thermo hydraulic optimisation of the eurisol

Project EURISOL

Title Thermo hydraulic optimisation of the EURISOL DS target

Registration TM-34-06-0

Author: Co-Author: M. Ashrafi-Nik

Issued 15.12.2006 / Issue 2

Summary :

The present document describes the thermal and the stress analysis of the final design of the EURISOL DS target. The preliminary design by Q. Prétet, R. Milenkovic and B. Smith was used as a starting point for further improvements to reduce stresses in the hull; the results of these computations are summarised in this document.

All variants studied to attain the objective are documented using CFD to assess the effects of different flow configurations on the temperature distribution in the target liquid metal and structural analysis for determining the stresses and temperatures in the target structure.

Abt. Empfänger / Empfängerinnen Expl. Abt. Emfpänger / Empfängerinnen Expl. Verteiler

CERN ASQ ASQ ASQ ASQ ASQ ASQ LTH FZK IPUL

Yacine Kadi Kurt Clausen Werner Wagner Friedrich Groeschel Karel Samec Jörg Neuhausen Luca Zanini Brian Smith Rade Milenkovic Ilgvars Platniecks

CERN EURISOL DS, Task2

Expl.

Bibliothek 1 Reserve Total 12 Seiten Beilagen Informationsliste

D 1 2 3 4 5 8 9 A

Visum Abt.-/Laborleitung:

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R e v i s i o n L i s t

Chapter Issue Author Date Modification

All 1 M. Ashrafi-Nik 15-12-06 Original version

All 2 K. Samec 16-12-06 Review and corrections

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C o n t e n t s R e v i s i o n L i s t ................................................................................................. 2 L i s t o f F i g u r e s ........................................................................................... 4 L i s t o f T a b l e s ............................................................................................... 4 L i s t o f S y m b o l s .......................................................................................... 5 R e f e r e n c e D o c u m e n t s ......................................................................... 6 1 Introduction............................................................................................................... 7 2 Scope........................................................................................................................... 8 3 Material properties ................................................................................................... 9

3.1 Physical properties of T91 .................................................................................. 9 3.1.1 Linear thermal expansion coefficient.....................................................9 3.1.2 Young`s Modulus...................................................................................9 3.1.3 Poisson Coefficient ................................................................................9 3.1.4 Specific heat, Density, Thermal conductivity......................................10 3.1.5 Allowable stress as a function of temperature .....................................10

3.2 Physical properties of the Liquid Metal............................................................ 11 3.3 Table of units conversion for Ansys ................................................................. 14

4 Numerical analysis and optimisation .................................................................... 15 4.1 Scope of the simulations ................................................................................... 15 4.2 CFD Model description..................................................................................... 15 4.3 Boundary conditions ......................................................................................... 16

4.3.1 Liquid Metal flow condition ................................................................16 4.3.2 Beam deposition applied to the model.................................................16

4.4 Optimisation Results......................................................................................... 17 4.4.1 2D detail model of window..................................................................17 4.4.2 3D detail model of the window............................................................21 4.4.3 Duct designs.........................................................................................22

4.4.3.1 Discussion ........................................................................................31 4.4.4 Stress Calculation.................................................................................33 4.4.5 Conclusion ...........................................................................................36

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L i s t o f F i g u r e s -

Figure 2-1. Cross-section of the Eurisol Target __________________________________________8 Figure 2-2. Investigated flow conditions _______________________________________________8 Figure 3-1. Steel material properties __________________________________________________10 Figure 3-2. Design stress vs. temperature acc. RCCMR, valid at doses < 2[dpa] ________________11 Figure 3-3. LBE material properties___________________________________________________12 Figure 3-4. Hg material properties ____________________________________________________13 Figure 4-1 Close-up view of the window region in the CFD model for the proposed initial design___15 Figure 4-2 Graphs representing the beam deposition______________________________________16 Figure 4-3 Effect on the peak stress of varying the opening angle of the window. ________________18 Figure 4-4 Effect on the peak stress of varying the curvature radius of the window. ______________19 Figure 4-5 1st and 3rd Principal stresses results; variable thickness of the window hull. ___________20 Figure 4-6 Graphs representing the Buckling Stress ______________________________________21 Figure 4-7 Eurisol Lower Target Configuration I_________________________________________23 Figure 4-8 Eurisol Lower Target Configuration II ________________________________________24 Figure 4-9 Eurisol Lower Target Configuration III _______________________________________25 Figure 4-10 Eurisol Lower Target Configuration IV ______________________________________26 Figure 4-11 Eurisol Lower Target Configuration V _______________________________________27 Figure 4-12 Eurisol Lower Target Configuration VI ______________________________________28 Figure 4-13 Eurisol Lower Target Configuration VII______________________________________29 Figure 4-14 Eurisol Lower Target Configuration VIII _____________________________________30 Figure 4-15 Von-Mises stress in the window corresponding to temperature distribution __________33 Figure 4-16 Von-Mises stress in the window corresponding to 10 bar Pressure & temperature distribution ______________________________________________________________________34 Figure 4-15 schematic of 3D geometry _________________________________________________35

L i s t o f T a b l e s -

Table 1: Linear thermal expansion coefficient for T91 martensitic steel, temperature dependency 9 Table 2: Young’s modulus for T91 martensitic steel, temperature dependency 9 Table 3: LBE material properties 12 Table 4: Hg material properties 13 Table 5: Conversion table from Ansys to SI 14

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L i s t o f S y m b o l s -

Parameters and variable:

Cp [J/kgK] Heat Capacity E [MPa] Young Modulus hf [W/mK] Heat transfer coefficient q [W] Heat T [°C] Temperature TRef [°C] Temperature of the LM entering the target t [sec.] Time UInlet [m/s] Inlet speed α [1/K] One-dimensional secant expansion coefficient λ [W/mK] Conductivity ν [kg/ms] Dynamic viscosity σv [MPa] Von-Mises stress ρ [kg/m3] Density

Subscripts:

Tb Bulk temperature of a fluid (first element close to wall) Tw Wall temperature

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R e f e r e n c e D o c u m e n t s -

[Ref1] MEGAPIE Declared Material List MPS-QA-GF34-002-5.doc F. Groeschel 2005

[Ref2] EURISOL Multi-MW Target Preliminary Study of the Liquid Metal Proton-to-Neutron Converter

A.Herrera-Martínez and Y. Kadi

[Ref3] EURISOL CFD optimisation Study of the Liquid Metal target Q. Pretet

R. Milenkovic B. Smith

2006

[Ref4] Best-estimate fit for EURISOL Heat Deposition Profiles, 17.10.06 Correlations to be used for the final design-phase CFD calculations

PSI Memorandum K. Samec 17.10.2006

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1 Introduction

The main objective of the analysis document is to increase the efficiency of cooling the window hull by optimising hydraulic design and flow conditions using liquid metal as a cooling medium

The following document describes the step by step optimization approach

which was taken, and which takes the previous optimisation study [Ref.3] as the point of departure.

The analysis predicts stress and temperature results for the projected nominal

configuration, as well as attempts at optimising the flow conditions to alleviate stress concentrations.

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2 Scope The stress analysis of the target covers nominal operations. The goal of the

optimisation is to reduce the stresses under nominal conditions by changing the detail of the window geometry, in particular at the point of entry of the proton beam.

The model uses axis-symmetric assumptions for both the flow and the stress; it concentrates on the main area of interest, i.e. the window as shown in the figure below. The analysis is carried out using the commercial codes CFX 10 for the thermal analysis and ANSYS 10 for the structural analysis.

Figure 2-1. Cross-section of the Eurisol Target

Window

Liquid Metal target

Beam Line

Dashed contour indicates location of the axis-symmetric model used in the following The liquid metal target structure is made up of two main components:

− A liquid metal cooled cylindrical hull with a concave conical shape at the point of entry of the beam.

− A Guide tube to propel the cooling fluid inside the hull towards the window and back.

As far as the liquid metal is concerned, there are two possibilities for flow direction in the target, one in which the inflow is conducted towards the window down the outer annulus; this is designated “outer annulus inflow”. In the other configuration the inflow occurs from the central Guide tube and flows back away from the window via the outer annulus; hence this condition is designated “Guide tube inflow”.

Outer annulus inflow Guide tube inflow Figure 2-2. Investigated flow conditions Note: Rotationally symmetric half-model is shown

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3 Material properties All material values are extracted from [Ref1]. Martensitic steel T91 is selected

for the cylinder hull and the Guide tube. The reasons for the choice are good radiation resistance and elevated temperature performance, as demonstrated in the Megapie project.

The effect of temperature on the material properties is accounted for. Linear approximations are used for the material behaviour as far as possible.

The choice of the coolant is limited to Mercury, as explained in the previous analysis documented in [Ref3]. LBE is kept aside for the time being.

3.1 Physical properties of T91 The temperature dependency of the steel is programmed both in the Ansys structural models and CFX fluid dynamic models.

3.1.1 Linear thermal expansion coefficient T ºC 20 100 200 300 400 500 600 700

αm 10-6/K 10.4 10.8 11.2 11.6 11.9 12.2 12.5 12.7

αi 10-6/K 10.4 11.1 11.9 12.4 13.0 13.6 13.8

Table 1: Linear thermal expansion coefficient for T91 martensitic steel, temperature dependency Where: αm mean coefficient between 20ºC and T αi instantaneous coefficient at T

3.1.2 Young`s Modulus Temperature dependency for the stiffness modulus follows the following relations;

E [MPa] = 207300 – 64.58 T for 20ºC < T < 500ºC

E [MPa] = 295000 – 240 T for 500ºC < T < 600ºC Hence, the Young’s modulus will be temperature dependant with the values below:

T ºC 20 100 200 300 400 500 600 700

Ε [MPa] 206000 199500 194400 187900 181500 175000 151000 127000

Table 2: Young’s modulus for T91 martensitic steel, temperature dependency

3.1.3 Poisson Coefficient The coefficient ν is 0.3 for all temperatures.

The shear modulus G [MPa] is calculated according to G = E/2(1+ν).

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3.1.4 Specific heat, Density, Thermal conductivity The density of T91 steel is taken from [Ref1] as depicted in the figure and table below.

Specific heat

y = 0.0004x2 + 0.2473x + 450.08R2 = 0.9968

0

100

200

300

400

500

600

700

800

0 100 200 300 400 500 600 700 Thermal conductivity

y = -2E-05x2 + 0.017x + 25.535R2 = 0.9988

25

25.5

26

26.5

27

27.5

28

28.5

29

29.5

0 100 200 300 400 500 600 700

Density

y = -0.3289x + 7742.5

7500

7550

7600

7650

7700

7750

7800

0 100 200 300 400 500 600 700 Figure 3-1. Steel material properties

The specific heat and the thermal conductivity, are temperature dependant,

however the variations are small in the temperature range considered for the final converged solution.

All the other properties, such as electric resistivity or magnetic properties are not used in this study because the software does not need them to perform a thermo structural analysis (all the electromagnetic forces are assumed to be negligible).

3.1.5 Allowable stress as a function of temperature Currently, the design assessment is carried out in accordance with the minimum RCCMR values. Such values have been derived for fast reactors at around 2 [dpa]. Since the window is expected to reach 25 [dpa], RCCMR may not be sufficiently conservative to cover the entire lifetime of the target, indeed the analysis is only valid for the first few months of irradiation. There are indications however that at temperatures around 500°C the material tends to “self-heal”. Hence using the

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RCCMR standards represents the best available estimate at the present stage of the project and using currently available test data.

The plasticity effect, when the stress exceeds the proportional limit, has not been considered in this study as the objective is to remain well within the proportional limit. Hence the calculations are conservative in designs where the stress level would lead to yielding and redistribution of stress.

0

50

100

150

200

250

0 100 200 300 400 500 600

Temperature [°C]

Allo

wab

le S

tres

s [M

Pa]

Figure 3-2. Design stress vs. temperature acc. RCCMR, valid at doses < 2[dpa]

3.2 Physical properties of the Liquid Metal The Liquid Metal (LM) properties are temperature dependent. Variations of

physical properties in the liquid metal are mostly small for the range of interest (300-500C). For project reasons driven by the experience of the partners involved, the initial study was limited to two liquid metals;

- Mercury (Hg) - Lead-Bismuth Eutectic (LBE)

Relevant properties are summarised in the next table; they have been tabulated for temperatures corresponding to the scope of interest. Small variations of 5-10 % over the temperature range are expected.

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T Pr ν λ ρ

150 0.04 3.05E-03 11.2 10550 200 0.0318 2.55E-03 11.7 10490 250 0.0262 2.19E-03 12.2 10430 300 0.0224 1.94E-03 12.7 10360 350 0.0197 1.76E-03 13.1 10300

Table 3: LBE material properties

Prandtl Number

y = 2.7072 T -0.8402

0.015

0.02

0.025

0.03

0.035

0.04

0.045

100 150 200 250 300 350 400

Dynamic viscpsity

y = 0.0807 T -0.6531

1.50E-03

1.70E-03

1.90E-03

2.10E-03

2.30E-03

2.50E-03

2.70E-03

2.90E-03

3.10E-03

3.30E-03

100 150 200 250 300 350 400 Thermal conductivity

y = 0.0096T + 9.78

11

11.5

12

12.5

13

13.5

100 150 200 250 300 350 400

Density

y = -1.26T + 10741

10250

10300

10350

10400

10450

10500

10550

10600

100 150 200 250 300 350 400 Figure 3-3. LBE material properties

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T Pr ν λ ρ 20 0.0249 1.55E-03 8.69 13579 50 0.0207 1.40E-03 9.4 13506 100 0.0162 1.24E-03 10.51 13384 150 0.0134 1.13E-03 11.49 13264 200 0.0116 1.05E-03 12.34 13145

Table 4: Hg material properties

Prandtl Number

y = 3E-07T2 - 0.0001T + 0.0275R2 = 0.9981

0

0.005

0.01

0.015

0.02

0.025

0.03

0 50 100 150 200 250

Dynamic viscpsity

y = 1E-08T2 - 5E-06T + 0.0016R2 = 0.9988

0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

1.40E-03

1.60E-03

1.80E-03

0 50 100 150 200 250 Thermal conductivity

y = 0.0203T + 8.371

0

2

4

6

8

10

12

14

0 50 100 150 200 250

Density

y = -2.4124T + 13626

13100

13150

13200

13250

13300

13350

13400

13450

13500

13550

13600

13650

0 50 100 150 200 250 Figure 3-4. Hg material properties

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3.3 Table of units conversion for Ansys Ansys as such does not use any particular units. The values entered into the

material property fields are pure numbers unrelated to units. It is up to the user therefore to enter the data in such a way that it is consistent, i.e. that the fundamental equations of continuity, momentum etc are valid. Choose for instance:

Unit length = mm Unit time = s Unit Force = N

Derived Mass: 1 Tonne (1 N = 1 Tonne x 1 mm/s2)

Derived Work: 1 mJ = 1 N x 1 mm

Hence the conversion table below for a system in Ansys using N, mm and s: Symbol SI Ansys SI→Ansys Ansys→SILength L [ m ] [ mm ] *103 *10-3

Time t [ sec ] [ sec ] - - Mass M [ kg ] [ to ] *10-3 *103

Temperature T [ K ] [ K ] - - Force F [ N ] [ N ] - - Work W [ J ] [ mJ ] *103 *10-3

Power P [ W ] [ mW ] *103 *10-3

Pressure p [ Pa ] [ [MPa] ] *10-6 *106

Density ρ [ kg / m3 ] [ to / mm3 ] *10-12 *1012

Thermal capacity C [ J / kg.K ] [ mJ / to.K ] *106 *10-6

Thermal conductivity λ [ W / m.K ] [ mW / m.K ] - - Film coefficient h [ W / m2.K ] [ mW / mm2.K ] *10-3 *103

Dynamic viscosity [ kg / m.s ] [ to / mm.s ] *10-6 *106

Power density Q [ W / m3 ] [ mW / mm3 ] *10-6 *106

Specific Heat Cp *106 *10-6[ J / kg.K ] [ mJ / to.K ]

Table 5: Conversion table from Ansys to SI Ansys conventions The designation of heat transfer variable, is defined in Ansys as follows;

Heat flow rate [ W ] (apply only to nodes or to keypoints) Heat flux [ W / m2 ] Heat Generation rate [ W / m3 ]

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4 Numerical analysis and optimisation

4.1 Scope of the simulations The simulation assesses the thermal distribution in the model under the

influence of both the proton beam and the cooling effect from the liquid metal flow within the target.

4.2 CFD Model description The model is primarily meshed with brick elements both in the fluid and in the solid domain. Note that the thermo-structural model is axis-symmetric to speed up convergence. The CFD model relies on finite volumes and hence contains brick element with a certain depth, the entire model being a wedge taken out of the circular symmetry. The axis-symmetric thermo-structural model is also wedge-shaped and is taken from the CFD model with the fluid removed. The influence of the cooling from the fluid is in the form of boundary conditions extracted from the CFD and draped onto the relevant surfaces in the thermo-structural model.

Figure 4-1 Close-up view of the window region in the CFD model for the proposed initial design

A wedge model with an opening angle of (1/72) perimeter or 5° opening angle has been created. The following geometric data describe the model in broad terms:

- Opening angle of the wedge: 5° degrees - Outer hull radius: 71 mm - Inner tube radius: 48 mm

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- Length of model: 300 mm (95% deposition length of the beam) - Inlet / Outlet axially symmetric (detail of connections to LM will be

addressed separately)

4.3 Boundary conditions The two main effects are the beam deposition on the one hand and the liquid metal coolant flow on the other. Radiative exchange has not been considered in this calculation. Such an assumption is conservative as the additional losses would further cool down the target. However most of the external hull is at a low enough temperature that this will not be a significant factor. As to the window, which will see a significant temperature rise, the emissivity factor is bound to vary with increasing radiation damage in a way that is difficult to predict. As the effect is purely local and can only be beneficial neglecting it is conservative.

4.3.1 Liquid Metal flow condition The flow rate of the liquid metal coolant is defined by; - Flow rate: 2.37 kg/s per 5° segment (171 kg/s for full model) - Static pressure: 0< P >5 bars (to avoid cavitation) - Entrance temperature of the cooling fluid: 60 C for Hg (240 C for LBE)

4.3.2 Beam deposition applied to the model

Proposed T91 designCFD M odel

Pow

er [W

/m3 ]

Radia l d irection [m m ] Axial d irection [m m ] Figure 4-2 Graphs representing the beam deposition

The beam deposition applied to Eurisol stems from the neutronic calculation in [Ref2]. The overall heat balance has been checked by integrating the profile over the entire domain and ensuring the deposited energy is within requirements. As documented in [Ref4] the bulk of the energy is deposited over 300mm and has no Bragg peak.

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The results from a series of CFD calculations for the initial design of the window are shown in the following, with many different flow configurations.

4.4 Optimisation Results The path chosen for optimising the design of Eurisol with a view to reducing stress was to proceed in several steps;

1. Optimise the thickness of the window with a simple 2D model and some basic assumptions on the cooling effect of the liquid metal.

2. Optimise the fluid flow inside the target to enhance cooling of the liquid metal and steel hull, whilst reducing pressure losses and the likelihood of cavitation.

3. Check the effect of static pressure on the outer hull, and if needed reinforce hull whilst conserving the beneficial effects of prior optimisation.

4.4.1 2D detail model of window The next following figures represent the Von Mises resultant stress along the hull for different designs of the window. A large number of configurations were examined with the help of log files in Ansys, to provide a clearer understanding of the effect of changing the angle, radius, thickness and taper of the window. The effects of cooling from the fluid are influencing this preliminary study through the application of convective thermal boundary conditions. As an example, the following values are extracted from a log file; Convective cooling at centre;

HTC1 = 15 [W/cm2K] TB1 = 200 [°C]

Convective cooling at base of cone:

HTC2 = 8 [W/cm2K] TB3 = 100 [°C]

Such values are fairly representative of the cooling effect expected from the liquid metal, and have been extracted from prior CFD calculations in [Ref3]. In the next following pages, geometric parameters in the window are changed, and the effects on the stress are studied. Note that the effect of pressure is not considered in this preliminary study, and may prove to rule out certain geometric configurations. This effect will be studied further in the next chapters.

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Effect of the opening angle: In Figure 4-3, the configurations studied clearly indicate that, varying the angle α of the window does not have a significant effect on the stresses along the window hull. This significant finding entails that the angle of the cone may be freely chosen so as to optimise cooling and prevent the formation of recirculation vortices in the fluid. Hence, the best angle will eventually arise out of a subsequent detail CFD calculation.

ά

σ Von Mises[Mpa]

σ Von Mises[Mpa]

Figure 4-3 Effect on the peak stress of varying the opening angle of the window.

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Effect of the curvature radius: Next, the effect of changing the radius is examined. In this case the effect is more significant. The radius chosen to minimise stress is determined to be around 60 [mm]. The effect of increasing the radius starts to taper off after 90 [mm]. Overall the gain in terms of lowering the stress is about 10%. Hence in this case again, the best possible choice of radius will be governed by the CFD calculations, although the radius should remain in a range between 50 and 100 [mm]

R

Figure 4-4 Effect on the peak stress of varying the curvature radius of the window.

Effect of the thickness taper: Hereafter, Figure 4-5 shows the 1st and 3rd principal stresses along the wall for two different configurations in terms of thickness. The thickness of 2mm with 1st (tension) and 3rd (compression) principal stresses of 355MPa and -210MPa respectively can be reduced significantly to stresses of 134MPa and -73Mpa, by reducing the window thickness to 0.8mm overall. This finding is quite significant in that it shows that no matter how strong the cooling from the liquid metal, stress will arise from the temperature gradients thru the thickness. The reduction in thickness should however be kept within bounds, as there could be stability problems due to internal pressure. Hence a taper is used, whereby the thickness along the outer edge of the window is higher than at the centre. Different

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ratios of centre thickness to edge thickness are studied in the following. Best results are obtained with a thickness of 0.8 [mm] at the centre, and 1-2 [mm] along the edge.

1st Pricipal Stress Vs HTC for thickness 2 - 1.5

353.8

354

354.2

354.4

354.6

354.8

355

355.2

355.4

355.6

355.8

0 5 10 15 20

HTC [W/cm2K]

Stre

ss [M

Pa]

1st Pricipal Stress Vs HTC for thickness 1 - 0.8

134

135

136

137

138

139

140

141

142

0 5 10 15 20

HTC [W/cm2K]

Stre

ss [M

Pa]

3rd Pricipal Stress Vs HTC for thickness 2 - 1.5

-224

-222

-220

-218

-216

-214

-212

-210

-2080 5 10 15 20

HTC [W/cm2K]

Stre

ss [M

Pa]

3rd Pricipal Stress Vs HTC for thickness 1 - 0.8

-86

-84

-82

-80

-78

-76

-74

-720 2 4 6 8 10 12 14 16

HTC [W/cm2K]

Stre

ss [M

Pa]

Figure 4-5 1st and 3rd Principal stresses results; variable thickness of the window hull.

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4.4.2 3D detail model of the window The findings in the previous section indicate it is desirable to reduce the thickness in the window. Hence structural stability under pressure may become a serious issue. In order to assess this problem, a 3D local model of the window has been produced. The structural boundary conditions are clamped at bottom, and the following geometric properties of the window apply; Centre thickness; 0.8 [mm] Edge thickness; 1 [mm] Opening angle; 20 [°] Curvature radius; 90 [mm] The figure blow shows the first buckling Eigen mode under 40 [Bar] of pressure (very conservative assumption). The Eigen mode of 6.36 indicates the safety margin is quite adequate. Assuming ideal clamping conditions and no initial waviness in the shape, the centre peak in the window could sustain 6.36 x 40 Bar = 254 [Bar]. Naturally, elasticity in the restraints and slight manufacturing imperfections would reduce this figure.

Normalised displacements

Figure 4-6 Graphs representing the Buckling Stress

The larger issue of pressure induced bending further down the section will be addressed further on in the next chapters.

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4.4.3 Duct designs The overall shape of the window has now being roughly assessed. The fluid flow inside the target must now be calculated, in order to optimise the duct shape hydraulically, whilst remaining within the geometric constraints imposed by the window optimisation. The primary objective is to reduce pressure losses whilst ensuring adequate cooling of the structure, preventing boiling of the Mercury and precluding the onset of cavitation along back-swept surfaces. The configuration of the flow may be improved significantly -as described in [Ref3]- by implementing one or several of the following ideas;

- Aerofoil-type end of guide tube to reduce friction at 180° turn whilst restricting the flow into the window area to increase velocity

- Cusp-shaped annular blades in the flow to enhance the 180° turn in the flow.

- Annular Blades along the window to accelerate liquid metal flow and cooling locally.

- Holes thru the guide tube to destroy recirculation vortices in the main flow, and thus reduce pressure loss and LM heating

Hereafter the different configurations, under steady-state conditions, were calculated in different CFD simulation steps. The optimisation process included several improvements tested independently to gauge their effect in terms of reducing hull stress, temperature, and pressure loses in the LM. Computational Fluid dynamics (CFD) are used to optimise flow conditions within the target. Thereafter an Ansys (FEM) runs uses the temperature distribution in the hull structure to calculate stresses. The next following figures show the most relevant design which yielded some success in terms of achieving the goals set out. A discussion of the relative merits of the different variants the follows.

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Aerofoil-type guide tube

Figure 4-7 Eurisol Lower Target Configuration I

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Cusp-shaped guide tube with holes

Figure 4-8 Eurisol Lower Target Configuration II

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Cusp-shaped guide tube with holes and blades

Figure 4-9 Eurisol Lower Target Configuration III

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Rounded guide tube with hydraulic blades along the window

Figure 4-10 Eurisol Lower Target Configuration IV

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Hydraulic blades reduced in length

Figure 4-11 Eurisol Lower Target Configuration V

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Slat added to the rounded guide tube

Figure 4-12 Eurisol Lower Target Configuration VI

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Thickened airfoil guide tube

Figure 4-13 Eurisol Lower Target Configuration VII

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Final optimized model, hollowed airfoil guide tube

Figure 4-14 Eurisol Lower Target Configuration VIII

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4.4.3.1 Discussion The merits of the different design variants are listed hereafter, in “historic” order, as the optimisation progresses. Configuration I: Central inflow with aerofoil type guide tube This design is typical of the preliminary studies performed on the liquid metal flow (see [Ref3]) and its behaviour within the lower target. The simulation performed, reveals clearly that restricting the central flow above the window produces high static pressure loss (ΔP=40.8bar) which is too far from the original assumption (5 Bar) used in the overall systems analysis. In addition, this type of guide tube introduces other problems such as recirculation vortices and detachment. Consequently, when the mercury passes back into the return channel, it contains very low momentum and hence it creates vortices with as a result the danger of generating cavitation. The highest temperatures on the hull are located where the proton beam impacts the window. A maximum temperature of around 425 C is reached, which shows that the cooling is moderately efficient. In terms of stress, this configuration does little to alleviate the thermal gradients which are the main cause for thermal stresses. Configuration II: Cusp shaped extended guide tube with inflow down the outer annulus In this configuration, a longer guide tube has been implemented to enhance cooling along the window hull by extending it closer to the critical point, i.e. the proton beam window. Initially, the pressure loss in this configuration is found to be quite high because of the restriction imposed on the flow. Subsequently, holes are also introduced along the guide tube in order to decrease this pressure loss. However, once these mercury jets spray out, they cause a great deal of recirculation; vortices appear in the central flow due to low momentum and low velocity in that particular area which could lead to cavitation. Configuration III: Guide tube vanes added to Configuration II This particular design is an optimized model of second configuration, with guide tube vanes inserted within the central flow at varied angles, in order to direct flow towards the centre and reduce recirculation. As a result, the number of vortices is reduced, lower pressure losses obtained and overall performance is slightly more satisfying, but the requested comprehensive objectives are not fully achieved. Configuration IV: Rounded guide tube with hydraulic blades along the window As far as manufacturing is concerned, the third configuration is extremely difficult to build, and is also slightly unstable from a hydraulic point of view. Hence the fourth configuration is essentially a simplified version, with less guide vanes and holes within system. The temperatures are slightly increased, but the pressure losses are significantly lowered.

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Configuration V: Hydraulic blades reduced in length This is an improvement on the previous version, in that the hydraulic blades have been shortened. The pressure losses are again reduced, to a very manageable 0.4 [Bar], the recirculation vortices are eliminated, however the LM temperature is increased. Configuration VI: Slat added to the rounded guide tube A slat has been added to the rounded end of the guide tube in an effort aimed at reducing the suction loss on the back-swept section of the guide tube as this would cause cavitation. The pressure losses are decreased by 20%. Configuration VII: Thickened airfoil guide tube The downstream section of the guide tube is restricted, thus causing an acceleration of the return flow of liquid metal. The purpose is to reduce the LM temperature to avoid boiling. This goal is achieved with a peak temperature of 257C, well below the boiling point for 5 Bar (460°C). An attempt was made to make the guide tube full rather than hollow. However the temperature lead to very high stresses, and it is recommended to go back to a hollow version for the guide tube (if need be with internal stiffening ribs)

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4.4.4 Stress Calculation

Temperature [C] Von Mises stress

Deformed shape x 5 Detail stress on window

Figure 4-15 Von-Mises stress in the window and corresponding temperature distribution

Prior 2D analyses proved that the introduction of thinning the window hull

could eventually reduce the stresses in the window. Also, efficiency in cooling the window has been demonstrated by the prior CFD analysis.

Figure 4-15, shows the Von-Mises stress in the window corresponding to the

temperature distribution calculated from the proton beam deposition. The maximum stress of 154MPa appears on the inner side of the window, which is admissible at the local applied temperature of 252 C. According to Figure 3-2, the admissible is; σ Adm = 190[MPa] The margin of safety is therefore:

23.01154190.. =−=SoM

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This margin is sufficient to guarantee the window will not break up to 2 [dpa], the limit validated by RCCMR. In addition to temperature, pressure is also exerted on the inner surface of the window: this is why the base of the container has been thickened locally to resist bending due to pressure. The most likely static pressure for the production unit is 5 bar; however in order to check the lower target reliability, 10 bar pressure is considered. The optimised design in this section is thus able to withstand a design pressure of: PDesign = 10 [Bar]

Calculations show that in actual fact the pressure is beneficial to the most stressed area of the window, as the compression of the cone reduces the tensile stress caused by differential thermal expansion through the thickness. Hence, with 10 Bar applied pressure, the maximum Von-mises Stress in the window reaches135MPa which is lower than without pressure (154 MPa). Hence the results without pressure are the most conservative and prove that stresses in the window up to 10 Bar static pressure actually benefit from applying pressure.

Temperature [C] Von Mises stress

Deformed shape x 5 Detail stress on window

Figure 4-16 Von-Mises stress in the window corresponding to 10 bar Pressure & temperature distribution

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4.4.5 Design considerations Hereafter figures generated with the help of I-Deas 12, show a schematic of the

assembly procedure for the target.

Blades welded on vanes which slot into guide tube

Slide tube over ribs E-weld in place

Figure 4-17 schematic of 3D geometry

Cut thru LM container

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4.4.6 Conclusion

The final optimisation has yielded a satisfactory solution to the problems brought about by the deposition of heat from the proton beam, most notably the issue of high stresses and temperatures in the hull and the danger of boiling and cavitation in the liquid metal.

To explore further the potential of this concept, it is recommended to repeat the same calculation in an extended 3D model, in order to ensure that gravitational loads and the presence of vanes does not lead to any perturbations in the flow.

In addition, tests are envisaged as the next logical step towards ensuring the

theoretical results are backed up by concrete proof.

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thermo hydraulic optimisation of the eurisol

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