The Centre for Advanced Studies, Research and Development in Sardinia (CRS4) is

participating to an Italian R&D program, together with Ansaldo, ENEA and INFN, devoted to the design of a 80 MW prototype of the Energy Amplifier proposed by C. Rubbia. The use of advanced numerical tools has been of practical support in the design of critical elements of the machine such as the fuel element and the beam target. The aim of this work is to study the sensitivity of beam window stresses to the beam distribution, size and interruption. In order to compute thermal stresses, the heat deposition in the window and in the coolant generated by the interaction with the proton beam is calculated and used as input data for the fluid dynamic simulation of the natural convection flow of the target coolant

Bellucci, Valter

Buono, Stefano

Fotia, Giorgio

Maciocco, Luca

Moreau, Vincent

Mulas, Marco

Siddi, Giuliana

Sorrentino, Luca

P-arch

THERMO-MECHANICAL STRESSES ON THE BEAM WINDOWV. Bellucci, S. Buono, G. Fotia, L. Maciocco, V. Moreau, M. Mulas, G. Siddi, L. SorrentinoCRS4 Research Centre ≠ Via N. Sauro, 10 ≠ Cagliari, ItalyAbstractThe Centre for Advanced Studies, Research and Development in Sardinia (CRS4) isparticipating to an Italian R&D program, together with Ansaldo, ENEA and INFN, devoted to thedesign of a 80 MW prototype of the Energy Amplifier proposed by C. Rubbia. The use ofadvanced numerical tools has been of practical support in the design of critical elements of themachine such as the fuel element and the beam target. The aim of this work is to study thesensitivity of beam window stresses to the beam distribution, size and interruption. In order tocompute thermal stresses, the heat deposition in the window and in the coolant generated by theinteraction with the proton beam is calculated and used as input data for the fluid dynamicsimulation of the natural convection flow of the target coolant.IntroductionThe Energy Amplifier (EA) [1,2] is a nuclear system in which a beam target, driven by aproton accelerator, supplies an external source of neutrons to the subcritical core. The beam targetrepresents one of the main technological problems related not only to the design of the EA, but toall High Power Spallation Sources currently under study or in construction world-wide [3,4].Neutrons come from the interaction of a high power proton beam with the material containedin the target. Such interaction, called spallation, has the undesirable effects of producing a largequantity of heat (typically some MW concentrated in a small volume) and inducing an intenseradiation damage in the structural materials. Liquid metals are currently considered the bestchoice in terms of target materials since they satisfy the important criteria of being the spallationmedium and the cooling fluid at the same time and since their structural and thermal propertiesare not degraded by the radiation damage induced by proton interactions. Nevertheless, thecorrosion of structural materials in a liquid metal environment is an important problem. Given thefact that the primary cooling loop of the EA is made of lead-bismuth eutectic (LBE), we considerthe same coolant for the beam target. The LBE flow is driven by natural convection whoseefficiency depends on the target height (which is related to the dimensions of the EA) and on thefluid dynamic design of the coolant circuit.In the EA prototype target a window separates the internal part of the beam pipe from thecoolant. Configurations using a beam window have additional problems of beam window cooling(in the window the highest temperatures and stresses are reached) and radiation damage inducedin the window material. This damage is of a slight different nature from that induced in the otherstructures, since the window is exposed not only to back-scattered high-energy neutrons, but alsoto the high-energy proton flux. While steels for low power applications keep a sufficient structuralresistance and are suitable candidates for the EA prototype [3-5], refractory alloys or moreadvanced materials are mandatory for high power applications [6,7].The EA prototype targetThe EA prototype target [5] is an axial symmetric device consisting of a ≥beam pipe≤enclosed in a coaxial ≥container≤ (see Fig. 1). The beam pipe is made of martensitic HT-9 steeland is a vertical cylinder of 10 cm radius, 635 cm height and 3 mm thickness closed at the bottomby an HT-9 ≥window≤. The window has a hemispherical external surface and an ellipsoidalinternal surface so that the thickness varies from a minimum of 1.5 mm in the beam pipe axis to amaximum of 3 mm in the junction with the cylindrical part of the beam pipe. The window is sotapered in order to reduce the beam heating in the beam pipe axis. The container is a verticalcylinder of 27 cm radius and 724 cm height with a hemispherical bottom. The region between thebeam pipe and the container is filled with LBE and ≥vacuum≤ is made inside the beam pipe.Having neglected the heat flux through the beam pipe and the container, the heat producedin the window and in the coolant is removed by a natural convection flow. This flow is guided bythe ≥flow guide≤, that is a 17 cm internal radius cylinder laying between the beam pipe and thecontainer. The flow guide separates the internal hot flow rising from the spallation region fromthe external cooled flow downcoming from the heat exchanger positioned on the top of thedowncoming duct. In the spallation region the flow guide assumes a funnel shape whichaccelerates the flow and enhances the cooling of the window. The flow guide is made of two HT-9layers 1 mm thick separated by a 1 mm layer of insulating material (Zirconium oxide). The heatexchanger is located at 25 cm from the container top, is 45 cm height and its outlet temperature isset to 180  C.CONTAINEREXCHANGERHEATVACUUMSPALLATIONREGIONWINDOWFLOW GUIDEBEAM PIPEFigure 1 ≠ Description of the EA prototype target.Neutronic analysisThe proton beam is injected through the top of the beam pipe and interacts with the window, thecoolant and the flow guide. The proton energy is 600 MeV and the beam size is assumed to be asa circular spot of radius r0  = 7.5 cm (the window radius allows a correct defocusing of the beamspot in order to prevent localised high power densities in the target materials). The beam currentdensity is given by the three-dimensional parabolic profile                                                 J Irrr= −2 1002202pi                                                              (1)where the beam current I0  ranges from about 2 to 6 mA. In the following we assume themaximum beam current of 6 mA corresponding to a beam power of 3.6 MW.The FLUKA Monte-Carlo code [8,9] is employed to calculate the heat source distribution,taking into account not only the electromagnetic interactions, but all kind of nuclear reactionsinduced by both protons and secondary generated particles. A 40∞70 orthogonal grid is used forthe FLUKA simulation. The heat generated inside the funnel is calculated by applying thedistribution for the coolant multiplied by the ratio between the flow guide density and the coolantdensity. According to the FLUKA computation, inside the window the proton beam deposits inform of heat about 22 kW (i.e. 0.6% of the beam power). The heat production in the coolant andin the flow guide is 72% and 1% of the beam power respectively, the rest of the beam energybeing contained in the particles escaping the system or in the binding energy of the targetnucleus. Fig. 2 illustrates the contours of the beam power released in the LBE.0.5 0.50.50.51101001000.510.50.50.5-20-15-10-505101520-10 0 10 20 30 40 50 60Distance from the beam axis (cm)Distance from the beam window (cm)Power in W / cm^3 / mAFigure 2 ≠ Neutronic calculation of the power generated in a thick LBE target by the protonbeam.Fluid dynamic analysisThe turbulent natural convection flow of the coolant and the thermal field in solids aresimulated using the STAR-CD fluid dynamic code [10] where the heat source distributioncalculated by the FLUKA code is used as input data. The vacuum inside the beam pipe issimulated by means of air at very low pressure. The heat exchanger is modelled as a thermal sinkuniformly distributed. The numerical model employs a third order scheme for the spatialdiscretisation of the convective terms. The Chen k-ε model with a two-layer algorithm in the nearwall region accounts for turbulence effects. The radiative heat flux through the beam pipe and thepressure losses in the heat exchanger are neglected. The container walls are assumed as adiabatic.The IDEAS CAD and mesh generator [11] is employed to create a mixedstructured/unstructured mesh. The fluid regions near the walls are meshed with structured grids,easier to handle and more suitable for the application of the turbulent near-wall algorithms.Structured meshing is also used for the discretisation of the solids. The total number of cells isabout 14000 and the discretisation is very accurate in the funnel zone, especially next to thewindow stagnation point.Fig. 3 shows the computed velocity and temperature fields in the funnel region. Therecirculation zone in the downcoming duct increases the temperature and reduces the naturalconvection pumping. However, the target height and the flow acceleration due to the convergentfunnel shape generate the coolant velocity necessary for cooling the beam window to a maximumtemperature of 427  C.Figure 3 ≠ Velocity and temperature fields in the funnel region.Structural analysisThe MSC/NASTRAN structural code [12] is employed to calculate the stresses induced in thewindow/pipe system by using a linear (elastic) model applied to the same window/pipe grid usedfor the fluid dynamic simulation. The temperature field is assigned to the elements of the modeland the coolant hydrostatic pressure distribution is applied onto the external surface.The maximum Von Mises stress is 109 MPa, the maximum ≥meridional≤ (i.e. tangent to thewindow profile) stress is 102 MPa and the maximum ≥hoop≤ (i.e. perpendicular to the plane ofstudy) stress is 101 MPa. The maximum window temperature is 427  C which corresponds to anUltimate Tensile Strength (UTS) of 610 MPa (this value is conservative due to the UTS decreasewhen the temperature increases). The values of temperature and stress are within the HT-9application range described in [13].Beam distribution effectsThe window stresses sensitivity to the beam distribution is studied by considering gaussianand uniform distributions having the same proton energy and beam current of the parabolicdistribution given by Eq. (1) (see Figs. 4 and 5). The corresponding heat flux to be removed fromthe window decreases in the beam axis according to the smaller window thickness.Fig. 6 shows the temperature distributions on the internal (window/vacuum) and external(window/coolant) surfaces as a function of the angle α between the target axis and the window (orpipe) circumference orthogonal to the axis (the proton beam crosses the window up to an angle of48.6  ).LLKKLKJGHHIDLLLKLHIJKEDEFGHIFEBCECDCDEHEDEDEBFGHFF H IIIHIIFGHIIFGHGHGFIFCHFHMHIHGHGFFFGHIFGHIIGHMGBE FECLEMBJICEGHHGFBHLLLILLIKKJJJ KKIMMMMMMFGMLLMJKLHHHI JGFGFGIEJKKELEIGHHKJ KJMK LLMMMDETEMPERATURE         ABSOLUTE            KELVIN              LOCAL MX=  600.9LOCAL MN=  470.5A   595.0B   585.0C   575.0D   565.0E   555.0F   545.0G   535.0H   525.0I   515.0J   505.0K   495.0L   485.0M   475.0Figures 4 and 5 ≠ Assigned proton beam particle distributions and corresponding heat fluxcalculated by FLUKA in the window for different beam distributions.0 10 20 30 40 50 60α (deg)externalinternalUNIFORM0 10 20 30 40 50 60GAUSSIANinternalexternalα (deg)0 10 20 30 40 50 60250300350400450500550α (deg)Temperature (o C)externalinternalPARABOLICFigure 6 ≠ Temperature distributions on the internal and external window surfaces.The gaussian distribution leads to window temperatures out of the HT-9 application range.With respect to the parabolic distribution, the gaussian and uniform distributions have greatertemperature gradients and therefore greater stresses close to the beam axis and edge respectively,as illustrated in Figs. 7 and 8 where the meridional and hoop stress components in the internal andexternal window fibres are reported. The maximum Von Mises stresses are 189 and 149 MPa forthe gaussian and uniform distribution respectively. The gaussian distribution produces stresses outof the HT-9 application range. The thinner part of the window, which is also the most loaded inthe non-uniform distribution case, undergoes strong bending moments (depending basically onthe temperature gradient along the thickness).00.050.10.150.20.250.30 1 2 3 4 5 6 7 8 9 101/N dn/dxDistance from the beam axis (cm)Gaussian distribution   (FWHM = 7 cm)r(max) = 7.5 cmParabolic distributionUniform distribution01020304050600 1 2 3 4 5 6 7 8 9 10Heat flux (W/cm^2/mA)Distance from the beam axis (cm)Gaussian DistributionUniform DistributionParabolic DistributionFigure 7 ≠ Meridional stress components in the internal and external window fibres.0 50 100 150α (deg)UNIFORMexternalinternal0 50 100 150α (deg)externalinternalGAUSSIAN0 50 100 150-180-120-60060120180α (deg)externalinternalHoop stresses (MPa)PARABOLICFigure 8 ≠ Hoop stress components in the internal and external window fibres.Beam size effectsOne of the most dangerous accidents expected in the beam window is a reduction of thebeam size. In order to analyse such effect we reduced the beam spot radius down to a dimensionof 3 cm. Fig. 9 shows that the maximum temperatures reached on the external and internalwindow surfaces in the beam axis are immediately out of the utilisation range of a HT-9 steel.The corresponding maximum meridional, hoop and Von Mises stresses normalised withrespect to the UTS are shown in Fig. 10 and illustrate that also stresses are immediately out of theapplication range when reducing the spot size.0 50 100 150α (deg)UNIFORMexternalinternal0 50 100 150α (deg)externalinternalGAUSSIAN0 50 100 150-180-120-60060120180α (deg)externalinternalMeridional stresses (MPa)PARABOLICFigure 9 ≠ Temperature on the window surfaces in the beam axis vs beam radius.Figure 10 ≠ Normalised maximum meridional, hoop and Von Mises stresses vs beam radius.Beam interruption effectsWhen the beam is interrupted, window temperatures decrease to the heat exchanger exittemperature. The beam interruption transient is calculated by a structural analysis decoupled bythe fluid dynamic transient. The MSC/NASTRAN code is used where the coolant temperature issupposed to decrease from 360  C (see Fig. 6) to 180  C in 0.15 s, according to the coolantvelocity field near the window. The window/coolant heat flux is computed by using a heat transfercoefficient of 20000 Wm −2 K −1 obtained by a forced convection fluid dynamic analysis of thewindow flow without the LBE heat source. Figs. 10 and 11 show the maximum temperature andVon Mises stress in the window during the transient.2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0300500700900110013001500Spot radius r0 (cm)Temperatures in the beam axis (o C)internalexternal2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.00.00.20.40.60.81.01.2Spot radius r0 (cm)Stresses / UTSmax meridionalmax hoopmax Von MisesFigures 10 and 11 ≠ Maximum window temperature and Von Mises stress during the beaminterruption transient.Under the approximation done on the coolant temperature transient, each beam interruptionlonger than about 4.5 s produces a stress cycle whose maximum Von Mises stress is 175 MPa. Byneglecting the creep damage, the fatigue life may be determined from a design curve based uponstrain cycling fatigue data generated at the maximum temperature [14]. In [15] a design curve formedium-strength pressure vessel steels is given, leading to a number of cycles to failure equal to10 5. However to predict thermal fatigue life with a higher degree of accuracy it is necessary tosimulate the coupled thermal and fluid-dynamic transient and to acquire data about the thermalstress behaviour of the specific steel, the irradiation damage and the corrosion effects.ConclusionsExtensive numerical calculations have been performed to study the thermo-fluid dynamicsand the structural loads on the EA 80 MW prototype target. In the limits of the geometricalconstraints of the system, a thermal hydraulic optimisation of the target allows the use of naturalconvection. The relatively low power beam of the machine (600 MeV of beam energy and 26mA of beam current) allows the use of a martensitic steel in the beam window. This deeplyalleviates the problems related to the construction, the assembly and the operation of the windowunder intense proton irradiation.When changing the uniform beam distribution from parabolic to gaussian or uniform,window temperatures and thermal stresses increase and eventually go out of the steel applicationrange. When reducing the beam size temperatures and stresses still increase but in this case areimmediately out of the steel utilisation range.A simplified study of the fatigue damage induced by cyclic beam interruptions (longer thanabout 4.5 s) leads to predict the allowable number of interruptions to failure. In this analysis themore critical points remain the need of data on steel thermal cycle fatigue, irradiation damage andcorrosion.    0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5150180210240270300330360390420450Max. temperature in the window (o C)Time (s)0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50306090120150180Time (s)Max. Von Mises stress in the window (MPa)References[1] C. Rubbia et al., ≥Conceptual Design of a Fast Neutron Operated High Power EnergyAmplifier≤, CERN Report, CERN/AT/95-44 (ET), Geneva, September 29, 1995.[2] C. Rubbia, ≥A High Gain Energy Amplifier Operated with Fast Neutrons≤, AIP ConferenceProceedings 346, International Conference on Accelerator-Driven Transmutation Technologiesand Applications, Las Vegas, July 1994.[3] Proceedings of the Meetings ICANS-XIII and ESS-PM4, edited by G. Bauer and R. Bercher,PSI proceedings 95-02, November 1995.[4] Proceedings of the ≥International Workshop on the Technology and Thermal Hydraulics ofHeavy Liquid Metals≤, compiled by B.R. Appleton and G.S. Bauer, Schruns, Montafon Valley,Austria, March 25-28, 1996.[5] L.Maciocco et al., ≥Design and Optimisation of a Liquid Metal Spallation Target for theEnergy Amplifier Prototype≤, 2nd International Topical Meeting on Nuclear Applications ofAccelerator Technology, Gatlinburg, TN, USA, September 20-23, 1998.[6] S. Buono and C. Rubbia, ≥A comparison of different materials for the beam window of theEnergy Amplifier≤, CERN/ET Internal Note 96-26, Geneva, August 27, 1996.[7] S. Buono and C. Rubbia, ≥A Tungsten-Rhenium Alloy as a beam window material for theEnergy Amplifier≤, CERN/ET Internal Note 96-24, Geneva, July 9, 1996.[8] A. FassÚ et al., ≥FLUKA92≤, Workshop on Simulating Accelerator Radiation Environments,Santa Fe, USA, January 11-15, 1993.[9] A. Ferrari and P.R. Sala, ≥Improvements to the Electromagnetic part of the FLUKA code≤,MC93 Int. Conf. on Monte-Carlo Simulation in High-Energy and Nuclear Physics, Tallahassee,February 22-26, 1993.[10] STAR-CD Version 3.05 User Guide, Computational Dynamics Limited, 1998.[11] IDEAS Master Series 5, Structural Dynamics Research Corporation.[12] MSC/NASTRAN Version 70.5, MacNeal-Schwendler Corporation.[13] Y. Dai, ≥Martensitic/ferritic Steels as Container Materials for Liquid Mercury Target of ESS'',International Workshop on the Technology and Thermal Hydraulics of Heavy Liquid Metals,Schruns, Austria, March 1996.[14] Thermal Stresses II, edited by R. Hetnarski, Elsevier Science Publishers, Amsterdam, TheNetherlands, 1987.[15] C. Osgood, Fatigue Design, John Wiley & Sons, New York, USA, 1970. 

Thermo-mechanical stresses on the beam window

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Thermo-mechanical stresses on the beam window

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