Influence of porous coatings on heat transfer in superfluid helium

ICEC 15 Proceedings

Influence of Porous Coatings on H e a t T r a n s f e r in Superfluid H e l i u m ,*

*

Yanzhong Li , Y u y u a n Wu I n g n d A r e n d , Klaus Liiders

, Udo Ruppert**

* Xi'an J i a o t o n g University, Xi'an, S h a a n x i 710049, China ** F r e e U n i v e r s i t y Berlin, A r n i m a l l e e 14, 14195 Berlin, G e r m a n y Different types of porous materials as surface coatings on samples (RhFe wire) are investigated at Hells and HeIIp in respect to their influences on the heat transfer. Experimental results of measurements on samples with and without coatings are presented. Wires covered with capillary filter plates as well as a mixture of gypsum and alumina abrasive show higher (up to 3.5 times) peak and recovery heat flux densities than those of the comparable bare wire at Hells. They show an increasing tendency of heat flux density with decreasing bath temperature at Hells similar to those at Hellp. A discussion of the results is also given in the' paper. INTRODUCTION The application of superconducting wires mainly relies on its cryostabilization affected by the external heat transfer performance between the conductor surface and the coolant. As a result, the improvement of heat exchange on the surface is of much interest for design and application• Though the use of superfluid helium with its outstanding heat transport properties could be an efficient way. The heat exchange is, in any case, heavily affected by the electrical insulation layer [1,2] which is mostly indispensable for the application of superconducting wires. Different experiments have been done at HeI [3-5] and Hell [6] to investigate the influence of material and thickness of insulation layers. Porous materials as coatings are investigated in HeI [4] but not so in superfluid helium up to now. In the work here for the improvement of the thermal stability of normal conducting RhFe wires, porous materials are investigated as electrical insulating coatings at Hells and Hellp. EXPERIMENTAL EQUIPMENT AND METHOD The experiments were carded out in a Hellp cryostat, which has a 2.35 liter volume HeIIp chamber. It can be operated from saturation pressure to 1 atm, and from 1.6 K to lambda point. The measuring samples are made of RhFe wires (O38p and O51p) with a length of about 30 ram. They are taken as heating elements and as temperature sensors. The heating power is supplied in form of a programmed voltage waveform. The current and voltage drop of the sample are measured while a triangular voltage waveform is supplied and recorded by a X-Y recorder. Peak heat flux qp, recovery heat flux ff and sample temperature are calculated from current and voltage drop measurement values. The temperature dependence of the resistivity was determined by previous calibration measurements [7]. Bath temperature and pressure were measured separately by a germanium resistor and a Siemens KPY-10 low temperature pressure transducer. Porous coatings used in the experiment are medical capillary filter plates, pure gypsum and gypsum mixed with alumina abrasive (A120a with particle size 0.05p). The capillary filter is a thin plate with a diameter of 50mm, brittle and not deformable. Therefore it cannot be attached closely to the sample surface. Figure 1 shows the design of two different samples. In case (a) the investigated section of the wire and all solder points of current and potential leads are placed between two fdter plates which are glued together along the rim. The sample wire is connected to the current leads by means of flexible NbTi foils. In case (b) gypsum or gypsum mixture is attached to the wire by using a special form at a 30 to 50 hours curing time. This design of porous coatings corresponds more to a technical Cryogenics 1994Vol 34 ICEC Supplement

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applicable method. In order to examine the He]] transparency of the coatings, flow measurements at samples of these materials were performed. The samples consist of disks of 8 mm effective diameter and 3 mm thickness separating a bath of superfluid helium at saturation pressure from a gas filled chamber, which is pumped (see figure 4). RESULTS AND DISCUSSION Figure 2a shows qp and qr for RhFe wires (~38p and O51p) at Hells and HeIIp, in which the influence of the wire diameter is shown. The experimental results for two different capillary filters (0.2p and 0.02la) are shown in Figure 2b. It can be seen that from the wire covered by smaller pore size filters larger values of Clp and qr are resulting. The results for RhFe wire (O381a) with different coatings are shown in figure 3. It is seen that the porous coatings in most cases are promoting the heat transfer by increasing the heat flux densities qp and ck. Especially at saturated superfluid helium, porous covered wires show better heat transfer performance than bare wire. The capillary covered wire shows the largest increase of peak heat flux density and the wire covered with gypsum mixture has a larger recovery heat flux density at Hells than others. It can be also seen in figure 3 that the tendencies of the curves qp and ck vs bath temperature measured at HeNs for the wires covered by porous coatings express the characteristics of those measured in HelIp, i.e. qp and qr are increasing with decreasing bath temperature. For the wire covered with gypsum mixture, qp as well as qr have the same value at Hells as at HeHp. These characteristics can be explained by a pressure zone produced inside the porous medium due to the thermomechanical effect pressurizing the superfluid helium. Also pure gypsum powder taken as porous coating on RhFe wire shows the same characteristic but with less effect on the heat transfer performance. The different behavior of gypsum mixture and pure gypsum can be explained by the results of mass flow measurement. Figure 4 shows the helium mass flow vs pressure difference between bath and gas chamber (phase boundary inside the sample) for a sample made from gypsum (curve 3 and 4) and for another made from gypsum mixed with A1203 powder (curve 1 and 2) at two different bath temperatures (1.7 K and 1.9 K). The higher flow rate for the mixture is caused by higher porosity and permeability. The porosity was determined by measuring the weight in dry as well as water filled state and results in 60% for the mixture and 48% for the gypsum. The value of the permeability is 8.48x10 "14 m 2 for the mixture and 1.17x10 -14 m 2 for the gypsum and was measured by means of helium gas flow at 4.2 K. From the Blake-Kozeny equation, which correlates the mean pore radius of a material composed of spheres of uniform size to the porosity and permeability, one can estimate that the pore size of the mixture is about 0.611 and that of the gypsum about 0.4p. Despite of the larger pore size the mixture has a better heat transfer performance due to the higher porosity. CONCLUSIONS Coating wires by porous layers of proper pore size can be a simple method for profiting by the outstanding cooling properties of HeIIp using a simple HeIIs cooling system. Porous coated wires allow large peak heat flux as well as recovery heat flux densities, which is of great importance for the improvement of cryostabilization of superconductors. However the effect of pore size and thickness of porous layers need to be further examined. REFERENCES

1

Meuris, C. Cryogenics (1991) 31 624-628

2 3 4 5 6 7

Funaki, K. et al ICEC 11 Berlin (1986) 730-734

302

Chandratiileke, G.R. et al Cryogenics (1989) 29 588-592 Andrianov, V.V. et al Cryogenics (1989) 29 168-178 Kubota, Y. et al ICEC 9 Kobe Japan (1982) CI2-6 Kobayashi, H. and Yasukochi, K. ICEC 8 (1980) 171-175 Wang, R. et al (not published) Cryogenics 1994 Vo134 ICECSupplement

ICEC 15 Proceedings

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ICEC 15 Proceedings

40

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Cryogenics 1994 Vol 34 ICEC S u p p l e m e n t

ICEC 15 Proceedings

Two Dimensional Numerical Simulation on He II Heat Transport

Tetsuji Okamura, Shinji Hamaguchi and Shigeharu Kabashima Dept. of Energy Sciences, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 227, Japan Heat transport characteristics in a helium channel for recovery processes have been investigated. The experimental results are analyzed by a two dimensional time dependent numerical calculation. One side wall of the channel is heated uniformly. The channel is placed vertically in a helium bath. The bath is atmospherically pressurized and is filled with He II or subcooled He I. It is clearly simulated that, when the bath is filled with He II, the generated He I in the channel recovers to He II near the top of the channel. On the other hand, when the bath is filled with subcooled He I, the heated helium flows out from the top of the channel and cooled in the bath.

Nomenclature ArM Cv g H L p q S T Tb

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2 transition temperature Time Velocity vector Thermal conductivity of He I Viscosity coefficient Density

Subscripts h Helium o Initial condition 2 2 transition

INTRODUCTION A two dimensional time dependent numerical calculation has been developed on the heat transport characteristics in an atmospherically pressurized He II channel with phase transition by the authors [1]. Experimental results for heating processes were analyzed by this calculation and changes of temperature distribution in a He II channel w e r e clearly simulated in Reference [1]. As an extension of the previous study, heat transport characteristics for recovery processes are focussed on in the present study. Temperature changes in the channel after stop of heating are measured in experiments. The experimental results are analyzed by the calculation which was used in the previous study. A finite element method and an explicit scheme are applied in the calculation. MODEL The present analyses are performed for a model channel shown in Figure l(a) and (b), where it should be noted that the scale in the vertical and horizontal directions are not the same. The dimensions of the channel for the analyses are the same as those used in the experiments except the width of the channel. The width is 7.0 mm in the experiments while it is infinite in the analyses. The dimensions of the helium bath for the analyses are smaller than those for the one used in experiments. The bath used in the experiments is cylindrical shape with 280 mm inner diameter and 365 mm depth. Cryogenics 1994Vol 34 ICEC Supplement 305

ICEC 15 Proceedings

A set of the following basic equations is solved in the present analyses. Equation of continuity;

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=o

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A set of Equations (1), (2) and (3) is solved in the region where the average temperature in a finite element is lower than Ta and a set of Equations (1), ( 2 ) a n d (4) is solved in the other region. Mass and momentum conservation is incorporated into a treatment of natural circulation. It is assumed in the present model that the temperature gradient in He II is associated with a diffusion of excitations of superfluid components, because the applied heat flux is comparatively large to induce a phase transition in the He II channel. This view is expressed in the right hand side term in Equation (3). All properties of helium which are needed in handling the above equations are given by temperature-dependent functions. The equations are solved under the following conditions: (1) temperature at the wall of the helium bath is kept at Tb; (2) all surfaces of the FRP blocks, except the heater surface, are kept adiabatic; (3) pressure gradient and velocity vector component in the direction normal to the wall are zero on all surfaces; and (4) heat is applied uniformly to the heater surface for 8 s before stop of heating as in the experiments. During this time, temperature distributions in the channel become almost constant in the present study. These temperature distributions are given as the initial conditions for the recovery processes. RESULTS The simulated and experimentally obtained results of traces of helium temperature in the channel after stop of heating are shown in Figure 2(a) and (b), respectively, where Tb is 2.05 K and applied heat flux in the heating process is 0.05 W cm 2. The both results indicate that the temperature decreases faster when the temperature is higher than T a as compared with when the temperature is lower than T a. This difference of the decreasing speed is considered to be lead from the difference of the value of specific heat of helium and fluid velocity of natural circulation. It is also observed that the temperature reaches T b from lower positions in the channel because of the natural circulation. The temperature distributions of helium simulated at times 0, 0.5, 1.0 ,and 2.0 s after the stop of heating are shown in Figure 3. It is clearly observed that the generated He I goes up in the channel and it recovers to He II near the top of the channel having a larger temperature gradient. The entire heated helium recovers to the bath temperature about 2 s in the channel in this case. On the other hand, when the bath temperature is 2.25 K, which is higher than T a, it takes more than 8 s that the entire helium in the channel recovers to the bath temperature in the experiment as shown in Figure 4(b). The simulated result of this case is shown in Figure 4(a). The simulated helium temperature decreases faster than the experimentally obtained one. The temperature 306

Cryogenics 1994 Vol 34 ICEC Supplement

ICEC 15 Proceedings

distributions simulated at times 0, 0.5, 1.0 and 2.0 s after the stop of heating are shown in Figure 5. In this figure, we can find a remarkable difference of temperature distributions at the top of the channel from those for the case of T b = 2.05 K as shown in Figure 3. The heated helium flows out from the top of the channel before it recovers to the bath temperature. The helium which flows out from the channel is cooled near the wall of the bath owing a larger temperature gradient as shown in Figure 5. The temperature gradient near the wall in the experiments may smaller than that in the simulation, because the helium bath used in the experiments is much larger than that for the analyses and it is assumed that the wall of the bath is kept T b in the present calculation. This difference may lead the fact that the simulated helium temperature decreases faster than that in the experiments as shown in Figure 4(a) and (b).

CONCLUSIONS Heat transport characteristics in a helium channel for recovery processes have been numerically and experimentally investigated. Changes of helium temperature distributions have been clearly simulated by the present numerical analyses. It is confirmed that heated helium is cooled while flowing up in the channel. The entire heated helium recovers to the bath temperature in the channel when the bath is filled with He II, having a larger temperature gradient near the top of the channel by the internal convection of He II. On the other hand, when the bath is filled with subcooled He I, the heated helimn flows out from the top of channel before it recovers to the bath temperature. This difference strongly affects the time which is required that the entire heated helium recovers to the initial bath temperature in the present case. REFERENCES 1

Okamura, T., Suzuki, T., Seki, N. and Kabashima, S., Heat transport in He II channel with phase transition Cryogenics (1993) 34 187-193

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ICEC 15 Proceedings

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Cryogenics

1994Vol

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