EP3004753B1

EP3004753B1 - Pulse tube cold head

Info

Publication number: EP3004753B1
Application number: EP14730968.6A
Authority: EP
Inventors: Michael William Dadd
Original assignee: Oxford University Innovation Ltd
Current assignee: Oxford University Innovation Ltd
Priority date: 2013-06-06
Filing date: 2014-06-06
Publication date: 2020-09-02
Anticipated expiration: 2034-06-06
Also published as: WO2014195725A3; US20160131399A1; WO2014195725A2; GB2514830A; EP3004753A2; GB2514830B; GB201310111D0

Description

The present invention relates to pulse tube coolers that have improved efficiency.
Pulse tube coolers have evolved as an alternative to Stirling cycle coolers. Their operation is very closely related; the main difference is that instead of using a "solid" piston or displacer to provide an expander component, this function is provided by a column of gas that acts as a springy, deformable displacer.
The motion of the gas column in a pulse tube can be controlled mechanically by a warm end piston/displacer but more often the motion is controlled by fluid "phase control" components. These avoid the need for extra moving components and control the mass flow in the way that they respond to the applied pressure variation. Various mechanisms have been employed to provide this function. These include designs that use orifices or inertance tubes in combination with reservoir volumes. In addition a second inlet and orifice combination can be connected between the compressor input and the warm end of the pulse tube to further modify the response.
Pulse tube coolers can be used in the same wide range of applications as Stirling cycle coolers. Examples include those for cooling optical components both for space and terrestrial applications. Their main advantage over Stirling cycle coolers is the elimination or simplification of the moving expander/ displacer components. This can improve overall reliability and reduce vibration. Potentially it also offers lower cost as a pulse tube cold head does not require high precision.
A good general description of present pulse tube technology is given in: Proceedings of the Institute of Refrigeration (London) 1999-2000, "Development of the Pulse Tube Refrigerator as an Efficient and Reliable Cryocooler, Ray Radebaugh, NIST.
Figure 1 shows the cold head 103 for a conventional Stirling cycle cooler. The cold head 103 consists of a regenerator 104 and an expander cylinder 105 that are connected via a heat exchanger 110 (which also acts as a fluid connection between the regenerator and the expander cylinder) at the cold end (at temperature Tc). An expander piston 113 is movably engaged within the expander cylinder 105. The working gas volume that includes the regenerator 104, cold end heat exchanger 110 and the expansion space 111 above the expander piston 113 is subjected to a pressure variation provided by an "AC" compressor (connected via connector 107). Typically, the compressor, or pressure wave generator, does not have valves and usually has an ambient heat exchanger (cooler) to reject heat from the gas before it enters the cold head 103. The compressor and cooler are not shown in Figure 1.
In operation, the movement of the expander piston 113 is arranged to be out of phase with the pressure variation so that net work is done by the gas on the piston 113. This loss of energy from the gas causes the gas temperature to decrease which in turn allows heat to be absorbed from the cold end heat exchanger 110. Over a cycle the net result is that heat can be absorbed from an external load via the heat exchanger 110 and this energy is transported to the warm end of the cold head (at temperature Th) as work done on the expander piston 113, which may in turn do work on gas in a compression space 115.
In the gamma configuration shown, the expander piston 113 becomes what is termed a displacer. The displacer takes energy from the gas at the cold end as an expander and directly transfers it back into a gas volume at the ambient end as a compressor. The additional gas volume is usually connected to the input from the compressor so that the expansion work is "recycled" to improve efficiency. This energy recovery is not essential; for low temperature coolers the expansion power is relatively small and can be just dissipated through a damping arrangement.
In Figure 1 there is no indication of how the movement of the displacer 113 is controlled in order to ensure that the work is done by the gas in the expansion space. In practice a small diameter shaft is usually attached to the displacer and taken through a seal in the ambient end to a mechanism that imparts the required motion. Various means are available for driving the displacer and these are generally well established in the literature.
In discussing Stirling cycle coolers and particularly pulse tube coolers, it is useful to consider the operation in terms of the phase relationship between the applied pressure variation and the mass flow of the gas between the cold end heat exchanger and the expansion space/volume.
The work done W by the expander piston is given by $W = \int P . dV over a cycle$
P is pressure, V is expander volume
For simplicity, sinusoidal* variations are assumed for pressure and volume. This integral has a maximum when the pressure and first derivative of volume are in phase. This is equivalent to requiring that the pressure variation and mass flow are in phase. (*Note: Actual pressure and mass flow variations will generally have additional harmonics but their magnitude will be small and they will not fundamentally change the operating mechanism).
It is noted that while this relationship will give the highest cooling effect it does not generally give the highest efficiency because losses in the cooler are also phase dependent. However it is generally the case that if the pressure and mass flow are 90 degrees out phase then there is no net work done on the gas and hence no cooling.
Figure 2 shows a conventional arrangement for a pulse tube cold head 102 in which the expansion work is transmitted via a column of gas contained in a tube 114 (which may be referred to as a pulse tube). The gas column can be considered to consist of three different zones. One zone 121 (which may be referred to as a first tidal volume) behaves like the expansion space 111 of a Stirling cooler in that gas has a tidal movement into and out of the cold end heat exchanger 110. At the other end of the pulse tube 114 is a similar zone of gas 125 (which may be referred to as a second tidal volume) that has a tidal movement into and out of the ambient temperature phase control components. This tidal volume 125 behaves in a similar way to the compression space 115 of the Stirling cycle cooler. In between there is a third gas zone 123 that separates the other two. Ideally this gas volume 123 simply acts as a deformable displacer that transmits work but at the same time provides thermal isolation.
Cooling is generated by appropriate phasing of the volume 121 with respect to the pressure variation. Achieving this is a more complex task than for a Stirling cycle machine and this aspect will be described more fully below.
For efficient operation of the pulse tube 114 it is desirable to minimise any turbulence so that the gas column remains stratified and convection by mixing is avoided. Flow straighteners 120 may be provided for this purpose, at either or both ends of the pulse tube 114 (as shown in the example of Figure 2). These provide low velocity, uniformly distributed axial flows.
In the above description of the Stirling cycle cooler it was shown that a key requirement for cooling is a combination of pressure and mass flow variations that are in phase. In a pulse tube the cooling process is more complicated for two reasons:

Firstly, the deformation of the "gas displacer" (labelled 123 in the example shown in Figure 2) with pressure requires additional mass flows into the pulse tube.
Secondly, as one of the main attractions of a pulse tube is the elimination of moving components, it is very desirable to control the mass flow using a system of fluid phase control components rather than using pistons/displacers.

In the following, the term "phase control device" is used to refer to any device which allows the relative phases of the pressure and mass flow variations to be such as to allow cooling to take place. The phase control device may operate using pistons/displacers, a system of fluid phase control components that may not comprise any moving parts, or a combination of the two.
The mass flows required into the pulse tube can be divided into two components: those in phase with the pressure pulse and those out of phase. If it is assumed that the pressure variation has a sinusoidal waveform: $P = P_{0} Sin (ωt)$
(Mean pressure level is ignored; pressure is assumed to be AC component only) then a general expression for the mass flow variation is: $\dot{m} = A . Sin (ωt) + B . Cos (ωt)$
The first component is in phase with the pressure pulse and this has already been established as the "cooling" component. The second component is mass flow required by the "deformation" of the "gas displacer". This component does not give rise to any work input or output; instead it acts as a spring component that stores energy during half the cycle and releases it in the other half.
This combination of two components of mass flow is illustrated in Figures 3A to 3C. The pulse tube in 3A has the total mass flow required for operation as a cooler. This can be likened to the combination of a displacer that is both

Reversibly expanding and contracting - the spring component
Displacing the tidal gas volumes into and out of the pulse tube

The operation of the pulse tube shown in Figure 3A can be imagined as the combination of the separate processes illustrated in Figures 3B and 3C.
Figure 3B represents the "spring" flows that occur when the mass flows are completely out of phase with the pressure variation and no net work is done on the gas. In 3B1 the pressure is increasing and all the gas flows are inward. In 3B2 the pressure is decreasing and all the gas flows are outward. It is seen that the "gas displacer" changes shape in accordance with the distribution of the mass flows.
Figure 3C shows the gas displacer considered as a solid displacer that is causing tidal mass flows into and out of the pulse tube by displacement without any pressure variation. In 3C1 the displacement is from the cold end at Tc (top) to the ambient end at Th (bottom). In 3C2 the displacement is the reverse of 3C1. The flows into and out of the pulse tube are consistent with these displacements.
In Figure 3B the mass flows associated with the gas spring are shown equally divided between the two ends of the pulse tube i.e. the mass flow from the cold end is the same as from the ambient end. This does not need to be the case; the mass flow could be entirely from either end or divided in any proportion. The key characteristic of the "spring" flows is that they are out of phase with the pressure variation. The direction from which the "spring" mass flows enter the pulse tube does not affect the amount of refrigeration generated, however it does affect the losses and hence the overall efficiency of the cooler. It is generally preferable for at least some of the "spring" mass flow to enter from the ambient end. If it comes in from the cold end it has to do so via the regenerator adding more thermal load to this component and hence increasing its losses.

Example of the Orifice Pulse Tube

One of the earliest designs used in pulse tube coolers is the orifice pulse tube, as shown in Figures 4A and 4B, in which gas is allowed to pass between the ambient end of the pulse tube and a reservoir 124 via an orifice 122. The orifice 122 is an example of a fluid phase control component. Figure 4A shows the pulse tube with the orifice 122 closed. There is no mass flow at the ambient end and the mass flow at the cold end consists of only the out of phase spring component; there is no net cooling:
For $\begin{matrix} P = P_{0} Sin (ωt) & {\dot{m}}_{spr} = B . Cos (ωt) & W = \int P . dV = 0 \end{matrix}$
If the orifice 122 is opened (Fig 4B) then the mass flow at the ambient end will be determined by the flow characteristics of the orifice 122. An orifice generally behaves as a resistive flow component where the mass flow is proportional to the pressure drop across it. As the reservoir volume 124 remains close to the mean DC level then the mass flow the through the orifice 122 and hence from the ambient end of the pulse tube will be given by ${\dot{m}}_{orif} = const . P . Sin (ωt) = A . Sin (ωt)$
The mass flow into the pulse tube at the cold end is a combination of the spring mass flow and the orifice mass flow: ${\dot{m}}_{coldend} = {\dot{m}}_{spr} + {\dot{m}}_{orif} = A . Sin (ωt) + B . Cos (ωt)$
The cold end now has a mass flow component that is in phase with the pressure variation and there is a net cooling effect at the cold end.
(Note: As might be expected, the cooling is equal to the work lost in pumping gas backwards and forwards through the orifice 122)

Other Types of Pulse Tube

The orifice pulse tube is probably the simplest design that has succeeded in producing reasonable levels of cooling at low temperatures. However it will be seen from Figure 4A that the spring mass flow enters the pulse tube entirely from the cold end. This flow adds a considerable burden to the regenerator and limits the ultimate performance. Two configurations that have been developed to overcome this limitation will be briefly described.

Double Inlet Pulse Tube

In the double inlet pulse tube configuration there is an additional connection between the ambient end of the pulse tube to the compressor via a second orifice. The effect of this is to cause a mass flow into the ambient end of the pulse tube that is in phase with the pressure drop across the regenerator and cold end heat exchanger. This can be used to allow some of the "spring" flow to enter from the ambient end. The reduction in flow through the regenerator reduces the regenerator loss and allows an overall improvement in performance.
Although good performance has been achieved with this arrangement it has been found that the second orifice is inclined to be asymmetric in its operation. This attribute tends to generate net DC flows that circulate around the pulse tube and regenerator. These flows do not undergo thermal regeneration as intended and even at low levels can produce unacceptable losses.

Inertance Tube

An alternative to the Double Inlet configuration that attracted interest is the inertance tube configuration. In this configuration the orifice of the Single orifice configuration described above is replaced by a tube or assembly of tubes that connect the ambient end of the pulse tube to a reservoir volume. The tube or assembly of tubes is a further example of a fluid phase control component(s).
The tube assembly is arranged to have both damping and significant inertia. It terms of an electrical analogy the inertance tube assembly is represented by a series combination of a resistor and an inductor whereas an orifice is represented by just a resistor. The inductive component has the effect of allowing some of the "spring" mass flow to enter the pulse tube from ambient end. This helps to reduce the thermal load on the regenerator without setting up the circulating flows that tend to occur with the Double Inlet design.

Coaxial Designs

In Figures 1 to 4 the cold head geometry is that of a U bend. Figure 5 shows a coaxial geometry applied to the general pulse tube arrangement shown in Figure 2. The operation is exactly the same except that the regenerator is now located in an annular volume surrounding the pulse tube. The wall of the pulse tube no longer has to withstand the full gas pressure instead it just acts as a partition. This arrangement is advantageous as it provides a more compact and convenient envelope for the cold head. Similar arrangements have also been widely used for Stirling cycle cold heads.

Pulse Tube Losses

There are four main loss mechanisms directly associated with the operation of a pulse tube:

Heat transfer through the bulk of the gas: The minimum value is set by thermal conduction in stratified layers but this can be greatly increased if there is significant mixing/turbulence.
Natural Convection: The temperature gradient produces a corresponding density gradient. The latter tends to drive a circulation of gas within the pulse tube. This effect causes pulse tube performance to be very dependent on orientation - pulse tubes generally work better with their cold ends pointing down.
There are two recognised losses associated with the interaction of the axial oscillation of the gas and the pulse tube wall.
- ∘ One loss, referred to as a type of shuttle loss, is due to the constantly reversing temperature gradient between the gas and the wall.
- ∘ A second loss that has been termed "Streaming convection" does not have any simple explanation but appears to derive from the velocity boundary conditions imposed at the interface between the gas and wall.

The "Streaming convection" loss is discussed in: J.R. Olsen, G.W.Swift, Acoustic Streaming in Pulse Tube Refrigerator: Tapered Pulse Tubes, Cryogenics, Volume 37, .
US 5 295 355 A discloses a multi-bypass pulse tube refrigerator comprising a pressure wave generator, a regenerator, a heat exchanger of cold ends, a pulse tube, an orifice means and a reservoir volume, connected in series. Matrix material made of material of high heat capacity is packed in the regenerator. Rectifying means are arranged at the ends of the pulse tube. The outlet of the pressure wave generator is connected with the hot end of the regenerator. The connection between the cold ends of the regenerator and the pulse tube forms the heat exchanger of cold ends. The reservoir volume is connected with the hot end of the pulse tube through the orifice means. Resistance means are properly arranged in the pulse tube, so as to allow gas to pass through the pulse tube uniformly and smoothly. At least one bypass with a throttling means is provided to connect the regenerator and the pulse tube.
It is an object of the present invention to provide an improved pulse tube cooler which at least partially address one or more of the problems with the prior art discussed above, for example by reducing losses.
According to an aspect of the invention, there is provided a cold head for a pulse tube cooler, according to claim 1.
Thus, an arrangement is provided in which a porous portion allows gas to enter or leave the pulse tube substantially laterally (which may also be referred to as "radially"). This provides a number of advantages relative to the prior art.
For example, there is a greater range of possibilities for the distribution of both the refrigeration process and the "spring" flows required:

i) In prior art arrangements such as that shown in Figure 5 for example, cooling only occurs at the cold end of the pulse tube. In contrast, the porous wall of embodiments of the present invention allows cooling to be additionally or alternatively distributed along the length of the pulse tube. The rate of cooling depends on the magnitude of the flow through the pores. Therefore, the spatial distribution of cooling can be set as desired by appropriate selection of the spatial distribution of porosity of the walls. Distributing some or all of the cooling along the porous wall can be advantageous as it allows the pulse tube to act as a multistage cooler. Cooling part way along the pulse tube can be used to remove heat at a higher temperature and hence with lower power requirement. This approach reduces the heat flow to the cold end and allows more of the low temperature refrigeration to be available for cooling of the load. Efficiency can therefore be improved.
ii) In the prior art the gas "spring" flows can only enter from the cold end or warm end (or both). However, the actual flow requirement is distributed along the length of the pulse tube. The provision of a porous wall allows the flow requirement to be fulfilled with more favourably distributed gas flows. The resulting pulse tube can be likened to a "multiple" inlet pulse tube.

A further advantage is related to the ability to reduce gas velocities and gas movement with respect to the thermal gradients:

i) In a conventional pulse tube all the gas flow has to be distributed across the end faces of the pulse tube. The flow straighteners are designed to provide low velocity, evenly distributed flows but there is clearly a lower limit set by the cross sectional area of the pulse tube. The provision of porous lateral walls allows the gas flows to be distributed over much larger areas allowing gas velocities to be considerably reduced. This helps to maintain streamlined flow with minimal mixing and turbulence
ii) In a conventional pulse tube the gas flows are all axial and this requires the gas to have significant velocities in the direction of the thermal gradient. The porous walls of the present invention allow much of the flow to be radial where the gas velocity is perpendicular to the thermal gradient. This reduces the axial gas velocities and allows the establishment of a more favourable temperature distribution.

A further advantage is that, where there is radial flow, the gas flow will be closer to being perpendicular to the wall than parallel to it. The axial velocity component that interacts with the tube wall will be much smaller than for a conventional axial flow design. This will result in lower losses that are dependent on the gas flow/wall interface. For example the "shuttle" loss will be reduced as this loss is proportional to the square of the axial displacement. The other loss related to the interaction between the pulse tube wall and the axial gas velocity is the "Streaming Convection" and it is also believed that the large reduction in axial gas velocity adjacent to the tube wall will also result in lower values for this loss.
Furthermore, there is the effect the radial gas velocity components have on natural convection losses. Natural convection occurs when buoyancy forces drive a circulation of gas. Typically this occurs when a hot surface is positioned below a cold surface - in a simple model the heated less dense fluid rises and the cooled denser fluid descends. The magnitude of the natural convection heat transfer is dependent on the Grashof Number - a measure of the balance between the buoyancy forces that drive the circulation and resistive processes that reduce it. In a conventional axial flow pulse tube, the tube's walls are the principal source of damping - the smaller the diameter the more the circulation is suppressed. The axial gas flows do not generally have much influence as they will add to the circulation on one side and subtract on the other. In the radial flow pulse tube it will be seen that there are two effects that will tend to reduce natural convection: firstly, the radial flows close to the wall will disturb the axial flow and will tend to suppress it; and, secondly, the core of the gas displacer where circulation could become established has a significantly reduced diameter which will also tend to suppress circulation.
In an embodiment, a phase control device is provided that comprises a piston configured to move within a cylinder. In comparison with prior art Stirling cycle coolers, the piston can be confined to a greater extent to the warm end of the tube than can the displacer of the Stirling cycle cooler. This allows the arrangement to be made lighter and/or easier to manufacture, while also tending to lower vibration and/or manufacturing cost. In comparison with prior art pulse tube coolers, this approach allows for a more compact arrangement because there is no need for a reservoir volume to be provided to implement the phase control.
Embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings in which corresponding reference symbols indicate corresponding parts, and in which:

Figure 1 depicts a cold head for a prior art Stirling cycle cooler;
Figure 2 depicts a pulse tube cold head according to the prior art;
Figures 3A-C depict operation of the pulse tube shown in Figure 2; Figure 3A illustrates a combination of spring action and displacement action, Figure 3B illustrates the spring action in isolation, Figure 3C illustrates the displacement action in isolation;
Figures 4A and 4B depict an orifice pulse tube according to the prior art; Figure 4A illustrates the pulse tube with the orifice closed, Figure 4B illustrates the pulse tube with the orifice open;
Figure 5 depicts a coaxial geometry version of the pulse tube cold head of Figure 2;
Figure 6 depicts an exemplary pulse tube cold head, in which a coaxial geometry is adopted;
Figures 7A-C show how the flow regime of the pulse tube cold head of Figure 6 can be seen as a combination of spring and displacement actions in an analogous manner to the flow regime depicted in Figures 3A-C; Figure 7A depicts the combination of spring action and displacement action, Figure 7B depicts the spring action in isolation, Figure 7C depicts the displacement action in isolation;
Figure 8 depicts a pulse tube cold head according to the invention in which the radial flows have been extended to the cold end heat exchanger and the connection to the phase control device;
Figure 9 depicts an embodiment in which a warm end displacer piston is used to control the mass flows in place of fluid components;
Figure 10A and 10B depict a heat exchanger configured to pass gas into the pulse tube in a radial direction; Figure 10A is a side sectional view, Figure 10B is an end view;
Figure 11 depicts an embodiment in which the pulse tube wall contains an electroformed screen that is solid at the warm end and then becomes more permeable towards the cold end;
Figure 12 depicts an embodiment in which the pulse tube and the regenerator are cylindrical and axially displaced relative to each other;
Figure 13 depicts an embodiment in which the pulse tube has an annular cross-section and coaxially surrounds a cylindrical regenerator;
Figure 14 depicts a cold head for use in a two stage cooler.

In an embodiment, a cold head for a pulse tube cooler is provided in which the flow of at least a portion of the working gas between the pulse tube and other components is diverted through a porous portion of a wall that is nearer to being parallel with the temperature gradient of the regenerator than being perpendicular to it. Preferably, the porous portion is within 5 degrees of being parallel, preferably within 1 degree of being parallel. The result of this arrangement is that the working gas enters or leaves the pulse tube in a predominantly lateral direction (perpendicular to the temperature gradient). As discussed above, this allows operational losses to be reduced. An example of such an arrangement is shown in Figure 6.
In this particular embodiment, the cold head 2 comprises a regenerator 4 which has a first end 6 and a second end 8. In use a temperature gradient will be maintained along the regenerator 4 such that the second end 8 will be colder (at Tc) than the first end 6 (at Th). The second end 8 may therefore be referred to as the cold end and the first end 6 may be referred to as the warm end. In an embodiment, the warm end 6 is at ambient temperature in which case it may be referred to as the ambient end.
The regenerator 4 is connectable via passageway 7 to a compressor (not shown in Figure 6) at the warm end 6. As described above with reference to Figures 1 and 2 the compressor may be configured for example to provide an AC pressure wave input, for example in the form of a sine wave (or a form in which the dominant component is a sine wave). The cold end 8 is connected to a heat exchanger 10 which in turn is connected to a first end 12 of a pulse tube 14, optionally via flow straightener 20.
The second end 16 of the pulse tube 14 is connected to a phase control device via connection 26, optionally via flow straightener 20. As described above with reference to Figure 2, a phase control device in this context refers to any device which allows the flow dynamics (e.g. the relative phases of the pressure and mass flow variations) to be such as to allow cooling to take place. The phase control device may operate using a piston/displacer, a system of one or more fluid phase control components without solid moving parts, or a combination of the two.
In the embodiment shown, the pulse tube 14 has a cylindrical form and comprises a wall 15 defining a pulse tube volume. In other embodiments, the pulse tube may take other forms. In the case where the pulse tube is cylindrical it will be understood that references to the axial direction refer to the axis of the cylinder. In the case where the pulse tube has an annular cross-section, the axial direction will refer to the axis of the cylinder formed by the inner or outer surfaces of the annular cross-section. In embodiments where the pulse tube is not cylindrical and does not have an annular cross-section it will be understood that references to the axial direction refer to an axis of elongation or "long axis" of the pulse tube. Typically, the axis of the pulse tube 14 will be substantially parallel to the direction of the temperature gradient in the regenerator (i.e. the direction of steepest temperature gradient - the vertical direction in the orientation of the figures).
In the particular embodiment shown the regenerator 4 coaxially surrounds the pulse tube 14 (as in the embodiment of Figure 5). However, this is not essential. In other embodiments, the regenerator may surround the pulse tube but not have a common axis, may only partly surround the pulse, coaxially or not, or simply be positioned adjacent to the pulse tube.
In an embodiment, the pulse tube shares a wall with one or both of the regenerator 4 and the heat exchanger 10 and/or, where provided, a flow distributer 11 between the second end of the pulse tube 14 and the phase control device (see Figure 8 for example). Any combination of these shared walls may comprise porous portions for allowing lateral passage of working gas into or out of the pulse tube 14 directly through the porous portion. In the embodiment shown in Figure 6, the pulse tube 14 shares a wall 16 with the regenerator 4 only. In the example shown the shared wall is a radially inner wall of the regenerator 4. Figure 8 shows an example embodiment in which the pulse tube shares a wall with the regenerator 4, the heat exchanger 10 and a flow distributer 11.
In an embodiment, at least a portion (the uppermost region in the marked range 28 in the example shown) of the shared wall 15 is porous to a working gas such that a portion of the working gas can enter or leave the pulse tube 14 (indicated by arrows 30) through the porous portion of the wall 15. Allowing some of the gas to enter into the pulse tube 14 directly from the regenerator in this way does not change the distinction between "spring" type mass flows that are out of phase with the pressure variation and "displacement" flows that are in phase, it just alters the way in which the gas displacer deforms and the distribution of the cooling effect. In the example shown, the additional radial inward flows in the range 28 effectively change the shape of the first tidal volume (the equivalent of the volume 121 of Figure 5 that does work on the gas displacer 123) so that it comprises both a component 121A in the form of a solid cylinder (as in Figure 5) and a component 121B having an annular form located adjacent to the wall 15.
Figures 7A to 7C show how the new flow regime can be considered as a combination of "spring" flows and "displacement" flows analogous to the purely axial flow arrangement illustrated in Figure 3.
Figure 7B represents the "spring" flows that occur when the mass flows are completely out of phase with the pressure variation and no net work is done on the gas. In 7B1 the pressure is increasing and all the gas flows are inward. In 7B2 the pressure is decreasing and all the gas flows are outward. It is seen that the "gas displacer" 23 changes shape in accordance with the distribution of the mass flows.
Figure 7C represents the mass flows when the gas displacer 23 is just displacing gas without any pressure variation. In 7C1 the displacement is from the cold end (at Tc) and the radial inlets (the pores in the wall 15), which are at intermediate temperatures, to the ambient end at Th. In 7C2 the displacement is the reverse of 7C1. The flows into and out of the pulse tube 14 are consistent with these displacements. Although the gas displacer 23 does change shape it is important to note that it does not change volume.
Figure 7A is intended to represent the combination of 7B and 7C when the pulse tube 14 is operating as a cooler with both in phase and out of phase flows occurring with respect to the pressure variation.
In an embodiment, the flows through the porous portion of the wall are such as to cause minimal mixing or turbulence. The ideal is that the gas flows follow streamlines so that over a cycle they tend to return to the point where they entered the pulse tube 14. This (or close to it) is achieved by having low gas velocities and well distributed apertures/pores.
In an embodiment, the porous portion of the wall 15 extends from the second end 8 (the cold end) of the regenerator 4 along a portion, but not all, of the regenerator 4 towards the first end 6 (the warm or ambient end) of the regenerator 4. This is the case for example in the arrangement of Figures 6 and 7A-C. In this and other embodiments the porosity of the porous portion of the wall 15 may be configured to decrease as a function of increasing separation from the second end of the regenerator, or vary in some other manner.
In the arrangement of Figures 6 and 7A-C the working gas flows into the pulse tube 14 through a combination of radial flows (through the porous wall) from the regenerator and axial flows from the heat exchanger 10. However, other combinations of flow, optionally of radial and axial flows or of flows directed in other ways, are possible. Figure 8 depicts an example in which the heat exchanger 10 is arranged to coaxially surround the pulse tube 14 at the cold end. A wall having a porous portion is provided (e.g. a mesh - see Figures 10A and 10B discussed below) to guide the flow from the heat exchanger 10 into the pulse tube in a radial direction.
In the example of Figure 8, a flow distributer 11 is provided for distributing flow from the second end of the pulse tube 14 to the phase control device. The flow distributer 11 may have a heat transfer function in addition to a flow distributer function. The flow distributer 11 may therefore optionally have the same or a similar configuration to the heat exchanger 10. The arrangement described below with reference to Figures 10A and 10B may be applied, for example, to the flow distributer 11.
In the embodiment shown, the flow distributer 11 comprises a wall having a porous portion that allows for a radial flow between the pulse tube 14 and the phase control device (via the flow distributer 11). In the arrangement of Figure 8, therefore, flows into and out of the pulse tube 14 are predominantly (or entirely) radial and the expansion and compression spaces 121,125 (first and second tidal volumes) are radially outside of the gas displacer 123.
All the pulse tube arrangements described above have assumed the use of a phase control device comprising a fluid phase control component, which avoids additional moving components. For example, a combination of inertance tube and gas reservoir may be used.
Figure 9 shows an example of a complete pulse tube cooler, including a compressor 45 and a phase control device 47, in which the phase control device comprises a piston 32 (which may be referred to as a warm end displacer) configured to move within a cylinder 34. A warm end tidal volume region is no longer required. The pressure variation within the cold head causes a net force to act on the warm end displacer 32 that is equal to the product of the pressure and piston face area. The dynamics of the piston assembly are arranged so that there is both inertia and damping. The resulting motion gives the desired mass flows at the boundary between the cold end heat exchanger 10 and the pulse tube 14. The damping is provided in this example by a damper piston 40, mounted via a shaft located by suspension spring 46, and a flow restrictor 42. The damping can be adjusted by varying the flow restrictor 42.
This use of a warm end displacer 32 can be regarded as a gamma configuration Stirling cycle cooler in which the thermal insulation function of a conventional displacer is transferred to a deformable "gas displacer" - the "gas displacer" effectively becomes an insulating piston crown. One advantage of this arrangement over a conventional Stirling cycle cooler is that the displacer 32 is confined to the warm end. This allows it to be both lighter and easier to make with lower vibration and lower manufacturing costs.
At the cold end the operation of the pulse tube 14 shown in Figure 9 is the same as the embodiment illustrated in Figure 8. Some of the gas flow enters the pulse tube 14 via a radial connection with the cold end heat exchanger 10. The remaining gas flow is distributed along a section of the pulse tube wall 16 and enters via connecting apertures between the regenerator 4 and the pulse tube 14.
The warm end displacer arrangement will not be the first choice for all pulse tube applications because of the additional moving components. However it possibly more compact as there is no longer a requirement for a reservoir gas volume which can occupy a significant volume.
In the example shown, the compressor 45 (which may also be referred to as a linear pressure wave generator) is configured to impart a modulating pressure on the cold head 2 via connector 7 (in this case a length of connecting tube). The compressor 45 comprises a piston cylinder assembly driven by a linear motor 50. The moving components are mounted on flexures (suspension springs) 46 so as to allow a close but non-touching fit between the compression piston 52 and cylinder 53. This arrangement is generally referred to as a "clearance seal" - there is leakage but it is small enough to be acceptable. The compressor 45 does not have valves and the modulating pressure can be regarded as analogous to a voltage that has both AC and DC components. The basic operating frequency may typically be in the range 50 to 100 Hz.
The configuration of the phase control device of the example of Figure 9 is independent of compressor configuration and could be replaced by one or more fluid phase control components without any modification to the compressor.

Implementation of Radial Flows

For the radial flows into the pulse tube 14 there are number of approaches that can be used. Figures 10A and 10B show one possible arrangement for the case where the flows enter from the heat exchanger 10 (arrows 61). In this embodiment, the axial gas flow 63 from the regenerator 4 enters slots 60 in the heat exchanger 10 that direct the flow radially into the pulse tube. A layer of mesh 64 between the slots 60 and the pulse tube 14 is used to even out and/or straighten the flow distribution. As mentioned above, a similar arrangement can be used for flows between a pulse tube and a flow distributer (e.g. flow distributer 11 of Figure 8).
For radial flows between the regenerator 4 and the pulse tube 14 the porosity of the pulse tube walls 16 needs to be controlled so as to give the required flow distribution. As the pressure drop across the pulse tube wall 15 varies along the regenerator 4 it is expected that porosity will also need to vary significantly. The gas flows within the regenerator 4 and porous wall 16 are expected to be laminar and this allows them to be modelled using simplified methods - e.g. software intended for mathematically similar processes.
A finite element thermal conduction model was used to estimate the range of permeability that would be needed to achieve the required gas flows. For a pulse tube 14 where the radial flow was comparable with the axial flow as per the arrangement shown in Figure 6, the range of local permeability varied by a factor of 100.
If the volume flow dV/dt through the regenerator 4 is given by: $\frac{dV}{dt} = A_{f} . \frac{κ_{R}}{μ} . \frac{dP}{dx}$
where A_f is flow area, κ_r is permeability of regenerator 4, µ is viscosity of gas and dP/dx is pressure gradient, the permeability of the pulse tube wall 15 would need to vary in the range 0.01κ_r to κ_r. The regenerator mesh used in pulse tube coolers is usually very fine. A typical mesh specification is:

Mesh Number (No. Of Wires per inch): #400

Wire diameter: 0.030 mm

Aperture dims: ∼ 0.034 x 0.034

Porosity: 0.59.
The permeability of porous material is generally:

Proportional to flow area and hence porosity
Inversely proportional to hydraulic diameter/aperture size.

As it is required to reduce the permeability by a factor of 100 from material that already has only 34 micron pore size it will be seen that it is necessary to produce a tube wall 16 with apertures of ∼ 1 micron or larger. A variation of 1 to 34 microns does not give the required permeability range so it is also necessary to alter the effective porosity.
Although there are a number of technologies that can be used to produce apertures in sheet material, many are not suited to the small dimensions required. One approach that is suited is the technology of electroforming. For example an electroformed screen can be made to give a varying permeability by controlling both the size and density of the apertures (the density effectively determines the flow area/porosity). The thickness of the screen needs to be between 5 and 10 microns to allow apertures of ∼ 1 micron to be defined. The screen is sandwiched between two layers of fine mesh which can then be formed into a tube and installed between the regenerator and pulse tube volume. The mesh is used for two reasons:

To produce a more robust assembly that can be handled
To give a symmetric flow characteristic so as to avoid any tendency to produce net circulations between the pulse tube and the regenerator as these will tend to generate losses.

The range of permeability that can be defined with a single electroformed screen is large but if necessary more than one screen can be used in conjunction with additional layers of mesh to further reduce the permeability.
Figure 11 shows an example where the pulse tube wall 15 comprises an electro formed screen that is solid at the warm end (portion 66) and then becomes more permeable towards the cold end (portion 64) so as to provide a controlled radial flow into pulse tube 14.
The embodiments described above relate to single stage pulse tubes where the regenerator 4 has an annular form and the pulse tube 14 is located concentrically within the regenerator 4. However, these features are not essential. Multi-stage pulse tubes may be provided. Additionally or alternatively, the regenerator and pulse tubes may take different forms. Some example configurations are described below with reference to Figures 12-14.
Figure 12 shows an embodiment in which the pulse tube 14 is provided outside of the regenerator 4. In the particular example shown, both the pulse tube 14 and the regenerator have a cylindrical form. In other embodiments, either or both may have different shapes. The pulse tube 14 is axially displaced relative to the regenerator, extending in an opposite direction relative to the regenerator than arrangements such as those shown in Figures 6 and 8. The second end 16 of the pulse tube 14 is further from the first end 6 of the regenerator 4 than the first end 12 of the pulse tube 14 rather than the other way round (as in Figures 6 and 8). In the particular example shown the regenerator 4 is coaxial to the pulse tube 14 but this is not essential. Providing the regenerator 4 outside and/or axially displaced relative to the pulse tube 14 removes constraints on the relative sizes and shapes of the regenerator 4 and pulse tube 14. For example, the regenerator 4 is not constrained to have a hollow (e.g. annular) form. Furthermore, the lengths of the regenerator 4 and pulse tube 14 are not constrained to be equal or nearly equal. This removal of constraints provides greater flexibility for optimising the properties of the cold head 2.
The embodiment of Figure 12 is an example of an embodiment in which the connection 26 to the phase control device is made at the opposite end of the cold head 2 (i.e. the warm end) compared with configurations discussed previously, for example with reference to Figures 6 and 8. Providing the connection 26 at the opposite end facilitates high performance.
In an embodiment, the pulse tube 14 comprises one or more flow shaping features 70. The flow shaping features 70 are configured to deflect flow towards the axial direction and/or make unavailable to the flow volumes of the pulse tube 14 in which the flow rate would otherwise be relatively low. Such volumes in which the flow rate would be relatively low are sometimes referred to as "dead volumes". The existence of dead volumes reduces efficiency and can cause undesirable stagnant and/or swirling flow patterns. The flow shaping features 70 improve efficiency by reducing dead volumes and helping to provide a smooth transition (arrows 80) between radial flow into the pulse tube (for example through meshes 64) and the predominantly axial flow (arrows 82) that exists in the bulk of the pulse tube. The embodiment of Figure 12 is an example of an embodiment comprising two of the flow shaping features 70: one at either end of the pulse tube 14.
In an embodiment, the pulse tube 14 is provided radially outside, optionally coaxially surrounding, the regenerator 4. In an example of such an embodiment the regenerator 4 has a cylindrical form and the pulse tube 14 has an annular form surrounding the regenerator 4. The porous wall through which the working gas can enter or leave the pulse tube 14 may in this embodiment comprise a part of a shared wall (e.g. shared between the pulse tube 14 and the regenerator 4) that is a radially inner wall of the pulse tube 14. An example of such an embodiment is depicted in Figure 13. In this embodiment, the working gas flows radially inwards from the pulse tube 14 into the regenerator 4. In the example shown, the flow passes through a mesh 64 (an example of a porous wall) connected between the regenerator 4 and the heat exchanger 10. It is expected that arrangements with the pulse tube 14 radially outside of the regenerator 4 will be more efficient than arrangements in which the pulse tube 14 is radially inside of the regenerator (for example as shown in Figures 6 and 8) for larger sizes of cold head 2.
In an embodiment, the cold head 2 is configured to operate as a multi stage cooler, with cooling at different temperatures being provided at different heat exchangers. The multi stage cooler may comprise a two stage cooler. Figure 14 depicts an example of such a two stage cooler.
The multi stage cooler comprises at least one additional regenerator 72 (one in the case of a two stage cooler), at least one additional pulse tube 74 (one in the case of a two stage cooler), and at least one additional heat exchanger 76 (one in the case of a two stage cooler). The original pulse tube 14, regenerator 4 and heat exchanger 10 may be referred to as a first stage pulse tube assembly. Each set of additional elements may be referred to as a second (or third, fourth etc.) stage pulse tube assembly. Thus, in the example of Figure 14, the second stage pulse tube assembly comprises one additional regenerator 72, one additional pulse tube 74 and one additional heat exchanger 76.
The second stage pulse tube assembly is attached to the cold end of the first stage pulse tube assembly (e.g. to the heat exchanger 10 of the first stage pulse tube assembly). The cold head 2 is configured so that a portion of the working gas from the first stage pulse tube assembly is directed, for example via appropriate passages 86, into the additional regenerator 72 of the second stage pulse tube assembly. The additional pulse tube 74 of the second stage pulse tube assembly is connected directly (i.e. has a continuous fluidic connection) to the pulse tube 14 of the first stage pulse tube assembly and shares the same connection 26 to the phase control device (via the pulse tube 14 of the first stage pulse tube assembly). It is noted that the phasing may not be simultaneously ideal for both stages. However, this is a workable arrangement as the performance of the first stage pulse tube assembly is not overly phase sensitive and the phase can therefore be adjusted to be close to ideal, or ideal, for the second stage pulse tube assembly. The portion of the flow that enters the additional regenerator 72 is cooled and input to the additional pulse tube 74 at the cold end of the additional pulse tube (the top of the additional pulse tube 74 in Figure 14). The first stage pulse tube assembly works between temperatures Th and Tc1, providing cooling at the heat exchanger 10. The second stage pulse tube assembly works between temperatures Tc1 and Tc2 and provides cooling at the heat exchanger 76. Th is warmer than Tc1 and Tc1 is warmer than Tc2. The arrangement can provide cooling more efficiently over the temperature range Th to Tc2 than a single stage cooler working directly between Th and Tc2. In the embodiment shown, three flow shaping features are provided: one at the hot end of the pulse tube 14, one at the cold end of the pulse tube 14, and one at the cold end of the additional pulse tube 74. The use of radial flows into and out of the pulse tubes in such multi stage coolers, according to embodiments of the invention such as that shown in Figure 14, allows multi stage coolers to operate particularly efficiently in comparison with otherwise equivalent arrangements that do not use radial flows.

Claims

A cold head (2) for a pulse tube cooler, comprising:
a regenerator (4) having a first end (6) connectable to a compressor (45);

a pulse tube (14) having a first end (12) and a second end (16);

a heat exchanger (10) connected between a second end (8) of the regenerator (4) and the first end (12) of the pulse tube (14); and

a phase control device connected at the second end (16) of the pulse tube (14) for controlling the flow dynamics in the pulse tube (14) to provide cooling at the heat exchanger (10), wherein:
the pulse tube (14) comprises a wall (15) having a porous portion for allowing a working gas to enter or leave the pulse tube (14) directly through the porous portion, the porous portion being nearer to being parallel than perpendicular to an axis of elongation of the pulse tube (14), characterized in that:
the heat exchanger coaxially surrounds the pulse tube.
A cold head (2) according to claim 1, wherein the porous portion is a part of a shared wall that is shared between the pulse tube (14) and one or more of the following: the regenerator (4), the heat exchanger (10), a flow distributer (11) between the pulse tube (14) and the phase control device.
A cold head (2) according to claim 2, wherein the regenerator (4) coaxially surrounds the pulse tube (14) and the porous portion is part of a shared wall that is a radially inner wall of the regenerator (4).
A cold head (2) according to claim 2, wherein the pulse tube (14) coaxially surrounds the regenerator (4) and the porous portion is part of a shared wall that is a radially inner wall of the pulse tube (14).
A cold head (2) according to claim 4, wherein the regenerator (4) is substantially cylindrical and the pulse tube (14) has a substantially annular cross-section.
A cold head (2) according to any of the preceding claims, wherein the porous portion extends from the second end (8) of the regenerator (4) along a portion of the regenerator (4) towards the first end (6) of the regenerator (4), without reaching the first end (6) of the regenerator (4).
A cold head (2) according to any of the preceding claims, wherein the porosity of the porous portion of the wall (15) decreases as a function of increasing separation from the second end (8) of the regenerator (4).
A cold head (2) according to claim 1, wherein the pulse tube (14) is orientated such that the second end (16) of the pulse tube (14) is further from the first end (6) of the regenerator (4) than the first end (12) of the pulse tube (14).
A cold head (2) according to any of the preceding claims, wherein the phase control device is configured to control the flow dynamics using one or more fluid phase control components to control the flow of gas into and out of the second end (16) of the pulse tube (14), the fluid phase control components being configured to operate without using any solid moving parts.
A cold head (2) according to any of the preceding claims, wherein the phase control device provides either or both of damping and inertia.
A cold head (2) according to any of the preceding claims, wherein the phase control device comprises a piston and cylinder in fluid communication with the second end (16) of the pulse tube (14).
A cold head (2) according to any of the preceding claims, wherein the porous portion of the wall (15) is formed from an electroformed sheet.
A cold head (2) according to claim 12, wherein the electroformed sheet is sandwiched between layers of mesh that act to even out and/or straighten the flow of gas passing through the porous portion of the wall (15).
A cold head (2) according to any of the preceding claims, wherein the cold head (2) is configured to operate as a multi stage cooler and has a first stage pulse tube assembly comprising:
a first regenerator (4) having a first end (6) connectable to a compressor (45);

a first pulse tube (14) having a first end (12) and a second end (16); and

a first heat exchanger (10) connected between a second end (8) of the first regenerator (4) and the first end (12) of the first pulse tube (14), wherein

the phase control device is connected at the second end (16) of the first pulse tube (14) for controlling the flow dynamics in the first pulse tube (14) to provide cooling at the first heat exchanger (10),

the first pulse tube (14) comprises the wall (15) having the porous portion for allowing the working gas to enter or leave the first pulse tube (14) directly through the porous portion, the porous portion being nearer to being parallel than perpendicular to an axis of elongation of the first pulse tube (10); and

the cold head (2) further comprises a second stage pulse tube assembly comprising:
an additional pulse tube (74) directly connected to the first pulse tube (14) in the region of the first heat exchanger (10) and in such a way that there is a continuous fluidic connection between the first pulse tube (14) and the additional pulse tube (74), the additional pulse tube (74) being fluidically coupled to the phase control device via said continuous fluidic connection;

an additional regenerator (72) configured to receive working gas from the first regenerator (4); and

an additional heat exchanger (76) configured to provide cooling at a lower temperature than the cooling provided at the first heat exchanger (10).
A pulse tube cooler comprising a cold head (2) according to any of the preceding claims and a compressor (45) connected to the first end (6) of the regenerator (4).