This invention relates to refrigerators, and, more particularly, to pulse tube refrigerators.
In a simplified view of the operation of the orifice pulse tube refrigerator, the gas in the pulse tube can be thought of as a long (and slightly compressible) piston, transmitting pressure and velocity oscillations from a cold heat exchanger to an orifice at higher temperature. In this view, the gas in the pulse tube must thermally insulate the cold heat exchanger from higher temperatures. Unfortunately, this simple picture can be spoiled by convective heat transfer within the pulse tube, which carries heat from a hot heat exchanger to the cold heat exchanger and thereby reduces the net cooling power. Such convection can be steady or oscillatory, and has causes as mundane as gravity or as subtle as jetting due to inadequate flow straightening at either end of the pulse tube.
The present invention is directed toward convection driven by streaming. Streaming conventionally denotes steady convection that is superimposed on and driven by oscillatory phenomena. In the context of a pulse tube, this driving can occur in the oscillatory boundary layer at the side wall of the pulse tube where both viscous and thermal phenomena are important.
For laminar oscillatory phenomena at angular frequency .omega., the relevant boundary-layer thicknesses are the viscous and thermal penetration depths .delta..sub.v and .delta..sub.k, respectively, defined by ##EQU1## where .mu. is the dynamic viscosity of the gas, .rho. is the density of the gas, c.sub.p is its isobaric specific heat per unit mass, and K is its thermal conductivity. In monatomic gases, the Prandtl number .sigma.&lt;1 so .delta..sub.v &lt;.delta..sub.K. Much farther from the wall than these penetration depths, the oscillatory temperature of the gas in the pulse tube is essentially adiabatic, and the axial oscillatory motion parallel to the wall is essentially independent of distance from the wall. Closer to the wall, the oscillatory temperature and motion are reduced by the thermal and viscous contact with the wall; at the wall, the oscillatory temperature and motion are zero.
In order to visualize streaming that is generated within these penetration depths, consider a small parcel of gas 10 located approximately a penetration depth .delta..sub.v 12 from wall 14 of pulse tube 18 oscillating up and down as shown in FIG. 1A. On average, the gas between parcel 10 and wall 14 will have a different temperature during the upward motion of parcel 10 than during its downward motion, which is due to thermal contact with wall 14 and the phasing between oscillatory pressure and motion. Since the viscosity depends on temperature, moving parcel 10 will experience a different amount of viscous drag during its upward motion than during its downward motion, and hence will undergo a different displacement during its upward motion than during its downward motion. After a full cycle, parcel 10 does not return to its starting point; it experiences a small net drift 16. Streaming is the sum of many processes, but this explanation provides an intuitive explanation for one such process.
Drifting parcel 10 close to wall 14 has a profound effect on all the gas in pulse tube 18 because it drags gas farther from wall 14 along with it. In the usual case, with pulse tube 18 radius much larger than penetration depth .delta..sub.v 12, an offset parabolic streaming velocity profile 22 results, shown in FIG. 1B. Gas parcel 10 has a velocity near the wall equal to the drift velocity just outside penetration depths 12, and has a velocity in the center 24 of the pulse tube determined by the requirement that the net mass flux along the tube must be zero.
The effect of parabolic-streaming profile 22 is shown in prior art pulse tube refrigerator 30 in FIG. 1C. Pulse tube refrigerator 30 includes hot heat exchangers 32 and 36, regenerator 34, cold heat exchanger 38, flow straightener 42, compliance volume 44, orifice valve 46, and pulse tube 48. The parabolic-streaming profile 22 shown in FIG. 1B produces a toroidal convection cell 50 that convects heat from hot heat exchanger 36 to cold heat exchanger 38. The toroidal velocity is much smaller than the oscillatory velocity that causes it.
Hence, oscillatory processes roughly a penetration depth from the wall cause a steady axial drift approximately a penetration depth away from the wall. This, in turn, establishes an offset parabolic mass-flux profile across the entire tube that convects heat.
The problem of heat convection caused by streaming is recognized in J. M. Lee et al., "Flow Patterns Intrinsic to the Pulse Tube Refrigerator", Proceedings of the 7.sup.th International Cryocooler Conference, pp. 125-139 (1993). In their final two paragraphs, Lee et al. discuss two methods for reducing this streaming: controlling the mass flow at the warm end of the pulse tube and using a tapered pulse tube configuration. It is suggested that the tapered pulse tube have a monotonic spatial variation in the pulse tube radius to reduce velocity amplitude differences. But there is no teaching on how to select an appropriate taper angle, nor is there presented any experimental evidence regarding a tapered pulse tube.
Accordingly, it is an object of the present invention to minimize or eliminate streaming mass flux near a pulse tube wall.
It is another object of the present invention to increase the cooling power of an orifice pulse tube refrigerator significantly by shaping the radius of a pulse tube wall along the axis of the pulse tube.
Yet another object of the present invention is to define an optimum taper angle of a pulse tube wall to suppress mass flow streaming.
Additional objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.