Cooling the thermal mirrors

The thermal mirrors (thermal cap, yellow; thermal wall, orange) are exposed to intense thermal radiation from the furnace opening or oculus (black line.) The black fringes represent 0 suns, 1000 suns, 2000 suns, etc., of back radiation when the the furnace is at the temperature of the sun.

The thermal mirrors—the cap and the wall—are exposed to intense thermal radiation. If the oculus were at the temperature of the sun, the cap would see about 9,000 suns of flux, and the wall about 1,000 suns. Of course, for the sake of efficiency, the furnace will actually operate at a much lower temperature, reducing these fluxes by about a factor of ten. The mirrors will reflect most of this heat, but perhaps about 5% will be absorbed. This absorbed heat needs to be dissipated from these surfaces to keep the mirrors cool—a thermal flux amounting to about 45 suns on the cap and 5 suns on the wall. The thermal wall may use passive cooling, but active convection is needed for the cap. For comparison, a 2-kw stove element heating a 20-cm diameter pot produces a thermal flux of about 64 suns.

Water is too dangerous to use directly above the furnace opening, so this significant cooling must be obtained by convected air. If the cap is segmented into smaller mirrors, each shingled over the other, a chimney extending to the top of the lamp may draft enough air between the mirrors to keep the mirrors cool.

The cap

Inside the lamp, or beam-down optics, of a telescopic heliostat field, the thermal cap is a mirror in the shape of a portion of a sphere centered on the oculus. Its purpose is to prevent thermal back radiation from the occulus from escaping skyward. 

In the far field, the thermal cap produces an umbral region (where view of the oculus is fully blocked) and also penumbral regions where view of the oculus is partially blocked.

A field of telescopic heliostats has its own sort of penumbral region due to the abrupt truncation of the heliostat field at its maximum radius. In order to balance forward and back radiation at the surface of the lamp, these two different kinds of penumbra must be coextensive.  

The lamp

Elliptical locus for the beam-down optics or lamp. The target point, in yellow, is a focal point of the ellipse. The telescopic heliostat field is in green, and the approximating cylinder is in cyan.

Zoom in on the center of figure above. The black fringes correspond to 0 suns, 100 suns, 200 suns, etc., of thermal radiation when the oculus is at the temperature of the sun. If the profile of the lamp follows the red, elliptical contour up to the height of the cylinder, it will be under about 200 suns of thermal back radiation over most of its surface. In an ideal concentrating system, there would be under an equal, counterbalancing, forward flux of solar radiation.

The profile of the transflective beam-down optics, or, more simply the lamp, is determined by both geometric and thermodynamic constraints.

When telescopic heliostats are aimed at a target point, the desirable geometric constraint that the angle of incidence equal the angle of transflection locates the surface of the lamp on an ellipse having one focus at the oculus and the other at the target point. The top figure shows the elliptical locus in red using the geometry of the previous post. The vertical cyan lines indicate the approximating cylinder.

The lamp needs to be supplemented by a thermal cap, a mirror in the shape of a portion of a sphere centered on the oculus, that reflects thermal radiation back to the oculus rather than letting it escape through the approximately 30° angular radius of open sky.