Convective Heat Losses in Pulse Tube Coolers: Effect of Pulse Tube Inclination

Abstract

In order to investigate the effect of pulse tube inclination on the performance of a pulse tube refrigerator (PTR), we have built a test rig in which the angle θ between the pulse tube axis and the direction of gravity can be varied between 0 and ± 180°. θ = 0° corresponds to the vertical orientation with the hot end up. The PTR was operated with orifice, reservoir and second inlet at the warm end using helium as working fluid. The pulse tube has a length of 250 mm and an inner diameter of 13.4 mm. Operating parameters are: average pressure 18 bar, peak to peak pressure variation 5.4 bar and frequency f = 1.6 – 4 Hz. Optimum cooler performance is obtained for θ = 0 and f = 2 Hz with a minimum no-load temperature of T(0°) = 52.5 K and a net cooling power of (0°) ≈ 2 W at 80 K. Upon tilting the pulse tube, T(θ) initially increases moderately up to T(70°)/T(0°) ≈ 1.2. Further increase of θ leads to a steep rise of T(θ)/T(O°) attaining a maximum of ≈ 3 for θ ≈ ±120° and finally a value of T(±180°)/T(0°) ≈ 2. The measured variation of T(θ) and (θ) indicates that tilting results in excess heat loads of up to 6 W. These losses are ascribed to an enhanced heat transfer by natural convection of He-gas occurring for θ ≠ 0°, which is superimposed on the oscillatory gas displacement in the empty pulse tube. This interpretation is supported by the calculated Nusselt number Nu(0) which can semi-quantitatively account for the observed inclination effect. At a frequency of 4 Hz the magnitude of T(θ)/T(0°) is reduced with a most pronounced effect at θ = ± 90°. The θ-dependence from convection is considerably weakened by filling the pulse tube with a porous material, but this also leads to a degradation of the cooler performance at θ = 0°.