At first, an algorithm which is capable of generating a fractal hydraulic network on a given area with fluid in — and outlet was developed (Fig. 2). Based on this algorithm, the com­puter programme FracTherm was written. The appearance of the structures is strongly in­fluenced by the net parameters chosen. This first step is a pure geometric process which does not yet include hydraulic or thermal calculations.

In order to assess the fractal structures with respect to their energy efficiency, it is neces­sary to carry out hydraulic as well as thermal simulations. For this purpose the structures are exported into a file format which can be read by the simulation environment ColSim that was originally developed for dynamic simulations of solar thermal systems [8]. ColSim was extended by the ability to calculate multiple branched hydraulic networks. This hy­draulic solver also takes pump characteristic curves into consideration.

Net parameters

Net generating algorithm

raclherm

Fig. 2: Generating fractal hydraulic networks with FracTherm

The results of the hydraulic simulations can be visualised within FracTherm. Fig. 3 shows a calculated volume flow distribution drawn on top of a fractal structure. The height as well as the colour indicate the volume flow of each branch.

The collector efficiency factor F is a common measure to evaluate the thermal efficiency of a solar absorber. Analytical approaches exist to calculate F for a conventional absorber fin with a tube attached to it [1, 2]. In order to make use of these formulae, the complex fractal structure is discretised into small absorber fins i. Afterwards, a collector efficiency

factor F is calculated for each absorber fin i, taking the local flow situation and the result­ing heat transfer coefficient into consideration (Fig. 4). Finally, a total collector efficiency factor F can be determined, which can act as a means of comparison between fractal hy­draulic structures and conventional ones.

Fig. 5 shows the calculated distribution of the collector efficiency factor F for an absorber with the dimensions 2500 mm x 2000 mm (working fluid: water; specific volume flow:

51.2 l/(m2h)). It can be seen that a uniform F distribution at a high level can be obtained; the total F amounts to 0.97, which is a rather high value (according to [3], measured val­ues range between 0.81 and 0.97). The detail in Fig. 5 (circle) reveals the influence of the fin width: F values in corners are lower due to the longer distance between the perpendic­ular edges and the curved fluid channel.

FracTherm also allows to visualise the fluid temperature distribution (Fig. 6). The temper­ature gradient between fluid in — and outlet can be recognised easily. Current values such as fluid in — and outlet temperatures, collector efficiency, hydraulic power and total volume flow are shown dynamically during a simulation (e. g. while pump stages are switched).