The cold mass of the LHC superconducting magnets, operating in pressurised superfluid helium at 1.9 K, must be shielded from the dynamic heat loads induced by the circulating particle beams, by means of beam screens maintained at higher temperature. The beam screens are cooled between 5 and 20 K by forced flow of weakly supercritical helium, a solution which avoids two-phase flow in the long, narr ow cooling channels, but still presents a potential risk of thermohydraulic instabilities. This problem has been studied by theoretical modelling and experiments performed on a full-scale dedicated te st loop

Hatchadourian, E

Lebrun, P

Tavian, L

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHEuropean Laboratory for Particle PhysicsLarge Hadron Collider ProjectLHC Project Report 212Supercritical Helium Cooling of the LHC Beam ScreensEmmanuel Hatchadourian1,2, Philippe Lebrun1 and Laurent Tavian1The cold mass of the LHC superconducting magnets, operating in pressurisedsuperfluid helium at 1.9 K, must be shielded from the dynamic heat loads inducedby the circulating particle beams, by means of beam screens maintained at highertemperature. The beam screens are cooled between 5 and 20 K by forced flow ofweakly supercritical helium, a solution which avoids two-phase flow in the long,narrow cooling channels, but still presents a potential risk of thermohydraulicinstabilities. This problem has been studied by theoretical modelling andexperiments performed on a full-scale dedicated test loop.1) CERN, LHC Division2) Centre de Recherches sur les Très Basses Températures, CNRS, Grenoble (France)Presented at ICEC 17 Conference, 14-17 July 1998, Bournemouth, UKAdministrative SecretariatLHC DivisionCERNCH - 1211 Geneva 23SwitzerlandGeneva, 29 July 1998Abstract2Supercritical Helium Cooling of the LHC Beam ScreensEmmanuel Hatchadourian1,2, Philippe Lebrun1 & Laurent Tavian11 LHC Division, CERN, Geneva (Switzerland)2 Centre de Recherches sur les Très Basses Températures, CNRS, Grenoble (France)The cold mass of the LHC superconducting magnets, operating in pressurisedsuperfluid helium at 1.9 K, must be shielded from the dynamic heat loads inducedby the circulating particle beams, by means of beam screens maintained at highertemperature. The beam screens are cooled between 5 and 20 K by forced flow ofweakly supercritical helium, a solution which avoids two-phase flow in the long,narrow cooling channels, but still presents a potential risk of thermohydraulicinstabilities. This problem has been studied by theoretical modelling andexperiments performed on a full-scale dedicated test loop.1 INTRODUCTIONThe high-energy, high-intensity proton beams of the future Large Hadron Collider (LHC), asuperconducting accelerator cooled by superfluid helium at 1.9 K, presently under construction at CERN[1], will induce heat loads into the cryogenic system through several mechanisms: synchrotron radiationfrom bending magnets, heating produced by image currents in the resistive wall and effective impedancedue to changes in cross-section of the beam channels, loss of stray particles from the beam halo, inelasticscattering by residual gas molecules, acceleration of photoemitted electrons by the beam electrical field. Inview of the large thermodynamic cost of refrigeration at 1.9 K, it is advisable to intercept the largestpossible fraction of the beam-induced heat loads on a beam screen, cooled by forced flow of supercriticalhelium between 4.6 and 20 K. The beam screen also acts as an intermediate-temperature baffle for theefficient cryopump constituted by the 1.9 K surface of the magnet cold bore, thus preventing desorption ofthe trapped gas molecules and avoiding breakdown of the beam vacuum [2].After recalling the operating constraints of the beam screen, in terms of heat loads and temperaturerange, we present the cooling scheme and hydraulic design retained. The use of weakly supercritical heliumflowing in long, parallel narrow channels with an aspect ration of 104, creates a risk of flow instabilities,which were carefully studied by theoretical modelling and confirmed by experiments on a full-scalethermohydraulic test loop.2 HEAT LOADS AND OPERATING TEMPERATUREThe heat loads deposited in the beam screens by synchrotron radiation, resistive heating andphotoelectrons, depend strongly on the energy E and intensity Ib of the circulating beams. Thermodynamicconsiderations favour the operation of the beam screens at a temperature well above the 1.9 K of themagnets. However, in order to limit the resistive heating, as well as the residual conductive and radiativeheat inleaks to the 1.9 K cold mass, the beam screens must operate at temperature below about 30 K.Moreover, the operating temperature must match the available interfaces at the existing cryogenic plants.Table 1 gives the heat loads in “nominal” (E = 7 TeV and Ib = 0.536 A) and “ultimate” (E = 7 TeV andIb = 0.848 A) conditions and their dependence on beam parameters.3Table 1  Heat loads in “nominal” and “ultimate” operating conditions (per aperture)Dependence Average per cell [W/m] Peak value [W/m]E Ib Nominal Ultimate Nominal UltimateSynchrotron radiation E4 Ib 0.164 0.260 0.206 0.326Resistive heating - Ib2 0.200 0.502 0.200 0.502Photoelectrons - Ib3 0.094 0.371 0.500 1.983 COOLING SCHEME AND HYDRAULIC DESIGNThe heat loads are extracted by a non-isothermal cooling loop operating between 4.6 K and 20 K, whichreduces by a factor 8 the entropic cost with respect to 1.9 K isothermal cooling. This cooling range hasbeen imposed by the availability of interface conditions of existing cryoplants, which will be reused for theproduction and distribution of the refrigeration. Due to very little space in the magnet aperture, longnarrow cooling channels in parallel [3] are required. Figure 1 shows the transverse cross-section of thebeam screen. Weakly supercritical helium is used to avoid potential problems of two-phase cooling. Avalve controls the outlet temperature of the beam screen circuits. Figure 2 shows the beam screen coolingscheme and the pressure vs. enthalpy diagram with the working line in “ultimate” conditions, which avoidscrossing the two-phase dome, however not far above the critical point. Such a loop is subject to controldifficulties and risks of instabilities, because of :- several circuits in parallel controlled by a single valve,- long cooling loop (53 m) giving a relativly long time response (about one minute),- strongly varying properties of helium close to the critical point.Magnet cold bore1.9 KDia. 50/53 mmBeam screen5 - 20 KDia. 45/47 mmCooling tubeDia. 3.7/4.5 mm36 mmPumping slots MoleculesPhotonFigure 1  Transverse cross-section of beam screen11.522.533.50 20 40 60 80 100 120Enthalpy, h [J/g]Pressure [bar]Beam screensSupports (0.27 W/m)Supply headerReturn headerP=3 bT=4.6 KP=1.3 bT=20 K12341 2 34T=10 K T=15 K T=20 KT=5 K T=6 KAperture 1Aperture 2control valve53 ma) Cooling schemeFigure 2  Beam screen coolingb) Working line on P-h diagram44 RISK OF THERMOHYDRAULIC INSTABILITIESThe properties of supercritical helium are quantitatively similar, within the pressure and temperature rangeof interest, to those of ordinary fluids in the neighbourhood of their respective critical points. Specific heat,compressibility and ratio of specific heats increase as the critical point is approached, while sound velocityand thermal diffusivity vanish [4]. However, as the state of the fluid gets some distance away from thecritical point, it behaves much like a pure liquid or an ideal gas. Therefore, the equation of state can beapproximated by two straight lines on a volume vs. enthalpy diagram as shown in Figure 3.ModelThis work examines the unidirectional propagation of a thermal pulse along the channel under a uniformheat flux. The dynamic state of the fluid in the test section can be described as follows.Mass conservation( ) 0=∂∂+∂∂xutρρEnergy conservation ρQxhuth =∂∂+∂∂Momentum conservation		frictiononacceleratiuDfxuutuxP 22ρρρ +∂∂+∂∂=∂∂−Equation of state ( )Phfv ,=Where D is the diameter, f the friction factor, x the length, Q  the total heat load, u the velocity, ρ thedensity and v the specific volume.The procedure adopted is to superimpose on a steady inlet velocity, a time-dependent velocity variationand then linearise the equation of flow [5]. The stability of the pertubated system is analysed by studyingthe variations of its transfer function. The mechanism of the density-wave oscillations is as follows : inletflow fluctuations create enthalpy perturbations in the “quasi-liquid” region. When these reach the “change-of-density” boundary they are transformed into void-fraction perturbations that travel with the flow alongthe channel, creating a dynamic oscillation in the “quasi-gas” region. With correct timing, the perturbationcan acquire appropriate phase and become self-sustained.A list of factors influencing stability, developed from the parametric analysis, is given in Table 2.Table 2  Factors influencing stabilityStabilising DestabilisingIncrease of tube diameter Subcooling of inlet temperatureIncrease of pressure level Restriction at tube outletIncrease of mass flow Increase of tube lengthExperimentWe fabricated a 53-m test section which reproduces one of the cooling tubes. The operating range in thisexperiment is P between 2 and 4 bar, T between 4.5 and 25 K with a flow-rate ranging from 0.1 to 1.5 g/s.Pressure and temperature were measured at the inlet and the outlet positions of the test section withpressure transmitters at ambient temperature and CernoxTM resistance thermometers, respectively.Compressed helium gas is precooled by two heat exchangers, and its temperature stabilised near 5 K by aliquid bath heat exchanger. Heat is deposited in the stainless-steel tube by direct Joule heating.Proportional-integral-differential (PID) controllers are installed in order to adjust the inlet and outlettemperatures. The inlet pressure is adjusted by a mechanical pressure regulator.502040600 10 20 30 40 50 60h [J/g]specific volume [cm3/g]quasi-liquid quasi-gas P=3 barP=5 bar00.10.20.30.40.50.60.70.80.910 5 10 15 20 25Q [W]mass flow rate [g/s]limit calculatedstableunstableP=3.1 bar, T=5 KP=3.1 bar, T=5 KFigure 3  Volume vs. enthalpy of supercritical helium Figure 4  Stability domain and experimental pointsResultsData from several experimental runs are plotted on Figure 4. It appears that the predictive power of themodel for the stability domain is correct. The unstable points correspond to oscillations with a periodbetween 1 and 5 minutes. The experimental data also shows that increasing the inlet temperature increasesthe domain of stability.5 CONCLUSIONS AND FURTHER WORKThe supercritical helium cooling scheme of the LHC beam screens has been validated - in steady stateoperation - on a full-scale geometry. Both theory and experiment have revealed the risk of flow instabilityby density wave oscillations, depending upon circuit geometry, applied heat load, and fluid inlet conditions,and the possible cures to the problem. First attempts have been made at controlling the beam screentemperature under application of strongly varying heat loads. This will be the subject of ongoing studiesand further experimental work.6 ACKNOWLEDGEMENTSWe would like to acknowledge the help of A. Bézaguet and his team on the experimental setup. Thanksalso go to L. Puech (CRTBT, CNRS, Grenoble) for guidance and helpful discussions. This work wasperformed in the framework of the CERN Doctoral Student programme, of which one of us (E.H.) is amember.7 REFERENCES1 Evans, L., The Large Hadron Collider Project, in Proc. ICEC16, Elsevier Science, Oxford, UK(1997) 45-522 Gröbner, O., The LHC Vacuum System, paper presented at the 1997 Particle AcceleratorConference, Vancouver3 Tavian, L., and Wagner, U., LHC sector heat loads and their conversion to LHC refrigerator, LHC Project Note 1404 Arp, V., Thermodynamics of single-phase one-dimensional fluid flow, Cryogenics (1984) 24 285-2895 Zuber, N., An analysis of thermally induced flow oscillations, Report NAS8-11422 (1966)6 Jones, M. C., and Peterson R.G., A study of flow stability in helium cooling systems, Journal of HeatTransfer (Nov. 1975) 521-527

Supercritical Helium Cooling of the LHC Beam Screens

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