Future large devices using superconducting magnets or RF cavities (e.g. LHC or TESLA) need He II two-phase flow for cooling. The research carried out into counter-current superfluid two-phase flow was the continuation of work on co-current flow and benefited from all the knowledge acquired both experimentally and theoretically. Experiments were conducted on two different pipe diameters (40 and 65 m m I.D. tube) for slopes ranging between 0 and 2%, and for temperatures ranging between 1.8 and 2 K. This paper introduces the theoretical model, describes the tests, and provides a critical review of the results obtained in He II counter current two-phase flow

Gauthier, A

Jäger, B

Rousset, B

Van Weelderen, R

Weisend, J G

CERN Document Server

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHEuropean Laboratory for Particle PhysicsLarge Hadron Collider ProjectLHC Project Report 217Hydraulic Behaviour of He II in Stratified Counter-Current Two-Phase FlowB. Rousset*, A. Gauthier*, B. Jager*, R. van Weelderen**, J.G. Weisend II***Future large devices using superconducting magnets or RF cavities (e.g. LHC orTESLA) need He II two-phase flow for cooling. The research carried out intocounter-current superfluid two-phase flow was the continuation of work on co-current flow and benefited from all the knowledge acquired both experimentallyand theoretically. Experiments were conducted on two different pipe diameters (40and 65 mm I.D. tube) for slopes ranging between 0 and 2%, and for temperaturesranging between 1.8 and 2 K. This paper introduces the theoretical model,describes the tests, and provides a critical review of the results obtained in He IIcounter current two-phase flow.* CEA-Grenoble/DRFMC/SBT, 17 rue des Martyrs, 38054 Grenoble Cedex 09, France** CERN, LHC Division, CH-1211 Geneva 23, Switzerland*** DESY, Hamburg GermanyPresented at ICEC 17, 14-17 July 1998, Bournemouth, UKAdministrative SecretariatLHC DivisionCERNCH - 1211 Geneva 23SwitzerlandGeneva, 31 July  1998Abstract2Hydraulic Behaviour of He II in Stratified Counter-Current Two-Phase FlowRousset Bernard*, Gauthier Alain*, Jager Bernard*, van Weelderen Rob**, Weisend II, J. G. ****CEA-Grenoble/DRFMC/SBT, 17 rue des Martyrs, 38054 Grenoble Cedex 09, France**CERN, LHC Division, CH-1211 Geneva 23, Switzerland***DESY, Hamburg GermanyFuture large devices using superconducting magnets or RF cavities (e.g. LHC orTESLA) need He II two-phase flow for cooling. The research carried out intocounter-current superfluid two-phase flow was the continuation of work on co-current flow and benefited from all the knowledge acquired both experimentallyand theoretically. Experiments were conducted on two different pipe diameters (40and 65 mm I.D. tube) for slopes ranging between 0 and 2%, and for temperaturesranging between 1.8 and 2 K. This paper introduces the theoretical model,describes the tests, and provides a critical review of the results obtained in He IIcounter current two-phase flow.INTRODUCTIONSuperconducting magnets in LHC [1] as well as superconducting RF cavities in TESLA [2] will use He IItwo-phase flow as the cold source. Furthermore, these two huge devices will be installed in a quasi-horizontal tunnel. The standard cooling configuration employs a co-current two-phase flow. However, ifspace for pumping at the outlet of the flow is not available or relatively costly to implement, countercurrent two-phase flow may be envisaged. This latter situation appeared more difficult to control [3] andtherefore required some preliminary investigations which were performed at Grenoble thanks to thesupport of CERN and DESY.A series of experiments were performed in order to investigate the limit of this cooling scheme and also tocompare the dependence on slope, diameter and temperature with reference to a simple model.CALCULATION MODELIn most cases, experiments on counter-current flows have been performed in vertical pipes. Extensiveresults have been reported for water and air mixture in such a configuration. In this case, the liquid flowsdown and the gas flows up. As the gas mass flow increases, the flow changes from annular film flow towavy annular flow until the flooding occurs. At this point, the counter current flow ceases and the liquidphase starts to be carried upwards. The best explanations and predictions of this flooding phenomenonhave been done using instability theory [4].In the present case, the pipe is slightly inclined, and the annular flow is replaced by stratified flow.Furthermore, the moving force (i.e. gravity) is very low compared to the vertical configuration and weinfer that limitation deduced from momentum balance occurs before the onset of instability. Consequently,we have developed a model based on mass and momentum balance. This model originated fromdiscussions with the CERN team and is also based on a study carried out by Guinaudeau [5]. It representsthe maximum mass flow rate allowed in such a configuration.3In this simple model, it is assumed that the flow is adiabatic, stratified, steady and established. Theliquid mass flow is supposed to be equal in magnitude to the vapour mass flow, but in the oppositedirection:  m m ml v≡ = (1)The momentum balance applied to the liquid phase and to the vapour phase yields:For the liquid phase:0 = − − + −τ τl l i i l l lS S A gsin APxρ β ( )dd           (2)For the vapour phase:0 = − − − − −τ τv v i i v v vS S A gsin APxρ β ( )dd (3)where x is the abscissa, A the area, ρ the density, g the gravity, S the perimeter, P the pressureand τ the shear stress. Index l is for liquid, v for vapour and i for interface.Resolving the problem involves determining the flow characteristics (liquid height, pressure drop,velocity of the liquid and that of the vapour) for a given mass flow wherever possible.When the mass flow increases, the liquid height also increases (because the prime mover termρ βl lA gsin  in equation (2) increases), leaving less and less space for the vapour flowing in the oppositedirection, which results in increasing the frictional forces due to the vapour (the term τ i iS  in equation(2)). The calculation is done in such a way as progressively increasing the mass flow. Once this exceeds acertain value, it is no longer possible for equations (2) and (3) to be satisfied simultaneously. The finalvalue of mass flow for which it is still possible to solve the system of equations (2) and (3) represents themaximum liquid that can flow against the same mass flow of vapour: this is the blocking flow.EXPERIMENTAL FACILITIESAll measurements were performed on the Superfluid Helium Test Facility at CEA Grenoble which has beendescribed previously [6]. A schematic diagram of the experimental line is given hereafter.T1W1C1 N1W2T2N2B1B2αC2C3VJTHe gasrecoverypumpingunitE101E1031 bar4.2KgαFigure 1 HeII counter current flow cooling scheme4Helium flows from the tank E101 at a temperature of about 4.2 K, passes through the heatexchanger E103 and exits at a temperature close to 2.2 K after being cooled by a counter-current of coldgas. The liquid then expands through the Joule-Thomson valve VJT. The resulting liquid-vapour mixturethen enters the settling chamber B1. Any liquid above the opening into the test line (40 mm or 65 mm I.D.tube) joining B1 to B2 flows under gravity to the chamber B2. It faces a counter current of vapourevaporated by the heater W2 operated by an electric current which is regulated to produce the requiredflow in the line. The vapour is then drawn through E103, after which it enters the pumping system.Temperature of the two-phase flow is measured using two carbon thermometers placed in B1 andB2.Pipe slope is measured either by using the “plumb line” method or the “lake” method describedhereafter. With all heaters and liquid supply shut off, a bath of liquid is obtained. The liquid-vapourinterface is then practically horizontal. Simply comparing the height of superfluid in the two viewing zonesgives the slope of the tube once the distance between the two zones is known. Pictures are taken usingblack-and-white CCD cameras positioned in the vacuum space in the vicinity of the line and operating at atemperature between 2 and 300 K.Since the liquid level in B2 is kept constant, the liquid mass flow entering B2 is equivalent to thevapour mass flow leaving. Its value is deduced from the power W2 necessary to regulate the level in B2:m Ll sat= W2RESULTS AND ANALYSISFlow behaviourIn all the counter-current experiments, the helium level in B2 was controlled and kept constant byregulating the power injected by the heater W2. The helium level in B1 was controlled (using the heaterW1) so as to allow a variable gravity-driven quantity of liquid helium (mass flow m1) to enter the line. Asthe level in the compartment B1 is raised, the flow in the line B1-B2 increases, together with the powerW2. However, above a certain liquid level in B1, the power W2 is seen to stabilise, signifying that the flowbetween B1 and B2 has reached a plateau: this is the blocking flow.The level in B1 can then continue to increase indefinitely without modifying the value of the flow inthe line. If liquid level in B1 goes higher than the top of the tube, the vapour leaving B2 creates a passagethrough the liquid. From this we conclude that blocking rather acts to limit the flow to a maximum valuethan to reduce the flow rate to zero.Comparison between model and experimentsThe figures 2 and 3 compare measurement and calculation. Dependence of the measured blocking massflow on slope, diameter and temperature agrees with the predictions. The dependence on slope anddiameter can be deduced from open-channel behaviour, but the trend with temperature is only two-phaseflow dependent. As the temperature increases, vapour velocity decreases (due to density growth) whichreduces the interfacial shear stress and blocking appears at higher flow rates.However, some differences between calculation and measurement can also be seen.At low values of slope, the calculated blocking mass flow rate is lower than the experimental one.This is certainly due to the poor ratio of length over diameter, which allows counter-current flow even forlow negative pipe slope. Thus, for a negative slope, counter-current flow remains possible, which is ofcourse impossible once the diameter/length ratio is less than the absolute value of this negative slope.On the other hand, for high values of slope, the calculation seems too optimistic, with thecalculated blocking mass flow higher than that measured. We explain this as follows: at the pipe entrance,the regime is not established and the liquid has to accelerate in order to reach a constant velocity. Sincemass flow is conserved, the height of liquid in this entry section is necessarily the highest (and, similarly,higher than that calculated for established flow). Hence, it is probably this entry condition that will fix thevalue of the blocking flow below the calculated value.5Slope and inner diameter influenceTube length 1.2 m  T=1.88 K04812-0.2 0.3 0.8 1.3 1.8 2.3Slope (%)Maximum mass flowrate (g/s)Calculations for diam 40Calculations for diam 65 Data for diam 40 Data for diam 65 Figure 2  Comparison between calculated and experimental blockingTemperature influenceTube length 1.2 m I.D. 40 mm012340 0.5 1 1.5 2Slope (%)Maximum mass flowrate (g/s)Data at 1.8 KData at 2 KCalculations at 1.8 KCalculations at 2KFigure 3 Comparison between calculated and experimental blockingCONCLUSIONThe overall trends (variation of blocking flow as a function of the two-phase flow temperature and ofdiameter and slope of the tube) are well reproduced by the calculation method. However, owing to the lowlength/diameter ratio, the experiment is not representative of a very long tube and comparisons with thecalculations should be treated with great caution.Further research will be necessary in order to refine our understanding, and the range of validity ofthe calculation method itself. Finally, more extensive data should make it possible to define a more precisecorrelation for the interfacial coefficient of friction.REFERENCES1 Lebrun, P., Superfluid helium cryogenics for the Large Hadron collider project at CERNCryogenics (1994) 34 1-82 Horlitz, G., et al, The TESLA 500 Cryogenic System & He II two-phase flow: issues & plannedexperiments Cryogenics (1997) 37, 719-725.3 Bézaguet, A., et al, In: International Cryogenics Engineering Conference – 16 Kitakyushu, Japan(1996) 91-944 Watson, M.J., and Hewitt, G.F., Experimental investigations of the diameter effect on flooding incountercurrent flow ICMF 98 Lyon, France (1998) to be published5 Guinaudeau, H. Modelling counter-current two-phase flow of saturated superfluid helium in quasi-horizontal tubes: application to the LHC cryogenic system LHC project note 69 (1996)6 Rousset, B., et al, Stratified two-phase superfluid helium flow: I Cryogenics (1997) 37 733-737

Hydraulic Behaviour of He II in Stratified Counter-Current Two-Phase Flow

Abstract

Similar works

Full text

Available Versions

CERN Document Server