Krafft, G.

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April 1972Institut für Experimentelle KernphysikKFK 1584Critical Heat Flux and Thermal Quenching of Helium I1in Very Lang ChannelsG. KrafftAls Manuskript vervielfältigtFür diesen Bericht behalten wir uns alle Rechte vorGESELLSCHAFT FüR KERN FORSCHUNG M. B. H.KARLSRUHEMai 1972KERNFORSCHUNGSZENTRUM KARLSRUHEKFK 158~Institut für Experimentelle KernphysikCritical Heat Flux and Thermal Quenching of Helium IIin Very Long Channels~)vonGerd KrafftGesellschaft für Kernforschung m.b.H., Karlsruhe~) Paper presented at the Low Temperature Conferenceof the European Physical Society, 6 - 8 April 1972,Freudenstadt, Germany.AbstractHeat-transport experiments with superfluid helium in pipesof 15 - 400 cm length and diameters between 0.3 - 1.0 cmshow, that in heat induced counterflow of He I1 the criticalheat flow density, i.e. the heat flux when superfluiditybreaks down and vaporization onset starts, is a function oftube length and bath temperature. It is mainly determinedby the amount of superheating required for bubble formation.ExperimentallY it is evident, that the degree of superheatis dependent of hydrostatic pressure and temperature.ZusammenfassungWärmetransport-Experimente mit superfluidem Helium in Kupfer-rohren mit Längen zwischen 15 und 400 cm und 0.3 bis 1.0 cmgroßen Durchmessern zeigen das Vorhandensein einer kritischenWärmeflußdichte, bei der Blasenbildung auftritt und der super-fluide Zustand zerstört wird. Der kritische Wärmefluß wirddurch die maximal mögliche "überhitzung" des Helium 11 be-stimmt und ist eine Funktion der Rohrlänge, des hydrostatischenDruckes und der Badtemperatur.CRITICAL HEAT FLUX AND THERMAL QUENCHING OF HELIUM I1 IN VERYLONG CHANNELSG. KrafftInstitut für Experimentelle Kernphysik, Universität und Kern-forschungs zentrum KarlsruheIntroductionThe following is a short report of some results concerning heat-transport experiments with superfluid helium in tubes of 15 -400 cm length and diameters between 0.3 - 1.0 cm.There were two general reasons for performing this research. Thefirst is a practical one: the people of our superconducting linearaccelerator group wanted to know the maximum removable heat fromtheir helically coiled niobium-tubes. These tubes, used as wave-guides and accelerating structures, have a total length of 3 meterand an inner diameter of 0.5 cm. They are cooled by helium 11 atT = 1.8 K without any mass transfer, i.e. only by the weIl known"int~rnal convection"-mechanism cf superfluid helium. The secondone is based on more theoretical questions. These are:a) Are the thermohydrodynamical equations of the two-fluid modelalso valid for large scale cooling systems?b) How can the often stated thermal break-down, or with other words,the limited heat-flux density in heat-induced counterflow ofhelium 11, be explained?Though there are two publications concerning heat-transport experi-ments with quite analogous geometries, we repeated the measurements,because the first one of CRITCHLOW and HEMSTEET 1) only dealt withvery low temperature differences (in the order of 20 mK) andtherefore very small heat-current densities. The second one of PASSOWet ale 2) gave only a rough technical survey and the results presentedcould not be accepted in general.- 2 -Experimental EquipmentAll the experiments were carried out in a cryostat and vacuumchamber, as shown in Fige 1. Two different copper helix tubeswere used:1. Tubes with both ends open to the helium bath.2. Tubes with only one end open to the helium bath.Also two kinds of heating have been studied: in the first caseheating was carried out with an outer coil wound continuouslyaround the helix tube; and in the second, local heaters weremounted at different places of the tube (for instance:~at theclosed end or in the middle).Temperature measurement was carried out with self-made carbonresistances distributed along the tube and calibrated againstvaporpressure.Experimental results and discussionFor turbulent flow thehydrodynamical equations yield the followingrelation between the temperature-gradient ~T and heat-currentdensity q 3):where~T =A •sq 3( ) , (1)S : entropy per gramPs: density of the super fluid componentPn: density of the normalfluid componentA : Gorter-Mellink constantFor numerical calculations we used the values of A as given byVINEN 4)As you can see from Fig. 2, gradientT has a minimum at ab out1.95 K. For T < 1.95 K it folIows, that for a fixed heat-- 3 -current density grad T is decreasing with increasing ternperatureand for T ~ 1.95 K grad T increases with rising temperatures.Consequently the temperature distribution alonga heated tube looksquite ~ifferent for bath-ternperatures above or below 1.95 K.Fig. 3 shows sorne characteristic temperature distributions alongthe one end-closed helix with the heater at the closed end. It isonly one specific example of our numerous rneasurernents for twoternperatures with opposite sign of grad T. The solid curves resultfrom step-by-step integration of the relation between grad T andheat-flux density q, where the constant bath temperature is thelower integration limit. The open and block circles indicate theexperirnentally measured temperatures, which fit the calculatedcurves quite weIl. By cornparison between the theoretically predictedcurves and the experimentally confirrned temperature distributions,two conclusions are evident:1. Within the experimental occuracy of ± 10 %and the measuredtemperature range between T = 1.4 K - 2.15 K the equations of thetwo-fluid model, including the Gorter-Mellink constant A, showno geometrical dependence, i.e. they are valid at least for tubeswith a diameter up to 1 cm~ The values of Aseern to agree with4'Vinen's data ) ± 10 %.2. The two-fluid model is also applicable to superheated rnetastablehelium II.The second statement has the following rneaning: for all liquidsexists an equilibrium-state between vapor and liquid. You can estirnatethe equilibrium pressure change 6Pn for an ternperature increase 6Ton the basis of the CLAUSIUS-CLAPEYRON equation (Fig. 4):6Pn 1 1 An • Pn• AD • • • ~.......... = PL PD J6T T PL - Pn TwithAD: heat of vaporizationPD: saturated vapor densityPL: liquid density.(2)- 4 -For superfluid helium under ideal conditions a temperaturedifference 6T produces according to LONDON 5) a thermodynamicalexcess pressure (or fountain pressure) of(3)For helium the corresponding pressure changes have been indicatedschematically in the P-T diagram of Fig. 4. Under the conditionthat ~PF > APD, you can see that point representing the liquidstate at a higher temperature is always displaced into the unsaturatedliquid regime of helium II. Further increase of temperature finallycauses a transition across the A-line between helium I1 and helium I.In our experiments - for bath temperatures TB < 2.0 K - we nevercould heat the helium at the end or in the midde of the tubes up tothe A-point. It was impossible to cross the A-line, because prior tothis event thermal quenching and break-down of superfluidity occured.From the just mentioned considerations one must conclude, that nofountain excess pressure is present in our pipes.Pressure measurements with a pressure-transducer confirmed theseresults up to an accuracy of ± O.i Torr.Heating up the helium is therefore simply crossing the equilibrium-line between the liquid and vapor-phase or superheating of the heliuminside the tubes, when the liquid state is still existing.This is illustrated in Fig. 5. The points left to the equilibrium-line represent the liquid state before heating, i.e. they are equalto the bath-temperature. The various degrees of subcooling correspondto different liquid levels above the tubes. The points on the rightare the measured temperatures when superfluidity breaks down.The above mentioned statement, that the two-fluid model is alsoapplicable to superheated metastable helium II, expresses the validityof the hydrodynamical equations between the saturation temperature,i.e. crossing the equilibrium line, and the thermal break-downtemperature. In Fig. 3 this can be seen explicitly from the fact,that above the saturation temperature the measured temperatures werein accordance with the calculated ones.= 5 -At the thermal break-down temperatures bubble formation andvaporization atar-t , 'As you can see (Pdg', 5) the degree of super-heat is dependent of hydrostatic pressure (or subcooling) andof temperature. First theoretical calculations indicate thatthe amount of superheating (and its temperature- and pressuredependence) perhaps can be explained by a homogenous nucleationprocess for bubble formation.Now we can make our last conclusion concerning the limited orcritical heat-flow density: the amount of the critical heat-current density qc or the termal quenching of helium I1 in finitetubes is only determinate by the maximum possible superheating,i.e. the difference between initial (or bath) temperature andvaporization onset temperature.In contrast to other investigations 6) no relation between qc andthe ratio LId (L, d: tube length and diameter) analogous to helium I 7)have been found for our geometries.The only way the tube length L influenees the eritieal heat-flowdensity qe is explained in Fig. 6. The point F in Fig. 6a representthe liquid state inside the tube before heating. The hydrostaticpressure Phydr• results from liquid level high. During heating up Fi8 displaced towards the equilibrium line and the temperature isshifted from Tba t h to Ts a t •• At Ts at• thermal quenching is expected,when no superheating is possible. For different tube lengths (orheater locations) YOti ean find the corresponding saturation heat-flux densities qsat. from the temperature distribution eurves inFig. 6b. YOti ean see for instance, that for a given saturationtemperature Tsa t• two different heat-flux densities follow for twodifferent pipe lengths. If one repeat this for bath temperaturesbetween T = 1.4 K and 2.1 K the curves 1 and 2 of Fig. 6c result,giving the eritieal heat-flux densities at saturation temperatures.So we must conclude,heat-flow density qcalong the tube or inof all parameters tothat the effect of tube length on the critiealis determined by the temperature distributionother words by the strong temperature variationbe found in the relation between VT and q,equation (1), whieh from the temperature distributions are derived.- 6 -The discrepancies between the saturation heat-flux densitiesq t and the experimentally measured values q indicate thatsa • csuperfluid helium can be superheated up to temperatures, whichwe called vaporization temperature Tva p•In order you get some feeling about the orders of magnitude,some values of the maximum removable heat are given: for acontinuously heated helix with a total length of 3.30 m and aninner diameter of 0.5 cm and with both ends open to the heliumbath at a temperature of T = 1.8 K you can remove a total ofabout 0.65 Watt corresponding to a critical heat-current densityof about 1.7 Watt/cm2•For niobium tubes with quite similar geometries these figureshave been fully verified during the first successful operationof the 1. stage of our superconducting proton linear accelerator,when for the first time in the world protons have been acceleratedby an superconducting device.References1) CRITCHLOW, P.R. and HEMSTEET, R.A., J. Appl. Phys. 40 (1969)2) PASSOW, C.H. et al., Cryogenics, April 19713) ARP, V., Cryogenics, Vol. 10, 96 (1970)4) VINEN, W.F., Proc. Roy. Soc. A240, 114 (1957)5) LONDON, F., "Superfluids", Vol. 1, 2, Wiley, New York(1950, 1954)6) CHAPMAN, R.G., GHANG, Y.W. and FREDERKING, T.H.K., Advanc.Gryog. Eng., Vol. 15, 290 (1970)7) LEHONGRE, S. et al., Proc. ICEC2, Brighton 1968, p. 2748) IREY, R.K. et al., Advanc. Cryog. Eng., Vol. 10, 361 (1965)ooLO--oLONHellVACUUMPUMPP =10 -6 Torr1-8llIIIIlI--------,.-- ,. ;; 300 -----~f--- -_.-He-DEWARVACUUM -TANK.. ihll10 -.............----'--- _ e __~-- 1iII8BI1CRYOSTAT WITH VACUUMTANK AND HELICESFIG.lgradT = A.~n.( q .)35 35-5-1q= 1.5 WIcm 2q :: 0, 5WIcm210'·410-210-1 j grad T (K'cm-1)10-3I . I I __ I I I , I , I ...1.5 116 '.7 1,8 1.9 2.0 2.1 T(K)'lemperoture gradient csu function of hect-current density and temperatureFIG.2.10-5 L.--! I , , , I • -'-------1.4q=0,55 WIcm 2- 'Sath ternpercture2,l1"'F- T (K)2.10.....,...,2,082091-/SaturationI . temperature--------2.05 LJ:=J-::::t; ---2,072,06t Positions of reslstcnces___----i~---- T ! q=0,7W/cm 2-- ;&-_ r r q=O,5W/cm 2__ ..-----'t"~-------Je-------SaturationItemperature14 r=l /Bath temperetute, A j! t I I I I I t I -L I J I t I ! , t I I ... L (rnl0,20 0,60 1,00 ',40 1,80 2,20 2,60 3,00 3.40Tempereture distribution along the helix (d : (),8cm, one end closedl for twobath temperatures and heat-current densities with heater location at L =3,30m1,5',61.71.8FIG.3""oC)-LL......,oc-Q)-8Ulo+Ja.:::J•11(Lu..<JI-<J.Cf)zo-~::JCWZoozo.....J•.....ICV\...-zo-~::::>ouizo~>-wCL<!.....JUiV):::>-(/):J«-JU-\wZ:::J•.< --(1)::cE:::J0--Q)s:'+-oEE0)d0-'Ut--•a...E:::J°i::-C0--CLIIIIIIII vaporIIIIII 'T".I .l\-2.172K,/IHelJI.-Iine~H 'fTeHo1,4 1.5 1.6 1.7 18 1.9 2.0 2.1 2.2 T(K)Superheat es a function of hydrostatic pressureand temperatureFIG.52103020pqc(Watt'cm-2)IT~ I+.~1.8 1,9 2,0 2.1 2.2---...... Tbath (K)~+~~1,5 1.6 1,7c)+meas. qc for l2== 3.30mand Phydr. :: 4 Torr?meas. qc for L, =O,6mand Phydr. == 2 Tor rCD qc == qsat. for L1:: 0,6 m~ qc:: q sat. for Lz==3.30m1,41,015 ,,-,0.520,,-•X==L zequllibrium - Une...-.----,. q sat.for L1b)a)-----,II,I II _ I __-1Tsct. Tvap.HellX:::L,TTsat. +- / §/' 7"= Y - qsat.for lzT , ..bcth. ..c:;; , XCRITICAL HEAT FLOW DENSITIES FOR DIFFERENT TUBE lENGTHS ANDBATH TEMPERATURES FIG.6

Critical Heat Flux and Thermal Qenching of Helium II in Very Long Channels

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Critical Heat Flux and Thermal Qenching of Helium II in Very Long Channels

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