Hot towers formation - A Simple Integral Model of Plume Rise

In a world where everything happens instantaneously, air surrounding a horizontal heated hot plate rushes in and mixes efficiently to ensure that the pressure difference caused by the buoyancy effect is nullified, an equilibrium situation. This is nearly achieved with small face-dimension hot or cold plates.

As the flat plate dimensions increase for the same process conditions, the equilibrium is disturbed until a steady state occurs where there is a constant pressure difference between the core of the plume and the ambient air. This is brought about by the buoyant plume diverting the entrained ambient air upwards, disallowing an equilibrium to be established.

It is by taking advantage of this non-equilibrium that one can create an ‘Effective Plume-chimney' that is invisible. Up until the year 2002, the empirical Doyle and Benkly formula had been the only method available in the open literature for estimating the ‘effective plume-chimney height' (EPCH) of an air-cooled heat exchanger operating under natural convection. In a previous work by Chu (1986) several possibilities of physically measuring an EPCH was investigated. It was experimentally determined using a laboratory size air-cooled heat exchanger that ho was negligibly small. Data from a fullsize industrial heat exchanger of 2.0 x 3.1 m2 face area and fitted with three hardware chimney heights of 0.30, 1.22 and 2.44 m appeared to support the laboratory result reasonably well. It was eventually recognised however that assuming the EPCH to be negligibly small when simulating a forced draft air-cooled heat exchanger with large face dimensions can lead to a very conservative result. An equation for predicting the EPCH was therefore developed by Chu (2002) and found to compare within acceptable error of the data obtained at an Industrial Test Rig (ITR).

Since the concept is based on a horizontal heated flat plate of sizable dimensions, it is therefore logical to apply the EPCH on natural convection phenomena that occur over objects or surfaces of similar geometrical characteristics, namely oceans, forest fire, nucleate pool boiling vessels and forced draft air-cooled heat exchangers. For a mesoscale plume source (10 -1000km) it was found necessary to develop an integral model derived from conservation of mass, momentum and energy equations to predict EPCH. The EPCH is determined using the necking height as suggested by Scorer (1959).

Hurricane intensification has been studied by scientists for decades and one phenomenon that appears to always accompany the intensification is the presence of hot towers of cumulous clouds that stretches from 10 km to 15 km high. Hot towers have been confirmed by scientists to accompany intensification of hurricanes (http://www.youtube.com/watch?v=kUG4-TEqPYc). While the mechanism as explained in the NASA video about Hot towers formation identifies the differential speeds around the tower wall as causing the tower to rise, the hypothesis proposed here favours the convective mechanism of a large plume source as the real cause, and appears to be supported by using a simple plume integral model on a dry basis, in a calm surrounding, to predict the tower height to be at 5km by equating it to EPCH, and the rising wind speed reaching 200 km/hr in the column.