|Figure 1: Graphical simulation of the added mass effect condition of a vessel (Courtesy: http://www.scmdt.mmu.ac.uk/cmmfa/images/ship.jpg)|
|Figure 2: (Copyright: Learn Ship Design)|
|Figure 3: Representation of added mass due to surrounding fluid (Courtesy: Googleimages)|
- Displacement of the object:
- Motion of the body:
Density of the Fluid:
- Hull Form:
|Figure 4: Finer and fuller hull form|
- Boundary Conditions:
|Figure 5: Ship moving through channel (Courtesy: Wikipedia)|
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)
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.
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
|Figure 6: (Copyright : ADDED MASSES OF SHIP STRUCTURES)|
- Analytical/Empirical Approach. (also including strip theory)
- Numerical Approach
|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
- · 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