The overall goal of this project is to develop a transient model for the start up time of a natural draft dry cooling tower (NDDCT). Such knowledge has many potential uses, most significantly in the renewable energy sector, such as solar thermal power. A critical literature review on cooling towers, heat exchangers and heat transfer and pressure drop correlations has been conducted. Choosing correlations that apply to the specific type of heat exchanger geometry being modeled is essential, therefore the Briggs and Young heat transfer and Robinson and Briggs pressure drop correlations have been selected.
A one dimensional finite element analysis, utilizing elements of air within the cooling tower, has been conducted. Such a model was most easily created using the MAT lab coding language. The tower is divided into a specified number of elements of equal height, and flow is initiated by an arbitrary velocity assigned to the first element, situated at the base of the tower. This element will then effectively pass through a heat exchanger heating the air (approximated using Briggs
and Young’s correlation) causing a density decrease and therefore a pressure difference between the tower and atmospheric conditions surrounding it. A key assumption is that density is only affected by temperature and not other factors, such as pressure. This pressure drop is the used with the Robinson and Briggs pressure drop correlation to convert density differences into flow velocity. The flow speed will then increase until the buoyant force is balanced with resistances at its steady state.
A base case using a 120m tall and 50m wide tower has been computed, resulting in a steady state velocity of 2.773 m/s and a time to steady state of 84.1 seconds. An investigation took place into the effects of varying some key parameters of the tower. Tower width was found to not affect the velocity plot at all, only the mass flow rate and therefore cooling capacity. In contrast changing the height of a tower resulted in changes to the steady state velocity and time to reach that speed. When comparing towers of equal radius, the shorter tower will have al ower steady state flow rate as the shorter a tower the less low density air it can contain, reducing the pressure drop experienced relative to outside air.
An additional investigation of the arbitrarily assigned initial velocity concluded that this velocity must be low to approximate zero, but not too low as to severely affect the final time to steady state. A velocity of 0.01 m/s was deemed appropriate for most cases. The height of the finite elements was also found to have a major affect both the shape of the velocity plot and the time to steady state. Smaller elements are more desirable as they allow the selection of a lower initial velocity. For the case of a 120m tall tower, 1000 finite elements were sufficient for accuracy.
Several issues are present with this model, most notably the absence of a heat transfer correlation for finned tube heat exchangers for flow at low Reynolds numbers. This issue together with the inability to initiate flow without an arbitrarily selected velocity results in an unusual and unrealistic velocity plot. The time scale is of the order of magnitude expected, as is steady state velocity, but the flow acceleration is not as expected. A distinctive ‘spike’ in velocity occurs before flow settles at its constant velocity. This is caused by excess heating of the first few elements due to the reasons discussed above. The Briggs and Young approximation estimates the heat transfer coefficient accurately at Reynolds numbers above 800 but over estimates it at slower speeds.
Overall the program does provide the desired results, however some verification would be desirable. Finally, more suitable ways of initiating flow, approximating heat transfer at low velocities and of discretising the finite elements would be beneficial to the accuracy of the program.