Partial geometric similarity for solar chimney power plant modeling

A solar chimney power plant derives its mechanical power from the kinetic power of the hot air which rises through a tall chimney, the air being heated by solar energy through a transparent roof surrounding the chimney. In our previous studies, the achievement of complete dynamic similarity between a prototype and its models imposed the use of different solar heat fluxes between them. It is difficult to conduct an experiment by using dissimilar heat fluxes with different physical models. Therefore, this study aimed to maintain dynamic similarity for a prototype and its models while using the same solar heat flux. The study showed that, to achieve the same-heat-flux condition, the roof radius between the prototype and its scaled models must be dissimilar, while all other remaining dimensions of the models are still similar to those of the prototype. In other words, the models are ‘partially’ geometrically similar to the prototype. The functional relationship that provides the condition for this partial similarity is proposed and its validity is proved by scaling the primitive numerical solutions of the flow. Engineering interpretations of the similarity variables are also presented.