Ray tracing results

The results of penetration for specular materials are depicted in Fig. 1. In all of them it is clearly shown that most of the absorption takes place in the first 5 to 20 mm of the duct, advancing an apparent lack of “volumetricity”. Parameters like reflectivity, pitch and view angle are influencing the profile of absorption and cumulated energy through the channel.

Fig. 1. Plots summarizing the profiles of absorbed energy through the specular channel for different values of view angle, channel pitch and reflectivity.

Specular reflectance model shows the maximum penetrability achievable within channels. Therefore a high reflectance material is strongly recommended since the flux distribution within duct is in these cases smoother. However in all cases higher incident flux values are reached within the first millimetres of the duct what will lead to the higher material temperature values closer to the channel entrance. This fact is by itself contrary to the volumetric philosophy.

Obviously the increment of channel pitch leads to a better penetration of photons, but this increment cannot be indefinite since we may presume that cumulated energy decreases because of higher radiation losses. View angles below 30° seem to be more adequate for volumetric receivers as well. High reflectivity materials lead to a change of penetration

profile and then a peak is registered a few mm inside the channel. On the contrary, when low reflectivities are used the maximum absorption is obtained at the front edge.

Fig. 2. Plots summarizing the profiles of absorbed energy through the channel for different values of reflectivity at diffuse and specular models.

In the case of the specular model the channels work as light traps, and therefore the cumulative energy through the channels increases to reach the total value of 1. When this value is not reached within the graph this is because the depth of the represented channel is not big enough.

In the case of the diffuse model part of the incident radiation is lost through the channel aperture (Fig. 2). The channel itself is of course a light trap increasing significantly the apparent absorptivity of the channel from the material absorptivity values (Fig. 3). The cumulated energy through the channels reaches an asymptotic value representing the apparent absorptivity of the duct. The diffuse model shows that apparent reflectivity is more sensitive to viewangle parameter than pitch length (Fig. 3 y Fig. 4).

The real case will be neither the specular model nor the diffuse model but something in between.

Ray tracing provides clues on internal behaviour of light, but only with a thermal analysis we may quantify some of the effects. Because of that we decided to analyze the influence of the previous photon penetration profiles on heat transfer figures.

Fig. 3. Apparent absorptivity of the channel as a function of material absorptivity and pitch length for the diffuse model

Fig. 4. Apparent absorptivity of the channel as a function of viewangle and pitch length for the diffuse model.