The optical analysis carried out through ray tracing techniques should be necessarily complemented with a thermal analysis of the duct to assess the eventual impact in terms of wall and air temperature, and radiation losses. A numerical analysis was performed to evaluate the forced convection heat transfer characteristics of air flowing through a rectangular channel with hydraulic diameter (pitch length) of 2 mm, length 100 mm and

0. 1 mm wall thickness under laminar flow regime (Reynolds number near 6). Wall and
fluid temperature and velocity profiles were analyzed for different profiles of radiation impinging onto the channel walls. A 3D numerical model was developed with the computer code FLUENT®. Heat transfer equations were solved simultaneously in the fluid and in the solid phase. The simulation is described with the following assumptions:

— The transport processes are considered to be steady-state and three-dimensional

— The flow is incompressible and laminar.

— Thermal forced convection and thermal radiation into the channels.

— Air physical properties are temperature dependent and solid properties are not temperature

dependent.

Boundary conditions for the fluid are: Constant mass flow, temperature and pressure at the inlet surface. Boundary conditions for the solid are: External walls adiabatic. The internal walls (in direct contact with the fluid) are considered as a heat source surface for different heat flux profiles as predicted by the ray tracing software. The channels were modeled with tetrahedrons (1 million for the fluid and 0.9 millions for the solid). Steady state solution of the laminar Navier-Stokes equations with conjugated heat transfer calculation was done. Inlet mass flow of 3.6.10-6 kg/s (0.77m/s) at 300 K was considered. Physical constants of the solid material were considered not temperature dependent (202.4 W/m-K thermal conductivity, 871 J/kg-k specific heat and 2719 kg/m3 density).

The air is considered as incompressible gas with physical constants as specific heat, thermal conductivity, viscosity and thermal diffusivity being temperature dependent.

Four different heat flux profiles on the wall were simulated corresponding to inlet aperture values of 250, 500, 1000 and 2000 kW/m2 respectively. Fig. 5 shows the heat flux distribution for each case. For the sake of simplicity we assume for all the cases equal heat flux profiles in the four channel walls (top, bottom, left and right). In addition, other cases analyzed were a wall with constant heat flux distribution from 1000 kW/m2 on channel aperture area for two different channels pitch (2×2 mm and 5×5 mm).

The consequences of the flux distributions abovementioned are represented in Fig. 6 and Fig. 7. As it can be observed in all the cases the temperature profiles are quite similar and only the absolute values differ, with the exception of the flat flux distribution.

The typical distributions of air and wall temperatures are represented in Fig. 8. When photon penetration takes place in the first 5 to 20 mm with the sharp profiles predicted by ray tracing techniques, the fluid gets a dramatic increase of temperature just at the entrance. The high concentration of photons at the front edge leads to some increment of wall temperature as well. It is therefore clearly observed that the limited penetration of photons inside the channel represents also a limited volumetricity of the absorber since the high temperatures are obtained too close to the inlet surface. Wall temperatures have also the maximum value extremely close to the edge. This behaviour differs from the theoretical performance of an ideal volumetric structure as depicted in Fig. 8. With those profiles radiation losses can raise up to non-negligible values of 7% (See Table 1).

The flat flux distribution is represented only for 1000 kW/m2 on the aperture, to visualize the dramatic effect on temperature profiles when a more volumetric behavior is given. For a highly porous absorber with specular surface, a more even distribution of photons would be obtained and then air and wall temperatures will show a continuous and steady increment throughout the whole channel. Maximum temperatures are in this case predicted at the channel outlet, temperatures are higher and radiation losses significantly lower (Table 1).

Based on the previous results we may confirm that Fluent® is a useful tool to determine the relevance of design parameters like the distribution of radiation flux inside the channel to quantify efficiencies and working temperatures. Since absorber reflectivity is considered one of the key factors regarding internal distribution of photons, we have analyzed in detail two different channels with reflectivities of 0.1 and 0.7 with penetration profiles as presented for the specular model in Fig. 2. The thermal analysis has been conducted for the specular case since it shows the higher photonic penetrability.

The plots depicted in Fig. 9 explain the reason for the higher radiation losses in lower reflectivity materials. As it can be observed, higher wall fluxes are obtained at the first part of the channel with the corresponding higher wall temperatures what leads to an increment in radiation losses2.

In these cases only the radiation absorbed on the first 50 mm of channel walls has been taken into account what is enough to represent the radiation losses through the aperture.

Conclusions

To assess the volumetricity and adequacy of a porous absorber as a 3D black body is not a trivial task. The optical and thermal performance of a monolithic structure are consequence of a number of design parameters like optical view angle between concentrator and receiver, absorber material reflectivity and specularity, channel pitch length, and other. The combined effect of those parameters needs to be known as it is clearly evidenced in the present analysis.

The proposed methodology integrating ray tracing techniques to determine the inner flux distribution throughout the channel and a CFD code for heat transfer simulation, reveals as a useful procedure to discern pros and cons of design parameters.

Even distributions of solar heat flux inside the channel, or in other words higher photon penetrations, lead to a higher volumetricity and more efficient design. This effect may be achieved working with larger pitch lengths and with lower view angles, but pitch cannot be indefinitely increased without penalizing radiation losses.

On the other hand, highly reflective and diffuse materials lead to counterproductive results since the penetrability improvement is neutralized by the increment in reflection losses at the channel entrance.

The results obtained under the present simulation confirm the difficulties to develop a monolith with operational behaviour close to that one from a theoretical volumetric absorber. The large gap of thermal efficiencies noticed nowadays at prototypes tested under real solar conditions and a theoretical volumetric receiver can be explained according to the previous contradictory effects predicted by the simulation.