Abstract
This dissertation presents a study of steady He II (superfluid helium) counterflow heat transfer in porous media. Porous insulations were suggested as potential alternatives to conventional fully impregnated insulations in superconducting magnet technology. Superconducting magnets are usually cooled with He II. Use of porous insulations requires thus a good knowledge of the behavior of He II within porous materials, when set in motion or exposed to a heat source. The present work was focused on the design of an apparatus capable of performing both steady and transient counterflow measurements in He II saturating a porous material with a geometry similar to potential candidate porous insulations. Those will most likely be composed of tapes of pre-impregnated woven ceramic fibers, forming a highly anisotropic compound, with a wide pore size distribution. The samples were provided by Composite Technology Development Inc. and are circular pellets (3.08 mm thick and 28.58 mm in diameter) of 20 compressed layers of pre-impregnated woven magnet insulation. The porous material was carefully characterized prior to experimental runs in He II. The samples exhibit a porosity and a permeability of respectively 20+-1% and 0.95x10^-14 m^2 for water measurements. The woven fiber rovings, composing the insulation, were found to be 0.04 mm^2 of average cross sectional area with fibers of average diameter of 10.6 micron. The He II experimental apparatus is composed of a vacuum insulated open channel whose top extremity is closed to a Minco heater. The temperature differences and pressure drops across the porous plug were measured by two Lakeshore barechip Cernox 1050BC thermometers and a Validyne DP10-20 differential pressure sensor. Applied heat fluxes ranged up to 0.5 kW/m^2 of sample cross section. Steady temperature differences, up to 570 mK, and pressure drops, up to 1800 Pa (limit of the sensor), measurements were performed at bath temperatures ranging from 1.6 to 2.1 K. In the low heat flux regime, the permeability data corroborate room temperature measurements. In the high heat flux regime however, we show evidence of the failure of previous models based on the inclusion of the tortuosity in the turbulent equation. We propose to include a constriction factor denoting an average maximum change in cross section in the heat path in addition to the increased path length denoted by the tortuosity. In the turbulent regime, this constriction factor is predominant as it enters in the model with a cubic power. Measurements of the critical characteristics, corresponding to the point of transition from the laminar regime, where Darcy law is applicable to the non-linear regime, where the heat flux adopts its characteristic cubic relationship, corresponding to the appearance of turbulence within He II are also reported. We obtained critical heat fluxes ranging from 20 to 70 W/m^2, Reynolds numbers of 0.5 to 4 and normal fluid velocities from 0.5 to 2.5 mm/s, varying with bath temperature. To confirm the room temperature measurements of permeability, we also conducted a forced flow experiment. Unfortunately, the flow range covered is outside of the laminar regime and does not permit an accurate estimation of the permeability. The results are however favorably comparable to earlier data recorded in the turbulent regime in similar flow conditions but with very different materials.
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