- Email: [email protected]
Development of helium coolant DEMO first wall model for SYCOMORE system code based on HCLL concept
Fusion Engineering and Design xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Development of helium coolant DEMO first wall model for SYCOMORE system code based on HCLL concept ⁎
Gandolfo Alessandro Spagnuoloa, , Giacomo Aiellob, Julien Aubertb a b
Karlsruhe Institute of Technology (KIT),Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany CEA-Saclay, F-91191 Gif-sur-Yvette, France
A R T I C LE I N FO
A B S T R A C T
Keywords: DEMO System code SYCOMORE Breeding blanket FW HCLL
The conceptual design of the demonstration fusion power reactor, known as DEMO, is ongoing and several reactor configurations have to be investigated by exploring different design parameters. For these reasons, within the European framework, systems codes like SYCOMORE (SYstem COde for MOdelling tokamak REactor) have been developed. SYCOMORE includes several specific modules, one of which is aimed to define a suitable design of the helium breeding blanket. The research activity has been devoted to improve the method to define automatically the First Wall design starting from thermal-hydraulic and thermo-mechanical considerations, using analytical design formulae and, also, taking into account the design criteria coming from Codes& Standards. Thanks to these considerations, it has been possible to derive the first dimensions of the First Wall channels from which all the other characteristics are deducted. Afterwards, it has been assessed the thermal and mechanical field using a theoretical approach. Therefore, in order to compare and validate the results, a 3D geometric model has been created and FEM analyses have been carried out finding out very satisfying results with maximum error of 6.06% for the thermal analysis while a maximum error of 20% for primary and secondary stresses.
1. Introduction
2. FW geometry and heat loads
Within the European framework, systems codes like SYCOMORE (SYstem COde for MOdelling tokamak REactor) have been developed [1] in order to investigate several DEMO design. It includes several specific modules (i.e. plasma physics, divertor, etc.). Among the different modules, the research activity has been focused on the development of the Breeding Blanket (BB) module because it is one of the most sensible components in relation to the associated functions [2]. The paper focuses on the improvement of the Helium Cooled Lithium Lead (HCLL) BB module of SYCOMORE and, in particular, on the First Wall (FW) geometrical design. The FW geometry is derived at first using the design limits on primary stresses (i.e. considering pressure loads only). Then a complete structural integrity assessment is performed by verifying that the thermal as well as the mechanical field are compliant with the design rules given in Codes&Standards (C&S). Finally, the methodology has been verified against the results of FEM calculations performed on 3D models of the FW geometry.
Within the framework of EUROfusion activities [2], four BB concepts are currently studied. The present study has been focused, in particular, on the HCLL BB but its application can be extended to the other concepts. The HCLL FW is made by U-shape steel plate where He circulates firstly and then it flows in series with the Breeding Zone (BZ). The structural material of the HCLL BB module is the Reduced Activation Ferritic/Martensitic steel Eurofer [3]. In Fig. 1, the 2D draw of the FW in the poloidal-radial direction [4] is reported and it has been selected as the representative geometry for the following discussion. The geometry of FW (Fig. 1) is characterized by: the radial Tungsten thickness (s), the overall FW thickness (t), the plasma facing wall thickness (e1), the BZ facing wall thickness (e2), the poloidal channel dimension (d1), the radial channel dimension (d2), the distance between two channels (2r, the rib) and the pitch between two channels (P). The additional notations are given in Table 1. The heat loads identified for the FW design [3] are: a) heat flux (HF)
⁎
Corresponding author. E-mail address: [email protected] (G.A. Spagnuolo).
https://doi.org/10.1016/j.fusengdes.2018.03.003 Received 9 August 2017; Received in revised form 13 February 2018; Accepted 2 March 2018 0920-3796/ © 2018 Published by Elsevier B.V.
Please cite this article as: Spagnuolo, G.A., Fusion Engineering and Design (2018), https://doi.org/10.1016/j.fusengdes.2018.03.003
Fusion Engineering and Design xxx (xxxx) xxx–xxx
G.A. Spagnuolo et al.
Table 1 Symbols used. fr fd fe fp
Ratio between 2r and d1. Dimensionless parameter. Ratio between d2 and d1. Dimensionless parameter. Ration between e1 and d1. Dimensionless parameter. Fraction of the thermal power used for the pumping power. Dimensionless parameter. Channel coolant velocity Concentrated pressure loss coefficient Darcy-Weisbach friction factor Channel lenght Helium density Number of FW parallel channels Cross section of FW channel Helium specific heat FW outlet bulk temperature
uc K f L ρ nc Sc cp FW Tout b
Tin
Fig. 1. FW section in the poloidal-radial plane.
coming from plasma, b) nuclear power directly deposited into FW structure and c) HF on the FW backside at boundary with the BZ. The total power deposited in the FW (PFW) is the sum of the three contributions. Contribution a) can be considered an input data, depending on the plasma characteristics and the poloidal position of the module, while contributions b) and c) are calculated in the neutronic model of SYCOMORE. A common assumption for the equatorial BB module is a constant HF equal to 0.5 MW/m2 [3]. The b) and c) contributions cannot be exactly determined without knowing respectively the geometry and the interaction between the FW and BZ. When running in SYCOMORE, these quantities are calculated iteratively starting from the total power deposited in the BB module [1]: they are therefore considered as input data for the development of the standalone FW model. Indeed, for the first iteration, it is assumed that 20% of the overall nuclear power is released in the FW [5]. Knowing the power deposited in the BB module and considering the operational coolant temperatures of HCLL BB (300 °C and 500 °C [3], inlet/outlet), it is possible to calculate the mass flow rate (m˙tot ) for each BB module. Then, knowing the fraction of the total power deposited in the FW (PFW), the bulk temperature (TFW out b ) to the outlet of FW can be obtained [5].
TwPL
FW inlet temperature Plasma facing wall channel temperature
TpPL
Plasma facing temperature
PL TArmour
Plasma facing armor temperature
TwBZ
BZ facing wall channel temperature
TpBZ
BZ facing temperature
TwPL1 − 2
Middle rib temperature
TwAV 1
Channel 1 wall temperature on the ribs
TwAV 2
Channel 2 wall temperature on the ribs
Tav qFW " qBZ "
Averaged temperature for allowable stress plasma heat flux
λEUR λArmor h Pdes Pm Pb Sm Sem Set St Ω φ Qm Qb εx − εy ν α X Y Z H
Thermal conductivity of EUROFER Thermal conductivity of Tungsten Convective heat transfer coefficient Design pressure Membrane primary stress Bending primary stress Allowable membrane stress Immediate plastic flow localization allowable stress Immediate fracture due to exhaustion of ductility allowable stress Creep differed excessive deformation allowable stress Factor for local membrane and multiaxial stress Neutron fluence Membrane secondary stress Bending secondary stress Strain in x and y direction Poisson's ratio Thermal expansion coefficient FW toroidal lenght FW poloidal lenght FW radial length (sidewall) Distance between two horizontal Stiffening Plates
BZ thermal flux
3. Determination of FW geometrical parameters dimensionless parameter introduced is fe, that is determined using the beam theory. The membrane and bending stresses acting on the thickness e1 due to the pressure on d2 can be evaluated considering the problem of a double-embedded beam on which, due to the coolant pressure, a distributed load acts:
In order to determine the FW channel dimensions, design limits on primary stresses are considered. Primary stresses are those due to external forces acting on the structure: in case of the FW this is the coolant pressure acting on the channels walls. The approach proposed in the following is based on beam theory taking into account criteria coming from C&S [6]. They can be calculated using dimensionless parameters for the FW geometric characteristics [5]. The first dimensionless parameter introduced is fr that can be estimated starting from the Pdes acting on d1. The resulting membrane stress Pm acting on the thickness 2r must verify the rule Pm < Sm in RCC-MRx [6]. This gives:
2⋅r P = des = fr d1 Sm
d ⋅f
Pm = Pdes⋅ 21⋅ e d ; Pb = Pdes⋅ 1
d12 ; 2 ⋅ e12
(2)
Using the criterion Pm +P b < 1.5Sm , with few steps, it is obtained the Eq. (3):
fe1,2 = (1)
fd ±
S
fd 2 + 12⋅ P m
des
S
6⋅ P m
des
(3)
The methodology, so far, provides couples of geometrical dimensions but not a unique design solution [5]. The innovative approach proposed here is to introduce the BB thermal-hydraulic aspects taking into account the requirements on the efficiency of DEMO reactor. It is common, in system codes [7], to calculate the pumping power as a
The second dimensionless parameter introduced is fd, corresponding to the “aspect ratio” of the channels in the FW. It cannot be determined only by considerations on primary stresses and it is considered as a user input which is bounded by manufacturing constraints. One can take fd equal to one as a starting point (square channels). The third 2
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(fixed) fraction of the recovered thermal power [7]. Indeed, for a given mass flow, the pumping power is related to geometry of the FW: smaller channels, with higher He velocity and heat transfer coefficients, insure better heat removal capability at the expense of the pumping power. For this, a new dimensionless parameter fp is introduced as the fraction of the FW pumping power in relation to the recovered FW thermal power. For information, this ratio is ∼3% in the current FW design of HCLL [3]. It is considered as an input data (given by the user) in the following. Taking into account that the channels of the FW are in parallel, they will experience the same pressure drop that is calculated as shown in Eq. (4) [5].
Δp ≡ ρ
⎞ fp ⋅PFW uc2 ⎛ f ⋅L ⋅⎜ + K⎟ = ρ 2 ⎜ 2⋅ fd ⋅d1 mtot ⎟ ⎝ 1 + fd ⎠
Fig. 2. Thermal field on FW.
flux, it is possible to calculate the temperatures in the thickness as described in the system of Eq. (8) and shown in Fig. 2 [5]. 1
PL FW " ⋅h ⎧Tw = Toutb + qFW ⎪ PL e1 PL " ⋅ λEUR ⎪Tp = Tw + qFW ⎪ PL s TArmour = TpPL + qFW " ⋅ λArmor ⎨ 1 FW ⎪TwBZ = Tout + qBZ " ⋅h b ⎪ ⎪TpBZ = TwBZ + q" ⋅ e2 BZ λEUR ⎩
(4)
The unknown factors are uc and d1. The equation necessary to solve the system is the power balance equation (Eq. (5)). FW PFW = ρ⋅nc⋅Sc⋅uc⋅cp⋅(Tout − Tin) b
(5)
Combining the previous equations, it is obtained an equation of the third order in which the unknown factor is d1, as shown in Eq. (6):
In order to estimate the thermal field on the ribs (Fig. 3), it is necessary to take into account that the adjacent channel are feed in counter-current, it means that there will be two different bulk temFW and Tin, respectively. Moreover, the highest temperature perature, Tout b will be to the FW side wall (SW) channel outlet but, conservatively, it has been assumed that the outlet FW temperature coincides with the SW one. Applying the same assumption discussed above, it is possible to figure out the temperature in the middle of the rib (TwPL1 − 2 ), as reported in Eq. (9).
2
FW Y ⋅fd ⋅ρ⋅cp⋅(Tout − Tin ) ⎤ 4⋅fd ⋅Δp 3 b 2⋅K ⋅fd ⋅PFW 2⋅d1 − ⎡ ⎢ ⎥ ⋅ ρ ⋅d1 = −f ⋅(X + 2⋅Z ) 1 + f r ⎣ ⎦ ⋅(1 + fd )⋅PFW 2 (6)
The solution of Eq. (6) [5] shows that only one result is real and also positive. Therefore it can be accepted as physical resolution of the problem. This equation allows determining the first dimension of the channels from which all the other characteristics (except e2) are deducted. In order to calculate e2, it is necessary to impose that it will sustain the increasing of the pressure in the BZ during an in-box LOCA [4]. Using the same approach for the calculation of the bending stress but considering, this time, a distance between two horizontal stiffening plates (H) [4], it is possible to calculate the maximum bending moment to the embedded joints, the second moment of inertia and, finally the bending stresses and applying the criteria P b ≤ 1.5⋅SD m , it is possible to estimate the thickness of the BZ facing wall, e2, as follows [5]:
e2 =
Pdes⋅
H2 3⋅SmD
(8)
(
⎡ qFW " ⋅ e1 + TwPL1 − 2 = TpPL − ⎢ λEUR ⎢ ⎣
d2 2
) ⎤⎥ ⎥ ⎦
(9)
Consequently, the assessment of the wall temperature on the ribs and TwAV ) can be pursed thanks to the Eq. (10) (Fig. 3, right-side). (TwAV 1 2
⎧ ⎪TwAV = 1 ⎪ ⎨ ⎪T AV = ⎪ w2 ⎩
(7)
PL Tw 1 − 2 ⋅ λEUR + h ⋅ T FW outb r λ h + EUR r PL Tw 1 − 2 ⋅ λEUR + h ⋅ T in r λ h + EUR r
(10)
SmD
is calculated according to the level D of The allowable stress RCC-MRx [6]. The membrane primary stress has not been taken into account because, during the LOCA, all the BZ is pressurized at the same pressure, it means that the plates will experience the same pressure in the poloidal direction. Only the last stiffening plates may have unbalanced pressurization but it has been assumed that the caps will sustain it [5].
4.2. Thermo-mechanical field assessment For assessing the thermo-mechanical field on the FW according to RCC-MRx methodology, three paths (Fig. 4) have been identified in which the primary and secondary stresses have been calculated.
4. Assessment of FW structural integrity The configuration obtained at the end of §3 is intrinsically able to withstand primary stresses. The main concern for the structural integrity of the FW are however thermo-mechanical stresses, especially because of the loss of ductility of the material in presence of neutron irradiation. To assess them, it is at first necessary to calculate the thermal field. 4.1. Thermal field assessment To determine the thermal field, a linear temperature distribution is assumed in the radial direction. This hypothesis is justified by the low thickness of the plasma-facing side, but is more delicate on the BZ side. However, temperature gradients are lower in this zone and the impact is limited. Making the balance of the conductive and convective thermal
Fig. 3. Thermal field on FW rib.
3
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and toroidal, respectively) according to the plate theory. The estimation of the εx and εy assumes an important relevance for a good calculation of the membrane secondary stress. In order to evaluate the differential expansion of the FW back and front, it has been studied a methodology [5] whereby, considering the front and the back of the FW displayable as two plates bonded to the extremities with different average temperatures Tm1 and Tm2 and indicating with ε1 and ε2 the “theoretical” expansion in absence of restraints, it is possible to determine the real deformation (Δε), as shown in Fig. 6, imposing a plane deformation to the boundaries. The two plates will exert a force according to the forbidden/imposed displacements. Imposing the force equilibrium, it is possible to calculate the real deformation, Δε (Eq. (14)).
Fig. 4. FW paths for stress assessment.
In the following, the paths will be used for stress calculation as well for checking level A criteria [6].
Δε =
1
d12 ; 4 ⋅ e12
Pm2 − 2 = Pdes⋅ 2 ⋅ 2e ; Pb2 − 2 = Pdes⋅
d12 ; 4 ⋅ e 22
d
d
2
5. Methodology application 5.1. Design rules The design rules contained in RCC-MRx [6] with respect to the specificities of the BB operating conditions in a fusion environment, and the allowable limits [11] have been implemented in SYCOMORE. In particular, for the type-P [11] damages: Immediate Excessive Deformation and Immediate Plastic Instability, Creep Differed Excessive Deformation, Immediate Plastic Flow Localization and Immediate Fracture due to Exhaustion of Ductility. While for the type-S [11] damages: Ratcheting in Negligible Creep end Fatigue in Non-Singular Zones.
d
Pm3 − 3 = Pdes⋅ 2 ⋅1r ;
(11)
4.2.2. Secondary stress Secondary stresses are those due to imposed displacements of the structure: in case of the FW those are the deformations due to the temperature field in the structures. The assessment of the secondary stresses may be very difficult due to the intrinsic 3D nature of the phenomenon [8]. For this reason, the plate theory has been selected for its study [9]. Two thermal regimes are identified in the FW that can be separately studied and then combined [10]: a uniform temperature variation and a temperature gradient through the thickness. Referring to Fig. 5, T0 is the reference temperature, Tm is the average temperature on thickness, T1 is the highest temperature on surface, T2 is the lowest temperature on surface, ΔTm is the difference between the average and the reference temperature and ΔT is the difference between surface temperatures. In the case of FW, a state of “co-action” will be aroused, in which the stress/deformation are associated to zero active force [10]. Using the Hooke’s law and considering a temperature difference between the two plate surfaces, it is possible to write the Eq. (12) [10]:
Qm =
5.2. Benchmark The methodology, the thermal and structural field assessment as well as the design rules of C&S have been coded in SYCOMORE using Python language [5]. In order to compare the results of Python script, a 3D geometric model has been created using CAST3M [12]. The simplified FEM model is shown in Fig. 7 [5] based on the model used in [13]. Several cases have been analysed varying the HF coming from the plasma. Considering a pumping power equal to 3% of the thermal power released into the FW, seven different heat fluxes have been studied from 0.1 MW/m2 to 0.7 MW/m2. While three cases (0.77, 0.82 and 1.0 MW/m2, respectively) have been studied considering a pumping power equal to the 10% of the FW thermal power [5]. Very satisfying results have been found for the thermal results with maximum error of 6.06% in all the cases with respect to the simplified FEM model [5]. Concerning the primary and secondary stresses, for paths 11 and 3-3 the maximum error is about the 20%. When the thickness
E⋅[ε y + ν⋅εx − (1 + ν)⋅α⋅ΔTm] (1 − ν 2)
(12)
For bending secondary stresses the governing equation is [8]:
Qb = ±
E ⋅α⋅ΔT 2⋅(1 − ν)
(14)
Assuming that εx and εy in Eq. (12) are equal to Δε in Eq. (14), it is possible to assess the membrane secondary stress for the three identified paths [5].
4.2.1. Primary stress Primary stresses are calculated with the same hypotheses used in §3. At this stage of the calculation, the FW geometry is intrinsically able to withstand them, but the numerical values are needed to combine them with secondary stresses and to apply C&S criteria. The membrane and bending primary stress have been estimated for Path 1-1, 2-2 and 3-3 (Eq. (11)) [5]. No bending stresses have been identified for the path 3-3 due to the same pressure on the rib in poloidal direction.
Pm1 − 1 = Pdes⋅ 2 ⋅ 2e ; Pb1 − 1 = Pdes⋅
E1⋅ε1⋅A1 − E2⋅ε2⋅A2 E1⋅A1 − E2⋅A2
(13)
Where x and y represent the principal normal directions (poloidal
Fig. 5. Thermal gradient and averaged temperatures.
Fig. 6. Differential expansion of FW plates.
4
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6. Conclusion
PYTHON
CAST3M
Error
Within the framework of EUROfusion activities, a research activity has been conducted in collaboration with KIT and CEA. It has been aimed to the improvement of HCLL BB module of SYCOMORE and, in particular, it has been focused on the FW geometrical design starting from thermal-hydraulic and structural considerations and taking into account, also, the criteria coming from C&S. For the first time, a methodology for determining the FW geometric characteristics has been developed by relating the thermal and structural stress fields to the (required) pumping power showing that the maximum value of the allowable surface heat flux increases with the one used in the FW until to reach the limit imposed by the requirements on the efficiency of DEMO reactor. Design criteria coming from nuclear C&S have been implemented, giving information to the designers from the early stage of the investigation. Therefore, in order to compare and validate the results, a 3D geometric model has been created and FEM analyses have been carried out finding out very satisfying results with maximum error of 6.06% for the thermal analysis while a maximum error of 20% for primary and secondary stresses. As future activities, the proposed approach might be extended to the other BB components such as stiffening plates, caps and cooling plates, providing, in this way, a powerful design tool for screening the possible reactor configuration.
TwPL [°C]
488.15
487.00
0.24%
Acknowledgments
TpPL [°C]
528.87
526.00
0.55%
PL [°C] TArmour
536.49
534.96
0.29%
TwBZ [°C]
407.85
397.00
2.73%
TpBZ [°C]
497.08
474.00
4.87%
Tav [°C] Pm + Pb [MPa] Qm + Qb [MPa] Pm/Sm (Pm + Pb)/Sm (Pm + Qm)/Sem (Pm + Pb + Qm + Qb)/Set (Ω*Pm)/St (Pm + φ*Pb)/St (Pm + Pb + Qm + Qb)/3Sm Allowable Stress at Tav Sm [MPa] Sem [MPa] Set [MPa] St [MPa]
508.51 105.60 245.10 0.14 0.50 0.90 0.20 0.15 0.68 0.83
506.20 108.30 286.80 0.10 0.51 0.94 0.22 0.11 0.69 0.92
0.46% −2.49% −14.54% 45.72% −1.25% −3.87% −9.64% 42.66% −0.87% −10.13%
Fig. 7. 3D FEM model of FW.
Table 2 Thermal-hydraulic and thermo-mechanical results for path 1-1 and for a heat flux of 0.5MW/m2 [5].
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] A. Li Puma, et al., Development of the breeding blanket and shield model for the fusion power reactors system SYCOMORE, Fusion Eng. Des. 89 (2014) 1195–1200. [2] C. Bachmann, et al., Initial DEMO tokamak design configuration studies, Fusion Eng. Des. 98–99 (2015) 1423–1426. [3] P. Arena, et al., Thermal optimization of the helium-cooled lithium lead breeding zone layout design regarding TBR enhancement, Fusion Eng. Des. 124 (2017) 827–831. [4] G. Bongiovì, et al., On the thermal and thermomechanical assessment of the optimized conservative helium-cooled lithium lead breeding blanket concept for DEMO, Fusion Eng. Des. (2017) (in press). [5] G. A. Spagnuolo, Report on the development of HCLL DEMO First Wall design for Sycomore Code, 2MVSRN. [6] RCC-MRx, 2015 edition – design and construction rules for mechanical components of nuclear installations, afcen. [7] M. Kovari, et al., PROCESS: a systems code for fusion power plants −Part 2: Engineering, Fusion Eng. Des. 104 (2016) 9–20. [8] Dennis R. Moss, et al., Pressure Vessel Design Manual (IV Edition), (2018) (ISBN: 978-0-12-387000-1). [9] Theory of Plates and Shells, McGraw-Hill Book Company, 1st Ed. 1940, 2nd Ed. 1959 (with S. Woinowsky-Krieger). [10] C. Sigmund, Elementi piastra e tubi – Quaderno Tecnico. [11] G. Aiello, et al. Proposal of a set of design rules for the Blanket Conceptual Design in WPBB, 2MMPLE. [12] CAST3M. http://www-cast3m.cea.fr. [13] J. Aubert, et al., Optimization of the first wall for the DEMO water cooled lithium lead blanket, Fusion Eng. Des. vol. 98–99, (2015) 1206–1210. [14] P. Arena, et al., Thermal optimization of the Helium-Cooled Lithium Lead breeding zone layout design regarding TBR enhancement, Fusion Eng. Des. 124 (2017) 827–831. [15] J. Aubert, et al., Thermo-mechanical analyses and ways of optimization of the helium cooled DEMO First Wall under RCC-MRx rules, Fusion Eng. Des. 124 (2017) 473–477.
142.00 257.00 1785.00 130.30
starts to be greater, the 3D effects have a strong impact on the results for path 2-2. In general, the most important zone, for the verification of the criteria, is the front plasma side thickness [5]. For path 1-1, considering the reference case at 0.5 MW/m2 [2], the results obtained with the Python script show a satisfactory agreement with the FEM calculation, with a maximum error of 14.54% [5]. A comparison has been also pursued with the detailed FEM models reported in [14] and [15]. Satisfactory results have been found comparing the maximum FW temperature (error lower than 1.01% [14]) as well as for Immediate Plastic Flow Localization and Ratcheting in Negligible Creep criteria with deviations comprised between the 5.88% and the 15.28% [15], respectively. The benchmark has demonstrated that the developed methodology reproduces the same behaviour of 3D model providing a tool useful for preliminary design [5]. As an example, in Table 2, the most important thermal-hydraulic and structural results are reported for the path 1-1 (see Fig. 4) and for a heat flux of 0.5 MW/m2.
5
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Development of helium coolant DEMO first wall model for SYCOMORE system code based on HCLL concept ⁎
Gandolfo Alessandro Spagnuoloa, , Giacomo Aiellob, Julien Aubertb a b
Karlsruhe Institute of Technology (KIT),Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany CEA-Saclay, F-91191 Gif-sur-Yvette, France
A R T I C LE I N FO
A B S T R A C T
Keywords: DEMO System code SYCOMORE Breeding blanket FW HCLL
The conceptual design of the demonstration fusion power reactor, known as DEMO, is ongoing and several reactor configurations have to be investigated by exploring different design parameters. For these reasons, within the European framework, systems codes like SYCOMORE (SYstem COde for MOdelling tokamak REactor) have been developed. SYCOMORE includes several specific modules, one of which is aimed to define a suitable design of the helium breeding blanket. The research activity has been devoted to improve the method to define automatically the First Wall design starting from thermal-hydraulic and thermo-mechanical considerations, using analytical design formulae and, also, taking into account the design criteria coming from Codes& Standards. Thanks to these considerations, it has been possible to derive the first dimensions of the First Wall channels from which all the other characteristics are deducted. Afterwards, it has been assessed the thermal and mechanical field using a theoretical approach. Therefore, in order to compare and validate the results, a 3D geometric model has been created and FEM analyses have been carried out finding out very satisfying results with maximum error of 6.06% for the thermal analysis while a maximum error of 20% for primary and secondary stresses.
1. Introduction
2. FW geometry and heat loads
Within the European framework, systems codes like SYCOMORE (SYstem COde for MOdelling tokamak REactor) have been developed [1] in order to investigate several DEMO design. It includes several specific modules (i.e. plasma physics, divertor, etc.). Among the different modules, the research activity has been focused on the development of the Breeding Blanket (BB) module because it is one of the most sensible components in relation to the associated functions [2]. The paper focuses on the improvement of the Helium Cooled Lithium Lead (HCLL) BB module of SYCOMORE and, in particular, on the First Wall (FW) geometrical design. The FW geometry is derived at first using the design limits on primary stresses (i.e. considering pressure loads only). Then a complete structural integrity assessment is performed by verifying that the thermal as well as the mechanical field are compliant with the design rules given in Codes&Standards (C&S). Finally, the methodology has been verified against the results of FEM calculations performed on 3D models of the FW geometry.
Within the framework of EUROfusion activities [2], four BB concepts are currently studied. The present study has been focused, in particular, on the HCLL BB but its application can be extended to the other concepts. The HCLL FW is made by U-shape steel plate where He circulates firstly and then it flows in series with the Breeding Zone (BZ). The structural material of the HCLL BB module is the Reduced Activation Ferritic/Martensitic steel Eurofer [3]. In Fig. 1, the 2D draw of the FW in the poloidal-radial direction [4] is reported and it has been selected as the representative geometry for the following discussion. The geometry of FW (Fig. 1) is characterized by: the radial Tungsten thickness (s), the overall FW thickness (t), the plasma facing wall thickness (e1), the BZ facing wall thickness (e2), the poloidal channel dimension (d1), the radial channel dimension (d2), the distance between two channels (2r, the rib) and the pitch between two channels (P). The additional notations are given in Table 1. The heat loads identified for the FW design [3] are: a) heat flux (HF)
⁎
Corresponding author. E-mail address: [email protected] (G.A. Spagnuolo).
https://doi.org/10.1016/j.fusengdes.2018.03.003 Received 9 August 2017; Received in revised form 13 February 2018; Accepted 2 March 2018 0920-3796/ © 2018 Published by Elsevier B.V.
Please cite this article as: Spagnuolo, G.A., Fusion Engineering and Design (2018), https://doi.org/10.1016/j.fusengdes.2018.03.003
Fusion Engineering and Design xxx (xxxx) xxx–xxx
G.A. Spagnuolo et al.
Table 1 Symbols used. fr fd fe fp
Ratio between 2r and d1. Dimensionless parameter. Ratio between d2 and d1. Dimensionless parameter. Ration between e1 and d1. Dimensionless parameter. Fraction of the thermal power used for the pumping power. Dimensionless parameter. Channel coolant velocity Concentrated pressure loss coefficient Darcy-Weisbach friction factor Channel lenght Helium density Number of FW parallel channels Cross section of FW channel Helium specific heat FW outlet bulk temperature
uc K f L ρ nc Sc cp FW Tout b
Tin
Fig. 1. FW section in the poloidal-radial plane.
coming from plasma, b) nuclear power directly deposited into FW structure and c) HF on the FW backside at boundary with the BZ. The total power deposited in the FW (PFW) is the sum of the three contributions. Contribution a) can be considered an input data, depending on the plasma characteristics and the poloidal position of the module, while contributions b) and c) are calculated in the neutronic model of SYCOMORE. A common assumption for the equatorial BB module is a constant HF equal to 0.5 MW/m2 [3]. The b) and c) contributions cannot be exactly determined without knowing respectively the geometry and the interaction between the FW and BZ. When running in SYCOMORE, these quantities are calculated iteratively starting from the total power deposited in the BB module [1]: they are therefore considered as input data for the development of the standalone FW model. Indeed, for the first iteration, it is assumed that 20% of the overall nuclear power is released in the FW [5]. Knowing the power deposited in the BB module and considering the operational coolant temperatures of HCLL BB (300 °C and 500 °C [3], inlet/outlet), it is possible to calculate the mass flow rate (m˙tot ) for each BB module. Then, knowing the fraction of the total power deposited in the FW (PFW), the bulk temperature (TFW out b ) to the outlet of FW can be obtained [5].
TwPL
FW inlet temperature Plasma facing wall channel temperature
TpPL
Plasma facing temperature
PL TArmour
Plasma facing armor temperature
TwBZ
BZ facing wall channel temperature
TpBZ
BZ facing temperature
TwPL1 − 2
Middle rib temperature
TwAV 1
Channel 1 wall temperature on the ribs
TwAV 2
Channel 2 wall temperature on the ribs
Tav qFW " qBZ "
Averaged temperature for allowable stress plasma heat flux
λEUR λArmor h Pdes Pm Pb Sm Sem Set St Ω φ Qm Qb εx − εy ν α X Y Z H
Thermal conductivity of EUROFER Thermal conductivity of Tungsten Convective heat transfer coefficient Design pressure Membrane primary stress Bending primary stress Allowable membrane stress Immediate plastic flow localization allowable stress Immediate fracture due to exhaustion of ductility allowable stress Creep differed excessive deformation allowable stress Factor for local membrane and multiaxial stress Neutron fluence Membrane secondary stress Bending secondary stress Strain in x and y direction Poisson's ratio Thermal expansion coefficient FW toroidal lenght FW poloidal lenght FW radial length (sidewall) Distance between two horizontal Stiffening Plates
BZ thermal flux
3. Determination of FW geometrical parameters dimensionless parameter introduced is fe, that is determined using the beam theory. The membrane and bending stresses acting on the thickness e1 due to the pressure on d2 can be evaluated considering the problem of a double-embedded beam on which, due to the coolant pressure, a distributed load acts:
In order to determine the FW channel dimensions, design limits on primary stresses are considered. Primary stresses are those due to external forces acting on the structure: in case of the FW this is the coolant pressure acting on the channels walls. The approach proposed in the following is based on beam theory taking into account criteria coming from C&S [6]. They can be calculated using dimensionless parameters for the FW geometric characteristics [5]. The first dimensionless parameter introduced is fr that can be estimated starting from the Pdes acting on d1. The resulting membrane stress Pm acting on the thickness 2r must verify the rule Pm < Sm in RCC-MRx [6]. This gives:
2⋅r P = des = fr d1 Sm
d ⋅f
Pm = Pdes⋅ 21⋅ e d ; Pb = Pdes⋅ 1
d12 ; 2 ⋅ e12
(2)
Using the criterion Pm +P b < 1.5Sm , with few steps, it is obtained the Eq. (3):
fe1,2 = (1)
fd ±
S
fd 2 + 12⋅ P m
des
S
6⋅ P m
des
(3)
The methodology, so far, provides couples of geometrical dimensions but not a unique design solution [5]. The innovative approach proposed here is to introduce the BB thermal-hydraulic aspects taking into account the requirements on the efficiency of DEMO reactor. It is common, in system codes [7], to calculate the pumping power as a
The second dimensionless parameter introduced is fd, corresponding to the “aspect ratio” of the channels in the FW. It cannot be determined only by considerations on primary stresses and it is considered as a user input which is bounded by manufacturing constraints. One can take fd equal to one as a starting point (square channels). The third 2
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(fixed) fraction of the recovered thermal power [7]. Indeed, for a given mass flow, the pumping power is related to geometry of the FW: smaller channels, with higher He velocity and heat transfer coefficients, insure better heat removal capability at the expense of the pumping power. For this, a new dimensionless parameter fp is introduced as the fraction of the FW pumping power in relation to the recovered FW thermal power. For information, this ratio is ∼3% in the current FW design of HCLL [3]. It is considered as an input data (given by the user) in the following. Taking into account that the channels of the FW are in parallel, they will experience the same pressure drop that is calculated as shown in Eq. (4) [5].
Δp ≡ ρ
⎞ fp ⋅PFW uc2 ⎛ f ⋅L ⋅⎜ + K⎟ = ρ 2 ⎜ 2⋅ fd ⋅d1 mtot ⎟ ⎝ 1 + fd ⎠
Fig. 2. Thermal field on FW.
flux, it is possible to calculate the temperatures in the thickness as described in the system of Eq. (8) and shown in Fig. 2 [5]. 1
PL FW " ⋅h ⎧Tw = Toutb + qFW ⎪ PL e1 PL " ⋅ λEUR ⎪Tp = Tw + qFW ⎪ PL s TArmour = TpPL + qFW " ⋅ λArmor ⎨ 1 FW ⎪TwBZ = Tout + qBZ " ⋅h b ⎪ ⎪TpBZ = TwBZ + q" ⋅ e2 BZ λEUR ⎩
(4)
The unknown factors are uc and d1. The equation necessary to solve the system is the power balance equation (Eq. (5)). FW PFW = ρ⋅nc⋅Sc⋅uc⋅cp⋅(Tout − Tin) b
(5)
Combining the previous equations, it is obtained an equation of the third order in which the unknown factor is d1, as shown in Eq. (6):
In order to estimate the thermal field on the ribs (Fig. 3), it is necessary to take into account that the adjacent channel are feed in counter-current, it means that there will be two different bulk temFW and Tin, respectively. Moreover, the highest temperature perature, Tout b will be to the FW side wall (SW) channel outlet but, conservatively, it has been assumed that the outlet FW temperature coincides with the SW one. Applying the same assumption discussed above, it is possible to figure out the temperature in the middle of the rib (TwPL1 − 2 ), as reported in Eq. (9).
2
FW Y ⋅fd ⋅ρ⋅cp⋅(Tout − Tin ) ⎤ 4⋅fd ⋅Δp 3 b 2⋅K ⋅fd ⋅PFW 2⋅d1 − ⎡ ⎢ ⎥ ⋅ ρ ⋅d1 = −f ⋅(X + 2⋅Z ) 1 + f r ⎣ ⎦ ⋅(1 + fd )⋅PFW 2 (6)
The solution of Eq. (6) [5] shows that only one result is real and also positive. Therefore it can be accepted as physical resolution of the problem. This equation allows determining the first dimension of the channels from which all the other characteristics (except e2) are deducted. In order to calculate e2, it is necessary to impose that it will sustain the increasing of the pressure in the BZ during an in-box LOCA [4]. Using the same approach for the calculation of the bending stress but considering, this time, a distance between two horizontal stiffening plates (H) [4], it is possible to calculate the maximum bending moment to the embedded joints, the second moment of inertia and, finally the bending stresses and applying the criteria P b ≤ 1.5⋅SD m , it is possible to estimate the thickness of the BZ facing wall, e2, as follows [5]:
e2 =
Pdes⋅
H2 3⋅SmD
(8)
(
⎡ qFW " ⋅ e1 + TwPL1 − 2 = TpPL − ⎢ λEUR ⎢ ⎣
d2 2
) ⎤⎥ ⎥ ⎦
(9)
Consequently, the assessment of the wall temperature on the ribs and TwAV ) can be pursed thanks to the Eq. (10) (Fig. 3, right-side). (TwAV 1 2
⎧ ⎪TwAV = 1 ⎪ ⎨ ⎪T AV = ⎪ w2 ⎩
(7)
PL Tw 1 − 2 ⋅ λEUR + h ⋅ T FW outb r λ h + EUR r PL Tw 1 − 2 ⋅ λEUR + h ⋅ T in r λ h + EUR r
(10)
SmD
is calculated according to the level D of The allowable stress RCC-MRx [6]. The membrane primary stress has not been taken into account because, during the LOCA, all the BZ is pressurized at the same pressure, it means that the plates will experience the same pressure in the poloidal direction. Only the last stiffening plates may have unbalanced pressurization but it has been assumed that the caps will sustain it [5].
4.2. Thermo-mechanical field assessment For assessing the thermo-mechanical field on the FW according to RCC-MRx methodology, three paths (Fig. 4) have been identified in which the primary and secondary stresses have been calculated.
4. Assessment of FW structural integrity The configuration obtained at the end of §3 is intrinsically able to withstand primary stresses. The main concern for the structural integrity of the FW are however thermo-mechanical stresses, especially because of the loss of ductility of the material in presence of neutron irradiation. To assess them, it is at first necessary to calculate the thermal field. 4.1. Thermal field assessment To determine the thermal field, a linear temperature distribution is assumed in the radial direction. This hypothesis is justified by the low thickness of the plasma-facing side, but is more delicate on the BZ side. However, temperature gradients are lower in this zone and the impact is limited. Making the balance of the conductive and convective thermal
Fig. 3. Thermal field on FW rib.
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and toroidal, respectively) according to the plate theory. The estimation of the εx and εy assumes an important relevance for a good calculation of the membrane secondary stress. In order to evaluate the differential expansion of the FW back and front, it has been studied a methodology [5] whereby, considering the front and the back of the FW displayable as two plates bonded to the extremities with different average temperatures Tm1 and Tm2 and indicating with ε1 and ε2 the “theoretical” expansion in absence of restraints, it is possible to determine the real deformation (Δε), as shown in Fig. 6, imposing a plane deformation to the boundaries. The two plates will exert a force according to the forbidden/imposed displacements. Imposing the force equilibrium, it is possible to calculate the real deformation, Δε (Eq. (14)).
Fig. 4. FW paths for stress assessment.
In the following, the paths will be used for stress calculation as well for checking level A criteria [6].
Δε =
1
d12 ; 4 ⋅ e12
Pm2 − 2 = Pdes⋅ 2 ⋅ 2e ; Pb2 − 2 = Pdes⋅
d12 ; 4 ⋅ e 22
d
d
2
5. Methodology application 5.1. Design rules The design rules contained in RCC-MRx [6] with respect to the specificities of the BB operating conditions in a fusion environment, and the allowable limits [11] have been implemented in SYCOMORE. In particular, for the type-P [11] damages: Immediate Excessive Deformation and Immediate Plastic Instability, Creep Differed Excessive Deformation, Immediate Plastic Flow Localization and Immediate Fracture due to Exhaustion of Ductility. While for the type-S [11] damages: Ratcheting in Negligible Creep end Fatigue in Non-Singular Zones.
d
Pm3 − 3 = Pdes⋅ 2 ⋅1r ;
(11)
4.2.2. Secondary stress Secondary stresses are those due to imposed displacements of the structure: in case of the FW those are the deformations due to the temperature field in the structures. The assessment of the secondary stresses may be very difficult due to the intrinsic 3D nature of the phenomenon [8]. For this reason, the plate theory has been selected for its study [9]. Two thermal regimes are identified in the FW that can be separately studied and then combined [10]: a uniform temperature variation and a temperature gradient through the thickness. Referring to Fig. 5, T0 is the reference temperature, Tm is the average temperature on thickness, T1 is the highest temperature on surface, T2 is the lowest temperature on surface, ΔTm is the difference between the average and the reference temperature and ΔT is the difference between surface temperatures. In the case of FW, a state of “co-action” will be aroused, in which the stress/deformation are associated to zero active force [10]. Using the Hooke’s law and considering a temperature difference between the two plate surfaces, it is possible to write the Eq. (12) [10]:
Qm =
5.2. Benchmark The methodology, the thermal and structural field assessment as well as the design rules of C&S have been coded in SYCOMORE using Python language [5]. In order to compare the results of Python script, a 3D geometric model has been created using CAST3M [12]. The simplified FEM model is shown in Fig. 7 [5] based on the model used in [13]. Several cases have been analysed varying the HF coming from the plasma. Considering a pumping power equal to 3% of the thermal power released into the FW, seven different heat fluxes have been studied from 0.1 MW/m2 to 0.7 MW/m2. While three cases (0.77, 0.82 and 1.0 MW/m2, respectively) have been studied considering a pumping power equal to the 10% of the FW thermal power [5]. Very satisfying results have been found for the thermal results with maximum error of 6.06% in all the cases with respect to the simplified FEM model [5]. Concerning the primary and secondary stresses, for paths 11 and 3-3 the maximum error is about the 20%. When the thickness
E⋅[ε y + ν⋅εx − (1 + ν)⋅α⋅ΔTm] (1 − ν 2)
(12)
For bending secondary stresses the governing equation is [8]:
Qb = ±
E ⋅α⋅ΔT 2⋅(1 − ν)
(14)
Assuming that εx and εy in Eq. (12) are equal to Δε in Eq. (14), it is possible to assess the membrane secondary stress for the three identified paths [5].
4.2.1. Primary stress Primary stresses are calculated with the same hypotheses used in §3. At this stage of the calculation, the FW geometry is intrinsically able to withstand them, but the numerical values are needed to combine them with secondary stresses and to apply C&S criteria. The membrane and bending primary stress have been estimated for Path 1-1, 2-2 and 3-3 (Eq. (11)) [5]. No bending stresses have been identified for the path 3-3 due to the same pressure on the rib in poloidal direction.
Pm1 − 1 = Pdes⋅ 2 ⋅ 2e ; Pb1 − 1 = Pdes⋅
E1⋅ε1⋅A1 − E2⋅ε2⋅A2 E1⋅A1 − E2⋅A2
(13)
Where x and y represent the principal normal directions (poloidal
Fig. 5. Thermal gradient and averaged temperatures.
Fig. 6. Differential expansion of FW plates.
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6. Conclusion
PYTHON
CAST3M
Error
Within the framework of EUROfusion activities, a research activity has been conducted in collaboration with KIT and CEA. It has been aimed to the improvement of HCLL BB module of SYCOMORE and, in particular, it has been focused on the FW geometrical design starting from thermal-hydraulic and structural considerations and taking into account, also, the criteria coming from C&S. For the first time, a methodology for determining the FW geometric characteristics has been developed by relating the thermal and structural stress fields to the (required) pumping power showing that the maximum value of the allowable surface heat flux increases with the one used in the FW until to reach the limit imposed by the requirements on the efficiency of DEMO reactor. Design criteria coming from nuclear C&S have been implemented, giving information to the designers from the early stage of the investigation. Therefore, in order to compare and validate the results, a 3D geometric model has been created and FEM analyses have been carried out finding out very satisfying results with maximum error of 6.06% for the thermal analysis while a maximum error of 20% for primary and secondary stresses. As future activities, the proposed approach might be extended to the other BB components such as stiffening plates, caps and cooling plates, providing, in this way, a powerful design tool for screening the possible reactor configuration.
TwPL [°C]
488.15
487.00
0.24%
Acknowledgments
TpPL [°C]
528.87
526.00
0.55%
PL [°C] TArmour
536.49
534.96
0.29%
TwBZ [°C]
407.85
397.00
2.73%
TpBZ [°C]
497.08
474.00
4.87%
Tav [°C] Pm + Pb [MPa] Qm + Qb [MPa] Pm/Sm (Pm + Pb)/Sm (Pm + Qm)/Sem (Pm + Pb + Qm + Qb)/Set (Ω*Pm)/St (Pm + φ*Pb)/St (Pm + Pb + Qm + Qb)/3Sm Allowable Stress at Tav Sm [MPa] Sem [MPa] Set [MPa] St [MPa]
508.51 105.60 245.10 0.14 0.50 0.90 0.20 0.15 0.68 0.83
506.20 108.30 286.80 0.10 0.51 0.94 0.22 0.11 0.69 0.92
0.46% −2.49% −14.54% 45.72% −1.25% −3.87% −9.64% 42.66% −0.87% −10.13%
Fig. 7. 3D FEM model of FW.
Table 2 Thermal-hydraulic and thermo-mechanical results for path 1-1 and for a heat flux of 0.5MW/m2 [5].
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] A. Li Puma, et al., Development of the breeding blanket and shield model for the fusion power reactors system SYCOMORE, Fusion Eng. Des. 89 (2014) 1195–1200. [2] C. Bachmann, et al., Initial DEMO tokamak design configuration studies, Fusion Eng. Des. 98–99 (2015) 1423–1426. [3] P. Arena, et al., Thermal optimization of the helium-cooled lithium lead breeding zone layout design regarding TBR enhancement, Fusion Eng. Des. 124 (2017) 827–831. [4] G. Bongiovì, et al., On the thermal and thermomechanical assessment of the optimized conservative helium-cooled lithium lead breeding blanket concept for DEMO, Fusion Eng. Des. (2017) (in press). [5] G. A. Spagnuolo, Report on the development of HCLL DEMO First Wall design for Sycomore Code, 2MVSRN. [6] RCC-MRx, 2015 edition – design and construction rules for mechanical components of nuclear installations, afcen. [7] M. Kovari, et al., PROCESS: a systems code for fusion power plants −Part 2: Engineering, Fusion Eng. Des. 104 (2016) 9–20. [8] Dennis R. Moss, et al., Pressure Vessel Design Manual (IV Edition), (2018) (ISBN: 978-0-12-387000-1). [9] Theory of Plates and Shells, McGraw-Hill Book Company, 1st Ed. 1940, 2nd Ed. 1959 (with S. Woinowsky-Krieger). [10] C. Sigmund, Elementi piastra e tubi – Quaderno Tecnico. [11] G. Aiello, et al. Proposal of a set of design rules for the Blanket Conceptual Design in WPBB, 2MMPLE. [12] CAST3M. http://www-cast3m.cea.fr. [13] J. Aubert, et al., Optimization of the first wall for the DEMO water cooled lithium lead blanket, Fusion Eng. Des. vol. 98–99, (2015) 1206–1210. [14] P. Arena, et al., Thermal optimization of the Helium-Cooled Lithium Lead breeding zone layout design regarding TBR enhancement, Fusion Eng. Des. 124 (2017) 827–831. [15] J. Aubert, et al., Thermo-mechanical analyses and ways of optimization of the helium cooled DEMO First Wall under RCC-MRx rules, Fusion Eng. Des. 124 (2017) 473–477.
142.00 257.00 1785.00 130.30
starts to be greater, the 3D effects have a strong impact on the results for path 2-2. In general, the most important zone, for the verification of the criteria, is the front plasma side thickness [5]. For path 1-1, considering the reference case at 0.5 MW/m2 [2], the results obtained with the Python script show a satisfactory agreement with the FEM calculation, with a maximum error of 14.54% [5]. A comparison has been also pursued with the detailed FEM models reported in [14] and [15]. Satisfactory results have been found comparing the maximum FW temperature (error lower than 1.01% [14]) as well as for Immediate Plastic Flow Localization and Ratcheting in Negligible Creep criteria with deviations comprised between the 5.88% and the 15.28% [15], respectively. The benchmark has demonstrated that the developed methodology reproduces the same behaviour of 3D model providing a tool useful for preliminary design [5]. As an example, in Table 2, the most important thermal-hydraulic and structural results are reported for the path 1-1 (see Fig. 4) and for a heat flux of 0.5 MW/m2.
5