ADDED MASSES IN SHIPS

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.

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.

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.

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.

•  Density of 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. 

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.

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: 

• 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. 

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