A single dimensionless variable for solar chimney power plant modeling

The solar chimney power plant is a relatively new technology for generating electricity from solar energy. In this paper dimensional analysis is used together with engineering intuition to combine eight primitive variables into only one dimensionless variable that establishes a dynamic similarity between a prototype and its scaled models. Three physical configurations of the plant were numerically tested for similarity: fully geometrically similar, partially geometrically similar, and dissimilar types. The values of the proposed dimensionless variable for all these cases were found to be nominally equal to unity. The value for the physical plant actually built and tested previously was also evaluated and found to be about the same as that of the numerical simulations, suggesting the validity of the proposition. The physical meaning of this dimensionless (similarity) variable is also interpreted; and the connection between the Richardson number and this new variable was found. It was found also that, for a fixed solar heat flux, different-sized models that are fully or partially geometrically similar share an equal excess temperature across the roof outlet.