Convective heat losses in pulse tube coolers: Effect of pulse tube inclination

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 theta between the pulse tube axis and the direction of gravity can be varied between 0 and +/- 180 degrees. theta = 0 degrees 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 theta = 0 and f = 2 Hz with a minimum no-load temperature of T(0 degrees) = 52.5 K and a net cooling power of (Q) over dot(0 degrees) approximate to 2 W at 80 It. Upon tilting the pulse tube, T(theta) initially increases moderately up to T(70 degrees)/T(0 degrees) approximate to 1.2. Further increase of theta leads to a steep rise of T(theta)/T(0 degrees) attaining a maximum of approximate to 3 for theta approximate to +/- 120 degrees and finally a value of T(+/- 180 degrees)/T(0 degrees) approximate to 2. The measured variation of T(theta) and (Q) over dot(theta) 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 theta not equal 0 degrees, which is superimposed on the oscillatory gas displacement in the empty pulse tube. This interpretation is supported by the calculated Nusselt number Nu(theta) which can semi-quantitatively account for the observed inclination effect. At a frequency of 4 Hz the magnitude of T(theta)/T(0 degrees) is reduced with a most pronounced effect at theta = +/- 90 degrees. The theta-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 theta = 0 degrees.