ANL/UI (Argonne National Laboratory / University of Illinois) is a one-dimensional steady-state integral model in which the independent variable is taken to be the distance along the plume centerline. It has been developed to evaluate cooling tower environmental impacts.
The model assumes the plume to be formed by three coaxial regions: the inner one is used to describe the plume water content (moisture core); the medium one, that surrounds the inner, provides the energetic content (heat o temperature core) and the external one, with the larger diameter, contains the mechanical properties (momentum core). This assumption can be justified because temperature and momentum have different spreading rates in radial direction (temperature mixes more slowly than does the momentum). The physical effect of assuming two radii for temperature and momentum is that the smaller heated region at the core provides the buoyancy for accelerating the larger momentum-containing region. As a result, buoyancy effect are lessened.
At the emission time, the three plumes have the same diameter. As far as the plume moves away from the stack, the radius of each region of the plume varies following its own equation. Moreover, close to the emission point, the dynamic variables have a top hat profile normally to the plume axis; far from the stack, they have instead a Gaussian distribution. Inside their own core, velocity, temperature and moisture are assumed to be constant.
The model solves a conservation equation for momentum in vertical direction. For the horizontal displacement, the model assumes the bentover hypothesis, meaning that the plume horizontal velocity is taken to be equal to the ambient velocity at plume height at all times, including immediately on exit from the tower. The bentover hypothesis has been introduced to take into account for the ambient air entrainment, that reduces plume’s vertical velocity due to the buoyancy force (entrained ambient air has zero vertical momentum, but causes the plume’s horizontal velocity to increase). The plume shape simulated using this hypothesis shows the correct natural plume’s bent.
The cooling tower or the building presence generates a pressure reduction down wind. The pressure gradient close to the stack and downwind to the stack generates a force that pushes the plumes downward. ANL/UI contains the physical concepts that are necessary to describe the downwash effect. This is done adding a term in the vertical momentum conservation equation. This term is different for emissions coming from NDCT (natural draft cooling towers) or MDCT (mechanical draft cooling towers). Moreover, due to the increase of downwind turbulence, an increasing of plume dilution is observed. The concentration decrease is described by the model through a multiplication factor. ANL/UI is one of the few models for cooling towers that can simulate the downwash effect.
The model also solves the conservation equation for mass, energy and water content. The visible part of the plume is obtained by determining the points where specific humidity is higher than specific saturation humidity at a given plume temperature.
From the physical point of view, the water content of the plume should freeze when it reaches a negative temperature. Actually, in order to have ice formation in the atmosphere, it is always necessary to go few degrees below zero (supercooling). The necessary supercooling is higher when less condensation nuclides are present (so supercooling is greater in clean atmosphere). It has been observed that a -10 °C supercooling causes a spontaneous nucleation and ice formation. The ANL/UI model simulates the liquid water freeze when the temperature is under 10 °C. When ice is present in the plume, the saturation mixing ratio is calculated over the ice instead than over the water.
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