https://hal.archives-ouvertes.fr/hal-00265717/document

A numerical approach for the study of glass furnace regenerators

An exact, general and algebraically simple solution is obtained to the classic model of the thermal regenerator—general in the sense of covering flushing ratios, A, of any magnitude, including the small values of interest in the context of Stirling cycle machines, and of depicting start-up and cyclic steady state operation.Specimen solutions turn the conventional picture of regenerator performance on its head: for a flushing ratio equal to or less than unity, for example, zero heat-transfer coefficient (NTU = 0) leads to a temperature recovery ratio of 100 per cent! At a thermal capacity ratio, NTCR, above a certain, minimal, value, the wall temperature distribution sits invariant between the extremes of gas temperature swing, and increased NTCR has no effect on temperature recovery ratio.The findings are sufficient to explain reports of unexpectedly good performance of Stirling machines with regenerators of cotton wool or glass fibre.

Solution of the Classic Thermal Regenerator Problem

The stationary, periodic solution to the problem of oscillating flow of a conducting fluid, in a duct closed at one end and with periodical mass flow rate at the other end, is known to exhibit a singularity in the mean temperature at the closed end when transverse conduction in the fluid and the duct wall is taken into account, but longitudinal conduction is neglected. For instance, a solution of that type was originally suggested by Gifford and Longsworth as a prototype for pulse-tube refrigeration. Whether these stationary singular solutions are physical or mere theoretical curiosities depend upon the existence of a scenario leading to such a limit cycle. To address that question, a transient theory is formulated, using the narrow duct approximation. The results show that at least for constant fluid thermal conductivity, all singular profiles generated by the mechanism under study are linearly stable. For round tubes, the temperature profile is shown to evolve, from an arbitrary initial value, toward an equilibrium profile which results in balanced energy fluxes.

Thermoacoustics: Transient regimes and singular temperature profiles

In order to select the most suitable phase shifting mechanism for the GM pulse tube coolers applied to cryoelectronic devices, we evaluated the performance of both double-inlet and four-valve type phase shifting mechanisms by using a single-stage GM pulse tube cooler and an on-off timing control system designed for valved cryocoolers. The lowest temperature achieved was 29.1K and the largest cooling capacity at 80K and 60K was 13 and 10W, respectively. For the four-valve type cooler, the cooling capacity at 80K was 72% of that for the double inlet type cooler.

Development of a 5 to 20 W at 80 K GM Pulse Tube Cryocooler

Mathematical models describing the operation of diabatic regenerators have been derived and solved numerically using finite-difference schemes for the prediction of system thermal performance. The present formulations include the effects of radial conduction and storage of heat in the regenerator walls as well as heat loss, which can be quite important in experimental situations but which were neglected in all previous investigations. The effects of the above phenomena are explored, and indications are given under what regenerator conditions these effects could be reduced. In addition, the models are used to examine the available experimental data for the contribution of such effects.

Thermal Performance of Diabatic Cyclic Regenerators

A simplified equation for calculating regenerator efficiency is derived. Derivation of the equation is based on the fact that most regenerators encountered in practice have very simple linear ternperature changes in their central portions. (B. O. G.)

W. F. Schalkwijk

Papers

A Simplified Regenerator Theory

A simplified regenerator theory