3. MATHEMETICAL MODELS

Rigorously tested and highly accurate mathematical models ensure highly accurate reproduction of specific behavioral characteristics and natural effects. Mathematical modeling is both an art and a science. A math model is the back bone of any simulation software. The better the quality of this core component, the more accurate and realistic the behavior. To ensure the quality of the mathematical models underlying its simulation products, ARI works in close consultation with domain experts and relevant functional specialists.

As a case in point, if we look at the ARI Cargo Handling simulator we find project development teams working closely with experts in fluid dynamics, tanker technologies, tanker operations, physics, mathematics and ship building. The result is a model that is robust, versatile, dynamic and above all, accurate, that takes into consideration:

• Physical and chemical properties of liquids and gases e.g. viscosity, vapour pressure, molecular weight, enthalpy and others.

• Fluid dynamics incorporating such variables as characteristics of different pumps (centrifugal, reciprocating, screw, eductors), change of flow with level, back pressure, valve setting, junctions & nodes (networks), level controllers, effect of list and trim on pump suction, mass conservation and many others.

• Thermodynamics including heat transfer at heat exchangers, tank walls (with and without insulation), two phase flows, vapour generation, flow through orifices and nozzles (atomization) and consequent heat transfer. Liquid/Vapour mass exchange is considered for establishing equilibrium levels within cargo tanks along with modeling of boundary layers to account for the non-equilibrium component.

• Stratification, both in liquid and vapour phases, to accurately demonstrate the compliance with MARPOL 73/78 (with amendments) for legal discharge of oil and the use of displacement or dilution methods for inerting/gas freeing of cargo tanks.

• Components of gas cargoes and preferential evaporation of the more volatile components including its effect on reliquefaction.

• NPSH requirements for cargo pumps and the effect of following (or not following) correct procedures for tank stripping on pump cavitation and ROB quantities.

ARI is working on further enhancement of the mathematical models by building a ready-to-use behavioral prediction tool for its navigation simulators. The tool will allow users to edit ship characteristics ‘on the fly’ through a convenient graphical interface, and observe the consequent changes in behavioral characteristics.