1. Ship Hydrodynamics - Resistance
İSTANBUL TEKNİK ÜNİVERSİTESİ
Naval Architecture and Marine Engineering – B.S.
GEM341E SHIP HYDRODYNAMICS
(Resistance – Viscous Resistance)
111
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2. Ship Hydrodynamics - Resistance
Viscous Effects and Viscous Resistance
Viscosity may be understood by considering friction between hypothetic layers of fluid which are in contact with solid boundaries
Deformed fluid particle under viscous effects
Here τxy is the shear stress, ∂u/∂y is the rate of change of velocity (strain) as a function of y from the solid boundary and μ is the dynamic viscosity coefficient
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3. Ship Hydrodynamics - Resistance
In 3-D flow; shear stress τxy is given by a total stress tansor together with normal stress (p) – which is called pressure -
The first term of τij gives the viscous pressure drag and the second term (the tangential stress component) is related to the frictional resistance. (Note that pressure (normal stress) due to the wave-making effects is not considered in this investigation).
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4. Let’s recall the decomposition of a ship’s resistance
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5. Frictional Drag (or Skin Friction)
Viscous Pressure Drag
Normal component causes a varying pressure distribution along the underwater part of the hull
A high pressure area is formed around the bow whilst there exists a low pressure zone at the aft
Hull shape is effective; i.e. fuller (blunt) forms have higher viscous pressure drag
Frictional Drag (or Skin Friction)
Tangential stress is parallel to the ship hull and causes a net force (skin friction) that opposes motion.
Skin friction drag or frictional drag of the ship can be assumed by using that of an equivalent length flat plate (note that in this case 3-D effects are discarded) .
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6. Recall that viscous flow is governed by two basic equations; one for the conservation of mass:
and one for the conservation of momentum, namely Navier-Stokes equation:
This is indeed a nonlinear differential equation and impossibility to solve the Navier-Stokes equation analytically comes from the nonlinearity in the convective term of
Computational solutions are possible, but as this is a very vast and complicated area of Fluid Mechanics, we will deal only with the practical/engineering aspects of the viscous flow characteristics.
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7. Boundary Layer
Prandtl was first who defined the boundary layer by dividing the flow field into two areas: one inside the boundary layer, dominated by viscousity and creating the majority of drag experienced by the boundary/solid body; and one outside the boundary layer, where viscosity can be neglected without significant effects on the solution. The velocity profile inside the boundary layer – dominated by viscous effects – zero at the solid boundary and reaches the inflow velocity at the outer boundary of the viscous layer:
L. Prandtl
( )
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8. Blasius Boundary Layer is due to 2-D steady flow over/along a flat plate. However 3-D effects are discarded, flat plate-flows help us to understand the pyhsics of the boundary layer flow.
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9. Approximating the wetted hull surface by an equivalent plank flat plate makes it possible to obtain frictional resistance by means of simpler mathematical/experimental expressions. 3-D effects in this case could be figured out by semi-empirical and/or experimental methods.
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10. More about boundary layers:
The frictional forces between the wall and the fluid due to the viscosity retards the motion of the fluid
The flow velocity gradually decreases closer to the wall and approaches to zero on the wall.
The effect of the wall friction is limited to a rather thin region near the wall and the friction force loses its effect gradually while departing from the wall.
The flow regains its momentum due to the interaction with the energetic outer flow and the streamwise velocity reaches to an almost equal value to that of the outer flow.
This thin region until the streamwise velocity reaches to the 99% of the outer flow velocity is called the boundary layer and the thickness of this region is referred as the boundary layer thickness (δ).
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11. Laminar Flow to Turbulent Flow
Laminar and Turbulent Boundary Layers – flow in a circular pipe
Laminar Flow to
Turbulent Flow
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12. Laminar boundary layers :
A boundary layer may be laminar or turbulent
Laminar boundary layers :
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13. Turbulent boundary layers :
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14. Boundary layer development and velocity profiles in laminar and turbulent regimes
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15. Of the various flat plate boundary layer thickness formulae, the following are the mostly used :
Skin friction is described in terms of the wall shear stress:
where the wall shear stress is the shear stress at the solid boundary:
Skin frictional drag (or frictional resistance) can then be obtained by the integration along the flat plate:
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16. Displacement and Momentum Thicknesses:
The momentum thickness, θ, may be defined as the loss of momentum in the boundary layer as compared with that of inviscid flow.
It is the distance that, when multiplied by the square of the free-stream velocity, equals the integral of the momentum defect.
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17. Skin friction drag can also be expressed in terms of the momentum thickness:
Shape Factor (or Shape Parameter):
Conventionally, H=2.59 (Blasius boundary layer) is typical of laminar flows, while H= is typical of turbulent flows.
A large shape factor may be taken as an indication for boundary layer separation.
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18. Roughness Effect Wall roughness affects the frictional drag:
Drag (frictional) coefficient of laminar and turbulent boundary layers on smooth and rough plates (L/ε; roughness parameter). (White, 1999)
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19. Wall (surface) roughness effect
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20. Flow around a ship hull
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21. Flow separation and vortex shedding
Flow separation means detachment of the streamline flow from a solid boundary
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22. Effect of pressure gradient upon the flow near the wall (White, 1999)
Negative pressure gradient (∂P/∂x<0) is termed a favourable pressure gradient. A positive pressure gradient, namely adverse pressure gradient, has the opposite effect
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23.
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24. Vortex shedding
The vortices create low-pressure zones which urge the vortex shedding body to move towards the vortices. In summary , flow separation and vortex shedding are the main sources of the viscous pressure resistance (or form drag).
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25. Viscous/Frictional Forces on Ships
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26. Viscous pressure resistance and roughness resistance:
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