Finite Element Modeling of Cryogenic Radiometer Temperature Field

In order to evaluate the non-equivalence of substitution of optical power (laser beam) by DC electric power in a 2nd generation cryogenic radiometer (see Figure 1), numerical modeling of steady-state temperature field using finite-element analysis code ANSYS 8 *see below has been performed. The principal difficulties of such an analysis consist of the following:

• Very small maximum allowable uncertainty of computation - not greater than several µK.
• The thickness of the cavity is 1000 times less than its length. It is necessary to keep the ratio of the largest to the smallest side of finite elements (FE) less than 2 in order to obtain a well-conditioned matrix of the resulting linear equations. Satisfying this rule for 3D brick-shaped or pyramidal FE leads to an increase of the matrix size and, as a result, decreases the accuracy of the solution. Because of this, curvilinear multilayer shell finite elements have been applied.
• Internal non-linearity: within the range of temperature from 4.5 K to 8 K, the thermal conductivity of Copper strongly depends on temperature.
• External non-linearity: radiation heat transfer from the cavity exterior to the cold (4.2 K) chamber and from the 300 K environment through the aperture to the cavity bottom.

The thermophysical model developed and the appropriate finite-element model are depicted in the picture above. The cavity internal walls are coated by Z302 specular black paint. About 5 % of the incident laser power is reflected by the slant bottom of the cavity and hits the cylindrical surface. The power substitution can be done by a chip heater, a wire-wound heater, or a combination. The purpose of modeling is to evaluate the significance of income of each component into steady-state temperature distribution, to perform the parametric studies with the imprecisely known thicknesses and thermal conductances, and to find the optium locations for temperature sensors to decrease the uncertainty due to substitution nonequivalence. The direction of coordinate x increase is designated by the arrows in the lower figure. A resulting temperature distribution is depicted below (right: complete distribution, left: expanded scale).

* Certain commercial software is identified in this web page in order to specify the computational procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the software identified is necessarily the best available for the purpose.