Sorption characterization and actuation of a gas-gap heat switch

Sensors and Actuators A 171 (2011) 324–331

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Sorption characterization and actuation of a gas-gap heat switch D. Martins a , L. Ribeiro a , D. Lopes a , I. Catarino a,∗ , I.A.A.C. Esteves b , J.P.B. Mota b , G. Bonfait a a b

Cefitec – Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal Requimte/CQFB, Departamento de Química, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

a r t i c l e

i n f o

Article history: Received 4 May 2011 Received in revised form 18 August 2011 Accepted 19 August 2011 Available online 27 August 2011 Keywords: Gas gap heat switches Cryogenic integration Sorption pumping Adsorption

a b s t r a c t Cryogenic gas-gap heat switches are rendered compact by using a sorption pump as actuating device. The sorption pump adsorbs gas when it is cooled and releases gas when it is heated. Upon desorption, the released gas lies in the gap between two blocks and increases the conduction heat transfer between them; in the reverse case – when the gas is adsorbed – the gap space between the two blocks behaves as an insulator. The temperatures at which there is sufficient desorption and adsorption of gas for actuating the ON an OFF states depend on several parameters of the gas-adsorbent system. The adsorption characteristics of helium gas on several carbon adsorbents were studied at pressures ranging from 50 Pa to 120 kPa and temperatures from 10 to 100 K. One of the carbons was successfully used in a heat switch at 6 K under different configurations in order to access different actuation characteristics. The experimental helium adsorption equilibrium data for each carbon were successfully fitted by a semi-empirical adsorption isotherm model. A thermal model of the heat switch, whose actuation can be tailored upon specifications, was developed based on the adsorption data. The thermal model was validated by reproducing the experimental data for two different configurations of a heat switch prototype. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Thermal switches (or heat switches) allow the user to toggle between states of poor and good thermal conduction, and are particularly convenient for thermal management in cryogenic systems. In these devices, the thermal conductions of the two states may differ by orders of magnitude, thereby approximating the discrete behavior of an on-off switch. Gas-gap heat switches (GGHS) use the filling and emptying of a gas in a gap between two blocks set apart to provide the different conduction states between the blocks. In a GGHS the gas can be managed in a compact way by using a sorption pump. By cooling the pump, it adsorbs the gas thereby producing the poor conduction (off) state; upon heating the adsorbent, the gas is desorbed and fills the gap between the two blocks thus providing the good conduction (on) state. Because the gas-gap heat switch does not have any moving parts, it is a very reliable cryogenic device and hence very attractive for certain types of applications, particularly for space applications [1–4]. Several cryogenic gasgap heat switches with sorption actuation have been presented [1–3,5–11], mostly using helium as an exchange gas, but also using some other gases. The heat transfer regime in a gas-gap heat switch is determined by the ratio of the mean free path of the gas molecules, which

∗ Corresponding author. E-mail address: [email protected] (I. Catarino). 0924-4247/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2011.08.017

is pressure and temperature dependent, and the gap width. The switch is turned on (maximum heat conductance) as the viscous regime is achieved; this happens when the mean free path is much smaller than the gap width. To turn off the switch, a molecular transfer regime must be established, in which the mean free path is much larger than the gap spacing; in this regime the heat transfer is linearly dependent on pressure and as the pressure decreases the conduction decreases asymptotically to a flat minimum that is set by the geometry and materials used for the design of the switch. Thus, the criterion for the conductance that establishes the off state defines an off limiting pressure. Since the pressure in the switch is controlled by the temperature of the sorption pump, the quantitative knowledge of the adsorption thermodynamics of the gas–solid system can be used to convert the on/off onset pressures into adsorbent temperatures that are easily assessed and controlled. Nevertheless the available adsorption data for cryogenic sorption pumps are very scarce [12] and the design of these pumps is frequently done by rough estimation based on previous experience or by trial and error. The main goal of the present work is to present the model-aided design of a carbon-based adsorbent pump for a gas-gap cryogenic thermal switch. This objective can only be achieved with accurate measurements of adsorption data and concomitant modeling work. Due to the lack of extensive and reliable adsorption data for the typical pressure and temperature ranges used in gas-gap cryogenic heat switches, we developed our own volumetric adsorption apparatus and started to build up a database of sorption properties for cryogenic applications [13].

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In the present study, five different carbon adsorbents were selected and their porosity characterized by standard nitrogen adsorption at 77 K. Helium adsorption measurements on the five carbons were performed at pressures ranging from 50 Pa to 120 kPa and temperatures from 10 to 100 K. The equilibrium relation between the measured temperature, pressure, and specific amount of adsorbed gas was accurately represented in an analytical form using a semi-empirical isotherm model proposed by Roubeau et al. [14]. The thermal model of a GGHS was developed to predict the conductance of the switch as a function of temperature of the sorption actuator. For the geometry of an available prototype [7], the model was validated by comparing its predictions with our own experimental data. Our model reproduces the entire experimental conductance curve for a helium GGHS as a function of the actuation temperature, including the intermediate regime. The behavior of the same switch was simulated for different types of carbon in the sorption pump. We also present design-aiding charts that summarize our calculations for the different types of adsorbents and/or their packing density in order to help dimensioning the actuators of similar switches. The paper is organized as follows: the adsorption experiments are presented and discussed in Section 2. In Section 3 we present the thermal model of the heat switch based on the adsorption equilibrium isotherm model developed in the previous section. The model is validated against experimental data obtained in an available GGHS prototype. Finally, in Section 4 we predict the effects of different carbon adsorbents on the GGHS. 2. Sorption 2.1. Sorption experiments Five different carbons1

were selected and characterized for their porosity and pore size distribution using standard nitrogen adsorption (77 K) on a Micromeritics® ASAP2010 surface area analyzer. The microporous properties of the various carbons are given here in terms of the commonly reported Brunauer–Emmett–Teller (BET) [15] surface area and Horvath–Kawazoe (HK) [16] pore volumes. This analysis was complemented by mercury porosimetry. The standard nitrogen adsorption isotherms for all carbons are Type I according to the IUPAC classification [17], which indicates that all carbons are essentially microporous. The characterization of the porosity of the carbon samples is given in Table 1. Our volumetric setup for adsorption measurements in the 10 k-300 K range is described in detail and validated elsewhere [13]. Only a brief description of the apparatus is given here for clarity. Briefly, it consists of a 5 cm3 cell filled up with adsorbent attached to a 10 K Gifford–Mac Mahon type cryocooler and connected to a temperature regulated calibrated volume (≈1000 cm3 ) by a capillary tube. The pressure in the whole system is measured at room temperature using two Baratron® type capacitor gauges. Since the initial amount of gas in the system before adsorption is known, the amount adsorbed in the cell can be determined from a material balance coupled with the equation of state for the ideal gas. The adsorption equilibrium data are recorded automatically at stable increasing temperature steps by means of an accurate temperature

Fig. 1. Adsorption isotherms of helium at 15.0 K on the five different carbons. The lines are a smooth interpolation of the experimental data (symbols) as serve as a guide to the eye. Unit for Q is gram of He per gram of carbon.

controller. Pressure gradients due to thermal transpiration were estimated using the empirical equation of Takaishi and Sensui [18], and found to be negligible for the geometry and pressure range used in this study. The adsorption isotherms of helium (4 He) on the five different carbon samples were measured at temperatures from 10 K to 100 K and pressures from 50 Pa to 120 kPa. As an example, Fig. 1 shows the isotherms at 15 K for all five carbon adsorbents. An analysis of these data with respect to the porosity and pore size distribution of the various carbons is outside the scope of this paper and will be addressed elsewhere.

2.2. Sorption data and fitting The measured adsorption data for each carbon were arranged into a table relating the three state variables: pressure (P), temperature (T), and amount of adsorbed gas per amount of adsorbent (Q). The various experiments in which different total amounts of gas were subjected to increasing temperature steps were concatenated into the form of adsorption isotherms (the relation between Q and P at a fixed value of T). The interpolation of Q across various isotherms allows the representation of adsorption isosteres (the relation between P and T for a given amount adsorbed). In order to obtain a relatively simple and tractable analytical equation of state for the adsorbed phase (i.e., an adsorption isotherm model), the adsorption data were fitted using a semiempirical equation proposed by Roubeau et al. [14] as described below. A link between the isosteric heat of adsorption, L, and experimental properties is made through the Clapeyron equation, which enables L to be found from the adsorption data. We take the usual assumption that the adsorbed phase will be much denser than the gas phase (in this case the molar volume of the former can be reasonably neglected in comparison with that of the latter); furthermore, over the temperature and pressure ranges of our measurements helium can be considered an ideal gas. These assumptions lead to the standard result:

 L = −R

1

Carbons A to D were supplied by Sutcliffe Speakman, Ltd., now part of Chemviron Carbon, Ltd. (Wigan, Lancashire, UK). Carbons B and D were produced by steam activation of selected grades of pulverized and then re-agglomerated, milled coconut shells; carbon D was subjected to a higher activation temperature than carbon B. Carbon C is a coal-based carbon produced by the same activation process as carbon D. Carbon A was synthesized from milled carbon fibers (isotropic pitch) and powdered phenolic resin, which was slurried in water and vacuum molded, and then heated to cure the phenolic resin and finally carbonized at 650 ◦ C.

325

∂ ln P ∂(1/T )

 (1) Q

where R is the ideal gas constant. The isosterical (constant Q) representation of the experimental adsorption data under the form of ln(P/Q) vs. 1/T yields straight lines for all carbon samples; a typical example is given in Fig. 2 for carbon B. The linear plots evidence the singular dependence of the

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Table 1 Characterization of the porosity of the carbon samples.

N2 77 K BET surface area (m2 /g) BET total pore volume (cm3 /g) ˚ BET avg pore diameter (A) ˚ HK total pore volume (cm3 /g; <200 A) ˚ HK micropore volume (cm3 /g; <20 A) ˚ HK narrow micropore volume (cm3 /g; <6 A) ˚ HK broad micropore volume (cm3 /g; 6–20 A) Hg porosimetry ˚ Total pore volume (cm3 /g; 66–105 A) ˚ Mesopore volume (cm3 /g; 66–500 A) ˚ Macropore volume (cm3 /g; 500–105 A)

A Monolith, compacted carbon fibers

B Granular, coconut shell carbon based

C Extruded pellets, coal based

D Granular, coconut shell carbon based

E Pellets, Prolabo®

1908 1.06 22.3 1.03 0.71 0.031 0.675

1144 0.61 21.9 0.60 0.54 0.031 0.514

1540 0.90 23.3 0.86 0.53 0.031 0.503

1891 1.07 22.7 1.06 1.02 0.771 0.248

1512 0.93 24.6 0.93 0.85 0.459 0.395

0.469 0.101 0.368

0.221 0.054 0.167

0.751 0.266 0.485

0.385 0.153 0.232

0.445 0.073 0.372

isosteric heat of adsorption on Q, i.e., L = L(Q). Roubeau et al. [13] noted that L(Q) is well described by a function of the form: −L = a + b ln(Q + c) R

(2)

where a, b and c are fitting constants. In the present work we confirm the adequacy of Eq. (2) for describing L(Q); this is demonstrated in Fig. 3 where the experimental values of L for sample B are plotted against Q and fitted using Eq. (2).

B -He

14

Q=10 Q=31

12

Q=62 Q=93

Ln P/Q

10

Q=124

8

Q=155

6

Q=186 Q=217

4

Q=248

2

Q=279

0 -2 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

1/T (K-1) Fig. 2. Adsorption isosteres (the relation between P and T for a given amount adsorbed) of helium on carbon B plotted as ln(P/Q) against 1/T (Pa and cm3 /g units are used for P and Q, respectively). The isosteres are well described by straight lines that share a common point. The slope of each line gives the isosteric heat, L/R, at the corresponding amount adsorbed.

Isosteric Enthalpy, B - He

3 2.5

fit

L(kJ/mol)

1 0.5

0

50

100

150

1 T



+ e + ln Q + ln 100

(3)

Here, d and e are fitting constants obtained from the mentioned common point: e = 1/T0 , where T0 is the temperature at which the common point occurs, and d = ln(P/Q)0 is the ordinate of the common point in the ln(P/Q) vs. 1/T plot. Eq. (3) is a very practical fitting equation that describes quite well the equation of state of the adsorbed phase as shown in Fig. 4. Table 2 lists the fitted values of the constants in Eq. (3) for the five different carbons; the units are Pa for P, K for T, and (cm3 STP gas)/(g carbon) for Q. The fittings shown in Fig. 4 may seem unsatisfactory at the lowest temperatures, but this is because the pressure is an especially sensitive variable at those temperatures. Actually, the large pressure discrepancies shown in the figure correspond to small relative temperature errors. Table 3 lists the temperature values calculated with the fitted equation of state using the experimental pressure (Pexp ) and adsorbed amount (Qexp ) as input variables. The calculated temperatures differ only slightly from the measured ones, for the lowest adsorbed amounts. As discussed in the next section, these errors are not very relevant for the purposes of the current work.

3.1. Heat switch characteristics

1.5

0



ln P = [a − b ln(Q + c)] d −

3. Gas gap heat switch

experimental

2

Fig. 2 shows that, to a good approximation, the isosteres plotted as ln(P/Q) against 1/T can be considered to cross at a single, common point. Although the data in Fig. 2 is for sample B, the plots for the other samples are qualitatively similar and also exhibit a quite defined crossing point. Presently, there is no precise known physical reason for the existence of the common point; however, the existence of such type of point is very advantageous, since it can be used as an integrating constant to solve Eq. (2):

200

250

3

Q(cm /g) Fig. 3. Isosteric heat of adsorption, L, of helium on carbon B, plotted as a function of the amount adsorbed, Q, and the corresponding fitting of Eq. (2). The values of L were calculated from the slopes of the isosteric plot of Fig. 2.

The heat switch under consideration here is the same prototype presented and detailed in previous works where it was filled with neon gas [7] and with helium for an energy storage unit [19]. Briefly, the switch comprises two concentric copper blocks separated by a 100 ␮m gap having 11.4 cm2 of facing area (Fig. 5). One of the blocks (“cold block”) is thermalized to the cold finger of a 4 K Gifford–Mac Mahon type cryocooler and is temperature controlled. The second block (“hot block”) is equipped with a thermometer and a heating resistor. A supporting shell (SS) holds the blocks in place and encloses the gas volume. This volume is connected to the cryopump (or sorption pump) whose temperature imposes the gas pressure. When the sorption pump is heated to a high temperature, it releases the gas to the gap (ON state); when the sorption pump is set at a low temperature it adsorbs the gas from the gap (OFF state). The

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327

Isotherrms, B - He e 0.1 12.5 K

15 K

20 K 25 K 30 K 35 K 40 K 45 K 50 K

Q (g/g)

0.01

60 K 70 K

0.001

0.0001

80 K

10

100

1000

0000 10

100000

P (Pa)

1000000

Fig. 4. Experimental (symbols, connected just as a guide for the eyes) and fitted adsorption isotherms (lines) of helium on carbon B.

Table 2 Curve fitting of Eq. (3) to the experimental helium adsorption data for the five carbon samples. Charcoal sample coefficients

A

B

C

D

E

a b c d e

409 42 19.1 0.013 5.2

484 56 17.8 0.012 5.65

376 41 5.7 0.016 4.9

461 51 30 0.012 5.4

600 81 34 0.014 5.6

Table 3 Fitting errors for the adsorption isotherms of helium at 12.5 K and 15.0 K on carbon B sample. The calculated temperature, Tcalc , is determined from the fitted equation of state using the measured pressure (Pexp ) and adsorbed amount (Qexp ) as input variables. Although there is a large difference in the estimated pressure (see Fig. 4), the estimated temperature is far more accurate, especially for the lowest values of Qexp . Texp (K)

Pexp (Pa)

Qexp (g/g)

Tcalc (Pexp , Qexp ) (K)

T (K)

T/T (%)

12.5

85.5 386 2460 50.4 169 644 2540 8260

0.0371 0.0463 0.0544 0.0186 0.02779 0.03685 0.04516 0.05147

13.1 13.8 15.4 15.5 15.2 15.6 16.5 17.9

0.6 1.3 2.9 0.5 0.2 0.6 1.5 2.9

4.8 10.4 23.2 3.3 1.3 4.0 10.0 19.3

15.0

Fig. 5. Schematic of the GGHS prototype (adapted from [7]).

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180

Q/ΔT (mW/K)

160

.

140 120 100 80 60

switch#1

40

switch#2

20 0

Tcryopump (K) Fig. 6. Effective conductance, Keff , as a function of the cryopump temperature, for the two switch configurations. In order to reach the molecular regime, switch #2 has to adsorb more gas than switch #1: its OFF state is hence obtained for a lower cryopump temperature.

developed molecular and viscous regimes) as well as the transition zone. The conductances for the two fully developed regimes are well established [19]. The present model of the heat switch includes the fully developed regimes but also accurately reproduces the whole transition zone as a function of the cryopump temperature. Using an equivalent model of association of thermal resistances, the heat path across the supporting shell (SS) is considered to be parallel to the heat path across the gas in the gap. For the intermediate regime, the gas conductance is modeled as the harmonic sum of the viscous and the molecular conductances [20]. The various conductances are summarized as follows [21]:

Km = A

 +1  −1

KV = k(T¯ ) sorption pump consists of a container equipped with its own thermometer (Tcryopump ) and heater; in the experiments reported here, the container was filled with 30 mg of carbon E (Prolabo® charcoal). In the present study, the switch was charged with helium (4 He) under two different configurations. In the first configuration, denoted switch #1,the switch was charged at room temperature up to a pressure of 74 kPa, and the total gas volume was minimized by pinching off and sealing the filling capillary very close to the switch itself [19]. In the second configuration (switch #2), the switch was charged up to a pressure of 50 kPa and the total volume of charged gas was significantly larger (it was approximately tripled) than that in the first configuration because the switch was sealed at the cryostat flange. The high-pressure configuration (switch #1) had a total switch volume of 1.1 cm3 , whereas the low-pressure one (switch #2) had a volume of 3.74 cm3 . Actually those configurations were not chosen for the purpose of this study, instead they were performed for something else and also studied according to the model under discussion. Joule power (Q˙ = RI 2 ) is applied to the hot block (HB), whereas the cold block (CB) is kept at a constant temperature. The temperature difference between the two blocks, THB − TCB , as well as the average temperature, T¯ = (THB + TCB )/2, are kept approximately constant by varying the applied thermal power. The cold block of the switch was kept at TCB = 6K while the hot block’s temperature was in the range THB = 10 ± 2K. The temperature of the sorption pump was varied and data recorded under equilibrium conditions. An effective thermal conductance keff is assessed as: Keff =

Q˙ THB − TCB

(4)

Fig. 6 shows the experimental values of Keff plotted as a function of the cryopump temperature for both switch configurations. Basically, the switch displays a low-conductance state at low pressure, obtained by lowering the temperature of the sorption pump, and a high-conductance state at high pressure when the sorption pump is heated. The molecular regime governs the heat transfer through the gas gap in the low-conductance state. The lowest conductance that can be attained is limited by the conductance of the supporting shell. Pressure-independent heat transfer in the viscous regime is predominant in the high-conductance state. In the midrange the conductance is dependent on pressure, and hence dependent on the sorption pump temperature. 3.2. Modeling the GGHS actuator A complete thermal model of the switch must necessarily include the two extreme values of the effective conductance (fully

Keff =



R P 8MT

A d

(5)

(6)

1 + KSS (1/Km ) + (1/Kv )

(7)

Here K = Q˙ /T , where Q˙ represents the thermal power and T the temperature difference between the two blocks; subscripts ‘m’ and ‘v’ stand for the molecular and viscous regimes, respectively, and SS denotes the supporting shell; A is the surface area for gas exchange, d is the gap width,  = Cp /CV is the heat capacity ratio, M is the molar mass of the gas, R is the ideal gas constant, P is the pressure, and k(T¯ ) is the gas conductivity at the average temperature T¯ . The thermal conductance of the cylindrical supporting shell is calculated by the following equation using the thermal conductivity of stainless steel taken from the NIST databank [22]: ASS Q˙ SS = lSS



TCB +T

kSS dT

(8)

TCB

Here ASS and lSS are the cross sectional area and height of the supporting shell. The value of Keff was computed using this model as a function of the gas pressure, P, which was in turn converted to the sorption pump temperature through the fitted adsorption isotherm model. In order to do so the total amount of gas was determined from the total switch volume (including sorption pump and dead volumes) and the filling pressure. From the range of block temperatures of the experimental runs, an average temperature of T¯ = 8K was considered for the gas. Using the ideal gas law, the amount of helium in the gas phase is easily calculated from the switch volume, gas pressure and temperature; this value is then subtracted from the total amount to determine the adsorbed amount Q. Finally, the temperature of the cryopump is determined from Eq. (3) using the values of P and Q as input variables. Using this procedure, the temperature of the cryopump can be calculated as a function of Keff . The experimental and calculated values of Keff for both GGHS configurations match quite well, as shown in Fig. 7. To our knowledge, this is the first time that the effective conductance of a GGHS is so precisely modeled over the complete temperature range of a cryopump. By reproducing the experimental conductance in both switch configurations, we validate the thermal model and also the fitted equation of state for the adsorbed phase, P(Q,T), over a range larger than that measured. Now that the GGHS thermal model is validated for both switch configurations, we can confidently employ it to predict the two onset temperatures TON and TOFF . The criterion for attaining the ON conductance state is that the Knudsen number reaches 0.01, the Knudsen number being the ratio of the mean free path to a

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329

Fig. 8. Predicted temperatures for onset of the ON and OFF states in switch #1 for the five carbons analyzed in this study. Each curve depends on the filling pressure: both TON and TOFF increase along the line as the filling pressure is decreased. For the experimental configuration of switch #1 (30 mg of carbon E and filling pressure of 74 kPa) the predicted values of TON and TOFF correspond to the solid square: the switch is turned on at 23.7 K and turned off at 11.9 K. These predicted temperatures match the experimental observations (see Fig. 7).

Fig. 7. Dependence of the effective conductance, Keff = Q¯ /T , on the cryopump temperature for the two configurations of the heat switch (switches #1 and #2). Experimental data are represented by dots and the computed data by the solid line. The logarithm (switch #1) and linear (switch #2) scales for the effective conductance allow emphasizing the good agreement between the experimental and calculated data in both low and high effective conductance range.

characteristic distance (d, the gap width). The mean free path () can be calculated as [23]: (T )  = 3.62 P



T M

(9)

in which M is the molar mass and  is the gas viscosity [24]. The value of TON is calculated from the pressure value that satisfies this criterion and is represented in Fig. 7 (open symbol). On the other hand, the onset of the OFF conductance state can be defined by the pressure value at which the gas conductance equals the supporting shell conductance. Experimentally, this criterion corresponds to a temperature TOFF at which the conductance is twice the supporting shell conductance (also represented in Fig. 7 as an open symbol). Using these criteria, we list in Table 4 the values of TON and TOFF for both switch configurations. These values are superimposed over the experimental data of Fig. 7 as open symbols. The gas pressures that define the criteria for the onset of the ON/OFF states are also given in Table 4. 4. Tailoring a GGHS actuator Our GGHS model can predict the values of TON and TOFF for hypothetical conditions which have not been analyzed experimentally, such as different filling pressures, different adsorbent or different mass of the adsorbent. The variation TON and TOFF with the filling pressure was calculated for the geometry of switch #1 with 30 mg of carbon E and

is plotted in Fig. 8 as the E curve. The upright-end point corresponds to the lowest filling pressure that still ensures a viscous ON conductance (∼11 kPa at room temperature); the left-end point corresponds to a filling pressure of 100 kPa at room temperature. Fig. 8 also shows the predicted performance of the heat switch when filled with the same amount (30 mg) of carbons A, B, C and D. From these curves it is possible to choose particular onset conditions for operating switch #1 with 30 mg of adsorbent; by changing the type of carbon and adjusting the gas pressure, TOFF can be varied by ≈5 K and TON by ≈25 K. Fig. 8 shows how the different adsorption properties can modify the actuation temperatures. The most extreme behaviors are assigned to charcoals B and C: using 30 mg of sorbent C may lead to TON /TOFF values as low as 10 K/20 K, whereas carbon B may lead to TON /TOFF values as high as 15 K/45 K. The possibility of being able to choose the appropriate higher or lower actuation temperatures may be very convenient for technical reasons. In practice, the mass of sorbent can also be adjusted to tune TON /TOFF . For the two carbons, B and C, which are those that exhibit the most extreme behaviors in Fig. 8, TON and TOFF were calculated for different amounts of adsorbent ranging from 10 mg up to 70 mg (corresponding to packing volumes from ≈15 mm3 up to ≈100 mm3 ). The results are displayed in Fig. 9. For a given carbon adsorbent, the dashed area shows the feasible domain of TON and TOFF temperatures, and also shows how it varies with pressure and amount of adsorbent. The chart shown in Fig. 9 is intended to be a design-aid for the cryopump. A quite interesting feature emphasized by this figure is that the two carbon adsorbents B and C lead to quite different TON × TOFF areas. For instance, a TOFF of 16 K can only be obtained with sorbent B. On the other hand, if a TOFF around 12 K is desired then carbon B provides only a narrow limited range for TON (≈24–26 K), whereas carbon C allows tuning TON from 25 K up to ≈30 K. The chart of Fig. 9 is a valuable tool for optimizing the functionalities of the GGHS. A good understanding of how the porosity and pore size distribution of the carbon influence its

Table 4 Actuation temperatures, TON and TOFF , and pressures, PON and POFF , for onset of the ON/OFF states of the two switch configurations.

Switch #1 Switch #2

Pfill (kPa)

Vswitch (cc)

Vdead (cc)

TON (K)

TOFF (K)

PON (Pa)

POFF (Pa)

74 50

0.95 0.95

0.15 2.79

23.7 20.8

11.9 10.1

300

5.8 × 10−3

330

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Acknowledgements This work was partially supported by Fundac¸ão para a Ciência e Tecnologia (PTDC/EME-MFE/66533/2006 and PTDC/EME-MFE/101448/2008). DM, DL, and LR acknowledge the Fundac¸ão para a Ciência e Tecnologia for granting (PTDC/EME-MFE/66533/2006) References

Fig. 9. Chart of actuation temperatures for the configuration of switch #1, for carbon loadings from 10 mg to 70 mg and filling pressures from ∼10 kPa to 100 kPa. Solid curves inside the shaded zones are the same as those in Fig. 8 (amount of carbon fixed at 30 mg). The left border of each shaded area corresponds to the 10 mg curve, while the right border is the 70 mg one. The bottom limit of each shaded area corresponds to an atmospheric filling pressure, whereas the top limit is the lowest filling pressure that still ensures the attainment of the viscous ON conduction state. This chart can be used to tailor a particular switch for a given application through the proper selection of the type and amount of carbon, as well as the filling pressure.

adsorption properties is desirable, as it can lead to a tailored manufacture of a carbon that enlarges further the range of actuation temperatures for this type of thermal switch.

5. Conclusion The adsorption characteristics of helium gas on five different carbons have been measured from 10 to 100 K and pressures from 50 Pa up to 120 kPa. A relatively simple and useful adsorption isotherm model that accurately fits the experimental adsorption equation of state for each carbon has been presented and validated for helium. A simple model that describes the effective conductance of a GGHS as a function of pressure was presented. By coupling this model to the adsorption isotherm model, the effective conductance of the GGHS was calculated as a function of the cryopump temperature; the model results match the whole experimental data for two different GGHS configurations. The good agreement between model predictions and experimental data validates our GGHS model and the extrapolation of the adsorption isotherm model to conditions outside those measured experimentally. A design chart was built in order to define the feasible values of TON and TOFF as a function of the amount of adsorbent mass and the amount of gas. This chart shows that different carbons can yield quite different TON /TOFF ranges. From this chart it is possible to choose the most convenient temperatures and to optimize the dimensioning of the cryopump. For example, for a given TOFF temperature, it is possible to choose by how much the cryopump must be heated in order to turn the switch on: the value of TON can range up to ≈12 K. Reversely, the heating temperature of the sorption pump can be more strictly limited; in this case there exist up to 3 K of freedom for choosing the value of TOFF . Finally, we note that whereas in the present study the fitted adsorption isotherm model was applied to the design of a GGHS, it can also be of valuable use to other applications such as in the optimization of large cryopumps or in the dimensioning of adsorption cryocoolers.

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Biographies Daniel Martins got his master’s degree in Engineering Physics from Universidade Nova de Lisboa (Portugal) in 2010. Currently he is a first year PhD student He has been dealing with in cryogenic devices for thermal management. Luis Ribeiro is completing his master’s degree course in Biomedical Engineering at the Faculty of Science and Technology, New University of Lisbon (Portugal). He has a bachelor’s degree in Biomedical Engineering Science, obtained from the same institution in 2009. He is currently developing a software application for radiation protection evaluation in nuclear medicine as a master’s final work. The fields of interest are programming and biomedical/physics engineering. Diogo Lopes got his masters in Engineering at the Universidade Nova de Lisboa, in 2008, started to work on his PhD project at CEA-Grenoble (France): the development of very high frequency pulse tube prototypes, which he will defend by September 2011. His interests include cryogenics, superconductivity and energetics. Isabel Catarino holds a PhD degree in Engineering Physics obtained from Universidade Nova de Lisboa (Portugal) in 2002. She had several scholarships at the Service des Basses Températures of the Commissariat à l’EnergieAtomique (CEA) in Grenoble (France), working with the design of cryocoolers and cryogenic thermal management devices. In 2009 she was Visiting Independent Advisor at the Jet Propulsion

D. Martins et al. / Sensors and Actuators A 171 (2011) 324–331 Laboratory (JPL-NASA/Caltech) in CA, USA, for one semester, also dealing with cryogenic thermal management devices. Presently she is an assistant professor in the UNL. Current fields of interest involve the design of cryogenic devices, namely heat switches and thermal storage units, and also the adsorption phenomena as a tool for the cryogenic devices. Along with D.L. and G.B., holds the Cryogenics 2010 (Elsevier) best paper award for their paper entitled “6 K solid state Energy Storage Unit”. Isabel Alexandra Esteves holds a PhD in Chemical Engineering obtained in Universidade Nova de Lisboa, 2005. Presently she is an Assistant researcher at FCT/UNL. Her current fields of interest include chemical engineering, adsorption science and technology as well as new materials and solvents. José Paulo Barbosa Mota PhD in Chemical Engineering, Institut National Polytechnique de Lorraine, Nancy, France, 1995, present employment as Senior Associate Professor of Chemical and Biochemical Engineering, Chemistry Department, FCT/UNL; Researcher at the Center for Fine Chemistry and Biotechnology

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(CQFB) of the National Laboratory REQUIMTE on Green Chemistry and Clean Processes. R&D interests: adsorption science and technology; transport phenomena; process simulation and optimization. Grégoire Bonfait is graduated in Physics (1978, Université Paris VII, France). He joined as researcher the “Center de Recherchessur Les Trèsbasses Températures” (CNRS laboratory, presently Neel Institute, Grenoble, France) in 1981 where he obtained his PhD (Solid State Physics, Quantumfluids and Solids) in 1987. From 1989 to 2000, as invited scientist, he worked at Nuclear Technological Institute (ITN, Portugal) on one dimensional materials and on High Tc superconductors at low temperature and high magnetic fields. In 1995, he joined the Physics department of Faculty of Sciences and Technology (Universidade Nova de Lisboa, Portugal), where he is presently associate professor habilitation in 2001 and the responsible of the Laboratory of Cryogenics (Laboratory of the Centre of Physics and Technological Research, same department). He is presently involved in cryogenic devices for thermal management and adsorption at low temperature.