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Low-heat input cryogenic temperature control with recuperative heat-exchanger in a Joule Thomson cryocooler
Cryogenics 44 (2004) 595–601 www.elsevier.com/locate/cryogenics
Low-heat input cryogenic temperature control with recuperative heat-exchanger in a Joule Thomson cryocooler M. Prina a
a,*
, J. Borders a, P. Bhandari a, G. Morgante b, D. Pearson a, C. Paine
a
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, CA 91109-8099, USA b IASF/CNR––Sezione di Bologna, Bologna 40129, Italy
Abstract The control of cryogenic temperatures is usually accomplished by a passive stage, exploiting the combined effect of a thermal mass connected to a thermal resistance; by an active control, often of a PID type, based on the combination of a dedicated sensor, a heater and a controller; or by a combination of the two. Such a system typically uses a controlled stage that is isolated from the source of the fluctuations by a thermal isolator. Controlled insertion of heat into this stage counters the temperature fluctuations reaching the stage. Inherent to this type of system is the insertion of heat into the controlled stage that eventually reaches the cold end of the cooler, reducing the net heat lift available. The larger the thermal isolation, the smaller the reduction of the net heat lift, but with the attendant increase in the interface temperature. Any scheme that can reduce the penalty associated with the loss of heat lift or the temperature offset would be attractive in terms of cooler performance. If the cooler system has a recuperative heat exchanger between the coldest heat sink and a higher temperature precooler, a different approach can be used. In this paper we describe a novel control approach capable of passively damping low frequency fluctuations, requiring minimal reduction of cooler heat lift and minimal temperature increase of the cold end interface. This alternative scheme is based on the idea of controlling the temperature of a section of the recuperative heat exchanger between the coldest precooler and the cold end of the cooler and it has been tested on a 20 K hydrogen sorption JT cooler. 2004 Elsevier Ltd. All rights reserved. Keywords: Joule Thomson coolers (E); Heat exchangers (E); Space cryogenics (F)
1. Introduction A Joule Thomson (JT) cooler is a simple thermodynamic machine that removes heat from a low temperature ðTC Þ source and moves to a sink at a higher temperature ðTH Þ by cycling a refrigerant with a compressor where work is applied. Generally the cooler is composed by four main devices: (1) a compressor where the refrigerant pressure is increased from a low pressure (LP) to a high pressure (HP), (2) a precooler/condenser that removes heat from the refrigerant stream reducing its temperature to TH , (3) a JT expansion valve that reduces temperature and pressure of the refrigerant to allow heat removal at the cold heat source through the evaporator, (4) the low pressure refrigerant is then recompressed to restart the cycle. Depending on the high pressure HP and on temperature TH at which the heat is
*
Corresponding author. E-mail address: [email protected] (M. Prina).
0011-2275/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2004.02.021
rejected the refrigerant can enter the JT valve in two states: gaseous or liquid. When the refrigerant starts the isenthalpic expansion in the liquid state the heat exchanger that previously removed heat is called a condenser while if it enter in a gaseous state it is generally called a precooler. JT coolers for cryogenic applications generally have precoolers. As an example shown in Fig. 1a, a cooler using hydrogen as refrigerant running between 40 and 5000 kPa where the refrigerant expands directly after the precooler (point A) to point CNO rec the minimum temperature achieved by the low pressure stream would only be 42.6 K and heat could only be removed from a sink at a higher temperature than that. The temperature difference between the precooler temperature TH and the evaporator temperature TC is maximized when TC is at the same temperature of the liquid refrigerant at LP (40 kPa). To achieve this condition the JT expansion needs to start at a lower temperature than TH . By inserting a recuperative heat exchanger between the high pressure refrigerant stream going to the JT valve and the refrigerant return from the
596
M. Prina et al. / Cryogenics 44 (2004) 595–601 Heat Rejection (TH)
BLIMIT
6 5 4
B
3
A Precooler / Condenser
45 K 35 K
2
80 K 70 K
1000
Compressor
Pressure [kPa]
30 K 6 5 4
60 K 25 K
3
100
Recuperative heat exchanger
20 K
6 5 4
17.5 K CLIMIT
3
E
A
55 K
2
C
CNO REC
E
B JT valve
2
C Evaporator
(a)
(b)
10 0
500
1000 1500 2000 "Normal Hydrogen" Enthalpy [J/g]
2500
3000 Heat Lift (TC)
Fig. 1. (a) Pressure–enthalpy representation of two ideal JT ‘‘normal’’ hydrogen cooler cycles with regenerative heat exchanger. The continuous lines represent isotherms; two different cycles are shown starting from the same point (A: high pressure of 5 MPa, 60 K) and ending at the same point (E: low pressure 40 kPa, 60 K): cycle ABCE and cycle ABLIMIT CLIMIT E (Point D and DLIMIT are not shown). (b) Schematic representation of a JT cooler with recuperative heat exchanger.
evaporator, as shown in Fig. 1b, the temperature in B can be lowered. The counter-flow heat exchanger recuperates part of the cooling available in the returning stream to the compressor by reducing the enthalpy of the HP stream: the expansion can start at a lower temperature than A (on the enthalpy–pressure diagram in Fig. 1b) such as B or BLIMIT , that are possible states of the system. The minimum temperature that can be reached before the JT expansion is the temperature of the liquid-phase mixture at LP (point BLIMIT ). Ideally, the fact that the expansion is not performed at the precooler temperature but at a lower one does not affect the heat lift of the system that can be calculated as a product of the refrigerant flow and the enthalpy difference between the point CNO rec and low point E. In reality, the non-perfect efficiency (<100%) of the recuperative heat exchanger, the pressure drop in the high and low pressure lines, and heat losses in the expansion valve reduce the amount of heat lift per unit of refrigerant flow going through the thermodynamic cycle. Non-ideal effects can be minimized by proper design and in the following general description of the system they will be neglected. By this assumption, a heat balanced system can have multiple energy-equivalent states defined by different temperature at the beginning of the expansion (point B can be everywhere between point A and point BLIMIT in Fig. 1a). Only temporary heat unbalances or non-ideal conditions can move point B once the system is balanced. However, the temperature
in B is very important in the determination of the flow through a JT valve [1]. In fact, the mass flow vs. pressure drop curve for an expansion valve is strongly dependent on the temperature and consequently on the density of the refrigerant entering the valve. Therefore, even if the two cycles represented in Fig. 1b, cycle ABCDE and cycle ABLIMIT CLIMIT DLIMIT E are energetically equivalent (they have the same specific heat lift), the flow through the same JT valve would be different as would the total cooling produced. The total cooling is the product of the specific heat lift and the refrigerant flow.
2. Temperature control of the cold source A cooler that produces a liquid–vapor mixture at the end of the JT expansion and that leaves some liquid at the exit of the evaporator after the heat absorption, will be the object of the following discussion on temperature and liquid level control. In an ideal system, the return pressure of the compressor is constant fixing the temperature of the evaporator. However, if the return pressure varies, if there are time variations in the heat load applied, in the refrigerant flow, and/or in the pressure drop in the lines, the evaporator temperature varies often requiring temperature stabilization systems. In general it is best to control the pressure at the evaporator to avoid burning precious liquid refrigerant. However this solution is not always available and three
M. Prina et al. / Cryogenics 44 (2004) 595–601
general approaches can be considered for thermal stabilization: (1) A passive temperature control that improves the thermal stability by means of a passive stage exploiting the damping due to the presence of a thermal mass attached at the evaporator that is directly connected to the cold source. The passive temperature control mass acts as a low pass filter: the low frequency harmonics are not damped by the control system while the high frequencies are efficiently suppressed. The transfer function of the controller is DT0 DTPass ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cosðxt þ uÞ 2 1 þ x2 R2 CPass
ð1Þ
where CPass is the thermal capacitance of the passive stage, R ¼ 1=G is the thermal resistance between the evaporator and the passively controlled stage, and x is the frequency (in rads/s) of the oscillations. For high frequency harmonics ðx 1=RCPass Þ the amplitude of the transmitted variations is greatly reduced by the filtering. Conversely, for low harmonic content the variations are hardly dampened at all. (2) An active control loop directly on the evaporator by close loop control that senses the evaporator temperature to control a heater mounted on it. Thermal conditioning of the evaporator by applying heat to the reservoir increases the liquid boil-off rate _ and consequently the pressure drop in ðdT =dmÞ, _ the return line and at the compressor ðdm=dP Þ. The pressure variation dictates the temperature variation at the evaporator ðdP =dT Þ and closes the control loop action, as shown in Eq. (2). This type of control however dissipates substantial amount of heat lift generated by the cooler by controlling the pressure at the evaporator and indirectly its temperature and it is generally not a viable option. dQ_ dQ_ dm_ dP ¼ ð2Þ dT dm_ dP dT (3) An active control system of an thermal stage that senses the temperature of the stage connected to the evaporator via a thermal resistance and that control a heater mounted on the same stage. This option does not require the same amount of heat as the previous one but it has the drawback of increasing the temperature at which the cooling is provided. In fact, heat is not removed directly at the evaporator but at the controlled stage. As an example of the efficiency of the three methods, their application on the Planck Sorption Cooler [2–5] is considered. The sorption cooler provides 1 W of cooling for 400 W of input power at 19 ± 0.225 K (main frequency 1.5 mHz). If the temperature stability
597
requirement of 0.1 K at a temperature below 22.5 K could be achieved through (1) a passive system with a thermal mass equivalent to 50 kg of Aluminum or 150 g of H2; (2) an active controller directly on the evaporator of the cooler using ½ðdQ=dmÞ ðdm=dP Þ
ðdP =dT Þ DT ¼ 1:6 ½W=K 0:45 ½K ¼ 0:72 W, corresponding to more than 70% of the entire cooling power provided by the cooler; (3) a temperature control stage isolated from the evaporator by a thermal resistance of 0.5 W/K using 150 mW. Independently of the three different approaches an additional phenomena should be considered: the cooler can become unstable when the amount of heat removed from the cold source exceeds the cooling provided by the refrigerator. In fact, when the heat load exceeds the heat lift, the liquid previously accumulated in the evaporator slowly boils off until there will be no more liquid left in it. Further heating of the vapor in the evaporator would increases the evaporator temperature and decreases the cooling provided to the incoming high pressure flow in the recuperator. The temperature at the inlet of the expansion valve increases as the flow through it decreases, as well as the amount of available cooling at the evaporator. This positive feedback loop drives the system to an unstable condition that could only be avoided by detecting incipient unstable conditions. By measuring the excess cooling power and off the load at the evaporator, a possible solution can be found.
3. Liquid level control Sirbi et al. [6] presented a creative method for controlling the liquid level in the evaporator by burning the excessive heat lift produced by a recuperative JT cooler with recuperative heat exchanger. The excess cooling power provided by the cooler is the control power to keep a section of the recuperative heat exchanger at a constant temperature (see Fig. 2). If the heat load applied at the evaporator is less than the heat lift provided by the cooler, the available cooling of the vapor in the return line of the recuperator-1 diminishes. The input stream is not cooled to the same temperature and therefore the temperature at the controller tends to rise. The controller senses the rise and it decreases the control power, reestablishing a heat balance. Conversely, when the amount of cooling power exceeds the load, the temperature at the controlled section tends to fall and the control system responds by applying more power. This system is based on the fact that the heat balance of the system can be performed in any section of the recuperative heat exchanger. The best control is obtained when it is performed on a section of the heat exchanger whose temperature is linearly dependent on the enthalpy of the refrigerant flowing through it (i.e. the refrigerant flowing through it
M. Prina et al. / Cryogenics 44 (2004) 595–601
Low High Pressure Pressure Section 2 Recuperator QCONTROL
Section 1 Recuperator
Fig. 2. Adriana Sirbi cold end design concept: the heat balance of the 50 K enclosure is performed in the heat exchanger before the JT expander and not in the two phase region (liquid–vapor) at the cold end.
is single phase). The Sirbi control system, to first order, is not dependent on the temperature setpoint of the control loop. The setpoint temperature affects only the amount of heat transferred from the high-pressure stream to the low-pressure one in the two sections of the recuperative heat exchanger. Assuming perfect efficiency of the heat exchangers, different setpoint temperatures between the liquid and pre-cooler temperatures define thermally equivalent system states. In reality the temperature cannot vary through the entire range, but only through a subset for which the assumption of high efficiency of the heat exchangers is valid. This design was tested on a hydrogen sorption cryocooler [4] that verified its reliability and robustness. The coupled control approach was introduced to take advantage of the liquid level control while simultaneously controlling the temperature of a thermal stage stood off from the evaporator, as previously described as third temperature stabilization method while minimizing the amount of control power.
4. Coupled control design The coupled control concept is based on the fact that the Sirbi design showed no sensitivity to the temperature setpoint of the liquid-level controller. It was deduced that: (1) all the controlled states are energetically equivalent, (2) the heat can be applied everywhere in the system and does not need to be applied at the temperature sensor location, and (3) the temperature sensor of the controller needs to be in one section of the recuperator where the return line is in the vapor phase. Based on the intuition that, if the system would be fast enough to allow temperature setpoint changes at the
same rate of the temperature variations at the evaporator, then no extra power for the controller would be needed. The concept of the coupled system was developed by thermally shorting the liquid level controller and an active temperature control at the evaporator (see Fig. 3). The design is based on the performance of the mid section of the recuperative heat exchanger, shown in Fig. 3. The heat balance of the this section, from now on called the clamp, can be calculated based on the thermal conditions of the points 1–4 (temperature, flow, enthalpy), on the temperature at which the clamp is controlled by the PID circuit, and on the mechanical design of the heat exchanger. An example of the coupled control design based on a particular application on the Planck sorption cooler that has two evaporators in series is shown in Fig. 3. The sorption cryocooler recuperative heat exchanger is simply a tube-in-tube configuration [2,3]. The inside tube carries the low-pressure line while the outside one carries the high pressure. This configuration was chosen to simplify the mechanical attachment of the pre-cooler section and is not optimized in terms of pressure drops and absolute minimum temperature achievable by the cooler. Assuming that the low pressure and high pressure flows are in first approximation identical, the heat balance of the system can be described as a function of only three parameters: the temperature of the incoming
.
.
mout,TPC3,PLP
min,TPC3,PHI
CFHX T2
T1
qclam isothermal T4
qpid
T3
Eva. 2
isothermal
598
Qeva2
Qresis
(thermal res.)
)( Eva.1 Qeva1 Fig. 3. Schematic of the coupled control system as applied to a JT cooler with two evaporator sections and the three sections of the recuperative heat exchanger.
M. Prina et al. / Cryogenics 44 (2004) 595–601
599
Clamp Heat Flow [W]
0.0
-0.2
2.5 cm clamp 2 cm clamp 1.25 cm clamp
-0.4
-0.6
20
25
30
35
40
Fig. 4. Heat exchanger performance for different copper clamp lengths as a function of the temperature of the incoming high-pressure gas (T 1) when the copper clamp is controlled at 20 K and the liquid temperature is 18 K.
high pressure gas (point 1), the temperature at which the clamp is controlled, and the length of the clamp. In this analysis the assumed heat transfer convective coefficient from the hydrogen streams to the tube walls has been assumed based on equivalent conditions of flow in empty tubes with equivalent hydraulic diameter. Different clamp lengths have been considered to evaluate various effects of the heat transfer mechanism: an improved heat transfer in the same clamp can be compared to an equivalent longer clamp; a degraded heat transfer effect can be analyzed as a shorter clamp (with the same heat transfer coefficient). Fig. 4 shows a representative plot of the heat flowing through the clamp for three different clamp lengths and for a wide range of incoming high pressure gas temperatures, T 1. It can be observed that the clamp is not very efficient in transferring heat to the high-pressure stream as it is in removing heat. Considering a baseline design of a 2 cm clamp but assuming the worst-case heat transfer mechanism in the clamp, the range of heat transferred (considering the positive and negative case) is 0.6 W. The range of the heat transferred through the clamp is used in designing the thermal strap between the clamp and the stage where the external heat load is applied. The range of heat transferred through the clamp is also used to determine the value of the thermal resistance (see Fig. 4) between the controlled stage and second evaporator. The heat transferred via the clamp to the evaporator is used to balance the temperature fluctuations of the controlled stage. When the controlled stage setpoint is colder than the clamp, heat flows from the warm incoming high-pressure gas, through the clamp and the thermal strap, to the second evaporator. Conversely,
when the controlled stage is warmer than the clamp, heat flows through the strap and the clamp, in the incoming cold high pressure gas. The heater of the control loop is only used to increase the response time of the system and to burn the possible excess cooling power provided by the cooler. From a cooler perspective, the choice of the thermal resistance affects only the selection of the setpoint of the PID loop that can be varied in different ranges depending on the sorption cooler’s actual cooling capacity and on the thermal resistance between the second evaporator (also caller liquid reservoir 2 or LR2) and the fixed load Qeva2 . The analysis of the tube-and-tube heat exchanger between the copper clamp and the reservoir has been performed to verify the sensitivity of the incoming highpressure gas temperature into the reservoir, and it has been concluded that for clamps positioned at a distance greater than 7.5 cm from the second evaporator, there is no sensible effect on the load change in the evaporator-2. The length of the recuperator between the clamp an the second evaporator is enough to precool the incoming high pressure gas below 20 K (temperature used in the design of the JT valve flow) for all the conditions of the hot high pressure gas after going through the clamp shown in Fig. 3.
5. Coupled control test results The coupled control was built and tested on the Elegant BreadBoard (EBB) sorption cooler [4] and its three main properties have been verified:
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M. Prina et al. / Cryogenics 44 (2004) 595–601
• The control power is the excess cooling power provided by the cooler. During the test the Qeva1 has been increased from 0 to 1.0 W linearly over a period of 8 h. During the same period the temperature of the controlled stage was kept stable while the power required by the control circuit was measured. It can be observed in Fig. 5 that while the Qeva was rising, the power used by the controller was reduced by the same amount such that the sum of the control power and the load applied, Qeva1 , was constant. Another feature that can be observed in Fig. 5 is the increase in the noise of LR2 (the second evaporator) when the load on the first evaporator (referred as LR1) increases. The cause of the increased fluctuations harmonic content is related to the ratio of the heat flowing from the controlled stage to the second evaporator and the amount of liquid in the low pressure stream returning from the LR1. The amount of heat flowing through the thermal resistance is the product of the temperature difference between the controlled stage and the evaporator and the thermal conductance between the two. As it can be observed the difference between those two temperatures is in first approximation constant, and consequently the heat flowing through the thermal resistance does not change. However, the amount of liquid hydrogen returning from the first evaporator decreases when more and more heat is applied on LR1 generating critical heat flux phenomena in LR2 (section of the evaporator have local surface heat flux higher than the local critical heat flux). This problem can be resolved by reducing the temperature of the setpoint, therefore reducing the amount of heat flowing though the thermal resistance (as can be observed in Fig. 6).
• The absolute minimum amount of excess cooling power to control the stage temperature is less than a similar control without the clamp. The minimum power consumption of the controller (40 mW) depends on the setpoint of the controlled stage. When heat is being inserted in the clamp, the system is inherently slow and the minimum power required increases. If heat is being pulled from the clamp to the evaporator-2, the curves shown in Fig. 3 are steeper implying that a small variation of the warm gas temperature in the clamp results in a large change in heat transfer. In this condition the control system is faster and it requires less power. • The control power was measured to be independent of the temperature setpoint. In fact, the setpoint temperature determines the fixed amount of heat being transferred to/from the section of the heat exchanger to the evaporator. Fig. 6 shows a test conducted on the hydrogen sorption cryocooler where the temperature of the setpoint was changed by 1.5 K, from 22 to 20.5 K when the temperature of the liquid hydrogen was at an average of 18.7 K with 400 mK peak-topeak temperature fluctuations. The variation of the controller behavior can be observed: when the setpoint temperature is lowered and less heat is removed from the clamp and dumped into the evaporator via the thermal resistance, the power profile of the controller has the same features the temperature of the evaporator, while when the controller is reacting faster to the evaporator temperature variation the power consumption is more constant. Another feature that differentiates the two setpoints is the reaction to ‘‘fast’’ changes in the evaporator temperature, namely the response to the peaks of the LR2 temperature
Fig. 5. Variation of the control power as a function of the Qeva1 applied.
M. Prina et al. / Cryogenics 44 (2004) 595–601 0.4
601
PID power [W]
0.3 0.2 0.1 0.0 0.8 0.6 0.4 0.2
LR2 heater power [W] LR1 heater power [W]
22.0 21.5 21.0
Setpoint Temperature [K]
20.5 20.0
Evaporator-2 Temperature [K]
19.5 19.0 11:00 AM 3/24/2003
12:00 PM
1:00 PM
2:00 PM
3:00 PM
Time
Fig. 6. Conservation of the average control power with different setpoint temperature.
curve shown in Fig. 6. When the controller is constantly pulling heat from the clamp the controller reaction is faster than the temperature variation and its power profile is not primarily determined by low frequency harmonics. Instead, when the controller is slow compared to the variations, its power profile is completely dictated by the profile of the temperature. 6. Conclusions The control scheme has been tested on a 20 K hydrogen cryocooler with a recuperative heat exchanger, demonstrating that reduction in heat lift is considerably smaller than typical temperature control methods such as PID on a thermal isolated stage for the same temperature difference between the controlled stage and the evaporator. In the specific cryocooler cold end on which it was tested (i.e. the hydrogen sorption cryocooler for the Planck mission) the coupled control demonstrated a minimum power requirement of 40 mW compared to the 80 mW required to run a regular stood-off temperature control stage with a PID controller. In addition, the coupled control was able to simultaneously heat balance the system and control the temperature of the evaporator on which it was mounted by applying excess heat to balance the amount of cooling produced by the cooler. Such a measurement is a key feedback in the control of the performance of the whole JT cryocooler with an evaporator. By adjusting the input power to always keep a minimum excess cooling power and not excessively burning extra cooling power produced the
cooler performance can be tuned while avoiding incipient dry-outs in the evaporator.
Acknowledgements This research was carried out by the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration.
References [1] Levy AR, Wade LA. Characterization of porous metal flow restrictors for use as the J-T expander in hydrogen sorption cryocoolers. In: Ross Jr RG, editor. Cryocoolers, vol. 10. New York: Kluwer Academic/Plenum; 1999. p. 545–52. [2] Wade Q-S et al. Hydrogen sorption cryocoolers for the Planck mission. editors. In: Advances in cryogenic engineering, vol. 45A. Kluwer New York: Academic/Plenum; 2000. p. 499–506. [3] Prina M, Morgante G, Loc A, Schmelzel M, Pearson D, Borders JW, et al. Initial test performance of a closed-cycle continuous hydrogen sorption cooler, the Planck sorption breadboard cooler. In: Cryocoolers, vol. 12. Plenum Publishers; p. 637–42. [4] Pearson D, Borders J, Prina M, Morgante G, Bhandari P, Bowman RC, et al. Planck engineering breadboard sorption cooler test results over its entire operating range. In: Proceedings of the 19th International Cryogenic Engineering Conference. Narosa Publishing House; 2003. p. 507–10. [5] Collaudin B, Passvogel T. Cryogenics 1999;39:157. [6] Sirbi A, Bowman Jr RC, Wade LA, Barber DS, et al. Cryogenic system design for a hydrogen sorption cooler. In: Breon S et al., editors. Advances in cryogenic engineering, vol. 47. New York: Am Inst Phys; 2002. p. 1217.
Low-heat input cryogenic temperature control with recuperative heat-exchanger in a Joule Thomson cryocooler M. Prina a
a,*
, J. Borders a, P. Bhandari a, G. Morgante b, D. Pearson a, C. Paine
a
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, CA 91109-8099, USA b IASF/CNR––Sezione di Bologna, Bologna 40129, Italy
Abstract The control of cryogenic temperatures is usually accomplished by a passive stage, exploiting the combined effect of a thermal mass connected to a thermal resistance; by an active control, often of a PID type, based on the combination of a dedicated sensor, a heater and a controller; or by a combination of the two. Such a system typically uses a controlled stage that is isolated from the source of the fluctuations by a thermal isolator. Controlled insertion of heat into this stage counters the temperature fluctuations reaching the stage. Inherent to this type of system is the insertion of heat into the controlled stage that eventually reaches the cold end of the cooler, reducing the net heat lift available. The larger the thermal isolation, the smaller the reduction of the net heat lift, but with the attendant increase in the interface temperature. Any scheme that can reduce the penalty associated with the loss of heat lift or the temperature offset would be attractive in terms of cooler performance. If the cooler system has a recuperative heat exchanger between the coldest heat sink and a higher temperature precooler, a different approach can be used. In this paper we describe a novel control approach capable of passively damping low frequency fluctuations, requiring minimal reduction of cooler heat lift and minimal temperature increase of the cold end interface. This alternative scheme is based on the idea of controlling the temperature of a section of the recuperative heat exchanger between the coldest precooler and the cold end of the cooler and it has been tested on a 20 K hydrogen sorption JT cooler. 2004 Elsevier Ltd. All rights reserved. Keywords: Joule Thomson coolers (E); Heat exchangers (E); Space cryogenics (F)
1. Introduction A Joule Thomson (JT) cooler is a simple thermodynamic machine that removes heat from a low temperature ðTC Þ source and moves to a sink at a higher temperature ðTH Þ by cycling a refrigerant with a compressor where work is applied. Generally the cooler is composed by four main devices: (1) a compressor where the refrigerant pressure is increased from a low pressure (LP) to a high pressure (HP), (2) a precooler/condenser that removes heat from the refrigerant stream reducing its temperature to TH , (3) a JT expansion valve that reduces temperature and pressure of the refrigerant to allow heat removal at the cold heat source through the evaporator, (4) the low pressure refrigerant is then recompressed to restart the cycle. Depending on the high pressure HP and on temperature TH at which the heat is
*
Corresponding author. E-mail address: [email protected] (M. Prina).
0011-2275/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2004.02.021
rejected the refrigerant can enter the JT valve in two states: gaseous or liquid. When the refrigerant starts the isenthalpic expansion in the liquid state the heat exchanger that previously removed heat is called a condenser while if it enter in a gaseous state it is generally called a precooler. JT coolers for cryogenic applications generally have precoolers. As an example shown in Fig. 1a, a cooler using hydrogen as refrigerant running between 40 and 5000 kPa where the refrigerant expands directly after the precooler (point A) to point CNO rec the minimum temperature achieved by the low pressure stream would only be 42.6 K and heat could only be removed from a sink at a higher temperature than that. The temperature difference between the precooler temperature TH and the evaporator temperature TC is maximized when TC is at the same temperature of the liquid refrigerant at LP (40 kPa). To achieve this condition the JT expansion needs to start at a lower temperature than TH . By inserting a recuperative heat exchanger between the high pressure refrigerant stream going to the JT valve and the refrigerant return from the
596
M. Prina et al. / Cryogenics 44 (2004) 595–601 Heat Rejection (TH)
BLIMIT
6 5 4
B
3
A Precooler / Condenser
45 K 35 K
2
80 K 70 K
1000
Compressor
Pressure [kPa]
30 K 6 5 4
60 K 25 K
3
100
Recuperative heat exchanger
20 K
6 5 4
17.5 K CLIMIT
3
E
A
55 K
2
C
CNO REC
E
B JT valve
2
C Evaporator
(a)
(b)
10 0
500
1000 1500 2000 "Normal Hydrogen" Enthalpy [J/g]
2500
3000 Heat Lift (TC)
Fig. 1. (a) Pressure–enthalpy representation of two ideal JT ‘‘normal’’ hydrogen cooler cycles with regenerative heat exchanger. The continuous lines represent isotherms; two different cycles are shown starting from the same point (A: high pressure of 5 MPa, 60 K) and ending at the same point (E: low pressure 40 kPa, 60 K): cycle ABCE and cycle ABLIMIT CLIMIT E (Point D and DLIMIT are not shown). (b) Schematic representation of a JT cooler with recuperative heat exchanger.
evaporator, as shown in Fig. 1b, the temperature in B can be lowered. The counter-flow heat exchanger recuperates part of the cooling available in the returning stream to the compressor by reducing the enthalpy of the HP stream: the expansion can start at a lower temperature than A (on the enthalpy–pressure diagram in Fig. 1b) such as B or BLIMIT , that are possible states of the system. The minimum temperature that can be reached before the JT expansion is the temperature of the liquid-phase mixture at LP (point BLIMIT ). Ideally, the fact that the expansion is not performed at the precooler temperature but at a lower one does not affect the heat lift of the system that can be calculated as a product of the refrigerant flow and the enthalpy difference between the point CNO rec and low point E. In reality, the non-perfect efficiency (<100%) of the recuperative heat exchanger, the pressure drop in the high and low pressure lines, and heat losses in the expansion valve reduce the amount of heat lift per unit of refrigerant flow going through the thermodynamic cycle. Non-ideal effects can be minimized by proper design and in the following general description of the system they will be neglected. By this assumption, a heat balanced system can have multiple energy-equivalent states defined by different temperature at the beginning of the expansion (point B can be everywhere between point A and point BLIMIT in Fig. 1a). Only temporary heat unbalances or non-ideal conditions can move point B once the system is balanced. However, the temperature
in B is very important in the determination of the flow through a JT valve [1]. In fact, the mass flow vs. pressure drop curve for an expansion valve is strongly dependent on the temperature and consequently on the density of the refrigerant entering the valve. Therefore, even if the two cycles represented in Fig. 1b, cycle ABCDE and cycle ABLIMIT CLIMIT DLIMIT E are energetically equivalent (they have the same specific heat lift), the flow through the same JT valve would be different as would the total cooling produced. The total cooling is the product of the specific heat lift and the refrigerant flow.
2. Temperature control of the cold source A cooler that produces a liquid–vapor mixture at the end of the JT expansion and that leaves some liquid at the exit of the evaporator after the heat absorption, will be the object of the following discussion on temperature and liquid level control. In an ideal system, the return pressure of the compressor is constant fixing the temperature of the evaporator. However, if the return pressure varies, if there are time variations in the heat load applied, in the refrigerant flow, and/or in the pressure drop in the lines, the evaporator temperature varies often requiring temperature stabilization systems. In general it is best to control the pressure at the evaporator to avoid burning precious liquid refrigerant. However this solution is not always available and three
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general approaches can be considered for thermal stabilization: (1) A passive temperature control that improves the thermal stability by means of a passive stage exploiting the damping due to the presence of a thermal mass attached at the evaporator that is directly connected to the cold source. The passive temperature control mass acts as a low pass filter: the low frequency harmonics are not damped by the control system while the high frequencies are efficiently suppressed. The transfer function of the controller is DT0 DTPass ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cosðxt þ uÞ 2 1 þ x2 R2 CPass
ð1Þ
where CPass is the thermal capacitance of the passive stage, R ¼ 1=G is the thermal resistance between the evaporator and the passively controlled stage, and x is the frequency (in rads/s) of the oscillations. For high frequency harmonics ðx 1=RCPass Þ the amplitude of the transmitted variations is greatly reduced by the filtering. Conversely, for low harmonic content the variations are hardly dampened at all. (2) An active control loop directly on the evaporator by close loop control that senses the evaporator temperature to control a heater mounted on it. Thermal conditioning of the evaporator by applying heat to the reservoir increases the liquid boil-off rate _ and consequently the pressure drop in ðdT =dmÞ, _ the return line and at the compressor ðdm=dP Þ. The pressure variation dictates the temperature variation at the evaporator ðdP =dT Þ and closes the control loop action, as shown in Eq. (2). This type of control however dissipates substantial amount of heat lift generated by the cooler by controlling the pressure at the evaporator and indirectly its temperature and it is generally not a viable option. dQ_ dQ_ dm_ dP ¼ ð2Þ dT dm_ dP dT (3) An active control system of an thermal stage that senses the temperature of the stage connected to the evaporator via a thermal resistance and that control a heater mounted on the same stage. This option does not require the same amount of heat as the previous one but it has the drawback of increasing the temperature at which the cooling is provided. In fact, heat is not removed directly at the evaporator but at the controlled stage. As an example of the efficiency of the three methods, their application on the Planck Sorption Cooler [2–5] is considered. The sorption cooler provides 1 W of cooling for 400 W of input power at 19 ± 0.225 K (main frequency 1.5 mHz). If the temperature stability
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requirement of 0.1 K at a temperature below 22.5 K could be achieved through (1) a passive system with a thermal mass equivalent to 50 kg of Aluminum or 150 g of H2; (2) an active controller directly on the evaporator of the cooler using ½ðdQ=dmÞ ðdm=dP Þ
ðdP =dT Þ DT ¼ 1:6 ½W=K 0:45 ½K ¼ 0:72 W, corresponding to more than 70% of the entire cooling power provided by the cooler; (3) a temperature control stage isolated from the evaporator by a thermal resistance of 0.5 W/K using 150 mW. Independently of the three different approaches an additional phenomena should be considered: the cooler can become unstable when the amount of heat removed from the cold source exceeds the cooling provided by the refrigerator. In fact, when the heat load exceeds the heat lift, the liquid previously accumulated in the evaporator slowly boils off until there will be no more liquid left in it. Further heating of the vapor in the evaporator would increases the evaporator temperature and decreases the cooling provided to the incoming high pressure flow in the recuperator. The temperature at the inlet of the expansion valve increases as the flow through it decreases, as well as the amount of available cooling at the evaporator. This positive feedback loop drives the system to an unstable condition that could only be avoided by detecting incipient unstable conditions. By measuring the excess cooling power and off the load at the evaporator, a possible solution can be found.
3. Liquid level control Sirbi et al. [6] presented a creative method for controlling the liquid level in the evaporator by burning the excessive heat lift produced by a recuperative JT cooler with recuperative heat exchanger. The excess cooling power provided by the cooler is the control power to keep a section of the recuperative heat exchanger at a constant temperature (see Fig. 2). If the heat load applied at the evaporator is less than the heat lift provided by the cooler, the available cooling of the vapor in the return line of the recuperator-1 diminishes. The input stream is not cooled to the same temperature and therefore the temperature at the controller tends to rise. The controller senses the rise and it decreases the control power, reestablishing a heat balance. Conversely, when the amount of cooling power exceeds the load, the temperature at the controlled section tends to fall and the control system responds by applying more power. This system is based on the fact that the heat balance of the system can be performed in any section of the recuperative heat exchanger. The best control is obtained when it is performed on a section of the heat exchanger whose temperature is linearly dependent on the enthalpy of the refrigerant flowing through it (i.e. the refrigerant flowing through it
M. Prina et al. / Cryogenics 44 (2004) 595–601
Low High Pressure Pressure Section 2 Recuperator QCONTROL
Section 1 Recuperator
Fig. 2. Adriana Sirbi cold end design concept: the heat balance of the 50 K enclosure is performed in the heat exchanger before the JT expander and not in the two phase region (liquid–vapor) at the cold end.
is single phase). The Sirbi control system, to first order, is not dependent on the temperature setpoint of the control loop. The setpoint temperature affects only the amount of heat transferred from the high-pressure stream to the low-pressure one in the two sections of the recuperative heat exchanger. Assuming perfect efficiency of the heat exchangers, different setpoint temperatures between the liquid and pre-cooler temperatures define thermally equivalent system states. In reality the temperature cannot vary through the entire range, but only through a subset for which the assumption of high efficiency of the heat exchangers is valid. This design was tested on a hydrogen sorption cryocooler [4] that verified its reliability and robustness. The coupled control approach was introduced to take advantage of the liquid level control while simultaneously controlling the temperature of a thermal stage stood off from the evaporator, as previously described as third temperature stabilization method while minimizing the amount of control power.
4. Coupled control design The coupled control concept is based on the fact that the Sirbi design showed no sensitivity to the temperature setpoint of the liquid-level controller. It was deduced that: (1) all the controlled states are energetically equivalent, (2) the heat can be applied everywhere in the system and does not need to be applied at the temperature sensor location, and (3) the temperature sensor of the controller needs to be in one section of the recuperator where the return line is in the vapor phase. Based on the intuition that, if the system would be fast enough to allow temperature setpoint changes at the
same rate of the temperature variations at the evaporator, then no extra power for the controller would be needed. The concept of the coupled system was developed by thermally shorting the liquid level controller and an active temperature control at the evaporator (see Fig. 3). The design is based on the performance of the mid section of the recuperative heat exchanger, shown in Fig. 3. The heat balance of the this section, from now on called the clamp, can be calculated based on the thermal conditions of the points 1–4 (temperature, flow, enthalpy), on the temperature at which the clamp is controlled by the PID circuit, and on the mechanical design of the heat exchanger. An example of the coupled control design based on a particular application on the Planck sorption cooler that has two evaporators in series is shown in Fig. 3. The sorption cryocooler recuperative heat exchanger is simply a tube-in-tube configuration [2,3]. The inside tube carries the low-pressure line while the outside one carries the high pressure. This configuration was chosen to simplify the mechanical attachment of the pre-cooler section and is not optimized in terms of pressure drops and absolute minimum temperature achievable by the cooler. Assuming that the low pressure and high pressure flows are in first approximation identical, the heat balance of the system can be described as a function of only three parameters: the temperature of the incoming
.
.
mout,TPC3,PLP
min,TPC3,PHI
CFHX T2
T1
qclam isothermal T4
qpid
T3
Eva. 2
isothermal
598
Qeva2
Qresis
(thermal res.)
)( Eva.1 Qeva1 Fig. 3. Schematic of the coupled control system as applied to a JT cooler with two evaporator sections and the three sections of the recuperative heat exchanger.
M. Prina et al. / Cryogenics 44 (2004) 595–601
599
Clamp Heat Flow [W]
0.0
-0.2
2.5 cm clamp 2 cm clamp 1.25 cm clamp
-0.4
-0.6
20
25
30
35
40
Fig. 4. Heat exchanger performance for different copper clamp lengths as a function of the temperature of the incoming high-pressure gas (T 1) when the copper clamp is controlled at 20 K and the liquid temperature is 18 K.
high pressure gas (point 1), the temperature at which the clamp is controlled, and the length of the clamp. In this analysis the assumed heat transfer convective coefficient from the hydrogen streams to the tube walls has been assumed based on equivalent conditions of flow in empty tubes with equivalent hydraulic diameter. Different clamp lengths have been considered to evaluate various effects of the heat transfer mechanism: an improved heat transfer in the same clamp can be compared to an equivalent longer clamp; a degraded heat transfer effect can be analyzed as a shorter clamp (with the same heat transfer coefficient). Fig. 4 shows a representative plot of the heat flowing through the clamp for three different clamp lengths and for a wide range of incoming high pressure gas temperatures, T 1. It can be observed that the clamp is not very efficient in transferring heat to the high-pressure stream as it is in removing heat. Considering a baseline design of a 2 cm clamp but assuming the worst-case heat transfer mechanism in the clamp, the range of heat transferred (considering the positive and negative case) is 0.6 W. The range of the heat transferred through the clamp is used in designing the thermal strap between the clamp and the stage where the external heat load is applied. The range of heat transferred through the clamp is also used to determine the value of the thermal resistance (see Fig. 4) between the controlled stage and second evaporator. The heat transferred via the clamp to the evaporator is used to balance the temperature fluctuations of the controlled stage. When the controlled stage setpoint is colder than the clamp, heat flows from the warm incoming high-pressure gas, through the clamp and the thermal strap, to the second evaporator. Conversely,
when the controlled stage is warmer than the clamp, heat flows through the strap and the clamp, in the incoming cold high pressure gas. The heater of the control loop is only used to increase the response time of the system and to burn the possible excess cooling power provided by the cooler. From a cooler perspective, the choice of the thermal resistance affects only the selection of the setpoint of the PID loop that can be varied in different ranges depending on the sorption cooler’s actual cooling capacity and on the thermal resistance between the second evaporator (also caller liquid reservoir 2 or LR2) and the fixed load Qeva2 . The analysis of the tube-and-tube heat exchanger between the copper clamp and the reservoir has been performed to verify the sensitivity of the incoming highpressure gas temperature into the reservoir, and it has been concluded that for clamps positioned at a distance greater than 7.5 cm from the second evaporator, there is no sensible effect on the load change in the evaporator-2. The length of the recuperator between the clamp an the second evaporator is enough to precool the incoming high pressure gas below 20 K (temperature used in the design of the JT valve flow) for all the conditions of the hot high pressure gas after going through the clamp shown in Fig. 3.
5. Coupled control test results The coupled control was built and tested on the Elegant BreadBoard (EBB) sorption cooler [4] and its three main properties have been verified:
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• The control power is the excess cooling power provided by the cooler. During the test the Qeva1 has been increased from 0 to 1.0 W linearly over a period of 8 h. During the same period the temperature of the controlled stage was kept stable while the power required by the control circuit was measured. It can be observed in Fig. 5 that while the Qeva was rising, the power used by the controller was reduced by the same amount such that the sum of the control power and the load applied, Qeva1 , was constant. Another feature that can be observed in Fig. 5 is the increase in the noise of LR2 (the second evaporator) when the load on the first evaporator (referred as LR1) increases. The cause of the increased fluctuations harmonic content is related to the ratio of the heat flowing from the controlled stage to the second evaporator and the amount of liquid in the low pressure stream returning from the LR1. The amount of heat flowing through the thermal resistance is the product of the temperature difference between the controlled stage and the evaporator and the thermal conductance between the two. As it can be observed the difference between those two temperatures is in first approximation constant, and consequently the heat flowing through the thermal resistance does not change. However, the amount of liquid hydrogen returning from the first evaporator decreases when more and more heat is applied on LR1 generating critical heat flux phenomena in LR2 (section of the evaporator have local surface heat flux higher than the local critical heat flux). This problem can be resolved by reducing the temperature of the setpoint, therefore reducing the amount of heat flowing though the thermal resistance (as can be observed in Fig. 6).
• The absolute minimum amount of excess cooling power to control the stage temperature is less than a similar control without the clamp. The minimum power consumption of the controller (40 mW) depends on the setpoint of the controlled stage. When heat is being inserted in the clamp, the system is inherently slow and the minimum power required increases. If heat is being pulled from the clamp to the evaporator-2, the curves shown in Fig. 3 are steeper implying that a small variation of the warm gas temperature in the clamp results in a large change in heat transfer. In this condition the control system is faster and it requires less power. • The control power was measured to be independent of the temperature setpoint. In fact, the setpoint temperature determines the fixed amount of heat being transferred to/from the section of the heat exchanger to the evaporator. Fig. 6 shows a test conducted on the hydrogen sorption cryocooler where the temperature of the setpoint was changed by 1.5 K, from 22 to 20.5 K when the temperature of the liquid hydrogen was at an average of 18.7 K with 400 mK peak-topeak temperature fluctuations. The variation of the controller behavior can be observed: when the setpoint temperature is lowered and less heat is removed from the clamp and dumped into the evaporator via the thermal resistance, the power profile of the controller has the same features the temperature of the evaporator, while when the controller is reacting faster to the evaporator temperature variation the power consumption is more constant. Another feature that differentiates the two setpoints is the reaction to ‘‘fast’’ changes in the evaporator temperature, namely the response to the peaks of the LR2 temperature
Fig. 5. Variation of the control power as a function of the Qeva1 applied.
M. Prina et al. / Cryogenics 44 (2004) 595–601 0.4
601
PID power [W]
0.3 0.2 0.1 0.0 0.8 0.6 0.4 0.2
LR2 heater power [W] LR1 heater power [W]
22.0 21.5 21.0
Setpoint Temperature [K]
20.5 20.0
Evaporator-2 Temperature [K]
19.5 19.0 11:00 AM 3/24/2003
12:00 PM
1:00 PM
2:00 PM
3:00 PM
Time
Fig. 6. Conservation of the average control power with different setpoint temperature.
curve shown in Fig. 6. When the controller is constantly pulling heat from the clamp the controller reaction is faster than the temperature variation and its power profile is not primarily determined by low frequency harmonics. Instead, when the controller is slow compared to the variations, its power profile is completely dictated by the profile of the temperature. 6. Conclusions The control scheme has been tested on a 20 K hydrogen cryocooler with a recuperative heat exchanger, demonstrating that reduction in heat lift is considerably smaller than typical temperature control methods such as PID on a thermal isolated stage for the same temperature difference between the controlled stage and the evaporator. In the specific cryocooler cold end on which it was tested (i.e. the hydrogen sorption cryocooler for the Planck mission) the coupled control demonstrated a minimum power requirement of 40 mW compared to the 80 mW required to run a regular stood-off temperature control stage with a PID controller. In addition, the coupled control was able to simultaneously heat balance the system and control the temperature of the evaporator on which it was mounted by applying excess heat to balance the amount of cooling produced by the cooler. Such a measurement is a key feedback in the control of the performance of the whole JT cryocooler with an evaporator. By adjusting the input power to always keep a minimum excess cooling power and not excessively burning extra cooling power produced the
cooler performance can be tuned while avoiding incipient dry-outs in the evaporator.
Acknowledgements This research was carried out by the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration.
References [1] Levy AR, Wade LA. Characterization of porous metal flow restrictors for use as the J-T expander in hydrogen sorption cryocoolers. In: Ross Jr RG, editor. Cryocoolers, vol. 10. New York: Kluwer Academic/Plenum; 1999. p. 545–52. [2] Wade Q-S et al. Hydrogen sorption cryocoolers for the Planck mission. editors. In: Advances in cryogenic engineering, vol. 45A. Kluwer New York: Academic/Plenum; 2000. p. 499–506. [3] Prina M, Morgante G, Loc A, Schmelzel M, Pearson D, Borders JW, et al. Initial test performance of a closed-cycle continuous hydrogen sorption cooler, the Planck sorption breadboard cooler. In: Cryocoolers, vol. 12. Plenum Publishers; p. 637–42. [4] Pearson D, Borders J, Prina M, Morgante G, Bhandari P, Bowman RC, et al. Planck engineering breadboard sorption cooler test results over its entire operating range. In: Proceedings of the 19th International Cryogenic Engineering Conference. Narosa Publishing House; 2003. p. 507–10. [5] Collaudin B, Passvogel T. Cryogenics 1999;39:157. [6] Sirbi A, Bowman Jr RC, Wade LA, Barber DS, et al. Cryogenic system design for a hydrogen sorption cooler. In: Breon S et al., editors. Advances in cryogenic engineering, vol. 47. New York: Am Inst Phys; 2002. p. 1217.