strength, the resultant circulation around the hydrofoil is zero. This is a case of
symmetrical hydrofoil with zero angle of attack. If the vorticity (also velocity
gradients) over the top surface exceeds that over the bottom, the resultant
circulation is a non-zero quantity. Velocities over the upper surface are higher
than under the lower surface. According to the Bernoulli equation, such a