A very typical feature associated with ships or any other
floating bodies is that unlike any land borne object, it has to overcome the
effect of the fluid it is floating in. Let us take a simple example. Suppose
you are wading through knee-deep water on a waterlogged road after a spell of
heavy rainshowers. Does it feel the same to walk the same stretch as compared
any other normal dry day?
The answer is a big no. Not only you take more time to tread
the same distance, but you also need somewhat extra effort to make your way.
The same physics applies to vessels. Water has a finite value of density.
Furthermore, when a vessel surges through the water, it creates a disturbance
to the surrounding fluid. The fluid which already has some ‘flow’, thanks to
its velocity potential gets an added acceleration triggered
off by the ship motion.
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| Figure 1: Graphical simulation of the added mass effect condition of a vessel (Courtesy: http://www.scmdt.mmu.ac.uk/cmmfa/images/ship.jpg) |
It is seen that when a vessel surges through water, it
creates a boundary layer in the surrounding fluid which always is viscous. What
is Boundary layer? A very critical aspect in fluid mechanics which ascribes the
phenomenon of flow separation due to the motion of a body in a real fluid. A
boundary layer is formed which demarcates the normal surrounding flow with the
‘flow affected by the body motion’. Thus the fluid content in this boundary
layer gets influenced by the ship motion.
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| Figure 2: (Copyright: Learn Ship Design) |
This accelerated fluid particles create forces on the
surface of contact of the vessel! As the
ship motion has already triggered off a disruption to the potential flow of the
fluid, the fluid particles possess some amount of kinetic energy. Thus apart
from accelerating itself, it also has to expend some amount of extra ‘kinetic
energy’ upon the surrounding fluid. This is realized in terms of propelling
with some extra amount of mass which gives rise to the concept of added mass or
virtual mass. Added masses arise simple from hydrodynamic considerations triggered mainly by waves and other external disturbances and
have no correlation with the structure or propulsive parameters of the vessel.
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| Figure 3: Representation of added mass due to surrounding fluid (Courtesy: Googleimages) |
Though added mass is essentially a wave phenomenon, it depends on several factors. Now
what does added mass of a body depend upon?
- Displacement of the object:
As well predicted, the added mass is a function of the mass
displacement of the body under consideration.
The larger is the displacement, more is the added mass measured. Though
it may be common to confuse it with buoyancy forces, it may be well noted that
buoyant forces are static properties of a floating body which solely depend
upon the geometry of the body and the fluid density. In other words, it is a hydrostatic
effect. This has no relation
with the added mass which is a hydrodynamic phenomenon limited to
finite sized floating bodies surging in water with some acceleration. For
symmetric bodies such as cylinder, cube etc., the added mass is mathematically
the displaced volume times the density of the fluid. But a ship being a complex
geometric object, the displaced water plus some extra amount of fluid in its
wake is taken into account for determination of added mass.
- Motion of the body:
· A ship or any other body has some definite value
of velocity and acceleration as well. This, in turn is reciprocated by the
pressure field of the displaced velocity in terms of kinetic work. To put it
simply, the more the velocity of the body, more is the reaction forces
generated by the fluid.
·
A ship or any other body has some definite value
of velocity and acceleration as well. This, in turn is reciprocated by the
pressure field of the displaced velocity in terms of kinetic work. To put it
simply, the more the velocity of the body, more is the reaction forces
generated by the fluid.
- Hull Form:
·
As the ship has a complex geometry, a detailed
analysis of the hull form exacts to the accurate determination of the added
mass. The sections at each station from fore to aft and their interaction with
the displaced fluid is studied in detail which gives the exact idea of the
added mass. It has been observed that finer hull forms have a reduction in added mass.
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| Figure 4: Finer and fuller hull form |
- Boundary Conditions:
·
There is an interesting physics behind the
behaviour of added mass properties in effect to the boundary conditions
persistent. In shallow waters, the added mass of any floating body is seen to
increase considerably. This effect is more pronounced when the vessel is
floating through a restricted water body like channel or canal. The reason is
quite simple. As the restrictions increase, the waves which are formed from the
moving body is reflected back continually until damped. This increasingly high
rate of wave incidence increases the added mass effect. Thus, it is worthwhile
to say that a ship finds more difficulty in passing through a canal or channel
as compared to the open sea.
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| Figure 5: Ship moving through channel (Courtesy: Wikipedia) |
DETERMINING
THE ADDED MASS
For symmetrical perfect objects like a solid sphere, cuboid,
ellipsoid the added mass in normal conditions is the mathematical equivalent of
its displacement. However, for complex shaped objects like a ship, the added
mass determination may be a difficult task to achieve. Here the added mass
comes out to be more than the mass displacement. Also the values are variant
from ship to ship and from time to time.
Figure 6: (Copyright : ADDED MASSES OF SHIP STRUCTURES)
Analogous
to the variation in buoyancy when a ship encounters waves, the added mass
varies from situation to situation. Thus it is valid to reason that there’s no
fixed algorithm to determine the added mass. As the added mass is directly
related to the kinetic energy of the surrounding fluid, it would involve terms
related to energy components.
In Newtonian terms, the drag, velocity and energy vartiation
may be expressed as:
This ρ*I term is the measure of the mass equivalent related
to the hydrodynamics of the disturbed fluid.
The evaluation of this mass term is carried out using these
classical techniques:
DETERMINING
THE ADDED MASS
For symmetrical perfect objects like a solid sphere, cuboid,
ellipsoid the added mass in normal conditions is the mathematical equivalent of
its displacement. However, for complex shaped objects like a ship, the added
mass determination may be a difficult task to achieve. Here the added mass
comes out to be more than the mass displacement. Also the values are variant
from ship to ship and from time to time.
 |
| Figure 6: (Copyright : ADDED MASSES OF SHIP STRUCTURES) |
Analogous
to the variation in buoyancy when a ship encounters waves, the added mass
varies from situation to situation. Thus it is valid to reason that there’s no
fixed algorithm to determine the added mass. As the added mass is directly
related to the kinetic energy of the surrounding fluid, it would involve terms
related to energy components.
In Newtonian terms, the drag, velocity and energy vartiation
may be expressed as:
This ρ*I term is the measure of the mass equivalent related
to the hydrodynamics of the disturbed fluid.
The evaluation of this mass term is carried out using these
classical techniques:
- Analytical/Empirical Approach. (also including strip theory)
- Numerical Approach
The methodology of these two approaches is a matter of scope
beyond our discussion. But now in recent the development of softwares such as
FEM packages, ABAQUS, NASTRAN and so on, the determination process has become
easier. The above two methods include intricate mathematical deductions along
with basic physical principles of boundary element method and infinite
potential flow.
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| Figure 7: 3D Modelling Patch(sample) for added mass calculation using FEM (Courtesy: Analytical and Numerical Computation of Added Mass in Ship Vibration Analysis) |
· IMPLICATIONS OF ADDED MASS
Now all of you must be wondering: why is the determination
of added mass so important?
The answer lies in its applicability. Added mass is mainly
aggravated by waves and other fluid inter actions in open water. And as the
ship has to face them inevitably, added mass calculations must be taken in
account. As added mass effects are virtually realized as ‘entrained’ mass, design
considerations must be taken in to account in the following ways:
- · Resistance of the hull. Thus the propulsive characteristics are modified accordingly to meet the surplus power required for added mass counterbalance.
- · Structural design modifications. As obvious, due to the hydrodynamic forces generated in the form of added mass incident upon the hull, the structural reliability factor must be enhanced manifold in strength and load-bearing capacity.
- · Design of hull form. Based on the type of ship, the hull form is decided where the minimization of added mass is also given adherence.
- · Maneuvering Characteristics: Added mass also causes difficulty in manoeuvring; extra rudder forces and more time required for a change of heading. Thus during fabrication of basic control surfaces like rudders or stabilizers, the added mass effect is taken for a better estimate of the manoeuvring characteristics and thus modifying its design.
- · Cost estimation and economy: As we know in ships, the resultant profit is the final aim for all parties. Added mass consumes more fuel, expends more engine power and also increases the time of voyage in the long run. But in shipping industry, economy is hard money. Thus the estimation of excess fuel consumption, cargo-carrying safety limits, voyage charter timings and increased engine power required due to added mass is mandatory as to give a better idea of the net expenditure.LSD
Article by : Subhodeep Ghosh
nice post
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