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Method (1): Two inter-penetrating continua: IPSA

In most circumstances, the two phases are taken as having the same pressure; but allowance can be made for the existence of a contact pressure between solid particles, when their volume fraction is close to unity.

This extra pressure is not shared by the fluid within which they move.

The IPSA method has been used in PHOENICS since 1981.

Click here for a lecture on IPSA.

Applications of IPSA

Applications of the use of this method include the simulation of:-

• steam-and-water flows in nuclear steam generators, and in pressurized-water nuclear reactors during loss-of-coolant accidents;
• combustion of pulverized-coal clouds in furnaces or of oil- droplet sprays in furnaces, diesel engines and gas-turbines;
• rain- and snow-fall phenomena in the atmosphere;
• the motion of sand, carried by the wind of by river flows;
• fluidized-bed phenomena.

An example from the PHOENICS Input Library:

DETAILS:

• A cylindrical tube-and-baffle steam generator is simulated
• The heat-flux distribution from hot water in the immersed tube bank is prescribed
• The flow is three-dimensional and steady
• Steam and water enthalpies, volume fractions and velocities have been calculated by use of the IPSA procedure
• A polar-coordinate grid is used
• Steam generators of this kind are employed in nuclear power plant of the pressurized-water-reactor kind

Contours of volume fraction of steam, formed from water entering at the bottom of the cylindrical vessel

The steam-generation pattern is not symmetrical because the temperature of the water in the immersed U-tubes falls between inlet and outlet.

The water enthalpy, measured above a base value corresponding to the entry temperature, just below boiling point. The water becomes super-saturated where the heating rate is most intense.

Contours of upward velocity of steam. The flow pattern is far from being axi- symmetrical.

Contours of upward velocity of water. Note that the water velocities are smaller than the steam velocities, because of inter-phase slip.

The distribution of pressure.

The pressure diminishes with increase in height partly because of gravity and partly to accelerate the steam-water mixture.

Another example: a coal-fired furnace

The IPSA method is used so as to simulate the different but interacting motions and exchanges of heat and mass between the coal and the burning gases.

Gas-phase temperature contours

Solid-phase temperature contours in the coal-fired furnace.

Note that the gas and coal temperatures are not the same.